estimating the loss of agricultural productivity in the amazon

Ecological Economics 31 (1999) 63–76

METHODS

Estimating the loss of agricultural productivity in theAmazon

Diana Weinhold *De6elopment Studies Institute, London School of Economics, Houghton Street, London, WC2A 2AE, UK

Received 23 November 1998; received in revised form 30 April 1999; accepted 7 May 1999

Abstract

We propose a procedure to obtain a general estimate of the rate at which agricultural productivity declines onnewly cleared land in the Brazilian Amazon. This estimated parameter has two advantages over conventionalestimates. First, it is a general, average estimate that can be used in macro-scale economic analysis. Second, theestimate is derived from regional data accessible to economists rather than from remote scientific stations. In the firststage a model is estimated that tracks the transition of land use from period to period for each municipality, allowingthe process to vary according to different characteristics of each municipality and time period. From this land usetransition model the percentage of crop land in each municipality that is recently cleared, 5-years old, 10 years oldor previously used for other purposes is calculated. These land vintage estimates are used with labor as inputs in aCobb–Douglas production function which is estimated using GLS. The estimated elasticities are allowed to vary byrelevant municipality characteristics and are then converted into a measure of productivity for each land vintage. Itis shown that the productivity of land drops in the first 5-years after clearing land and stabilizes thereafter. Severaleconomic arguments are given to support the empirical results. © 1999 Elsevier Science B.V. All rights reserved.

Keywords: Agricultural productivity; Amazon; Panel data; Heterogeneity

www.elsevier.com/locate/ecolecon

1. Introduction

Over the past 15-years both the scientific estab-lishment and the general public have become in-creasingly concerned about deforestation in theBrazilian Amazon. The possibility of global cli-mactic change and the loss of biodiversity are

only two of the more serious consequences of theclearing of virgin forest. Although estimates of theextent of deforestation vary depending on themethodology of the study1, there is good evidence

1 As of 1985 estimates of the total percentage of land clearedranged from 5% to 12% depending on whether land-basedmeasures or satellite information was used (and how it wasinterpreted). For more discussion about the range of measure-ment see Andersen et al. (1996).

* Tel.: +44-171-9556331; fax: +44-171-9556844.E-mail address: [email protected] (D. Weinhold)

0921-8009/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved.

PII: S 0921 -8009 (99 )00055 -5

D. Weinhold / Ecological Economics 31 (1999) 63–7664

Table 1Literature values for decay rates of yields following land clearinga

(a)

Paddy Rice Ground-nuts CassavaCrop Maize/Cassava

Zaire Zaire GhanaZaireLocation Malaysiakg/ha kg/ha kg/haYields lb/acre

1750 2341 1363 45000Year 1 X30000191565Year 2 1200

Year 3 800X/2Year 89%76% 86% 33%Decay rate of yield 32%

(b)Maize CattleCrop Yucca, pineapple, plantainMaize

Honduras East AmazoniaVenezuela GuatemalaLocationYields lb/acre t/ha/yr head/ha

X5.1 0.4900Year 1700 X/2Year 2500 3.1 0.2Year 3

Year 850%Decay rate of yield 26% 30%22%

a Source: Robert Schneider (1995).

that after a decade of relatively slower rates ofdeforestation, clearing activity in the Amazon hasshown a marked increase over the last 2 years.Generally, the cleared land is used for agriculturalpurposes, with land use following patterns dis-cussed below. Many scientists have argued thatthe economic benefits accruing from the agricul-tural output and associated activities will notcompensate for the costs of deforestation.2 Otherresearchers, however, have estimated that in somecases land clearing can provide a net benefit to thelocal economy.3 Given the sensitive nature (bothfiguratively and literally) of this situation there isan acute need for policy makers to have accurateinformation about the economics of deforestationin order to make policy decisions with sociallydesirable outcomes. Although such policy adviceis well beyond the scope of this paper, we attemptto contribute to the stock of relevant knowledgeby providing an estimate of the mean rate atwhich agricultural productivity declines after land

clearing. The proposed methodology may be usedfor estimating a variety of parameters when di-rect, time series data is not available.

Previous estimates of rates of agricultural pro-ductivity decline have relied on careful field stud-ies conducted at many different tropical scientificstations around the world. Schneider (1995) sum-marizes several of these studies and we reproducehis results here in Table 1 for convenience.

In general these studies are characterized bycareful, controlled experiments focusing on partic-ular agricultural methods and crops over a periodof 1–3 years.4 As can be observed, the rates ofland degradation range anywhere from 9 to 86%per year. Given the existence of these studies, onepossible way to estimate a general average rate ofland degradation for the Amazon would be topool the results of these studies (one would eitherhave to assume similar agricultural conditionsacross tropical countries or limit the analysis tostudies from the Amazon) and conduct a meta-analysis. From an economist’s point of view there

2 See, for example, Mahar (1989).3 See Andersen (1996).

4 For another recent example of this type of study seeMoran et al. (1996).

D. Weinhold / Ecological Economics 31 (1999) 63–76 65

are several limitations associated with this ap-proach, however. The first obstacle is a practicalone. Many of the relevant studies conducted atscientific stations in Bolivia, Peru, and Brazil (inSpanish and Portuguese) have never been pub-lished in the U.S.5 Second, since these studies usevery specific crop varieties and agricultural tech-nologies such a meta-analysis would require acareful pooling methodology and special technicalknowledge. In addition, the rate of land degrada-tion thus calculated may or may not reflect actualrates of land degradation faced by common agri-culturists following normal patterns of land use inthe Amazon.

This paper provides an alternative measure ofthe rate of agricultural productivity decline thatcan be estimated from less specific data that ismore widely available. We do not intend theproposed methodology to serve as a substitute forcareful field analysis, but rather as a complemen-tary form of analysis. As we shall discuss, ourapproach lacks the ability that field studies haveto provide advice (on optimal cropping patterns,for example) on how to improve productivity.However it does have the advantage of being amore general, average measure that is relativelyeasier to compute.

The paper continues as follows. Section 2 pro-vides a very brief history of agricultural policy inthe Amazon. Section 3 describes the data set andoutlines the basic procedure to calculate the rateof degradation. Section 4 discusses some specificestimation and data issues and presents the mainresults. Finally, Section 5 summarizes theconclusions.

2. A brief economic history of agriculture in theAmazon

As documented in the literature6 it is generallyaccepted that the initial, primary causes of humanincursions into the Brazilian Amazon were gov-

ernmental policies that encouraged settlement andland clearing. Although these policies began in1958 with the opening of the Brasilia–Belem high-way, settlement and the consequent deforestationwas minimal until the mid 1970s when the govern-ment embarked on a more aggressive pro-settle-ment program designed to increase population ofthe interior. Amazonian settlers cleared forest togain title to the land, generally practicing smallscale shifting agriculture or low-quality cattleranching.7 Fiscal incentives insured that manyeconomic activities with low or even negativeeconomic rates of return would be profitable,leading to excessive investment in clearing land.Road building on the part of the government andtimber companies opened up new tracts of land tothe agriculturists.

As the frontier moved further and further intothe interior, a typical pattern of land use emerged.This began with land clearing by timber compa-nies, followed by the arrival of colonists attractedby the easy availability of cheap land. These earlycolonists generally practiced shifting cultivation,leaving the land fallow and moving on to clearnew land after the land was exhausted (usually3–4 years). As the frontier progressed outward,these early settlers found themselves surroundedby improved rural infrastructures or even urbancenters with the value of their land correspond-ingly higher. At that point many colonists soldtheir plots to second-wave colonists, usually cattleranchers or capital-intensive agricultural enter-prises. The first-wave colonists then moved on tothe new frontier of newly cleared forest to beginthe sequence anew, leaving the better-endowedsecond wave colonists to more intensively workthe older lands (Andersen et al., 1996).

Considerable international pressure since 1992has led to the removal or even reversal of many ofthe policies that had encouraged land clearing andsettlement in the 1970s and 1980s (see Andersen etal., 1996). Indeed, deforestation slowed consider-ably between 1985 and 1994, although many ob-servers attribute this change more to the economicrecession and hyperinflation than to changing

5 The author has only indirectly heard of the existence ofthese studies through informal conversations with scientistswho have spent time in the Amazon region.

6 See, for example, Mahar (1989), Schneider (1992) orBinswanger (1991). 7 Mahar (1989), Schneider (1992).


government policies (Moran, 1993). With a suc-cessful stabilization program now beginning tobear economic fruit in Brazil, figures for 1995 and1996 reveal an alarming increase in deforestationrates.8

Indeed, currently 16 million people live andwork in legal Amazonia, with over 1.4 millionliving in the city of Manaus (Andersen et al.,1996). The process of deforestation has, in asense, taken on a life of its own responding tolocal and national economic forces of populationgrowth, landlessness, and the need for producerand household goods, food and building supplies.Despite recent national ‘environmentally friendly’legislation, further land clearing and local roadbuilding occurs due to these endogenous eco-nomic pressures. The co-movement of deforesta-tion and national economic performanceunderlines this point: the process of environmen-tal degradation may no longer respond primarilyto changes in national land policy (although theseare certainly important) but rather is part of thecomplex interaction of the local and nationaleconomies.

While it is beyond the scope of this paper toelucidate the complexities of this relationship, wedo believe that a necessary ingredient of a dy-namic, macroeconomic model of the economics ofdeforestation is some aggregate parameter esti-mate of how crop land degrades over time. Themethodology described below is presented as analternative form to estimate this parameter.

3. Methodology

3.1. Description of the data

The data available for this study was derivedlargely from Brazilian National Agricultural Cen-sus. The original database included municipality-level figures on economic, demographic,ecological and agricultural variables collected for

the years 1970, 1975, 1980, and 1985 for 316municipalities in the Brazilian Legal Amazonia.The data were cleaned, standardized and mergedwith data from other sources9 in a painstakingexercise undertaken by Dr. Eustaquio Reis of theInstitute of Applied Economic Research (IPEA)in Rio de Janeiro, without whose work this papercould not have been written.10 For each munici-pality in each time period the variables11 that areused for this analysis include total crop land, totalplanted pasture land, total fallow land, total laborforce, value of total crop output, density of roads,population density, percentage land of high qual-ity soil, relative price of land, and finally, the stateto which the municipality belongs. The variablesand their definitions are reproduced for conve-nience in Table 2. Figs. 1–9 show the aggregateevolution from 1970 to 1985 of the percentage of

Table 2Variable definitions

Total crop land in municipality i in time tcropit

pastureit Total planted pasture land in municipality i intime t

fallowit Total fallow land in municipality i in time tlaborit Total labor force in municipality i in time t

Value of total crop output in municipality i inoutputit

time troadit Density of roads in municipality i in time tdenit Population density in municipality i in time t

Percentage land of high quality soil in munici-soilitpality I

relprit Relative price of land in municipality i in timet

stateit The state to which municipality i belongs

9 Other variables in the original data set at IPEA coveringsatellite deforestation measures and migration come from thepopulation census and IBGE as well as some other govern-ment agencies. For this paper the data that was used werefrom the Agricultural Census, however.

10 For an extensive discussion of the entire database seeAndersen et al. (1996).

11 Some variables appear as logs of the described data inlater parts of the paper and are so noted.

8 See Andersen et al. (1996) for 1995 figures. Statements on1996 deforestation rates are based on newly released statisticsfrom IBGE, Rio de Janeiro Brazil.


Fig. 1. Brazilian legal Amazonia.

land used (out of total land area) for crop land,planted pasture and fallow land, respectively,for each of the eight states represented in theanalysis.

3.2. O6er6iew of the proposed methodology

The purpose of this paper is to estimate theextent to which the value of crop output declineswith time after forest has been cut and the landplanted in crops. As described above, data isavailable in each period on the area of land usedfor crops and other agricultural activities in eachmunicipality. However, in order to estimate therate of land degradation directly we would haveto know exactly what land was used for eachactivity, not just the share of the municipality

dedicated to each use. For example, if crop landincreases from 20 to 25% between 1980 and 1985,we cannot know how much of the old crop land isstill being used and how much is newly cleared orconverted land. Thus it is necessary to estimate

Fig. 2. Acre.


Fig. 3. Amazonas. Fig. 5. Roraima.

land that was in crops in time t−1, land that wasin pasture in time t−1, or land that was fallow intime t−1. Analogously both pasture and fallowland in time t must also come from these foursources, although the proportion from eachsource may vary. The land use model is thus:

cropit=b1Dclearit+b2cropit−1+b3pastureit−1

+b4 fallowit−1 (1)

pastureit=f1Dclearit+f2cropit−1+f3pastureit−1

+f4 fallowit−1 (2)

fallowit=h1Dclearit+h2cropit−1+h3pastureit−1

+h4 fallowit−1 (3)

where bj, fj, and hj are parameters that indicate,at time t, what proportion of crop land, pastureland, and fallow land, respectively, come fromsource j, where j is an index that maps to Dclear( j=1), crop ( j=2), pasture ( j=3) and fallow( j=4) in time t−1. The closed nature of themodel implies that bj+fj+hj=1 for j=1, 2, 3,4. Eq. (1) holds in all time periods t so we can lagall variables by one period to obtain:

cropit−1=b1Dclearit−1+b2cropit−2

+b3pastureit−2+b4 fallowi t−2 (4)

the pattern of land use and land vintage (i.e. toestimate the proportion of crop land that derivesfrom newly cleared land, from old crop land,from pasture land or from fallow land) in eachmunicipality in order to compute the rate ofproductivity decline.

This estimation is accomplished by first con-structing a land use transition model.12 We distin-guish between natural land which is defined asplanted forest, virgin forest and natural pasture,and cleared land which is comprised of crop land,planted pasture and fallow land. As this is aclosed system the definitions of cleared land(clear), and the change in cleared land13 (Dclear),can be constructed as:

clearit=cropit+pastureit+ fallowit

Dclearit=clearit−clearit−1

Crop land in municipality i at time t must comefrom four possible sources: newly cleared land(i.e. land that was in a natural state in time t−1),

Fig. 4. Maranhao.

Fig. 6. Mato Grosso.

12 This model was originally proposed by Clive Granger andexplored in Andersen and Granger (1995) for the Amazon.

13 i.e. newly cleared land, converted from its natural state.


Fig. 7. Amapa. Fig. 9. Para.

If we then substitute Eq. (4) into Eq. (1) it is thenpossible to expand the crop land Eq. (1)14 to get:

cropit=b1Dclearit

+b2(b1Dclearit−1+b2cropit−2

+b3pastureit−2+b4 fallowit−2)

+b3pasturet−1+b4 fallowit−1 (5)

We then collect terms and interpret the compo-nents of Eq. (5) as corresponding to differentvintages of crop land in time t. For example, thefirst term b1Dclearit is defined as the area of cropland that comes from land that has been newlycleared during the current 5-year period (We notethat since our data periodicity is every 5-yearstime ‘t’ actually corresponds in practice to a 5-year period. Thus time t−1 would correspond tothe preceding 5-year period, and so on). We callthis NEWLAND. The second term, b2b1Dclearit−

1, corresponds to land that was newly cleared inthe previous 5-year period (time t−1) andplanted in crops at that time, and which has

remained in crop land to the present. Thus thisland has been in crops for at least 5-years and wedenote it 5YRLAND. The third term is b2

2cropit−2

which is the current crop land area that wasplanted in crops in both the previous 5-year pe-riod and the 5-year period before that. This landhas been cultivated for at least 10 years and wethus denote it 10YRLAND. We define the remain-der of the components of the expanded Eq. (5) ina similar fashion, with the definitions summarizedin Table 3.

Thus the coefficient estimates from the cropland Eq. (1) in the land transition model definedabove can be used to construct an estimate of theproportion of total crop land that comes fromnewly cleared land, NEWLAND, from land thatwas cleared in the previous 5-year period,5YRLAND, from land that was cleared two 5-year periods ago, 10YRLAND, and from landthat has had other uses in the previous timeperiods, CRPPAS, CRPFAL, PAS and FAL asdescribed in Table 3. We refer to these categoriesas different 6intages of crop land. We then assumeCobb–Douglas agricultural production:

CROPOUTPUT=A�LABORy1LANDjyj

where A is a technological constant and the nj

denote elasticities that give the percentage changein output that results from a unit percentagechange in input j. Taking logs of both sides anddefining lower case variables as the log of upper-case variables, we can then estimate these elastic-ities from the regression:

outputit=a+y1laborit+y2newlandit+y35yrlandit

+y410yrlandit+y5crppasit+y6crpfalit

+y7pasit+y8 falit+oit (6)

Fig. 8. Goias.

14 It would, of course, be possible to expand out the last twoequations as well, which would enable us to estimate thedynamics of pasture productivity from data on cattle herd.However, this is not necessary for the task at hand.


Table 3Constructed land type (‘vintage’) definitions

Variable nameTerm from Eq. Variable definition(5)

NEWLANDb1Dclearit Land that has been newly cleared sometime during the current 5-year period and plantedin crops

b2b1Dclearit−1 Land that was newly cleared sometime during the previous 5-year period and been used5YRLANDas crop land continuously since

10YRLANDb22cropit−2 Land that has been in crops for the past 10 years continuously. It is not known what the

original form of this land was before thatb2b3pastureit−2 CRPPAS Land that was used as crop land for the current and previous 5-year periods, but which

had been used as pasture land before thatb2b4 fallowt−2 CRPFAL Land that was used as crop land for the current and previous 5-year periods, but which

had been used as fallow land before thatLand that was pasture during the previous 5-year period but has now been converted tob3pasturet−1 PAScrop landLand that was left fallow during the previous 5-year period but has now been convertedb4 fallowt−1 FALto crop land

The estimated coefficients from this regression, 61to 67, give us an estimate of the percentage changein output for a 1% change in the correspondingland area. We can easily calculate the percentagechange represented by an increase of a given areaunit in one land category and the consequentchange in output, which will give us an idea of theproductivity of that land.

3.3. Estimation procedure for the land usetransition model

As described in the previous subsection, theland use transition model has the theoreticalproperty that bj+fj+hj=1. Also, it is clear thattheoretically all the coefficients should lie betweenzero and one since no less than 0% and no morethan 100% of the land of a given type can beconverted to crop land. When the basic model isestimated by a heteroskedasticity consistent gener-alized least squares procedure15 (henceforth sim-ply GLS) separately on each equation, thecoefficients do indeed sum to one. Two problemsemerge, however. First, Andersen and Granger(1995) show that the heterogeneity in the panelcan lead to bias in the GLS estimates. Second, thesumming up property is an artifact of the data,

and in the presence of heterogeneity comes at thecost of coefficient estimates that occasionally falloutside the [0, 1] bound. We will discuss the het-erogeneity problem first and then how it relates tothe second problem of negative coefficient values.

Land transition patterns could be expected tovary from municipality to municipality dependingon any number of characteristics such as soilquality, population density, land type (savannaetc.), land area, and distance to nearby markets.In addition, the coefficients might be expected tochange through time and from state to state. Wethus try to control for these factors in the regres-sions. In addition to the above characteristics, wealso control for the average price of land. Landprices serve as an excellent proxy for many unob-served (or imperfectly observed) characteristicsthat impact the desirability of land, such as pres-ence of a rural infrastructure or economic proxim-ity to an urban center. In particular, Andersen etal. (1996) have found that land prices are very

Table 4Productivity estimates of the value of additional crop outputfrom a one hectacre increase of each given land vintagea

NEWLAND 5YRLAND 10YRLAND

993.42919.76Estimate 4955.2641.18103.06St. Dev. 1832.9

a Sample mean, 1671.60; sample SD, 1569.15.

15 We use White’s Generalized Heteroskedasticity-Consis-tent Feasible Least Squares (see White (1980)).


strongly correlated with subsidized credit andother fiscal incentives for the region. The data onland prices is in current prices so in order to avoidany biases from using a deflator, only relativeprices in each year are used, so that each pricerepresents that municipality’s share of total landprices for that year.

It is clearly necessary to take all of this infor-mation into account if meaningful estimates ofland degradation are to be calculated. In addition,Andersen and Granger (1995) show that estimateswill be biased if the heterogeneity is ignored.However, if we allow the b ’s to vary according todifferent characteristics of the municipality, thismultiplies the coefficients to be estimated andincreases the probability of coefficient estimatesfalling outside the theoretical [0, 1] bound.16 Thisin turn may exacerbate a second problem, whichis that the Cobb–Douglas production functionthat will be estimated must have only non-nega-tive inputs. However GLS on the land transitionmodel does not put any constraints on the coeffi-cient estimates, leading in some cases to negativevalues.

Thus, although GLS yields the ‘summing up’property referred to earlier, this is an artifact ofthe data construction and is achieved at the costof coefficient estimates that occasionally lie out-side of the [0, 1] interval. While in theory coeffi-cients shouldn’t fall outside this interval, therecould be measurement problems and actual cir-cumstances not controlled for in our simple modelthat could lead to negative GLS estimates. Forexample, the original census land use data iscompiled from people who own agricultural es-

tablishments and report to the census taker howthe land is used. In some cases the boundariesbetween the municipalities is not well defined, andagriculturists and census takers may attribute landto one municipality that actually lies in a neigh-boring municipality. This over-measuring ofcleared land in one period may lead in subsequentperiods to negative values for the change incleared land for a particular municipality. Thisproblem occurs most frequently where it would beexpected: in the smaller municipalities. Negativevalues for the change in cleared land is a suffi-ciently common problem that simply eliminatingall observations with this property can lead tosevere sample selection bias in the estimates. Wecall this problem ‘shrinking’ and introduce a‘shrinking’ dummy variable that interacts with theprimary variables to allow the coefficients to varybetween municipalities which display this prop-erty and those that do not. We thus allow boththe land use coefficients and the elasticity esti-mates from the Cobb–Douglas production func-tion to vary according to whether or not amunicipality exhibits ‘shrinking’ over time.

In sum, the estimation process thus entails us-ing GLS to estimate the initial land use transitionsystem. Not truncating the coefficient estimates soas to enforce the [0, 1] bound actually accentuatesthe final results presented below. Therefore, tosave space and in the interests of keeping theestimation consistent with the theory, only thoseresults using truncated coefficients are presentedin Table 5.17 After the land use transition coeffi-cients have been estimated, they are used to con-struct the different vintages of crop land asdescribed in Table 3, and these are in turn used asinputs into a time- and municipality-varyingCobb–Douglas production function in which theelasticities are allowed to vary according to mu-nicipality specific characteristics. Thus we have:

outputit=a+y1itlaborit+y2itnewlandit

+y3it5yrlandit+y4it10yrlandit

+y5itcrppasit+y6itcrpfalit+y7itpasit

+y8it falit+oit (7)

16 Previous versions of this paper have used nonlinear leastsquares to impose the restriction of the 0,1 bound on thecoefficients. There were several problems associated with thismethod, however. The models were very difficult to estimateand often did not converge, leading to artificially restricted setsof explanatory variables. The estimates were also very sensitiveto the choice of explanatory variables and often producedestimated betas with extremely bimodal distributions. A num-ber of trials were run in which betas estimated with GLS gavesimilar results to the betas estimated with nonlinear leastsquares with similar variables. However, by allowing forgreater heterogeneity, more complex GLS estimation yieldscoefficients which are distributed with a unimodal bell shape.

17 Primarily the untruncated productivity estimates differ inthat the productivity of NEWLAND is considerable higher.


Table 5Land use regression results: dependent variable=crop land (1985)a,b

T for H0:ParameterVariable Variable Parameter T for H0:estimateparameter =0 parameter =0estimate

−1.589 CROPS8DCLEAR 0.571888−0.072620 6.014***0.506CROPL1 PASSAV0.127855 0.021368 3.828***2.852*** PASSOI0.170512 −0.029589FALLOL1 −2.020***

0.015924PASTUL1 0.739 PASDEN −0.000083341 −0.186−0.066628CLEARSAV −4.055*** PASARE −0.001302 −0.769

0.095 PAS50.003818 0.009524CLEARSOI 2.571***1.285CLEARDEN PAS800.000869 −0.011756 −2.518***2.858*** PAS850.010913 −0.006182CLEARARE −1.335

0.015403CLEAR80 1.375 PASPR 1.697775 0.642−0.033775CLEAR85 −2.608*** PASSQ 17.702235 0.074

1.478 PASTURS27.112195 0.040851CLEARPR 0.5930.041 PASTURS3CLEARSQ −0.09573515.281006 −1.983**1.628*** PASTURS50.072107 0.000803DCLEARS2 0.094

0.084827DCLEARS3 2.901*** PASTURS6 −0.022572 −1.1160.011887DCLEARS5 0.664 PASTURS7 0.003730 0.317

0.127 PASTURS80.003950 −0.011261DCLEARS6 −1.937**1.386 FALSAVDCLEARS7 −0.0185540.028833 −0.7953.962*** FALSOI0.047039 0.040522DCLEARS8 0.978

0.143347CROPSAV 1.285 FALDEN −0.000540 −1.242−0.197411CROPSOI −1.451 FALARE −0.013747 −2.738***

−0.512 FAL5−0.000796 −0.010793CROPDEN −0.8773.983*** FAL80CROPARE 0.0281010.073664 1.907**

−3.583*** FAL85−0.204976 −0.059743CROP5 −4.081***−0.101815CROP80 −1.325 FALPR 22.797138 3.621***−0.051464CROP85 −0.738 FALSQ −304.697179 −0.894

−1.906* FALLOWS2−24.030320 0.008875CROPPR 0.0850.932 FALLOWS3 −0.017157 −0.485CROPSQ 233.998902

−0.010 FALLOWS5−0.003254 −0.016179CROPS2 −0.6410.294712CROPS3 2.252** FALLOWS6 0.096211 0.9790.260649CROPS5 2.164** FALLOWS7 −0.031654 −1.271

0.359 FALLOWS80.161712 −0.093095CROPS6 −3.837***2.660**CROPS7 0.332501

a Regression N, 945.b R-square, 0.9497, Adj R-sq, 0.9462

Finally, the productivity estimates are derived us-ing the estimated elasticities from this regression.For example, we can calculate the additional out-put that would be obtained from increasing eachland type input by one hectacre and comparethese yields across the different vintages of land.The difference between the yields on newlycleared land and land that has been in crops forlonger periods will give us an estimate of the rateat which agricultural productivity is changingover time.

4. Results

4.1. Construction and estimation of the land usetransition model

As discussed earlier we wish to allow the coeffi-cients to vary from municipality to municipalityand over time depending on various characteris-tics of the location and land.

Thus each coefficient in the model is defined asvarying by year, state, share of savanna land,


Table 6Cobb–Douglas regression resultsa,b

Dependent variable= log(real crop output)

ParameterVariable T for H0: Variable Parameter T for H0:estimateestimate parameter=0parameter=0

23.950*** YR105INTERCEPT −0.3057277.462146 −4.139***−0.025811T85 −0.331 YR106 −0.276502 −1.263

13.414*** YR1070.687467 −0.062654LLABOR −0.958−0.018486LABSH −0.310 YR108 −0.160449 −2.383**0.021742NEWLAND 0.925 CRPPAS2 −0.197825 −0.777

0.204 CRPPAS50.005104 −0.066042YR5LAND −1.340−0.003567YR5SH −0.179 CRPPAS7 0.019352 0.445

4.894** CRPPAS80.323511 0.126619Y10LAND 2.199**0.009743YR10SH 0.125 CRPFAL2 0.124595 0.384−0.021759CRPFAL −0.478 CRPFAL3 0.179939 2.610***

0.889 CRPFAL50.031160 0.305736CRPFSH 4.636***0.186 CRPFAL6PAS −0.1839710.007579 −1.017−0.365 CRPFAL7−0.012335 0.022055PASSH 0.408

0.012004CRPPAS 0.285 CRPFAL8 0.082920 1.5580.038276CRPSH 1.268 PAS2 0.142451 0.686

0.501 PAS50.011520 −0.033912FAL −0.725FALSH 0.027226 1.549 PAS7 −0.039818 −0.912

−0.383 PAS8−0.029738 0.042607NEW2 0.7260.010081NEW3 0.268 FAL2 0.078883 0.6870.045140NEW5 1.418 FAL3 −0.016650 −0.529

1.467 FAL50.109607 0.050125NEW6 1.673−0.053 FAL6NEW7 0.488438−0.001562 2.491***2.286** FAL70.082432 −0.021756NEW8 −0.875

−0.016530YR52 −0.356 FAL8 −0.090620 −2.653***0.003639YR53 0.116 NEWSOI 0.049929 1.249

1.267 YR5SOI0.041157 −0.028029YR55 −0.705−3.473***YR56 YR10SOI−0.294741 0.049763 0.4890.716 CRPPSOI0.020344 −0.212787YR57 −2.166***

0.094037YR58 2.902*** CRPFSOI −0.129868 −1.595YR102 −0.428−0.060895 PASSOI −0.031603 −0.349

−1.863* FALSOI 0.078401 1.564−0.133088YR103

a Regression N, 629.b R-square, 0.8093, Adj R-sq, 0.7888.

share of good soil, population density, area,whether or not the municipality crop land is‘shrinking,’ and by relative price of land and thesquare of the relative price of land in thatmunicipality.

GLS regression results from the land use tran-sition model are presented in Table 6. Variablenames are easily deciphered as the first part cor-responds to the type of land (new, crop, fallow,or pasture) and the second part to the interac-tion variable. Percentage of good soil is denotedby soi, percentage of savanna land is sa6, log of

area of the municipality is are, population den-sity is den, relative prices are denoted by pr andthe square of relative prices is sq. Each state isdenoted by its corresponding number, and timeshifts are clearly named by the year. The modelexplains about 94% of the variation in cropland (although since there is no intercept in themodel due care must be exercised in interpretingthe R-squared statistics). These coefficient esti-mates are then used to calculate the land usetransition b ’s for each municipality in each sam-ple period.


The estimated b ’s are in turn themselves used toconstruct the land categories described in Section3. If the technique is accurate, the sum of all sevenland categories ought to be close to the actual areaof crop land in 1985. For both truncated anduntruncated b ’s the percentage error between actualand predicted area of crop land is quite similar. Themean percentage error is −0.308 for the truncatedb ’s and −0.2216 for the untruncated b ’s, withrespective standard deviations 1.954 and 1.717.These seemingly high and variable percentage errorsare almost completely determined by a very fewoutliers (most caused by large errors in the estima-tion of CRPPAS and CRPFAL), however, as thecorresponding medians are 0.038 and 0.068, respec-tively. If the worst offenders of these outliers aredeleted, the mean errors fall dramatically. This isclearly illustrated in the case of the untruncated b ‘s,whose mean error, when the ten largest percentageerror outliers are deleted, falls to −0.040 with astandard deviation of 0.735. At any rate, althoughsome of these large outliers may lead to large errorsin the estimates of productivity of CRPPAS andCRPFAL, they have very little impact on theestimated productivity of NEWLAND, 5YRLANDor 10YRLAND. The fundamental results on pro-ductivity reported below are extremely robust to theinclusion or exclusion of any of these outliers.

4.2. Estimation of the loss of crop producti6ity

The estimated b ’s are different for each munic-ipality and over time. These estimated coefficientsare in turn used to estimate the land categoriesdescribed in Section 3 for each municipality. Takinglogs of both the land categories, labor and outputa heteroskedasticity-consistent18 GLS estimation ofa Cobb–Douglas production function (Eq. (7))produces estimates of the relative elasticities foreach land category.

As with the land transition model, it could beexpected that productivity of various land typescould vary across municipalities. For this reason theelasticity estimates are allowed to vary by soil type,state, and whether or not the municipality displaysthe measurement problem we call ‘shrinking’. In

addition each coefficient is allowed to vary over timeto capture any general shift between sample periods.The relative price variable was not included in thisregression due to the possibility of endogeneitybetween the value of crop output and land prices.For example, it could be the case that higher levelsof agricultural output led to higher land pricesrather than the reverse. If this is the case thenincluding land prices on the right-hand side of theregression could induce bias in the coefficientestimates.

Table 6 presents the results of the Cobb–DouglasGLS regression of the log of crop output on the logsof the different land types, allowing the coefficientsto vary according to the variables described above.Although the names of the variables seem a bitdifficult, again in fact, they are simply a compoundof the two variables compromising the interactionvariable. The first part of the name corresponds tothe land type, the second part to the interactionvariable. Shrink is denoted by sh, percentage ofgood soil is soi and each state is represented by itscorresponding number. The time shift dummyvariable is represented by t85.

The final elasticities are calculated for eachmunicipality in each time period using the estimatedcoefficients. Each of these elasticities is multipliedby (100/landj) which gives the percentage change inoutput produced by an increase of 1 area units ofland in any given land category j. This percentageis then converted into an actual monetary changein output for the 1 area unit increase in crop land.These productivities are then averaged over allmunicipalities for each land category. In order toavoid letting a few outliers impact the mean exces-sively, each observation that falls outside of 2 SDsof the mean is deleted before averaging, leaving amean that is closer to the median.19

The percentage change in output estimates aremultiplied by the actual real output in each munic-ipality to give a monetary unit estimate of theincrease in output for a 1 area unit increase in eachtype of land (i.e. marginal output). The main resultsare presented in Table 4 which focuses on

19 Including the outliers essentially increases the productivityestimates of NEWLAND but does not impact much the esti-mates of 5YRLAND or 10YRLAND.18 White’s heteroskedasticity consistent methodology.


the calculated productivity estimates (after delet-ing outliers as described above) for NEWLAND,5YRLAND and 10YRLAND, and provides thesample standard deviation as a point of compari-son.20 In particular, we find that:� an additional hectacre of newly cleared land

planted in crops will increase agricultural out-put an average of almost 5000 R$ (1985prices);

� increasing 5-year-old crop land area by onehectacre will increase output by an average ofonly 920 R$;

� increasing 10-year-old crop land area by onehectacre will increase output by an average ofabout 1000 R$; it is important to note, how-ever, that this figure is not statistically differentfrom the estimate of 920 R$ from increasing5-year-old crop land.The results imply a dramatic fall in productivity

in the first 5-years after initial land clearing. Theadditional output from a 1 unit area increase in5-year-old crop land is only 20% of the value ofan additional unit of newly cleared land. Since thetime span between periods is 5-years, these figuresyield an annualized rate of just over 30% declinein agricultural productivity per year. This figurecorresponds closely to the rates predicted by fieldresearch and to the general consensus of expertsin the region of what the average rate of landdegradation has been during the sample period.

The productivity decline levels out, however,between 5- and 10-year-old crop land. One expla-nation for this is that the land that was cultivatedfirst (i.e. the oldest land) was the best quality landsettlers could find. In addition, the result couldalso be expected given the common land usepatterns that prevailed at the time. Early colonistswould clear land and practice low-capital shiftingagriculture for a few years until the land wasexhausted, then abandoning or selling the land to

better-endowed second-wave settlers who usedmore intensive agricultural practices to keepyields at sustainable levels.

5. Conclusions

This paper has presented an estimation proce-dure that uses data on areas of crop, pasture, andfallow from 1970, 1975, 1980, and 1985 and com-bines this with estimates of crop output value, thelabor force and a variety of natural and demo-graphic municipality characteristics to calculate ageneral estimate of the average rate of decline ofagricultural productivity that prevailed in theAmazon during the sample period. The procedurehas two primary steps, and although data hetero-geneity may be a problem throughout both ofthese steps, it is shown that the estimated patternand magnitude of land degradation does not varymuch as the sample is restricted to only thoseobservations without large outliers included intheir construction. Measurement problems arealso a serious concern with this data set. Never-theless, the actual money figures that are derivedare within the neighborhood of sample averagesand the calculated rate of land degradation isconsistent with field research in this area. Theresults show strong evidence for a precipitousdrop in productivity in the first 5-years after landhas been cleared for crops, with an estimated fallof 30% per year in productivity. The productivityestimates increase slightly between 5-year-old cropland and 10-year-old crop land, although thisincrease is not statistically significant. The stabi-lization of productivity between 5 and 10 yearsmay be explained by several observations. First, itis expected that the best land will be cultivatedfirst. In addition, it has been noted that after thefirst few years a second wave of more permanentsettlers move into the area and proceed to culti-vate the land more intensively and use more fertil-izer. Finally, land that has been continuously incultivation for 10 years is most likely planted withperennial crops which do not deplete the soil asrapidly.

The estimates of the rate of land degradationpresented in this paper differ in several ways from

20 Readers should note that the reported standard deviationsshould not be interpreted as confidence intervals. Appropriateconfidence intervals would have to be constructed taking intoaccount confidence levels associated with the estimated coeffi-cients used in the construction of these numbers, which due tothe complexity of the problem, they do not. Rather, thismeasure gives us an idea of how the mean estimate variesacross municipalities.


the estimates derived from scientific field studiesor case studies. A disadvantage of the estimatespresented here is that they do not give an indica-tion of where the productivity frontier is, i.e. whatagricultural productivity could be under idealconditions. They cannot be used to derive whatthe optimal cropping patterns are, nor to comparethe economic performance of different crops.Thus the proposed methodology is in no waymeant as a substitute for careful field analysis.

On the other hand, the methodology proposedhere has some advantages over field research aswell. The average rates of land degradation thuscalculated contain dynamic information from amuch longer time period (15-years) and muchlarger area (Brazilian Legal Amazonia) than mostfield studies. Despite the extensive dynamic andspatial coverage, the models allow for the factthat land use patterns and methods of cultivationdiffer across space and have changed over time.Thus, to a much greater extent than is possible ina specific field study, the methodology outlined inthis paper incorporates the actual distribution ofagricultural activity that existed over the sampleperiod in the Brazilian Amazon. The methodol-ogy produces estimates of the a6erage rate ofagricultural productivity decline that prevailedover the sample period, given the pattern of cropsand land use that existed, rather than the exactrate of land degradation for a particular crop,agricultural intensity and/or location.

Acknowledgements

The author acknowledges the partial support ofNSF (Grant ¯cSBR-930081). The much appreci-

ated support and advice of Eustaquio Ries, CliveW.J. Granger and Lykke Andersen, as well threeanonymous referees, have all been invaluable. Inaddition, the author gratefully recognizes thehelpful comments of participants of workshops atIndiana University, University of Houston, andSouthern Methodist University and at the Econo-metric Society Meetings in Rio de Janeiro and theSouthern Economic Association Meetings inWashington D.C. All errors are my own.

References

Andersen, L.E. 1996. A cost-benefit analysis of deforestationin the Brazilian Amazon. Discussion Paper, IPEA, Rio deJaneiro, Brazil.

Andersen, L.E., Granger, C.W.J., 1995. A random coefficientVAR transition model of the changes in land use in theBrazilian Amazon. UCSD Discussion Paper no. 95–35,Department of Economics, University of California, SanDiego.

Andersen, L.E., Granger, C.W.J., Reis, E.J., Huang, L.-L.,Weinhold, D., 1996. Report on Amazon deforestation.UCSD Discussion paper c96-40, Department of Econom-ics, University of California, San Diego.

Binswanger, H.P., 1991. Brazilian policies that encourage de-forestation in the Amazon. World Dev. 7 (19), 821–829.

Mahar, D.J., 1989. Government policies and deforestation inBrazil’s Amazon region. The World Bank.

Moran, E.F., 1993. Deforestation and land use in the BrazilianAmazon. Hum. Ecol. 21, 1–21.

Moran, E.F., Packer, A., Brondizio, E., Tucker, J., 1996.Restoration of vegetation cover in the Eastern Amazon.Ecol. Econom. 1 (18), 41–51.

Schneider, R.R., 1992. An economic analysis of environmentalproblems in the Amazon. The World Bank.

Schneider, R.R., 1995. Government and the economy on theAmazon frontier. World Bank Environment Paper, no.11.

White, H., 1980. Heteroscedasticity—consistent covariancematrix estimator. Econometrica 48 (4), 817–838.

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estimating the loss of agricultural productivity in the amazon

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