partial equilibrium analysis of policy impacts (part i)

With the support of

TRAINING MATERIALS

Partial Equilibrium Analysis of Policy Impacts (part I)

Federico Perali


i

Foreword

The present volume is part of the series “Training Materials”, published by the National Agriculture Policy Center (NAPC) with the support of the FAO Project GCP/SYR/OO6/ITA. The series includes notes and handouts produced as part of the training activities carried out at the NAPC by the international experts recruited by the Project. Even though they cannot be considered as comprehensive textbooks, the NAPC decided to make these materials available for a wider public, considering them as a useful reference for the study and the practice of agricultural economics and policy analysis.

The FAO Project, which is generously funded by the Italian Government and executed in close coordination with the Syrian Ministry of Agriculture and Agrarian Reform (MAAR) has been supporting the establishment of a cadre of professional agricultural policy analysts for the NAPC and other institutions involved in the Syrian agricultural policy making process. This undertaking encompassed an intensive training activity articulated over two programs involving, in a five year period, a total of about 130 officials of the MAAR. Each training program comprised a set of intensive courses to provide theoretical background and familiarize with issues, concepts, methods and tools needed to carry out policy analyses. The set of courses was completed by on-the-job research experiences on issues of relevance for Syrian agricultural development, whose results have been published by the NAPC’s Working Papers series. The formal training programs were also accompanied by seminars, shorter intensive courses and participation in research activities, which are still on-going as part of NAPC’s staff capacity building process.

Training was part of a wider undertaking in institutions’ building for agricultural policy analysis. Indeed, the Project has been providing support to the institutional development of the NAPC, its technical capacity to analyze, formulate and monitor agricultural policies, and its capacity to maintain and develop a comprehensive set of statistical information for the economic analysis of policies (the Syrian Agriculture Database).

The program of study on “Partial Equilibrium Analysis” has been delivered in two modules. In module I, Prof Perali illustrated the analysis of supply and demand within a partial equilibrium setting, while in module II Prof Conforti focuses on the theory of market equilibrium, with reference to the analysis of agricultural policies, within the most common quantitative frameworks.

This volume presents part of the training material of the module I of the program of study on “Partial Equilibrium Analysis”. In it, Prof Perali provides the theoretical foundations of demand, supply and market behavior, both at the individual and aggregate levels. This is a necessary step to build the readers’ capacity to apply demand, supply and market analysis to real cases, within the economic, social and institutional context of Syria. The analytical tools applied are those used by analysts to interpret economic results,

The reader should note that exercises pertaining the issues presented in the volume are available at NAPC in electronic format. Furthermore, at NAPC, are also available the slides used in class during the lectures and the slides of the seminar Prof Perali delivered on Drug Consumption and Intra-household Resource Allocation: the case of Djibouti.

Damascus, December 2003


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Table of Contents

Chapter 1 - Introduction .............................................................................. 1 1.1. Motivation and Objectives of the Course.......................................................................... 1 1.2. An example of Applied Partial Equilibrium Analysis...................................................... 2

1.2.2. The Model .......................................................................................................................................... 3 1.2.3. Results ................................................................................................................................................ 4

1.3. A Methodological Note ..................................................................................................... 6 1.3.1. Data Collection.................................................................................................................................. 6 1.3.2. Familiarization with the Data........................................................................................................ 7

1.4. Description of the Aggregate Data Base (the Colombian Rice Economy) ...................... 8 Chapter 2 - Demand Analysis..................................................................... 19

2.1. Introductory Demand Analysis .......................................................................................19 2.1.1. Some Basic Notions ........................................................................................................................ 20 2.1.2. Introductory Applications............................................................................................................. 23

2.2. Advanced Demand Analysis ............................................................................................35 2.2.1. Duality Theory ................................................................................................................................ 36 2.2.2. Empirical Implementation: The Almost Ideal Demand System (AIDS)................................ 37 2.2.3. Cost of Living Indexes and Compensating Variations ............................................................. 39 2.2.4. A GAUSSX program for advanced demand analysis............................................................... 40

Chapter 3 - Supply Response .....................................................................45 3.1. Introductory Supply Analysis......................................................................................... 45

3.1.1. Approaches to the estimation of supply response ..................................................................... 45 3.2. An Introductory Exercise ............................................................................................... 49

3.2.1. The Colombian Rice Economy: Supply side ............................................................................... 49 3.2.2. Estimation of a Nerlovian Supply Response Model for groundnuts in Senegal .................. 53

Chapter 4 - The Market Model ................................................................... 61 4.1. Causality in Economic Analysis ......................................................................................61

4.1.1. Exogenous and Endogenous Variables in a Model ................................................................... 61 4.2. A Structural Market Model with Exogenous Variables ................................................. 62

4.2.1. Structural and Reduced Form Models ........................................................................................ 63 4.3. The Colombian Rice Economy: the market model ........................................................ 65 4.4. Welfare Analysis of Technical Change ........................................................................... 66

References ............................................................................................... 69


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Chapter 1 - Introduction

1.1. Motivation and Objectives of the Course

The specific objectives of the module in “Partial Equilibrium Analysis” aim at (a) providing the theoretical foundations of demand, supply and market behavior both at the individual and aggregate levels, (b) building the capacity to apply demand, supply and market analysis to real cases within the economic, social and institutional context of Syria, and (c) enabling the analyst to interpret the economic results, to verify the robustness of the applied methodology and to provide sound policy recommendations. To pursue these objectives the course provides basic theory notions required to specify, estimate and interpret demand, supply and market models illustrated by means of computer based applications. This learning by doing approach is a necessary step if the objective to bridge the gap between basic theory and applied analysis to real economic problems is to be attained.

The learning process is intended to be incremental. The material is proposed both at the basic and advanced level. The advanced material is not required for the exam. It is intended to be a complete reference for both the future applied work of the trainees and the future activities of the Center of Policy Analysis. Special emphasis is placed on a) concepts, b) methodology, and c) economic intuition and interpretation. The presentation of the teaching material follows rigorously this sequence. Active participation to the discussion is expected.

Let us start our journey through the analysis of partial market equilibrium with a definition.

Definition.

Partial Equilibrium Analysis:

It is the analysis of a market in equilibrium considered in isolation from other product or input markets.

In general, the existence of an equilibrium implies competitive (Walrasian) conditions. Our study will be confined to the situation of a perfectly functioning market satisfying both Fundamental Theorems of Welfare Economics. The working assumption of Pareto efficiency is far from the reality of imperfect markets. It is adopted because it is instructive. It is useful to sharpen the understanding of the market paradigm. Also, it is of practical interest as a benchmark reference model that can be used to gauge how far second best solutions are from their first best.

The market, being the sum of individual demand and supply functions, describes the aggregate behavior of both consumers and producers as summed up by the behavior of a representative consumer. Consumers and producers are not distinct by their characteristics. Not all consumers consume a little bit of all goods and producers do not produce in some positive quantities all the products. As a matter of fact, the effects of a consumer or producer subsidy on a good reach only those who consume or produce the good. This limitation of the aggregate analysis is a major shortcoming for the implementation of a policy interesting welfare and distributive analysis.

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Every market is both vertically and horizontally integrated with both the product and factor markets. Consider the corn market. It is vertically connected from below to the labor, capital, land and other inputs markets such as fertilizers and pesticides. It can be directly used for human consumption and be itself an input of the feed industry for livestock production or of the industry producing combustible from biomass. It is horizontally integrated with those markets that are close substitutes or complements in production or consumption such as soybean. The partial equilibrium analysis can be static or dynamic as we will see in the second part of the course.

The advantage of the approach lies on its empirical simplicity. When the vertical and horizontal links are weak, then the partial equilibrium effects are a reasonable approximation of the general effects. If the linkages are expected to be strong, then the markets are better analyzed jointly through a multi-market approach which is a partial equilibrium approach extended vertically or horizontally to include other markets. However, the analysis is partial also in the sense that only the price effect is considered. Income and cost changes that shift the demand and supply functions, exchange rate effects, savings-investment, public investments, government transfers are out of the classical graphical market analysis. To capture these indirect effects the partial analysis must be extended to the general equilibrium analysis taking under considerations all the markets in the economy.

To implement the partial equilibrium approach we need first to learn how the two sides of the markets behave and how to estimate them. Finally, we will combine demand and supply to understand the basic mechanics of market equilibrium and the fundament of welfare analysis applying the concepts of consumer and producer surplus to the measurement of the welfare effects of technological change. This is the organization of the course.

To appreciate the power of the partial equilibrium approach as an analytical tool, let us consider an example that we will implement together and will accompany us throughout the course.

1.2. An example of Applied Partial Equilibrium Analysis

This example is taken from a seminal article in the analysis of partial equilibrium written by Scobie and

Posada (1977) as the product of a research conducted at CIAT (International Center of Tropical Agriculture based in Cali - Colombia) on the impact of high-yielding rice varieties in Latin America with special emphasis to Colombia. This study is a precursor of the modern debate on the effects induced by genetically modified material and the value of indigenous genetic patrimony.

The generation of technical change through public and private agricultural research is an economic activity raising both efficiency, expressed in terms of rate of returns from the investment, and equity issues. The study is concerned with the measurement of the distribution of social benefits derived from public investments of the international community on agricultural research. The authors elect Colombian rice production as the industry of interest and examine the distributive impact on both producers and households considering both costs and benefits of the research program. The rice example can be adapted to other economic realities. Syrian trainees, for example, may find many similarities between the Colombian rice industry and the local wheat industry.

1.2.1. Background

In the late 1950s Colombian rice production was plagued by a virus disease causing large losses. Imports of rice rose and the real retail price of rice increased dramatically. This critical situation primed the formation and funding of a national rice research program with the objective of selecting varieties resistant to the virus capable of increasing productivity thus reducing the


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dependence on imports and curbing the upward pressure on prices. In 1967 the newly founded Centro Internacional de Agricultura Tropical (CIAT) joined in a collaborative effort with the Colombian program contributing the dwarf lines developed at the International Rice Research Institute (IRRI) in the Philippines. This effort led to the development of disease resistant dwarf rices. These modern varieties were widely and rapidly adopted mainly by the irrigated rice sector. Because in rainfed rice areas located in the uplands the modern varieties could not express their potential. Rationally, they were not adopted in non irrigated rice fields. As a consequence, while the irrigated sector increased both yields and production, the disadvantaged upland sector did not enjoy the advantages pf the technological evolution and declined in importance from 50 percent of the national output in 1966 to 10 percent in 1974. Rice is the most important foodstuff in Colombia. Rice is the major source of calories and the second major source of protein (beef is the first) in the Colombian diet.

1.2.2. The Model

The model can be represented as a set of demand and supply equations with an exponential form (linear in the logarithms):

Inverse Demand: P = A QD 1/η

Supply: QS = B P β

Equilibrium QS = QD

where P is the price of the good, Q is the quantity demanded or supplied, A and B are exogenous shifters. In the demand equations, A includes exogenous variables such as income and demographic effects. The B shifters, on the other hand, includes technical change. Note that in general the demand function is specified as:

Q = (A* P) η

where A*=1/A The demand function is here inverted to be represented in a two dimensional space while keeping all other exogenous factors such as other prices, income, tastes, and income distribution data constant. A partial equilibrium model always assumes the coeteris paribus (everything else equal) condition.

Figure 1.1 The market model of the rice economy with technical change

S’S D

Q

P

P0

P1

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The model showing the impact of high yield varieties on equilibrium prices and quantities can be represented as in Figure 1.1 The curves are exponential. The model can be represented in linear form after taking a logarithmic transformation.

The graph also shows the welfare impact of technical change. It visualizes both the change of consumer surplus and the and producer surplus. These concepts along with the definition and neutral or factor biased nature of technical change have been developed already in other courses and will be taken up again in the part of the course devoted to the analysis and welfare interpretation of the market. The graph is aggregate because it refers to a representative consumer and producer. Interestingly, we may distinguish the supply of upland rice producers from the one of irrigated rice producers in order to separate the different impacts. Similarly, we can proceed for the consumers trying to do as best as we can give the aggregate information we have. Our goal is to build this graph using the same data set of the authors by estimating both the demand and the supply curve and the shift in technical change.

1.2.3. Results

Table 1 shows the changes in consumer and producer surpluses resulting from the introduction of virus-resistant and dwarf varieties estimated for the period 1964-1974. Consumers benefit from the introduction of the modern varieties. If the modern varieties were not developed, the quantity of rice produced would have been markedly lower and domestic prices would have been higher. Producers suffered a substantial loss. However, it is likely that “early birds,” that is farmers of the irrigated sector, which first adopted the modern varieties, enjoyed some short run benefits. It must be emphasized that the partial equilibrium framework does not allow us to judge whether higher imports would have curbed the upward pressure on prices due to a lower availability of domestic rice. Higher imports would have increased the demand for foreign exchange and would have pushed up the exchange rate. These side effects can be properly accounted for only within a general equilibrium framework.

Table 1. Gross Benefits of modern rice varieties in Colombia ($ Col. Million)

Gross benefits

1964-69 1970-74

Consumers 1404 17542 Producers Irrigated -368 -6468 Upland -517 -3878 Total 519 7196

Gross benefits include also the research costs that are borne by the Colombian taxpayer (both consumers and producers) funding the national rice research institutions and the international community funding the international research centers. Table 2 reports the distribution of gross social benefits, research costs and net benefits for producers and consumers for the period 1957-1974 without accounting for the international research costs. Producers borne about two times the cost of the research financed by consumers taxes.

Table 2. Size and Distribution of Benefits and Costs of modern rice varieties in Colombia 1957-1974 ($ Col. Million)

Producers Item Upland Irrigated Total

Consumer

s

Colombia

Intl Cooper

Gross Benefits -3542 -5293 -8835 14939 6104 Costs of research

9 32 40 22 63 19

Net Benefits -3551 -5235 -8875 14917 6042


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It is of paramount importance that the estimates of producer and consumer surpluses critically depend on the quality of the estimated demand and supply slopes. This point is clearly shown in table 3. The net benefits are more than halved when the demand elasticity moves from -0.3 to -0.449. The internal rate of return from the investment on rice research, shown in italic in Table 3, remains high independently from the choice of the demand and supply elasticity. Such high returns are not infrequent in agriculture.

Table 3 Net Benefits in 1974 and Internal Rates of return for differing elasticities

Elasticity of demand η Elasticity of supply ε -0.3 -0.449 -0.754

9052 3981 2174 0.235 89% 94% 89%

8627 3556 1749 1.5 96% 87% 79%

Note: Internal rate of returns are in italic; net benefits are in bold; results in table 1 and 2 use ε =-0.449 and ε =0.235 as in the shadow area.

Net benefits and costs have been distributed across income deciles of consumers and rainfed and irrigated producers as illustrated in table 4. A decile corresponds to 1/10 of the income range. Each income decile is equally spaced. For example, the first decile counts 19 percent of the household accounting for only 2 percent of total household income. The benefits accruing to each income group were assumed to be proportional to the quantity of rice consumed. Of course, the benefits received depend on whether all consumers consume at least some rice and on the frequency of consumption. This information is in general not available from aggregate Time series data. A higher disaggregation can be achieved only by combining the market data with household level consumption information.

Table 4 Distribution of Net Benefits across income deciles Cumulative % of

Income deciles

Annual avg net benefits

Net benefits as

% of income Net Benefits Households Total Hh

Income I 385 12.8 18 19 2 II 642 7.1 50 39 8 III 530 3.5 67 52 15 IV 333 1.6 77 64 23 V 348 1.3 83 71 29 VI 353 1.2 88 76 35 VII 342 0.8 93 82 43 VIII 200 0.4 95 86 51 IX 128 0.2 96 89 57 X 138 0.2 100 100 100

Rice in Colombia is consumed in higher proportion by the poor. Considering that the poor make a smaller tax contribution, the net benefits were reaching mostly the poor. Poor Colombian households may consume also 70-80 percent of their total budget on food and about 50 percent of food expenses on rice. This reasoning provides an explanation for the fact that net benefits accruing to very poor consumers range around 10 percent of the household income.

Rice is a staple food If we assume as an acceptable poverty line PL the level of income corresponding to PL= 0.5 mean(income), then the poverty line is close to the upper bound of the third decile. If so, about 50 percent of the Colombian population would be in poverty. Note also that the income distribution in Colombia is highly concentrated. The affluent Colombians living in the upper two deciles own 50 percent of household income.

The lowest 50 percent of Colombian households belonging to the three lowest deciles of the income distribution account for 15 percent of household income but receive almost 70 percent of the net benefits generated by the research program. This is in line with our expectations because

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a decline in the price of a food staple due to technological change targets those most in need and tends to reduce the income polarization.

In contrast, if we consider the distribution of benefits accruing to producers disaggregated by farm size (and farm incomes) shown in Table, the group most severely hit was the small rainfed producer. Small upland producers participating to the market were “takers” of lower prices without receiving the benefits stemming from the technological advances. The irrigated producers, on the other hand also had a substantial reduction of producer surplus that were partially offset by the cost reducing and output increasing effects of technical change.

Table 5 Annual average Distributional Impact of rice research program on producers

Change in Prod Surplus+Research costs (% income)

Farm Size (Ha)

Avg Income

Upland Sector Irrigated Sector 0-1 1500 -58% -56 1-2 3647 -53 -39 ...... ...... ...... ......

1000-2000 532389 -19 -49 2000+ 1480199 -11 -36

In conclusion, small producers were the most severely affected while poor households benefitted the most. In terms of social welfare, given that the losses were distributed across about 12000 small producers with less than 5 hectares while the gains reached more than one-million households belonging to the lowest deciles, the economic situation with technical change is socially preferable.

Let us now try to estimate the partial equilibrium model used by Scobie and Posada to carry out their study. We first need to delineate some of the main traits of a general methodology that should be followed when carrying out applied partial equilibrium analysis.

1.3. A Methodological Note

The first step to be undertaken is data collection and preparation for the econometric analysis. Before starting the econometric execution we have to be familiar with the data and be sure that the data reflect rational behavior of both producers and consumers.

In market economies characterized by a strong government intervention or in economies in transition, the data are not generated by an efficient market mechanism. In such situations, neoclassical economic theory has a very weak explanatory power. Prices are not expression of a market equilibrium signaling consumers desire for a specific good and its relative scarcity in the market, but is the realization of government decisions. Government rather than market behavior should be more properly modeled in such occasions.

Let us keep in mind that our objective is to interpret the data as best we can using both economic and econometric theory.

1.3.1. Data Collection

Nowadays, economic data is commonly available from national statistical sources and international sources such as FAO Statistical Data Base and the World Bank Economic Indicators. Data are available through the internet or can be obtained upon request at low cost.

To gather the proper data we first need the appropriate specification of the demand and supply functions. Theory is a necessary condition. What data would we collect if we do not know what we should look for? Economic theory tells us that quantity demanded is affected by the own price, price of close substitutes, income and demographic variables and quantity supplied varies


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with the g(output price, price of other outputs, input prices, characteristics:

QD = f (P | Pj, Y, D) = f (own good price, price of other goods, income, demographic factors)

QS = g (P | Pj, Pi, O, D) = g(output price, price of other outputs, input prices, characteristics).

Note that the theory does not help regarding the choice of demographic variables and other characteristics of the production process or the producer. What is important is that other factors that can be included such as demographic variables, advertising effects, income distribution indexes for the demand, and farm size, concentration indexes, decision making process information for the production side, be exogenous, that is not determined by the model, and relevant.

We now need to organize our information in a matrix form where each rows corresponds to an observation and each column is a variable to be included in the model.

There are 2 type of data sets:

(1) TIME SERIES aggregate data set at the market level. Data figures can be found in the official publications of the National Statistical Office. They are usually organized by years, or quarters, or month. N=number of years.

(2) CROSS SECTION DATA at the individual household levels. Data come from household expenditure and income surveys or farm/firm surveys. The level of detail of commodities is very high. N= number of households in the sample (for a population of 60 mil., sample size can be 25000).

Note that prices in cross section analysis are unit values given by the ratio between expenditure and quantities. Unit values vary in relation to the household location and time of purchase. They are household or firm specific and embed quality information. We can think at unit values as prices that are slightly dispersed around a mean price that should be close to the nominal price used in time series analysis for the survey year.

Time series data is commonly used to estimate aggregate demand at the market or sector level. It describes the behavior of a representative consumer. Cross Section data allows for disaggregate demand and policy analysis at the level of individuals. It describes the behavior of specific households. Because of the because of the high level of commodity detail, it is necessary to deal with the econometric problem of dealing with zero realizations. Consumers do not consume all the goods or producers do not produce all goods. The analysis explaining why some consumers do not consume certain goods is of great policy interest. It allows one to know the price level at which consumers are willing to buy the good (e.g. how the government may subsidize that good). Consider also that those who do not consume do not receive policy benefits because their consumer surplus is of course zero.

1.3.2. Familiarization with the Data

Before starting an econometric estimation it is necessary to be familiar with the data aiming at knowing whether the data gathered have been generated through a theoretically consistent economic process. In essence, we would like to answer the following question:

ARE DATA RATIONAL?

If data are rational then we may expect to obtain estimates that are consistent with economic theory.

Before estimating a demand or a supply relationship, it is important to verify whether the data reflect rational (optimizing behavior) of the consumer or the producer using graphical analysis. The objective is to verify, before estimation, whether the data reflect optimizing behavior of the consumer or the producer after controlling for the effects of the other exogenous factors.

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An extremely simple check to verify the rationality or optimizing behavior of the data consists in graphing the data. Visual inspection should provide an answer to the following type of questions: a) do price slopes slope as we expect? , b) are Engel curves (the relation between the share consumed of a good and the logarithm of income) negatively sloped? Using graphs, we are verifying, in a quite crude way, whether the behavior comply with the axioms of revealed preferences and if it obeys the Slutsky law describing price and income demand effects and price and output production effects.

This is important for at least 2 reasons:

(1) either we did not collect the data well, because, for example, the quality control of survey data was not very precise, or,

(2) the institution that we are studying, such as the market, may not be working properly. As an example, consider a market where prices are administered. It is the government setting the prices, not the exchanges between producers and consumers in a market!

Note that the theory does not help regarding the role of demographic variables and other factors. In such cases we may use our economic intuition: e.g. as number of children increase in the family, consumption of food is expected to increase. Or let us think at an index of inequality: if inequality increases through time, this may have a positive effect on luxury goods and a negative effect on necessary goods. For production, the age of the head of the farm may be reasonably expected to be negatively correlated with productivity.

Let us apply this methodology to the construction and the analysis of the data base referring to the rice economy in Colombia.

1.4. Description of the Aggregate Data Base (the Colombian Rice Economy)

The data are from Scobie and Posada (1977), Fao Disappearance data and data from DANE, the national Colombian statistical institute.

Table 6 presents the production data of the Colombian rice market both for the upland rice sector depending on rainfalls and the irrigated sector during the period 1954-1974. In twenty years, rainfed production decreases the area planted and yields increase relatively little if compared with the yield growth enjoyed by an increasingly growing irrigated sector during the same period. the supply increases also when the price decreases. Technical change decreases the costs of production and increases productivity so that it is still remunerative to produce.

As a result, irrigated rice production increased from 58.1 percent in 1954 to 90.5 percent in 1974 as it is shown in Table 6 referring to the supply side of the rice economy. Yields and total area planted more than doubled during the period under consideration. Inspection of table 6 further reveals that real prices at the farm gate level increased until the mid 1960s and then declined slightly. Despite the price decrease irrigated farmers were still investing in rice and increasing the area planted. This is an apparent inconsistency. The new technology, in fact, allows farmers to reduce production costs while increasing the yields, thus maintaining the relative profitability of rice production even at lower prices. The continued adoption of new technology in the face of falling farm prices is often referred to as Cochrane’s “agricultural treadmill.” Farmers are able to undertake such a habitual and laborious course of action (treadmill) because farmers, being price takers, have nothing else to do than always trying to reduce costs adopting technologies that are also yield increasing. Note that those irrigated and better informed rice farmers, who adopted the modern varieties in the early sixties, were also able to capture extra benefits from rising prices. In this sense they are called “early birds” evoking those birds waking up earlier in the morning and leaving no “feed” for the late comers.


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The treadmill argument is crucial for us. It helps “rationalizing” why farmers have increased production in spite of lower prices. In the estimation phase, it will then be important to control for the role of technical change. Interestingly, inspecting the yield pattern we notice that yields grew at a constant rate as a linear trend by the time modern varieties were introduced. This evidence supports the introduction of a linear trend in the supply analysis to control for the role of technical change. We can also note that we may reasonably expect a structural break due to the introduction of high-yield varieties that may justify the introduction of a dummy variable in the model.

Table 8 and related graphs show marketing margins at the wholesale and retail level and the pattern of net exports. Marketing margins capture the costs of intermediaries, often acting as speculators, and of the passages linking farm gate production to the consumer via the production chain. The production and distribution of milled rice involves transport, storage, insurance, milling, packaging, wholesaling, and retailing before it gets into the hands of the consumers. The farm to retail margin increased from 147 percent (obtained as: (retail price-farm price)/farm price) from 1954 to about 190 percent at the end of the period. At the beginning of the period the Colombian rice industry was importing rice, while at the end of the period was an exporter. The analysis of marketing margins is relevant. A reduction of the margin is often a strict Pareto improvement in the sense that producers, consumers and the government all gain from more efficient markets.

Table 9 reports the demand side of the rice economy. Per capita consumption increased steadily as income levels were also increasing thanks also to greater domestic availability. The decreasing share of rice as income increases throughout the period is in line with Engel law (an Engel curve describes the relationship between budget share and the logarithm of income). As prices decrease, consumption increases as required by the Slutsky law. Part of this increase can be explained by a change in taste as can be captured by the increase from 37 percent to about 60 percent of the proportion of the urban population. These regularities of the data are important. It means that there exists evidence supporting the hypothesis that the data set is rational. The important implication is that we can rely on our data set as we develop our experiment. For example, if the regression analysis does not show the correct sign, it means that the problem does not belong to the data but to our experimental conduct. Either we are making a programming mistake or we are not interpreting the data correctly using both economic and econometric theory.

This data set is a standard design for the aggregate market analysis. It can be reproduced to any market.

Now we need to apply very basic econometric techniques to estimate the demand and supply relationships of interest.

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Table 6. The Rice Market in Colombia (1954-1974): rice production

Upland Sector Irrigated Sector Year Area Prod Yield Area Prod Yield

(ha) (m.t.) (t/Ha) (ha) (m.t.) (t/Ha) 54 111580 123600 1.1077 63420 171200 2.6995 55 103920 124328 1.1964 84070 195872 2.3299 56 119960 130210 1.0854 70040 212290 3.0310 57 110250 130042 1.1795 79750 220158 2.7606 58 124800 147779 1.1841 71200 232621 3.2671 59 153610 180366 1.1742 52190 241734 4.6318 60 160230 186770 1.1656 67070 263230 3.9247 61 132100 200150 1.5151 105000 273450 2.6043 62 154200 231310 1.5001 125350 353690 2.8216 63 138600 206000 1.4863 115400 344000 2.9809 64 178300 215000 1.2058 124200 385000 3.0998 65 244750 275600 1.1260 130000 396400 3.0492 66 236000 338600 1.4347 114000 341400 2.9947 67 180850 280500 1.5510 109850 381000 3.4684 68 150200 250600 1.6684 126925 535000 4.2151 69 134570 220275 1.6369 115890 474225 4.0920 70 121113 198248 1.6369 112100 554347 4.9451 71 109130 173696 1.5916 144380 730652 5.0606 72 103220 160524 1.5552 170620 882724 5.1736 73 98840 154769 1.5659 192020 1021102 5.3177 74 95600 149830 1.5673 272950 1420110 5.2028 75 95000 152000 1.6000 273650 1480100 5.4087 Note: m.t.= millions of tons (t), ha=hectares

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(ha)

Area Upland Sector(ha) Area Irrigated Sector(ha) AreaTotal(ha)

Production of Rice

0

200000

400000

600000

800000

1000000

1200000

1400000

1600000

1800000

54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75

Years

M.T

Prod(m.t.) of Upland Area Prod(m.t.) of Irrigated Area Prod(m.t.) of Total Area

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Yield of Rice

0.0000

1.0000

2.0000

3.0000

4.0000

5.0000

6.0000

54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75

Years

M.T/

HA

Yield of Upland (M.t/Ha) Yield of Irrigated land (M.t/Ha) Total Yield(M.t/Ha)

Table 7. The Rice Market in Colombia (1954-1974): the supply side

Total Production Real Prices Area Prod Yield Irrigated Farm (ha) (m.t.) (t/Ha) % $/t.

175000 294800 1.6846 58.1 1270 187990 320200 1.7033 61.2 1284 190000 342500 1.8026 62.0 1244 190000 350200 1.8432 62.9 1337 196000 380400 1.9408 61.2 1471 205800 422100 2.0510 57.3 1375 227300 450000 1.9798 58.5 1497 237100 473600 1.9975 57.7 1490 279550 585000 2.0926 60.5 1372 254000 550000 2.1654 62.5 1321 302500 600000 1.9835 64.2 1347 374750 672000 1.7932 59.0 1592 350000 680000 1.9429 50.2 1507 290700 661500 2.2755 57.6 1418 277125 785600 2.8348 68.1 1452 250460 694500 2.7729 68.3 1217 233213 752595 3.2271 73.7 1121 253510 904348 3.5673 80.8 1044 273840 1043248 3.8097 84.6 893 290860 1175871 4.0427 86.8 978 368550 1569940 4.2598 90.5 1151 368650 1632100 4.4272 90.7


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0

200000

400000

600000

800000

1000000

1200000

1400000

1600000

1800000

years0

200

400

600

800

1000

1200

1400

1600

1800


Table 8. The Rice Market in Colombia (1954-1974): market margin and net exports

Real Prices Marketing Margin Exports Imports Net Exports

Year Wholesale Retail Farm to Retail $/t. $/t. $/t. % (m.t.) (m.t.) (m.t.)

54 2789 3135 1865 146.9 0 31000 -31000 55 2508 3135 1851 144.2 0 2000 -2000 56 2687 3026 1782 143.2 0 0 0 57 3200 3696 2359 176.4 0 10000 -10000 58 2902 3529 2058 139.9 0 0 0 59 2600 3071 1696 123.3 0 0 0 60 3281 3695 2198 146.8 0 0 0 61 2913 3688 2198 147.5 0 39000 -39000 62 2579 3522 2150 156.7 4000 3000 1000 63 2626 3012 1691 128.0 3000 0 3000 64 2928 3480 2133 158.4 0 0 0 65 3379 3850 2258 141.8 0 0 0 66 3059 3568 2061 136.8 0 0 0 67 2850 3259 1841 129.8 0 0 0 68 2780 3117 1665 114.7 0 0 0 69 2415 2877 1660 136.4 16000 0 16000 70 2545 2727 1606 143.3 5000 0 5000 71 2309 2735 1691 162.0 0 0 0 72 2089 2493 1600 179.2 3000 0 3000 73 2755 3113 2135 218.3 20000 0 20000 74 2783 3311 2160 187.7 1000 0 1000

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Farm, Wholesale, Retail Price of Rice

0

500

1000

1500

2000

2500

3000

3500

4000

4500

54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74

M.T/$Farm Real Prices$/t. Wholesale($/t.) Retail($/t.)

Marketing Margin %

0.0

50.0

100.0

150.0

200.0

250.0

54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74

years

%


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Imports,EXports of Rice

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74

Years

M.T

Exports(m.t.) Imports(m.t.)

Table 9. The Rice Market in Colombia (1954-1974): the demand side

Consumption Population Population Per capita consumption

Income Rice Share

Total Urban % Urb/Tot kg/month Pesos/mth 325800 12486 4639 37.154 2.174 83.48 0.0817 322200 13027 5073 38.942 2.061 85.18 0.0759 342500 13627 5552 40.743 2.094 89.19 0.0711 360200 14372 6068 42.221 2.089 109.52 0.0705 380400 14892 6612 44.400 2.129 112.69 0.0667 422100 15387 7171 46.604 2.286 114.91 0.0611 450000 15901 7623 47.940 2.358 144 0.0605 512600 16421 8082 49.217 2.601 164.83 0.0582 584000 16918 8503 50.260 2.877 177.77 0.0570 547000 17430 8945 51.320 2.615 178.63 0.0441 600000 17959 9412 52.408 2.784 191.82 0.0505 672000 18506 9904 53.518 3.026 236.9 0.0492 680000 19074 10345 54.236 2.971 237.6 0.0446 661500 19659 10805 54.962 2.804 208.2 0.0439 785600 20246 11277 55.700 3.234 232.7 0.0433 678500 20817 11750 56.444 2.716 213.6 0.0366 747595 21360 12218 57.200 2.917 219.8 0.0362 904348 21869 12659 57.886 3.446 267.5 0.0352 1040248 22348 13091 58.578 3.879 281.8 0.0343 1155871 22813 13523 59.278 4.222 388.6 0.0338 1568940 23283 13968 59.992 5.615 561.1 0.0331

Note: the mean of the rice share is: mean(w)=0.052.

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Evolution of Rice Consumption and Prices

0

1

2

3

4

5

6

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

years

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Per capita Consumpt. (kg/month) Retail Prices($/kg.)

I Engel Law: As log income rises, the share of necessities decrease

0

100

200

300

400

500

600

1.921.95

2.052.16

2.252.28

2.382.37

2.342.45

Log Income

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

Income Pesos/mth Rice Share


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Chapter 2 - Demand Analysis

The section on demand analysis is organized in an introductory and an advanced part.

In the introductory part the concepts of income and price elasticities are introduced in the context of Engel curve analysis and then estimated using the class experiment related to the Colombian rice economy. Own and cross price elasticities have been defined and derived both for a time series aggregate application and for a disaggregate cross section application where a complete demand system, in its simplest form, is estimated within the laboratory experiment.

In the advanced section, it is introduced the Almost Ideal Demand System (AIDS) which is the most popular applied demand system. The economic interpretation of demand policy parameters is developed using estimates of empirical applications. The welfare analysis of consumption introduces the concepts of living standard, cost of living indexes and compensating variation, an exact measure of consumer surplus.

The objective is to apply the experimental methodology very pragmatically simulating within a participatory class experiment the steps that an applied economist would have to follow in order to estimate a demand system that complies with the requirements of economic theory. The lab experiment is the estimation of Scobie and Posada model (1977) and the application of disaggregate demand analysis using Italian rural consumption data.

2.1. Introductory Demand Analysis

Demand analysis can be used to understand consumer behavior alone if the interest is simply in forecasting. Interestingly, we can build a partial equilibrium model for a public good such as a park or a child accounting for habits, heterogeneity and tastes of the consumer. Or about a quality characteristic or about the market for leisure time. We may apply a distributive (equity) analysis both within society and within the family seen as a micro society.

The demand estimates can also be used to implement welfare analysis that is to use the information on observed demand behavior to deduce utility (welfare) levels and develop exact welfare analysis of markets, poverty and inequality measurement, the estimation of social welfare function given by the sum of producer and consumer surpluses and to carry out taxation analysis.

Follows a non exhaustive list of possible uses:

Study of BEHAVIOR (POSITIVE ANALYSIS).

• Demand for goods (it is specific to each good):

o Demand for Wheat flour, Bread, alcool or tobacco (theory of addiction), nutrients, durables, cotton, public goods such as parks, or clean air.

• Analysis of structural change: habits, heterogenity or tastes? And advertisement?

• Demand for quality characteristics

• Intrahousehold distribution: adults vs children good, gender specific demand

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• Demand for children

• Demand for leisure (labor supply)

Notice that these applications can be described using a partial equilibrium framework.

Implementation of WELFARE ANALYSIS

• Estimation of the Expenditure function and utility in order to derive the Compensating Variation which is an exact measure of Consumer Surplus

• Estimates of the “Cost of Children”: demographic targeting and welfare reform.

• Poverty and Inequality: from demand to Y(u,p,d) => microsimulations on p and d!

• Social welfare functions: W=Producer Surplus (PS)+Consumer Surplus (CS) corresponding to the sum of all individual utilities

• Demand and Optimal taxation It is relevant to be aware that demand analysis can serve both to understand behavior and to implement welfare analysis. From a practical standpoint, our choices regarding the specification of the model and the choice of the functional form may depend on the objective of our study. For example, if the objective is to implement also a welfare analysis than greater accuracy is achieved by estimating a system of demand equations rather than a single demand equation. A system approach corresponds to a multi-market approach; a single equation approach is used to implement a partial equilibrium framework. These concepts are going to be described below after a brief description of some basic notions in demand analysis.

2.1.1. Some Basic Notions

DEFINITION OF ELASTICITY

Suppose that q=f(x) is a demand (or a supply curve) where x is an exogenous variable such as income, price, fixed factors, etc. and q is the quantity demanded or supplied. Marginal changes such as dq /dx are in the measurement unit of q and x and so difficult to compare across marginal changes. In contrast, the elasticity is unit free.

Elasticity: is the percentage change in the dependent variable due to a percentage change in the independent variable.

Elasticity of q with respect to x:

qx

dxdq

xxdqqd

xdqd

xqEx ====

ln ln

in change %in change %

Note: The elasticity can be computed at the mean or at each data point. It can be a constant or a function.

If the absolute value of the elasticity |Ex| >1 = elastic

If the absolute value of the elasticity 0<|Ex| <1 = inelastic.

INCOME ELASTICITY OF DEMAND

consume topropensity averageconsume topropensity marginal

ln ln

====qy

dydq

yydqqd

ydqdEy

If Ey>1, demand increases more than proportionally with income, so, the expenditure share of this good increases as income increases. If Ey<1, the expenditure share declines as income increases. This is the case for food.


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OWN PRICE ELASTICITY OF DEMAND

Own price elasticities must be negative.

qipi

dpidqi

pipidqiqid

pidqidEpi ===

ln ln

If Ep>-1, (inelastic demand) an increase in price induces an increase in expenditure (pq) (d (pq)/dp>0) despite a decrease in demand. The change in quantity is smaller than the change in price.

If Ep<-1, (elastic demand) the expenditure (pq) decreases with a price increase (d (pq)/dp<0) because the decline in demand is larger than the price increase.

Explanation:

( ) ( )Epqdqdppq

dppqd

+=+= 1

The same reasoning applys to factor demand in production.

CROSS PRICE ELASTICITY OF DEMAND

pjqi

qipj

dpjdqiEpij

in change %in change %

==

If Ep ij > 0, i and j are gross substitutes

If Ep ij < 0, i and j are gross complements.

This concept is especially appropriate to a system (multi-market demand approach). Consider the following two demand equations exhausting the full budget: food and nonfood expressed in shares rather than in quantities:

wfood = d0 + d00 ln d +d11 ln pf + d12 ln pnf + d2 ln y

wnonfood = e0 + e00 ln d +e11 ln pf + e12 ln pnf + e2 ln y

In a single equation framework, we only have the cross effect of a price of a substitute or complement good such as, looking at the first equation, non-food on food, but we do not know how the price of food affects the demand for non-food and vice versa. This full matrix of effects is possible to obtain only with a system approach. From a behavioral standpoint it is interesting to test whether the cross-price relationships are symmetric.

CLASSIFICATION OF GOODS

Goods are defined in terms of the type of response with respect to prices and incomes. These definitions are fundamental to interpret the results.

1) Classification in terms of price response

Giffen Ep>0

Normal with inelastic demand 0>Ep>-1

Normal good with elastic demand Ep<-1

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2) Classification in terms of income response

Inferior Ey<0

Necessity 0<Ey<1

Luxury Ey>1

THE I AND II ENGEL LAWS

I Engel Law: As the log of income increases, the food share decreases.

Note: This empirical regularity linking consumption to income can be found in the data of all societies and explains why food is an indirect measure of welfare.

Ex. Italian Household budget data 1995. Obs: 33400.

Food Share

Quo

ta A

limen

tare

Log della Spesa Totale

12 14 16 18

.1

.2

.3

.4

log income

Definition. II Engel Law: As family size increases, the share of expenditure allocated to food also increases.

Food share

Quo

ta A

lim

enta

re

Log della Spesa Totale

13 14 15 16 17

.1

.2

.3

.4

.5

log income

The shape of the data suggests that a correct functional representation of the Engel curve is linear in the logarithm:

wi = αi + δi ln di + βi ln y

where w=food share, d=number of children, y=income.


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2.1.2. Introductory Applications

THE TIME SERIES EXERCISE: AGGREGATE MARKET DEMAND FOR RICE IN COLOMBIA

This exercise is meant for illustrating a practical method to estimating the price and income elasticity of consumption using aggregate time series data. We use price, consumption and income data from the data set that we assembled together for the Colombian rice economy. The demographic variable is the percentage of urban population. It is included in the analysis to account for tastes.

The data are transformed in logarithms both to ensure e better fit and for analytical convenience. In a Cobb-Douglas demand specification expressed in terms of quantity, the parameters are directly interpreted as elasticities. In the Engel type of demand functions expressed in share form, the logarithmic specification come from the theoretical derivation of the model.

Notation

Consider a general demand system specified using the Colombian data set:

q = f ( p, y, N, d) or w=pq/y = f ( p, y, N, d)

where:

q is quantity demanded in kg/month

p is the real retail price of rice in Pesos/Kg (the Peso is the Colombian currency)

y is total income

w is the budget share of rice: w=p q/y

N is population size

d is the urban/N ratio.

• Specification and Choice of Functional Form

At this point of our project, we collected the time series data base and familiarized with our data. It is time to implement the econometric analysis. In doing this, we have to make two important choices:

1. Model Specification: What is the best model specification, that is what is the set of relevant variables to include in the model and how should we include the selected variables in the model? For example, income, prices and demographic effects may be included both linearly and nonlinearly as quadratic terms. Prices, income and demographic variables also interact with each other. Nonlinearities in demographic effects may imply the existence of household economies of scale. A quadratic income term may be justified by the shape of the Engel curve. A quadratic income term would make the elasticity change across the income distribution: the same good can be a luxury at low income levels and a necessity at high income levels.

2. Choice of the appropriate functional form: for example, what is the functional form that interprets the data better? A double log or a semilog model or other functional forms? It is important to emphasize that the choice of the functional form (for example between a ad hoc single equation double log model and a semilog system of share equations derived from utility theory ) often depends on the objectives of the research. For partial equilibrium analysis a single equation approach may suffice. In contrast, multimarket analysis and accurate welfare analysis requires a system approach consistent with utility theory.

The exercise is designed to illustrate these topics through a learning by doing process.

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• Representation of preferences

First, we need to choose how to represent preferences

• “Ad hoc,” that is specified for the specific purpose at hand

Ex. linear single equation models

Ad hoc models are not based on theory: if a model is single equation cannot represent preferences for all goods we buy, so we cannot derive the total expenditure function and utility based on the consumption of the complete basket.

• Utility based complete demand systems are based on theory: this type of model allows one to recover the unobservable U(x). This is necessary for welfare analysis!

• Choice of the functional form

Ex. of a ad hoc reduced form model

ln Q = a + a1 ln d + b ln p + c ln y +d ln y*y

Ex. of a utility based structural model (system of demand equations)

wi = a0 + Σk ak ln dk + Σj bj ln pj + c ln y for k=1,..,K; i=j=1,..,N

where wi = share of good i, pj=price of good j, dk = k-th demographic variable, y= income, K is the number of demographic variables and N is the number of goods (and prices) included in the system of demand equations.

• Flexibility

In some empirical situations where the presence of nonlinearities in the data is significant, in order to correctly interpret the data, it is useful to add more flexibility to the model:

Is the model linear in p?

Is the model linear in y?

Is the model linear in d: are there economies of scale (nonlinear demographic effects)?

Answer: let us learn from the data by graphing them! If not linear, add a quadratic income term or nonlinearity in p or quadratic demographic effects.

Note: this is crucial to obtain estimates that agree with the theory requirements (Ex. Own price demand elasticities must be negative!)

• Econometric Execution

We have the option to estimate either in quantity q or in share form w. We will estimate and analyze five specifications of an aggregate demand function:

Cobb-Douglas (univariate double log regression)

ln q = ln A + A1 ln p = A pA1

Cobb-Douglas (multivariate) ln q = (a0 + a00 ln d + a2 ln (y/N) ) + a1 ln p

Working-Leser (WL) Engel curve (semi-log) w = b0 + b2 ln (y/N)

WL Engel curve with prices w = c0 + c1 ln p + c2 ln (y/N)

WL Engel curve with prices and demographics

w = d0 + d00 ln d +d1 ln p + d2 ln (y/N)


25

Note: the double-log and the semi-log are not directly comparable because the double-log and semi-log models are not nested into each other. The dependent variables are different.

Specification 1: Cobb-Douglas (univariate double log regression)

• ln q = ln A + a1 ln p

Coefficients

Standard Error

t Stat

Intercept 1.682 0.578 2.911

Prices $/t -0.557 0.492 -1.133

R2=0.063, N. Obs. 21

This is the functional form closest to our representation of the partial equilibrium model. The results show a clear misspecification problem. The fit is very low and the price parameter is not statistically significantly different from zero at all levels of significance. The price here explaiins only 6 percent of the variation observed for demand (R2=0.063).

Many relevant variables are omitted. The theory tell us that income, acting as an exogenous shifter, should be included in the specification. Other exogenous factors can be relevant in the sense that, if omitted, a bias may result. So, considering that our level of familiarization with the data allows us to have confidence on our data, than it means that we can do better either by improving the specification and/or through adopting a functional form more appropriate to interpret correctly our data. Let us work on the specification first.

Specification 2: Cobb-Douglas (multivariate double log regression)

• ln q = a0 + a00 ln d + a1 ln p + a2 ln (y/N)

Coefficients Standard Error

t Stat

Intercept 1.823 0.527 3.461

urb/tot % -1.151 0.187 -6.151

Prices $/t -0.361 0.084 -4.296

Income/mth 0.796 0.053 14.975

R2=0.979, N. Obs. 21

Note that model 2 can be rewritten as model 1 using the following change in notation:

ln q = ln A + a1 ln p where A=exp( a0 + a00 ln d + a2 ln y - a2 ln N).

Model 2 controls for relevant exogenous factors such as income and demographic trends.

The set of regressors explains .979 percent of the variation observed (R2=0.979). The estimated coefficients are all statistically significantly different from 0 at the 5 percent confidence level.

Statistical significance is analyzed using the t-distribution. The table of the t-distribution gives the values of t which limits the interval of the acceptance region. In our case, we may look at the table referring to a 5 percent significance level and 17 degrees of freedom (df=(n obs)-(n Param)=21-4). For example, the t-value for the price coefficient is 2.12. This means that with t-values less than -2.12 and greater than +2.12 the coefficients can be accepted.

Note that the t-values is equal to the ratio between the coefficients and the standard error:

Ex. Price: H0 : β=0; b - β / s = (-0.361-0)/0.084=-4.296

Then we conclude that the price coefficient is significantly different from 0 at the 5 percent

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significance level. (Note that β is the population parameter).

Suppose now that we want to test whether the income coefficient is significantly different from 1 at the 5 percent significance level:

Ex. Income: H0 : β =1; b - β / s = (0.796-1)/0.053=-3.85

In the case of a t-test the null hypothesis is in general the statistical difference of the parameter of interest with respect to 0. If the null hypothesis is accepted than the parameter is not statistically significantly different from 0 at the selected level of confidence.

The signs comply with the theory: the own price effect is negative and the income effect is positive. According to these estimates rice is a normal good with respect to the price effect and a necessary good with respect to the income effect.

Note that with respect to model 1 we maintained the same functional form. The improved specification changed the overall performance of the model.

Elasticity calculation

Ed = ∆ ln q / ∆ ln d = (∆ q / ∆ d) (d / q) = a00 = - 1.151

Ep = ∆ ln q / ∆ ln p = (∆ q / ∆ p) (p / q) = a1 = -0.361

Ey = ∆ ln q / ln y = (∆ q / ∆ y) (y / q) = a2 = 0.796

Specification 3: Working-Leser (WL) Engel curve (semi-log)

• w = b0 + b2 ln (y/N)


t Stat

Intercept 0.198 0.014 13.733

Income/mth -0.028 0.003 -10.191

R2=0.845, N. Obs. 21 mean(w)=0.052


w = pq / y → ln w = ln p + ln q - ln y →

ln q = ln w(p,y,d) - ln p + ln y

ln q = ln (b0 + b2 ln y - b2 ln N) - ln p + ln y

So, taking the derivative we respect to y we derive the elasticity of income:

Ey = ∆ ln q / ∆ ln y = (∆ ln w / ∆ w) (∆ w / ∆ ln y) +1 = b2 / w + 1 = 0.458

where: (∆ ln w / ∆ w) = 1/w

(∆ w / ∆ ln y) = b2.

Note 1: The elasticity of a demand equation in share form is a function not a constant as we had in the case of a double logarithmic specification. In particular, it is a function of the level of the share. This implies that we can derive an elasticity for the poor and one for the rich consumer. In our time series example, it means that we can compute the elasticity for the beginning of the period when Colombia was less rich and the share of rice consumed was higher and for the end of the period. This greater flexibility is highly desirable.


27

Note 2:

If b2<0 and b2>w, the good is an inferior good (Ey<0)

If b2<0 and b2<w, the good is a necessity (0<Ey<1).

If b2>0 ,the good is a luxury (Ey>1).

Specification 4: WL Engel curve with prices

• w = c0 + c1 ln p + c2 ln (y/N)


t Stat

Intercept 0.152 0.017 8.762

Prices $/t 0.034 0.009 3.532

Income/mth -0.027 0.002 -12.100

R2=0.909, N. Obs. 21, mean(w)=0.052


w = pq / y ln w = ln p + ln q - ln y ln q = ln w(p,y,d) - ln p + ln y

Ep = ∆ ln q / ∆ ln p = (∆ ln w / ∆ w) (∆ w / ∆ ln p ) - 1 = c1 / w - 1 = -0.355

Ey = ∆ ln q / ∆ ln y = (∆ ln w / ∆ w) (∆ w / ∆ ln y) +1 = c2 / w + 1 = 0.484

where: (∆ ln w / ∆ w) = 1/w

(∆ w / ∆ ln p ) = c1

(∆ w / ∆ ln y) = c2.

The interpretation of the function Ep tell us that:

if c1 <0, the good is normal with elastic demand

if c1 >0 and c1 >w, the good is a Giffen good

if c1 >0 and c1 <w, the good is normal with inelastic demand.

In our case, rice is a normal good with inelastic demand. Rice is a necessity. This evidence is in line with the prior information that we gathered from the data. Let us see if we can do better by controlling for taste changes due to rural-urban migration.

Specification 5: WL Engel curve with prices and demographics

• w = d0 + d00 ln d +d1 ln p + d2 ln (y/N)


t Stat

Intercept 0.389 0.025 15.801

urb/tot % -0.088 0.009 -10.015

Prices $/t 0.021 0.004 5.302

Income/mth -0.003 0.002 -1.397

R2=0.987, N. Obs. 21 mean(w)=0.052

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w = pq / y → ln w = ln p + ln q - ln y → ln q = ln w(p,y,d) - ln p + ln y

Ed = ∆ ln q / ∆ ln d = (∆ ln w / ∆ w) (∆ w / ∆ ln d ) = d00 / w = -1.686

Ep = ∆ ln q / ∆ ln p = (∆ ln w / ∆ w) (∆ w / ∆ ln p ) - 1 = d1 / w - 1 = -0.600

Ey = ∆ ln q / ∆ ln y = (∆ ln w / ∆ w) (∆ w / ∆ ln y) +1 = d2 / w + 1 = 0.933

where: (∆ ln w / ∆ w) = 1/w

(∆ w / ∆ ln d ) = d00

(∆ w / ∆ ln p ) = d1

(∆ w / ∆ ln y) = d2.

Note: both income and demographic effects are trends. Because of this relationship, the income coefficient is no longer significantly different from zero at the 10 percent significance level.

Note: the results are consistent both with the expectations we built looking at the data and with economic theory.

Next, an example applying a detailed demand analysis is presented using cross section (household specific) data. This information allows us to move away from the representative consumer assumption by estimating disaggregate demand parameters. Ultimately, to answer the question: who is eating how much of what or, stated in other way, to identify the potential beneficiaries of policy interventions.

So we leave the rice example to get back to it later when we will deal with the supply analysis.

• Disaggregate Demand Analysis

This approach is needed for carrying out exact welfare analyses that requires a multi-equation (multimarket) approach.

Plan of the exercise:

1) Estimate Engel Kernel regressions

2) Estimate a complete demand system equation by equation

3) restrictions from sum(share of cereals + meat + others) =1; (homogeneity)

4) test for income and demographic quadratic effects

5) role of demographic effects

6) Interpret

• Engel curve analysis

Learning from the data. nonparametric Engel curves for Cereals, Meat and Other food items - Italian Rural Household Data (ISMEA 1995). Observe the nonlinearities of cereals and meat. It is likely that to interpret the data correctly we may need to add a quadratic income term to the Engel curve. If we do not, we may not obtain estimates consistent with the theory.

The data set counts 1777 units of observations (households).

Next, we analyze empirically the behavioral response to income using the concept of Engel curves describing how consumption, in terms of expenditure shares, varies with respect to the logarithm of income. The analysis is carried out using a Gaussian kernel regression. It is a non parametric technique that interprets the data without prior assumptions about the functional form of the regression relationship. For this reason, this instrument is very helpful in providing pre-estimation information about the most appropriate functional form to adopt.


29

An example may help clarifying the concept. If we run a linear regression, the prediction will be of course linear. If we run a nonparametric regression, then the graph of the non parametric regression shows if the relationship is linear or nonlinear and what type of nonlinearities.

The Engel curve nonparametric analysis is also an example of how to use graphical analysis as a tool helping making specification decisions. If the Engel curves are nonlinear, then it can be appropriate to include a quadratic income term in the demand function. A similar analysis can be carried out for price and demographic effects.

Inspection of the kernel graphs presented below shows that the nonparametric Engel curves of the Italian rural consumption of cereals, meat and other food are linear. On the basis of this evidence, we may reasonably expect that the inclusion of a quadratic income term in the parametric demand specification may not be significant. We will test this hypothesis at the end of the exercise.

Engel curves of the system of Cereal (1), Meat (2) and Other Food (3) consumption (ISMEA - 1995)

Kernel regression, bw = 1.8, k = 6

Grid points6.43053 9.71057

.207115

.208118

1


Grid points6.43053 9.71057

.370864

.373115

2


Grid points6.43053 9.71057

.418767

.422021

3

Training Materials

30

A CROSS-SECTION APPLICATION: THE DISAGGREGATE DOMAND FOR FOOD IN ITALY

Prices in cross-section demand analysis are household specific because they are derived as expenditures spent on a good i by household h divided by quantities consumed by household h. We no longer have one aggregate price per year as in time-series analysis. Cross-section prices are called unit values.

Bre

ad &

Cer

eals

Sha

re

Market Bread & Cereals Price0 12459.3

0

1

However, as the graph relating the share spent on cereals and the cereal unit value shows that prices are highly concentrated around an average price that can be compared to the aggregate price for the survey year. Interestingly, the graph reveals that the unit value increases as the share spent on cereal increases. This evidence supports the fact that unit values contain information about the quality of the good.

• Functional form:

++++= ∑∑ Nypdw ij

jijk

kikii lnlnln βγδα

where i=j=1,..,N indexes the number of goods and prices, k=1,..,K indexes the number of demographic variables. The above equation represents one equation of a N-system of equations.


31

The STATA program

#delimit; /* ----------------------------------- Estimate of Engel regressions ISMEA data on rural consumption Federico Perali Cham, September 2002 --------------------------------------- */ capture clear; capture log close; set more off; set mem 5m; /* ----------------------------------- OPENING DATASET AND OUT FILE -----------------------*/ use C:\docs\Papers\papers02\siria02\fao_syria_9_02\exercises\ismea_fao1\ismea_syr.dta; capture log using C:\docs\Papers\papers02\siria02\fao_syria_9_02\exercises\ismea_fao1\disag_dem.log, replace; sum w_panal w_carni wother p_panal p_carni p_food red_glo_hh ireg area5 area3 sex edu cprof age fsize nmales nfemales nchild spesa; gen nord=1 if area3==1; recode nord .=0; gen centro=1 if area3==2; recode centro .=0; gen sud=1 if area3==3; recode sud .=0; gen spesa2=spesa*spesa; gen nchild2=nchild*nchild; /* take logs */ gen lp_panal=log(p_panal); gen lp_carni=log(p_carni); gen lp_food=log(p_food); gen lspesa=log(spesa); gen lspesa2=log(spesa2); sum; /* ------------------ Plan:------------------------------- 1) Estimate Engel Kernel regressions 2) Estimate a complete demand system equation by equation 3) restrictions from sum(share of cereals + meat + others) =1 (homogeneity) 4) income and demographic quadratic effects 5) role of demographic effects 6) Interpret ---------------------------------------------------------- */ /* Unit values */ graph w_panal p_panal; /* Estimate Engel Kernel (Gaussian) regressions */ kernreg w_panal lspesa, b(1.8) k(6) np(200) saving(eng_cereal,replace) ;

Training Materials

32

kernreg w_carni lspesa, b(1.8) k(6) np(200) saving(eng_meat,replace) ; kernreg wother lspesa, b(1.8) k(6) np(200) saving(eng_other,replace) ; /* Complete Demand System (multimarket) equation by equation */ reg w_panal nchild age edu nord centro lp_panal lp_carni lp_food lspesa; reg w_carni nchild age edu nord centro lp_panal lp_carni lp_food lspesa; reg wother nchild age edu nord centro lp_panal lp_carni lp_food lspesa; /* income and demographic quadratic effects */ reg w_panal nchild nchild2 age edu nord centro lp_panal lp_carni lp_food lspesa lspesa2; log close; Table 10 . The ISMEA 1995 data base on the Socioeconomic Conditions of Italian Agriculture -

Rural Consumption Variable Definition Mean Std. Dev. Min Max

w_panal Cereal share 0.2077 0.1152 0.00 1 w_carni Meat share 0.3721 0.1653 0.00 0.858 wother Other Food share 0.4202 0.1439 0.00 1 p_panal Price for Cereals (££/Kg) 900.53 889.75 0.00 12459.29 p_carni Price for Meat (££/Kg) 6842.99 3741.05 0.00 42904.29 p_food Price for Other Food

(££/Kg) 10993.91 3538.47 2000.00 43370.74

ireg Region (1, .., 20 regions) 11.2510 6.0202 1.00 20 sex male 1.0456 0.2086 1.00 2 edu education level 3.5768 0.9443 1.00 6 cprof professional condition 2.4513 2.8832 1.00 9 age age 51.1216 13.0113 18.00 89 fsize Family Size 3.4682 1.4617 1.00 11 nmales Number of Males 1.9387 0.9669 0.00 6 nfemales Number of Females 1.5295 0.9623 0.00 7 nchild Number of Children 1.1660 1.0957 0.00 7 spesa Total Food Expend. (££000) 2885.77 1822.55 620.50 16491 nord 1 if North 0.3832 0.4863 0.00 1 centro 1 if Center 0.2212 0.4151 0.00 1 sud 1 if South 0.3956 0.4891 0.00 1 lp_panal ln Price for Cereals 6.4519 0.8694 3.63 9.43 lp_carni ln of price for Meat 8.6938 0.6858 3.68 10.67 lp_food ln of price for other food 9.2548 0.3230 7.60 10.68 lspesa Ln tot Food exp 7.8201 0.5227 6.43 9.71

Table 11. Estimates of the cereal equation (Obs: 1777, R2=0.716)

w_panal Coef. Std. Err. t P>|t| [95% Conf. Interval]

nchild 0.0016 0.0014 1.1300 0.2590 -0.0012 0.0043 age -0.0001 0.0001 -0.7900 0.4310 -0.0003 0.0001 edu 0.0024 0.0016 1.4900 0.1380 -0.0008 0.0057 nord 0.0067 0.0032 2.1200 0.0340 0.0005 0.0130 centro -0.0061 0.0037 -1.6400 0.1020 -0.0133 0.0012 lp_panal 0.0897 0.0017 51.9500 0.0000 0.0863 0.0931 lp_carni -0.0004 0.0030 -0.1400 0.8890 -0.0062 0.0054 lp_food -0.0954 0.0067 -14.3000 0.0000 -0.1084 -0.0823 lspesa -0.0118 0.0030 -3.9700 0.0000 -0.0176 -0.0060 _cons 0.5977 0.0544 10.9800 0.0000 0.4910 0.7045


33

Table 12. Estimates of the meat equation (Obs: 1777, R2=0.747) w_carni Coef. Std. Err. t P>|t| [95% Conf. Interval]

nchild -0.0039 0.0019 -2.0500 0.0400 -0.0077 -0.0002 age -0.0002 0.0002 -1.4100 0.1590 -0.0006 0.0001 edu 0.0029 0.0023 1.2900 0.1970 -0.0015 0.0073 nord -0.0296 0.0044 -6.7800 0.0000 -0.0382 -0.0210 centro -0.0009 0.0051 -0.1800 0.8570 -0.0109 0.0091 lp_panal -0.0354 0.0024 -14.9200 0.0000 -0.0401 -0.0308 lp_carni 0.1843 0.0041 45.1800 0.0000 0.1763 0.1923 lp_food -0.0421 0.0092 -4.5900 0.0000 -0.0600 -0.0241 lspesa 0.0033 0.0041 0.8100 0.4200 -0.0047 0.0113 _cons -0.6081 0.0748 -8.1300 0.0000 -0.7547 -0.4615

Table 13. Estimates of the other food equation (Obs: 1777, R2=0.491)

wother Coef. Std. Err. t P>|t| [95% Conf. Interval]

nchild 0.0024 0.0025 0.9600 0.3370 -0.0025 0.0072 age 0.0003 0.0002 1.5400 0.1230 -0.0001 0.0007 edu -0.0054 0.0029 -1.8500 0.0650 -0.0110 0.0003 nord 0.0229 0.0056 4.0800 0.0000 0.0119 0.0339 centro 0.0070 0.0065 1.0700 0.2850 -0.0058 0.0198 lp_panal -0.0543 0.0030 -17.8400 0.0000 -0.0603 -0.0484 lp_carni -0.1838 0.0052 -35.1200 0.0000 -0.1941 -0.1736 lp_food 0.1374 0.0118 11.6900 0.0000 0.1144 0.1605 lspesa 0.0085 0.0052 1.6200 0.1050 -0.0018 0.0188 _cons 1.0104 0.0960 10.5300 0.0000 0.8222 1.1986

The interpretation of these results follows the same guidelines provided in the previous exercise. It is left to the reader to compute elasticities and to interpret the statistical and economic significance of the results.

• Restrictions

When a complete demand system is estimated in share form, the following adding-up restriction holds:

Σi wi =1.

Let us show how this restriction operates. Consider the following set of share demand equations for k=1,..,K; i=j=1,..,N where K=2 and N=3 (1=cereals, 2=meat, 3=other food):

w1 = α10 + ( δ11 ln d1 + δ12 ln d2 ) + ( γ11 ln p1 + γ12 ln p2 + γ13 ln p3 ) + β1 ln y

w2 = α20 + (δ21 ln d1 + δ22 ln d2 ) + (γ21 ln p1 + γ 22 ln p2 + γ23 ln p3 ) + β2 ln y

w3 = α 30 + (δ31 ln d1 + δ32 ln d2 ) + (γ31 ln p1 +γγ32 ln p2 + γ33 ln p3 ) + β3 ln y

Notice that in the application K=5, but the line of the argument does not change. Now, the adding-up restriction ∑i wi =1 implies the following:

w1 + w2 +w3 = (α10 + (δ11 ln d1 + δ12 ln d2 ) + (γ11 ln p1 + γ12 ln p2 + γ13 ln p3 ) + β1 ln y ) +

(α20 + (δ21 ln d1 + δ22 ln d2 ) + (γ21 ln p1 + γ22 ln p2 + γ23 ln p3 ) + β2 ln y ) +

(α30 + (δ31 ln d1 + δ32 ln d2 ) + (γ31 ln p1 + γ32 ln p2 + γ33 ln p3 ) + β3 ln y ) = 1.

Collecting terms, we obtain:

w1 + w2 + w3 = (α10 + α20 + α30 ) + (δ11 + δ21 +δ31 ) ln d1 + (δ12 + δ22 + δ32 ) ln d2 +

Training Materials

34

(γ11 + γ21 + γ31 ) ln p1 + (γ12 +γ22 + γ32 ) ln p2 + (γ13 + γ23 + γ33 ) ln p3 ) +

(β1 + β2 + β3 ) ln y = 1.

For the adding-up equality to hold, it must be that:

Restrictions Σi αi =1; Σi γij = Σ βi = Σk δ k=0

Note, that given this set of restrictions, we may estimate only two equations and derive the parameters of the omitted equation.

This property also guarantees the absence of what is called in the economic terminology “money illusion”. That is, if all prices and income are increased by the same proportion, demand remains unchanged. In other words, the homogeneity property holds and is implied by the adding-up condition.

The homogeneity property also applies to demographic effects. If all prices, income, and demographic effects are increased by the same proportion, demand remains unchanged. Demographic effects do sum to 0 as well. The property provides an interesting interpretation of demographic effects as demographic substitution effects. Suppose that the effect of the number of children for the cereals and other food equation is positive. Because of the budget constraints requiring that the shares sum to 1, it must be that larger families with more children buy relatively less meat. The sign associated with the variable number of children must in fact be negative in the meat equation.

Another implication of the homogeneity property is that the sum of all price, income and demographic elasticities must sum to 0.

Table 14. Restrictions implied by adding up of the shares (homogeneity) nchild age edu north centre lp_panal lp_meat lp_food lspesa _cons δ δ δ δ δ γ γ γ β α

w_cereal 0.0016 -0.0001 0.0024 0.0067 -0.0061 0.0897 -0.0004 -0.0954 -0.0118 0.5977 w_meat -0.0039 -0.0002 0.0029 -0.0296 -0.0009 -0.0354 0.1843 -0.0421 0.0033 -0.6081 w_other 0.0024 0.0003 -0.0054 0.0229 0.0070 -0.0543 -0.1838 0.1374 0.0085 1.0104

restrictio

ns 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000

mean(wcereal=0.208), mean(wmeat=0.372), mean(wother food=0.42)

• Exercise calculation of Detailed Demand Elasticity

Table 15. Price, Income and Demographic Demand Elasticities - ISMEA Data

nchild age edu north centre lp_panal lp_meat lp_food lspesa Mean w w_cereal 0.0088 -0.0231 0.0420 0.0124 -0.0065 -0.5680 -0.0020 -0.4591 0.9433 0.2077 w_meat -0.0123 -0.0317 0.0280 -0.0305 -0.0005 -0.0952 -0.5048 -0.1130 1.0088 0.3721 w_other 0.0065 0.0395 -0.0456 0.0208 0.0037 -0.1293 -0.4375 -0.6730 1.0202 0.4202

mean 1.166 51.1216 3.5768 0.3832 0.2212

The elasticities have been calculated as in the semi-log specification in share form of the time-series exercise:

Recall: ln q = ln w(p,y,d) - ln p + ln y

Ep = ∆ ln q / ∆ ln p = (∆ ln w / ∆ w) (∆ w / ∆ ln p ) - 1 = γij / wi - 1

Ey = ∆ ln q / ∆ ln y = (∆ ln w / ∆ w) (∆ w / ∆ ln y) +1 = βi / wi + 1

• A Note on the Calculation of the Demographic Elasticity


35

We need to consider two possible cases according to whether the demographic variables enters in the demand function in the logarithms or in the anti logarithms :

1. Logarithm: ln d

Ed = ∆ ln q / ∆ ln d = (∆ ln w / ∆ w) (∆ w / ∆ ln d ) = δ ik / wi

2. Antilogarithm: d

a) ∆ ln q / ∆ d = (∆ q / ∆ d) (1 / q) = (∆ ln w / ∆ w) (∆ w / ∆ d ) = δ ik / wi

b) Ed = ∆ ln q / ∆ ln d = [(∆ q / ∆ d) (1 / q)] d = (δ ik / wi ) d.

As you can see by looking at table 10 reporting the descriptive statistics of the Italian household survey, our case is case 2. The mean of the demographic variables are also reported at the bottom of the table with the results.

The interpretation of these results is left to the reader.

• Quadratic (nonlinear) demographic and income effects

Table 16. Estimates of the cereal equation with quadratic demographic and income effects (R2=.716)

w_panal Coef. Std. Err. t P>|t| [95% Conf. Interval]

nchild 0.0053 0.0030 1.7700 0.0770 -0.0006 0.0111 nchild2 -0.0011 0.0008 -1.4000 0.1600 -0.0026 0.0004 age -0.0001 0.0001 -0.8100 0.4180 -0.0003 0.0001 edu 0.0025 0.0016 1.5300 0.1260 -0.0007 0.0057 nord 0.0070 0.0032 2.2000 0.0280 0.0008 0.0132 centro -0.0061 0.0037 -1.6600 0.0970 -0.0134 0.0011 lp_panal 0.0897 0.0017 51.9500 0.0000 0.0863 0.0931 lp_carni -0.0003 0.0030 -0.1100 0.9090 -0.0062 0.0055 lp_food -0.0956 0.0067 -14.3400 0.0000 -0.1087 -0.0826 lspesa (dropped) lspesa2 -0.0061 0.0015 -4.1100 0.0000 -0.0091 -0.0032 _cons 0.6021 0.0545 11.0500 0.0000 0.4952 0.7090

The results show that there are no economies of scale in cereal consumption due to the presence of extra children because the parameter associated with the quadratic demographic variable nchild2 is not significantly different from zero. The presence of a quadratic income term lspesa2 is redundant to the point the lspesa is dropped from the estimation. This evidence favors the hypothesis of linearity of the income effect as we were expecting from the results of the nonparametric Engel curve analysis. Overall, the nonlinear specification adds no further explanatory power with respect to the linear model. The R2 of the linear and nonlinear specification of the cereal equations are virtually the same.

2.2. Advanced Demand Analysis

• The Consumer Maximization Problem

• Let U(x) be an ordinal utility function representing household preferences (how a consumer trades one good for another as described by an indifference curve) increasing and concave in the quantities x.

• In general, the consumer maximize his own utility subject to the budget (total expenditure) constraint:

Training Materials

36

== ∑ yxptosubjectxUMaxypVi

iix : )(),(

where V(p,y) is the observable indirect utility function. The solution of the maximization problem by solving the Lagrangean expression gives the Marshallian demands

x*(p,y)

Note that when we substitute the optimal choices x*(p,y) we obtain the indirect utility V(p,y).

Note further that the Max of U(x) subject to total expenditure is equivalent to minimize total expenditure subject to a utility level u=U(x).

2.2.1. Duality Theory

A demand system derived from a known utility (preference) allows us to recover the unobservable cost function using the theory of duality.

The EXPENDITURE function C ( p, u ) is the minimum expenditure that can be attained while maintaining a given level of utility:

{ }),( '),,( dxUtoUsubjectxpMindupCY −+=

The solution to this minimization problem gives the Hicksian demand functions:

Xc (p, u) (which is not observable)

Note: the expenditure function C(p,u,d) is increasing in p, u, homogenous of degree 1 and concave in p; demands Xc (p, u) are homogenous of degree 0.

The INDIRECT UTILITY function V(p,y)

C(p,u)=Y and V(p,y) are inverse functions, where u=V.

• Why own price elasticities must be negatively sloped?

Answer: Because the cost function is concave

DERIVATIVE RESULTS

Shephard’ s Lemma to obtain Hicksian demands from the cost function

),(),( upxpupC c

ii

=∂

∂

Or, in the logarithms:

iiii

iiw

ypx

Cp

pupC

pupC

==∂

∂=

∂∂ ),(

ln),(ln

Roy’s identity to obtain Marshallian demands from the indirect utility function

),(*),(),(

ypxyypVpypV

ii =

∂∂∂∂

−

Note: the price elasticities [( ∂ x/ ∂p) p/x] are the matrix of second derivatives of the cost function multiplied by p/x. The component ( ∂ 2 C(u,p) / ∂p2) = ( ∂ xc/ ∂p) is a symmetric negative matrix. This explains why the own price elasticities must be negative!

• The Slutsky equation: price (substitution) and income effects

The reader may also refer above were substitution and income effects have been studied using a


37

graphical approach. The illustration here is analytical.

By duality theory, at the optimum, holds the following equality:

Xc (p,u) = X*(p,y)=X*(p,C(p,u))

Non observable Observable

By differentiating with respect to p:

iii

c

pupC

yypx

pypx

pupx

∂∂

∂∂

+∂

∂=

∂∂ ),(),(*),(*),(

or, using the derivative property (Shephard’s Lemma):

Compensated non compensated

),(*),(*),(*),( ypxyypx

pypx

pupx

ii

c

∂∂

+∂

∂=

∂∂

Price Income effect

(Non observable) Observable

which is the Slutsky matrix of first derivatives of the Hicksian quantities (= the elasticities if we take logarithms, and derive the matrix of second derivatives of the cost function). As before, it must be symmetric and negative (that is, all the elements in the diagonal must be negative). Note: the hicksian quantities are compensated by the income effect. Hicksian effects are not directly observable but can be estimated as the sum of the observable Marshallian price effect and the income elasticity.

The total effect of a price change can be decomposed in two components:

(1) the income effect, which is the change in quantity demanded resulting from a change in income holding prices constant;

(2) the substitution effect, which is the change in quantity demanded resulting exclusively from a relative price change ( a change in terms at which one product can be exchanged for another) after compensating the consumer for the change in real income.

Intuitively, when a price changes, everything else held constant, the real purchasing power of the or real income of the consumer also changes. For example, if a product price falls, real income rises to maintain indirect utility constant and vice versa.

2.2.2. Empirical Implementation: The Almost Ideal Demand System (AIDS)

Let us choose a general representation of preferences (They are unobservable since utility cannot be observed directly, but we estimate observable demands and then we recover C(u,p) and U(x), V(p,y) by going back to the preferences we derived demand from)! So,

Y=C(u,p,d)=(A(p)uB(p))D(p,d)

where u is a utility level, p are prices, and d are demographic variables. In the logarithms:

lnC(u,p,d)=(lnA(p)+B(p) lnu)+lnD(p,d)

We need first to specify a functional form also for the index functions A(p) and B(p):

∑ ∑∑++=i i j

jiijii ppppA lnlnln5.)(ln 0 γαα

Training Materials

38

∑∏ ==i

kiii

i dpdpDppB i lnln),(ln and ,)( 0 ββ β

So, let us derive the demand in share form w= (p x)/y by taking the derivative with respect to prices of ln C(u,p,d) by using the derivative property (Shephard’s Lemma):

ii

wpdpuC

=∂

∂ln

),,(ln

and after substitution for u, we obtain:

∑ ∑

+++=

ki

jjijkkii pA

ypdw)(

lnlnln βγδα

which is the AIDS system of demand equations.

Observe that they are like Engel functions with the inclusion of prices!.

• Estimation

The AIDS specification provides the basis for an econometric estimation of the demand parameters

Note: the specification of ln A(p) makes the model non linear. We can linearize the model using Stone’s approximation:

ln A(p) ≈ iΣ w i ln p i = P

Stochastic Specification:

ik

ij

jijkkii epAypdw +

+++= ∑ ∑ )(

lnlnln βγδα

where e is a random variable (error) with mean zero and finite variance.

• Theoretical Restrictions

The structure about the shape of C(u,p,d) (must be concave) and the requirement of homogeneity 1 in prices implies the following restrictions:

∑ ∑∑∑∑ =====i j

ji

ij

iji

iji 0,0;1 δβγγα

and symmetry: γij = γji .

Note 1. The theoretical restrictions implied by consumer theory: homogeneity and symmetry can be tested using standard statistical tests.

Note 2. Because by definition the shares sum to 1, the dependent variables are linearly dependent, so the variance of the error e is singular. Hence, when estimating we must drop one equation. The parameters from the equation dropped can be recovered from the restrictions. The parameter estimates are invariant to the equation dropped if maximum likelihood is used.

• Elasticities in the AIDS model

Matrix of Own price elasticities

ii

ijii wE β

γ−+−= 1


39

Matrix of Cross price elasticities

ji

i

i

ijij w

wwE

βγ−=

Vector of income elasticities

i

ii w

βη +=1

Note: if β < 0 => the good is a NECESSITY

If β > 0 => the good is a LUXURY

Trick to derive the elasticities: Try it!

Let w=pq/y → ln w = ln p + ln q - ln y → ln q = ln w -ln p + ln y.

Then,

pypw

pq

ln)lnln(ln

lnln

∂−−∂

=∂∂

price elasticity

yypw

yq

ln)lnln(ln

lnln

∂−−∂

=∂∂

income elasticity

2.2.3. Cost of Living Indexes and Compensating Variations

The Cost of living index measures the relative costs of reaching a given standard of living under two different situations.

The most convenient scale with which to measure welfare is the expenditure necessary at constant prices to maintain the various welfare levels being considered.

These concepts which use money to measure changes in welfare are limited to the measurement of quantities and prices that arise in the market. So, we do not consider goods that are important for consumers’ well being but are not purchased through the market. Examples are health care, natural areas, clean air, or the smile of a child in a household.

Definition. The Cost of Living Index: A cost of living index (CLI) is the ratio of the minimum expenditure necessary to reach the reference indifference curve at the two sets of prices.

Hence, if ur is the label of the indifference curve taken as reference, the true CLI is:

P(u, p1,p0) = C(u, p1) / C(u,p0)

• The Compensating Variation

Since the Hicksian demand functions are the derivatives of the cost function, integration gives the difference in costs of reaching the same indifference curves at two different price vectors. This is an exact measure of consumer surplus.

Instead of using index numbers based on ratios, we have compensating variations (CV) in terms of differences expressed as money measures rather than pure numbers. This is usefully to compare welfare effects of government policies.

Definition. Compensating Variation: CV is the minimum amount by which consumers should be compensated after a price change in order to be as well off as before the change:

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CV = C(u, p1) - C(u,p0)

The GAUSSX program that follows implements all the above concepts applied to a time series data base of consumption data for the United States. As an exercise interprets the results.

2.2.4. A GAUSSX program for advanced demand analysis

CREATE (a) 1950 1992 ; ? We are interested in analyzing US Consumption behavior. So, we obtained ? time series data on aggregate consumption during the period 1950-1992. ? The data includes price (pi) and quantity (Qi) information on 3 ? commodity groups: 1=food; 2= durable goods; and 3= non durable goods. LOAD YEAR = 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 ; LOAD P1= 25.4 28.2 28.7 28.3 28.2 27.8 28.0 28.9 30.2 29.7 30.0 30.4 30.6 31.1 31.5 32.2 33.8 34.1 35.3 37.1 39.2 40.4 42.1 48.2 55.1 59.8 61.6 65.5 72.0 79.9 86.8 93.6 97.4 99.4 103.2 105.6 109.0 113.5 108.2 125.1 132.4 136.3 137.9 ; LOAD P2= 34.9 37.9 38.0 37.7 36.8 36.1 36.1 37.2 37.8 38.4 38.1 38.1 38.5 38.6 39.0 38.8 38.9 39.4 40.7 42.2 44.1 46.0 46.9 48.1 51.5 57.4 60.9 64.4 68.6 75.4 83.0 89.6 95.1 99.8 105.1 106.8 106.6 108.2 110.4 112.2 113.4 116.0 118.6; LOAD P3= 27.0 29.5 29.8 29.7 29.7 29.5 29.9 30.9 31.7 31.5 32.0 32.2 32.5 32.9 33.2 33.8 35.1 35.7 37.1 38.9 40.8 42.1 43.5 47.5 54.0 58.3 60.5 64.0 68.6 77.2 87.6 95.2 97.8 99.7 102.5 104.8 103.5 107.5 111.8 118.2 126.0 130.3 132.8; LOAD Q1 = 2.122 2.152 2.233 2.311 2.368 2.467 2.550 2.598 2.579 2.717 2.753 2.789 2.846 2.877 3.003 3.136 3.224 3.293 3.444 3.517 3.625 3.651 3.764 3.653 3.595 3.653 3.831 3.906 3.897 3.917 3.937 3.924 3.963 4.086 4.168 4.271 4.374 4.411 4.514 4.517 4.568 4.559 4.595; LOAD Q2 = 0.882 0.797 0.771 0.867 0.871 1.077 1.057 1.067 0.984 1.114 1.141 1.100 1.220 1.341 1.456 1.636 1.760 1.7922 1.990 2.042 1.934 2.113 2.360 2.579 2.388 2.339 2.627 2.835 2.949 2.840 2.560 2.550 2.486 2.755 3.024 3.304 3.654 3.731 3.959 4.094 4.0942 4.002 3.914; LOAD Q3 = 3.637 3.699 3.849 3.966 4.028 4.227 4.373 4.436 4.470 4.714 4.782 4.889 5.040 5.147 5.414 5.677 5.940 6.076 6.334 6.483


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6.627 6.729 7.016 7.148 7.051 7.136 7.468 7.663 7.893 7.944 7.795 7.817 7.896 8.202 8.517 8.772 9.200 9.405 9.604 9.725 9.718 9.397 9.220; ? Data generation section GENR E1 = P1.*Q1; ? expenditure on food GENR E2 = P2.*Q2; ? expenditure on durables GENR E3 = P3.*Q3; ? expenditure on other goods GENR II = E1+E2+E3; ? Total expenditure GENR W1= E1./II; ? food share GENR W2= E2./II; ? durables share GENR W3= E3./II; ? other goods share GENR LNII=LN(II); ? ln of tot expenditure GENR LNP1=LN(P1); ? ln of p1 ? This is the Stone's Price Index to linearize the model GENR LP = W1.*LN(P1)+W2.*LN(P2)+W3.*LN(P3); ? Descriptive statistics of all the data cova(d) P1 P2 P3 Q1 Q2 Q3 W1 W2 W3 E1 E2 E3 II LP ; ? Let us learn from the data non parametrically, ? that is, without choosing a functional form for f: w=f(p,y,d) h = 0; genr w1s = sortc(w1,1); ? we sort the data to order it for plotting genr w1shat = npe(w1s,w1s,h); ? we smooth the series plot (p,d) w1s w1shat; ? we plot the food share and food price h=0; genr p1s = sortc(p1,1); genr p1shat = npe(p1s,p1s,h); plot (p,d) p1s p1shat; ? I. non parametric relation (npr) between w and p npr (d,p) w1 lnp1; ? command asking for NonParametric Regression replic = 50; window = 2; oplist = cv direct; ? or cv print (fourier default) title = "Non parametric w and ln p relation"; forcst yhatwp; ? nonparametric forecast oplist = nocv; graph (p,h,m) yhatwp lnp1; ? II. relation between w and y (The Engel relation) npr (d,p) w1 lnii; ? command asking for NonParametric Regression replic = 50; window = 2; oplist = cv direct; ? or cv print (fourier default) title = "Non parametric Engel curve"; forcst yhateng; ? nonparametric forecast oplist = nocv;

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graph (p,h,m) yhateng lnii; ? Estimation of a complete demand system PARAM a0 a1 a2 a3 a11 a12 a13 a21 a22 a23 a31 a32 a33 b1 b2 b3 ; ? Unrestricted model FRML eq1a W1= a1+ a11*LN(P1) + a12*LN(P2) + a13*LN(P3) +b1*(LN(II)-LP); FRML eq2a W2= a2+ a21*LN(P1) + a22*LN(P2) + a23*LN(P3) +b2*(LN(II)-LP); NLS (i,d) eq1a eq2a ; LLU = LLF ; ? Homogeneity restriction (a13=-a11-a12) imposed FRML eq1b W1= a1+ a11*LN(P1) + a12*LN(P2) + (-a11-a12)*LN(P3) + b1*(LN(II) -LP); FRML eq2b W2= a2+ a21*LN(P1) + a22*LN(P2) + (-a21-a22)*LN(P3) + b2*(LN(II)-LP); NLS (i,d) eq1b eq2b ; LLH = LLF ; ? Symmetry restriction (a12=a21) imposed FRML eq1c W1= a1+ a11*LN(P1) + a12*LN(P2) + a13*LN(P3) +b1*(LN(II)-LP); FRML eq2c W2= a2+ a12*LN(P1) + a22*LN(P2) + a23*LN(P3) +b2*(LN(II)-LP); NLS (i,d) eq1c eq2c ; LLS = LLF ; ? Both homogeneity and symmetry restrictions imposed FRML eq1d W1= a1+ a11*LN(P1) + a12*LN(P2) + (-a11-a12)*LN(P3) +b1*(LN(II)-LP); FRML eq2d W2= a2+ a12*LN(P1) + a22*LN(P2) + (-a21-a22)*LN(P3) +b2*(LN(II)-LP); NLS (i,d) eq1d eq2d ; LLHS = LLF ; ? Hyppothesis testing TEST LLU LLH ; METHOD = LRT ; order = 2; TEST LLU LLS ; METHOD = LRT ; order = 1; TEST LLU LLHS ; METHOD = LRT ; order = 3; TEST LLH LLHS ; METHOD = LRT ; order = 1; ? recovery of the parameters of the omitted equation ? (see your note: implementation) a3 = (1 -a1 -a2); ? from the adding up to 1 of the shares b3= (-b1 -b2); a31= (-a11 -a12); ? from homog of degree 0 in prices a32= (-a21 -a22);


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a33= (-a13 -a23); ? Computation of the std errors of the omitted parameters ? ANALYZ (p,d,v) eqp1 eqp2 eqp3 eqp4 eqp5; cova (p,d) w1 w2 w3; fetch w1 w2 w3 II p1 p2 p3; ? Computation of the elasticities at the data means w1m=meanc(w1); w2m=meanc(w2); w3m=meanc(w3); ey1=1+b1/w1m; ? income elasticities ey2=1+b2/w2m; ey3=1+b3/w3m; e11=-1+a11/w1m-b1; ? own price elasticities e22=-1+a22/w2m-b2; e33=-1+a33/w3m-b3; e12=a12/w1m-b1*(w2m/w1m); ? cross price elasticities e13=a13/w1m-b1*(w3m/w1m); e21=a12/w2m-b1*(w1m/w2m); e23=a23/w2m-b1*(w3m/w2m); e31=a31/w3m-b1*(w1m/w3m); e32=a32/w3m-b1*(w2m/w3m); eyy=ey1|ey2|ey3; @@ "vector of income elasticities" eyy; mat_e=e11~e12~e13|e21~e22~e23|e31~e32~e33; @@ "matrix of price elasticities" mat_e; ? The Slutsky equation in elasticity form: matrix of compensated elasticities ? That is, compensated by the income effect! ? e11_c=e11+ey1*w1; ? compensated price elasticity ? e12_c=e12+ey1*w2; .... ? w1*e11_c; ? own term of the Slutsky equation ? The recovery of the cost function A_p=exp( a1*ln(p1)+a2*ln(p2)+a3*ln(p3)+ 1/2*( a11*ln(p1).*ln(p1)+a12*ln(p1).*ln(p2)+a31*ln(p1).*ln(p3)+ a12*ln(p2).*ln(p1)+a22*ln(p2).*ln(p2)+a32*ln(p2).*ln(p3)+ a31*ln(p3).*ln(p1)+a32*ln(p3).*ln(p2)+a33*ln(p3).*ln(p3) ) ); B_p=(p1^b1).*(p2^b2).*(p3^b3); lnu=(ln(meanc(II))-ln(meanc(A_P)))/meanc(B_p); ? the mean level of u Costf=exp(ln(A_p)+B_p*lnu); @@ "The mean of total expenditure=income" meanc(costf); ? The cost of living

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Output

Estimated Elasticities and Welfare Analysis

Vector of income elasticities

ey1 0.7554 Food

ey2 1.6398 Durables

ey3 0.9164 Other goods

Matrix of Marshallian own and cross price elasticities

Food Durables Other goods

Food -0.483 -0.104 -0.184

Durables -0.124 -0.553 -0.174

Other goods -0.121 -0.110 -0.663

Note 1: all own price elasticities in the diagonal are negative as required by the theory!!

Note 2: goods can be defined as

Complements: if the cross price elasticity is < 0.

(Ex. coffee and sugar).

Substitutes: if the cross price elasticity is > 0.

(Ex. butter and margarine).

The mean of total expenditure=income

C(u,p) = Y = 847.04417807

The cost of living index of 1951/1950

C(u,p_1951)/C(u,p_1950) = 1.09099598

The compensating variation

CV=C(u,p_1951)-C(u,p_1950) = 37.11242740


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Chapter 3 - Supply Response

3.1. Introductory Supply Analysis

The supply response for crops can be studied for yield, area, or output in the short or in the long run.

Definition. Short run: producers can alter only the level of variable factors. Land and household labor supply, for example, cannot be changed.

Definition. Long Run: producers can vary all factors of production and producers and resources can enter or leave the industry.

The elasticity of supply response is smaller in the short run since fixed factors are not a decision variable. Long run elasticities of supply response can be very high since fixed factors become increasingly variable and can be reallocated. Further, if output grows as a consequence of new entrant firms or farms, then an expansion of supply can be achieved without large price rises and the supply curve can be quite flat.

In general, the elasticity of yield is smaller and more unstable than the elasticity of area and, of course, of output which is the sum of the two.

• Risk and Uncertainty

Farmers operate under uncertainty with respect to yields, and prices of inputs and outputs. Failing to recognize this fact in the modeling strategy may result in inadequate analysis.

The perception of uncertainty is subjective. For this reason, when uncertainty is taken into account, the utility of profit rather than profit itself, is the object of interest. Therefore, in un uncertain environment where outcomes realize with a probability of occurrence, the producer maximize expected utility. Utility describes the farmer’s attitude to the variability of outcomes (risk).

In general, the farmer in developing countries is risk averse. The farmer is willing to pay in order to avoiding risk. If farmer is risk averse and the product price is uncertain, then a smaller level of output is produced than under perfect certainty. The farmer does not equate marginal cost to (average) price but produce at a point where marginal cost is less than that price. The difference is the equivalent amount of money the farmer is willing to pay to “buy” certainty.

3.1.1. Approaches to the estimation of supply response

There are two approaches to the estimation of supply response:

A) Indirect Structural Form Approach

we first estimate the structure (a profit or a cost function), then we derive the input demand and output supply response -This approach is more theoretically rigorous but fails to take into account the partial adjustment in production and the mechanism used by farmers in forming expectations.

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B) Direct Reduced Form Approach

Direct Estimation of the Supply Response including Partial Adjustment and Expectations Formation -The Nerlovian Model

We study method B.

The Nerlovian Models of Supply Response

How do agricultural producers make decisions?

In agriculture the OBSERVED PRICES are known after production has occurred, while planting decisions are based on the prices farmers EXPECT to prevail later at harvest time. Because of this time lag, it is crucial to model the formation of expectations in the analysis of agricultural supply response.

Similarly, OBSERVED QUANTITIES may differ from the DESIRED ones because of the adjustment lags of variable factors. When a price changes, it may take several years (or never) before farmers can reach their desired production patterns given the new price setting.

The specification of these adjustment lags is the essence of Marc Nerlove’s (University of Maryland) model.

• The Nerlove specification

Let us suppose that we are interested in the supply response of a DESIRED area to be allocated to a crop at time t. The relation of interest can be expressed as a function of expected relative prices and exogenous shifters as follows:

qtd = α1 + α2 pt

e + α3zt + ut

where:

qtd = desired cultivated area in period t

pte = a set of expected relative prices including the p of the crop, competing crops, and

factor prices

zt = set of exogenous shifter (analogous to demographic information in demand analysis) such as weather, political factors, farmers education, technical change

ut = accounts for unobserved random factors; it has an expected value of zero

α2 = is the long run coefficient (or elasticity in a double log model) of supply response.

Notation: the d superscript means desired, the e superscript means expected.

Note: both expected prices and desired quantities are not observable.

• The AREA adjustment

Full adjustment of the DESIRED allocation of land may not be complete in the short run. Therefore, the ACTUAL adjustment in area will only be a fraction δ of the desired adjustment:

qt -qt-1 = δ ( qtd -qt-1 ) + vt,

where:

qt = actual area planted of the crop,

δ = PARTIAL ADJUSTMENT coeffic. with 0 ≤δ ≤ 1,

vt = spheric random error (with mean zero and finite variance).

• The PRICE adjustment

The farmer’s expected price at harvest time cannot be observed. So, we have to formally


47

describe how decision makers form expectations based on the knowledge of actual and past prices and other observable information. We may think that farmers maintain in their memory the magnitude of the mistake they made the previous period and LEARN by adjusting the difference between actual and expected p in t-1 by a fraction γ:

pte -pt-1

e = γ ( pt-1 -pt-1e ) + wt, with 0 ≤ γ ≤ 1, or

pte = γ pt-1 + (1 - γ ) pt-1

e + wt,

where:

pt-1 is the price at the time decisions are made, γ is the ADAPTIVE expectation coefficient, and wt is a spheric random error, that is with zero expectation. An alternative interpretation of this learning process is that the expected price pt

e is the weighted sum of all past prices of which farmers have memory with a geometrically declining set of weights:

pte = γ ∑

∞

i

(1-γ)i-1 pt-i .

Note: for i=1, .., 3, pte = γ pt-1 +γ (1 - γ ) pt-2 + γ (1 - γ )2 pt-3.

• The REDUCED form

Since pte and qt

d are not observable, we need to derive an estimable expression. Take the pte

equation expressed as the weighted sum of all past prices and insert in qtd. Then insert the qt

d equation into the partial area adjustment equation qt. Rearranging we obtain the following ESTIMABLE reduced form:

qt = π1 +π2 pt-1 + π3 qt-1 + π4 qt-2 +π5 zt +π6 zt-1 + et, where:

π1 = α1 δ γ,

π2 = α2 δ γ, short run coefficient (elasticity) of supply response,

π3 = (1-δ)+(1-γ),

π4 = -(1-δ)(1-γ),

π5 = α3 δ,

π6 = α3 δ(1-γ), and

et = vt-(1-γ)vt-1+δut-δ(1-γ)ut-1+α2δwt.

The reduced form is overidentified: there are 6 reduced form coeff. π and 5 structural parameters α1, α2, α3, γ, and δ. So for a unique solution we need an extra restriction:

π62 -π4π5

2 + π3 π5 π6 = 0.

• Derivation of the reduced form

Objective: Estimate Short run and Long run supply elasticities

Structural Form (non estimable):

1) qtd=α1+α2 pt

e+α3zt+ut; α2 = long run elasticity

The desired area equation as a PARTIAL ADJUSTMENT process:

2) qt -qt-1 = δ ( qtd -qt-1 ) +vt

The expected price equation as an ADAPTIVE process:

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3) pte = γ ∑

∞

i

(1 - γ )i-1 pt-i

Estimable Reduced Form obtained after substitution of (1) and (3) into (2):

qt = π1 +π2 pt-1 + π3 qt-1 + π4 qt-2 +π5 zt +π6 zt-1 + et ; π2 = short Run elasticity

• Estimation and Recovery of the Structural Form

The model should be estimated by Maximum Likelihood techniques correcting for serial correlations in the error term. The structural coefficients can be recovered using the following set of equalities:

δ2 + (π3 - 2) δ + 1 - π3 - π4 = 0, ≥ δ=1- π3 using –b ± ( b2-4ac)½ /2a and π4=0

γ= 1 + π4/(1-δ),

α1 = π1 / δγ,

α2 = π2 / δγ, the long run coef. (elasticity) of supply response,

α3 = π5 / δ.

Note that the short run price response π2<α2= π2 / δγ , the long run price response since both δ and γ are less than 1, as expected!

• Simplified models with either no Partial Adjustment or no Price Expectations

The Nerlove models admits several estimable versions depending on the economic and institutional situations that we are studying. These situations help model identification (the possibility to uniquely determine the parameters of the structural form) because we have either no partial adjustment δ = 1 or no expectation formation γ=1.

In some cases, areas are fully adjusted in a year span, implying qtd=qt and δ = 1. In cases when

administered prices are announced at planting time so are known with certainty by farmers implying pt

e=pt-1 and γ = 1.

Note: when γ = 1, the model is exactly identified. In all models, though, with either γ = 1 or δ = 1, the long run supply elasticity of supply response is

α2 = π2 / δγ= π2 / (1- π3)

Note: in all these models pt-1, qt-1 are exogenous variables.

• Critique of the Nerlovian Model

Nerlove’s adaptive expectations are based on the history of past prices with weights declining geometrically over time:

pte = f ( past prices ) = γ ∑

∞

i

(1 - γ )i-1 pt-i

This approach has been criticized because:

A. Price weights are ad hoc instead of being determined optimally or actually corresponding to the length of farmers’ memory;

B. Price predictions do not take fully account of the information available to farmers:

1) price predictions are formed using structural market information, that is information on both supply and demand;

2) farmers may use available forecasts about prices and about exogenous variables


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affecting the process such as rain;

3) farmers may take into account anticipated policy changes affecting price formation: Lucas’ critique (Lucas, 1976).

The Rational Expectation Model

Rational expectations (Muth, 1961) reproduce the process of formation of expectations based on both sides of market information. We assume that farmers do not make decisions only on past prices, but forecasts are based on

a) knowledge of a structural model of price determination, that is they think as if they understood the market,

b) exogenous forecasts of the independent variables in the model, and

c) expectations about the policy instruments in the model. Rational expectations thus use the model prediction’s of the endogenous variables, including PRICES, to form expectations:

pte = f ( model prediction I exogenous variables forecasts and expected policy changes ).

• Critique of the Rational Expectation Model

In general, the approach relies too heavily on rational behavior in forming expectations and on an easy access to information.

A. Agents may not use all the information that is potentially available to them, because acquiring it is costly (Farmers’ organization play an important role in distributing information and forming farmers in interpreting it!). Sometimes, though they are fully informed still do not act rationally (in the sense, as expected) because they may face constraints not revealed in market behavior.

B. Agents may not use the information as intelligently as the model. They do not know the model, but interpret the market signal subjectively. So the same market signal may be interpreted differently by farmers. After all, they have incomplete information. At the same time, farmers subjective predictions may perform better than the model ....

C. Agents may not know how to forecast the exogenous variables and policy changes.

Empirically rational expectations has not proved its superiority to ad hoc specifications such as the Nerlovian adaptive hypothesis. But adaptive expectations are too naive. We may improve our formal understanding of the formation of expectations if we can account for how farmers think about the future, the cost of accessing information and their ability to process it, quality and expected benefits from the use of information.

3.2. An Introductory Exercise

3.2.1. The Colombian Rice Economy: Supply side

Purpose of the Exercise:

Obtain an unbiased estimate of the price elasticity of supply to complete the market model of the Colombian rice industry.

Farmers do not respond only to prices. The state of technology, the natural, economic and institutional environment should be taken into account as well. Yield and price (of both outputs and inputs) uncertainty are also very important. Rational farmers are in general risk averse and may be very prudent towards innovations that may increase uncertainty. Small farmers are more sensitive to risk with respect to rich farmers. In the case of Colombia, rice producers in

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rainfed areas where more cautious in adopting because the modern varieties were not appropriate for their environment, and therefore more risky, and experienced a more difficult access to information. Let us see what the data are going to tell us about our conjectures.

In our data base we do not have production or price information about competing crops such as corn or sorghum or other crops. Therefore, we will first estimate a model with no behavioral assumptions with just price information. We then add more information about technical change and the proportion of irrigated area. Our specification exercise for the selected double-log functional form, that was maintained the same for all models, continues by adopting a Nerlovian specification. We then estimate the same specification both for the rainfed and irrigated production. The interpretation and comparison of the results are left to the reader as an exercise.

Plan of the exercise:

Cobb-Douglas (univariate double log regression)

ln q = ln B + B1 ln p = B pB1

Cobb-Douglas with technical change and other shifters

ln q = (b0 + b01 ln %Irr + b02 DT) + b1 ln p

Nerlove model: Dynamic Cobb-Douglas with technical change and other shifters

ln q= (b0 + b01 ln %Irr + b02 DT) + b1 ln p(-1)+ b2 ln q(-1)

where D T is a linear trend capturing the effect of technical change and %Irr is the proportion of irrigated rice production. Now, let us refer back to our Colombian data base.

Regression of Rice Production | Price (Total Production)

Let us specify a double logarithmic specification:

• ln q = ln B + B1 ln p = B pB1

Coefficients

Standard Error

t Stat

Intercept 24.0887 4.1898 5.7494

Price -1.5076 0.5848 -2.5779

R2=0.259

The price explains only 26 percent of the observed variation of supply (R2=0.259). The price coefficient is significant, but has the wrong sign. The elasticity (-1.51) is quite high.

The negative sign of the price coefficient is not surprising if we remind the “treadmill” effect that we found exploring the data. Quantity produced was indeed increasing in spite of decreasing prices. We need to control for other effects such as technical change and the differential rate of adoption between rainfed and irrigated producers.

As we learned from the data, we can now improve our specification by adding the variable describing the effect of linear technical change and of other shifters such as the proportion of irrigated production.

Regression of Rice Production | Price controlling for Technical Change

Recalling our observations about the characteristic of technical change when we were familiarizing with the data, we found reasonable to represent technical change as a linear trend, that is, increasing at a constant rate.


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Technology acted also as a structural break. When modern varieties were introduced, the technology previously used to produce rice changed radically especially in the irrigated sector. To account for the effect of the adoption of new varieties after 1966, we may construct a dummy taking the value of zero before 1966, and 1 after 1966 capturing the effect of the adoption of new varieties after 1966. The variable used in the regression analysis DT as a proxy for technical change is the interaction of the dummy and the trend because, as a matter of fact, technical change occurred only after the institutional change also took place, that is the creation of the Colombian National Research Institute and of CIAT that had a key role in making the modern varieties available to farmers, and, of course, after the adoption. Therefore, the variable DT is a vector with elements = 0 until 1966, and sequence from 1 to 8 with increments of 1 from 1967 to 1974.

• ln q = (b0 + b01 ln %Irr + b02 DT ) + b1 ln p

Coefficients

Standard Error

t Stat

Intercept 4.5534 6.7955 0.6701

%Irrig -0.4359 0.9566 -0.4557

Year=tech 0.2317 0.0516 4.4950

Price 1.4185 0.5780 2.4542

R2=0.814

The model with technical change explains a much greater variation than the previous model does and the sign of the price coefficient is now coherent with the theory. This is another example supporting the importance of the pre-estimation phase that requires a thorough knowledge of the market and of the collected data.

The elasticity associated to the shifter corresponding to the proportion irrigated is not significantly different from zero. In the context of the present specification, technology is highly significant. The price elasticity of supply (1.42) has the correct sign, is significant and quite elastic.

The Nerlove Model:

Regression of Rice Production | lag(prod), lag(price) while controlling for Technical Change

• ln q= (b0 + b01 ln %Irr + b02 DT) + b1 ln p(-1)+ b2 ln q(-1)

Coefficients

Standard Error

t Stat

Intercept 0.7888 3.8753 0.2036

%Irrig 0.1623 0.4895 0.3316

Year=tech 0.0128 0.0336 0.3823

Prod(-1) 0.9265 0.1143 8.1023

Price(-1) -0.0604 0.3405 -0.1775

R2=0.966

The Nerlove model explains a greater proportion of the supply variation if compared to the previous specifications. Technical change and the proportion of irrigated rice production are not significantly different from zero. The effect of technical change is absorbed by the effect of the change in previous year production. The signs comply with the theory.

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Short and Long Run Supply Elasticities

Short Run Price Elasticity: (b1) = -0.06

Long Run Price Elasticity: b1/(1-b2) = -0.0604/(1-0.9265) = -0.8218.

In line with our expectations, the long run supply elasticity is higher than the short run elasticity which is, in our example, not significantly different from zero. However, the sign of the long run elasticity is wrong. We may hypothesize that this is the result of aggregate behavior. So, let us see what the separate analysis of rainfed and irrigated production tell us. First, a simple simulation.

Suppose now that the Colombian government would like to increase the price of rice by 10 percent in 1975. What would you expect the production to be in 1975, 1976 and 1977?

Year Index of price change

% Expected changes in prod

Rice price Rice production

1974 100 100 1151 1569940 1975 110 99.396 1266.1 1560451 1976 110 108.660 1266.1 1695587 1977 110 117.925 1266.1 1999513

Note that the price effect works only in the first year, when it is replaced by the past production impulse.

The Nerlove Model for Rainfed and Irrigated Colombian Rice Producers

Rainfed Producers

Coefficients

Standard Error

t Stat

Intercept 0.4184 2.2974 0.1821

Year=tech -0.0098 0.0229 -0.4274

Prod(-1) 0.7971 0.1329 5.9985

Price(-1) 0.2892 0.4478 0.6459

R2=0.866

Irrigated Producers

Coefficients

Standard Error

t Stat

Intercept 2.4781 2.2703 1.0915

Year=tech 0.0610 0.0335 1.8233

Prod(-1) 0.7898 0.1314 6.0121

Price(-1) 0.0290 0.3359 0.0862

R2=0.965

Home exercise: Compute the short run and long run price elasticity of supply and the impact of technical change for both rainfed and irrigated rice production. Interpret, compare and contrast your results across upland, rainfed and total production.


53

Price Elasticity of Supply of Agricultural Products in Syria

Product Period Short runPrice el.

Long runPrice el.

R2

Wheat 1961-72 0.64 3.23 .57Barley 1961-72 0.27 0.40 .50 Maize 1947-60 0.51 0.69 .84Millet 1961-72 1.21 1.60 -Potatoes 1950-60 0.65 1.30 .87

Source: Scandizzo and Bruce, 1980. 2 2

3.2.2. Estimation of a Nerlovian Supply Response Model for groundnuts in Senegal

First, let us share some background information about the economic and institutional situation of the Senegales Groundnut Market 1960-1988. Groundnuts represent the major source of income for Senegalese farmers and the main source of export earnings for the country. The government administers the price and extracts the positive difference between world price and producer price as government revenue. (So, we do not to explain how farmers form expectations about groundnut prices, since the government announces the price before planting time)!

The dramatic decline of world peanuts prices in the 1980s, also coinciding with the adoption of a structural adjustment program, forced the government to subsidize the sector.

Our main questions are:

What is the impact on farmer from the removal of this costly subsidy?

What is an acceptable combination between market AND state?

What is the impact of structural adjustment?

Further information:

millet market is free and farmers do not know the price at planting time (so, we need to model how farmers form expected prices for millet).

We use a lagged price to model expectations. Similarly for rainfall.

Note: This is very important for both a statistically and economically sound specification of the model!!!

Training Materials

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The data set

Current prices Real prices Year Area in groundnuts (1,000 ha) Groundnuts

(CFA/mt) Millet

Rainfall (mm)

Cons. price index

Groundnuts (1961 CFA/mt)

Millet

1960 1323 20500 22000 817 0.95 21652 23236 1961 1230 22000 22500 685 1.00 22000 22500 1962 1233 21500 23000 609 1.07 20101 21503 1963 1185 21500 25000 699 1.14 18873 21945 1964 1055 20600 25000 830 1.21 17039 20678 1965 1016 20600 25800 660 1.26 16401 20541 1966 1017 21000 22000 897 1.28 16355 17134 1967 1064 18000 23000 886 1.32 13678 17477 1968 1091 18000 23000 457 1.31 13730 17544 1969 1097 21200 24000 841 1.37 15520 17570 1970 1051 23100 23000 496 1.42 16256 16186 1971 1060 23100 29000 745 1.51 15288 19193 1972 1087 25500 22000 428 1.60 15977 13784 1973 1280 41500 37000 461 1.69 24513 21855 1974 1020 41500 35000 556 1.95 21282 17949 1975 1201 41500 42000 801 2.37 17533 17744 1976 1175 41500 55000 573 2.51 16508 21877 1977 1079 41500 65000 437 2.67 15520 24308 1978 970 41500 45000 637 2.87 14445 15663 1979 995 41500 45000 666 3.11 13344 14469 1980 1097 50000 45000 418 3.52 14209 12788 1981 1216 60000 55000 573 3.73 16100 14759 1982 1148 60000 75000 553 4.37 13730 17162 1983 925 60000 85000 337 4.88 12303 17429 1984 873 75000 95000 492 5.46 13741 17406 1985 750 75000 100000 546 6.16 12175 16234 1986 789 90000 100000 735 6.54 13761 15291 1987 823 90000 110000 809 6.82 13191 16122 1988 787 70000 115000 500 6.54 10700 17579


55

Data Preparation

Prices (1961 CFA) Last year

Year Area in groundnuts (1,000 ha)

Lag area in groundnuts

Groundnuts Millet

Rainfall last year

Previous three years mean

rainfall

Agricultural structural

adjustment 1979 - 88

t ln At ln At-1 ln Pg,t ln Pm,t-1 ln Rt-1 ln Rt-(1-3) DUM 1960 7.19 9.98 0 1961 7.11 7.19 10.00 10.05 6.71 0 1962 7.12 7.11 9.91 10.02 6.53 0 1963 7.08 7.12 9.85 9.98 6.41 6.56 0 1964 6.96 7.08 9.74 10.00 6.55 6.50 0 1965 6.92 6.96 9.71 9.94 6.72 6.57 0 1966 6.92 6.92 9.70 9.93 6.49 6.59 0 1967 6.97 6.92 9.52 9.75 6.80 6.68 0 1968 6.99 6.97 9.53 9.77 6.79 6.70 0 1969 7.00 6.99 9.65 9.77 6.12 6.62 0 1970 6.96 7.00 9.70 9.77 6.73 6.59 0 1971 6.97 6.96 9.63 9.69 6.21 6.39 0 1972 6.99 6.97 9.68 9.86 6.61 6.54 0 1973 7.15 6.99 10.11 9.53 6.06 6.32 0 1974 6.93 7.15 9.97 9.99 6.13 6.30 0 1975 7.09 6.93 9.77 9.80 6.32 6.18 0 1976 7.07 7.09 9.71 9.78 6.69 6.41 0 1977 6.98 7.07 9.65 9.99 6.35 6.47 0 1978 6.88 6.98 9.58 10.10 6.08 6.40 0 1979 6.90 6.88 9.50 9.66 6.46 6.31 1 1980 7.00 6.90 9.56 9.58 6.50 6.36 1 1981 7.10 7.00 9.69 9.46 6.04 6.35 1 1982 7.05 7.10 9.53 9.60 6.35 6.31 1 1983 6.83 7.05 9.42 9.75 6.32 6.24 1 1984 6.77 6.83 9.53 9.77 5.82 6.19 1 1985 6.62 6.77 9.41 9.76 6.20 6.13 1 1986 6.67 6.62 9.53 9.69 6.30 6.13 1 1987 6.71 6.67 9.49 9.63 6.60 6.38 1 1988 6.67 6.71 9.28 9.69 6.70 6.55 1

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Evolution of Acreage and Price of Groundnut

6.00

6.50

7.00

7.50

8.00

8.50

9.00

9.50

10.00

10.50

11.00

1960

1962

1964

1966

1968

1970

1972

1974

1976

1978

1980

1982

1984

1986

1988

Years

ln At

ln Pg,t

Lineare (ln At)

Log. (ln Pg,t)

Lineare (ln Pg,t)

Evolution of Groundnut Price

8.80

9.00

9.20

9.40

9.60

9.80

10.00

10.20

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

years

ln(P

gt)

Serie1


57

Acreage supply

6.30

6.40

6.50

6.60

6.70

6.80

6.90

7.00

7.10

7.20

7.30

1960

1962

1964

1966

1968

1970

1972

1974

1976

1978

1980

1982

1984

1986

1988

years

ln(A

t) Acreage supply

Acreage and price

6.50

6.60

6.70

6.80

6.90

7.00

7.10

7.20

7.30

9.20 9.30 9.40 9.50 9.60 9.70 9.80 9.90 10.00 10.10 10.20

ln(Pgt)

ln(A

t)

ln At

Log. (ln At)

Log. (ln At)

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Acreage Supply Response Equation for groundnuts in Sub-Saharan Africa

Regression Results: Estimates

(See Excel file 4supply fed2)

Dependent Lag area ln At-1

Prices (1961 CFA) Rainfall Structural adjustment 1979 - 88

variable Constant Current groundnut

ln Pgt

Millet ln Pm,t-1

last year ln Rt-1

Three-year average ln

Rt-(1-3)

Additive DUM

On price DUM*ln

Pgt

R2 adjusted

Short Run elast

1. lnAt 1.623 0.675 0.349 -0.341 0.091 0.821 1.804 5.387 3.865 -3.878 1.814 0.789

2. lnAt 1.668 0.621 0.338 -0.368 0.202 0.825 1.642 4.951 3.708 -4.125 2.420 0.792

3. lnAt 3.852 0.645 0.252 -0.423 0.052 -0.087 0.855 2.997 5.552 2.692 -4.771 1.064 -2.268 0.822

4. lnAt 4.136 0.648 0.239 -0.441 0.053 -0.009 0.852 2.889 5.531 2.425 -4.699 1.075 -2.161 0.818

5. lnAt 4.293 0.595 0.177 -0.372 0.075 -4.866 0.502 0.886 3.330 5.539 1.925 -4.201 1.653 -2.488 2.442 0.853

Note1: t-statistics in italic; adjusted R2 in italic = 1-[T/(T-K)](1-R2), where T is the number of observations and K the number of exogenous variables.

Note2: 1) since groundnut price is administered, then gamma=1, so delta=1-PI3=1-b1=>Long run el=pi2/(1-b1) (Hint: watch your definiton of pi3 in your notes).

2) when there is the interaction term DUM*ln Pgt, then the price elasticity=coeff(Pgt) +coeff(DUM*ln Pgt) when DUM=1.


59

Acreage Supply Response Equation for groundnuts in Sub-Saharan Africa

Regression Results: Elasticities

(See Excel file 4supply fed2)

Elasticities (at mean values) w.r.t. Groundnut price Millet price

Model Short Long pi2/(gam*delta)

Short Long

1 0.349 0.464 -0.341 -1.050 2 0.338 0.327 -0.368 -0.971 3 0.252 0.561 -0.423 -1.190 4 0.239 0.650 -0.441 -1.250 5 0.177 1.678 -0.372 -0.920

Actual and Estimated area of groundnuts: Model 1

6.3

6.4

6.5

6.6

6.7

6.8

6.9

7

7.1

7.2

7.3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

Years

Ln(A

t)

Y actual

Y predicted

Training Materials

60

Simulation and price policy analysis

1.5% increase/year

Estimated area in groundnuts Estimated area in groundnuts under alternative policy

Model 1 (1,000 ha)

best model 5 High price of groundnuts

new Pg,t (CFA/mt)

High price with struct.

adj. (1,000 ha)

No structural adjustment(1,

000 ha)

1323 1323 20808 1266 1274 22330 1215 1215 1213 1207 21823 1158 1158 1202 1189 21823 1169 1169 1152 1147 20909 1136 1136 1088 1093 20909 1098 1098 1072 1062 21315 1061 1061 1055 1063 18270 1131 1131 1071 1079 18270 1153 1153 1116 1083 21518 1144 1144 1108 1114 23447 1220 1220 1094 1067 23447 1178 1178 1071 1070 25883 1166 1166 1200 1162 42123 1400 1400 1191 1160 42123 1306 1306 1055 1036 42123 1246 1246 1090 1095 42123 1417 1417 1048 1033 42123 1262 1262 989 959 42123 1130 1130 964 991 42123 1170 1285 982 1050 50750 1309 1393 1052 1176 60900 1542 1542 1043 1087 60900 1469 1591 972 949 60900 1267 1450 900 908 76125 1174 1270 847 815 76125 1098 1264 804 833 91350 1140 1233 812 835 91350 1203 1329 791 727 71050 1049 1287


61

Chapter 4 - The Market Model

We are now ready to combine the two sides of the market to find an equilibrium price. First, it is instructive to review some basic notions of market equilibrium and analysis.

4.1. Causality in Economic Analysis

Let us think at the familiar supply and demand model. The price P0 is an equilibrium price because at this price all buyers are able to buy as much as they like and all suppliers are able to sell as much as they like. No other price will satisfy these conditions.

At a price above P0, for example, sellers could not sell as much as they desire. Each can remedy the problem by lowering the price a bit. Buyers will discover sellers are receptive to price discounts. The result is downward pressure on price and the pressure will continue as long as price remains above P0.

This analysis of demand and supply is of limited interest. The real significance of the model resides in a set of hypotheses not explicitly shown in the classic diagram as to variables that expand or contract demand and supply and therefore CAUSE price and quantity to change called shifters.

Demand shifters: population, per capita income, prices of related goods and consumer preferences.

Supply shifters: Number of sellers, input prices, weather, and technology.

4.1.1. Exogenous and Endogenous Variables in a Model

Definition. Exogenous Variable: Variables are EXOGENOUS to a model or theory if their values are determined by processes not described by the model.

Example: Demand and supply shifters.

Note: whereas changes in exogenous variables CAUSE changes in endogenous variables, changes in endogenous variables have NO EFFECT on exogenous variables. CAUSALITY flows in one direction. For example, weather can greatly influence grain prices BUT grain prices have no perceptible impact on weather .....

Definition. Endogenous Variables: Variables are said to be ENDOGENOUS if their values are determined jointly by processes described by the theory (a model).

Example: Price and quantities are endogenous variables because jointly determined by the model.

Note: the value of one does not imply the value of the other. It would be nonsensical to ask whether an increase in price would CAUSE quantity to fall ..... Price might rise because of a decrease in supply, in which case quantity falls.

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The interest in POLICY ANALYSIS is to ask how a change in an exogenous variable affects the values and the direction of change of an endogenous variable.

To ask how a change in one endogenous variable affects the value of another endogenous variable is a WRONG question.

A simple algebraic representation of a demand-supply model

The well-known graphical description of a market can be represented with a simple set of equations:

Qd = β0 -β1 Pd Demand

Qs = γ0 + γ1 Ps Supply

Qs = Qd = Q Equilibrium Condition

Pd = Ps = P Equilibrium Condition

This system consists of 6 equations and 6 endogenous variables: Qd, Qs, Pd, Ps, Q, P.

Definition. Equilibrium Condition: a market is in equilibrium when the excess demand is zero (Qd -Qs )=0, that is when the market is cleared.

At the equilibrium, there is no tendency to change. For this reason, the analysis of what the equilibrium state is like is referred to as comparative statics analysis.

Note: the variables Q and P are introduced to allow expressing the model in equilibrium values only, as shown below:

Q = β0 -β1 P Demand

Q = γ0 + γ1 P Supply

• Solution of the Market Model

In order to obtain the previous model in equilibrium values, we have used the equilibrium conditions to rid the system of four endogenous variables that is Qd, Qs, Pd, Ps. In general, a standard algebraic procedure is to reduce the size of a system of equations by eliminating variables through substitution (that is, getting rid of variables through giving up equations).

If this process is carried out to its logical conclusion, we can find the solution of a consistent system of equations. So, solving the equilibrium model for the solution values of P and Q yields:

11

00

γβγβ

+−

=P

11

0110

γβγβγβ

++

=Q

These are the equilibrium values for Q and P as in the graphical representation.

4.2. A Structural Market Model with Exogenous Variables

Let us insert exogenous shifters in the model! Suppose that:

Z1 = population (expanding demand) , and

Z2 = technological change (expanding supply), then we have the:

STRUCTURAL MODEL

Q = β0 -β1 P + β2 Z1 Demand


63

Q = γ0 + γ1 P + γ2 Z2 Supply

Solving the system for P and Q, we obtain the:

REDUCED FORM MODEL

( )22120011

1 ZZP γβγβγβ

−+−+

=

( )221122011011

1 ZZQ γββγγβγβγβ

++++

=

4.2.1. Structural and Reduced Form Models

Question: How do we do POLICY analysis?

Definition. Structural Model: The distinguishing feature of a STRUCTURAL MODEL is that AT LEAST ONE of its equations contains two or more endogenous variables.

Note: both equations of our structural model contain two endogenous variables.

Definition. Reduced Form Model: The distinguishing feature of a REDUCED FORM MODEL is that each equation has NO MORE than ONE endogenous variables.

Note: All the exogenous variables are on the right hand side.

Structural models are expressions of economic theories. They provide simplified description of real world processes such as market, consumption or production behavior.

Reduced models are of great use to derive the hypothesis that are derived from the theory. Only once the reduced form equations have been derived, one for each endogenous variable, the theorist can do the POLICY ANALYSIS by finding the partial derivatives describing the impact of a change in the exogenous variables on the endogenous variables!

Determining whether the partial derivatives are positive, negative or equal to zero is the essence of qualitative policy analysis!

• Causality

An example

Suppose we let demand increase because of population growth. As a result equilibrium price and quantities increase. Our hypothesis, then, asserts that population growth CAUSES P and Q to rise. From the solution of our structural model it is apparent that an increase in Z1 (population) also causes P and Q to increase. Similarly, an increase in technological progress (Z2) uses P to fall and Q to rise (just looking at our reduced form model).

The graphic and algebraic approaches lead to the same result!

The advantage of the graphic approach is that it allows for easy derivation of hypothesis when the structural model is simple and consists of a few equations.

The advantage of the algebraic approach is that it allows derivation of hypotheses in case of complex structural models.

In our reduced form model, it is clear that changes in P and Q are CAUSED by Z1 and Z2.

What role is played by the structural parameters β and γ?

An example: suppose that β1 is very close to zero (not statistically and economically significantly different from zero). That is to say that the demand for output is perfectly vertical or inelastic.

Now, let technological change shift supply from S0 to S1. The effect of technical change is to

Training Materials

64

decrease P but Q does not change at all! So, the importance of β1 is that it conditions then price and quantity effects of technical change.

If it were true world wide that the demand for food is highly inelastic, then technological progress would not affect output very much at least for very short periods of time. It would mainly tend of lower food prices.

$ Structural parameters are important in explaining real world events because they condition the effects of changes in exogenous variables.

This explains why it is important to have reliable estimates of structural parameters such as the elasticities of demand and supply.

Market examples: Demand and Supply Shift

Demand shift: a population increase

P

Q

D0

D1

S

P0

P1

Q0 Q1

Supply shift: technological progress with rigid demand

QQ0

S1

S0DP

P0

P1


65

4.3. The Colombian Rice Economy: the market model

We choose the double-log specification for both demand and supply because this is the specification selected by Scobie and Posada (1977) in our reference article. The summary of our results follows.

Demand Side

• ln q = a0 + a00 ln d + a1 ln p + a2 ln (y/N)


t Stat

Intercept 1.823 0.527 3.461

urb/tot % -1.151 0.187 -6.151

Prices $/t -0.361 0.084 -4.296

Income/mth 0.796 0.053 14.975

R2=0.979, N. Obs. 21

Let ln A= a0 + a00 ln d + a2 ln (y/N)

So, A = exp(ln A) and mean(A)= 4.402944

Therefore, the exponential specification is:

QD = A P η

with the associated inverse demand

P = (1/A QD ) 1/ η

Supply side with technical change

• ln q = (b0 + b01 ln %Irr + b02 DT ) + b1 ln p

Coefficients

Standard Error

t Stat

Intercept 4.5534 6.7955 0.6701

%Irrig -0.4359 0.9566 -0.4557

Year=tech 0.2317 0.0516 4.4950

Price 1.4185 0.5780 2.4542

R2=0.814

with technical change

ln Bt = b0 + b01 ln %Irr + b02 DT and mean(exp(Bt)) = 2.727727

without technical change

ln B = b0 + b01 ln %Irr and mean(exp(B)) = 1.540489

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The Market

Finally, our estimated market model for the Colombian rice industry is:

without technical change with technical change

QD = A P � = 4.4 P -0.36 QD = A P � = 4.4 P -0.36

QS = B P � = 1.5 P 1.42 QS = Bt P � = 2.7 P 1.42

QD = QS QD = QS

The graph is presented in the following page.

Exercise: Compute the equilibrium for both the situation with and without technical change and check the analytical solution with the graphical solution shown in the graph. Interpret.

Solution: For convenience, let us linearize the model taking logarithms:

ln QD = ln A + η ln P

ln QS = ln B + β ln P

Then, let us use the market clearing condition to obtain the analytical solution for the equilibrium price Pe :

ln A + η ln P = ln B + β ln P → ln A - ln B = ln P ( β - η )

ln Pe = ( ln A - ln B ) / ( β - η ) = ln A/B / ( β - η )

Pe = exp ( ln A/B / ( β - η ) )

So, to find the equilibrium price Pe without technical change:

Pent = exp ( ln A/B / ( β - η ) ) = exp ( ln 1.63 / 1.78 ) = exp (1.08 / 1.78 ) = exp( 0.6 ) =

1.83

and with technical change:

Pet = exp ( ln A/Bt / ( β - η ) ) = exp ( ln 2.93 / 1.78 ) = exp (0.49 / 1.78 ) = exp ( 0.27 ) =

1.32

To find the equilibrium quantity Qe corresponding to Pe substitute ln Pe into either equation of the system:

ln Qe = ln A + η (ln A/B / ( β - η ) ) = (ln A ( β - η ) + η ln A - η ln B) / ( β - η ) =

= (β ln A - η ln B) / ( β - η ).

4.4. Welfare Analysis of Technical Change

In the market model with technical change consumers are the main gainers by visually appreciating the change in Consumer Surplus (∆CS=1+2=area below the demand curve delimited by the price change before and after technical change has occurred). The gain to consumers increase as the demand is more inelastic. The effect on producers is small (∆PS=(4+3)-(1+3)(area above the supply curve after technical change)-(area above the supply curve before technical change)). The Net Social Gains (NSG=2+4=area below the demand curve comprised between the before and after technical change supply curve) are captured mostly by


67

consumers. If demand is completely inelastic, only consumers gain because NSG=∆CS. For this reason, there is nothing surprising if consumers invest through tax transfers to the government on agricultural research.

If demand is infinitely elastic (parallel to the horizontal axis), because rice is a tradable commodity on open global markets or because the government intervenes in the market buying and stocking all increases in production at a target price, then technical change is neutral to consumers. Then, producers gain the full NSG= ∆PS=2. If the good is tradable, the country gains from increased exports and foreign earnings. In this case, farmers should be very supportive of technical change when the good is tradable. If the good is non tradable, farmers may still gain if the government supports the price.

The measurement of the welfare gains from technological change, as shown in the article by Scobie and Posada, is important because, by dividing the welfare gains from research by the social costs of generating innovations, we obtain the rate of return from investment in agricultural research.

Technical change for non tradable goods

Technical change for tradable goods or price support

∆CS=1+2; ∆PS=(4+3)-1+3); NSG≈∆CS=2+4

∆CS=0; ∆PS=2; NSG=∆PS=2

Q

S1

S0DP

P0

P11 2

34

QQ0

S1

S0P

P0

1 2

The Colombian Rice Market

01020304050607080

1 2 3 4 5 6 7 8 9 10

Q

P

Series1Series2Series3


69

References

Berndt, E. (1996): “The practice of Econometrics. Classics and Contemporary,” Addison-Wesley Publishing Company, Reading, Mass., USA.

Colman, D. and T. Young “Principles of Agricultural Economics. Market and Prices in Less Developed Countries ,” Cambridge University Press, 1989.

Deaton, A. and J. Muellbauer (1980): “Economics of Consumer Behavior,” Cambridge University Press, Cambridge.

Deaton, A. (1997): “The Analysis of Household Surveys. A Micro-econometric Approach to Development Policy Analysis,” The John Hopkins University Press, Baltimore, USA.

De Janvry, A. and E. Saudolet (1995): “Quantitative Development Policy Analysis ,“ The John Hopkins University Press, Baltimore, USA..

Helmberger, P. and J.P. Chavas (1997): “Economics of Agriculture: Production, Marketing and Prices,” Addison-Wesley Publishing Company, Reading, Mass., USA.

FAO/TCAS ID8 (1992): Agricultural Policies Analysis. Exercises. Rome.

Johansson, Per-Olov (1991): “An Introduction to Modern Welfare Economics,” Cambridge University press, Cambridge.

Rivas, L., J. Garcia, C. Serè, T. Jarvis, and L.R. Sanint (1999): “Economic Surplus Analysis Model”, Centro Internacional de Agricultura Tropical (CIAT), Cali, Colombia.

Scobie, G. and R. Posada (1977): “The Impact of High-Yielding Rice Varieties in Latin America,” Centro Internacional de Agricultura Tropical (CIAT), Cali, Colombia, Series JE-01.

partial equilibrium analysis of policy impacts (part i)

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