multiproduct rational expectations forecasting of … · the land allocation model is based on...

MULTIPRODUCT RATIONAL EXPECTATIONS FORECASTING OF IRRIGATION

WATER DEMAND: AN APPLICATION TO THE FLINT RIVER BASIN IN GEORGIA

by

SWAGATA “BAN” BANERJEE

(Under the Direction of Michael E. Wetzstein)

ABSTRACT

Limited water supply in many parts of the U.S. is a serious problem in agriculture.

Policymakers need better tools to devise programs and policies to deal with such shortages. A

model is built to estimate irrigation water demand. This model combines a land allocation model

with the crop- and region-specific Blaney-Criddle coefficients of net irrigation water

requirements. The land allocation model is based on portfolio analysis that combines measures of

risks and returns, but it also allows for agronomic and other influences.

Two economic methods – a simple statistical method and an alternative method using

futures prices and a modified weighted average of past yields – are employed to generate price

and yield expectations. The better of the two methods, based on the “root mean square error”

criterion, is used in the land allocation model to generate measures of risks and returns.

The overall model allows for the effect of economic factors on irrigation water demand.

This is important because different crops require different amounts of water for their proper

growth, and so the crop mix affects water demand in differing degrees.

The model is applied to analyze a program used in Georgia to conserve agricultural water

use by taking bids from farmers to reduce irrigated acreage. Results from this analysis show that

accounting for changes in the crop mix due to expectations about risks and returns for major

crops can have significant effects on estimates of water savings from reducing irrigated acreage.

This model should allow policymakers to better calibrate acreage reduction programs to meet

targeted levels for reductions in agricultural water use.

INDEX WORDS: Acreage Response Models, Corn, Cotton, Econometric Approach,

Engineering Approach, Flint River Basin, Forecasting, Forecasts, Futures

Prices, Irrigation Water Demand, Peanuts, Prediction, Prices, Scenarios,

Sequential Simulation, Simulation, Simultaneous Simulation, Slippage,

Soybeans, Yields



by


B.Sc. (Honors), University of Calcutta, India, 1987

M.Sc., University of Calcutta, India, 1989

M.S., University of Nevada, Reno, Nevada, 1999

A Dissertation Submitted to the Graduate Faculty of The University of Georgia in Partial

Fulfillment of the Requirements for the Degree

DOCTOR OF PHILOSOPHY

ATHENS, GEORGIA

2004

© 2004

Swagata “Ban” Banerjee

All Rights Reserved



by


Major Professor: Michael E. Wetzstein

Committee: Lewell F. Gunter Chung L. Huang

Electronic Version Approved: Maureen Grasso Dean of the Graduate School The University of Georgia May 2004

DEDICATION

This doctoral dissertation is dedicated to my dear parents and family back in India.

iv

ACKNOWLEDGEMENTS

This would be a long list if I had to mention every single person’s name in this section.

At the outset, therefore, I would like to thank everybody (including the names I might miss) for

their help, support, encouragement and patience throughout the entire process of working on this

research and preparing this manuscript. Thanks also to the ones who have helped me shape my

academic career.

Specifically, I would first like to thank my major professor, Dr. Michael Wetzstein,

whose patience, humor and caring attitude towards me during the entire duration I have been a

student in the Department of Agricultural and Applied Economics made my days go by faster

and easier. In fact, by his unique nature, often times he has reminded me of my dad whom I lost

on December 19, 1999 – at the end of my first semester in this department.

Then I will absolutely have to acknowledge the help I received from my committee

member, Dr. Lewell Gunter, without whose deep interest in my research I would definitely not

be able to complete this daunting task in a prompt and efficient manner. I will forever be

indebted to him for his great show of support and for confiding in me to push the envelope a

little bit farther whenever I thought I had reached my limit. Thank you, thank you, thank you, Dr.

Gunter!

I wish to thank my other committee member, Dr, Charlie Huang, who has at times forced

me to put on my thinking cap real tight and study the basics of microeconomic principles and

other fun stuff. I also wish to thank two other people I originally had on my committee but in the

end had to miss out on them due to their family emergencies. They are Mr. Jimmy Bramblett and

v

Dr. Jeff Mullen. Jimmy helped me absolutely unconditionally and deserves cheers for that! There

were so many other faculty members in this department whom I have come to know closely

during my tenure as a student here. Dr. James Epperson is one of them, with whom I have also

worked as a part-time assistant in one of his agribusiness classes. I will always remember his

student-friendly and supportive nature. His often-sarcastic ways of speaking are very unique and

different! Dr. Cesar Escalante, Dr. Andy Keeler, Dr. John Bergstrom, Dr. Jack Houston, Dr.

Forrest Stegelin, Dr. Dmitry Vedenov, and certainly our department head, Dr. Fred White, have

often given me hope and inspiration, and lauded me for my efforts.

In the same breath, I also wish to mention the name of a statistics instructor, Dr. Jem

Corcoran, of the Department of Statistics, who had not only been the best instructor I have had in

the United States, but also was a good friend!

There are many students, colleagues and friends in the Agricultural and Applied

Economics Department who have directly or indirectly helped me at some point or the other and

made my journey easier, sometimes even without them knowing. They include Daniel Muturi

George Ngugi (‘mi mejor amigo’… I’m glad I remember your full name … or do I? …ha-ha-ha),

Wei Bai, Xiaohui “Sarah” Deng, Yingzhuo Yu, Mawar Andromeda Tresna, Shaikh Mahfuzur

Rahman, Vahe Heboyan, Arusyak Alavardyan, Byung-Joon Woo, Christa Galloway, Tim

Meeks, Rodney Brooks, Dilshod Abdulhamidov, Adelin John Semali, Bella Ablaeva, Hongsin

Park, Willard Phillips, So Jin Hwang, Jinghua “Lumina” Cao, Anderson Saito, Wesley Zwirn,

Gabriela Cardenas, Nirmala Devkota, Augustus Nyako Matekole, Josh Gill, Areg Azoyan, R.J.

Byrne, Chris Allen, Li Zhang, Feng “Frank” Zhang, Rui “Carolyn” Zhang, Murali Adhikari,

Laxmi Paudel, Horacio Saravia, Oleksiy Tokovenko, Zana Constantin Somda, Mohammed

Ibrahim, Katy Swickard, Mark Byrd, Vijay Subramaniam, Quinn Kelley, Bethany Lavigno,

vi

Shanna Damken, Vernisha Bethea, Laci Banks, Dmitriy Volinskiy, Tatiana Gubanova, Mariana

Arzangulyan, Irfan Yousuf Tareen, Ecio de Farias Costa, Ruth Claudia Allport, Laura Knight,

Leah Camps, Yvonne Juliet Acheampong, Marionette Charisse Holmes, Christina, Yassert

Arafat Gonzalez-Alvarez, Anil Sulgham, and so many others. There are others in the school at

large, like Siew-Hoon (my friend and guitar student) and her hubby Zhulu Lim, who have been

great friends too. And who can forget the timely help and friendship of Dr. Don McLellan and

his office staff (Julia Adkins, Jessica, Nusaiba) and others in the Rock House!

I wish to acknowledge also the instruction and support of the Economics Department

faculty, and the help and support of the entire Ag & Applied Econ Department staff – especially

Jan Hamala, Donna Ross, Doris Strickland, Jo Anne Norris, Kim Waters, Jennifer, Dianne

O’Kelley, Christy Porterfield and Laura Alfonso; and the computer support staff – Chris Peters,

Tony Garcia, and Yanping Chen. Tony, I will remember some of your magic tricks and your

skills in ventriloquism, but will miss the endless conversions we used to have on almost anything

and everything. Hope you’ll remember the card trick I taught you too!

I would also like to thank our custodians, including Sarah, whom I have been friends with

all along. I will miss you and your smiles, Sarah.

Then there is the International Student Life Office – Saehee Chang, Marcus Longmuir,

Leigh Poole, Ana Bonfante-Bossak, Nancy Dodson, Jackie Minus, Jeongyi Lee, and so many

others I have met in and through that office. Some of the friendships I have made there will most

certainly be life-long! Roy Fenoff, Gautam Pandhiyan, Sarah Nicole Julia Hemmings, Michelle

Fonseca, Farah Mahmud, Jennifer Kyle, Vicky Wong, Jesse Jones, Allison Krache, Cindy Lim

are just a few of them. Roy humbles me with his comments about my character and personality!

vii

He truly does! Amazing is his spirit and forthrightness! I have learned a lot from him while being

amused by his style at the same time!

There are quite a few outstanding families that I have come to know very closely and

become friends with during my stay in Athens. They include my first host family, the

Lipscombes (Hugh, Leigh Ann and Devin…hope you are all doing well, wherever you are, and I

do hope you now have another healthy little one in your family, which I knew was on its way the

last time I talked with you), the Dahls (Eric, Margaret, Maddie, Miranda and Gavin), the

Thompsons (Jeff, Caroline and George) and Maya Mukherjee and her family in Atlanta, Georgia.

I will never ever forget any of you! Eric and Margaret, your family has become my family over

the last fifteen months or so (since the Thanksgiving of 2003)! That’s the least I can say about

you!

I also cannot but mention the names of some of the friends I made while being a Masters

student at the University of Nevada, Reno – for example, Laura Ashkin-Stanton and her family

(Chris, Miriam and Ethan), Gautam Priyadarshan, Doug Robertson, Aditi and Aniruddha Mitra

and their family, April Joy Meservy, Hellen Esperanza Quan-Lopez and Naoko Kimura, who

have all been in constant touch with me until now.

So many great acquaintances and friendships I have made through my songwriting

association in Nashville (Nashville Songwriters Association International) and the Athens

chapter of its regional workshops, which I had the privilege of founding in August 2000 and

coordinating since then (for about 3½ years)! Liesl Villegas is one such songwriter friend who

has helped lift my spirits up from long distance ever since we met. Then there are Jamie Creech

(my co-coordinator for a while), Carter Betz, Brian Edwards, Martha Phillips, Charlotte “Chip”

McDaniel, Linda Wycheslavzoff, Barbara Dial, Dodd Ferrelle, Troy Aubrey, Julie Phillips-

viii

Jordan (the entertainment editor of Athens Banner-Herald) are some of the folks who have

believed in me and supported me in my efforts in academia along with my musical career.

Thanks also to Matthew Comegys, David Harris, Katie Goodrum, Devin Carlen, Jonathan Liang

and Heidi Kathryn Millington for playing music and/or forming songwriting partnerships with

me.

My first and foremost true economics mentor in India, Santanu Ghosh, deserves a special

mention in this section because he is the one who showed me the true light of this enlightening

and dynamic field. It is through him that I found Dr. Basudeb Biswas, who was so instrumental

in finding me a department (Applied Economics and Statistics, University of Nevada, Reno)

where, in the Masters program with Resource and Applied Economics major, I started this long

journey towards fulfilling my dreams of obtaining my doctoral degree. Dr. Anima Basu and her

family, and many others in India also helped make this transition possible. You all know who

you are!

Among my friends all over the world, one Ella Nugraha from Indonesia considers me as

her “best friend.” She has been a great inspiration to me lately! We have several common

interests, the most important being music!

Last but certainly not least, I have to admit that, even though my entire life has been

replete with struggles, it is my well-knit family’s moral support that has kept me going all along

the way! Specifically, my mom’s support, in every possible way, is something I am very proud

of having like an umbrella over my head. My dad passed away without knowing the news of my

completing my doctoral degree, and that is definitely going to be one of the deepest regrets I will

always have. I believe it is my paternal grandfather’s foresight in sending me (and my two

brothers) to an Irish Catholic school in Kolkata, India, with English as the medium of instruction

ix

(so English happened to be our first language), that enabled me towards knowing and

understanding the Western world better and ultimately drove me here. Thanks to my guru,

Trishan Moharaj, his guru, Guruji Swami Paramananda (the founder of Paramananda Mission in

India and Peace University in Norway) and God for making my dream of successfully pursuing

graduate study in the United States a reality!

x

TABLE OF CONTENTS

Page

ACKNOWLEDGEMENTS.............................................................................................................v

LIST OF TABLES....................................................................................................................... xiv

LIST OF FIGURES ................................................................................................................... xviii

CHAPTER

1 INTRODUCTION .........................................................................................................1

Overview ...................................................................................................................1

Historical Background...............................................................................................4

Some Problems Rarely Addressed ..........................................................................11

The Region Studied .................................................................................................17

Problem Statement ..................................................................................................17

Objectives................................................................................................................21

Procedures ...............................................................................................................22

2 LITERATURE REVIEW ............................................................................................25

Literature on Acreage Response..............................................................................25

Forecasting Literature..............................................................................................30

Literature on Rational Expectations ........................................................................32

Focus of this Study ..................................................................................................35

3 THEORETICAL MODELING OF ACREAGE RESPONSE.....................................37

The Expected Utility Theory...................................................................................38

xi

Assumptions and Properties of a Representative Utility Function..........................43

Theoretical Framework for Irrigation Decision ......................................................46

Rational Expectations Hypothesis...........................................................................53

4 DATA SOURCES AND TRANSFORMATIONS, AND CHOICE OF

METHODOLOGY ......................................................................................................56

Acreage Data ...........................................................................................................57

Profits Data..............................................................................................................59

Government Program Variables..............................................................................72

Counties Studied and the Dummy Variables ..........................................................78

5 EMPIRICAL MODEL AND ESTIMATION RESULTS ...........................................85

Data Span Used in Empirical Model .......................................................................85

Econometric Model for Irrigated Acreage Allocation ............................................86

Hypothesized Signs on Estimated Parameters ........................................................88

Estimation Results...................................................................................................90

6 WATER DEMAND ESTIMATION AND FORECASTING ...................................112

Water Demand Estimation ....................................................................................112

The Flint River Drought Protection Act................................................................115

Scenarios for Simulations......................................................................................117

Acreage of Other Crops Not Modeled ..................................................................118

Simulation Methods ..............................................................................................119

Slippage .................................................................................................................127

7 SUMMARY, CONCLUSIONS, IMPLICATIONS AND FURTHER

RESEARCH...............................................................................................................141

xii

Summary ...............................................................................................................141

Conclusions and Policy Implications ....................................................................146

A Summary of Suggestions for Further Research.................................................149

REFERENCES ............................................................................................................................152

APPENDICES .............................................................................................................................172

A TABLES A.1a THROUGH A.16: 1998 – 2000 IRRIGATED ACRES AND WATER

DEMAND..................................................................................................................173

B FORECASTING COVARIANCES...........................................................................194

Literature on Forecasting Covariances..................................................................194

Generalized Autoregressive Conditional Heteroskedasticity................................196

Forecasting Net Return Covariances and Variances .............................................200

C A NOTE ON VECTOR AUTOREGRESSION ........................................................205

xiii

LIST OF TABLES

Page

Table 4.1: Data Types, Periods and Sources..................................................................................81

Table 4.2a: In-Sample (1982-1998) Comparison of Prices and Yields between Method 1 and

Method 2.....................................................................................................................82

Table 4.2b: Out-of-Sample (1999-2001) Comparison of Prices and Yields between Method 1 and

Method2......................................................................................................................82

Table 4.3: Summary Statistics for Method 2 Data: Variables Used in the Empirical Model........83

Table 5.1: Hypothesized Signs on Estimated Parameters..............................................................97

Table 5.2: List of Variables Used in the Empirical Model ............................................................98

Table 5.3: Estimated Corn Irrigated Acreage: 1982 – 1998 ........................................................100

Table 5.4: Estimated Cotton Irrigated Acreage: 1982 – 1998 .....................................................103

Table 5.5: Estimated Peanut Irrigated Acreage: 1982 – 1998 .....................................................106

Table 5.6: Estimated Soybean Irrigated Acreage: 1982 – 1998 ..................................................109

Table 6.1: Net Irrigation Requirements (acre-inches) in Normal and Dry Years by Crop and

Region of the Flint River Basin as given by Blaney-Criddle Coefficients ................130

Table 6.2: Reduction in Total Irrigated Acres (TIA) in the Flint River Basin by County from

2000 to 2001 Caused by the Flint River Drought Protection Act...............................131

Table 6.3a: Irrigated Acres for Scenario 1: Expected Returns Updated in 2001 and 2002, Total

Irrigated Acres Constant for 2000-2002 ...................................................................132

xiv

Table 6.3b: Water Demand (acre-feet) for Scenario 1: Expected Returns Updated in 2001 and

2002, Total Irrigated Acres Constant for 2000-2002 ...............................................133

Table 6.4a: Irrigated Acres for Scenario 2: Expected Returns Updated in 2001 and 2002, Total

Irrigated Acres Reduced by 33,006 Acres.................................................................134

Table 6.4b1: Water Demand (acre-feet) in Normal Year for Scenario 2: Expected Returns

Updated in 2001 and 2002, Total Irrigated Acres Reduced by 33,006 Acres ........135

Table 6.4b2: Water Demand (acre-feet) in Dry Year for Scenario 2: Expected Returns Updated

in 2001 and 2002, Total Irrigated Acres Reduced by 33,006 Acres.......................136

Table 6.5a: Irrigated Acres for Scenario 3: Expected Returns Updated Using FAPRI 2010 Prices,

Total Irrigated Acres (TIA) Set at 2000 Level and at Reduced Level (Reduced by

33,006 Acres).............................................................................................................137

Table 6.5b1: Water Demand (acre-feet) in Normal Year for Scenario 3: Expected Returns

Updated Using FAPRI 2010 Prices, Total Irrigated Acres (TIA) Set at 2000 Level

and at Reduced Level (Reduced by 33,006 Acres).................................................138

Table 6.5b2: Water Demand (acre-feet) in Dry Year for Scenario 3: Expected Returns Updated

Using FAPRI 2010 Prices, Total Irrigated Acres (TIA) Set at 2000 Level and at

Reduced Level (Reduced by 33,006 Acres) ...........................................................139

Table 6.6: Slippage Comparison of Economic “Sequential” and “Simultaneous” Simulations

under Three Different Price Situations........................................................................140

Table A.1a: 1998 Corn Irrigated Acres and Water Demand Observed for Normal and Dry

Years…………………………………………………………………………… ...174

Table A.1b: 1998 Corn Irrigated Acres and Water Demand Predicted for Normal and Dry

Years…………………………………………………………………………….....175

xv

Table A.2a: 1998 Cotton Irrigated Acres and Water Demand Observed for Normal and Dry

Years……………………………………………………………………………….176

Table A.2b: 1998 Cotton Irrigated Acres and Water Demand Predicted for Normal and Dry

Years.............................................................................................................……….177

Table A.3a: 1998 Peanut Irrigated Acres and Water Demand Observed for Normal and Dry

Years……………………………………………………………………………….178

Table A.3b: 1998 Peanut Irrigated Acres and Water Demand Predicted for Normal and Dry

Years……………………………………………………………………………….179

Table A.4a: 1998 Soybean Irrigated Acres and Water Demand Observed for Normal and Dry

Years……………………………………………………………………………….180

Table A.4b: 1998 Soybean Irrigated Acres and Water Demand Predicted for Normal and Dry

Years..........................................................................................................................181

Table A.5: 1998 Simulation for Corn without Peanut Quotas: Irrigated Acres and Water Demand

Predicted for Normal and Dry Years...........................................................................182

Table A.6: 1998 Simulation for Cotton without Peanut Quotas: Irrigated Acres and Water

Demand Predicted for Normal and Dry Years ............................................................183

Table A.7: 1998 Simulation for Peanuts without Peanut Quotas: Irrigated Acres and Water


Table A.8: 1998 Simulation for Soybeans without Peanut Quotas: Irrigated Acres and Water


Table A.9: 1999 Corn Irrigated Acres and Water Demand Predicted for Normal and Dry

Years............................................................................................................................186

Table A.10: 1999 Cotton Irrigated Acres and Water Demand Predicted for Normal and Dry

xvi

Years………………………………………………………………………………..187

Table A.11: 1999 Peanut Irrigated Acres and Water Demand Predicted for Normal and Dry

Years………………………………………………………………………………..188

Table A.12: 1999 Soybean Irrigated Acres and Water Demand Predicted for Normal and Dry

Years..........................................................................................................................189


Years..........................................................................................................................190


Years..........................................................................................................................191


Years..........................................................................................................................192


Years..........................................................................................................................193

xvii

LIST OF FIGURES

Page

Figure 1.1: Georgia Irrigated Acreage: 1970–1998.........................................................................8

Figure 1.2: The 31 Georgia Counties that Approximate the Flint River Basin .............................18

Figure 3.1: Indifference Curves for Risk-Averse, Risk-Neutral and Risk-Seeking Individuals in

an Expected Utility and Variance Space .....................................................................45

Figure 4.1: U.S. National Peanut Poundage Quotas 1978–1998 ...................................................76

Figure 4.2: U.S. National Corn and Cotton Set-Asides 1978–1998 ..............................................78

Figure 4.3: Upper and Lower Flint River Basin Counties .............................................................79

xviii

CHAPTER 1

INTRODUCTION

Overview

Production of crops requires land, and land requires water for the crops to grow. The

natural source of water for land is precipitation, mostly in the form of rain. But when

precipitation is less than normal or less than necessary for the healthy growth of crops, farmers

resort to the artificial source of water called irrigation. Other than augmenting precipitation,

irrigation is sometimes used to artificially extend a growing season or enable farming in dry

seasons or regions. According to Karadi (1998), farmers, in general, the world over rely on

precipitation for crop production. However, irrigation is considered necessary in crop production

wherever and whenever precipitation amounts to less than ten inches a year.

If annual precipitation is between ten and twenty inches, dry-land farming methods may

be used to grow some crops, but the farmer has to resort to irrigation in order to obtain larger and

more dependable yields.

Uneven seasonal distribution of rainfall is one important aspect necessitating irrigation

even in regions with adequate annual rainfall. If the seasonal distribution is such that the growing

season coincides with a dry period, irrigation becomes necessary.

Even though the total rainfall during the growing season may be adequate, supplemental

irrigation is also desirable in regions that are subject to short droughts. Therefore, irrigation is

practiced by more than 50% of all farmers in the world.

1

According to Karadi (1998), modern irrigation methods vary widely among five general

types, from flooding to furrow irrigation to sub-irrigation to sprinkling to drip irrigation. This is

because they depend on local conditions, including topography, the particular crops to be

irrigated, the nature and location of the water supply and drainage characteristics of the soil. We

may now take a closer look at each of these five categories of irrigation methods used in the

world.

1. Flooding Method: In this method, also known as flood-and-border irrigation, the

surface of the irrigation plot is continually submerged in water and the plot contains small dikes

(dams/embankments) or ridges. The process used to maintain this is the following. First, the

fields to be irrigated are divided into smaller basins. Then, water is released from field ditches

either through siphons or by making temporary gaps cut in through the earthen ridge of

secondary ditches. Once a basin is filled with water, the siphons or gaps are closed and the

procedure is repeated at the next basin.

2. Furrowing Method: This is another traditional technology employed to irrigate some

crops. Furrows are ditches between the ridges on which crops are planted. Water, channeled

through laterals, is admitted to each furrow by cutting away a small earthen dike, thus opening a

gap. When the water in each of the furrows has reached the desired level, its supply is cut off by

closing the dike again. Thus, water is allowed to seep into the soil and feed the roots of the

plants. Traditional technologies such as flooding and furrowing require substantial volumes of

water over a short period of time. But the furrowing method is more expensive to build and

operate compared to the flooding method. But it is normally used to produce high-value crops

such as vegetables.

2

3. Sub-irrigation Method: This method, also known as under-bed irrigation, is used if soil

conditions are favorable and the groundwater table is near the surface. In this method, water is

delivered to the field in ditches and allowed to seep into the ground to reach the desired

groundwater level to feed the roots of plants. Compared to the flooding method, the amount of

irrigation water required for this method is a lot less. But, since the roots are under direct

exposure to the water, sub-irrigation also requires water with low salt content. Because this

method enables the farmers to keep the tops of the plants dry, thus preventing spoilage through

rot or mildew, this approach turns out to be effective for delicate plants, like strawberries, small

fruits and vegetables.

4. Sprinkling Method: This is one of the modern technologies used in irrigation.

Introduced in the 1950s, this method is used for field crops, fruits and vegetables. In some ways,

the sprinkler method is the most convenient and the most efficient irrigation system. There are

many different kinds of sprinklers. But most of them require piping and pumps. The advantages

of this method are that water can be delivered exactly where it is required, and the flow rate can

be regulated more accurately than in other systems. Also, the sprinkling method can be used

applied quite effectively on rough and hilly land without resorting to smoothing or grading.

Sprinklers are available in the market as portable, permanent or semi-permanent. Rotary

sprinkler systems that are widely used in the United States consist of sprinklers mounted on a

radial pipeline supported by towers. The towers are mounted on two wheels or small trucks to

enable movement across a field. At each tower, the pipeline is slowly rotated about a central

pivot by electric motors. In self-propelled systems, this is being done by water pressure

actuators. A single rotary unit can irrigate an area of 24 to 260 acres. Georgia has adopted this

3

method to be the preferred method of irrigation. In 1998, about 57% of all farmers in Georgia

used sprinkler irrigation techniques like the center pivot (or rotary) system.

5. Drip Irrigation Method: In drip irrigation, otherwise called trickle irrigation, a

perforated plastic pipe is laid on the ground. The perforations are so designed that they release

only a controlled amount of water near the roots of plants. Thus, this method enables water

losses due to evaporation and deep seepage below the root level to a minimum. Obviously, it is

practiced mainly in areas where water supplies are limited. Introduced in the 1970s, this method

is most commonly used in the production of high-value fruits and vegetables and in regions with

low water quality or with high water cost.

How does the farmer decide on how much water to use in irrigation of the crop(s) he or

she is producing? Well, some of the factors that may affect that decision and other decisions

related to irrigation may easily be attributed to expected crop price, cost of water – usually the

fixed cost of installing the irrigation system and the cost associated with operating that system,

risk perception, expected yield response, role of government programs designed to minimize risk

to farmer income, and water availability. Management of irrigation requires an understanding

not only of irrigation technologies, but also of soil-plant-water processes and economic factors

that affect the choice of crop planted.

Historical Background

Irrigation is a technique that has historically augmented the natural availability of water

for crop production or farming in general around the world. As noted by Boggess et al. (1993),

although irrigation has evolved through time, there have been significant changes in irrigation

technology over the last half a century or so. Not only have new technologies, such as sprinkler

4

and drip irrigation, been introduced, there have also been improvements made in water pumping

and conveyance technologies. Adoption of these technologies has had dramatic impacts on water

use, crop yields, crop production patterns, and the trade and market conditions of many crops

(Boggess et al., 1993).

Irrigation dates as far back as about 5000 BC, when the Egyptians are known to have first

used irrigation techniques. The founder of the first Egyptian dynasty Menes undertook the first

major irrigation project in about 3100 BC. In many countries of the Middle East, there still exist

ruins of elaborate irrigation projects that were built 2,000 to 4,000 years ago. For example, the

Marib Dam in Yemen, built in about 500 BC to store water for a large irrigation system, was in

operation for more than 1,000 years. A large irrigation project in the Sichuan province of China

dates to the third century BC and is still in use (Karadi, 1998).

Irrigation in agriculture is known to have flourished in the Western Hemisphere more

than 2,000 years ago. For instance, the Incas in Peru developed an advanced agricultural

civilization based on irrigation. The Hohokam Indians in Arizona constructed extensive

irrigation systems around 1200 AD. Built at about 1400 AD, ditches in the Salt River Valley of

Arizona are still in use.

But the credit for establishing the first large-scale irrigation project in the United States

goes to the Mormon settlers in Utah in 1847. More and more irrigation works began to be built

as other settlers moved to the West. Early on, they were small and crude. But as associations of

farmers and commercial firms began to be formed, the projects became larger and sophisticated.

In 1868, the federal government undertook the construction of an irrigation project to

provide water for the land on the Mojave Indian Reservation in Arizona. By 1900, about 9.5

million acres were being irrigated in the West (Karadi, 1998). In 1902, the National Reclamation

5

Act was passed. Through this Act, the government began to finance large projects that were not

possible for individuals, groups or even states to construct. Nowadays most large irrigation

projects are initiated and directed by national governments. By 1980, irrigation in the U.S. had

become a major component of agriculture: the total agricultural products from irrigated land

accounted for over a third of the total value of agricultural output (Day and Horner, 1987).

Historically speaking, the southeastern U.S. is considered water-abundant, and the

farmers rely heavily on precipitation for crop production.

In this dissertation, the area studied falls in the Flint River Basin, which passes through

Georgia, Alabama and Tennessee. Specifically, the area studied consists of 31 Georgia counties

that approximate the Flint River Basin.

In general, Georgia has both abundant water resources and significant rainfall. With

annual precipitation of 50 inches per year and an extensive system of surface water sources and

aquifers, Georgia still experiences water-related problems. Water use estimates for 1995 show

the largest increase in water withdrawals for irrigation purposes. Irrigation in 1995 was estimated

to be 720 million gallons per day (mgd), up by 63% from 1990. Public water supply use

increased by 19% from 1990. The increase in irrigation use was particularly felt by Georgia’s

ground water resources. Ground water irrigation use increased 81% by 1995 over 1990 and 36%

for surface water irrigation (Jordan, 1998).

According to a survey in 2000 conducted by county Extension agents in all of Georgia’s

159 counties, the water sources for irrigation systems have continued the same trend as in the

past. Ground water supplies about 61% and surface water about 31% of the agriculture water in

the state. The other 1% comes from wastewater sources (Georgia Faces, 2001).

6

There are only a few records of water use in Georgia. So it is difficult to assess

agricultural water use directly. What is relatively better in respect of availability is a time series

of irrigated acres. A careful study of recent trends in agricultural water use in Georgia reveals

that through most of the 1970s there have been sharp increases in irrigated acreage, and this

trend continued well into the 1990s (Figure 1.1).

A couple of possible explanations can be provided for this fact. One is that credit

agencies began requiring farmers to irrigate a certain proportion of their land to minimize the

downside risk associated with a poor yield. Second, historically speaking, irrigated production

of corn, soybeans and peanuts is generally found to be more profitable in Georgia relative to

non-irrigated production (Moss and Saunders, 1982; Mackert et al., 1980a-c).

This historical trend is demonstrated by remarkable changes in acreage under irrigation

for these three commodities, viz., corn, soybeans and peanuts. According to the Proceedings of

the 1999 Georgia Water Resources Conference, between 1970 and 1980, the acreage increased

from 30,418 to 410,241 acres for corn, from 38,227 to 271,323 acres for soybeans, and from 795

to 133,695 acres for peanuts.

According to Kerry Harrison (2001), an irrigation engineer with the UGA College of

Agricultural and Environmental Sciences, the recent increase in irrigated acres is modest

compared to the mid-’80s and early-’90s. During that period, irrigated acreage grew about 20

percent per year. In contrast, between 1998 and 2000, the number of irrigated acres in the state of

Georgia increased about 2 percent, according to the UGA Extension Service 2000 Irrigation

Survey. The 1.5 million acres of irrigated farmland in 2000 is a 31,000-acre increase since the

previous survey in 1998 (Harrison, 2001).

7

Moreover, Tew (1984) observes that what makes irrigation a desirable technology is the

expectation of profits rather than the absolute levels of profits. The 1990s were a decade of

declining price supports. So there was a motivation on the part of the farmer to bring larger

amounts of land under irrigation to boost the expectation of profits (Tew, 1984).

The U.S. Department of Agriculture - Natural Resource Conservation Services (USDA -

NRCS) conducted a comprehensive study in 1995 on agricultural water demand in the Alabama-

Cossa-Tallapoosa (ACT) and Apalachicola-Chattahoochee-Flint (ACF) (ACT/ACF) River

Basins. According to that study, the state of Georgia had 7.5 million acres of farmland (over 37%

of which were planted for crops), and agriculture constituted its major consumptive water user.

Georgia Irrigated Acres: 1970 - 1998

0

0.2

0.4

0.6

0.8

19

1

1.2

1.4

1.6

7019

7119

7219

7319

7419

7519

7619

7719

7819

7919

8019

8119

8219

8319

8419

8519

8619

8719

8819

8919

9019

9119

9219

9319

9419

9519

9619

9719

98

Years

Irrig

ated

Acr

es (M

illio

ns)

Figure 1.1. Georgia Irrigated Acreage: 1970–1998

Source: USDA – Natural Resource Conservation Service

8

However, despite the large consumption, it is unknown precisely how much wate

agriculture uses on a county by commodity basis. Information on a crop by county basis

facilitates a better, clearer and more precise understanding of agricultural water demand.

Therefore, this level of disaggregation is not only desirable but also required. This is so because

crop by county information can help us identify the variation in water demand owing to uniqu

soil, climate and market cond

r

e

itions in a county in question. Furthermore, information on a

commo ons

In

gate

ted with policymaking under incomplete information were

mphas

e

e (Tareen, 2001).

)

dity level enables us to more accurately predict the agricultural water demand projecti

in the face of changing government commodity programs and profitability of different crops.

the absence of such information, policy proposals and decisions regarding which crops to irri

and in what quantities tend to be potentially inaccurate (Tareen, 2001).

The problems associa

e ized in a 1995 water summit in Southwest Georgia, where engineers and economists

expressed similar views on the desire and necessity for additional information regarding

agricultural water use in the state of Georgia. The participants at the water summit agreed that

more temporal and site-specific information was required for understanding Georgia’s futur

agricultural water demands.

In vulnerable areas, site-specific, temporal information is especially required both in

terms of water quantity and quality. In regards of water quantity, it is important to assess the

effect of withdrawals on competing users of the watershed. In Southwest Georgia, the Flint

River is inextricably linked with the ground water tables. So the issue of water quality is also a

critical on

The Alabama-Cossa-Tallapoosa (ACT) and Apalachicola-Chattahoochee-Flint (ACF

River Basins that pass through the three southern states of Alabama, Florida and Georgia may be

9

considered as a specific example of rising pressure on agricultural water demand. Precisely,

ACT-ACF River Basins are comprised of 62 Georgia counties, 34 Alabama counties and 6

the

ss was

luded

imately 400 mgd in 1992. Of this amount, Georgia farmers used 72%,

ions

in

has

ds for water, there are

demand

y and

With the goal to achieve an equitable allocation of water among the states of Alabama,

Florida and Georgia, there have been negotiations and studies going on for more than ten years.

In 1999, when all attempts failed to bring a settlement to the issue, it appeared that it was

Florida counties. In an attempt to address interstate water resource issues and promote

coordinated system-wide management of water resources, the Governors of Alabama, Florida

and Georgia and the Assistant Secretary of the Army for Civil Works came together in 1992 and

signed a Memorandum of Agreement to establish a partnership. A key part of this proce

to conduct a comprehensive study of the ACT and ACF River Basins. The study was conc

in 1997.

According to the study, the total agricultural water withdrawals from the ACT-ACF

River Basins were approx

while farmers in Alabama and Florida accounted for 21% and 7%, respectively. They also

forecasted a 40% increase in agricultural water demand from 1992 to 2000 in the tri-state area.

As is clear from the USDA-NRCS study, the moot cause of ongoing water negotiat

amongst the states of Alabama, Florida and Georgia is greater pressure on the water resources

the tri-state area. The current long spell of drought in Georgia – 1998 through present time –

resulted in greater uncertainty in agricultural yield, which has accentuated the need for

agricultural water use in this state. Coupled with its internal deman

s from its neighboring states. These conflicting demands have been the cause of

problems in water allocation among these states. These problems do not seem to be readil

quite easily addressed.

10

heading to federal courts. However, the southeastern region of the U.S. has learned numerous

bitter lessons of water litigation from the western U.S., and more recently, from Colorado,

Kansas and Nebraska over the failure of the Republican River Compact.1 These provided enough

disincentives against litigation and paved the way for mediation.

The Republican River Compact resulted in a judgment that led Colorado to pay Kansas

aking that grave lesson, Georgia and Florida have

ion

teps

associated with agricultural water demand is a serious

lack of

ence

e, but

huge amounts of money in damages. T

considered mediation as a better alternative. In late October 2000, Dr. Talbot D'Alemberte, the

President of Florida State University, was selected as the mediator to assist with the ACF port

of the ACT/ACF River Basins between Georgia and Florida. These mediation attempts are s

towards a potential ACF Compact among the states of Alabama, Florida and Georgia, hopefully

with a more positive and better vision than the Republican River Compact.

Some Problems Rarely Addressed

The first and foremost problem

information on agricultural water use. The past, present and future water demands of

farmers are not what the policymakers have a clear knowledge and understanding about. In

order for the state to have improved decision-making and policy development that will influ

agricultural water use, an understanding of historical agricultural water use patterns in Georgia is

imperative. Some efforts have been made in the recent past to bridge the gap in knowledg

1 The Republican River Compact was designed in 1943 to improve efficiency of water use and remove potential water conflicts in the region. The Compact has resulted in limited success. Recently, Colorado, Kansas and Nebraska sued and counter-sued each other over issues of water flow and inclusion of ground water in the definition of water rights. According to the last court decision in favor of Kansas, the judge assessed damages to be paid by Colorado in the order of $66 million for lost economic activity, lost yields and resulting loss in Kansas state and local tax revenue from 1965 onwards (Norton, 2000; Tareen, 2001).

11

there st

esearch

.)

ted data and reflect

easur

n

ill remain numerous problems to date associated with estimating agricultural water

demand in Georgia (Tareen, 2001).

Tareen’s (2001) dissertation addressed some of those problems. In particular, his r

focused on the following four areas: i.) the limited number of data sources and lack of consistent

data; ii.) the absence of an economic model of agricultural water demand; iii.) the lack of a

proper linkage between the economics and engineering models of agricultural water use; and iv

the lack of dynamics in agricultural water demand, or the lack of predictability of future

agricultural water demand.2

In estimating and forecasting agricultural water demand, the first and foremost problem

encountered is the limitation of available data sources. As Tareen (2001) notes, the first source

of information that is potentially being used in practice is the estimation done by county

Extension agents on irrigation patterns on a county basis. These are aggrega

m es of irrigation behavior for a given crop either for the entire state or the total irrigation in

the entire county for all crops combined. Using these data, irrigated acreage cannot be broken

down on a county by crop level – i.e., the irrigated acreage for each crop in each county – and,

therefore, site-specific irrigation patterns remain unknown.

Also, the agents tend to misestimate (underestimate) the irrigated acreage. Under ope

area irrigation systems, which are accounted through aerial photo observation, some areas may

be unobservable when under tree cover in the orchards. Thus one possible reason for the

underestimation might be undercounting of the orchards that are irrigated.

pendices B and C for alternative forecasting methods. In particular, as noted in Appendix B of this

methods. Tareen (2001) used the first method, the method of full covariance matrix forecasting. This method that takes an averaging scheme has its inherent disadvantages (see the section “Forecasting Net Return Covariances and Variances” in Appendix B), and tends to wash away the variability in the forecasts. The second method, the method of obtaining covariance forecasts from factor models (see the section “Forecasting Net Return Covariances and

2 See Apdissertation, the variances and covariances of net returns from crop production can be forecasted using three

Variances” in Appendix B), may be used to avoid those problems in future research.

12

A second potential source of information for estimating and forecasting agricultur

demand is the irrig

al water

ation permit database of Georgia. This database, established in the late 1980s,

mana

nd used to irrigate a different area than claimed on the permit application. As a sequel to

the

attempt

al commodities, the USGS estimates define all water use,

such as y using

iated with

is ged by the Environmental Protection Department (EPD). Initially, EPD required farmers

using over 100,000 gallons per day to apply for these irrigation permits. Currently, the database

has information on more than 18,000 producers reporting their intended irrigated acres with

certain irrigation systems. This is a potential source that could have been used to disaggregate

the acreage by counties. But, in order to guarantee a bigger share of water, there is a tendency of

farmers to over-report the area to be irrigated, often to an extent that exceeds the physical limits.

Another limitation to the establishment of a clear link between the permit and irrigated

acreage is that irrigation systems are not static. They may be moved from, say, one pond to the

other a

the above limitations, the claimed irrigated acres by county in Georgia may, in fact, be a

nebulous picture.

The United States Geological Survey (USGS) estimates of agricultural water use for

years 1980, 1985, 1987, 1990 and 1995 constitute the third potential source of data. In an

to parse the agricultural component of the estimates into ground water and surface water as well

as into livestock and other agricultur

agricultural, municipal and thermoelectric, in the state of Georgia. They do this b

the two data sources mentioned a while ago, namely, the EPD irrigation permit database and the

irrigation survey conducted by the county Extension agents. However, in using these two data

sources, the USGS estimates also carry over the problems (as mentioned earlier) assoc

them.

13

Obviously, we have insufficient available potential sources to quantify irrigation w

use and to forecast water demand in Georgia. Also, with regards to the main problem of inter

in this current study, which is forecasting, current models of agricultural wa

ater

est

ter use have an

an

e is obtained by subtracting the effective precipitation from the consumptive

orgia

of

ntent

s

of Southwest Georgia for the 1995-96 growing season (Fanning, 2000;

m

engineering slant and examine only the physical parameters, such as weather. In reality,

forecasting water demand requires economic and institutional variables, such as expected profits

and role of government programs.

Models based on physical parameters estimating water requirements for different

agricultural commodities were based on a formula called Blaney-Criddle (BC) formula, named

after Blaney and Criddle (1962), who found that the amount of water consumptively used by

crops during their normal growing season was closely correlated with mean monthly

temperatures and daylight hours. The coefficients they developed through this observation c

be used to convert the consumptive use data for a given area to other areas for which only

climatological data are available. The net amount of irrigation water necessary to satisfy

consumptive us

water requirement during the growing or irrigation season (Tareen, 2001).

There have been attempts to update the BC formula by more precise measures of Ge

water application rates. In Georgia, the U.S. Geological Survey (USGS) made the first study

this type. It was called Benchmark Farms Study (Fanning, 1995; Tareen, 2001). With an i

to build a monitoring network for the entire state and to improve irrigation estimation technique

based on the BC formula, USGS randomly selected and studied 200 irrigation systems in an area

covering 32 counties

Tareen, 2001). In order to measure water use, they strapped monitors to the irrigation syste

and measured the time the systems operated and calculated the associated application rate.

14

Application rates were used as a measure of water use. This way of measuring water use was

aimed at better approximating the application rates. Till date, the final results from the

not available.

study are

g

oxy for water demand. When

comple this models for water demand put

forth by US

ter for Remote

Sensing M lint River Basin with

the aid - rate measure of agricultural irrigated acres in the

mporal scope and

or water

(iii.) the downside risk associated with choosing not to irrigate,

Currently, a similar ongoing study by the University of Georgia-Agricultural Engineerin

(UGA-AE) department is examining 400 sites for three years. Focusing on the center pivot

irrigation system and examining a larger number of farms over the entire state, the study by

UGA-AE is intended to provide relatively precise measures of the application rates. The

estimates of the rates of application are supposed to serve as a pr

ted, research will contribute to the existing engineering

the GS.

Yet another study was conducted by the University of Georgia-Cen

and apping Science (UGA-CRMS). It took place in the lower F

of low level photography to get an accu

study area. This study was aimed at further improving the estimates of irrigation water

application rate by using remote sensing devices.

The studies of USGS, UGA-AE and UGA-CRMS discussed above are very valuable in

providing a benchmark for water use. However, these studies have a limited te

are also limited in the sense that they only examine the physical relationships. Demand f

is a derived demand. It is driven by several economic factors related to the decision a farmer

makes regarding irrigating a particular crop, like the following:

(i.) the market price the producer expects for the crop,

(ii.) the cost of irrigation,

15

(iv.) the effect of government support programs on prices, and

(v.) total irrigable land available.

A more precise examination of water demand in agriculture must, thus, allow for these economic

e

, are

tly and requires certain physical and economic

determ

ly a model that traces changes in the acreage due to

hanges in the economic parameters. The appropriate modeling strategy is to examine the

g mix patterns committed to irrigation when the economic and

institut of

ation is

factors in addition to the physical relationship examined by the above two studies. Moreover, th

physical models, by ignoring the economic forces that drive the choice of crop to be planted

prone to slippage,3 and hence do not do justice to forecasting water demand.

The demand for irrigation water is a derived demand evolving from the value of

agricultural product produced (Boggess et al., 1993). A key variable required in estimating

agricultural demand for water directly is price of water. For Georgia, this is zero. Therefore,

irrigation water demand cannot be modeled direc

inants. Rather, the planted acres of the crop may be used to act as the major determinant

for the derived demand for irrigation water. This entails that the relevant model uses planted

acres as the dependent variable. In the literature, such models are referred to as acreage response

models.

An acreage response model is simp

c

changes in the croppin

ional parameters of the problem, such as profitability of different crops and availability

total irrigated acreage, change. Farmers apply water on a per-acre basis and water applic

a function of the crop planted to those acres. This makes these models theoretically consistent

with the farmer’s decision-making framework.

3 In the context of agricultural water demand, “slippage” refers to a situation where a reduction in irrigated acreage takes place, with no corresponding reduction in water use (Ericksen, 1976).

16

Another desirable characteristic of acreage response models is their independence from

r conditions. Furthermore, a site-specific acreage response model, based

on coun

sed

e

contain a representative crop mix for the state and consumed approximately 51% of the irrigation

water in the state of Georgia in 1995. That is the main reason why this region is chosen for the

study. The crops under study are corn, cotton, peanuts and soybeans.

Problem Statement

Dependable and predictable water supply is vitally important for the farmers and hence

for the general well-being and economic development of the state or region under question.

There have been several proposals to develop water resource projects and to protect the use of

water for various municipal and industrial purposes in the North Georgia region, but they have

created serious problems among other water user groups in the state.

Expected profits are an important component of the acreage response model. But,

assuming prices and yields are stochastic when predicted and costs are known with certainty, the

certainty-equivalent expected profits comprise expected prices and expected yields, along with

the subsequent weathe

ty by commodity data, is considerably more useful than one on an aggregate level, such

as the state. Currently, irrigation data are available only on a state level. They need to be par

on a county by crop level (Tareen, 2001).

The Region Studied

To better understand agricultural water demand in the context of cropping mix in th

ACF River Basin, this analysis focuses closely on a 31-county region in Georgia, which

approximates the Flint River Basin (Figure 1.2). The counties, comprising the Flint River Basin,

17

Figure 1.2. The 31 Georgia Counties that Approximate the Flint River Basin

18

the covariances between them and constant costs. Therefore, it is necessary to predict the prices

and yields with as much accuracy as possible, taking all available information at hand and

conforming to economic theory. Accurately forecasting these prices and yields will enable us to

incorporate these forecasts into projections of future irrigated crop acreage. This will

significantly improve the forecast of irrigation water demand. This constitutes the first problem

we address in this research by utilizing two methods that carry two different sets of price and

yield data.

The second problem we look at is inherent in the fact that we have chosen to forecast

prices and yields by two methods. In an attempt to make the irrigated acreage predictions and

hence the water demand estimates the best possible for policymaking purposes, we perform a

simple test of performance of the two methods both in- and out-of-sample. Only the method that

better predicts out of the sample are carried over to estimate and forecast water demand.

Thirdly, the irrigated acreage response model used by Tareen (2001) included terms

involving variances and covariances of net returns. But he obtained those higher moments of

expected profits around the means of net profits. Given that forecasting involves inevitable errors

and that means are a stable measure of central tendency, forecasting around means (dispersion of

predictions from means) may give us relatively stable, unrealistic predictions and hence are

likely to render us erroneous parameter estimates. Following Holt (1999), we address this

problem by calculating variances and covariances of expected profits around forecast errors

(dispersion of predictions around observed values) and hence make the estimates from the

acreage response model more efficient. The same goes for calculating the covariances between

prices and yields.

19

This leads us to the fourth problem of accurately translating irrigated acreage predictions

to water demand predictions by applying the Blaney-Criddle (BC) formula. Blaney and Criddle

(1962), working on the quantitative estimation of vegetation water usages, found the amount of

water consumptively used by crops during their normal growing season was closely correlated

with mean monthly temperatures and daylight hours. The BC formula is that the consumptive

use (U) is equal to a seasonal coefficient (K) times a monthly consumptive use factor (F), or

U=K*F. Here, F is a function of the mean monthly air temperature in degrees Fahrenheit (t)

times the monthly percent of daytime hours (p) divided by 100, or F=t*p/100. K is a factor

relating the plant water usage for a specific species. K=Kt*Kc, where Kt=a climatic coefficient

related to the mean air temperature (t)=0.0173t-0.314 and Kc=a coefficient reflecting the growth

stage of the crop. K factors are generated under experimental conditions, where F and U in the

above formula are measured under tightly controlled conditions (K=U/F). Consumptive

irrigation requirement is given as the difference between U and the mean monthly effective

precipitation. Tareen (2001) calls this the BC coefficient. The same terminology is maintained in

this dissertation. Water demand for each crop by county is calculated by multiplying the irrigated

acres by the relevant BC coefficient, and divided by 12 to obtain the unit in acre-feet. Hence, if

the estimation of irrigated acres were made erroneously, so would the calculation of water

demand be.

Finally, using the estimates of irrigation water demand, Tareen (2001) conducts what he

calls a “sensitivity analysis” on the parameters of the acreage response model to see how

irrigated acres change with respect to prices and institution.4 This results in what Tareen (2001)

4 In this research, we would simply call this the “responsiveness” of irrigated acres to changes in economic and institutional factors.

20

calls “slippage.” Obviously, inaccurate estimates of parameters from the acreage response model

would result in inaccurate figures of “slippage.”

In essence, the crux of the problem is that agricultural economists have so far either

neglected the idea of forecasting irrigation water demand or not been successful in achieving this

with a reasonable amount of accuracy. Under the assumption of rational expectations and

utilizing the expected utility theory, this study attempts to estimate current irrigation water

demand and, given certain conditions, forecast the same using a model that predicts out of

sample better vis-à-vis an alternate model. Thus this study attempts to rectify the problems

previously encountered and make forecasting agricultural water demand for irrigation more

robust. However, forecasting is considered on a year-to-year basis and not for a long time

horizon.

Objectives

The overall objective of this study is to develop a method of precisely forecasting at least

a year in advance agricultural water demand for irrigating corn, cotton, peanuts and soybeans on

county-level basis in Georgia. In particular, the following are done in the order noted to fulfill

the basic objective of developing such a forecasting method:

1. Develop a simple statistical method and an alternative method for generating expected

prices and yields.

2. Given the price and yield forecasts generated by each of these two methods, test for the

in-sample and out-of-sample predictive power of each method as regards prices and

yields. Compare and contrast these two methods and choose one of them based on their

out-of-sample predictive power.

21

3. Develop an econometric model of crop acreage allocation based on the projected

expected prices, expected yields, expected crop returns, variances and covariances of

crop returns, calculated around forecast errors, and some government program variables.

4. Employ the acreage forecasts from the estimated econometric model to the relevant BC

coefficients to estimate water demand, and compare and contrast the forecasting and

estimation results for this rational expectations-based econometric approach against the

traditional engineering approach. Calculation of “slippage” enables us to visualize this

difference.

5. From the above water demand estimates for the econometric and engineering approaches,

use simulated forecasting scenarios to determine responsiveness of the econometric

approach vis-à-vis the engineering approach to some of the economic and institutional

variables used in the study, and precisely calculate “slippage” as a measure to distinguish

between the two approaches.

Procedures

Objective 1 is accomplished by (a) developing a statistical method for determining prices

and yields based on historical data, and (b) developing an alternative method, following Holt

(1999), with futures prices and a modified weighted average of past yields.

To achieve objective 2, the root-mean-square-error (RMSE) criterion is used to test the

in-sample and out-of-sample forecasting power of the econometric model when each of the two

methods is used. Since prices and yields are the two main economic components that determine

expected profits, the predictive power of prices and yields for both methods will be tested using

the RMSE criterion.

22

Once expected prices and yields are selected, we can easily calculate expected profits and

the variances and covariances of expected profits. On the assumption of uncorrelatedness of

disturbance terms and orthogonality of regressors to residuals, the third objective is

accomplished by linearly regressing irrigated acreages of each of the four crops (corn, cotton,

peanuts and soybeans) on expected profits, variances and covariances of profits, county-specific

dummy variables and total irrigated acreages obtained from the better of the two methods

(statistical and its alternative), judged on the basis of its out-of-sample predictive power. This

yields a set of crop acreage predictions.

Irrigated acreage forecasts obtained as estimates from the acreage allocation equations

are employed to the Blaney-Criddle (BC) (1962) formula for obtaining the current and future

water demand estimates. This lets us achieve objective 4 of this research. Specifically, predicted

acreage times the relevant BC water requirement coefficient divided by 12 gives us the monthly

water demand in acre-feet. A comparison of the water demand estimates by this econometric

approach with the engineering approach yields insights into the appropriate model for forecasting

crop acreage, and hence for forecasting agricultural water demand for irrigation.

Finally, for objective 5, by changing some of the economic and institutional variables, the

responsiveness of irrigated acres is determined. Specifically, once the base simulation is created

at the end point within the sample, several kinds of simulations are conducted. One, the variable

on peanut quotas is removed. Two, prices, yields, costs and total irrigated acreages are altered to

reflect the new out-of-sample data for three consecutive years out of the sample. Three,

embedded in the simulation for the third out-of-sample year, 2001, the institutionally forced

reduction in available total irrigated acres is considered. Three different scenarios are considered

for this third kind of simulation, and they form the basis of comparison between the engineering

23

approach and the econometric approach. A simple formula involving the water demand estimates

by the engineering approach and the econometric approach is used to calculate “slippage.”

Though objectives 4 and 5 follow a logical sequence, they are achieved almost simultaneously.

24

CHAPTER 2

LITERATURE REVIEW

Agricultural economists have basically been interested in policy analysis and forecasts

under government intervention. They have employed elasticity estimates as the guiding tool to

achieve these goals. Thus they have focused in modeling agricultural commodity response,

which have generally taken the shape of two types of model categories: one, acreage response

models; and two, supply response models.

Previous literature consists of a larger number of acreage response models in relation to

supply response models for estimating crop production. This could possibly be attributed to the

fact that planting decisions are independent of the subsequent weather conditions and, therefore,

provide an accurate forecast of planned production compared with observed output (Tareen,

2001). In this chapter, we would like to review some of the past research done on acreage

response, on forecasting in agricultural economics, and on rational expectations, particularly as it

pertains to agricultural economics. An attempt is also made in this chapter to find the linkages in

the literature among models of acreage response and forecasting. [See Appendix B for some

literature on forecasting variances and covariances.]

Literature on Acreage Response

Nerlove (1956) wrote a seminal paper on partial adjustment and adaptive expectations

models. Since that time, estimation of acreage response has resulted in a whole body of

25

literature, wherein the basic Nerlovian framework has been extended in various ways. Following

are some of the extensions that have taken place.

First, some studies have incorporated the role of government programs. Examples are

Houck and Ryan (1972); Morzuch et al. (1980); Duffy, Richardson and Wöhlgenant (1987);

Shideed, White and Brannen (1987); McIntosh and Shideed (1989); Chembezi and Womack

(1992); Massow and Weersink (1993).

Second, some other studies have considered alternative expected market price in the

model where the suggestions range from simple one-period lag (as done by Duffy et al., 1987),

to a higher of the geometric lagged function of the previous seven years’ market price or current

weighted support price (as in the case of Shumway, 1983), futures prices (as in Gardner, 1976;

Morzuch et al., 1980), and a combination of cash and futures prices (as by Chavas et al., 1983).

Thirdly, the Nerlove model has also been extended by considering the role of risk in

acreage allocation, for instance, by Just (1974); Lin (1977); Traill (1978); Nieuwoud et al.

(1988); Chavas and Holt (1990); Pope and Just (1991); Duffy et al. (1994); Krause et al. (1995).

In this type of an extension of Nerlove model, risk typically enters the model through an agent

whose objective is to optimize his/her expected utility. This concept will be looked into in

greater detail in the chapter on model development, Chapter 3.

A major portion of the literature focuses primarily on the acreage response for a single

commodity, for instance, Houck and Ryan (1972); Morzuch et al. (1980); Bailey and Womack

(1985); Duffy et al. (1987); Ahouissoussi et al. (1995); Govindasamy and Jin (1998). Single

commodity studies are potentially incomplete because they fail to incorporate all alternative uses

of land. Unlike multiple-equation models, single-equation models fail to capture the interaction

among the error terms. Hence a single-equation model is limited in providing information on

26

substitutability, even if it were to include all alternatives (Tareen, 2001). Acreage response in

multiproduct setting has comparatively fewer studies. Binkley and McKinzie (1984) have the

credit for conducting one such study.

To improve upon the single-commodity studies, Binkley and McKinzie specify a system

of crop acreage demands. Given that land is fixed in supply, a system of equations provides

information about the allocation of land to any one use and its substitutability to other uses.

However, Binkley and McKinzie’s analysis is not without serious limitations. In particular, even

though they consider behaviorial matters such as convexity and linear homogeneity, they fail to

take account of separability,5 adding-up,6 duality and assumptions necessary for reciprocity7 in

an acreage demand model. Moreover, Binkley and McKinzie discuss symmetry conditions, but

apparently do not use or otherwise test for reciprocity in their empirical analysis.

Models with multiple outputs deal with allocation of land for those outputs. They fall in

the category of land allocation models. In such models, the shares allocated to each of the crops

act as probabilities. Thus, the actual shares as well as the predicted shares are non-negative and

they all add up to unity. There can be several different specifications to ensure that the shares

sum to one, but the dual problem of adding-up and non-negativity requires the use of highly non-

5 The notion of separability is used in terms of output and refers to the technical feasibility of aggregating groups of outputs. Separability is a measure of how the marginal rate of product transformation (MRPT) is independent between two outputs, i.e., the MRPT for one output is independent of the level of another output.

6 In production theory, adding-up restrictions are typically for imposition of homogeneity. Homogenous technologies are of interest since they put specific restrictions on how the technical rate of substitution changes as the scale of production changes. This restriction is often seen in translog models. Models which use normalized quadratic functional forms (or any normalized model, such as the translog) will not have them as the restriction is imposed by normalization. The proof is based on the definition of linear homogeneity.

7 Reciprocity refers to symmetry of the cross-partial derivatives. Symmetry is an artifact of assuming that your response can be modeled using a twice-continuously-differentiable function. According to Young's theorem, the second partial derivatives of any twice-continuously-differentiable function are invariant to the order of differentiation.

27

linear equation systems. Logistic type functions have been used in literature to take care of that,

since they have the characteristic of non-linearity.

Theil’s (1969) multinomial extension of the linear logit model is a possible model to

fulfill the basic requirement. Colman (1979); Kraker and Paddock (1985); and Bewley et al.

(1987) have all adopted the multinomial logit model to strategically specify a system of crop

acreage demands conditional on all crop output prices and total crop acreage. However, the

multinomial logit models tend to become increasingly complex with the increase of the number

of crops. This could be a potential disadvantage of this strategy. Also, the authors of the above

three articles have failed to highlight the role of separability as a means of simplifying the model

structure, as noted by Tareen (2001).

Another aspect of multioutput models of agricultural firms dealt with in the literature is

the issue of land fixity, for example, Binkley and McKinzie (1984). Moore and Negri (1992)

have also modeled surface water as a fixed, allocable input to a multioutput firm. Their model

has the following three basic assumptions: (i) land and surface water are fixed, allocable inputs;

(ii) inputs are allocated to specific crop production activities; and (iii) production is technically

non-joint so the allocation of inputs uniquely determines crop-specific output levels. Moore and

Negri have derived their model specifications by assuming expected profit maximization, but

they have not imposed or even discussed the implied symmetry conditions in their estimated

acreage allocations model.

Model diagnostic issues such as multicollinearity are common in multiproduct models of

the crop acreage response system. They have been largely been addressed by adopting highly

restrictive functional forms. In so doing, these models have overlooked many of the possible

cross-price effects between crops. However, there is an alternative to these restrictive functional

28

forms, and that is to adopt restrictions on coefficients implied by fundamental behavioral theory

(Tareen, 2001).

Coyle (1993) makes an effort in that direction. His is an alternative approach to the

specification of systems of crop acreage response. Given the assumption of weak separability

between the enterprises, Coyle’s two-stage aggregation model is by far appropriate. It is simple

for estimation of a lag in a single acreage variable, but at the same time, the system of individual

crop acreage demands specified by Coyle relates demands to lags in adjustment of the overall

crop rotation. The effects of multicollinearity in the system are reduced because the derived

demands of acreage for individual crops are specified as conditional on total crop acreage, and

also because of separability and dynamic specifications. Coyle’s framework also takes into

account the reciprocity restrictions and duality relations. From the standpoint of behavioral

consistency, this is a significant addition to the previous contributions by Colman (1979); Kraker

and Paddock (1985); and Bewley et al. (1987).

The acreage response models that incorporate risk effects have been modeled for

commodities on a case-by-case basis, without consideration of the system-wide impact of these

response models, for instance, by Traill (1978); Just (1974); Pope (1982); Chavas and Holt

(1990); and Krause et al. (1995). In other words, the constraints imposed by total acreage have

not been incorporated into model specifications as they have been for other agricultural supply

models, for instance, by Chambers and Lee (1986).

Since acreage decisions are made among competing commodities, a systems framework

is the appropriate modeling technique. Such a technique incorporates contemporaneous

covariance of disturbances across the equations and yields efficient estimators (Tareen, 2001).

29

Studies by Bettendorf and Blomme (1994); Barten and Vanloot (1996); and Holt (1999) are

some notable examples, since they examine acreage response with risk in a systems framework

Bettendorf and Blomme (BB) (1994); and Barten and Vanloot (BV) (1996) have

generalized the cobweb theorem8 for markets of eight agricultural products. They represent the

supply side by an acreage allotment model, the latter describing the areas under cultivation for

various crops in response to price expectations. The demand side has been modeled as an

inverse demand system. These two systems are estimated for historical data for Belgium in the

early part of this century. Barten and Vanloot’s conclusion is that the strength of the response is

dependent on substitution possibilities. In agriculture, the latter might be restricted for a number

of reasons: for example, one, the lack of quality of the soil; two, the lack of knowledge of the

farmer; and three, the specificity of consumer preferences.

BB and BV’s (1994, 1996) model was developed as a first-order differential acreage

allocation model that uses the basic mean-variance utility framework. It is consistent with

certainty equivalent profit maximization and constant absolute risk aversion. The BB-BV

specification is useful in estimating acreage response with time-series data but has limited

application with cross-sectional or panel data. Holt (1999) extends BB-BV’s (1994, 1996)

analysis to deal with cross-sectional and panel data. Holt’s extension is also useful for

maintaining the theoretically useful properties of homogeneity, symmetry and adding-up.

Forecasting Literature

In general, forecasting literature may be divided into two broad groups: one, structural

econometric models; and two, time-series models that use Box-Jenkins (1976) techniques.

8 The cobweb theorem is one that links supply reacting to the lagged price to demand reacting to the current price. One can generalize this idea to a set of interdependent markets.

30

According to Allen (1994), forecasting in agricultural economics may similarly be categorized

into two groups. Moore (1917) is credited with having done the first econometric forecast for

agricultural commodities. His was structural forecasting with regression of cotton yield on

rainfall and temperature in selected months. It outperformed the USDA models of forecast based

on condition reports (Tareen, 2001).

In its infancy, econometric forecasting was characterized by single-equation forecasting

models. For instance, hog prices were forecasted by Sarle (1925), cotton acreage by Smith

(1925), and cattle prices by Hopkins (1927). One of the few early efforts of pure forecasting

using a single equation was done by Cox and Luby (1956), whose specifications for 6- and 12-

month ahead price forecasts also relied on explanatory variables known non-stochastically at the

time of forecasting. Nerlove (1958) developed adaptive expectations for prices, thus introducing

dynamic structure to the field of agricultural economics. He modeled expected prices as an

exponentially decaying function of past prices. An excellent review of this line of research has

been done by Askari and Cummings (1977).

Estimating time-series models and comparing these models to their structural counterpart

have picked up an interest among economists since the sixties. Time-series models in their

earliest form aimed at deterministic trend extrapolation. Jarret’s (1965) study of Australian wool

prices is one such earlier application of time-series methods in agricultural economics. Probably

the earliest application of time-series methods to U.S. agriculture is the forecast of wheat yield

by Schmitz and Watts (1970). They apply Box-Jenkins and exponential smoothing to annual

data. When we compare the extrapolation and the smoothing methods, we may consider

exponential smoothing to produce better out-of-sample forecasts. However, unlike business

31

forecasting, this standard has not been followed in the agricultural economics literature (Tareen,

2001).

Also, at about the same time, in the 1970s, spectral analysis was used to explain the

historical patterns, for example, by Rausser and Cargill (1970); Cargill and Rausser (1972); and

Hinchy (1978). In the 1980s, Shonkwiler and Spreen (1982) used a transfer function to study

multivariate time series.

Vector autoregression (VAR), an atheoretical approach to modeling, is often criticized as

causing the problem of over-parameterization. Nevertheless, Bessler (1984) introduced it in the

field of agricultural economics. Several articles have been written in the 1980s suggesting ways

to overcome the undesirable effects of over-parameterization. Kaylen (1988) has reviewed those

articles. It is still a popular approach in microeconometrics. [See Appendix C for a note on vector

autoregression.]

Literature on Rational Expectations

Throughout the seventies and eighties formation of expectations has been the core of a

lot of macroeconomic research. Following Muth (1961), attention has been concentrated

particularly on the concept of rational expectations (RE), i.e., that “agents form expectations

consistent with their knowledge of the underlying processes of the economic system and taking

into account all available information” (Fisher, 1992). According to Begg (1982), the RE

hypothesis has sufficiently penetrated all areas of macroeconomic theory and applied work to

have caused a “revolution in macroeconomics.” Large-scale, empirical macroeconomic models,

such as forecasting models, sooner or later incorporate rational expectations in their basic

structure.

32

Rational Expectations in microeconomics in general and agriculture or agricultural

economics in particular have been studied by quite a few researchers, for instance, Ezekiel

(1938), Nerlove (1958), Muth (1960), Askari and Cummings (1977), Shonkwiler and Emerson

(1982), Holt (1992), Ahouissoussi et al. (1995).

Agricultural supply models can be conveniently broken down into two categories: one,

models without storage – the ones for which storage of the commodity is not possible (see, for

example, Nelson, 1975; McCallum, 1976; Huntzinger, 1979; Goodwin and Sheffrin, 1982;

Cumby et al., 1983), and two, models with storage – the ones for which storage of the

commodity is possible (see, for example, Kendall, 1953; Muth, 1961; Cox, 1976; Peck, 1976;

Turnovsky, 1979). The existing empirical evidence pertains mostly to the former category –

models without storage.

Models with storage are more complicated with inventories of commodities being held

for anticipated profit. These models can also be employed for futures trading (see, for example,

Cox, 1976; Peck, 1976). Turnovsky (1979) analyzed a shochastic model with RE, but he

assumed price expectations would be formed adaptively in the absence of futures markets. This

assumption essentially meant that the introduction of futures markets would, in itself, convert a

market with non-RE to one with RE.

Some of these models (of the storage type) feature expectations and sophisticated

dynamics. Eckstein (1984) examined Egyptian data on cotton and wheat prices and production

from 1913 to 1969. Following a technology shock, the data on crop areas exhibited an interesting

path to equilibrium. With a change in the relative prices of the crops, cotton and wheat areas

responded in opposite directions and fluctuated frequently until reaching their means. Eckstein

tested if a RE model that accounted for production constraints could simulate the unique

33

properties of the Egyptian data. The RE model sufficiently reproduced the oscillation in crop

areas observed in the data due to expectations about the future.

Also, using Greek, Turkish and U.S. tobacco data for 1953-1980, Zanias (1987) modeled

the demand for tobacco exports by tobacco manufacturing firms that faced adjustment costs.

Treating tobacco as a heterogeneous product, i.e., assuming different types and varieties of

tobacco were imperfect substitutes in manufacturing, substitution possibilities were limited due

to adjustment costs, except in the long run and through technical progress. Because the estimated

short-run price elasticity was much smaller than the long-run value, the model confirmed that

tobacco manufacturers adjusted slowly to the new equilibrium following a price change.

Therefore, the tobacco firm lost less by being in disequilibrium than by adjusting rapidly to

prices. Zanias’ conclusion was that studies disregarding adjustment costs would produce

elasticities underestimating true responses.

Holt (1992) examined the demand and production of corn and soybeans in a RE model

that accounted for agricultural price supports and acreage set-aside programs. Previous research

had studied price supports using a single market, but this was the first application of a

multimarket model with bounded prices under RE. Since both corn and soybeans used many of

the same resources, production decisions were made jointly, and so Holt argued that cross-price

effects were important in studying the markets for those two crops.

Holt’s (1992) model consisted of two each of demand and production equations, with the

corn-production equation being of particular interest. It was assumed that expected corn and

soybean prices and corn area diverted (a proxy for the set-aside program) would affect corn

supply. Annual data from Agricultural Statistics (1950-1985) were used to estimate the demand

34

and supply models. All of the estimated own- and cross-price elasticities had the usual signs, and

most were statistically significant.

By estimating alternative models with less-restrictive price-expectations processes, Holt

then tested for the appropriateness of the RE assumption and found the model incorporating RE

to be performing as well as the alternative models. Also, testing for the usefulness of the

multimarket context while estimating corn and soybean models, the hypothesis that the corn and

soybean markets were unrelated was rejected.

Finally, Holt (1992) simulated his model over the sample period, removing the price-

support and acreage set-aside program effects. These “free-market” simulations showed that

removing price supports had a larger impact on the corn than on the soybean market. The

simulation showed that, without government intervention, corn prices were well below the

observed market prices for 27 out of the 35 periods studied (the first period lost with the creation

of a lag). Also, corn production was above actual production for a large portion of the sample

period. In the soybean market, the effects of removing government intervention were smaller,

but, like in the corn market, soybean prices were lower.

More on the concept of RE and its use in microeconomics, agriculture and agricultural

economics appears in the last section (“Rational Expectations Hypothesis”) of Chapter 3.

Focus of this Study

Forecasting in the literature of agricultural economics has mostly focused on prices and

production. Allen (1994) has an excellent review of forecasting in agriculture articles. There is

some literature on derived demand for agricultural inputs in general and for irrigation water in

particular, as by Lynne (1978); Apland et al. (1980); Nieswiadomy (1985); and Kulshreshta and

35

Tewari (1991). However, focus of much of this literature is agricultural production in the

western United States, for instance, by Gisser (1970); Connor et al. (1989); and Ogg and

Gollehon (1989).

Very little research appears to have been done on irrigation water demand in the

southeastern regions of the U.S. (for instance, by Pierce et al., 1984; Duffy et al., 1994; Moss and

DeBodisco, 1999; and Houston et al., 1999).

More scarce seems to be research on forecasting irrigation water demand, either on a

national or a regional level. Tareen (2001) develops a method to forecast Georgia agricultural

water demand for corn, cotton, peanuts and soybeans on a county basis. Tareen’s (2001) method

employs the irrigated acreage response to changes in the economic climate of Georgia on a

county by commodity basis. More on this methodology is discussed in the next chapter.

The current study maintains almost the same irrigated acreage model specification, but

expands its scope and realism by adding a set of three government program variables and an

extra set of dummy variables, and utilizes the same underlying theory (namely, of expected

utility) as Tareen’s (2001), but it addresses the above problem in the light of more precisely

estimating and forecasting the acreage allocation on a county-by-commodity basis using a

statistical method and another alternative method, and consequently estimating current water

demand and forecasting future water demand more precisely. The theoretical models utilized to

attempt this are presented in the following chapter.

36

CHAPTER 3

THEORETICAL MODELING OF ACREAGE RESPONSE

In this chapter, we lay out the theoretical bases for the empirical analyses to follow. In

particular, this chapter has the following sections. First, expected utility theory is defined as a

general case. Next, the properties of a representative utility function are formalized with a

Taylor series expansion. Then, a theoretical model of acreage response is derived based on

expected utility function of a farming enterprise. The rational expectations hypothesis, with its

specific relevance to agricultural economics, is laid out at the end.

The demand for irrigation water is a derived demand that evolves from the value of

agricultural commodities produced. The value of agricultural commodities, on the other hand,

may depend on several things. Static and deterministic empirical models of water demand

indicate that the adoption of modern irrigation technologies depends on price of water, labor,

output level, output prices, soil slope, water-holding capacity and climate (Tareen, 2001). Studies

by Caswell and Zilberman (1985); Nieswiadomy (1988); Negri and Brooks (1988); Lichtenberg

(1989); and Schaible, Kim and Whittlesey (1990) suggest that, with the introduction of modern

technology, irrigation tends to use less water and at the same time render an increase in yields.

With its application on poorer land qualities, both these effects appear to be stronger.

Deterministic models are effective in assessing seasonal water demand and the choices in

irrigation technology that risk-neutral producers would undertake. (A note on risk-neutral, risk-

averse, and risk-seeking individuals will follow in the next section.) However, given that yields

37

and prices are “risky,” the profits of an enterprise involve uncertainty. Irrigation may be

considered a risk-reducing technology. Then, the decision to irrigate by a risk-averse individual

is appropriately modeled, in decision-making models, through techniques allowing for the effects

of risk.

The major analytic tool for solving decision problems under risk is the expected utility

model. The expected utility hypothesis states that the individual assigns a utility value to each

mutually exclusive activity with an associated probability distribution that is an outcome of a

decision. The preferred choice has maximum expected utility. The expected utility theorem

provides a complete theory of choice under uncertainty. Therefore, it is widely used by

economists to formally describe individual decisions under risk and uncertainty.

It was Bernoulli who first formulated the expected utility theorem in 1738, when he

postulated that an extra dollar has more value to a poor man than to a rich man. Using a set of

behavioral axioms, von Neumann and Morgenstern (1944) extended the concept to the case of an

expected utility model, where a representative agent maximizes expected utility subject to an

endowment constraint.

The Expected Utility Theory

Let us suppose we have a representative firm that wants to make future investment plans.

In so doing, it will consider the probability of possible outcomes. Probability may be defined as

a measure of the likelihood an outcome will occur, where an outcome is a particular result when

undertaking an action. If an outcome is certainly going to happen, then the probability is one, and

when an outcome cannot happen at all, the probability is zero.

38

Now, depending on perception and past experience, we may consider two kinds of

probabilities: subjective and objective. Subjective probability is where a firm or household has

some perception if an event will occur. This perception may be based on current market prices,

preferences, income, and so on. Thus, through time and across individuals and firms, subjective

probabilities are likely to vary. Objective probability is an alternate type of probability that

measures the frequency with which a certain outcome will occur. This is based on past

experiences.

A firm chooses alternatives with uncertain outcomes by means of known probabilities.

These risky alternatives are called states of nature or lotteries. In this discussion, the letter S

denotes a state of nature. A state of nature is a set of probabilities, summing to one, with a

probability assigned to each of the n outcomes. In general, a state of nature is a set of

probabilities associated with all n outcomes.

Commodities and states of nature are fundamentally different in that commodities can be,

and generally are, consumed jointly. An example of joint consumption of commodities is

driving and listening to the radio at the same time. On the other hand, states of nature, by

definition are mutually exclusive, and hence cannot be consumed jointly. Thus, with two

possible states of nature, we cannot have a 20% probability of rain and an 80% probability of

rain simultaneously.

This notion that two or more states of nature cannot be jointly consumed is a fundamental

assumption of many theories that deal with choice under uncertainty. This assumption may be

summarized by the following axiom, called the “Independence Axiom”:

39

If S, S’, and S” are alternative states of nature and D is the probability of the states of nature S

and S’ occurring, then S š S’ if and only if DS + (1 - D)S” š DS’ + (1 - D)S”. 9

To explain the above axiom, the preference a firm has for one state of nature, S, over

another state, S’, should be independent from other states of nature, say, S”. This other state of

nature, S”, should be irrelevant to the firm’s choice between the other two states of nature, S and

S’. For example, the preferences associated with a 2/5 probability of studying and a 3/5

probability of watching a movie versus a 1/3 probability of studying and a 2/3 probability of

watching a movie are independent of a 1/4 probability of studying and 3/4 probability of watching

a movie. In other words, what does not happen or is impossible has no effect on the level of

preferences between two possible states of nature.

Based on the Independence Axiom stated above, choice under uncertainty has a utility

function that is additive for consumption in each possible state of nature. This means that, for all

possible states of nature, utility from consumption in one state of nature is added to the utility

from consumption in another state. Such a utility function is called the expected utility function

or the von Neuman-Morgenstern utility function. Mathematically, for two possible states of

nature, 1 and 2, the expected utility function is written as

U(x1, x2, D1, D2) = D1U(x1) + D2U(x2), (3.1)

where

U1 and U2 are utility functions associated with contingent commodity10 bundles x1 and x2

consumed in states of nature 1 and 2, respectively, and

D1 and D2 are the probabilities of the states of nature occurring. Note that D1 + D2 = 1.

9 The symbol š indicates “preferred to or indifferent to.” 10 A contingent commodity is a commodity whose level of consumption depends on which state of nature occurs. For example, the amount of popcorn you consume depends on if you go to the movies or not.

40

What the expression (1) above states is that expected utility is the weighted sum of the

utility from consumption in the two states of nature, where the weights are the probabilities of

the states occurring. So, if only one of the states of nature occurs, say state two, then D1 = 0 and

D2 = 1, and the utility function reduces to U = U(x2). Alternatively, if state one occurs, then D1 =

1 and D2 = 0, and the utility function reduces to U = U(x1).

With uncertainty, both the probabilities lie between 0 and 1, i.e., 0 < D1, D2 < 1, and,

given the alternative possible states of nature, the utility function represents the average or

expected utility.

In contrast, for certainty utility functions, which are ordinal measures of utility, expected

utility measures utility on an interval scale.11 Thus, unlike certainty utility functions, the changes

in the marginal utilities of expected utility do represent changes in preferences. For example,

specifically speaking, MU1 = MU/Mx1 = D1MU1/Mx1

represents the change in utility from a change in the consumption bundle x1. Thus, any

monotonic transformation of the expected utility function may not yield the same measure of

firm preferences. The reason for this result is the independence axiom may be violated by a

monotonic transformation.

However, there are some transformations that do not violate the Independence Axiom.

They are increasing linear transformations, and are also called positive affine transformations or

positive linear transformations. A positive linear transformation is written in the form

V(U) = aU + b, a > 0. (3.2)

For instance, consider the following expected utility function:

U(x1, x2, D1, D2) = D1 ln(x1) + D2 ln(x2). (3.3)

11 At an interval scale, the magnitude of the relation between the different levels of utility is known.

41

A linear transformation of (3) is

V(U) = aD1 ln(x1) + aD2 ln(x2) + b. (3.4)

The marginal utilities associated with this function (3.4) above are

MU1 = aD1/x1, MU2 = aD2/x2,

and these do not violate the Independence Axiom.

Firms’ preferences are conveniently represented by expected utility under uncertainty.

Hence it is widely used throughout economic theory, yielding positive as well as normative

implications. However, expected utility cannot offer universally reasonable explanations of firm

behavior. For one thing, in practice, we may experience some paradoxes that invalidate the

foundations of expected utility theory. One example is the Allais Paradox. In Allais Paradox, an

individual is shown to prefer a sure return as compared to a lottery with a higher expected return

(see Allais, 1953).

Another example is Machina’s Paradox. Let’s say, for instance, there is a disappointed

fan, who is unable to get a ticket for the Super Bowl. He might rather go entirely without

watching the Super Bowl, even on television. He might think that watching the game on the

television would reinforce his disappointment. Thus, he might end up choosing an alternative

with a lower expected return (see Machina, 1987).

These paradoxes illustrate that there may exist individual examples of preferences that

violate the Independence Axiom. They limit expected utility as a model of preferences. These

paradoxes may look analogous to the Giffen Paradox in the aggregate investigation of markets,

but expected utility can still be assumed to represent preferences.

42

Assumptions and Properties of a Representative Utility Function

Following are some of the assumptions about individual preferences and the distribution

of returns made to simplify the expected utility model for empirical analysis:

1.) If returns are normally distributed, the decision maker can rank alternatives using only two

parameters, expected value and variance, without concern to the higher moments of the

distribution.

2.) The individual is assumed to behave as if he or she were an expected utility maximizer, and

maximizing expected value, ceteris paribus, is an appropriate goal.

3.) The decision maker is assumed to be a risk averter, so that the individual wants to minimize

the dispersion of returns.

To see the properties of the representative utility function, it helps to formalize the

results of expected utility maximization. The usual way of formalization is to derive a

multivariate Taylor series expansion of the utility of profits, denoted U(Bi), for the four crops

under the current study (i = corn, cotton, peanuts and soybeans) around the expected value, h =

E[B].

In order to proceed with the Taylor series expansion, we need to define a couple of

notations. One, a gradient vector, G(B), is defined to have components given by

Gi(B) = MU(B)/MBi, i = 1, . . . , 4, (3.5)

And, two, a Hessian matrix, H(B), is defined with components

Hij(B) = M2U(B)/MBi MBj, i, j = 1, . . . , 4. (3.6)

Both G and H are functions of B: the G(B) is interpreted as a four-component vector and H(B) as

a four-by-four matrix.

Thus, using (3.5) and (3.6), the Taylor series for U in vector-matrix form reads

43

U(B + h) = U(B) + G(B)T h + ½ hT H(B) h + . . .. (3.7)

Here, U is the fixed point of expansion in the four-dimensional space, sometimes written as ú4,

and h is the variable vector in ú4 with the components h1, h2, h3 and h4.

By Young’s theorem, insofar as the partial derivatives are all continuous, they are

invariant to the order of differentiation. As a special case, if the second partial derivatives of U

are all continuous, then H is a symmetric matrix; i.e.,

Hij(B) = M2U(B)/MBi MBj = M2U(B)/MBj MBi = Hji(B), (3.8)

with

hT Hii(B) h = Fii = Var(Bi), (3.9a)

hT Hij(B) h = Fij = Cov(Bi,Bj). (3.9b)

Expression (3.7) illustrates that the expected utility of a risky project can be expressed in

terms of the mean and a series of higher moments of the associated probability distribution. The

appropriate number of higher moments is determined by several factors, like the complexity of

the utility function, the desired accuracy of the approximation and the characteristics of the

distribution of returns.

However, if we trust the Central Limit Theorem, we have to believe that the normally

distributed returns are more likely than any other type of distribution (Samuelson, 1970).

According to Hogg and Craig (1970), if the first two moments completely specify a normal

distribution, a functional form that incorporates only the first two moments is sufficient.

In agricultural situations, however, the normality of agricultural returns is not assured.

Thus, a quadratic expected utility function poses to be a possible alternative assumption. For one

thing, for a quadratic function, the third derivative of U, denoted U’’’, and its higher derivatives

are zero. So higher moments of such functions are irrelevant: the first and second moments are

44

Risk AverterE(B)

Risk Neutral

Risk Seeker

F2B

Figure 3.1. Indifference Curves for Risk-Averse, Risk-Neutral and Risk-Seeking Individuals in an Expected Utility and Variance Space

sufficient to characterize the function entirely. Given the assumption of risk aversion, the

expected utility of profits, EU(B), is an increasing function of the first moment of expansion

(“gradient”) and a decreasing function of the second moment of rate of expansion (“Hessian”)

for the risk-averse decision maker.

Figure 3.1 illustrates the respective indifference curves for risk-averse, risk-seeking and

risk-neutral decision makers. The basis for these three different types of curves is that expected

utility functions for an individual are typically categorized in those three ways. They are defined

below, as done by Binger and Hoffman (1997).

1.) Risk-Averse: An individual is said to be risk-averse if for constant wealth, a certain

45

sure outcome is always preferred to a lottery with the same expected value but for

some positive variance.

2.) Risk-Neutral: An individual is risk-neutral if he or she is indifferent between the

certain outcome and the gamble.

3.) Risk-Seeking: An individual is risk-seeking if the lottery is preferred.

We may note that the fact that the indifference curves for the risk-averse individual are

convex to the horizontal axis indicates that the direction of increasing expected utility is upward

and to the left. We assume diminishing marginal rate of substitution (MRS) for a risk averter and

increasing MRS for a risk seeker. Hence we get the shapes of the indifference curves as shown in

Figure 3.1.

Having identified the assumptions and properties of a representative expected utility

function in general, we may now proceed with the development of the specific expected utility

function for the farming enterprise.

Theoretical Framework for Irrigation Decision

Irrigated acreage decision-making considers two theoretical issues, viz., expected utility

maximization and agronomic consideration. Once the expected utility maximization is laid out,

the agronomic considerations are incorporated in the theoretical framework for irrigation

decision-making. Basically what follows is the acreage supply response model developed under

expected utility maximization by Chavas and Holt (1990) specify and estimate a system of risk-

responsive acreage equations for corn and soybeans in the United States.

Let us consider a farming enterprise in a given county that produces n crops over A acres

of irrigated land. Let Ai denote the number of acres of the ith irrigated crop with a corresponding

46

yield of Yi per acre. Let Yi be sold at the market price of Pi per unit of yield. This activity

results in the following revenue function, R, for the farm:

nR = E PiYiAi. (3.10) i=1

Equation (3.10) implies that revenue (R) is a linear function of stochastic prices and yields. By

assumption, the vectors of prices P = P1, ..., Pn and yields Y = Y1, ..., Yn, respectively, are

unobserved at the time of acreage allocation. This makes R a risky variable.

Assuming that the total variable costs, C, for the farming enterprise are known with certainty, the

input prices being given, and per acre costs are known at the time of irrigated acreage

commitment, the costs of such an enterprise can be defined as

nC = E ciAi, (3.11) i=1

where ci is the variable cost of production per irrigated acre of the ith crop.

Now we may talk about the constraints on the irrigated acreage. The irrigated acreage

requires that all land be allocated to one of the n enterprises, and also that total irrigated acreage

does not exceed the total available acreage. These constraints may be written down as the

equations (3.12a) and (3.12b) below:

f(A) = 0, (3.12a)

which is the production frontier representing the multiproduct, multifactor technology of the

firm, and

n

EAiy = Ay, (3.12b) i=1

where variable Aiy denotes the irrigated acres of the ith crop in a county y, and Ay is the total

irrigated acres available in the yth county.

47

Assuming the representative firm maximizes expected utility under competition, the

decision model is given by

n

Max EU(B) = Max EU[(GBiAi)], (3.13) A Ai i=1

subject to the acreage constraints in equations (12a) and (12b). Thus, the profit per acre accruing

from the ith crop is

Bi = PiYi - ci. (3.14)

The way the decision model (3.13) is formulated indicates that the acreage decision A is

made under uncertainties in both price and production. With given subjective probability

distributions, both yields and output prices are random variables. Therefore, the expectation

operator (E) in (3.13) over the stochastic variables Y and P is based on the information available

to the firm at the time of planting.

It is obvious that the optimization model in equation (13) has direct economic

implications for the optimal irrigated acreage allocation, Ai*. For instance, in the case that the

firm is not risk-neutral, the optimal acreage decision will depend not only on expected profits,

but also on higher moments of the profit distributions. For normally distributed returns, the

expected utility criteria are completely specified by the expected value and variance of returns.

It is fitting in this context to introduce the concept of the expected value-variance (EV)

rule. Markowitz (1952) developed the EV theory as a portfolio selection tool in an optimization

setting. Since then, it has been a popular method of ordering choices into efficient and inefficient

sets. The EV set is defined as the choices or sets of choices that provide the minimum variance

for alternative levels of expected returns. The efficient set contains the preferred choice for a

well-defined set of producers, whereas the inefficient set does not contain the preferred choice.

48

More explicitly, the EV rule is based on the proposition that, if the expected value of the

choice, say X, is greater than or equal to the expected value of choice Y, and the variance of X is

less than or equal to the variance of Y, and there is at least one strict inequality, then X is

preferred to Y by the decision maker (Tareen, 2001).

In literature, the use of the EV approach is justified on the basis of the following four

conditions:

(1) quadratic utility,

(2) normality,

(3) choices involving a single random variable, and

(4) choices involving linear combinations of the random variables.

Unfortunately, only condition (4) characterizes most empirical situations. First, the implication

of quadratic utility is that, beyond a certain monetary outcome, marginal utility becomes

negative and the investor in the model is characterized by increasing absolute risk aversion.

Second, in real life situations, seldom do we find random variables taking on symmetrically

distributed values ranging from negative to positive infinity as implied by normal distribution.

Third, the relatively more important portfolio decisions concern choices involving more than one

risky asset.

Because the conditions underlying the EV approach have the above shortcomings, the

justification of this approach in empirical analysis has become dependent on its ability to

approximate results from the more general EU models. Levy and Markowitz (1979) have

demonstrated that the EV model is appropriate as a second-order Taylor series approximation to

all risk-averse utility functions. Modeling acreage response as in this study is one such

49

application of the EV theory that is being used in approximating expected utility as a function

profits and variance-covariance of profits.

According to the EV theory, an increase in the profits of the ith crop increases the

expected utility of the producer. This drives the producers to add more irrigated acres of the ith

crop by substituting away from the jth crop and vice versa for all crops where i…j. On the other

hand, an increase in the variance of the ith crop increases risk and drives expected utility of the

producer down. With higher variance, therefore, the producer will reduce irrigated acreage of a

crop. However, increased variance of the jth crop, with j…i, indicates an increased risk associated

with crop j. Thus, reducing irrigated acreage of the jth crop is a possible strategy adopted to free

up resources to commit to crop i.

A negative correlation between two crops in a producer’s portfolio signifies reduced risk.

A rising covariance between crops and i and j, with i…j, means more exposure to risk to a

producer who has both crops i and j in his or her portfolio. Expected utility may be increased by

reducing irrigated acreage of both i and j. However, according to portfolio theory, with a rising

covariance between crops j and k, with j, k…i, a producer may increase his or her expected utility

by reducing irrigated acreage of both j and k and committing resources to crop i.

Decision making in irrigated acreage takes into serious consideration such agronomic

factors as rotation of crops, which is the successive planting of different crops in the same field.

Rotations usually range from two to five years in duration, with a farmer planting part of his or

her land to each crop in successive rotation (National Research Council, 1989).

Rotations provide well-documented economic and environmental benefits to agricultural

producers (Heady, 1948; Heady and Jensen, 1951; Power, 1987). While some of the benefits of

rotation are inherent to all rotations, there are some others that depend on the crops planted and

50

the length of the rotation, and yet others that depend on the types of tillage, cultivation,

fertilization and pest control practices used in the rotation (National Research Council, 1989).

Much of the literature on crop rotation refers to the “rotational effect” (Power, 1987).

This term is used to describe the fact that in most cases rotations will increase yields of a grain

crop beyond yields achieved with continuous cropping under similar conditions. Many factors

are thought to contribute to the rotational effect, including soil moisture, pest control and the

availability of nutrients. It is generally agreed that the most important component of this effect is

the insect and disease control benefits of rotations (Cook, 1986; Tareen, 2001).

In respect of insect and disease control, rotation is used in Georgia against the potential

damage caused by white molds and nematodes. The typical rotation cycle is three years, with

corn, cotton, peanut and soybeans planted alternately. Specifically, cotton works the best against

the infestation of nematodes. Rotating corn with soybean virtually eliminates the damage caused

by corn rootworms. According to the University of Georgia Extension Services, in order to

minimize the risk of nematodes to peanuts, planting peanuts after corn may be practiced (Tareen,

2001).

The irrigated acreage (IA) allocation equation emerges from the solution to the decision

model expression in (3.13). The optimal choice of A (denoted as Ai*) is a function of the

following variables and their estimated parameters: (a) total irrigated acres available (TIA), (b)

expected profits for each commodity ( π ), (c) variances of these profits (Fii), and (d) cross-

commodity covariances of profits (Fij). Therefore,

Ai* = f (TIA, π , Fii, Fij,) œ i, j = 1, ... , n, (3.15)

where TIA = total irrigated acres available,

π = expected profits,

51

Fii = variance of expected profits for crop i, and

Fij = covariance of expected profits between crops i and j.

The acreage response model in (3.15) may be decomposed into two parts:

substitution effects and expansion effects. They are defined as follows:-

i.) Substitution Effects: In making decisions about irrigated acreage allocations,

producers may compare the first and second moments of profits of alternative

enterprises. The substitution among crops for a utility-maximizing firm are assumed

to be driven by a comparison of expected per-acre profits, and the variances and

covariances of recent profits of alternate enterprises. These are called substitution

effects.

ii.) Expansion Effects: Along with substitutions between irrigated crops, over time there

has been an increase in irrigated acreage due to changes in irrigation technology,

costs of irrigation, irrigation policy, lender practices relative to irrigation, and

producers’ assessments of future economic conditions in agriculture, all of which may

stimulate expansion or contraction of total irrigated acreage, partly or wholly

independent of year-to-year variations in relative expected prices, yields, and costs of

a set of crops. This means that even if relative profits of a set of crops were expected

to remain constant, changes in total irrigated acreage will be reflected in changes in

the irrigated acreages of individual crops. These impacts represent an expansion

effect. They are captured by the parameters of the total irrigated acreage variable

included in the equation for each commodity. The derived irrigation allocation

function in equation (3.15) will be of primary interest later in this research.

52

Rational Expectations Hypothesis

The econometric literature on testing for rationality (or the hypothesis of RE) is not very

clear because of the seemingly different tests employed. But basically there are four different

tests used extensively. Where t-kE(Xt) indicates the expectation reported in the survey for a

variable Xt made at time t – k, following are the four tests of rationality:-

1.) Unbiasedness: The survey expectation should be an unbiased predictor of the variable.

That is, in a regression of the form

Xt = a + b t-kE(Xt) + є t, (3.16)

the coefficient estimates should be a = 0 and b = 1.

2.) Efficiency: The survey expectation should use information about the past history of the

variable in the same way that the variable actually evolves through time. That is, in the

two regressions

t-1E(Xt) = a1 Xt-1 + a2 Xt-2 + … + an Xt-n + є t (3.17)

and

Xt = b1 Xt-1 + b2 Xt-2 + … + bn Xt-n + u t, (3.18)

it must be true that ai = bi for all i (i = 1, 2, …, n).

3.) Forecast-Error Unpredictability: The forecast error, i.e., the difference between the

survey expectation and the actual realization of the variable, should be uncorrelated with

‘any’ information available at the time the forecast is made.

4.) Consistency: Forecasts for the same variable given at different times in the future should

be consistent with one another. For example, in the regressions

t-2E(Xt) = c1 t-2E(Xt-1) + c2 Xt-2 + … + cn Xt-n + є t (3.19)

and

53

t-1E(Xt) = a1 Xt-1 + a2 Xt-2 + … + an Xt-n + u t (3.20)

it must be true that ci = ai for all i (i = 1, 2, …, n).

Even though the above tests might seem quite dissimilar, they are simply different

devices to test the consistency of the reported survey expectations with being conditional

expectations. All the tests are in fact just different ways of testing properties of conditional

expectations. For example, in the efficiency test above, consider a situation where a1 ≠ b1.

Subtracting equation (3.17) from equation (3.18) renders the expression

Xt – t-1E(Xt) = forecast error = (a1 – b1) Xt-1. (3.21)

Since by hypothesis a1 ≠ b1, the forecast error is correlated with Xt-1, which violates the

orthogonality property of conditional expectations as long as Xt-1 is contained in the information

set. Although it would be desirable for any expectation mechanism to satisfy at least some of the

above four properties, conditional expectations must satisfy all of them (Sheffrin, 1996).

The concept of RE has mostly been used in macroeconomics and finance (see, for

example, Bell, 1985; Moore and Meyers, 1986; Kollintzas, 1989). Its use in microeconomics is

relatively recent. Three areas where the concept has been used the most in empirical

microeconomic modeling are agriculture (see “Literature on Rational Expectations” section of

Chapter 2 for literature), housing investment and price appreciation (see, for example, Witte,

1963; Kearl, 1979; Poterba, 1980; Abel, 1980; deLeeuw and Ozanne, 1981; Blanchard, 1981;

Topel and Rosen, 1988) and micro decision making (see, for example, Rust, 1987; Wolpin,

1987). [For a fuller exposition of the microeconomics of RE, efficiency gains or otherwise

through aggregation or averaging of information, see Sheffrin, 1996.]

Askari and Cummings (1977) have listed over 500 studies on agricultural-supply

response in which variants of Nerlove’s (1958) model were used. Given this large body of work,

54

even though one may naively assume that the adaptive expectations hypothesis was clearly

established, the conclusion would not be warranted. There are only a few studies that even

attempt to estimate an agricultural-supply function that assumes rational expectations and still

fewer that test for rational expectations (Sheffrin, 1996).

This research only assumes but does not test for rational expectations insofar as the price

and yield forecasts are concerned and hence in the modeling of acreage allocation that lead us

into the simulations allowing us to estimate current water demand and forecast future water

demand.

55

CHAPTER 4

DATA SOURCES AND TRANSFORMATIONS,

AND CHOICE OF METHODOLOGY

One-year-ahead prediction of irrigated acreages of each of the four crops under study by

county essentially entails the estimation of an irrigated acreage response model (equation (3.15)).

This in turn requires data on irrigated acreage on a crop-by-county basis, and data on prices,

yields, costs and government program variables. The specific data requirements for the analysis

and available data sources are identified, and the assumptions and techniques used in going from

the available to the required data are described in this chapter. Also, the better of the two

methods of forecasting prices and yields is chosen. The first section is devoted to a discussion on

acreage data, its sources, methods and assumptions for imputing irrigated acreage by crop and

county, as done by Tareen (2001). The data sources for prices, yields and costs are identified in

the second section for the two sets of expected prices and expected yields (coined above and in

other places of this dissertation as the two “methods”). The three government program variables

used in this research are described in the third section. Then, the choice of one of the two

methods used in forecasting prices and yields based on their forecasting power is made in the

fourth section and further data imputation is conducted as a preparation for the acreage allocation

model. Finally, the region under study and the dummy variables used are discussed. Table 4.1

summarizes the data sources. A comparative report on the forecasting power of the two methods

is presented in Table 4.2a (in-sample forecast comparison) and Table 4.2b (out-of-sample

56

forecast comparison) before the summary statistics for the more powerful method, given by its

out-of-sample forecasting power, are presented in Table 4.3.

Acreage Data

The data on acreage used in this research are the same as used by Tareen (2001). There

are two major data sources for this data, viz., the University of Georgia - Cooperative Extension

Service (UGA-CES) and the U.S. Department of Agriculture - National Agricultural Statistics

Service (USDA-NASS).12

In equation (3.15) of Chapter 3, the dependent variable Ai (or we may call it CIAiyt)

represents irrigated acreage of crop i on county y in year t. Given that data is only available on

state irrigated acreage by crop (SIAit), state total irrigated acreage by year (STIAt), total irrigated

acreage by county by year (TIAyt), state harvested acreage by crop (SHAit) and county harvested

acreage by crop by county (CHAiyt), there were two possible alternatives to construct a proxy for

CIAiyt:-

12 The data on state and county irrigated acres were obtained from the UGA-CES. The state irrigated acreage of the ith crop at time period t (SIAit), which includes all commodity and recreational irrigation groups, is a subset of these data. Summing these categories gives us the state total irrigated acres at time period t (STIAt). Unfortunately, these data are available discretely for the years 1970, 75, 77, 80, 82, 86, 89, 92, 95 and 98. Another irrigation data subset consists of total irrigated acres for all commodities combined, by county at time t (TIAyt). Data for TIAyt are available for the years 1974, 78 – 82, 84, 86, 89, 92, 95, 98 and 2000 and are reported in the annual publications of the Georgia County Guide.

All harvest data came from NASS. These data are available for 1970 through 1998 and were downloaded from the USDA - NASS website http://www.usda.gov/nass/. They are data on commodity harvested acreage by county at time t (CHAiyt). Summing over all the 159 Georgia counties, the state commodity harvested acres (SHAit) were arrived at. A strong linear trend was observed in the available irrigation data (see Figure 1.1). Thus, data interpolation for the missing SIAit and TIAyt assumes that irrigation acreage increases or decreases linearly between two time intervals. This assumption of linearity on data for the missing years might be a potential source of error, but it would be difficult to quantify this error (Tareen, 2001).

As apparent from Table 4.1, the time intervals vary among the state- and county-level irrigation data sets. But, in order to conduct this study, it was necessary to have a common time period for all data sets (i.e., a balanced time series and cross section). Therefore, the sample period used is 1974-1998, as imposed by the range of the TIAyt and SIAit data sets. As mentioned later in this chapter and as seen in Chapter 4, with the first eight years lost having to take lags of different variables, the estimation proceeded from 1982 through 1998, and years 1999 through 2001 were considered out-of-sample forecasting years.

57

i.) Assume that the proportion of crop i irrigated in county y is the same as that irrigated

in the state. Algebraically,

CIAiyt = (SIAit/SHAit) * CHAiyt. (4.1)

ii.) Assume that the proportion of irrigated acreage used in the production of crop i in

county y is the same as in the state. Algebraically,

CIAiyt = (SIAit/STIAt) * TIAyt. (4.2)

While the first alternative has the conceptual advantage of being linked with the observed

crop mix in a given county, the obvious problem with it is that employing state proportion of

each crop irrigated might underestimate the proportion of each crop irrigated in the river basin

counties under study. On the other hand, with the use of total irrigated acres by county in its

calculation, alternative 2 accounts for higher levels of irrigation expected in river basin counties.

But this alternative is conceptually disadvantaged in that by imputing the county-by-crop

irrigation acreage, the acres lack the link with the crop mix in a county (Tareen, 2001). However,

like Tareen (2001), this current research is based on the second alternative with the following

restriction to account for available county-level crop mix data:

CIA*iyt = Min(CIA’

iyt, CHAiyt), (4.3)

where CIA*iyt = the county irrigated acres data of the ith crop to be used in the study, and

CIA’iyt = the unrestricted county irrigated acres of the ith crop at time t, given by the

relation (4.2) above.

Relation (4.3) is a restriction that ensures that the irrigated acreage data used for the ith

crop in the yth county does not exceed the harvested acres of the ith crop in that county. Thus, this

modification of alternative 2 emphasizes the importance of available data on total irrigated

58

acreage by county and year, but seeks to minimize possible errors related to the crop mix by

incorporating county-level data on harvested acreage by crop and year (Tareen, 2001).

Profits Data

Like Tareen (2001), a major contribution of this analysis is to account for the influence of

economic variables on water demand, which requires the incorporation of profitability of

competing farming enterprises. This in turn requires information on prices, yields and costs for a

given enterprise. Two methods are used to obtain data on expected prices and expected yields –

named as steps 1 and 2 in the sequence of the analysis. Then a forecasting power test is

performed on both the data sets. The rest of the steps use only the data set (or the method) that

performs better in forecasting out-of-sample vis-à-vis the other. This makes sense because the

rest of the analysis will focus on estimating and forecasting acreage and water demand, and on

simulating different scenarios based on the estimation results. So only the better of the two

economic methods is supposed to measure up to the challenge of the alternative engineering

approach.

Following are the steps followed in obtaining the data on expected prices and expected

yields:-

Method 1: Statistical Method

Step 1. Price Forecasts: Data for prices were obtained from USDA-NASS. Following Tareen

(2001), we assume expected supply-inducing prices (SIP) for producers making cropping

decisions for period t to be a simple linear function of the announced government price (GP) for

year t, the lagged supply-inducing price and a time trend (T):

E[SIPit] = $0 + $1 GPt + $2 SIPi,t-1 + $3 T, (4.4)

59

and thus estimate

SIPit = $0 + $1 GPt + $2 SIPi,t-1 + $3 T + ε1, (4.5)

where $0, $1, $2 and $3 are parameters to be estimated with the price data, and

SIPit = Max(GPit, SAPit), (4.6)

where SAPit is the seasonal average price for commodity i in year t and

GPit = Max(LRit, TPit) (4.7)

for corn and cotton at time t. Seasonal average price (SAPit) for a given crop is reported as a

simple average of the prices of that crop in Georgia during the cropping season or crop

marketing year. SAPit data were collected from the 1970 - 2001 editions of Georgia Agricultural

Facts, published annually by USDA-NASS. Government prices (GPit) were proxied as in (4.7)

above by the loan rates (LR) and target prices (TP), whichever were larger. GPit for peanuts and

soybeans do not have target prices and were, therefore, proxied using the loan rates (LRit). These

data were collected from 1970 - 2002 editions of the Agricultural Statistics published by USDA-

NASS.

The idea behind the relation (4.7) is that generally a producer’s revenue per unit of output

i in year t will be higher of the government price, GPit, and the market price for that output

(Shumway, 1983). The government price for a given commodity is usually known to producers

before planting decisions are made, but market prices for the crops to be planted are not known

in advance. Therefore, planting decisions need to be based on expected revenue or expected

profit per unit.

Equation (4.5) was estimated for each crop using ordinary least squares (OLS). For the

sake of brevity, we will be substituting SIP by P from this point on and by prices we will mean

60

SIP, unless otherwise stated. Prices predicted from the above estimation are the expected prices,

denoted E(P), from Method 1.

Note: The expected prices thus obtained are the same across counties for any given time period

and any given crop.

Step 2. Yield Forecasts: Yield data were collected for each of the 16 counties and the

conglomerate county “Other” from USDA-NASS and Georgia Agricultural Facts. Yields

account for cross-sectional heterogeneity in terms of irrigated acreage and thus enter the

empirical model on a county-by-crop basis over time. In predicting yields, Tareen (2001)

assumed expected yields to be a function of the past year’s yields and a trend term:

E[Yiyt] = "0 + "1Yt-1 + "2 T, (4.8)

and hence he estimated

Yiyt = "0 + "1Yt-1 + "2 T + ε2. (4.9)

With the purpose of obtaining better fit, a county-specific dummy variable (Dy with y = county)

was added to Tareen’s (2001) estimated yield equation, thus rendering us the following:

Yiyt = "0 + "1Yt-1 + "2 T + "3 Dy + ε3, (4.10)

where "0, "1, "2 and "3 are parameters to be estimated using the data on yield, T is the time

trend, and Dy is the county-specific dummy variable, y = 1, 2, …, 17.13

Equation (4.10) was regressed using OLS.

Note: Unlike prices, the expected yields thus obtained are not the same across counties for any

given time period and any given crop.

13 Note: In this research, there are 17 counties under study as against 19 for Tareen’s (2001) study. The fact is two of the smaller counties, as given by their smaller number of irrigated acres, viz., Grady and Webster, were clubbed into the aggregate county called “Other.”

61

A problem encountered in executing this step with all 17 counties is that the degrees of

freedom for the parameter estimates of the intercept term ("0) and the first 16 dummies would be

biased, and the same for the 17th dummy would be zero. The reason is that the covariance matrix

associated with the error terms would be singular and not of full rank, i.e., one or more of the

variables could be expressed as a linear combination of the rest of the variables. Such a situation

in practice can be taken care of by eliminating one of the relatively unimportant variables, which

becomes redundant for the purpose of the regression (Barten, 1969; Holt, 1999). We eliminated

the dummy for the county dubbed “Other.” With a total of 16 dummies, expected results were

obtained for yield forecasts.

Method 2: Futures Method

Step 1. Price Forecasts: The data source used to collect the price data for this method is a CD-

Rom called “Historical Futures Data 1959-Present” © 1999 Prophet Financial Systems, Inc.

Following Gardner (1976), Chavas, Pope and Kao (1983), Eales et al. (1990), Choi and

Helmberger (1993), and Holt (1999), futures prices are used to represent expected prices by this

method. To be specific, weighted average prices in March for harvest-time futures contracts for

corn, cotton and soybeans [December Chicago Board of Trade (CBOT) contract for corn and

cotton, November CBOT contract for soybeans] are used as a measure of expected prices for

these commodities. Each set of data is an Excel spreadsheet with the following information (in

columns): Date, Open, High, Low, Close, Volume, and Open Interest. To obtain the weighted

average prices, we multiplied the “close” values for each crop by the corresponding “volumes”

traded (weights), added over the entire month of March and divided by the sum of the volumes.

62

Although the futures price used in the analysis should be the one observed at the time of

the acreage decision, it is not clear exactly when such decisions are made. But to account for the

time required to procure all the necessary inputs, one may expect the farmers to decide how

many acres to plant several weeks before planting (Chavas, Pope and Kao, 1983). Normally,

corn and cotton are planted between April and May, and soybeans are planted between April and

June each year in Georgia. Thus, the month of March was arbitrarily chosen on the assumption

that planting decisions for all those three crops would be made at any time during that month.

Futures market for peanuts does not exist. Therefore, expected price data for that crop were

chosen from in-sample price predictions of Method 1 (i.e., the SIPit forecasts from equation (4.5)

for i = peanuts).

Step 2. Yield Forecasts: Following Holt (1999), an estimate of expected yields per acre by crop

and county was obtained using the formula:

^ 6Yiyt = δiy + (1/4)*['Yiyt-k – Max(Yiyt-1, …, Yiyt-6) – Min(Yiyt-1, …, Yiyt-6)], (4.11) k=1

where δiy is an adjustment parameter, and it assures that deviations between observed and

expected yields sum to zero over the sample period. Expression (4.11) implicitly assumes that

farmers view historically very high and low yields as being unrepresentative when forming

expectations.

Step 3. In-Sample and Out-of-Sample Forecasting Comparison: The Root Mean Square

Error (RMSE) criterion was chosen to compare the forecasting power of the two methods.

Though in-sample (i.e., for the sample period used in the regressions, 1982-98) price and yield

forecasts are consistently better with Method 1, as demonstrated by lower RMSE values in Table

63

4.2a, it is Method 2 that wins in terms of providing better out-of-sample forecasts for yields and

prices in general (Table 4.2b).

As seen from Table 4.2b, Method 2 cotton and soybean prices have lower RMSE, peanut

prices have the same RMSE for both methods, obviously because the same data set was used

(since peanut futures do not exist), and only corn prices have a lower RMSE in Method 1. Also,

all but soybean yields have lower RMSE using Method 2, the RMSE value for soybean yields

being about the same for both methods.

Since the rest of the analysis has to do with data imputation, estimation, forecasting and

data simulation based on the estimated results, the overall out-of-sample forecasting strength was

given priority while choosing the method to use for the rest of the research.14 Therefore, Method

2 (futures prices and Holt-yields15) data were considered for further analysis. The rest of the

steps taken in preparing the stage for the acreage response model estimation follow.

Step 4. COVariances between P and Y or COV(P, Y): Covariances between prices P and

yields Y, or COV(P, Y), are an important component of net expected profits. Thus it is important

to compute those covariances. There are at least two ways of doing this. The first, adopted by

Tareen (2001), is to take them around the means or averages:

^ _ ^ _ COV(P, Y) = (P – P)*(Y – Y) (4.12)

for each pair of crops by county,

14 Ideally, however, data on corn expected prices and soybean expected yields could be taken from Method 1 and the rest from Method 2. It might be interesting in the future to see if any of the results from this research change with that variant of the data pool. 15 “Holt-yields” are a term coined here for expected yields from expression (4.11), as calculated by Holt (1999).

64

where a ^ symbol indicates ‘predicted’ and ¯ indicates ‘average’ or ‘expected’ (statistically

speaking).

Therefore, there was a value of COV(P, Y) for each of the 19 counties for each of the

four crops, so there were a total of 19 x 4 = 76 of these covariances for Tareen (2001).

Obviously, they were assumed to be the same over time for any given county and crop.

The second way, used in this dissertation, is a more detailed method and is to obtain the

covariances using the forecast errors of prices and yields, as done by Holt (1999) using futures

prices. In this method, we take the product of the forecast errors (differences of predicted values

from their observed counterparts) or, stated otherwise, expectation errors (differences of

observed values from their expected counterparts) of prices and yields. Holt (1999) determines

COV(P, Y) as a weighted rolling average of the product of three years’ historical price and yield

expectation errors, with weights of 1/2, 1/3 and 1/6, respectively, for the three preceding years.

Following Holt (1999), we take the same weights for each of the past three periods, thus ending

up calculating:

^ ^ 3 COV(Piyt, Yiyt) = ' ωk(Piyt-k – Piyt-k)*(Yiyt-k – Yiyt-k), (4.13) k=1

3 = ' ωk Uiyt-k Viyt-k, (4.14) k=1

^ where Uiyt = Piyt – Piyt = price expectation error, (4.15)

^ Viyt = Yiyt – Yiyt = yield expectation error, (4.16)

i indexing crops, y indexing counties, and t indexing time.

Obviously, the first four observations were lost in the process of this operation for each

county by crop. This is because the predicted prices are reported from the second observation,

65

and the operation in (4.14) inherently cannot be reported without having at least the past years’

observations, thus giving us a loss of one plus three equals four degrees of freedom for each

county by crop. With the use of Method 2 data, however, there was a starting loss of six

observations per county and crop in yield calculations (1974-79), plus these four in COV(P, Y)

calculations (1980-83). Three years’ observations were artificially recovered by taking the

rolling average of COV(P, Y) for the next three years for 1980-82.

Step 5. Costs of Production: The cost data used in this research are “historical” variable costs

of production based on the actual costs incurred by producers in the southeastern U.S. during

each year. In considering profitability of competing enterprises, these actual measures of costs

are more relevant to the present analysis than the projection-based budgets put forth by land-

grant universities to assist farmers in planning. Variable cost of production data were collected

from the USDA - Economic Research Service (USDA-ERS). The same variable cost data were

used as used by Tareen (2001), without the deflating or any other adjustments. Cost data were

observed to be quite stable over the sample period and beyond. Again, the cost data are the same

across counties for any given time period and any given crop. They were obtained from the

USDA-ERS website:

http://www.ers.usda.gov/briefing/farmincome/costsandreturns.htm.

Step 6. Expected Net Returns: Expected net returns or profits, π it, are expressed as

Et-1[Biyt] = Et-1[(Pit)y* Yiyt] – (cit)y, (4.17)

where cit is the total variable cost of production of the ith crop in time period t.

66

Given covariance between yields and prices (see, e.g., Bohrnstedt and Goldberger, 1969; Chavas

and Holt, 1990), expected profits are calculated using the relation

Et-1[Biyt] = Et-1[Pit]y*Et-1[Yiyt] + Cov(Piyt, Yiyt) – (cit)y, (4.18)

where Cov(Piyt, Yiyt) is the covariance between price and yield of the ith crop in county y at time

period t.

With the first four observations by county by crop lost in calculating COV(P, Y) in Step

4, the expected net returns produced a matching loss of the first four observations, which

appeared to be a loss too many. But that could be easily taken care of by stating in the SAS

program

if Cov(Piyt, Yiyt) = . (i.e., missing) then Et-1[Biyt] = Et-1[Pit]y*Et-1[Yiyt] – (cit)y. (4.19)16

As a preparation for the next step, three lags were defined for expected net returns, as

obtained from (4.17) and (4.18), and through SAS coding, those lagged values were prevented

from running into subsequent counties. This is essential when dealing with time-series and cross-

section data at the same time (or ‘panel’ or ‘longitudinal’ data, for example, when the same units

are surveyed over time) consisting of multiple time series stacked one on top of the other across

a cross section and hence sometimes called cross-sectional time series. [Note: The same care was

taken in obtaining the forecasts of prices and yields in Steps 1 and 2.]

Also as a preparation for the next step, three lags were defined for observed profits, and

appropriate coding in the SAS program was made to prevent them from running into subsequent

counties. Using Method 2 data, expected profits data were available from 1980, but like in Step 16 If Method 1 was used, the fact that the first few (first four in calculating COV(P, Y), then three more in calculating COV(E(B)), total seven) observations were lost in the covariance calculations would not matter in the later part of the research as the acreage allocation models were regressed using data starting from 1982 (i.e., eight years past the starting year of the sample, 1974). In choosing Method 2, however, the yield calculations gave a starting loss of six observations and more while calculating covariances. This was avoided by calculating COV(P, Y) for 1980-82 and E(B) for 1977-79 as rolling averages of the next three years, thus giving us the data for use starting in 1980. However, as described in Chapter 5, the regressions were run using data starting in 1982. This further reduced the use of artificial data in the analysis.

67

5, the first three years’ data (1977-79) for expected profits were artificially recovered using the

rolling average of the initial available three years.

Step 7. Variances and Covariances of Expected Net Returns: While expected net returns

constitute the first moment of net returns, the second moments are their variances and

covariances.

Variances in profits for crops capture the risk aversion of the farmers, and are thus

included in the model. Tareen (2001) defined variance associated with net profits for the three-

year period preceding year t as dispersion of observed profits about their means, i.e.,

3 VarEt-1[Biyt] = FB

iyt = ' 8k [Bi,y,t-k - Et(Biyt)]2, (4.20) k=1

where

Et(Biyt) = (1/3)*[(Bi,y,t-1 + Bi,y,t-2 + Bi,y,t-3)] (4.21)

is a three-year moving average of observed profits, and 81, 82 and 83 represent the weights from

an adaptive expectations model similar to the one used in Chavas and Holt (1990). He assumed

an approximately equally weighted scheme for the data with the three time periods weighted at

0.34, 0.33 and 0.33 for the first, second and third year, respectively.

On the contrary, we define variance based on forecast errors, and, for each county y is

given by

3 VarEt-1[Biyt] = FB

iyt = ' 8k [Bi,y,t-k - Et-k(Biyt)] , (4.22) 2

k=1

where

Bi,y,t-k = observed net profit for crop i in time t-k, with k = 1, 2, 3,

68

Et-k(Biyt) = expected net profit in time t-k, with k = 1, 2, 3, as obtained from operation (4.18) in

Step 6 above, and

8k = weight for period k, with k = 1, 2, 3.

For the sake of being consistent with the weights ωk used in Step 3 above, we choose 8k = 1/2,

1/3 and 1/6, respectively, for the three past years.

However, as Tareen (2001) noted, using variance directly in the estimation has a demerit

in that if a random variable has an upward trend its variance will increase due to scale effect even

though its relative risk, i.e., variance standardized by the mean, may not be increasing. Using

coefficient of variation standardizes variance and eliminates this scale effect. Following Tareen

(2001), we calculate coefficient of variation (or standardized variance) as follows:

C.V.E(Biyt) or VarS(Biyt) = FBiyt / Et(Biyt), (4.23)

where

FBiyt = unstandardized variance of the ith crop in county y at time t, and

Et(Bit) = expected profit derived from the ith crop in county y at time t.

In an expected value-variance (EV) setting, there is a mechanism of risk-spreading by

farmers via the portfolio effect. This is accounted for in acreage allocation models by the

inclusion of covariances between crops. According to this mechanism, a negative correlation

between two crops in a farmer’s portfolio reduces the farmer’s risk. Therefore, in the equation

for the ith crop we may expect a negative sign associated with the variable for covariance, which

evidences that the farmer will commit more resources to the irrigated acres of the ith crop.

However, in the same equation, comparing the covariance between other non-i crops, and hence

a reduced-risk scenario, suggests taking irrigated acres out of the production for the ith crop and

69

committing them to some combination of the other two crops. Thus, a positive relationship

would be the expected sign in the latter case.

Tareen (2001) calculates covariance using the following equation:

3 Cov(Biyt,jyt) = FB = ' 8k [[Bi,y,t-k - Et(Biyt)] [Bj,y,t-k - Et(Bjyt)]], (4.24) iyt,jyt k=1 i…j

where

Et(Biyt) = (1/3)*(Bi,y,t-1 + Bi,y,t-2 + Bi,y,t-3) (4.25)

Et(Bjyt) = (1/3)*(Bj,y,t-1 + Bj,y,t-2 + Bj,y,t-3) (4.26)

We define covariance using forecast errors as in Step 4 above, and hence

3 Cov(Biyt,jyt) = FB

iyt,jyt = ' 8k [[Bi,y,t-k - Et-k(Biyt)] [Bj,y,t-k - Et-k(Bjyt)]], (4.27) k=1 i…j

where Bi,y,t-k = observed net profit for crop i in county y at time t-k, with k = 1, 2, 3,

Bj,y,t-k = observed net profit for crop j in county y at time t-k, with k = 1, 2, 3,

Et-k(Biyt) = expected net profit for crop i in county y at time t-k, with k = 1, 2, 3, as obtained from

operation (4.18) in Step 6 above,

Et-k(Bjyt) = expected net profit for crop j in county y at time t-k, with k = 1, 2, 3, as obtained from

operation (4.18) in Step 6 above,

8k = a scalar coefficient of absolute risk aversion, chosen to be 1/2, 1/3 and 1/6 for the three years

t-1, t-2 and t-3, respectively, if t is considered the current year.

Like variances, covariances are standardized, to eliminate the trend effect, as follows:

70

FB iyt,jytCovS(Biyt,jyt) = ______________________________, (4.28)

(1/2)*[Et(Biyt) + Et(Bjyt)]

and we follow Tareen (2001) in that operation.

We may note that, having artificially recovered the expected profits data for 1977-79, the

possible starting year of our data after calculating variances and covariances of expected profits

becomes 1980. As will be seen in Chapter 5, the regressions for the allocation equations are

considered from 1982, which means only one year of artificial data on expected profits per

county and crop are used in the estimation equations using Method 2 data, viz., the data on

standardized variances and covariances of expected profits for 1982, which use expected profit

data for 1979-82, 1979 being the year of artificial data.

The years 1983-85 still have embedded artificial data, but let us assume for now we can

trust the data on COV(P, Y) for the later years, which will entail that we trust the earlier COV(P,

Y) calculated from the later years and hence the sanctity from the whole data set is maintained at

an assumed satisfactory level. The possibilities of abnormalities can arise from the

unstandardized and standardized variances and covariances, and they will be dealt with at the

appropriate time. At this point, let us consider all standardized variances carry their absolute

values, since, theoretically speaking, expression (4.23) could turn out to be negative if the

denominator, Et(Biyt), i.e., current expected profit, turns out to be negative, which is quite

possible.

The next step (Step 8) is to run the irrigated acreage allocation models (one for each of

the four crops) and that will be talked about in Chapter 5. It is befitting at this point to introduce

the government program variables used in the allocation model structure.

71

Government Program Variables17

Three government program variables are considered for this research: a variable on

peanut quotas and two set-aside variables, one each for corn and cotton.

Peanut Quota Variable

A brief discussion on the peanut quota program:

One of the two mechanisms that limit the amount of peanuts allowed to be sold in the

domestic market is the national poundage quota (the other being import restrictions). Both tools

serve to manage the supply of peanuts primarily for food use in the U.S.

The federal government supports the farm price of peanuts primarily by limiting the

amount of “quota” peanuts that can be sold at a specified “high” price support level. Farmers

may sell peanuts produced in excess of their “quota” (called “non-quota” peanuts or

“additionals”) for export or crushing into peanut oil and meal. Farmers without quotas may

produce as much as they want, but they must market them as additionals for export or crushing.

However, as a result of lower production due to poor weather and/or changing manufacturer

preferences for peanut type, when quota peanuts fall short in meeting domestic food demand

farmers may sell additionals as quota peanuts under the buyback provision.

A national poundage quota limits the quantity that producers can sell for domestic

consumption with the exception of “buybacks.” The changes introduced in the 1996 Farm Bill

have created a new environment for producers, shellers and users. As the latter have adjusted to

the changes, the buybacks for the 1996-1998 marketing years accounted for a much higher share

(10-15%) of domestic peanut sales for food than in previous years (1-3%). In 1999-2000,

17 It may be noted that this is a portfolio approach with rational expectations assumptions, and because of the assumed inter-connected nature of the approach, it is considered legitimate to use each of these government program variables in all the four acreage allocation models.

72

buyback activity fell significantly in reaction to farmer concern about the losses they would

likely need to absorb as a result of such activity associated with the 1998 crop.

The 1996 law required USDA to announce a national poundage quota equal to projected

U.S. peanut consumption for food and related uses, excluding seed. Use of this quota tool was

intended to guard against a surplus and to limit the program’s budget exposure. The 1996 law

eliminated the “statutory minimum” provision specified under previous farm bills, under which

USDA was required each year to set the national quota, defined then to include seed use, at not

less than that minimum, even if USDA’s projection showed food use would lower.

Under the revised definition, USDA announced on December 13, 1999 that the 2000 crop

national poundage quota would be 1.18 million tons, the same as set for the 1999 quota. The

decision not to increase the quota reflected USDA’s assessment that (1) U.S. domestic peanut

consumption for food had leveled off, and (2) projected increased peanut imports allowed under

trade agreements would continue to displace domestically-produced peanuts that otherwise

would have entered the U.S. food marketing channels. The 2000 quota level is a 12.6% reduction

from the minimum 1.35-million-ton national poundage quota that was in effect for the years

1991 through 1995.18

The national quota is distributed among eligible states based on the share of the quota for

each state for the previous year, and then distributed by the “farm” to quota-holders based largely

on past production history. A producer holding or leasing farm quota receives price protection at

the high price support level, whether by selling to commercial buyers or effectively transferring

18 Another key change in the 1996-2002 Farm Program is that the “undermarketings” provision that allows any producer who experiences a production shortfall because of poor weather to carry forward that year’s unused quota to market a portion of future years’ output as “quota” peanuts. Previously, USDA had no discretion on how to handle undermarketings in setting the national quota level. This means that sales of “undermarketed” peanuts in recent years contributed to domestic marketings being higher than domestic food demand for peanuts (Jurenas, 2001).

73

ownership of their unsold peanuts to USDA’s designated marketing agent in return for price

support benefits.

Each state’s poundage quota is further distributed among individual peanut operations

based on past production history. In general, a poundage quota is established for each farm that

(1) had a quota in the previous year, and (2) produced peanuts to sell in at least two of the three

preceding crop years, if a state’s poundage quota is increased.

The 1996 act allowed an owner of farm poundage quota, or a producer with the

permission of a quota owner, to lease or sell such quota across county lines within the same state.

The law also phased in stages through 2000 the aggregate amount of quota that could be

‘transferred’ out of a county, but limited such transfers to not more than 40%. This limit on the

share of each county’s quota that could be transferred did not apply to those states that received

small amounts of the national poundage quota and to those counties with less than 100,000

pounds of quota. Though relaxed, these restrictions continue to ensure that farmers do not move

too much poundage quota away from those areas where handlers have developed an extensive

infrastructure to market peanuts (Jurenas, 1998; Jurenas, 2001).

The data availability problem and data used:

The peanut quota data at the county level is not readily available. USDA did not seem to

have the information on file when contacted. They do not seem to keep such records by county

(Robison, 2003). When the Farm Service Agency (FSA) at Georgia State Office was contacted in

this regard, we were told they were in the practice of saving records for only five years (Carey,

2003). However, we do know that Georgia has historically been one of the largest producers of

peanuts, accounting for 38% of total peanut output in 1997-99, when the Southeast (Georgia,

Alabama, Florida and South Carolina) accounted for 55% of U.S. peanut output, the Southwest

74

(Texas, Oklahoma and New Mexico) 30%, and the Virginia- North Carolina region 15%.

According to an FSA notice, Georgia’s state poundage quota allocations were about 41.29% of

the total national quota (FSA, 1997). For the purpose of this research, a flat 38% of the national

quotas during the available period, 1978 through 1998 (the end period being chosen because it is

the end period of the sample under study) are assumed to apply to Georgia. Figure 4.1 depicts the

national poundage quotas over the period 1978-1998.

After 1998, the quotas have nothing but declined, before being abolished 2001.

According to the Census of Agriculture, peanut producers in the U.S. declined from 16,194 in

1992 to 12,211 in 1997. Nationwide production, while fluctuating from year to year due to

variable weather, went down from an annual average of 4.3 billion pounds (2.14 million tons) in

1990-92 to almost 3.8 billion pounds (1.89 million tons)19 annually in the 1997-99 period. The

2000 quota level was a 12.6% reduction from the minimum 1.35-million-ton national poundage

quota that was in effect for the 1991-95 crops (Jurenas, 2001).

The specification used here and its justification:

Since the counties used in the study are of various sizes and are thus likely to be

variously affected by this quota imposition, the specification of the quota variable used in this

study is the state peanut quota times per-year average irrigated acres allotted to peanut

production in each county. This is then divided by a million to scale down the estimated

coefficients to comparable levels.

19 The conversion rate from pounds to tons is 2000 lbs. = 1 ton.

75

U.S. National Peanut Poundage Quotas 1978-98

100011001200130014001500160017001800

1978

1979

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

Year

Quo

ta ('

000

tons

)

Figure 4.1. U.S. National Peanut Poundage Quotas 1978–1998 Sources: Georgia Farm Service Agency; CRS Report and Issue Brief for Congress

Set-Aside Variables

There are two such variables considered in this analysis: one each for corn and cotton.

A brief history/discussion of the set-aside or acreage reduction program:

This is a production control program, according to which farmers were required to physically set

aside a certain percentage (specified by the program on an annual basis) of their cropland out of

production in return for the right to receive farm program benefits. To induce farmers to take out

cropland from production, program benefits had to be sufficient to offset the income that a

farmer had to forgo from not producing on the set-aside acres.

Introduced in 1970, in addition to “set-aside,” the 1981 Farm Bill used the term “acreage

reduction” without changing the basic concept of the program. Apart from the fact that the

program is voluntary in nature, set-aside had the advantage of reducing government costs of

76

controlling production. This is because the government could avoid both the payments involved

in retiring land as well as the income support payments that would otherwise have been meted

out to farmers who chose not to participate in the program.

However, the set-aside program was not very effective at controlling production because

not all farmers participated. Among the ones who did, many set aside their poorest land and then

applied more inputs to the remaining land they farmed. It was often the case in the 1970s that a

15% set-aside would result in only about 3% reduction in production, this relationship assuming

no supplementary diversion incentive and no effective means of enforcing farmers to set aside

land of at least average productivity (Knutson et al., 1983).

The data:

The program was started in 1978 with a 10% set-aside for corn only, discontinued in

1980 and 1981, restarted with corn and cotton in 1982, and eliminated in 1996 by the 1996 Farm

Bill. Figure 4.2 depicts the data used for corn and cotton set-aside variables, respectively.

The specification used here is just the variable itself, with the assumption that size will

not matter much to create any abnormal trends.

77

The Set-Aside Program for Corn and Cotton 1978-98

0

5

10

15

20

25

30

1978

1979

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

Year

Cor

n an

d C

otto

n se

t-as

ide

%ag

es

Corn Cotton

Figure 4.2. U.S. National Corn and Cotton Set-Asides 1978–1998 Source: USDA – Economic Research Service

Counties Studied and the Dummy Variables

The counties used in this study are all of the 31 Flint River Basin counties in Georgia.

However, 15 upper Flint River Basin counties – 14 geographically contiguous upper Flint River

Basin counties and one lower Flint River Basin county, viz., Grady – have very small numbers of

irrigated acres of each crop and are thus lumped into one separate county called “Other.” Thus,

the counties under study are Baker, Calhoun, Crisp, Decatur, Dooly, Dougherty, Early, Lee,

Macon, Miller, Mitchell, Randolph, Seminole, Sumter, Terrell, Worth and Other, the Other

county being comprised of Clayton, Coweta, Crawford, Fayette, Grady, Lamar, Marion,

Meriwether, Pike, Schley, Spalding, Talbot, Taylor, Upson and Webster counties.

78

Figure 4.3 Upper and Lower Flint River Basin Counties

79

Like in the prediction of yields, there is obviously the need to capture the differences

among counties in the Flint River Basin. We can easily do this by using intercept-shifting

indicator or dummy variables as our regressors – one for each of the 17 counties studied less one

(to avoid perfect collinearity) equals 16 dummy variables.

The acreage data for cotton demonstrated a sudden upward leap after 1992 across all

counties in general.20 So we use a second set of 16 dummy variables after 1992 to justify this

jump (this explains the high range of the standardized variance of expected profits for this crop

as seen from Table 4.3). In reality, we may expect this change in model specification in the

cotton acreage allocation equation will affect other crops in a farmer’s portfolio, and hence we

include these dummies in all four equations. As with the estimated dummies in yield prediction,

we cannot assign a priori signs on the estimated dummy variables in the irrigated acreage

response model in general.

20 One possible reason for this could be the success of the Boll Weevil Eradication Program in Georgia. Boll weevils (or anthonomus grandis grandis) – beetles measuring an average length of six millimeters – arrived in the United States from Mexico in 1892 and have caused an estimated $14 billion in yield losses and control costs to the U.S. cotton industry since then. In the cooperative boll weevil eradication program, Animal and Plant Health Inspection Service (APHIS) supplies equipment, technical and administrative support and funds up to 30 percent of program costs. Growers pay at least 70 percent of program costs. The program has been successful in eradicating weevils from Virginia, the Carolinas, Georgia, Florida, south Alabama, California, and Arizona (USDA – APHIS, 1999). To-date boll weevils remain the most destructive cotton pest in North America

80

Table 4.1. Data Types, Periods and Sources

Variable Data Span Source Acreage Data State Irrigated Acres 1970, 75, 77, 80, UGA – Cooperative Extension by crop (SIAit) 82, 86, 89, 92, 95, 98 Service State Total Irrigated 1970, 75, 77, 80, UGA – Cooperative Extension Acres, all crops (STIAt) 82, 86, 89, 92, 95, 98 Service Total County Irrigated 1974, 78-82, 84, 86, UGA – Cooperative Extension Acres, all crops (TIAyt) 89, 92, 95, 98, 2000 Service / Georgia County Guide State Harvested Acres 1970 - 1998 U.S.D.A. – National by crop (SHAit) Agricultural Statistics Service County Harvested Acres 1970 - 1998 U.S.D.A. – National by crop (CHAiyt) Agricultural Statistics Service Profits Data Season Average Prices 1970 - 2001 U.S.D.A. – National by crop (SAPit) Agricultural Statistics Service Loan Rates, Target Prices 1970 - 2002 U.S.D.A. – Agricultural Statistics (LRit, TPit) Yields per acre by crop 1970 - 2001 U.S.D.A. – National and county (Yiyt) Agricultural Statistics Service Variable Costs per acre 1975 - 2001 U.S.D.A. – Economic Research by crop (cit) Service Futures Prices by crop 1970 - 2002 Prophet Financial Systems, Inc. (FPit or SIPit or E(P)) CD-Rom “Historical Futures Data

1959-Present” Government Program Data Peanut Quotas by year 1978 - 1998 Georgia Farm Service Agency and

CRS Report and Issue Brief for Congress Set-Asides by year 1974 - 1998 U.S.D.A. – Economic Research (corn and cotton) Service

81

Table 4.2a. In-Sample (1982-1998) RMSE Comparison of Prices and Yields between

Method 1 and Method 2

Price Yield

Method 1 Method 2 Method 1 Method 2 (1982-98) (1982-98) (1982-98) (1982-98) Corn 0.3147 0.5617 18.4427 20.1288

Cotton 0.0219 0.1466 159.7490 181.8962

Peanuts 0.0093 0.0164 413.6100 439.4367

Soybeans 0.8254 0.9211 5.7814 6.5656

Table 4.2b. Out-of-Sample (1999-2001) RMSE Comparison of Prices and Yields

between Method 1 and Method 2

Price Yield

Method 1 Method 2 Method 1 Method 2 (1999-01) (1999-01) (1999-01) (1999-01) Corn 0.2632 0.3137 76.5008 21.4382

Cotton 0.1046 0.0601 274.1454 126.4009

Peanuts 0.0086 0.0086 679.0792 544.0171

Soybeans 0.8595 0.4663 8.2316 8.2337

82

Table 4.3. Summary Statistics for Method 2 Data: Variables Used in the Empirical Model

Variable Label Mean Std Dev Minimum Maximum Irrigated Acres

Corn CICNST 7,257.93 4,305.92 500.00 20,197.52

Cotton CICTST 6,551.89 7,495.47 0.00 36,201.20

Peanut CIPNST 10,042.25 5,143.44 2,178.56 25,292.97

Soybean CISBST 2,551.99 2,318.96 279.91 12,939.66

Expected Profits

Corn XPROFCN 119.73 66.59 -12.87 312.46

Cotton XPROFCT 171.91 127.67 -87.82 515.32

Peanut XPROFPN 510.49 136.93 147.73 817.50

Soybean XPROFSB 71.61 28.79 4.69 151.25

Standardized Variances

Corn VSCN 86.81 175.12 1.44 2,416.78

Cotton VSCT 11,720.96 184,055.01 0.50 3,129,282.50

Peanut VSPN 43.12 53.02 1.33 431.95

Soybean VSSB 32.80 56.69 0.36 718.07

Standardized Covariances

Corn-Cotton COVSCNCT 94.30 353.67 -4,051.13 2,239.38

Corn-Peanut COVSCNPN 11.46 24.27 -32.88 156.05

Corn-Soybean COVSCNSB 15.24 39.53 -133.78 354.13

Cotton-Peanut COVSCTPN 30.84 61.15 -63.43 333.97

83

Table 4.3. Summary Statistics for Method 2 Data (Continued)

Variable Label Mean Std Dev Minimum Maximum Cotton-Soybean COVSCTSB -2.43 298.58 -4,341.23 929.05

Peanut-Soybean COVSPNSB 9.12 21.55 -19.81 162.63

Peanut Quota * Peanut Average

PNQUOTAPNAVG 3,994.04 2,021.89 1,532.04 10,232.53

Corn Set-Aside

CNSA 8.68 6.26 0.00 20.00

Cotton Set-Aside

CTSA 12.56 9.28 0.00 25.00

Total Irrigated Acres

TIA 36,501.91 18,562.87 8,288.00 92,508.00

Note: With the regression data selected to start from 1982 and end in 1998, the number of observations for all variables has been made equal, viz., N = 289 (17 years x 17 counties) for all variables.

84

CHAPTER 5

EMPIRICAL MODEL AND ESTIMATION RESULTS

In this chapter, the econometric model used in estimating acreage response for corn,

cotton, peanuts and soybeans in the 17-county region of southwest Georgia for the years 1982-98

is presented. Since two sets of price and yield forecasting methods were used in obtaining

expected returns and their second moments, there were two possible sets of estimation results

from the econometric model. But since, based on the out-of-sample forecasting power as given

by the RMSE criterion, we chose Method 2 (using futures prices and an alternative set of

expected yields) over Method 1, the goodness-of-fit statistics and parameter estimates emanating

from the econometric model using Method 2 only are presented and discussed.

Data Span Used in Empirical Model

The data on irrigated acreage are not available at a regular interval. Though state irrigated

and harvested acres start from 1970, the same at a county level are not available earlier than

1974. To create a balanced set of time-series and cross-section data, therefore, the entire data was

initially read from 1974. Then, in the process of obtaining expected profits (through expected

prices – one lag – and expected yields – six lags), and the variances and covariances of expected

profits (three lags), a series of lags were encountered, so much so that artificial data needed to be

generated for the initial few years of the study with sufficiently reasonable assumptions on

variability of expected profits. Also the peanut quota data were available starting only as early as

85

1978. To maintain a reasonable level of sanctity in the data and credibility in the analysis, the

year 1982 was chosen as the starting period for the empirical analysis. As for the end period,

while data on some prices (preliminary seasonal average prices and government prices), yields,

costs and government program variables are available until 2002, some others, especially

irrigated acres by county and crop and total irrigated acres (TIA) by county are not available

after 2000. Thus, for the sake of making out-of-sample predictions on irrigated acres and water

demand (and also for us to be able to compare the predictive power of the two methods using

prices and yields, as talked about in Chapter 4), the year 1998 was chosen as the cut-off point (or

end point) in the data. Beyond this, three years (1999-2001) were considered for out-of-sample

comparison and forecasting exercises, as will be discussed in Chapter 6.

Econometric Model for Irrigated Acreage Allocation

The theoretical model was developed in Chapter 3 based on a representative farm. Since

farm level data are not readily available to study an individual farm’s irrigation acreage response

when faced with risk, the empirical model of acreage response is based on some reasonable level

of aggregation. When you use aggregated data, you implicitly assume the producers of a given

commodity are homogeneous in their behavioral characteristics. This can be a strong assumption

on the characteristic of the land and particularly over-simplifying with regard to irrigation

responsiveness. Moreover, aggregation limits the degrees of freedom available for hypothesis

testing. The current analysis uses a more disaggregated, county-level data for irrigated acreage

and yield, and promises to alleviate the negative effects of aggregation.

86

Recall and rewrite the optimal irrigated acreage equation (3.15):

— — — A*

iyt = f (Πjyt, Fjyt, CovΠijyt, TIAyt) (5.1)

Given the hypothesis of expected utility maximization and the functional relationship between

the optimal irrigated acreage and the components of expected utility in (5.1), the empirical model

for optimal irrigated acreage equations may be estimated with the following econometric model:-

4 — 4 — 4 — 4 4 — 3 16 16 A*

iyt="i+E$Π +E& F +E*j jyt j jyt ijyt jk yt m mt iy y

ijCovΠ +EE. CovΠjkyt+0iTIA +G' G +G2 D +G2’iyD’y+,iytj=1 j=1 j=1 j=1 k=1 m=1 y=1 y=1

j…i j…i,k k…i,j

(5.2)

for i, j, k (i…j…k) = 1, . . ., 4 (crops); y = 1, …, 17 (counties); and t = 1, …, 17 (1982-1998)

where

A*iyt = irrigated acreage of the ith crop in the yth county at time t,

"i = intercept term for the ith equation,

— Πiyt = mean expected net return per acre of the ith crop in the yth county at time t,

—Fjyt = standardized variance of expected profits of the jth crop in the yth county at time t,

—CovΠijyt = standardized covariance of expected profits between the ith and jth crops in the yth

county at time t, j…i

—CovΠjkyt = standardized covariance of expected profits between the jth and kth crops in the yth

county at time t, j…i,k, k…i,j

TIAyt = total irrigated acres in the yth county at time t,

Gmt = three government program variables:

one, m = 1 is (peanut quota)*(peanut average acres by county),

87

two, m = 2 is set-aside variable for corn,

three, m = 3 is set-aside variable for cotton,

Dy = county-specific indicator variable (dummy),

D’y = county-specific indicator variable (dummy), for t > 1992,

used to justify a sudden leap in irrigated acreage of cotton after 1992 across

counties, and

,iyt = stochastic mean-zero random error term for the ith equation.

For the sake of easy comparison, the symbols used in the acreage allocation models by

Chavas and Holt (1990) and Tareen (2001) have more or less been maintained above. In

addition, this research expands the scope and realism of the acreage allocation estimation by

incorporating three government program variables, viz., some specification of peanut quotas,

corn set-aside variable and cotton set-aside variable. A brief explanation of each of these

program variables is provided in the last section of Chapter 4.

Hypothesized Signs on Estimated Parameters

The economic theory of expected value - variance (EV) and agronomic relationships,

such as rotational consideration, between the crops (as described in Chapter 3) determine the

hypothesized relationships between irrigated acreage of a given crop and each of the parameters

in equation (5.2).

A risk-averse producer under competition has a concave expected utility function.

Concavity in the context of the expected utility model indicates a monotonically increasing

function of own profits. A positive sign is thus expected on the coefficient associated with

expected profits for the ith crop. The second moment of profits is captured by the own variances

88

of expected profits. Due to risk aversion, expected utility is a decreasing function of this variance

of the ith crop. Therefore, an inverse relationship is hypothesized between irrigated acres

committed to the ith crop and variance in its own expected profits.

An acreage allocation model characterizes crops as having any of three kinds of

relationships: substitute, complementary or none. The assumed nature of these relationships and

agronomic considerations of the crop determine the hypothesized signs assigned on the variances

and covariances of expected profits (the second moments of profits).

Let the crop modeled be labeled i, and let j be an alternative, competing or substitute

crop. Substitutes are expected to be negatively related to each other in the producers’ acreage

allocation decision and hence increasing profitability in the jth crop is expected to lower acreage

commitments for crop i. On the contrary, rising profits in the ith crop may result in rising levels

of acreage committed to the kth crop that serves as a rotation crop.

On the contrary, when the standardized variance of expected profits of j rises, the

irrigated acreage of the ith crop also rises. In this case, the variation in profitability of a

competing crop positively influences the acreage committed to a crop and hence the expected

relationship reverses; i.e., rising variability of a substitute crop is likely to increase the acreage

committed to the ith crop. For a complementary crop, however, rising variability in expected

profits will tend to decrease the irrigated acres in the ith crop (Tareen, 2001).

As for the covariance terms, a negative correlation between two crops in a producer=s

portfolio reduces the farmer=s risk. In the equation for the ith crop, the associated covariance

variable is thus expected to have a negative sign. However, in the same equation, comparing the

covariance between other non-i crops, i.e., between crops j and k, a reduced risk scenario

suggests taking irrigated acres out of the production of the ith crop and committing them to some

89

combination of the other two crops. Thus, we may expect a positive sign on this estimated

covariance parameter (Tareen et al., 2001).

With regard to the program variables, peanut quotas set a ceiling on the maximum

amount of peanuts the farmers are allowed to sell. A rise (fall) in quotas will likely increase

(decrease) the acreage of peanuts, hence a positive sign on the estimated parameter for this quota

variable is expected in the model for peanuts. For obvious reasons, for each of the other crop

models we will expect this variable to be associated with a negative sign. As the name suggests,

the set-aside variables specify a floor on the amount of the relevant crop (corn or cotton) acreage

the farmer needs to set aside to be able to obtain the benefits under that program. Thus, an

inverse relationship exists between this amount to be set aside and the acreage of the relevant

crop, meaning the higher (lower) the set-aside requirement, the lower (higher) the own acreage.

Each of these estimated parameters is, therefore, expected to have a negative sign in its own

model and, for obvious reasons, a positive sign in other crop models.

As stated in the last section of Chapter 4, there is no a priori sign assignment on

intercept-shifting, county-specific dummy variables – they are merely indicator variables. The

expected signs on the estimated regression coefficients of the rest of the variables are

summarized in Table 5.1 and a nomenclature and description of the variables used in the analysis

are listed in Table 5.2 at the end of this chapter.

Estimation Results

Since four crops are considered in this research, equation (5.2) essentially models a

system of four risk-responsive irrigated acreage response equations, one each for the four crops

under study: corn, cotton, peanuts, soybeans. Further, all four equations have the same

90

independent variables. Assuming the error terms are independently and identically distributed

(i.i.d.), therefore, we may estimate (5.2) equation by equation using ordinary least squares

(OLS). Each of the four equations is specified as a function of an intercept term, expected

profits, variances and covariances of expected profits, the total irrigated acreage in a county,

three government program variables and two sets of county-specific dummy variables, one for

the full length of the sample size and one starting from 1993. Parameter estimates for each crop

along with their standard errors, t ratios and p-values are presented in Tables 5.3 through 5.6 at

the end of this chapter.

The F-values in all acreage equations are statistically significant at the 1% level of

significance, suggesting the null hypothesis that all parameters except the intercept are zero is

strongly rejected for all the four allocation models. The coefficients of determination, R2, for the

corn, cotton, peanuts and soybeans equations are about 0.94, 0.93, 0.99 and 0.84, respectively,

indicating the regressors in each of the models explain 94%, 93%, 99% and 84%, respectively, of

the variation in irrigated acreage of the corresponding crop.

The estimated coefficient for expected profit of corn (XPROFCN) is 9.88 in the corn

equation, has the hypothesized (positive) sign, as seen in Table 5.3, and it is statistically

significant at the 5% level. In the corn equation, the estimate of expected corn profit is positive

and significant at the 5% level, the estimate of expected cotton profit is negative and significant

at the 1% level, and the estimate of expected soybean profit is negative and significant at the

10% level. Expected peanut profit estimate is positive but insignificant in the corn equation.

Standardized variance of soybeans and standardized covariance between peanuts and soybeans

are significant at the 10% level. The rest of the variability terms are estimated to be statistically

insignificant. Among the government program variables in the corn equation, the peanut quota

91

variable has a negative sign on the estimated parameter, as expected, and is significant at the 1%

level, and the cotton set-aside variable has a positive sign, as expected, with statistical

significance also at the 1% level. The coefficient of the corn set-aside variable was hypothesized

to be negative in the corn equation, but it is not significantly different from zero in our results.

But the positive sign on the own variable of corn set-aside is not as hypothesized, though the

estimated coefficient is statistically insignificant. The estimated coefficient of the total irrigated

acres parameter has the expected positive sign and is significant at the 1% level.

Expected profit of cotton, with an estimated coefficient of 18.25, is positively related to

the irrigated acres of cotton and the coefficient of expected cotton profit is statistically significant

at the 1% level (see Table 5.4). Coefficients for corn and peanut expected profits are

insignificant in the cotton acreage equation, and expected soybean profit estimate is positive and

significant at the 10% level. Coefficients of standardized variances are all insignificant in the

cotton equation. Coefficients of standardized covariances between corn and peanuts, between

corn and soybeans and between peanuts and soybeans are significant at the 1%, 5% and 10%

levels, respectively. The rest of the variability terms are estimated to be statistically insignificant.

Among the government program variables in the cotton equation, the peanut quota variable is

insignificant, and both the set-aside variables have negative estimated parameters (the cotton set-

aside result being as hypothesized) that are both statistically significant at the 1% level. The

coefficient of the total irrigated acres parameter has the expected positive sign and is significant

at the 10% level in the cotton equation.

As shown in Table 5.5, the peanut model is different from the other three models in that

the acreage response of peanuts to its own profit (XPROFPN) has the counter-hypothesized

negative sign but is statistically insignificant. This may be explained by the constraining role of

92

the government poundage quota variable on peanuts. Producers of quota peanuts lacked the

flexibility to adjust their acreage in response to the changes in profitability. Since quota prices

and a quota variable are both included here, the statistical insignificance of the expected peanut

profits parameter may not be a surprising outcome.

In the peanut equation, the most important results are the following: the estimate of

expected profit of peanuts is negative (counter-hypothesized) but insignificant at the 1% level,

with a coefficient of 0.71, the estimate of the peanut quota variable is positive and significant (as

hypothesized), the total irrigated acres parameter has a coefficient estimate of 0.26 and is

significant at the 1% level. Among estimated expected profit parameters in the peanut equation,

only corn has a significant coefficient estimate, and is positive with a large coefficient of 5.42,

indicating a strong relation between the profitability of corn and the irrigated acreage of peanuts.

Both the set-aside terms have a high estimated coefficient with high levels of significance (1%

level), suggesting the substitution possibilities between any of these crops under government

program and peanut acreage. Among the variability terms, only estimates of standardized

covariances between cotton and peanuts and between peanuts and soybeans are significant, both

at the 10% level.

Finally, in the soybean equation, the expected soybean profit coefficient has the

hypothesized (positive) sign but is insignificant even at the 10% level, as shown in Table 5.6.

However, estimates of expected profit coefficients of corn and cotton are both negative and

significant at the 1% level, suggesting that the increasing profitability of these two crops may

drive farmers to shift acres from soybeans to corn and/or cotton. The estimate of expected profit

for peanuts also has a negative sign in the soybean equation but is insignificant. All but three

variability terms are estimated with statistical significance: covariances between corn and

93

peanuts, corn and soybeans, and cotton and peanuts. The peanut quota variable has an estimated

negative and significant (at the 1% level) coefficient, and both set-aside variable coefficients are

insignificant. The total irrigated acres parameter has a positive estimate with a very low

coefficient of 0.05, and is significant at the 5% level.

On the whole, estimated coefficients of variation (or standardized variances) of expected

profits are not significantly different from zero even at the 10% level of significance for any

crops with the exception of soybeans in the corn equation (at the 5% level) (see Table 5.3) and

peanuts in the soybean equation (at the 10% level) (see Table 5.6). Lack of statistical

significance on the estimated coefficients of variation suggests that Georgia producers are not

risk-averse with respect to profits, and government price supports enable them to emphasize

expected profits in making acreage allocation decisions (Tareen, 2001).

Standardized covariance between crops was included to capture the risk-spreading or

diversifying behavior of the farmers. Out of a total of 24 (six in each of the four models) such

terms, the estimated coefficient of this parameter is significantly different from zero in 12

(exactly half) of the instances. For example, the standardized covariance between corn and

soybeans is statistically significantly different from zero at the 1% level in the soybean equation.

This relationship suggests the portfolio effect between the two crops.

Total irrigated acreage in a county, TIAyt, has the expected (positive) sign associated with

its parameter estimate and is significantly different from zero at the 1% level in the corn and

peanut equations, at the 5% level in the soybean equation, and at the 10% level in the cotton

equation. As far as responsiveness to TIA is concerned, peanuts are the most responsive among

the four crops, with a coefficient estimate of 0.26, meaning that an acre increase in TIA induces

0.26 acre increase in peanut irrigated acreage in a county, ceteris paribus. Similarly, an acre

94

increase in TIA induces 0.177 acre increase in corn, 0.079 acre increase in cotton, and 0.046 acre

increase in soybeans, as given by the estimated TIA coefficients in the relevant crop equations.

There were three government program variables considered in the study: corn set-aside

(CNSA), cotton set-aside (CTSA), and the peanut quota variable weighted by average peanut

acreage per county (PNQUOTAPNAVG). Out of these three variables, only one – viz., CNSA–

does not have the expected (negative) sign associated with its parameter estimate in the corn

equation. But this estimate is statistically highly insignificant. Thus the corn set-aside program

does not seem to affect the response in irrigated acreage of corn.

But the CTSA estimate is highly significant (at the 1% level) and negative, as expected,

in the cotton equation. Also, the relevant coefficient is high, -175.22, indicating 175.22 acres of

cotton being taken out of production with a one percent increase in the set-aside requirement.

The estimated coefficient of CNSA is negative and significant in the cotton equation

(counter-hypothesized), positive and significant in the peanut equation (as hypothesized), and

insignificant in the soybean equation. The wrong sign for CNSA in the cotton equation may be

due to fact that the set-aside requirements for corn and cotton generally move together – both

tightened and relaxed – and the combined effect of both is negative for cotton.

The CTSA coefficient estimate is positive and significant for both corn and peanuts, as

expected, but insignificant in soybeans. The cotton set-aside program seems to positively affect

corn irrigated acreage, as given by the positive sign and the high level of significance (at the 1%

level) of the CTSA estimate in the corn equation. The relevant coefficient estimate of 77.88

suggests that one percent increase in cotton specified by the cotton set-aside program raises the

irrigated acreage of corn by 77.88 acres, ceteris paribus.

95

The parameter estimate of the peanut quota variable, PNQUOTAPNAVG, is positive and

significant in the peanut equation, as expected, negative (as expected) and significant in corn and

soybean, but insignificant in the cotton equation.

As regards the dummy variables, two sets of those were included in the analysis. The first

set, D1, …, D16, was included in the econometric model to account for any heterogeneous

“county effects” across the counties, including differences in size, soil, climate and economic

conditions. Each is an indicator variable contrasted against the county group categorized as

Other. Most of these variables (49 out of a possible 64, which is 76.5625%) are significant at the

1%, 5% or 10% level of significance. In particular, soybeans have 14/16 of this first set of

dummies all significant at the 1% level. Peanuts have the minimum of nine dummies from this

first set statistically significant (producers of peanuts show the least amount of heterogeneity in

production relative to county group Other as compared to the other three crops, possibly due to

the restrictive nature of peanut production as given by the poundage quotas), and corn and cotton

have 13 of each significant.

The second set of intercept-shifting dummy variables, called DZ1, …, DZ16, was

included to control for a sudden unexplained upward jump in acres data for cotton across

counties after 1992. Out of a total of 64 possible estimates, 38 (i.e., 59.375%) of the dummies

demonstrate statistical significance at the 1%, 5% or 10% level – nine each for corn, cotton and

soybeans, and 11 for peanuts.

96

Table 5.1. Hypothesized Signs on Estimated Parameters

______________________________________________________________________________ Variable Expected Directional Impact on Irrigated Acreage of Crop i ________________________________________________ EV Theory Agronomic ______________________________________________________________________________

Profits

Expected, ith crop ( π iyt) +

Expected, jth crop ( π jyt) – – , if substitute crop

+, if rotation crop

Variance, ith crop (Fiyt) –

Variance, jth crop (Fjyt) + +, if substitute crop

–, if rotation crop

Covariance, ith and jth crops –

Covariance, jth and kth crops +

Peanut Quota Variable, ith crop is peanut +

ith crop is other than peanut –

Corn Set-Aside, ith crop is corn –

ith crop is other than corn +

Cotton Set-Aside, ith crop is cotton –

ith crop is other than cotton +

Total Irrigated Acres (TIAyt) + ______________________________________________________________________________

Note: The ith crop refers to the crop associated with the dependent variable and jth and kth crops refer to any two of the remaining three crops at a time.

97

Table 5.2. List of Variables Used in the Empirical Model _____________________________________________________________________________ Variables Description Dependent Variables:

CICNST Irrigated Acres of Corn by County

CICTST Irrigated Acres of Cotton by County

CIPNST Irrigated Acres of Peanuts by County

CISBST Irrigated Acres of Soybeans by County

Independent Variables:

XPROFCN Expected Profits of Corn by County

XPROFCT Expected Profits of Cotton by County

XPROFPN Expected Profits of Peanuts by County

XPROFSB Expected Profits of Soybeans by County

VSCN Standardized Variance of Corn by County

VSCT Standardized Variance of Cotton by County

VSPN Standardized Variance of Peanuts by County

VSSB Standardized Variance of Soybeans by County

COVSCNCT Standardized Covariance between Corn and Cotton

by County

COVSCNPN Standardized Covariance between Corn and Peanuts

by County

98

Table 5.2. List of Variables (Continued)

______________________________________________________________________________ Variables Description Independent Variables (Continued):

COVSCNSB Standardized Covariance between Corn and

Soybeans by County

COVSCTPN Standardized Covariance between Cotton and

Peanuts by County

COVSCTSB Standardized Covariance between Cotton and

Soybeans by County

COVSPNSB Standardized Covariance between Peanuts and

Soybeans by County

TIA Total Irrigated Acres by County

PNQUOTAPNAVG Peanut Quotas by Year Weighted by Average

Irrigated Acres of Peanuts by County

CNSA Corn Set-Aside by Year

CTSA Cotton Set-Aside by Year

D1, …, D16 County-specific Dummies, one for each of the

following counties, respectively: Baker, Calhoun,

Crisp, Decatur, Dooly, Dougherty, Early, Lee,

Macon, Miller, Mitchell, Randolph, Seminole,

Sumter, Terrell, Worth and Other21

DZ1, …, DZ16 Same as D1-D16, only for t > 1992 (i.e., 1993-98) 21 As mentioned in Chapter 4, the county named “Other” consists of the following 15 counties: Clayton, Coweta, Crawford, Fayette, Grady, Lamar, Marion, Meriwether, Pike, Schley, Spalding, Talbot, Taylor, Upson and Webster.

99

Table 5.3. Estimated Corn Irrigated Acreage: 1982 – 1998

Parameter Standard Variate Estimate Error t Ratio Pr > |t| INTERCEPT 5134.3013 1239.1672 4.1433 <.0001

XPROFCN 9.8840 3.9016 2.5333 0.0119

XPROFCT -9.0360 1.5623 -5.7839 <.0001

XPROFPN 1.2855 2.0808 0.6178 0.5373

XPROFSB -11.1261 5.4521 -2.0407 0.0424

VSCN -0.2841 0.4957 -0.5731 0.5671

VSCT 0.0002 0.0004 0.5649 0.5727

VSPN -0.9760 3.8692 -0.2523 0.8011

VSSB -4.6890 2.3438 -2.0006 0.0466

COVSCNCT -0.0911 0.2204 -0.4134 0.6797

COVSCNPN -9.0236 5.1705 -1.7452 0.0822

COVSCNSB 4.9001 2.7951 1.7531 0.0809

COVSCTPN 3.1100 2.1720 1.4318 0.1535

COVSCTSB -0.1388 0.2687 -0.5164 0.6061

COVSPNSB 19.4007 9.5581 2.0298 0.0435

PNQUOTAPNAVG -0.9845 0.2815 -3.4968 0.0006

CNSA 16.2194 25.5164 0.6356 0.5256

CTSA 77.8808 17.8141 4.3719 <.0001

TIA 0.1771 0.0229 7.7235 <.0001

D1 1582.3981 580.9750 2.7237 0.0069

100

Table 5.3. Estimated Corn Irrigated Acreage: 1982 – 1998 (Continued)

Parameter Standard Variate Estimate Error t Ratio Pr > |t| D2 -1419.8319 723.3054 -1.9630 0.0508

D3 -3855.1052 773.2793 -4.9854 <.0001

D4 7318.8899 1292.6347 5.6620 <.0001

D5 -5307.9328 662.8701 -8.0075 <.0001

D6 -3961.0427 934.1880 -4.2401 <.0001

D7 1718.2699 513.9932 3.3430 0.001

D8 765.9716 521.3533 1.4692 0.1431

D9 -4202.5853 823.8344 -5.1013 <.0001

D10 1398.0787 856.2511 1.6328 0.1038

D11 5286.3520 960.3565 5.5046 <.0001

D12 -2338.2822 789.5282 -2.9616 0.0034

D13 2561.9118 784.0479 3.2675 0.0012

D14 735.9009 502.3070 1.4650 0.1442

D15 -3369.3142 799.2554 -4.2156 <.0001

D16 -1769.8106 700.2584 -2.5274 0.0121

DZ1 -3053.5484 641.7185 -4.7584 <.0001

DZ2 -1372.9362 659.2890 -2.0824 0.0384

DZ3 -251.1909 665.7346 -0.3773 0.7063

DZ4 -8272.9796 711.3076 -11.6307 <.0001

DZ5 -615.4827 720.2846 -0.8545 0.3937

101

Table 5.3. Estimated Corn Irrigated Acreage: 1982 – 1998 (Continued)

Parameter Standard Variate Estimate Error t Ratio Pr > |t| DZ6 710.5197 694.4957 1.0231 0.3073

DZ7 -3153.4210 622.5257 -5.0655 <.0001

DZ8 -2904.2564 632.6276 -4.5908 <.0001

DZ9 -322.0785 649.7945 -0.4957 0.6206

DZ10 -1930.1523 694.1254 -2.7807 0.0059

DZ11 -7113.6560 666.5769 -10.6719 <.0001

DZ12 -334.3187 641.7728 -0.5209 0.6029

DZ13 -3596.8229 640.1218 -5.6190 <.0001

DZ14 -2878.7837 654.6755 -4.3973 <.0001

DZ15 -232.6689 633.9626 -0.3670 0.7139

DZ16 -778.5957 663.3648 -1.1737 0.2417

Number of Observations: 289

F-value: 75.89 (Pr > F: <0.001)

R2: 0.9410; Adjusted R2: 0.9286

Root Mean Square Error: 1150.70082

Durbin-Watson D: 1.618

First-Order Autocorrelation: 0.189

102

Table 5.4. Estimated Cotton Irrigated Acreage: 1982 – 1998

Parameter Standard Variate Estimate Error t Ratio Pr > |t| INTERCEPT 6191.7591 2330.3307 2.6570 0.0084

XPROFCN -4.4968 7.3372 -0.6129 0.5405

XPROFCT 18.2456 2.9380 6.2103 <.0001

XPROFPN 0.8855 3.9130 0.2263 0.8212

XPROFSB 19.0679 10.2531 1.8597 0.0642

VSCN 1.1183 0.9321 1.1997 0.2314

VSCT 0.0003 0.0008 0.4038 0.6867

VSPN 6.9052 7.2763 0.9490 0.3436

VSSB 6.4788 4.4077 1.4699 0.1429

COVSCNCT 0.1251 0.4145 0.3018 0.7631

COVSCNPN 26.0079 9.7235 2.6748 0.0080

COVSCNSB -12.1621 5.2563 -2.3138 0.0215

COVSCTPN 3.3797 4.0846 0.8274 0.4088

COVSCTSB 0.0921 0.5054 0.1822 0.8556

COVSPNSB -61.7782 17.9746 -3.4370 0.0007

PNQUOTAPNAVG -0.4738 0.5294 -0.8948 0.3718

CNSA -159.4732 47.9851 -3.3234 0.0010

CTSA -175.2197 33.5006 -5.2303 <.0001

TIA 0.0787 0.0431 1.8244 0.0694

D1 -3995.6206 1092.5595 -3.6571 0.0003

103

Table 5.4. Estimated Cotton Irrigated Acreage: 1982 – 1998 (Continued)


D3 -1615.8268 1454.1997 -1.1111 0.2676

D4 -3978.0449 2430.8797 -1.6365 0.1031

D5 -2145.4284 1246.5683 -1.7211 0.0865

D6 -4057.4056 1756.7985 -2.3095 0.0218

D7 -3884.6538 966.5961 -4.0189 <.0001

D8 -3962.5775 980.4372 -4.0416 <.0001

D9 -2861.0573 1549.2717 -1.8467 0.0660

D10 -3981.1010 1610.2333 -2.4724 0.0141

D11 -2443.4769 1806.0100 -1.3530 0.1773

D12 -3784.4085 1484.7567 -2.5488 0.0114

D13 -2564.7973 1474.4507 -1.7395 0.0832

D14 -3282.4527 944.6195 -3.4749 0.0006

D15 -2816.9823 1503.0493 -1.8742 0.0621

D16 -3872.5719 1316.8794 -2.9407 0.0036

DZ1 5575.6886 1206.7914 4.6203 <.0001

DZ2 1684.1003 1239.8339 1.3583 0.1756

DZ3 -1404.6063 1251.9551 -1.1219 0.2630

DZ4 15996.0000 1337.6580 11.9582 <.0001

DZ5 1898.9676 1354.5398 1.4019 0.1622

104

Table 5.4. Estimated Cotton Irrigated Acreage: 1982 – 1998 (Continued)

Parameter Standard Variate Estimate Error t Ratio Pr > |t| DZ6 -2720.4378 1306.0421 -2.0830 0.0383

DZ7 5747.7906 1170.6982 4.9097 <.0001

DZ8 5409.0458 1189.6955 4.5466 <.0001

DZ9 781.9984 1221.9789 0.6399 0.5228

DZ10 9900.4888 1305.3459 7.5846 <.0001

DZ11 13206.0000 1253.5392 10.5350 <.0001

DZ12 -1363.7210 1206.8935 -1.1299 0.2596

DZ13 7462.5390 1203.7888 6.1992 <.0001

DZ14 6257.8568 1231.1579 5.0829 <.0001

DZ15 -187.2717 1192.2060 -0.1571 0.8753

DZ16 1051.6694 1247.4985 0.8430 0.4001


F-value: 64.35 (Pr > F: <0.001)

R2: 0.9311; Adjusted R2: 0.9167




105

Table 5.5. Estimated Peanut Irrigated Acreage: 1982 – 1998

Parameter Standard Variate Estimate Error t Ratio Pr > |t| INTERCEPT -3861.0156 624.1507 -6.1860 <.0001

XPROFCN 5.4192 1.9652 2.7576 0.0063

XPROFCT -0.2599 0.7869 -0.3303 0.7415

XPROFPN -0.7181 1.0481 -0.6851 0.4939

XPROFSB 1.7291 2.7462 0.6297 0.5295

VSCN -0.3915 0.2497 -1.5683 0.1181

VSCT 0.0000 0.0002 0.1941 0.8463

VSPN -0.7634 1.9489 -0.3917 0.6956

VSSB -1.8877 1.1805 -1.5990 0.1111

COVSCNCT -0.0603 0.1110 -0.5430 0.5876

COVSCNPN 3.9023 2.6043 1.4984 0.1354

COVSCNSB -1.3766 1.4078 -0.9778 0.3292

COVSCTPN 2.2005 1.0940 2.0114 0.0454

COVSCTSB 0.1145 0.1354 0.8457 0.3986

COVSPNSB 8.8419 4.8143 1.8366 0.0675

PNQUOTAPNAVG 0.7122 0.1418 5.0221 <.0001

CNSA 82.9599 12.8522 6.4549 <.0001

CTSA 57.4843 8.9727 6.4066 <.0001

TIA 0.2601 0.0116 22.5186 <.0001

D1 -479.2219 292.6288 -1.6376 0.1028

106

Table 5.5. Estimated Peanut Irrigated Acreage: 1982 – 1998 (Continued)

Parameter Standard Variate Estimate Error t Ratio Pr > |t| D2 587.0353 364.3186 1.6113 0.1084

D3 1043.8089 389.4897 2.6799 0.0079

D4 -1894.5762 651.0815 -2.9099 0.0040

D5 968.7300 333.8781 2.9014 0.0041

D6 746.3617 470.5371 1.5862 0.1140

D7 -103.8085 258.8910 -0.4010 0.6888

D8 226.4039 262.5982 0.8622 0.3895

D9 1023.6345 414.9535 2.4669 0.0143

D10 -876.4290 431.2814 -2.0322 0.0432

D11 -1141.5076 483.7178 -2.3599 0.0191

D12 635.1052 397.6740 1.5970 0.1116

D13 -907.2562 394.9137 -2.2974 0.0225

D14 65.9404 253.0048 0.2606 0.7946

D15 729.0015 402.5735 1.8109 0.0714

D16 795.5227 352.7101 2.2555 0.0250

DZ1 -1270.8634 323.2244 -3.9318 0.0001

DZ2 -549.7347 332.0744 -1.6555 0.0991

DZ3 -5.7865 335.3209 -0.0173 0.9862

DZ4 -3161.4342 358.2754 -8.8240 <.0001

DZ5 -872.9783 362.7970 -2.4062 0.0169

107

Table 5.5. Estimated Peanut Irrigated Acreage: 1982 – 1998 (Continued)


DZ7 -1272.6736 313.5572 -4.0588 <.0001

DZ8 -1184.5573 318.6455 -3.7175 0.0003

DZ9 -562.5264 327.2922 -1.7187 0.0870

DZ10 -2220.4631 349.6210 -6.3511 <.0001

DZ11 -2852.5713 335.7452 -8.4962 <.0001

DZ12 -122.3918 323.2517 -0.3786 0.7053

DZ13 -1926.4241 322.4202 -5.9749 <.0001

DZ14 -1073.3920 329.7506 -3.2552 0.0013

DZ15 49.0765 319.3179 0.1537 0.8780

DZ16 -478.1489 334.1273 -1.4310 0.1537


F-value: 448.85 (Pr > F: <0.001)

R2: 0.9895; Adjusted R2: 0.9873




108

Table 5.6. Estimated Soybean Irrigated Acreage: 1982 – 1998

Parameter Standard Variate Estimate Error t Ratio Pr > |t| INTERCEPT 8868.6126 1094.6469 8.1018 <.0001

XPROFCN -12.8763 3.4466 -3.7359 0.0002

XPROFCT -7.9172 1.3801 -5.7368 <.0001

XPROFPN -2.5095 1.8381 -1.3653 0.1734

XPROFSB 6.8258 4.8163 1.4172 0.1577

VSCN -0.3257 0.4379 -0.7437 0.4578

VSCT 0.0000 0.0004 0.0618 0.9508

VSPN -6.4735 3.4180 -1.8940 0.0594

VSSB -2.0942 2.0705 -1.0115 0.3128

COVSCNCT 0.0435 0.1947 0.2232 0.8235

COVSCNPN -10.9893 4.5675 -2.4060 0.0169

COVSCNSB 8.2939 2.4691 3.3591 0.0009

COVSCTPN -3.9532 1.9187 -2.0604 0.0405

COVSCTSB -0.2295 0.2374 -0.9669 0.3346

COVSPNSB 16.0697 8.4433 1.9032 0.0582

PNQUOTAPNAVG -1.1540 0.2487 -4.6400 <.0001

CNSA -9.2084 22.5405 -0.4085 0.6833

CTSA 5.4072 15.7365 0.3436 0.7314

TIA 0.0459 0.0203 2.2675 0.0242

D1 3558.9157 513.2176 6.9345 <.0001

109

Table 5.6. Estimated Soybean Irrigated Acreage: 1982 – 1998 (Continued)


D3 -4380.5777 683.0941 -6.4128 <.0001

D4 8447.5323 1141.8786 7.3979 <.0001

D5 -2257.5644 585.5616 -3.8554 0.0001

D6 -2532.2928 825.2365 -3.0686 0.0024

D7 2702.5596 454.0477 5.9521 <.0001

D8 1316.3851 460.5495 2.8583 0.0046

D9 -3483.8229 727.7531 -4.7871 <.0001

D10 5834.9381 756.3892 7.7142 <.0001

D11 6770.9146 848.3530 7.9812 <.0001

D12 -1050.9344 697.4479 -1.5068 0.1332

D13 4337.0415 692.6068 6.2619 <.0001

D14 1908.6996 443.7245 4.3015 <.0001

D15 -2835.8226 706.0406 -4.0165 <.0001

D16 -2138.9150 618.5894 -3.4577 0.0006

DZ1 -1494.7177 566.8768 -2.6368 0.0089

DZ2 -31.8087 582.3981 -0.0546 0.9565

DZ3 425.4028 588.0919 0.7234 0.4702

DZ4 -2590.2467 628.3499 -4.1223 <.0001

DZ5 -222.0874 636.2800 -0.3490 0.7274

110

Table 5.6. Estimated Soybean Irrigated Acreage: 1982 – 1998 (Continued)


DZ7 -1464.7200 549.9224 -2.6635 0.0083

DZ8 -1361.4162 558.8462 -2.4361 0.0156

DZ9 521.9605 574.0110 0.9093 0.3641

DZ10 -2066.6189 613.1717 -3.3704 0.0009

DZ11 -3065.0763 588.8361 -5.2053 <.0001

DZ12 426.7583 566.9248 0.7528 0.4523

DZ13 -1371.1829 565.4663 -2.4249 0.0161

DZ14 -2438.0212 578.3227 -4.2157 <.0001

DZ15 567.9858 560.0255 1.0142 0.3115

DZ16 399.8883 585.9985 0.6824 0.4956


F-value: 25.22 (Pr > F: <0.001)

R2: 0.8412; Adjusted R2: 0.8079




111

CHAPTER 6

WATER DEMAND ESTIMATION AND FORECASTING

In this chapter, the results from estimated irrigated acreage obtained in Chapter 5 are

applied to the Blaney-Criddle (BC) net water requirement coefficients to model water demand.

The econometric approach of modeling water demand is compared and contrasted with the

physical, engineering approach via their respective measures of irrigated acreage and water

demand. Next, the substitution and expansion effects in irrigated acres and water demand are

studied by varying economic (prices, costs, yields) and institutional (total irrigated acreage)

factors. Several different scenarios are used to simulate forecasts of irrigated acreage and water

demand using a base simulation. Slippage estimates the difference between these two measures.

Water Demand Estimation

Irrigation specialists use climatological data to estimate consumptive and irrigated crop

acreage trends of water by crop. As discussed in Chapter 1, Blaney and Criddle (1962) found the

amount of water consumptively used by crops during their normal growing season was closely

correlated with mean monthly temperatures and daylight hours. They developed coefficients that

could be used to transpose the consumptive use data for a given area to other areas for which

only climatological data are available. The net amount of irrigation water necessary to satisfy

consumptive use is obtained by simply subtracting the effective precipitation from the

112

consumptive water requirement during the growing or irrigation season (USDA-Soil

Conservation Service, 1967).

With a normal year defined as a growing season having average rainfall of 49, 44 and 55

inches of rain in Lower, Middle and Upper Flint River Basin regions, respectively, and a dry

year defined as a drought on the magnitude of 20% or an average of the two driest years in a ten-

year period over the last 30 years, the net irrigation requirements for corn, cotton, peanuts and

soybeans in normal and dry years are listed in Table 6.1. These net irrigation requirement data

are based on 30-year averages of climatological data. As seen from Table 6.1, the differences in

water usage by crop are larger than the differences among the regions.

Tables A.1a through A.16 in the Appendices list the by-crop by-county irrigated acres

and the corresponding water demand for ‘normal’ and ‘dry’ years for 1998 through 2000. The

year 1998 is the last year within the sample. So both irrigated acres observed and predicted for

that year are listed. Tables A.1a, A.2a, A.3a and A.4a list the observed irrigated acres and water

demand for 1998, and A.1b, A.2b, A.3b and A.4b list the predicted irrigated acres and water

demand for 1998. The observed values of irrigated acreage were generated using equation (4.3)

(see Chapter 4) and the predicted values are predictions of the dependent variable in equation

(5.1) (see Chapter 5) with the predicted acreage modeled as a function of expected profits,

variances and covariances of expected profits, total irrigated acreage, the three government

variables, and two sets of dummy variables. Though not for 1998, within the sample, the models

for cotton and soybeans predicted some counties with low acreage as having negative acres of

irrigated land in some time periods. In particular, 26 for cotton and 10 for soybeans out of a total

of 289 predictions for each crop were negative. One possible reason for this could be that the

113

ordinary least squares assume a linear relationship between the dependent variable and the

explanatory variables when the reality might be a non-linear relationship.

Tables A.5 through A.8 list irrigated acres and water demand predictions for 1998 with

the peanut quota variable removed . The set-aside figures for this year are zero. So essentially

Tables A.5 through A.8 list acres and demand based on the total absence of government program

variables.

Beyond that, for the years 1999 through 2001, the parameter estimates from the

regression for each crop model were applied to predicted values of the variables (under certain

assumptions) to obtain the predicted irrigated acres and the corresponding water demand. The

negative predicted irrigated acres were set to zero so the corresponding water demand figures

were also zero. Total irrigated acres data for the year 1999 were not available. Harrison (2001) in

Georgia Faces reports that, according to the UGA Extension Service 2000 Irrigation Survey,

“the number of irrigated acres in the state of Georgia increased about 2 percent” between 1998

and 2000. The 2000 figure is 1.5 million acres of irrigated farmland – a 31,000-acre increase

since the survey in 1998. For the counties under study, the overall TIA for 2000 increased 5.93%

over 1998, i.e., the increase was at the compound rate of 2.92% per year. Using these figures and

the available by-county total irrigated acres (TIA) distribution in 1998, the by-county TIA

figures for 1999 were extrapolated by multiplying each TIA figure of 1998 by a multiplicative

factor of 1.029, assuming the TIA for each county increased by the same factor.

The water demand for each of the years 1998 through 2000 by crop and county was

derived by multiplying the relevant irrigated acres in a county by the relevant crop- and region-

specific BC coefficient of net irrigation water requirement. For example, predicted water

demand for corn in Baker County in 1998 was calculated by multiplying the 6641.95 predicted

114

irrigated acres in that county by the BC coefficients of 11.14 acre-inches and 12.71 acre-inches

for normal and dry years, respectively, and then dividing by 12 (to get the measure in terms of

acre-feet), to arrive at 6165.95 and 7034.93 acre-feet of water demand, respectively, as shown in

Table A.1b (1 acre-foot = 325,800 gallons per day). We may note that these predictions are

comparable with the corresponding observed acres of 7000 and water demand of 6498.33 ac-ft

(normal year) and 7414.17 ac-ft (dry year) for 1998, as shown in Table A.1a.

The Flint River Drought Protection Act

In March 2000, the Georgia Legislature passed the Flint River Drought Protection Act

(FRDPA). In April of that year, the Governor signed it into law. Beginning in June 2000, the

Environmental Protection Division (EPD) initiated a series of open public meetings, through

which it sought extensive participation and comments about the proposed rules from farmers,

farm organizations and other interested individuals. In these public meetings, the EPD received

many recommendations from agricultural interests, and modifications were made to the original

proposal to reflect these concerns. For example, the original proposal included the rule limiting

participation to both surface water and ground water users in the lower Flint River Basin. The

rule was modified to limit surface water users in the entire Flint River Basin. After the drought in

1999, the impact on Flint River flows caused by groundwater use was considered uncertain. On

the contrary, the impact on flows caused by direct surface water withdrawals from perennial

streams was considered much clearer by the EPD. In December 2000, the Board of Natural

Resources adopted the recommended final rules to implement the Flint River Drought Protection

Act.

115

Following the passage of FRDPA, auction registration was held at eight sites throughout

southwest Georgia. A total of 194 farmers holding 347 surface water permits, out of the potential

575 eligible permits, registered to participate in the auction. Bids to suspend irrigation were

submitted on these 347 permits on the designated auction date of March 17, 2001. After five

rounds of auction, the EPD declared the auction closed and announced the following final

results.

a.) Out of the 347 permits registered, the EPD accepted offers on 209 permits.

b.) The average price of an offer for this entire accepted acreage was $135.70 per acre,

leading to a cumulative expense of $4.5 million.

c.) The highest offer price accepted by the EPD was $200 per acre.

The initial estimates in 2001 were that the auction withdrew more than 33,006 acres of

farmland from irrigation using perennial surface water sources.22 The breakdown of these 33,006

acres by county is listed in Table 6.2. Out of these 33,006 acres, a total of 9,903 acres had been

reduced from the county category “Other” between the years 2000 and 2001. The breakdown of

these 9,903 acres reduction in the “Other” counties is also listed in Table 6.2. Four (Decatur,

Dougherty, Miller and Mitchell) of the 16 counties classified individually and eight (Clayton,

Coweta, Crawford, Fayette, Grady, Meriwether, Spalding and Talbot) of the “Other” counties

did not face a reduction in total irrigated acreage, meaning these counties are assumed to

maintain the same total irrigated acreage in 2001 as in 2000. Using physical models, the EPD

estimated that the removal of 33,006 acres from direct surface water irrigation would mean

conserving approximately 130 million gallons per day of water. This amount that would

22 Note: The drop in irrigated acreage in 2001 appears as a reduction ‘from the 2000 level’ of irrigated acreage. Farmers will not plan on irrigating a higher amount in 2001 than they irrigated in 2000 and then reduce their irrigated acres. These decisions are most likely made before the planting season and the farmers will know about the announced drop in acres at the outset of the planting season.

116

otherwise have been consumed in irrigation would remain flowing in the Flint River and its

tributaries with the reduction in irrigated acreage forced by FRDPA (Georgia Environmental

Protection Division, 2001; Tareen, 2001).

Scenarios for Simulations

Base Scenario

Year 2000: Irrigated acreage calculated from results of estimating equation (5.2) using

TIAy,2000 from Georgia County Guide, and expected returns based on expected price and

expected yield calculations from Chapter 4; water demand calculated by applying BC

coefficients to predicted irrigated acreage in each county.

Additional Scenarios

Scenario 1: Years 2001 and 2002 irrigated acreage and water demand assuming new

expected returns based on updated futures prices, forecasted peanut prices, and calculated

expected yields assuming TIA constant at 2000 level.

Scenario 2: Years 2001 and 2002 irrigated acreage and water demand assuming new

expected returns based on updated futures prices, forecasted peanut prices, and calculated

expected yields assuming a 33,006-acre TIA reduction from level in 2000.

Scenario 3: Year 2010 irrigated acreage and water demand assuming 2010 FAPRI price

forecasts, assumed non-program peanut prices, 2001 yield forecasts, and TIAy’s set at constant

2000 level and at the new level with a 33,006-acre TIA reduction from the level in 2000.

For all of the above simulations, we assume: variable costs constant at the 2000 level;

COV(P, Y) – covariances between prices and yields – fixed at the average level of 1996-98;

unstandardized variances and covariances of expected profits fixed at average level of 1996-98,

117

standardized variances and covariances being calculated by the simulation model; and

government program variables remain at the 2000 level. In all simulations, absolute values of

standardized variances are used.

Acreage of Other Crops Not Modeled

The econometric model in Chapter 5 estimated irrigated acreage of four specific crops for

each county: corn, cotton, peanuts, and soybeans. Other, usually minor or specialty crops,

however, are also irrigated in Georgia. These other crops include orchard crops (e.g., peaches

and pecans), and various vegetable crops, among others. Sufficient data to estimate irrigated

acreage of these crops were not available while conducting this research. In the acreage

estimations for the four modeled crops, these “other” crops were included in county-level total

irrigated acreage (TIA), an independent variable in each crop-specific equation.

These “other” crops gain particular importance when we observe the responsiveness of

the econometric model vis-à-vis the engineering model with respect to changes in some of the

regression variables. This research takes into account those “other” left-out crops through the

inclusion of TIA.

In the simulation models, acreage of “other” crops is treated as a residual – as the

difference between total irrigated acreage and the sum of the estimated acreage of corn, cotton,

peanuts, and soybeans. We also assume that the BC coefficient for the “other” crops is equal to

the mean of the BC coefficients of the four modeled crops in each county.

118

Simulation Methods23

The base simulation results for 2000 serve as the starting point for analyzing the impacts

of changes in expected returns and reductions in total irrigated acreage on acreage allocations

and irrigation water demand. Base simulation acres and water demand are shown in the results

tables (6.3a through 6.5b2) at the end of this chapter for the additional simulations to facilitate

comparison.

Three simulation models were applied for each of the scenarios analyzed. These models

include an engineering or physical model of water demand and two economic water demand

models based on the econometric results reported in Chapter 5.

The engineering model assumes that the proportion of irrigated acreage devoted to each

crop in each county is constant at its base year (2000) level. This assumption ignores possible

changes in crop allocations from changes in economic conditions, so changes in irrigation water

demand occur only when total irrigated acreage changes. The possibilities of substitution among

crops that may arise, for example, due to price changes are thus ignored.

Mathematically, water demand (WD) estimates by county for the base 2000 simulation

and for the 2001 engineering simulation can be shown, respectively, as:

5 5

WDy,2000 = ΣA*i,y,2000 * BC i,y = Σ[A*

i,y,2000 / TIAy,2000] * TIAy,2000 * BC i,y (6.1) i=1 i=1

and 5

WDENGy,2001 = Σ[A*

i,y,2000 / TIAy,2000] * TIAy,2001 * BC i,y. (6.2) i=1

The economic approach developed in this study is based on econometric modeling and

can easily renew the crop distribution to reflect the new prices and thus take into consideration 23 It may be noted that the simulations used in this analysis are not simulations in the traditional (Monte Carlo or bootstrapping) sense, but are called “simulations” in a loose sense of the term to define different methods of handling the problem at hand with the intent to provide different options.

119

the substitution effect among crops. The economic approach is more sophisticated than the

engineering approach in the sense that it recognizes that the farmer may alter his/her portfolio at

any point in time beyond the sample in response to changing economic conditions.

The two versions of the economic simulation models differ with respect to how

producers are assumed to allocate their irrigation acres to different crops when total irrigation

acreage is reduced. During the estimation period for the econometric model, total irrigation

acreage increased monotonically. Including TIAy,t as an independent variable in each crop-

specific acreage equation accounted for the impacts of increases in total irrigated acres on

individual crop acres in addition to responses to changes in expected returns and risks for each

crop. Allocation of additional irrigation acres to each crop, assuming constant returns and risks in

the current period, would theoretically be based on marginal returns and risks of assigning new

irrigation capacity to each crop, on agronomic considerations discussed earlier, and possibly on

equipment capacity and field size. The estimated coefficients of TIAy,t in Chapter 5 measured the

responsiveness of acreage of each modeled crop to a one-acre increase in total irrigated acreage,

ceteris paribus.

The Flint River Drought Protection Act of 2000 resulted in a decrease in total irrigated

acreage in 2001, and any irrigation water planning model should indeed be capable of simulating

decreases in water availability. Without historical data on responses of acreage to irrigation

capacity decreases, however, there is no empirical basis for modeling such a response. For this

reason we use two alternative assumptions to simulate acreage responses to reduction in

irrigation capacity: one, the “Sequential” assumption, and two, the “Simultaneous” assumption.

In the “Sequential” (SEQ) economic simulation model, the base 2000-level of TIA is

used with the new level of expected returns and risks, for 2001, for example, to estimate the

120

proportion of irrigated acres that would be allocated to each crop given expected changes in

returns and risks. Under this simulation method, these crop acreage proportions are then applied

to the new reduced level of TIA to generate the estimates of acreage allocations for calculating

water demand. This “Sequential” method thus assumes that producers respond to a decrease in

irrigation capacity by optimizing their base acreage allocation in response to changes in expected

risks and returns of each crop, and then applying the new allocation proportions to the reduced

level of irrigation capacity.

An alternative economic simulation model, which we will refer to as the “Simultaneous”

(SIM) model, simply includes the new, reduced level of TIA in the acreage allocation simulation

simultaneously with the new levels of expected returns and risks. This version of the simulation

thus assumes that the impact of a one-acre decrease in TIA on each crop acreage is simply the

opposite of the effect of a one-acre increase in TIA, as measured by the relevant estimated

coefficient of TIA in equation (5.2).

The base year water demand estimate is the same for the engineering (ENG) and both

economic simulations (SEQ and SIM), and is as shown in equation (6.1) above.

The “Sequential” economic model water demand estimates by county for the 2001

simulation can be shown as:

5

WDSEQy,2001 = Σ[(A*′i,y,2001| TIAy,2000) / TIAy,2000] * TIAy,2001 * BC i,y. (6.3)

i=1

The “Simultaneous” economic model water demand estimates by county for the 2001

simulation can be shown as:

5

WDSIMy,2001 = Σ[(A*′i,y,2001| TIAy,2001) / TIAy,2001] * TIAy,2001 * BC i,y

i=1

121

5

= Σ[A*′i,y,2001| TIAy,2001] * BC i,y, (6.4) i=1

where

[A*′i,y,2001| TIAy,2000] and [A*′i,y,2001| TIAy,2001] are estimated irrigated acreages of each crop in

2001 assuming year 2000 TIA and year 2001 TIA after the 33,006-acre reduction, respectively.

Summing irrigated acres by crop across all 17 counties (including the “Other” county)

gives us the sum total of irrigated acres by crop and are shown in Tables 6.3a, 6.4a and 6.5a for

the three scenarios, respectively. Crop distribution percentages are also shown along with

irrigated acres in those tables. Similarly, summing water demand in equations (6.2) through (6.4)

across all 17 counties (including the “Other” county) gives us the sum total of water demand by

crop and are shown in Tables 6.3b, 6.4b1-2 and 6.5b1-2 for the three scenarios, respectively.

Summing across counties in equation (6.1) provides the total base year 2000-level water demand

by crop as shown in Tables 6.3a through 6.5b2. Both normal and dry year water demand results

are provided.

Abnormally small acres numbers were often the result of abnormally high standardized or

unstandardized variances and/or covariances. In the case of standardized variances-covariances,

these numbers were often the result of corresponding low expected profits. When expected

profits per acre were near zero, dividing variances and covariances by expected profits to obtain

standardized variances and covariances resulted in extremely large and unrepresentative values.

These few outlying observations were assigned reasonable, credible values (as given by the

corresponding observations in other counties) to obtain reasonable, credible irrigated acres and

water demand estimates and forecasts.

Ceteris paribus, price (and hence expected return) changes result in substitution effects –

i.e., the way farmers will substitute one crop for another due to an expected change in prices (and

122

hence expected returns). Ceteris paribus, TIA changes result in expansion effects – i.e., the way

farmers will expand their cultivable land or irrigated acreage in the face of a change in TIA.

The simulation results demonstrating responsiveness of irrigated acres and the corresponding

water demand by crop to changes in expected returns and irrigation capacity (TIA) are briefly

discussed in the paragraphs below by scenario.

The results discussed here are for totals of the entire Flint River Basin. The results by

crop by county are available from the author upon request. Tables 6.3a through 6.5b2 at the end

of this chapter provide simulation results for irrigated acres, percentages of acres (tables marked

“a”), and water demand for dry and normal years (tables marked “b”). The crop category “Other”

in all of these tables include all crops not modeled – i.e., crops other than the four under study

that are grown in the Flint River Basin.

Scenario 1 (Tables 6.3a-b): This is the effect of a change in expected returns (prices,

yields, and costs) only, ceteris paribus, meaning no change in TIA is considered along with it.

This effect provides us with results for irrigated acres and water demand by county by crop. The

irrigated acres by crop are added over counties to obtain the Flint River Basin total irrigated

acres by crop for the years 2000 through 2002. The water demand in each case (by county) is

derived in the way described in the “Water Demand Estimation” section of this chapter above.

The water demand numbers in acre-feet by crop for normal and dry years are then added over

counties to obtain the Flint River Basin total water demand by crop for the years 2000 through

2002.

As seen from Table 6.3a, between 2000 and 2001, the irrigated acres for corn, soybeans

and “other” crops go up while those for cotton and peanuts go down. The pattern is repeated for

a change in the price vector between 2000 and 2002. As clear from Table 6.1, corn and cotton

123

are crops with relatively higher BC coefficients than peanuts and soybeans. So we may say that

corn and cotton are high BC crops, and peanuts and soybeans are low BC crops. Compared to the

engineering solution, the economic solution has 24,774 fewer acres of high BC crops and 8,807

more acres of low BC crops, so the economic solution gives more water savings. Table 6.3b

reflects the corresponding water demand numbers for each crop, the direction of changes for

each crop and year obviously remaining the same as that of irrigated acres and their

distributional percentages.

Scenario 2 (Tables 6.4a-b2): Under assumptions mentioned in the “Scenarios for

Simulations” section above, total irrigated acres (TIA) are altered along with the change in the

price vector. The FRDPA-stipulated 33,006 total acres decrease is imposed at the outset and the

new irrigated acres, crop distribution and water demand are studied under the new expected

returns-risks-and-TIA environment for responsiveness. The expected price vector for the base

2000 simulation given by (2.569, 0.624, 0.296, 5.446)′ for (corn, cotton, peanuts, soybeans) is

replaced in turn by the 2001 expected price vector (2.389, 0.523, 0.297, 4.505)′ and the 2002

expected price vector (2.620, 0.556, 0.248, 4.953)′.24 The engineering approach takes the old

crop mix (of 2000) and distributes the decrease in acres among the five crops according to that

mix.

The total acres by crop after the TIA change and the new crop distribution for the

“Sequential” economic model are shown in Table 6.4a and water demand for dry and normal

years under this new price-and-TIA environment appear in Tables 6.4b1 and 6.4b2, respectively.

The direction of change by crop totals is the same as in Scenario 1. Compared to the engineering

solution, in 2001, the economic solution has 23,423 fewer acres of high BC crops (corn and

24 The cost vector used in the base 2000 simulation (with a lag of one period) given by (143.81, 248.65, 328.51, 88.94)′ for (corn, cotton, peanuts, soybeans) is replaced by the cost vector (155.93, 300.52, 337.63, 91.41)′ of 2000 level, for calculation of both 2001 and 2002 expected returns. Expected yields vary by county and crop.

124

cotton) and 8,311 more acres of low BC crops (peanuts and soybeans), so the economic solution

gives more water savings. In 2002, the economic solution has 22,004 fewer acres of high BC

crops (corn and cotton) and 12,073 more acres of low BC crops (peanuts and soybeans), so the

economic solution still gives more water savings.

Under the “Simultaneous” economic model for Scenario 2, the direction of change by

crop totals is the same as in Scenario 1. Compared to the engineering solution, in 2001, the

economic solution has 17,904 fewer acres of high BC crops (corn and cotton) and 7,773 more

acres of low BC crops (peanuts and soybeans), so the economic solution gives more water

savings. In 2002, the economic solution has 16,480 fewer acres of high BC crops (corn and

cotton) and 11,902 more acres of low BC crops (peanuts and soybeans), so the economic

solution still gives more water savings. Tables 6.4b1-2 depict the corresponding water demand

numbers for each crop. The direction of shift in water demand is obviously the same as the

direction of shift in irrigated acres.

Comparing these numbers with those in the alternative economic simulation, we see that

with the “Sequential” assumption a higher number of acres is taken away from high BC crops

and a higher number of acres is planted of low BC crops than with “Simultaneous” assumption

as a result of the contraction in irrigation capacity. Thus, the shift in acres from high BC crops to

low BC crops and hence more water savings predicted by the economic approach vis-à-vis the

engineering approach as a result of the reduction in TIA become more prominent in the

“Sequential” simulation than in the “Simultaneous” simulation.

Scenario 3 (Tables 6.5a-b2): In this simulation, the original expected price vector (2.569,

0.624, 0.296, 5.446)′ for 2000 is replaced by the Food and Agricultural Policy Research Institute

(FAPRI)-projected 2010 raw price vector (2.990, 0.770, 0.175, 5.940)′ for the crops (corn,

125

cotton, peanuts, soybeans)′ with peanut price being substituted by an assumed no-government

program price of $0.175 per lb., since FAPRI does not report peanut price projections.

Obviously, all but peanut prices have gone up in 2010 from those in 2000. The rise in prices of

both of the high BC crops (corn and cotton) suggests growing those crops replacing low BC

crops, particularly peanuts. All the three scenarios are repeated with these new prices: first, with

TIA constant at base (year 2000) level, then with TIA reduced by 33,006 acres. The engineering

approach still fixes its crop mix, and with only a price change that approach suggests no change

in irrigated acres, whereas the economic approach allows for this price change and redistributes

the irrigated acres among the competing crops. As evident from Table 6.5a, under constant TIA,

both economic approaches predict 7,854 less acres of corn and 24,664 more acres of cotton,

totaling 16,810 more acres of high BC crops than the engineering approach predicts. Similarly,

the economic approach predicts 7,357 more acres of peanuts and 13,896 less acres of soybeans,

totaling 6,539 less acres of low BC crops than the engineering approach predicts. Further, the

economic approach suggests taking away 10,271 irrigated acres from “Other” crops and

distributing them between cotton and peanuts. Tables 6.5b1 and 6.5b2 give the corresponding

water demand predictions for normal and dry years, respectively.

For the scenario with TIA reduced by 33,006 acres, under “Sequential” assumption with

FAPRI 2010 prices, the direction of all changes remain the same as in the constant TIA case,

with slight differences in magnitude. A total of 16,274 more acres of high BC crops (7,515 less

of corn and 23,789 more of cotton) are irrigated, replacing 6,283 less acres of low BC crops

(6,974 more of peanuts and 13,257 less of soybeans) and 9,992 less acres of “other” crops.

For the scenario with TIA reduced by 33,006 acres, and under “Simultaneous”

assumption with FAPRI 2010 prices, direction-wise changes similar to those described above in

126

the “FAPRI no-TIA-change” economic effect and the “Sequential” effect occur. However, under

reduced TIA, compared to the “Sequential” case, the “Simultaneous” assumption leads FAPRI

prices to demonstrate a more shift in acres in favor of high BC crops. A total of 23,747 more

acres of high BC crops (8,072 less of corn and 31,819 more of cotton) are irrigated, replacing

7,374 less acres of low BC crops (6,315 more of peanuts and 13,689 less of soybeans) and

16,373 less acres of “other” crops.

In all the simulations with FAPRI prices, the most notable departure in results using

FAPRI prices in place of futures prices is that the direction of change among crop acreages has

reversed for all crops. Previously, 2001 and 2002 experienced a shift in irrigated acres from

cotton and peanuts to corn, soybeans and “other” crops. Consequently, in those years, the

economic approach vis-à-vis the engineering approach predicted shifting of irrigated acres from

high BC crops to low BC and “other” crops. With FAPRI 2010 prices, however, the situation is

completely reversed: all three scenarios now suggest a shift of acres under irrigation in corn,

soybeans and “other” crops to those under irrigation in cotton and peanuts. A rise in prices of

high BC crops makes those crops on the whole more lucrative to farmers to irrigate vis-à-vis the

low BC and “other” crops.

Slippage

As we have seen so far, total available irrigated acreage and expected profitability of

crops affect the crop mix in the farmer’s portfolio each year. This, in turn, determines the

possible changes in water demand. Conventionally physical models have been used to determine

agricultural water demand. They do not consider the possibilities of substitution effects that exist

in such determination. The econometric (also termed “economic”) model, on the contrary, does

127

consider these effects. The difference in the estimates of water demand measures “slippage”

(Tareen, 2001). Depending on the effect of relative profitability, this measure predicts a higher

or lower level of water use than the physical model.

Slippage is calculated by comparing the econometric forecast of a change in water

demand with the forecast from the physical model following a reduction in total irrigated acreage

(TIA), such as occurred after the passage of the Flint River Drought Protection Act (FRDPA).

Reduction in TIA available by county is considered in examining slippage in water use

estimation.

Specifically, as shown in equation (6.5) below, Tareen calculated slippage as the ratio of

the total econometric change to the total physical change subtracted from unity. That is,

Econometric Change in Total Water Demand Slippage = 1 – __________________________________________________________, (6.5) Physical Change in Total Water Demand

In an extreme case where both econometric and physical measures predict the exact same change

in total water demand, slippage will be zero. In another extreme case, when both changes are in

the same direction, let us say if the econometric change is twice the physical change, slippage

will be negative one, and when physical change is twice the econometric change, slippage equals

one-half. With no change in econometric prediction and any change in physical prediction,

slippage will be one.

As long as econometric and physical estimated changes occur in the same direction, and

the econometrically predicted change in water use is greater than the change predicted by the

physical model, slippage will be negative as seen under Scenario 2 (with 2001 and 2002 prices)

in Table 6.6. In contrast, when the econometrically estimated change in water demand is smaller

than that estimated by the physical model, and in the same direction, slippage is positive, as seen

under Scenario 3 (with 2010 prices) of Table 6.6. When economists and engineers predict

128

changes in total water demand in opposite directions, the sign and magnitude of slippage cannot

be predicted without knowing the sign and magnitude of the changes in both economic and

engineering predictions.

We may note that slippage cannot be calculated for Scenario 1, when TIA remains fixed,

since no change in engineering acres is recorded and thus the divisor in the slippage formula is

zero (see relation (6.5)).

The differences in estimation techniques between the physical and the econometric

measures result in a slippage amount of approximately -17.66% for the “Simultaneous”

economic model under Scenario 2 with 2001 expected prices. The amount of slippage in this

case, as obtained from this current research, suggests that a physical model under-predicts water

savings by approximately 50.96 million gallons per day for this scenario.

The slippage results under three different price situations for the two economic

simulation forecasts are shown in Table 6.6 at the end of this chapter. However, the discussion

on the strength of the econometric model vis-à-vis the engineering model becomes relatively

easier when we compare total irrigated acres and total water demand in the entire Flint River

Basin than on a formula such as “slippage,” as seen from the discussion on forecasting through

the simulation exercises. In this research, therefore, more stress is placed on irrigated acres and

water demand than on slippage.

129

Table 6.1. Net Irrigation Requirements (acre-inches) in Normal and Dry Years by Crop

and Region of the Flint River Basin as given by Blaney-Criddle Coefficients

______________________________________________________________________________

Crop Lowera Middleb Upperc Wtd. Avg. (L,M,U)d

______________________________________________________________________________

Corn

Normal Yeare 11.14 12.15 12.32 11.75

Dry Yearf 12.71 13.65 3.69 13.23

Cotton

Normal Year 11.74 13.22 11.85 12.00

Dry Year 13.68 15.04 13.38 13.78

Peanuts

Normal Year 6.58 7.69 n/a 7.13

Dry Year 7.97 9.01 n/a 8.49

Soybeans

Normal Year 7.58 8.38 7.65 7.72

Dry Year 9.04 9.75 8.79 9.06 ______________________________________________________________________________ Source: Georgia Irrigation Guide, USDA – Soil Conservation Service

a Lower Flint consists of Baker, Calhoun, Decatur, Dougherty, Early, Grady, Lee, Miller, Mitchell, Seminole and Worth counties. bMiddle Flint consists of Crawford, Crisp, Dooly, Macon, Marion, Randolph, Schley, Sumter, Taylor, Terrell and Webster counties. c Upper Flint consists of Clayton, Coweta, Fayette, Lamar, Meriwether, Pike, Spalding, Talbot and Upson counties. d The weighted average of the Lower, Middle and Upper Flint River Basin regions were calculated based on the weights defined by the percentage distribution of irrigated acres of a given crop in each region. e A normal year is defined as a growing season with average rainfall of 49, 44 and 55 inches of rain in Lower, Middle and Upper Flint River Basin regions, respectively. f Dry year is defined as a drought on the magnitude of 20% or an average of the two driest years in a ten-year period over the last 30 years of weather data. Note: Conversion rate: 1 ac-in = 27,150 gallons per day 1 ac-ft = 325,800 gallons per day

130

Table 6.2. Reduction in Total Irrigated Acres (TIA) in the Flint River Basin by County

from 2000 to 2001 Caused by the Flint River Drought Protection Act

County Acres Reduced Other County* Acres Reduced Baker 1,288 Lamar 90 Calhoun 2,400 Marion 3,004 Crisp 1,524 Pike 167 Dooly 377 Schley 1,297 Early 2,884 Taylor 275 Lee 1,010 Upson 237 Macon 1,402 Webster 4,833 Randolph 681 Total 9,903 Seminole 91 Sumter 4,595 Terrell 5,109 Worth 1,742 Other* 9,903 Total 33,006 Source: Georgia Department of Natural Resources * This gives the distribution of TIA reduced for counties clubbed in the composite county “Other.” Note: The following counties did not face any acres reduction (# indicates that county is clubbed in “Other”): Clayton#, Coweta#, Crawford#, Decatur, Dougherty, Fayette#, Grady#, Meriwether#, Miller, Mitchell, Spalding# and Talbot#.

131

Table 6.3a. Irrigated Acresa for Scenario 1: Expected Returns Updated in 2001and 2002,

Total Irrigated Acres Constant for 2000-2002

Flint Totals (Acre Percentages) Simulation Results Base ECON Modelsb

Acres Acres AcresCrop 2000 2001 2002

Corn 119,044 130,772 129,330 (0.152) (0.167) (0.165) Cotton 237,140 200,638 223,601 (0.302) (0.256) (0.285) Peanuts 177,184 169,658 171,307 (0.226) (0.216) (0.218) Soybeans 29,291 45,624 41,630 (0.037) (0.058) (0.053) Other 222,157 238,124 218,948 (0.283) (0.303) (0.279) Total 784,816 784,816 784,816 (1.000) (1.000) (1.000)

a Engineering model predicts no change in acreage allocation for Scenario 1. b Economic “Sequential” and “Simultaneous” simulation models predict identical acreage allocation for Scenario 1.

132

Table 6.3b. Water Demanda (acre-feet) for Scenario 1: Expected Returns Updated in 2001

and 2002, Total Irrigated Acres Constant for 2000-2002

Water Demand (Normal) Water Demand (Dry) Simulation Results Simulation Results Base ECON Modelsb Base ECON Models Crop 2000 2001 2002 2000 2001 2002

Corn 1,335,424 1,467,126 1,451,571 1,519,457 1,669,209 1,651,091 Cotton 2,799,159 2,366,845 2,635,599 3,246,064 2,746,260 3,060,366 Peanuts 1,177,829 1,127,350 1,139,199 1,420,286 1,359,727 1,373,406 Soybeans 223,566 348,455 317,882 264,857 412,556 376,445 Other 1,383,995 1,327,444 1,386,062 1,612,666 1,546,938 1,615,327 Total 6,919,973 6,637,220 6,930,312 8,063,328 7,734,690 8,076,636

a Engineering model predicts no change in water demand for Scenario 1. b Economic “Sequential” and “Simultaneous” simulation models predict identical water demand for Scenario 1.

133

Table 6.4a. Irrigated Acres for Scenario 2: Expected Returns Updated in 2001 and 2002,

Total Irrigated Acres Reduced by 33,006 Acres

Flint Totals (Acre Percentages) Simulation Results Base 2000 2001 Acres 2002 Acres Crop Acres ENG SEQ SIM ENG SEQ SIM

Corn 119,044 113,483 124,778 124,927 113,483 128,321 128,847 (0.152) (0.152) (0.166) (0.166) (0.152) (0.171) (0.171) Cotton 237,140 227,389 192,671 198,042 227,389 190,547 195,545 (0.302) (0.302) (0.256) (0.263) (0.302) (0.253) (0.260) Peanuts 177,184 169,641 162,600 161,073 169,641 170,688 169,680 (0.226) (0.226) (0.216) (0.214) (0.226) (0.227) (0.226) Soybeans 29,291 27,766 43,118 44,107 27,766 38,791 39,629 (0.037) (0.037) (0.057) (0.059) (0.037) (0.052) (0.053) Other 222,157 213,531 228,642 223,661 213,531 223,462 218,109 (0.283) (0.283) (0.304) (0.297) (0.283) (0.297) (0.290) Total 784,816 751,810 751,810 751,810 751,810 751,810 751,810 (1.000) (1.000) (1.000) (1.000) (1.000) (1.000) (1.000)

134

Table 6.4b1. Water Demand (acre-feet) in Normal Year for Scenario 2: Expected Returns

Updated in 2001 and 2002, Total Irrigated Acres Reduced by 33,006 Acres

Water Demand (Normal) Simulation Results 2001 2002 Crop Base 2000 ENG SEQ SIM ENG SEQ SIM

Corn 1,335,424 1,272,090 1,398,834 1,400,692 1,272,090 1,438,960 1,445,065 Cotton 2,799,159 2,683,320 2,272,266 2,335,997 2,683,320 2,246,443 2,305,752 Peanuts 1,177,829 1,126,549 1,079,362 1,069,037 1,126,549 1,133,553 1,126,737 Soybeans 223,566 211,870 329,232 336,846 211,870 296,168 302,614 Other 2,069,579 1,988,423 2,129,666 2,082,583 1,988,423 2,081,126 2,030,540 Total 7,605,557 7,282,251 7,209,361 7,225,155 7,282,251 7,196,248 7,210,708

135

Table 6.4b2. Water Demand (acre-feet) in Dry Year for Scenario 2: Expected Returns

Updated in 2001 and 2002, Total Irrigated Acres Reduced by 33,006 Acres

Water Demand ( Dry) Simulation Results 2001 2002 Crop Base 2000 ENG SEQ SIM ENG SEQ SIM


136

Table 6.5a. Irrigated Acres for Scenario 3: Expected Returns Updated Using FAPRI 2010

Prices,a Total Irrigated Acres (TIA) Set at 2000 Level and at Reduced Level (Reduced by

33,006 Acres)

Flint Totals (Acre Percentages) Simulation Results with 2010 FAPRI Pricesa Base 2000 TIA at Base Level TIA at Reduced Level Crop Acres ENG SEQ SIM ENG SEQ SIM Corn 119,044 119,044 111,190 111,190 113,483 105,968 105,411 (0.152) (0.152) (0.142) (0.142) (0.152) (0.141) (0.140) Cotton 237,140 237,140 261,804 261,804 227,389 251,178 259,208 (0.302) (0.302) (0.334) (0.334) (0.302) (0.334) (0.345) Peanuts 177,184 177,184 184,541 184,541 169,641 176,615 175,956 (0.226) (0.226) (0.235) (0.235) (0.226) (0.235) (0.234) Soybeans 29,291 29,291 15,395 15,395 27,766 14,509 14,077 (0.037) (0.037) (0.020) (0.020) (0.037) (0.019) (0.019) Other 222,157 222,157 211,886 211,886 213,531 203,539 197,158 (0.283) (0.283) (0.270) (0.270) (0.283) (0.271) (0.262) Total 784,816 784,816 784,816 784,816 751,810 751,810 751,810 (1.000) (1.000) (1.000) (1.000) (1.000) (1.000) (1.000)

a Raw FAPRI prices were used for corn ($2.99/bu.), cotton ($0.77/lb.) and soybeans ($5.94/bu.); FAPRI prices are not available for peanuts. A non-program peanut price was assumed at $0.175/lb.

137

Table 6.5b1. Water Demand (acre-feet) in Normal Year for Scenario 3: Expected Returns

Updated Using FAPRI 2010 Prices,a Total Irrigated Acres (TIA) Set at 2000 Level and at

Reduced Level (Reduced by 33,006 Acres)

Water Demand (Dd) Normal Simulation Results with 2010 FAPRI Pricesa Base 2000 TIA at Base Level TIA at Reduced Level Crop Water Dd ENG SEQ SIM ENG SEQ SIM



138

Table 6.5b2. Water Demand (acre-feet) in Dry Year for Scenario 3: Expected Returns

Updated Using FAPRI 2010 Prices,a Total Irrigated Acres (TIA) Set at 2000 Level and at

Reduced Level (Reduced by 33,006 Acres)

Water Demand (Dd) Dry Simulation Results with 2010 FAPRI Pricesa Base 2000 TIA at Base Level TIA at Reduced Level Crop Water Dd ENG SEQ SIM ENG SEQ SIM



139

Table 6.6. Slippage Comparison of Economic “Sequential” and “Simultaneous”

Simulations under Three Different Price Situations

Expected “Simultaneous” “Sequential”

Prices (Effectsa Together) (Effectsa Separated)

2001 Normal -0.176603232 -0.225454818

(futures) Dry -0.178431695 -0.225361760

2002 Normal -0.221286558 -0.266011192

(futures)* Dry -0.220500977 -0.263398893

2010 Normal 0.215491298 0.149993860

(FAPRI raw) Dry 0.219399134 0.155633007

* The 2002 futures prices for corn, cotton and soybeans were preliminary data available during the time of this research. Since peanut contracts do not exist, peanut prices were substituted by peanut price forecasts from Chapter 4 using Method 1 price forecasting (from historical data). a These are effects of changing expected returns and total irrigated acreage (TIA).

Note: Slippage under Scenario 1 (expected returns updated, no TIA change) cannot be calculated because the divisor (change in engineering irrigated acres) will be zero, since in the context of this study engineers do not consider a change in crop acres distribution based on price changes. The 2001 and 2002 cases depicted in the table above are essentially Scenario 2 and the 2010 case is Scenario 3 described in this chapter.

140

CHAPTER 7

SUMMARY, CONCLUSIONS, IMPLICATIONS AND FURTHER RESEARCH

Summary

With approximately 1.5 million irrigated acres of farmland, agriculture is the major

consumptive water user in the state of Georgia (Georgia Water Resources Conference

Proceedings, 2001; Georgia Faces, 2001). However, in spite of this large consumption, the

precise agricultural water uses on a county by commodity basis are not known in general. Thus,

policy proposals and decisions regarding irrigation water management are made under

incomplete, and potentially inaccurate, information. Tareen (2001) addressed the problem of

limited data on irrigated acreage as part of his dissertation. The current research used that data on

irrigated acreage and further developed Tareen’s (2001) allocation model, introduced an

alternate price and yield forecasting method, and based on its performance in forecasting out of

the sample, carried forward the price and yield forecasts from that alternate method to the

allocation model, then addressed the problem of the existing lack of linkages between water

demand and physical models of agricultural water use and the resulting “slippage” occurring

from the differences between the physical and the econometric measurements of agricultural

water demand for irrigation purposes. The gap in information about water allocation and between

water allocation and water demand as regards its use in irrigation is thus addressed.

Specifically speaking, the present study starts from Tareen’s (2001) dissertation and

further develops a method for forecasting Georgia irrigation water demand for corn, cotton,

peanuts and soybeans on county basis under different scenarios. First, prices and yields of the

141

four crops were forecasted by two methods – one, statistical, and two, following Holt (1992).

Second, using the irrigated acreage data disaggregated by Tareen (2001), the irrigated acreage

for responsiveness of each of the four crops – corn, cotton, peanuts and soybeans – was modeled

and estimated as a function of profits, variance-covariance of profits, the total irrigated acreage

available to producers in a county, and county-specific dummy variables. Third, the irrigated

acreage estimates, which in essence gave the predictions of acreage allocation, were used in

conjunction with the crop- and region-specific Blaney-Criddle (BC) coefficients of net irrigation

water requirements to forecast water demand. Finally, simulations were conducted on the

parameters of the acreage response model to trace the effects of alternative expected returns

(prices, yields and costs) and institutional arrangements (specifically, the withdrawal of specified

government programs, the results of which appear in Appendix A, and a forced change in total

irrigated acreage), resulting in slippage.

The main theory that underlies the whole analysis is that of expected utility

maximization. According to this theory, the producer is assumed to be a risk-averse expected

utility maximizer who operates in a competitive market facing uncertain output prices and yields.

He or she maximizes expected utility by allocating the total irrigated acreage available among

competing enterprises. Under the assumption of risk aversion and an acreage constraint, the

resulting empirical model of irrigated acreage is a function of profits, variance-covariance of

profits and the total irrigated acreage.

Data for estimating the empirical model for an individual producer are not readily

available and the highest degree of disaggregation in data is on a county level. Data on irrigated

acreage are also not available on a county-by-crop level. Tareen (2001) disaggregated the state-

142

level crop irrigation data on a county level by assuming the county total irrigated acreage of the

ith crop is proportional to the state irrigated acres of the ith crop.25

Rational expectations were also assumed. With this assumption, all available information

is taken into consideration while making planting decisions. Thus, the results are expected to

conform to those indicated by economic theory. In that sense, this framework provides an

appropriate way of incorporating the effects of uncertainty about future prices (Ahouissoussi,

1995).

Assuming the error terms were independently and identically distributed (i.i.d.) allowed

us the estimation of the equations for crop acreage using ordinary least squares (OLS). For four

crops we had four equations, respectively. Each of the four crop equations were specified as

functions of an intercept term, profits, variance of each of the crops, covariances between any

two crops, the total irrigated acreage in a county, and county-specific intercept-shifting dummy

variables. The overall goodness-of-fit was considered by examining the F-test statistic and the

coefficient of determination, R2, and a linear fit was imposed. The F-values in all crop equations

were found to be highly significant (all at the 1% level), and so were the R2 values:

approximately 94%, 93%, 99% and 84% in corn, cotton, peanut and soybean equations,

respectively. Most estimated parameters in all equations had their expected signs.

The estimated total irrigated acreage (TIA) coefficient in each of the four crop irrigated

acreage response equations was significant with the correct sign, i.e., positive. Own expected

profit estimates were as hypothesized (i.e., positive) and significant for corn and cotton, and

insignificant for peanuts and soybeans. The peanut quota variable gave a positive (as expected)

and significant coefficient estimate in the peanut model, negative (also as expected) and

25 A problem with this method, as recognized by Tareen (2001) himself, is that it is not linked with the crop mix in a county. Thus, he adopts this method with a modification to account for the crop mix in a county. That modified data set is used in the present analysis as well.

143

significant estimates in the corn and soybean models, respectively, and was insignificant in the

cotton model. The corn set-aside program variable produced an insignificant coefficient estimate

in the corn model, negative (counter-hypothesized) and significant estimate in the cotton

equation, positive (as expected) and significant estimate in the peanut equation, and was

insignificant in the soybean equation. The cotton set-aside gave a negative (as expected) and

significant coefficient estimate in the model for cotton, positive (also as expected) and significant

coefficient estimate in the models for corn and peanuts, respectively, and was insignificant in the

model for soybeans.

Apart from that, most of the 32 dummy variables (two sets of 16 in each set) were

significant in each of the four crop model equations. This proved the heterogeneity among the

counties under study, both with respect to size or irrigated acres (as shown by the first set of

dummies) and with respect to the leap in cotton acreage after 1992 (as shown by the second set

of dummies).

The results from estimating irrigated acreage in each of the four equations were used in

conjunction with the Blaney-Criddle (BC) net water requirement coefficients for modeling water

demand. The parameter estimates were then used to forecast one-year-ahead irrigated acreage

and water demand for three consecutive years out of the sample (1999 – 2001). Considering the

fact that the Flint River Drought Protection Act (FRDPA) was passed in year 2000 and it

decreased the irrigation capacity of the farmers in the Flint River Basin by a total of 33,006 acres

in 2001, the effect it had on the acreage allocation by crop by county and as a whole (specifically

as regards the four crops and the 17 counties under this study) was an important issue. The

econometric approach of modeling water demand was compared and contrasted with the

physical, engineering approach via their respective measures of irrigated acreage and water

144

demand. Next, the substitution and expansion effects in irrigated acres and water demand were

studied by varying economic (prices, costs, yields) and institutional (total irrigated acreage)

factors.

Three different scenarios were used to simulate forecasts of irrigated acreage and water

demand using a base simulation of year 2000. For each scenario, three simulations were looked

at: the engineering approach, the economic “Sequential” (SEQ) approach, and the economic

“Simultaneous” (SIM) approach. The engineering approach does not change the crop acreage

mix by county. It uses the exact same proportion of the initial allocation to reduce the total

irrigated acres (TIA) by crop by county. On the contrary, both the economic simulation

approaches change the acreage allocation, but in different ways.

For the SEQ approach, first, the base 2000 level of TIA was used with the new level of

expected returns and risks, for another out-of-sample year, say 2001, to estimate the proportion

of irrigated acres that would be allocated to each crop given expected changes in returns and

risks. Under this simulation method, these crop acreage proportions were then applied to the new

reduced level of TIA to generate the estimates of acreage allocations for calculating water

demand. This method thus assumed that producers would respond to a decrease in irrigation

capacity by optimizing their base acreage allocation in response to changes in expected risks and

returns of each crop, and then applying the new allocation proportions to the reduced level of

irrigation capacity.

The SIM model, an alternative economic simulation model, simply includes the new,

reduced level of TIA in the acreage allocation simulation simultaneously with the new levels of

expected returns and risks. With this version of the simulation, we thus assumed that the impact

of a one-acre decrease in TIA on each crop acreage was simply the opposite of the effect of a

145

one-acre increase in TIA.

Slippage estimates the difference between the engineering measure and each of the two

economic measures – SEQ and SIM. Slippage occurs when, based on economic or institutional

effects, producers switch to crops with higher or lower supplemental water requirements. This

research placed more emphasis, however, on the comparison of the physical model with the two

economic models based on total irrigated acreage and water demand (for both normal and dry

years) by crop, summed across counties.

Conclusions and Policy Implications

A major contribution of this research is incorporating substitution effects through price

changes along with expansion effects through total irrigated acreage changes in a producer’s

acreage allocation decision. Producers’ decision-making process is primarily based on the

expected net returns from the competing enterprises. Probably due to lack of evidence in favor of

risk aversion coupled with price supports afforded by the government, the focus in literature thus

far has primarily been on the first moments of an expected utility function, with minimal regard

for the riskiness of competing crops. In the context of a farming enterprise, the first moments are

expected returns. But, along with expected returns, this study included a risk-averse farming

enterprise’s regard for risks associated with each crop as well as with its substitutes and

complements, as given by the second moments of expected returns, viz., variances and

covariances of expected returns.

Through two economic simulations against an engineering simulation for each of the

three different scenarios (according to different expected returns and TIA situations), this study

attempted to identify the distinction between the conventional water use model and the modern

146

economic model. Further, two different versions of the economic model were studied and

compared. This gave us the choice of a better technical method in the presence of declining

irrigation capacity. Incorporating price and cross-price effects in the acreage allocation decision

led to “slippage” in the measurement of water demand. The FRDPA was a water-conserving

initiative on the part of the government. The effectiveness of such a policy could be determined

using a measure such as slippage.

The pitfalls associated with disregarding the updated irrigated acreage allocation by crop

and by county are clearly established through this research. The model development and the

simulation exercises provide insights into the importance of economic theory in the estimation

and forecasting of water use. Moreover, it paves the path for further research with more

sophisticated techniques and precision forecasting. Under a reduced acres scenario, the overall

model developed in this research will aid environmental, natural resource and land allocation

policy specialists better assess the impact of a change in irrigation capacity on irrigated acres and

irrigation water demand for the future on a crop-by-county basis.

As a result of reducing the total irrigated acreage, policymakers have been anticipating a

certain level of decrease in irrigation water demand. The decrease in water demand is then, in

turn, assumed to benefit both the interstate and intrastate allocation of water from the Flint River.

With decreased demand, policymakers anticipate increased water flows for Alabama and Florida

as well as more water for the competing users within the state of Georgia.

In considering the dynamic price effects in acreage allocation, policymakers will be

better equipped to assess the net change in water demand. Greater precision in information is

beneficial because, as Tareen (2001) notes, a smaller than expected reduction in water demand

implies increased government expenditures on payments to farmers to not irrigate in auctions

147

such as the one used in the FRDPA, so not only will the government expenditure increase, but

also will the intended reduction in water demand not be met. Failure to make adjustments, as

suggested by the economic approach in this dissertation, would lead to erroneous policy

analyses.

This research has its strengths over previous studies in that it is an improvement over the

engineering approach to estimating water demand. The engineering approach cannot change the

crop mix in any year beyond the base year, while our economic approaches can do so according

to the new predicted acres.

Furthermore, it is an improvement over Tareen’s (2001) work in several aspects. First, it

uses forecast errors instead of means to calculate covariances between prices and yields to

capture risks involved in the calculation of expected profits and to calculate the higher moments

(variances and covariances) of expected profits. This is theoretically superior because the risks

the farmer faces are risks from inaccurately forecasting prices and yields (and hence returns)

rather than the variability of returns around their means.

Second, the current research used two alternative methods to forecast prices and yields

and chose the better option, which turned out to be the one with futures prices and an alternative

yield calculation as done by Holt (1999) to include representative yields from the previous six

years. Tareen’s (2001) approach used only one method – the one using historical data – to

forecast prices and yields, and it turned out to perform worse of the two methods used in this

research.

Third, the current study introduces the “Sequential” simulation method, which considers

a change in expected returns and a decrease in TIA in sequence. Thus it offers an alternative way

of modeling the farmer’s response to reductions in TIA, which may be superior to simply

148

assuming that farmers respond to decreased TIA by just doing the opposite of what they would

do with an increase in TIA. Previous literature, including Tareen (2001), considered a single

economic approach to contrast against the traditional, engineering approach. Thus our current

study improves on that front as well.

However, admittedly, one of the weaknesses of this study has been the unavailability of

data, especially irrigation data, by crop and by county. For this reason, we had to depend on data

smoothing by interpolation methods. Future research could benefit from the use of more frequent

irrigation and actual water use data at the county level by crop. More precise policy analyses will

thus be possible through the exploitation of interactions between time-series and cross-section

data.

Better data should focus on what the policymakers might be able to collect and provide

the economists if they wanted to use this tool. Ideally, the overall model developed in this

research should render more accurate results if a program is set up to collect irrigated acreage

data annually on a county-by-crop basis so the allocation model can be re-estimated over time to

better reflect the water consumption pattern of the farmers. Further, if the policymakers can

provide data on water use by crop and county each year, the economists might be able to

improve on the BC coefficients indicating net irrigation water requirements and obtain better

water demand estimates. Data on irrigated acreage, water use and BC coefficients for “other”

(minor) crops would also improve accuracy.

A Summary of Suggestions for Further Research

1.) Obtaining more frequent data on irrigated acreage by crop and by county will render us

more confidence in the estimation and forecasting exercises.

149

2.) Obtaining county-level data on peanut quotas for the Georgia counties under study will

provide us with a more reliable data set on peanut quotas.

3.) Obtaining actual water use data for the region under study will allow us to determine the

accuracy of our predictions.

4.) Taking total irrigated acres so they equal the sum of the irrigated acres of the crops

studied will allow us to model the crop irrigated acreage response equations as share

equations. One can model the acreage allocation equations with all variables as shares of

total irrigated acres, so that the sum of all crop shares (i.e., the sum of the left-hand-side

variables in all the crop model equations) add up to one, thus imposing a restriction on

each of the parameters estimated. Estimation of such share equations has appeared in

recent years in the literature.

5.) Standardizing variances and covariances of expected net crop returns may be done using

a slightly different formula – for example, the standardization (i.e., dividing the

unstandardized counterpart) by the mean expected profits of the previous three years

instead of the current year.

6.) Assumption of linearity has been inherent in the modeling structure of the acreage

allocation equations. This might have been the cause of negative predictions of irrigated

acreage in some cases. Running non-linear regressions – two-stage or three-stage least

squares – for efficiency gains might be a way to obtain better acreage and hence water

demand predictions.

7.) In the simulation exercises described in Chapter 6, the crop category “Other” (consisting

of all crops other than the four crops under study) was assumed to have a BC coefficient

that approximates the average of the BC coefficients of the four crops studied. It would

150

be more precise to obtain the actual BC coefficients of those “Other” crops in further

research.

8.) Different specifications for the set-aside variables, for example, more in the lines of the

one used for the peanut quota variable, may be used. This will place some importance to

the fact that the counties under study are heterogeneous with respect to irrigation

capacity.

9.) More simulations with program variables may be performed.

10.) More sophisticated forecasting methods may be utilized. A couple of possible methods

are explained in the “Appendices” (B and C) of this dissertation.

11.) Rational expectations were assumed to exist in this research. To better explain the

phenomena of the market as it pertains to the supply and demand interactions (e.g., the

cross-price effects) of the crops under study, a test of the rational expectations hypothesis

would be recommended. Sheffrin (1996) notes, “It is important to test the hypothesis of

rational expectations in several ways. For agricultural markets, futures markets will be

useful for these tests. Where futures markets are not available, the likelihood and

predictive tests are still possible. Perhaps many of the over five hundred studies that used

adaptive expectations would, in fact, be consistent with rational expectations.” The

Rational Expectations Hypothesis (REH) had been a working assumption for the purpose

of this dissertation, and it might be explored and tested in future research.

151

REFERENCES

Abel, Andrew B. “ Empirical Investment Equations: An Integrative Framework.” In On the State

of Macro-Economics, edited by K. Brunner and A. Meltzer, 39-91. Carnegie-Rochester

Conference Series on Public Policy, No. 12. Amsterdam: North Holland, 1980.

Agricultural Statistics. United States Department of Agriculture – National Agricultural

Statistics Service, 1970 – 2002.

Ahouissoussi, Nicolas B.C., Christopher S. McIntosh and Michael E. Wetzstein. “Rational

Expectations Estimation of Georgia Soybean Acreage Response.” Journal of

Agricultural and Applied Economics 27(1995): 500-09.

Allen, P.G. “Economic Forecasting in Agriculture.” International Journal of Forecasting

10(1994): 81-135.

Allais, M. “Le Comportement de L’homme Rationel Devant Le Risque, Critique des

Postulates Axiomes de L’école Américaine.” Econometrica 21(1953): 503-46.

Apland, J., B. McCarl and W. Miller “Risk and the Demand for Supplemental Irrigation: A Case

Study in the Corn Belt.” American Journal of Agricultural Economics 62(1980): 142-45.

Askari, H. and J.T. Cummings. “Estimating Agricultural Supply Response with the Nerlove

Model: A Survey.” International Economic Review 18(1977): 257-92.

Bailey, K.W. and A.W. Womack. “Wheat Acreage Response: A Regional Econometric

Investigation.” Southern Journal of Agricultural Economics 17(1985): 171-80.

152

Baillie, Richard T. and Tim Bollerslev. “Multivariate Generalized ARCH Approach to Modeling

Risk Premia in Foreign Exchange Markets.” Journal of International Money and Finance

(September 1990): 309-24.

Banerjee, Swagata. “A Disaggregated Time-Series Analysis of Export-Base Models in Elko

County of Nevada.” Unpublished M.S. Thesis, Department of Applied Economics and

Statistics, University of Nevada, Reno, 1999.

Barsky, R.B. “The Fisher Hypothesis and the Forecastability and Persistence of Inflation.”

Journal of Monetary Economics 19(1: Jan. 1987): 3-24.

Barten, A.P. “Maximum Likelihood Estimation of a Complete System of Demand Equations.”

European Economic Review 1(Fall 1969): 7-73.

Barten, A.P. and C. Vanloot. “Price Dynamics in Agriculture: An Exercise in Historical

Econometrics.” Econometric Modelling 13(1996): 315-31.

Begg, D.K.H. The Rational Expectations Revolution in Macroeconomics. Oxford: Philip Allan,

1982.

Bell, Walter Howard. Rational and Adaptive Expectations, the Phillips Curve and the

International Transmission of Inflation. Geneva: Institut Universitaire de Hautes Études

Internationales, 1985.

Bernoulli, D. translation by L. Somer. “Exposition of a New Theory on Measurement of Risk.”

Econometrica 22(1954): 23-36.

Bessler, D. “An Analysis of Dynamic Economic Relationship: An Application to the U.S. Hog

Market.” Canadian Journal of Agricultural Economics 32(1984): 109-24.

Bettendorf, L. and J. Blomme. “An Empirical Study of the Distribution of Crops in Agricultural

Land in Belgium: 1900 – 1939.” Historical Social Research 19(2: 1994): 53 - 63.

153

Bewley, R., T. Young and D. Colman. “A Systems Approach to Modelling Supply Equations in

Agriculture.” Journal of Agricultural Economics 38(1987): 151-66.

Binger, B.R. and E. Hoffman. Microeconomics with Calculus 2nd edition. Glenview, IL: Scott,

Foresman and Co., 1997.

Binkley, J.K. and L. McKinzie. “Improving Acreage Response Analysis with Multiple

Equations.” North Central Journal of Agricultural Economics 6(1984): 91-98.

Blanchard, Olivier J. “Output, the Stock Market, and Interest Rates.” American Economic

Review 71(1981): 132-43.

Blaney, H.F. and W.D. Criddle. “Determining Consumptive Use and Irrigation Water

Requirements,” Agriculture Research Service, U.S. Department of Agriculture, Technical

Bulletin No. 1275, Washington, D.C.: U.S. Government Printing Office, 1962.

Boggess, W. R. Lacewell and D. Zilberman “Economics of Water Use in Agriculture.”

Agricultural and Environmental Resource Economics edited by G. Carlson, D. Zilberman

and J. Miranowski. Oxford: Oxford University Press, 1993.

Bollerslev, T. “Generalized Autoregressive Conditional Heteroskedasticity.” Journal of

Econometrics 31(April 1986): 307-27.

Box, G.E.P. and G.M. Jenkins. Time Series Analysis: Forecasting and Control. San Francisco,

CA: Holden-Day, 1970.

Box, G.E.P. and G.M. Jenkins. Time Series Analysis: Forecasting and Control, revised edition,

San Francisco, CA: Holden-Day, 1976.

Carey, Ronald O. “Re: Thanks, and Question.” Personal communication via electronic mail, July

29, 2003.

154

Cargill, T.F. and G.C. Rausser. “Time and Frequency Domain Representation of Futures Prices

as a Stochastic Process.” Journal of American Statistical Association 67(1972): 23-30.

Caswell, M. and D. Zilberman. “The Choices of Irrigation Technologies in California.”

American Journal of Agricultural Economics 67(1985): 224-34.

Chamberlain, G. “Panel Data.” In Handbook of Econometrics, edited by Z. Griliches and M.

Intriligator. Amsterdam: North-Holland, 1983.

Chambers, R.G. and H. Lee. “Constrained Output Maximization and U.S. Agriculture,” Applied

Economics 18(1986): 347-57.

Chan, Louis K.C., Jason Karceski and Josef Lakonishok. “On Portfolio Optimization:

Forecasting Covariances and Choosing the Model.” Review of Financial Studies 12(5:

Winter 1999a): 937-74.

Chan, Louis K.C., Jason Karceski and Josef Lakonishok. “On Portfolio Optimization:

Forecasting Covariances and Choosing the Model.” National Bureau of Economic

Research Working Paper 7039(1999b): http://www.nber.org/papers/w7039.

Chavas, Jean-Paul, R.D. Pope and R.S. Kao. “An Analysis of the Role of Futures Prices, Cash

Prices, and Government Programs in Acreage Response.” Western Journal of

Agricultural Economics 8(July 1983): 27-33.

Chavas, Jean-Paul and Matthew T. Holt. “Acreage Decision Under Risk: The Case of Corn and

Soybeans.” American Journal of Agricultural Economics 72(1990): 529-38.

Chembezi, D.M. and A.W. Womack. “Regional Acreage Response for U.S. Corn and Wheat:

The Effects of Government Programs.” Southern Journal of Agricultural Economics

24(1992): 187-98.

155

Choi, J.-S. and P.G. Helmberger. “Acreage Response, Expected Price Functions, and

Endogenous Price Expectations.” Journal of Agricultural and Resource Economics

18(July 1993): 37-46.

Colman, D. “Prairie Grain and Oilseed Acreage Response.” Working Paper No. 7, Policy,

Planning and Economics Branch, Agriculture Canada, Ottawa, 1979.

Connor, Jeffery D., Richard M. Adams and J. David Glyer. “Some Further Evidence on the

Derived Demand for Irrigation Electricity: A Dual Cost Function Approach.” Water

Resources Research 25(7: 1989): 1461-68.

Connor, G. and R.A. Korajczyk. “A Test for the Number of Factors in an Approximate Factor

Model.” Journal of Finance 48(1993): 1263-91.

Cook, R.J. “Wheat Management Systems in the Pacific Northwest.” Plant Disease 70(1986):

894-8.

Coulson, N. and R. Robins. “Aggregate Economic Activity and the Variance of Inflation:

Another Look.” Economic Letters 17(1985): 71-75.

Cragg, J. “Estimation and Testing in Time Series Regression Models with Heteroscedastic

Disturbances.” Journal of Econometrics 20(1982): 135-57.

Cox, C.B. and P.J. Luby. “Predicting Hog Prices.” Journal of Farm Economics 38(1956): 931-

39.

Cox, C.C. “Futures Trading and Market Information.” Journal of Political Economy 84(1976):

1215-36.

Coyle, B.T. “On Modeling Systems of Crop Acreage Demands.” Journal of Agricultural and

Resource Economics 18(July 1993): 57- 69.

156

Cumby, R.E., J. Huizinga and M. Obstfeld. “Two-Step Two-Stage Least Squares Estimation in

Models with Rational Expectations.” Journal of Econometrics 21(1983): 333-55.

Day, J.C. and G.L. Horner. “U.S. Irrigation Extent and Economic Importance.” Agriculture

Information Bulletin No. 523, Economic Research Service, USDA, Washington, D.C.,

1987.

deLeeuw, F.D. and L. Ozanne. “Housing.” In How Taxes Affect Economic Behavior, edited by

H. Aaron and J. Pechman, 283-326. Washington, DC: Brookings Institution, 1981.

Domowitz, I. and C. Hakkio. Conditional Variance and the Risk Premium in the Foreign

Exchange Market.” Journal of International Economics 19(1985): 47-66.

Duffy, P.A., J.W. Richardson and M.K. Wöhlgenant. “Regional Cotton Acreage Response.”

Southern Journal of Agricultural Economics 19(1987): 99-108.

Duffy, P.A., K. Shalshali and H.W. Kinnucan. “Acreage Response Under Farm Programs for

Major Southeastern Field Crops.” Journal of Agricultural Applied Economics 26(1994):

367-78.

Eales, J.S., B.K. Engel, R.J. Hauser and S.R. Thompson. “Grain Price Expectations of Illinois

Farmers and Grain Merchandisers.” American Journal of Agricultural Economics

72(1990): 701-08.

Eckstein, Z. “A Rational Expectations Model of Agricultural Supply.” Journal of Political

Economy 92(1984): 1-19.

Engle, Robert F. “Autoregressive Conditional Heteroscedasticity with Estimates of the Variance

of United Kingdom Inflations.” Econometrica 50(1982): 987-1008.

Engle, Robert F. “Estimates of the Variance of U.S. Inflation Based on the ARCH Model.”

Journal of Money, Credit, and Banking 15(1983): 286-301.

157

Engle, Robert F. and D. Kraft. “Multiperiod Forecast Error Variances of Inflation Estimated

From ARCH Models.” In Applied Time Series Analysis of Economic Data, edited by A.

Zellner. Washington, DC: Bureau of the Census, 1983.

Engle, Robert F., D. Lilien and R. Robins. “Estimation of Time Varying Risk Premiums in the

Term Structure.” University of California, San Diego, Department of Economics,

Discussion Paper 85-17, 1985.

Engle, Robert F. and Kenneth F. Kroner. “Multivariate Simultaneous Generalized ARCH.”

Unpublished Manuscript, 1993.

Engle, Robert F. and M. Rothschild. “ARCH Models in Finance.” Journal of Econometrics 52,

1/2, 1992.

Ericksen, M.H. “Use of Land Reserves to Control Agricultural Production.” U.S. Department of

Agriculture – Economic Research Service, ERS-635, September1976.

Ezekiel, Mordecai. “The Cobweb Theorem.” Quarterly Journal of Economics 52(1938): 255-80.

Fanning, J. “Benchmark Farms for Estimating Irrigation Water Use in Georgia.” Proceedings of

the 1995 Georgia Water Resources Conference, The University of Georgia (K.J. Hatcher,

editor, Carl Vinson Institute of Government), Athens, Georgia (1995): 274-75.

Fanning, J. Referenced in Tareen, 2001: Telephone interview by Irfan Y. Tareen, November 13,

2000.

Farm Service Agency. “Notice PN-618, dated 12-22-97, State Peanut Quota Allocations

(Conituned).” Obtained through personal communication (facsimile message) with

Ronald O. Carey, Chief, Production Adjustment Section, Farm Service Agency, Georgia

State Office, July 17, 2003.

Flint River Drought Protection Act. House Resolution 17, Georgia General Assembly, 2001.

158

Food and Agricultural Policy Research Institute (FAPRI). “Commodity Price Projections.”

Center for Agricultural and Rural Development (CARD), Iowa State University.

Website: http://www.fapri.org/Outlook2001/Tables/CPrices.xls.

Frost, P.A. and J.E. Savarino. “An Empirical Bayes Approach to Efficient Portfolio Selection.”

Journal of Financial and Quantitative Analysis 21(1986): 293-305.

Gardner, B.L. “Futures Prices in Supply Analysis.” American Journal of Agricultural Economics

58(1976): 81-84.

Georgia Agricultural Facts. Georgia Department of Agriculture – Georgia Agricultural Statistics

Service, in cooperation with USDA – NASS. Website: http://www.nass.usda.gov/ga/,

1970 – 2001.

Georgia Department of Natural Resources. Atlanta, Georgia, August 2001.

Georgia Environmental Protection Division. Geological Survey Branch, Atlanta, Georgia,

August 2001.

Georgia Faces. “Irrigated Acres Slightly Up In Georgia.” The University of Georgia College of

Agricultural and Environmental Sciences, 2001.

Georgia Florida Peanut Producers Association. Obtained through personal communication

(facsimile message) with Ronald O. Carey, Chief, Production Adjustment Section, Farm

Service Agency, Georgia State Office, July 17, 2003.

Gibson, W.E. “Interest Rates and Inflationary Expectations: New Evidence.” American

Economic Review 62(1972): 854-65.

Gisser, M. “Linear Programming Models for Estimating the Agricultural Demand Function for

Imported Water in the Pecos River Basin.” Water Resources Research 6(1970): 1025-32.

159

Goodwin, T. and S.M. Sheffrin. “Testing with Rational Expectations Hypothesis in an

Agricultural Market.” Review of Economics and Statistics 64(1982): 658-67.

Govindasamy, R. and S. Jin. “Fresh Sweet Corn Acreage Response in the Selected States of the

U.S.A.” Applied Economics Letters 5(1998): 555-57.

Green, R.J. and B. Hollifield. “When Will Mean-Variance Efficient Portfolios be Well

Diversified?” Journal of Finance 47(1992): 1785-1809.

Greene, William H. Econometric Analysis 2nd edition. Englewood Cliffs, NJ: Prentice Hall, Inc.,

1993.

Greene, William H. Econometric Analysis 3rd edition. Englewood Cliffs, NJ: Prentice Hall, Inc.,

1997.

Harrison, Kerry. “Irrigated Acres Slightly Up in Georgia.” Georgia Faces, February 28, 2001.

Hansen. L.P. “Large Sample Properties of Generalized Method of Moments Estimators.”

Econometrica 50(1982): 1029-54.

Heady, E.O. “The economics of rotations with farm and production policy applications.” Journal

of Farm Economics 30(1948): 645-64.

Heady, E.O. and H.R. Jensen. The Economics of Crop Rotations and Land Use: A Fundamental

Study in Efficiency with Emphasis on Economic Balance and Forage and Grain Crops.

Research Bulletin 383, August 1951, Ames, Iowa: Agricultural Experiment Station, Iowa

State University.

Hinchy, M. “The Relationship Between Beef Prices in Export Markets and Australian Saleyard

Prices.” Quarterly Review of Agricultural Economics 31(1978): 83-105.

Hogg, R. and A. Craig. Introduction to Mathematical Statistics 4th edition. New York, NY:

Macmillan Publishing Co., Inc., 1978.

160

Holt, Matthew T. “A Multimarket Bounded Price Variation Model Under Rational Expectations:

Corn and Soybeans in the United States.” American Journal of Agricultural Economics

74(1:1992): 10-20.

Holt, Matthew T. “A Linear Approximate Acreage Allocation Model.” Journal of Agricultural

and Resource Economics 24(2:1999): 383-397.

Hopkins, J.A., Jr. “Forecasting Cattle Prices.” Journal of Farm Economics 9(1927): 433-46.

Houck, J.P. and M.E. Ryan. “Supply Analysis of Corn in the United States: The Impact of

Changing Government Programs.” American Journal of Agricultural Economics

54(1972): 184-91.

Houston, J.E., C.S. McIntosh, P.A. Stavriotis and S.C. Turner. “Leading Indicators of Regional

Cotton Acreage Response: Structural and Time Series Modeling Results.” Journal of

Agricultural and Applied Economics 31(1999): 507-17.

Huber, P.J. “Robust Covariances.” In Statistical Decision Theory and Related Topics II, edited

by S.S. Gupta and Dennis S. Moore. New York: Academic Press, 1977.

Huntzinger, R.L. “Market Analysis with Rational Expectations.” Journal of Econometrics

10(1979): 127-45.

Jurenas, Remy. “Farm Commodity Programs: Peanuts.” Congressional Research Service Report

for Congress, August 26, 1998.

Jurenas, Remy. “IB95118: Peanuts: Policy Issues.” Congressional Research Service Issue Brief

for Congress, January 19, 2001.

Jarret, F. “Short-term Forecasting of Australian Wool Prices.” Australian Economics Paper

4(1965): 93-102.

161

Jobson, J.D. and B. Korkie. “Putting Markowitz Theory to Work.” Journal of Portfolio

Management 7(1981): 70-74.

Jordan, Jeffrey L. “Georgia Water Series Issue 1: An Introduction to Water: Economic Concepts,

Water Supply and Water Use.” Faculty Series 98-13, Department of Agricultural and

Applied Economics, The University of Georgia, 1998.

Just, R.E. “The Investigation of the Importance of Risk in Farmers’ Decision.” American Journal

of Agricultural Economics 56(1974): 14-25.

Karadi, G. “History of Irrigation.” Compton's Encyclopedia Online v3.0 1998. The Learning

Company, Inc., 1998.

Kaylen, M.S. “Vector Autoregression Forecasting Models: Recent Developments Applied to the

U.S. Hog Markets.” American Journal of Agricultural Economics 70(1988): 701-12.

Kraker, E. and B. Paddock. “A Systems Approach to Estimating Prairie Crop Acreage.” Working

Paper No. 15, Marketing and Economics Branch, Agriculture Canada, Ottawa, 1985.

Kearl, J. “Inflation, Mortgages, Housing.” Journal of Political Economy 87(1979): 1115-38.

Kendall, M.G. “The Analysis of Economic Time-Series, Part I: Prices.” Journal of the Royal

Statistical Society 96(1953): 11-25.

Knutson, Ronald D., J.B. Penn and William T. Boehm. Agricultural and Food Policy Englewood

Cliffs, NJ: Prentice Hall, Inc., 1983.

Kollintzas, Tryphonus. The Rational Expectations Equilibrium Inventory Model: Theory and

Applications. (Ed.) New York: Springer-Verlag New York, Inc., 1989.

Krause, M.A., J.-H. Lee and W.W. Koo. “Program and Nonprogram Wheat Acreage Responses

to Price and Price Risk.” Journal of Agricultural and Resource Economics 20(1995): 96-

107.

162

Krikelas, Andrew.C. Industry Structure and Regional Growth: A Vector Autoregression

Forecasting Model of Wisconsin Regional Economy. Ph.D. Dissertation, University of

Wisconsin, Madison, 1991.

Kroner, Kenneth F. and William D. Lastrapes. “The Impact of Exchange Rate Volatility on

International Trade: Reduced Form Estimates Using the GARCH-in-mean Model.”

Journal of International Money and Finance 12(1993): 298-318.

Kulshreshta S. and D. Tewari. “Value of Water in Irrigated Crop Production Using Derived

Demand Functions: A Case Study of South Saskatchewan River Irrigation District.”

Water Resources Bulletin 27(1991): 227-36.

Levy, H. and H. Markowitz. “Approximating Expected Utility by a Function of Mean and

Variance.” American Economic Review 69(1979): 308-17.

Lichtenberg, E. “Land Quality, Irrigation Development, and Cropping Patterns in the Northern

High Plains.” American Journal of Agricultural Economics 71(1989): 187-94.

Litterman, R. B. “Forecasting with Bayesian Vector Autoregression – Five Years of

Experience.” Working Paper 274, July 1985.

Lynne, G. “Issues and Problems in Agricultural Water Demand Estimation from Secondary Data

Sources.” Southern Journal of Agricultural Economics 10(1978): 101-06.

Machina, M. “Choice Under Uncertainty: Problems Solved and Unsolved.” The Journal of

Perspective 1(1987): 121-54.

Mackert, J.R, B.R. Miller and J.A. Meier “Peanut Production Costs and Returns in Selected

Georgia Counties, 1979.” Faculty Series 80-4, Department of Agricultural Economics,

The University of Georgia, 1980a.

Mackert, J.R, B.R. Miller and J.A. Meier “Corn Production Costs and Returns in Selected

163


The University of Georgia, 1980b.

Mackert, J.R, B.R. Miller and J.A. Meier “Soybean Production Costs and Returns in Selected


The University of Georgia, 1980c.

Markowitz, Harry. “Portfolio Selection.” Journal of Finance 7(1952): 77-91.

Masanao, A. “Two Complementary Representations of Multiple Time Series in State

Space Innovation Forms.” Journal of Forecasting 13(1994a): 69-90.

Masanao, A. “Modeling Economic Time Series by Forward and Backward State Space

Innovation Models and Instrumental Variable Estimator.” European Journal of

Operations Research 73(1994b): 265-78.

Massow, M. and A. Weersink. “Acreage Response to Government Stabilization Programs in

Ontario.” Canadian Journal of Agricultural Economics 41(1) 1993: 13-26.

McCallum, B.T. “Rational Expectations and the Natural Rate Hypothesis: Some Consistent

Estimates.” Econometrica 44(1976): 43-52.

McLeod, I.A. “Distribution of the Residual Cross Correlations in Univariate ARMA Time Series

Models.” Journal of the American Statistical Association 74(1979): 849-855.

Moore, Henry Ludwell. Forecasting the Yield and Price of Cotton. New York, NY: McMillan,

1917.

Moore, M.R. and D. H. Negri. “A Multicrop Production Model of Irrigated Agriculture, Applied

to Water Allocation Policy of the Bureau of Reclamation.” Journal of Agricultural and

Resource Economics 17(1992): 30-43.

164

Moore, Kevin Clare and William H. Meyers. Predictive Econometric Modeling of the U.S.

Farmland Market: An Empirical Test of the Rational Expectations Hypothesis. The

Center for Agricultural and Rural Development (CARD) Report 133, Iowa State

University, Ames, Iowa, 1986.

Morzuch, B.J., R.D. Weaver and P.G. Helmberger, “Wheat Acreage Supply Response under

Changing Farm Program.” American Journal of Agricultural Economics 62(1: 1980): 29-

37.

Moss, C. and C. DeBodisco. “Estimation of Agricultural Water Demand in Northwest Florida:

Valuing Water Using Quasi-fixed Variables.” Staff Paper, Food and Resource Economics

Department, Institute of Food and Agricultural Sciences, University of Florida,

Gainesville, Florida, 1999.

Moss, R.B. and F.B. Saunders. “Costs and Returns for Selected Crop Enterprises at the

Southwest Georgia Branch Station, 1978-80, With Comparison for the 18-Year Period,

1963-80.” Research Report 398, College of Agriculture, The University of Georgia,

Athens, Georgia, 1982.

Muth, John F. “Optimal Properties of Exponentially Weighted Forecasts.” Journal of the

American Statistical Association 55(1960): 299-306.

Muth, John F. “Rational Expectations and the Theory of Price Movements.” Econometrica

29(1961): 315-35.

National Research Council – Alternative Agriculture. Washington, DC: National Academy

Press, 1989.

Negri, D. and D. Brooks. “The Determinants of Irrigation Technology Choice.” Staff Paper,

USDA – Economic Research Service, 1988.

165

Nelson, Charles R. “Rational Expectations and the Predictive Efficiency of Economic Models.”

Journal of Business 48(1975): 331-43.

Nerlove, Marc. “Estimates of the Elasticities of Supply of Selected Agricultural Commodities.”

Journal of Farm Economics 38(1956): 496-509.

Nerlove, M. The Dynamics of Supply: Estimation of Farmer’s Response to Price. Baltimore,

MD: John Hopkins Press, 1958.

Nieswiadomy, M. “The Demand for Irrigation Water in the High Plains of Texas, 1957 – 1980.”

American Journal of Agricultural Economics 67(1985): 619-26.

Nieswiadomy, M. “Input Substitution in Irrigated Agriculture in the High Plains of Texas, 1979-

80.” Western Journal of Agricultural Economics 13(1988): 63-70.

Nieuwoud, W.L., A.W. Womack and S.R. Johnson. “Measurement of Importance of Risk on

Supply Response of Corn and Soybeans.” North Central Journal of Agricultural

Economics 10(1988): 281-92.

Norton, V. “Water Resource Management: A Critical Issue for Farmers and Rural Communities

in the 21st Century.” Paper presented at the 2001 Annual J.W. Fanning Lecture at the

University of Georgia, November 14, 2000.

Ogg, C. and N. Gollehon. “Western Irrigation Response to Pumping Costs: A Water Demand

Analysis Using Climatic Regions.” Water Resources Research 25(1989): 767-73.

Peck, Anne E. “Future Markets, Supply Response, and Price Stability.” Quarterly Journal of

Economics 90(1976): 407-23.

Pierce, R., N. Barber and H. Stiles. “Georgia Irrigation, 1970-80: A Decade of Growth.” U.S.

Geological Survey Water Resources Investigation Report 83-4117, 1984.

166

Pope, Rulon D. “Empirical Estimation and Use of Risk Preferences: An Appraisal of Estimation

Methods That Use Actual Economic Decisions.” American Journal of Agricultural

Economics 64(1982): 376-83.

Poterba, James M. “Inflation, Income Taxes, and Owner Occupied Housing.” National Bureau of

Economic Research Working Paper No. 553, 1980.

Power, J.F. “Legumes: Their Potential Role in Agricultural Production.” American Journal of

Alternative Agriculture 2(1987): 69-73.

Proceedings of the 1999 Georgia Water Resources Conference, held at the University of

Georgia, March 29-31, 1999.

Proceedings of the 2001 Georgia Water Resources Conference, held at the University of

Georgia, March 26-27, 2001.

Prophet Financial Systems, Inc. “Historical Futures Data 1959-Present.” CD-Rom © 1999.

Rausser G.C. and T.F. Cargill “The Existence of Broiler Cycle: A Spectral Analysis.” American

Journal of Agricultural Economics 52(1970): 109-21.

Rich, Robert W. “Another Look at the Rationality of the Livingston Price Expectations Data.”

Applied Economics 22(Issue 4, April 1990): 477-85.

Robison, K. “Re: Research Data Help Sought.” Personal communication via electronic mail,

August 13, 2003.

Rust, John. “Optimal Replacement of GMC Bus Engines: An Empirical Model of Harold

Zurcher.” Econometrica 55(1987): 999-1033.

Samuelson, Paul Anthony. “The Fundamental Approximation Theorem of Portfolio Analysis in

Terms of Means, Variances and Higher Moments.” Review of Economic Studies

37(1970): 537-42.

167

Sarle, C.F. “The Forecasting of the Price of Hogs.” American Economic Review 15(1925): 1-22.

Schaible, G., C. Kim and N. Whittlesey. “Water Conservation Potential from Irrigation

Technology Transitions in the Pacific Northwest.” Western Journal of Agricultural

Economics 16(1990): 194-206.

Schmitz, A. and D.G. Watts. “Forecasting Wheat Yield: An Application of Parametric Time

Series Modeling.” American Journal of Agricultural Economics 52(2: May1970): 247-

54.

Schroeter, J.R. and S.L. Smith. “A Reexamination of the Livingston Price Expectations.”

Journal of Money, Credit, and Banking 18(1986): 239-46.

Sheffrin, Steven M. Rational Expectations 2nd edition. Cambridge Surveys of Economic

Literature.Cambridge: Cambridge University Press, 1996.

Shideed, K. H., F.C. White and S.J. Brannen. “The Responsiveness of U.S. Corn and Soybean

Acreage to Conditional Price Expectations: An Application to the 1985 Farm Bill.”

Southern Journal of Agricultural Economics 19(1987): 153-67.

Shonkwiler, J. Scott and Robert D. Emerson. “Imports and the Supply of Winter Tomatoes: An

Application of Rational Expectations.” American Journal of Agricultural Economics

64(4: Nov. 1982): 634-41.

Shonkwiler, J. Scott and T.H. Spreen. “A Dynamic Regression Model of the U.S. Hog Market.”

Canadian Journal of Agricultural Economics 30(1982): 37-48.

Shumway, C.R. “Supply, Demand, and Technology in a Multiproduct Industry: Texas Field

Crops.” American Journal of Agricultural Economics 65(1983): 748-60.

Smith, B.B. “Forecasting the Acreage of Cotton.” Journal of American Statistical Association

20(1925): 31-47.

168

Tareen, Irfan Yousuf. Forecasting Irrigation Water Demand: An Application to the Flint River

Basin. Unpublished PhD Dissertation, Department of Agricultural and Applied

Economics, The University of Georgia, Athens, 2001.

Tareen, Irfan Y., Lewell F. Gunter, Jimmy Bramblett and Michael E. Wetzstein. “Slippage in

Forecasting Irrigation Water Demand: An Application to the Georgia Flint River Basin.”

Unpublished Manuscript, 2002.

Tew, B.V. An Expected Value-Variance Analysis of Alternative Production Systems: A Study of

Irrigation Schedules in the Georgia Coastal Plain. Unpublished Ph.D. Dissertation,

Department of Agricultural Economics, The University of Georgia, Athens, 1984.

Theil, H. “A Multinomial Extension of the Linear Logit Model.” International Economic Review

10(1969): 251-59.

Topel, Robert and Sherwin Rosen. “Housing Investment in the United States.” Journal of

Political Economy 96(1988): 718-40.

Traill, B. “Risk Variables in Econometric Supply Models.” Journal of Agricultural Economics

29(1978): 53-61.

Turnovsky, Stephen J. “Some Empirical Evidence on the Formation of Price Expectations.”

Journal of the American Statistical Association 65(1970): 1441-54.

Turnovsky, Stephen J. “Futures Markets, Private Storage, and Price Stabilization.” Journal of

Public Economics 12(1979): 301-27.

United States Department of Agriculture – Animal and Plant Health Inspection Service. “Boll

Weevil Eradication.” 1999. Website: http://www.aphis.usda.gov/ppq/weevil/.

169

United States Department of Agriculture – Economic Research Service. “Briefing Room Farm

Income and Costs: Commodity Costs and Returns.” Website:

http://www.ers.usda.gov/briefing/farmincome/costsandreturns.htm.

United States Department of Agriculture – National Agricultural Statistics Service. Website:

http://www.usda.gov/nass/.

United States Department of Agriculture – Natural Resource Conservation Service. “ACT/ACF

River Basins Comprehensive Study: Agricultural Water Demand.” 1995.

United States Department of Agriculture – Soil Conservation Service, Engineering Division.

“Irrigation Water Requirements: Technical Release No. 21.” April 1967, revised

September 1970 (Citation for Blaney-Criddle).

University of Georgia – Cooperative Extension Service. “Georgia Irrigation Survey.” Biological

and Agricultural Engineering, Tifton, Georgia, 1999.

Van Tassel, W.H. A Comparison of GLS, BVAR and Composite Forecasts of Nevada Alfalfa Hay

Prices. Unpublished M.S. Thesis, Department of Applied Economics and Statistics,

University of Nevada, Reno, 1990.

Von Neumann, J. and O. Morgenstern. Theory of Games and Economic Behavior. Princeton, NJ:

Princeton University Press, 1980 (original 1944).

Witte, James. “The Microfoundations of the Social Investment Function.” Journal of Political

Economy 71(1963): 441-56.

Wolpin, Kenneth I. “Estimating a Structural Search Model: The Transition from School to

Work.” Econometrica 55(1987): 801-17.

Zanias, George. “Adjustment Costs and Rational Expectations: An Application to a Tobacco

Export Model.” American Journal of Agricultural Economics 69(1987): 22-29.

170

Zapata, Hector O. and P. Garcia. “Price Forecasting with Time-Series Methods and Non-

Stationary Data: An Application to Monthly U.S. Cattle Prices.” Western

Journal of Agricultural Economics 15(1: 1990): 123-132.

171

APPENDICES

172

APPENDIX A.

TABLES A.1a THROUGH A.16:

1998 – 2000 IRRIGATED ACRES AND WATER DEMAND

173

Table A.1a. 1998 Corn Irrigated Acres and Water Demand Observed for Normal and Dry

Years

CORN Acres Observed Water Demand (ac-ft)

County 1998 Normal Dry Baker 7,000.00 6,498.33 7,414.17

Calhoun 4,706.53 4,369.23 4,985.00

Crisp 1,700.00 1,578.17 1,800.58

Decatur 7,500.00 6,962.50 7,943.75

Dooly 500.00 464.17 529.58

Dougherty 1,800.00 1,671.00 1,906.50

Early 7,117.26 6,607.19 7,538.36

Lee 4,000.00 3,713.33 4,236.67

Macon 3,600.00 3,342.00 3,813.00

Miller 8,035.24 7,459.38 8,510.66

Mitchell 5,500.00 5,105.83 5,825.42

Randolph 3,539.04 3,285.41 3,748.43

Seminole 8,835.69 8,202.47 9,358.47

Sumter 6,703.36 6,222.95 7,099.97

Terrell 4,313.53 4,004.39 4,568.74

Worth 4,500.00 4,177.50 4,766.25

Other 6,634.38 6,494.92 7,315.00

Total 85,985.03 80,158.77 91,360.56

174

Table A.1b. 1998 Corn Irrigated Acres and Water Demand Predicted for Normal and Dry

Years

CORN Acres Predicted Water Demand (ac-ft)

County 1998 Normal Dry

Baker 6,641.95 6,165.95 7,034.93

Calhoun 4,056.39 3,765.68 4,296.40

Crisp 1,384.16 1,284.96 1,466.05

Decatur 9,835.90 9,130.99 10,417.86

Dooly 788.90 732.36 835.58

Dougherty 2,201.28 2,043.52 2,331.53

Early 6,374.88 5,918.02 6,752.06

Lee 5,681.78 5,274.58 6,017.95

Macon 3,045.65 2,827.38 3,225.85

Miller 7,228.90 6,710.82 7,656.60

Mitchell 9,978.26 9,263.15 10,568.64

Randolph 3,468.85 3,220.25 3,674.09

Seminole 8,100.03 7,519.53 8,579.28

Sumter 5,582.33 5,182.26 5,912.61

Terrell 3,421.88 3,176.64 3,624.34

Worth 5,502.71 5,108.35 5,828.29

Other 7,561.77 7,402.82 8,337.53

Total 90,855.60 84,727.26 96,559.59

175

Table A.2a. 1998 Cotton Irrigated Acres and Water Demand Observed for Normal and

Dry Years

COTTON Acres Observed Water Demand (ac-ft) County 1998 Normal Dry Baker 18,500.00 18,099.17 21,090.00

Calhoun 12,380.84 12,112.59 14,114.16

Crisp 8,281.51 8,102.08 9,440.92

Decatur 36,000.00 35,220.00 41,040.00

Dooly 16,095.42 15,746.68 18,348.78

Dougherty 8,972.21 8,777.81 10,228.32

Early 18,722.42 18,316.76 21,343.55

Lee 17,904.81 17,516.88 20,411.49

Macon 10,916.19 10,679.67 12,444.46

Miller 21,000.00 20,545.00 23,940.00

Mitchell 32,736.44 32,027.15 37,319.54

Randolph 8,500.00 8,315.83 9,690.00

Seminole 17,000.00 16,631.67 19,380.00

Sumter 17,633.63 17,251.56 20,102.33

Terrell 11,347.02 11,101.16 12,935.60

Worth 16,693.97 16,332.27 19,031.12

Other 17,452.16 17,450.72 20,038.62

Total 290,136.61 284,227.01 330,898.90

176

Table A.2b. 1998 Cotton Irrigated Acres and Water Demand Predicted for Normal and

Dry Years

COTTON Acres Predicted Water Demand (ac-ft) County 1998 Normal Dry Baker 17,707.94 17,324.27 20,187.05

Calhoun 12,189.92 11,925.80 13,896.50

Crisp 9,318.76 9,116.85 10,623.38

Decatur 33,723.56 32,992.88 38,444.86

Dooly 16,830.82 16,466.15 19,187.13

Dougherty 8,866.64 8,674.53 10,107.97

Early 17,947.71 17,558.84 20,460.38

Lee 16,489.98 16,132.70 18,798.58

Macon 10,355.76 10,131.38 11,805.56

Miller 20,985.17 20,530.50 23,923.10

Mitchell 29,011.91 28,383.32 33,073.58

Randolph 8,752.27 8,562.64 9,977.59

Seminole 20,743.11 20,293.68 23,647.14

Sumter 17,236.38 16,862.93 19,649.47

Terrell 11,413.70 11,166.41 13,011.62

Worth 12,594.26 12,321.39 14,357.46

Other 14,043.50 14,042.34 16,124.79

Total 278,211.39 272,486.60 317,276.19

177

Table A.3a. 1998 Peanut Irrigated Acres and Water Demand Observed for Normal and

Dry Years

PEANUTS Acres Observed Water Demand (ac-ft) County 1998 Normal Dry Baker 10,552.04 5,786.03 7,008.31

Calhoun 6,802.42 3,730.00 4,517.94

Crisp 4,550.12 2,494.98 3,022.04

Decatur 20,541.83 11,263.77 13,643.20

Dooly 8,843.33 4,849.09 5,873.44

Dougherty 4,929.61 2,703.07 3,274.09

Early 10,286.68 5,640.53 6,832.07

Lee 9,837.47 5,394.21 6,533.72

Macon 4,600.00 2,522.33 3,055.17

Miller 11,613.46 6,368.05 7,713.27

Mitchell 17,986.43 9,862.56 11,945.99

Randolph 5,115.03 2,804.74 3,397.23

Seminole 12,770.36 7,002.42 8,481.65

Sumter 9,688.47 5,312.51 6,434.76

Terrell 6,234.41 3,418.53 4,140.69

Worth 9,172.19 5,029.42 6,091.86

Other 9,588.77 5,698.77 6,781.66

Total 163,112.61 89,881.01 108,747.08

178

Table A.3b. 1998 Peanut Irrigated Acres and Water Demand Predicted for Normal and

Dry Years

PEANUTS Acres Predicted Water Demand (ac-ft)County 1998 Normal Dry Baker 10,852.27 5,950.66 7,207.72

Calhoun 6,908.21 3,788.00 4,588.21

Crisp 4,103.46 2,250.06 2,725.38

Decatur 21,011.04 11,521.05 13,954.83

Dooly 8,488.80 4,654.69 5,637.98

Dougherty 4,681.08 2,566.79 3,109.02

Early 10,431.26 5,719.81 6,928.10

Lee 9,969.51 5,466.62 6,621.42

Macon 5,531.43 3,033.07 3,673.79

Miller 11,777.35 6,457.91 7,822.12

Mitchell 18,911.42 10,369.76 12,560.34

Randolph 5,268.43 2,888.86 3,499.12

Seminole 12,853.74 7,048.13 8,537.03

Sumter 9,880.34 5,417.72 6,562.19

Terrell 6,159.82 3,377.64 4,091.15

Worth 9,409.69 5,159.65 6,249.60

Other 10,695.33 6,356.41 7,564.27

Total 166,933.19 92,026.84 111,332.26

179

Table A.4a. 1998 Soybean Irrigated Acres and Water Demand Observed for Normal and

Dry Years

SOYBEANS Acres Observed Water Demand (ac-ft)County 1998 Normal Dry Baker 897.53 566.94 676.14

Calhoun 578.60 365.48 435.88

Crisp 387.02 244.47 291.56

Decatur 1,747.24 1,103.67 1,316.26

Dooly 752.19 475.14 566.65

Doughert 400.00 252.67 301.33

Early 874.96 552.68 659.14

Lee 836.75 528.55 630.35

Macon 510.15 322.25 384.31

Miller 987.81 623.97 744.15

Mitchell 1,529.89 966.38 1,152.51

Randolph 435.07 274.82 327.75

Seminole 1,086.22 686.13 818.28

Sumter 824.08 520.54 620.81

Terrell 530.28 334.96 399.48

Worth 780.17 492.80 587.73

Other 815.60 524.93 615.70

Total 13,973.58 8,836.39 10,528.04

180

Table A.4b. 1998 Soybean Irrigated Acres and Water Demand Predicted for Normal and

Dry Years

SOYBEANS Acres Predicted Water Demand (ac-ft)County 1998 Normal Dry Baker 666.10 420.75 501.79

Calhoun 230.77 145.77 173.85

Crisp 570.32 360.25 429.64

Decatur 2,090.31 1,320.38 1,574.70

Dooly 401.74 253.76 302.64

Dougherty 528.17 333.63 397.89

Early 582.88 368.19 439.10

Lee 830.33 524.49 625.51

Macon 610.26 385.48 459.73

Miller 858.25 542.13 646.55

Mitchell 1,417.06 895.11 1,067.52

Randolph 115.85 73.18 87.27

Seminole 1,167.38 737.39 879.43

Sumter 700.65 442.58 527.82

Terrell 31.43 19.85 23.68

Worth 1,542.84 974.56 1,162.27

Other 1,598.96 1,029.12 1,207.06

Total 13,943.28 8,826.61 10,506.45

181

Table A.5. 1998 Simulation for Corn without Peanut Quotas: Irrigated Acres and Water

Demand Predicted for Normal and Dry Years


County 1998 Normal Dry

Baker 10,924.31 10,141.40 11,570.66

Calhoun 6,597.35 6,124.54 6,987.70

Crisp 3,020.69 2,804.21 3,199.41

Decatur 17,371.97 16,126.98 18,399.82

Dooly 3,174.78 2,947.25 3,362.62

Dougherty 3,801.45 3,529.01 4,026.37

Early 10,400.02 9,654.69 11,015.36

Lee 9,391.03 8,718.01 9,946.67

Macon 4,657.42 4,323.64 4,932.98

Miller 13,063.76 12,127.52 13,836.70

Mitchell 16,330.66 15,160.30 17,296.89

Randolph 5,687.78 5,280.15 6,024.31

Seminole 13,279.47 12,327.78 14,065.18

Sumter 9,408.35 8,734.08 9,965.01

Terrell 5,220.90 4,846.73 5,529.80

Worth 7,830.88 7,269.67 8,294.21

Other 11,346.56 11,108.06 12,510.61

Total 151,507.40 141,224.03 160,964.30

182

Table A.6. 1998 Simulation for Cotton without Peanut Quotas: Irrigated Acres and Water


COTTON Acres Predicted Water Demand (ac-ft) County 1998 Normal Dry Baker 19,768.70 19,340.37 22,536.31

Calhoun 13,412.68 13,122.07 15,290.45

Crisp 10,106.29 9,887.32 11,521.17

Decatur 37,350.07 36,540.82 42,579.08

Dooly 17,978.95 17,589.41 20,496.01

Dougherty 9,636.67 9,427.88 10,985.80

Early 19,884.68 19,453.85 22,668.54

Lee 18,274.95 17,878.99 20,833.44

Macon 11,131.37 10,890.19 12,689.76

Miller 23,793.03 23,277.51 27,124.05

Mitchell 32,068.81 31,373.99 36,558.45

Randolph 9,820.07 9,607.30 11,194.88

Seminole 23,235.56 22,732.12 26,488.54

Sumter 19,077.54 18,664.19 21,748.39

Terrell 12,279.43 12,013.37 13,998.55

Worth 13,714.63 13,417.48 15,634.67

Other 15,864.82 15,863.51 18,216.03

Total 307,398.23 301,080.37 350,564.12

183

Table A.7. 1998 Simulation for Peanuts without Peanut Quotas: Irrigated Acres and Water


PEANUTS Acres Predicted Water Demand (ac-ft) County 1998 Normal Dry Baker 7,754.41 4,252.00 5,150.22

Calhoun 5,070.08 2,780.09 3,367.38

Crisp 2,919.59 1,600.91 1,939.09

Decatur 15,559.43 8,531.75 10,334.06

Dooly 6,762.85 3,708.30 4,491.66

Dougherty 3,523.52 1,932.06 2,340.20

Early 7,519.47 4,123.17 4,994.18

Lee 7,286.23 3,995.28 4,839.27

Macon 4,365.48 2,393.74 2,899.40

Miller 7,556.40 4,143.43 5,018.71

Mitchell 14,316.08 7,849.99 9,508.27

Randolph 3,663.26 2,008.69 2,433.01

Seminole 9,106.92 4,993.63 6,048.51

Sumter 7,112.58 3,900.07 4,723.94

Terrell 4,858.41 2,664.03 3,226.79

Worth 7,725.49 4,236.14 5,131.01

Other 7,957.40 4,729.22 5,627.87

Total 123,057.59 67,842.49 82,073.58

184

Table A.8. 1998 Simulation for Soybeans without Peanut Quotas: Irrigated Acres and

Water Demand Predicted for Normal and Dry Years

SOYBEANS Acres Predicted Water Demand (ac-ft) County 1998 Normal Dry Baker 5,685.61 3,591.41 4,283.16

Calhoun 3,209.13 2,027.10 2,417.55

Crisp 2,488.56 1,571.94 1,874.72

Decatur 10,923.63 6,900.09 8,229.14

Dooly 3,198.32 2,020.27 2,409.40

Dougherty 2,403.79 1,518.39 1,810.85

Early 5,300.91 3,348.41 3,993.35

Lee 5,178.09 3,270.83 3,900.83

Macon 2,499.47 1,578.83 1,882.93

Miller 7,697.52 4,862.26 5,798.80

Mitchell 8,862.96 5,598.44 6,676.76

Randolph 2,716.74 1,716.08 2,046.61

Seminole 7,238.41 4,572.26 5,452.93

Sumter 5,185.28 3,275.37 3,906.25

Terrell 2,140.13 1,351.85 1,612.23

Worth 4,271.78 2,698.34 3,218.07

Other 6,035.27 3,884.38 4,556.05

Total 85,035.60 53,786.26 64,069.63

185

Table A.9. 1999 Corn Irrigated Acres and Water Demand Predicted for Normal and Dry

Years



Calhoun 5,492.45 5,098.82 5,817.42

Crisp 2,823.34 2,621.00 2,990.38

Decatur 11,832.92 10,984.89 12,533.03

Dooly 1,341.45 1,245.31 1,420.82

Dougherty 3,668.16 3,405.27 3,885.19

Early 8,061.51 7,483.76 8,538.48

Lee 6,869.33 6,377.03 7,275.76

Macon 4,760.75 4,419.57 5,042.43

Miller 8,451.64 7,845.94 8,951.69

Mitchell 11,715.38 10,875.77 12,408.54

Randolph 4,760.79 4,419.60 5,042.47

Seminole 9,653.75 8,961.90 10,224.93

Sumter 6,697.10 6,217.14 7,093.35

Terrell 4,722.32 4,383.89 5,001.73

Worth 6,898.92 6,404.49 7,307.10

Other 8,927.48 8,739.82 9,843.36

Total 114,603.36 106,842.26 121,771.72

186

Table A.10. 1999 Cotton Irrigated Acres and Water Demand Predicted for Normal and

Dry Years

COTTON Acres Predicted Water Demand (ac-ft)


Calhoun 8,777.43 8,587.25 10,006.27

Crisp 5,835.68 5,709.24 6,652.67

Decatur 30,135.10 29,482.17 34,354.01

Dooly 14,413.62 14,101.33 16,431.53

Dougherty 5,573.10 5,452.35 6,353.34

Early 14,242.46 13,933.87 16,236.40

Lee 14,063.04 13,758.34 16,031.87

Macon 7,018.99 6,866.91 8,001.65

Miller 18,373.69 17,975.59 20,946.01

Mitchell 25,956.06 25,393.68 29,589.91

Randolph 5,701.34 5,577.81 6,499.53

Seminole 17,878.06 17,490.71 20,380.99

Sumter 14,505.37 14,191.08 16,536.12

Terrell 8,026.23 7,852.33 9,149.91

Worth 9,638.71 9,429.87 10,988.12

Other 11,205.33 11,204.41 12,865.99

Total 226,300.85 221,639.52 258,074.88

187

Table A.11. 1999 Peanut Irrigated Acres and Water Demand Predicted for Normal and

Dry Years

PEANUTS Acres Predicted Water Demand (ac-ft)


Calhoun 6,742.03 3,696.88 4,477.83

Crisp 4,249.94 2,330.38 2,822.67

Decatur 21,340.16 11,701.52 14,173.42

Dooly 8,110.20 4,447.09 5,386.52

Dougherty 4,541.62 2,490.32 3,016.39

Early 10,462.94 5,737.18 6,949.13

Lee 10,091.18 5,533.33 6,702.23

Macon 5,716.59 3,134.59 3,796.77

Miller 11,929.37 6,541.27 7,923.09

Mitchell 19,280.83 10,572.32 12,805.69

Randolph 5,072.80 2,781.59 3,369.19

Seminole 13,091.41 7,178.45 8,694.88

Sumter 9,944.00 5,452.63 6,604.47

Terrell 6,048.33 3,316.50 4,017.10

Worth 9,480.07 5,198.24 6,296.35

Other 10,769.95 6,400.77 7,617.05

Total 167,715.10 92,459.02 111,854.79

188

Table A.12. 1999 Soybean Irrigated Acres and Water Demand Predicted for Normal and

Dry Years

SOYBEANS Acres Predicted Water Demand (ac-ft)


Calhoun 1,770.11 1,118.12 1,333.49

Crisp 1,803.21 1,139.03 1,358.42

Decatur 3,743.51 2,364.65 2,820.11

Dooly 900.29 568.68 678.22

Dougherty 1,923.39 1,214.94 1,448.95

Early 2,252.36 1,422.74 1,696.78

Lee 1,987.54 1,255.46 1,497.28

Macon 1,875.34 1,184.59 1,412.75

Miller 2,346.82 1,482.41 1,767.94

Mitchell 2,882.49 1,820.77 2,171.47

Randolph 1,667.06 1,053.02 1,255.85

Seminole 2,486.37 1,570.56 1,873.07

Sumter 2,193.55 1,385.59 1,652.48

Terrell 1,718.81 1,085.72 1,294.84

Worth 2,920.21 1,844.60 2,199.89

Other 2,945.63 1,895.85 2,223.67

Total 37,357.21 23,632.50 28,147.06

189

Table A.13. 2000 Corn Irrigated Acres and Water Demand Predicted for Normal and Dry

Years



Calhoun 6,894.72 6,400.60 7,302.66

Crisp 2,708.53 2,514.42 2,868.78

Decatur 9,757.02 9,057.77 10,334.31

Dooly 1,493.33 1,386.31 1,581.68

Dougherty 3,898.26 3,618.88 4,128.91

Early 10,321.73 9,582.01 10,932.43

Lee 6,768.06 6,283.02 7,168.51

Macon 4,474.81 4,154.12 4,739.57

Miller 11,671.58 10,835.12 12,362.15

Mitchell 12,208.46 11,333.52 12,930.79

Randolph 5,062.29 4,699.49 5,361.80

Seminole 9,279.96 8,614.90 9,829.03

Sumter 6,329.07 5,875.49 6,703.54

Terrell 4,697.32 4,360.68 4,975.25

Worth 7,692.88 7,141.55 8,148.04

Other 7,826.13 7,661.62 8,629.02

Total 119,043.83 110,908.72 126,427.10

190

Table A.14. 2000 Cotton Irrigated Acres and Water Demand Predicted for Normal and

Dry Years

COTTON Acres Predicted Water Demand (ac-ft)


Calhoun 10,032.35 9,814.98 11,436.88

Crisp 6,787.61 6,640.54 7,737.87

Decatur 29,214.63 28,581.64 33,304.67

Dooly 12,120.62 11,858.01 13,817.51

Doughert 5,876.58 5,749.25 6,699.30

Early 15,581.91 15,244.30 17,763.37

Lee 14,750.76 14,431.16 16,815.86

Macon 8,119.73 7,943.81 9,256.50

Miller 21,070.57 20,614.04 24,020.45

Mitchell 26,792.69 26,212.18 30,543.67

Randolph 6,099.69 5,967.53 6,953.65

Seminole 18,663.42 18,259.05 21,276.30

Sumter 14,940.77 14,617.05 17,032.47

Terrell 8,555.65 8,370.28 9,753.44

Worth 10,713.99 10,481.85 12,213.95

Other 12,019.85 12,018.85 13,801.22

Total 237,140.44 232,261.84 270,438.70

191


Dry Years

PEANUTS Acres Predicted Water Demand (ac-ft)


Calhoun 8,976.97 4,922.37 5,962.20

Crisp 4,520.22 2,478.59 3,002.18

Decatur 18,113.97 9,932.49 12,030.69

Dooly 6,926.98 3,798.29 4,600.67

Dougherty 4,734.53 2,596.10 3,144.52

Early 13,840.34 7,589.12 9,192.29

Lee 10,238.30 5,614.00 6,799.94

Macon 5,878.23 3,223.23 3,904.13

Miller 17,333.66 9,504.62 11,512.44

Mitchell 20,278.13 11,119.17 13,468.05

Randolph 5,505.69 3,018.95 3,656.69

Seminole 12,902.46 7,074.85 8,569.38

Sumter 9,723.17 5,331.54 6,457.81

Terrell 6,241.95 3,422.67 4,145.70

Worth 10,856.94 5,953.22 7,210.82

Other 9,848.08 5,852.88 6,965.06

Total 177,183.81 97,608.64 118,103.87

192


Dry Years

SOYBEANS Acres Predicted Water Demand (ac-ft) County 2000 Normal Dry Baker 1,297.90 819.84 977.75

Calhoun 1,390.07 878.06 1,047.18

Crisp 1,462.86 924.04 1,102.02

Decatur 2,643.15 1,669.59 1,991.18

Dooly 1,068.91 675.19 805.25

Dougherty 880.57 556.23 663.36

Early 2,285.65 1,443.77 1,721.85

Lee 1,183.35 747.48 891.46

Macon 1,536.60 970.62 1,157.57

Miller 2,645.50 1,671.07 1,992.94

Mitchell 2,640.99 1,668.23 1,989.55

Randolph 1,015.65 641.56 765.13

Seminole 1,537.95 971.47 1,158.59

Sumter 1,876.35 1,185.23 1,413.52

Terrell 1,269.97 802.20 956.71

Worth 2,359.11 1,490.17 1,777.20

Other 2,195.94 1,413.34 1,657.73

Total 29,290.51 18,528.08 22,068.97

193

APPENDIX B.

FORECASTING COVARIANCES

Literature on Forecasting Covariances

Literature on forecasting covariances is real scant, particularly in the field of agricultural

economics. The field of finance has some literature geared toward forecasting variances and

covariances. Chan et al. (1999a) have evaluated the performance of models for the covariance

structure of stock returns, focusing on their use for optimal portfolio selection. In an effort to

minimize tracking error volatility, they have applied portfolio optimization for risk control and

selection of minimum-variance portfolio. They have done this by forecasting covariances in the

risk models. They have compared the models’ forecasts of future covariances and the optimized

portfolios’ out-of-sample performance. They have found that a few factors capture the general

covariance structure but adding more factors does not improve forecast power (Chan et al.,

1999b). Portfolio optimization helps for risk control, but the different covariance models yield

similar results. So they conclude that a three-factor model is adequate for selecting the

minimum-variance portfolio. Under a tracking error volatility criterion, which is widely used in

practice, larger differences emerge across the models, with particularly favorable results for a

heuristic approach based on matching the benchmark’s attributes. In general, more factors are

necessary when the objective is to minimize tracking error volatility (Chan et al., 1999a; 1999b).

In testing the rationality of the Livingston price series, Turnovsky (1970) and Gibson

(1972) found evidence of a structural break in the price survey series around 1960, the existence

194

of a break in the series suggesting that results obtained using the full sample may not be robust

across sub-samples and therefore could lead to incorrect statistical inference.

Rich (1990) looks at the rationality of the Livingston price expectations data. Using

Hansen’s (1982) generalized method of moments (GMM) estimator, Rich (1990) tests the data

for the property of unbiasedness over the sample period 1947-84. He also examines the survey

series for evidence of a structural break in 1960. The results strongly reject the absence of bias in

three out of the four survey series over the full sample period. To account for a possible

structural break in the survey series, the full sample period is divided into two sub-periods at the

June 1960 survey. There are two findings from Rich’s (1990) sub-period analysis. First, while

there is strong evidence of a structural break in the 14-month price forecasts, the results of the

unbiasedness tests are generally robust across sub-periods. Second, the forecastability of

inflation by the Livingston respondents increased dramatically after 1960. This latter finding is

consistent with the results of Barsky (1987) who attributes the increased forecastability of post-

1960 inflation to an increase in the persistence of inflation.

One advantage of the GMM estimation procedure is that it is computationally easier than

many other methods, as the one of Schroeter and Smith (1986). More importantly, it does not

require any specification of the form that the conditional heteroskedasticity might take.

Therefore, the GMM estimator is robust to this type of specification error and will yield

consistent estimates of both parameters and their covariances. McLeod (1979); and Masanao

(1994a, 1994b) also have some related research in this regard in the field of finance.

Tareen (2001) develops a method to forecast Georgia agricultural water demand for corn,

cotton, peanuts and soybeans on a county basis. Tareen’s (2001) method employs the irrigated

acreage response to changes in the economic climate of Georgia on a county by commodity

195

basis. He had variance and covariance terms on the right hand side of the econometric model he

estimated and used for forecasting. With variances and covariances of mean expected net returns

per acre for each crop and between crops, respectively, in each county at each time period, there

was a problem encountered with forecasting. Specifically, forecasting irrigated acreage (the

dependent variable in his model) makes the forecasts of the variances and covariances look

linear, with forecast errors washed out. Our knowledge of reality tells us that this could not be

the case. Forecasting in the way mentioned above, we lose the year-to-year bounces in the

variances and covariances. The two theoretical concepts described below, viz., Generalized

Autoregressive Conditional Heteroskedasticity (GARCH) in Appendix B and a Vector

AutoRegressive framework in Appendix C, may provide a solution to the problem of forecasting

moments of second order (i.e., variances and covariances) in the pursuit of more accurate

forecasts of acreage allocation and water demand. It is believed that will be a new ground

covered in the field of agricultural economics.

Generalized Autoregressive Conditional Heteroskedasticity

This theory may primarily be used to forecast the variances and covariances of expected

net returns before estimating the irrigated acreage and hence forecast irrigation water demand.

Tim Bollerslev (1986) propounded this theory through a paper published in Journal of

Econometrics. As is true with most areas of econometrics, the line of research on Generalized

Autoregressive Conditional Heteroskedasticity (GARCH) models has progressed rapidly in

recent years and is expected to continue to do so. There have been many recent extensions to the

model, for example, a multivariate GARCH approach by Baillie and Bollerslev (1990), and a

multivariate simultaneous GARCH theory by Engle and Kroner (1993), but in order to introduce

196

the topic as a bridge to the literature, and also for the purpose of this research, we may take a

look at it as done by William H. Greene (1993) in his book “Econometric Analysis, 2nd edition.”

As is apparent from the name, GARCH is a generalized formulation of AutoRegressive

Conditional Heteroskedasticity (ARCH). So a short discussion of ARCH seems in order. It was

suggested by Robert Engle as an alternative to the usual time-series process. In analyzing

macroeconomic data, Engle (1982, 1983) and Cragg (1982) found evidence that for some

phenomena the disturbance variances in time-series models are less stable than usually

assumed.26 Engle’s results were suggestive of the fact that in analyzing models of inflation, large

and small forecast errors appear to occur in clusters, indicating a form of heteroskedasticity in

which the variance of the forecast error depends on the size of preceding disturbance.

As mentioned by Greene (1993), the ARCH model has proven to be useful in studying a

variety of macroeconomic phenomena, including the volatility of inflation (Coulson and Robins,

1985), the term structure of interest rates (Engle et al., 1985), and foreign exchange markets

(Domowitz and Hakkio, 1985), to name a few.27 One common element in these studies has been

the observation of clusters of small and large regression residuals, which cannot be adequately

described by the conventional regression models.

Under usual, standard notations of a regression model, the most simple version of the

ARCH model, ARCH(1), or an ARCH model of the first order, may be written down as the

following:

yt = β′xt + εt, (A.1)

εt|εt-1 ~ N[0, σt2], (A.1a)

23 Heteroskedasticity is usually associated with cross-sectional data, while time series are typically studied in the context of homoskedastic processes (Greene, 1993). 24 Engle and Rothschild (1992) have a survey of this literature.

197

σt2 = α0 + α1εt-1

2. (A.1b)

If |α1| < 1, then unconditionally,

εt ~ N[0, α0/(1- α1)]. (A.2)

Expression (16a) states that ‘conditional’ on εt-1, εt is heteroskedastic. The ‘unconditional’

variance of εt is given by

Var[εt] = E[Var[εt|εt-1]]

= E[α0 + α1εt-12]

= α0 + α1E[εt-12]

= α0 + α1Var[εt-1].

If the process generating the variances is variance stationary, the unconditional variance remains

the same over time. In that case, we have,

Var[εt] = Var[εt-1]

= α0 + α1Var[εt-1]

= α0/(1- α1).

That is how we get the variance term under normality in (A.2) above. With the above restriction

on α1, the model still obeys the classical assumption, and ordinary least squares (OLS) is the

most efficient ‘linear’ estimator of β.28 [See Greene (1993), Section 15.9, for a more detailed

exposition of the above formulaton.] Many of the empirical studies, as of Engle and Kraft

(1983), have used the more general form of ARCH, known as ARCH(q) model, which is a slight

modification of (A.1b) with a moving average (MA) process of order q:

σt2 = α0 + α1εt-1

2 + α2εt-22 + α3εt-3

2 + ... + αqεt-q2. (A.3)

25 However, the log-likelihood function for this model, or the generalized least squares (GLS) estimator, as given by Engle (1982), is a more efficient ‘non-linear’ estimator.

198

The GARCH is an even more generalization of (A.3) above. The underlying regression is

the usual one in (A.1). But, with GARCH, an information set at time t, denoted by ψt, is

considered. Conditioned on that information set, the distribution of the disturbance is assumed to

be the following:

εt|ψt ~ N[0, σt2],

where the conditional variance is given by

σt2 = α0 + α1εt-1

2 + α2εt-22 + ... + αqεt-q

2 + δ1σt-12 + δ2σt-2

2 + ... + δpσt-p2. (A.4)

If we define

zt = [1, εt-12, εt-2

2, ... , εt-q2, σt-1

2, σt-22, ... , σt-p

2]’

and

γ = [α0, α1, α2, ... , αq, δ1, δ2, ... , δp]′ = [α′, δ′]’,

we may shrink (A.4) and write in matrix notation as

σt2 = γ′zt. (A.5)

Relation (A.5) forms the core of the GARCH model.

We may note that the conditional variance is defined by an autoregressive (AR)-moving

average (MA), or ARMA(p,q), process in the εt2 ‘innovations,’ as they are called for such

processes, with p autoregressive (lagged dependent variable) terms and q lagged moving average

terms. The AR part is of order p, and the MA part is of order q. Depending on the parameter

values and the values of p and q, the conditional variance evolves over time in what may be a

very complicated manner. The difference of GARCH with ARMA, though, is that the mean of

the random variable of interest, yt, is described completely by a heteroskedastic, but otherwise

ordinary, regression model in GARCH (Greene, 1993).

199

The virtue of GARCH is that, with a small number of terms, it appears to perform equally

well or even better than an ARCH with many terms (Bollerslev, 1986; Greene, 1993). Moreover,

the GARCH specification allows for shocks to variance to be persistent. Thus, assuming the

GARCH model is valid, at least in a time-series context, the one-step variance is a good proxy

for longer horizons (Kroner and Lastrapes, 1993). Last but not least, as it incorporates elements

of both time series (autoregression) and cross section (heteroskedasticity), some form of a

GARCH model seems to be the most ideal econometric method to go about doing the

“forecasting of variability of net returns” part of the analysis, since the study proposed is one

using time-series and cross-section data simultaneously.

Forecasting Net Return Covariances and Variances

In the finance literature, covariances of stock returns are predicted by the following three

alternative methods (refer, for example, to Chan et al., 1999a):

1.) Full Covariance Matrix Forecasting Method,

2.) Covariance Forecasting from Factor Models, and

3.) Forecasting from a Constant Covariance Model.

In the following discussion, consider stocks to be crops in order to translate the research in

securities to agricultural crops.

First, with the full covariance matrix forecasting method, the sample covariances are

based on the estimation period, so the sample covariance of net returns from crops i and j will be

given by

m _ _

Cov Bij = (1/(m-1)) E (rit-k – ri)(rjt-k – rj), (A.6) k=1

200

where rit = net return for crop i in period t, _ ri = sample mean net return for crop i, and

m = the number of periods of prior data (i.e., the estimation period).

Tareen (2001) used m as 3 in his analysis and forecasted covariances of net returns in that

manner. Tareen’s (2001) calculation, however, was slightly different in that he did not use 1/(m-

1) as the weight but “λk” (with k = 1, 2, 3) and did an approximately equal weighting of each

time period (viz., 0.34, 0.33 and 0.33 for the first, second and third years, respectively).

Statistically speaking, m may be used for m-1 with a small number of observations, say m = 3.

Chan et al. (1999a) had 60 observations, and so it would not make a whole lot of difference

between m and m-1. Moreover, this factor is a scalar and only does a shift in scale, without

causing any real difference.

This method of forecasting covariances has a potential problem of averaging out the

errors in the forecasts and project the covariances in the future as is expected in physical models.

Thus a linear forecast in the covariances may be well expected, as did in Tareen’s (2001) study.

This belies reality and gives us an unrealistic picture.

In addition, sample covariances are very sensitive to outlier observations (Chan et al.,

1999a; Huber, 1977). This means just one or two outliers can cause a significant difference in the

forecast due to large forecast errors caused by the outliers. Thus, forecasts from the full

covariance matrix model may reflect farming enterprise-specific events that happen to affect

several crops at the same time, but which are not expected to persist in the future.

An alternative approach is to introduce only the pervasive factors that drive returns in

common. One such model used in the finance literature is called the “factor model of security

returns” (in the proposed study this translates to the factor model of net crop returns):

201

K

rit = βi0 + E βij fjt + εit, (A.7) j =1

where fjt = the jth common factor at time t,

βij = loadings or sensitivities of stock (crop, in the present study) i on each of the K

factors, and

εit = a residual term.

Assuming the K factors are uncorrelated with the residual net returns and that the residual net

returns are mutually uncorrelated, the covariance matrix, denoted by V, of the net returns on a set

of N stocks (in our case, N = 4 crops) is given by

V = BΩB΄ + D, (A.8)

where B = the matrix of factor loadings of the stocks (crops, in this research),

Ω = the covariance matrix of the factors, and

D = a diagonal matrix containing the residual net return variances.

It appears that the matrix V in (A.8) will contain elements of the forecasted covariances.

The third procedure of forecasting covariances assumes that all pairwise covariances

between stocks (or crops) are identical. Using that option, an estimated constant covariance is the

simple mean across all pairwise covariances from the estimation period. This model can be

thought of as a version of what is called the James-Stein estimator, which shrinks each pairwise

covariance to the global mean covariance while giving no weight otherwise to the specific pair of

stocks (or crops) under consideration. One motivation for this approach may be that the noise in

returns and the resulting estimation error suggest that it may be unwise to make distinctions

between stocks (or crops) on the basis of their sample covariances. Instead, it may be more

fruitful to assume all stocks (or crops) are identical in terms of their covariation (Chan et al.,

202

1999a). In the literature of finance, Frost and Savarino (1986) and Jobson and Korkie (1981)

provide evidence that using the common sample mean return as the expected return for each

stock improves the out-of-sample performance of optimized portfolios relative to assuming that

historical average returns will persist.

Chan et al. (1999a) also applies several methods to forecast return variances. Their results

suggest that variances are relatively more stable, and hence easier to predict, than covariances. In

their study, past and future return covariances (measured over the subsequent 36 months) have a

correlation of 33.94%, while the same for variances is 52.25%. For both variances and

covariances, higher dimensional models do not necessarily raise forecasting power. After

accounting for the dominant influence of the first factor, further refinements do not offer a great

deal of improvement.

The results of a factor-model study by Connor and Korajczyk (1993) also suggest that

after the first factor the marginal explanatory power of additional factors is relatively low. This

can be interpreted in the following way: There is a “major factor” which is more important than

the other influences on returns (Chan et al., 1999a). In the case of stocks, this dominant influence

is the market, and it tends to overpower the remaining factors, so their incremental

informativeness becomes increasingly difficult to detect. This accounts for why the different

factor models generate similar forecast results. A similar interpretation is offered by Green and

Hollifield (1992), who provide conditions under which well-diversified portfolios are mean-

variance efficient.

Chan et al. (1999a) conclude the following in terms of forecasting return covariances and

variances: “There is some stable underlying structure in return covariances. Factor models help

to improve forecast power, but there is little to distinguish between the performance of a 3-factor

203

model and a 10-factor model. Modifications of the factor model structure, such as relaxing the

model’s linear structure or having more timely information on loadings and attributes, do not

salvage the models. The situation improves somewhat when it comes to forecasting variances.

Future variances are relatively more predictable from past variances, and so the models’ forecast

power is relatively stronger.”

For precise forecasts with the problem at hand, it is believed most useful to use the

second method described above (the factor method), assume a GARCH model structure (to get

more efficient estimates) and run vector autoregression on net returns with one, two, or three

lags. A more complex (and not necessarily better) alternative would be to model the price of

each crop by county separately and use the relevant factors fjt on the right-hand-side of (A.7) as

the factors that govern the process of each crop, with restrictive assumptions on both yields and

costs. The knowledge of what factors drive the future prices of each crop will be required to use

that alternative. Also, in that case, we will need to use the price forecast covariances and derive

from them the covariances of net returns using information on yield and cost forecasts, since net

returns equal prices times yields minus variable costs.

Other choices are to model prices, yields and variable costs separately in the left-hand-

side of (A.7), or price times yields with an assumption of constancy on variable costs. As we

know, yields are heavily dependent on the weather conditions and other exogenous factors, using

these other methods might be extremely difficult to handle. Thus, the most convenient way may

be to use the past known values of net returns, assume they are the most dominant factors

determining future net returns, and forecast net returns. The covariance matrix of net returns thus

obtained will contain the elements of the forecasted covariances that are of interest. A note on

vector autoregresssion (VAR) is presented in Appendix C.

204

APPENDIX C.

A NOTE ON VECTOR AUTOREGRESSION

Statistically speaking, Vector Autoregression (abbreviated as VAR) procedure is a linear

dynamic system with a k x 1 vector of outputs, Y, generated by a stochastic difference equation

(Litterman, 1985). The vector Y includes all endogenous, as well as exogenous variables in the

system. Each variable, in turn, is expressed as a linear function of its own lagged values and the

lagged values of each of the other variables, plus a random disturbance term. Mathematically

speaking, a k-dimensional VAR(p) process can be specified as:

Yt = Dt + ΣAjYt-j + et, (A.9) j

where

et = (e1, …, ek)/ are vectors of k components,

A1, …, Ap are k x k matrices of unknown parameters,

j = 1, …, p,

Dt is the deterministic component referred to as the intercept, and

L is a lag operator such that LpYt = Yt-p.

The estimation of a VAR model is done by applying OLS separately to each equation (Zapata

and Garcia, 1990; Van Tassel, 1990).

Let us make a simple illustration of the above. Consider a two-variable (Y, X) VAR(2) of

order 1 and 2. VAR(2) specifies a VAR model with an optimal lag structure of two; those two

lags being of order 1 and 2. The matrix form of the example model is:

205

Yt = Dt + A11Yt-1 + A12Yt-2 + A13Xt-1 + A14Xt-2 + et, (A.10)

and

Xt = Dt + A21Xt-1 + A22Xt-2 + A23Yt-1 + A23Yt-2 + et. (A.11)

VARs have been appearing in the microeconometrics literature for a while now.

According to Chamberlain (1983), a useful approach to the analysis of panel data is to treat the

observations of each period as a separate equation. Thus, for a two-period time-horizon, i.e., for

t=2,

yi1 = αi + β′xi1 + ei1 (A.12)

yi2 = αi + β′xi2 + ei2, (A.13)

where i indexes individuals and αi are unobserved individual effects. This produces a

multivariate regression, to which Chamberlain added restrictions related to the individual effects.

Notice the similarity of (A.12) and (A.13) to the model described by (A.1), which is ARCH or

GARCH depending on the structure of the conditional variance.

Vector autoregression offers applicable advantages over traditional structural regression

analysis. Two distinct advantages are specified by Litterman (1985). First, VAR does not require

judgmental adjustment; thus the forecast and the method can be evaluated objectively, without

reference to forecaster bias. Second, the VAR technique incorporates attributes from linear

specification and Box-Jenkins (1970)29 type time-series analysis. Specifically, VAR accounts for

both the linear relationship between the dependent and explanatory variables and the

autoregressive nature of many economic time series. Furthermore, VAR models are less difficult

29 For a detailed discussion of Box-Jenkins type of time-series analysis, see G. E. P. Box and G. M. Jenkins’ book “Time Series Analysis: Forecasting and Control.” For a simple application of the VAR technique, see William H. Van Tassel (1990)’s Master’s thesis entitled “A Comparison of GLS, BVAR and Composite Forecasts of Nevada Alfalfa Hay Prices.” For a detailed and more sophisticated VAR test, see Andrew Constantine Krikelas (1991)’s doctoral dissertation entitled “Industry Structure and Regional Growth: A Vector Autoregression Forecasting Model of the Wisconsin Regional Economy.”

206

to construct and maintain than multi-equation large-scale econometric models (Van Tassel,

1990).

But this technique is not without disadvantages. Most economic time series are highly

correlated with their own lags and the current and previous values of other time series.

Therefore, as more variables are added, multicollinearity can be a problem. With the increase in

the number of variables used in the model, the number of coefficients to be estimated increase by

a factor of m, where m is the length of the lag. For instance, consider a two-variable VAR model

with a lag length of 2. The addition of one variable to the model increases the number of

coefficients to be estimated by two. This problem may decrease the degrees of freedom rapidly.

This, in theory, is referred to as “overparameterization” (Banerjee, 1999).

207

multiproduct rational expectations forecasting of … · the land allocation model is based on...

Documents