METHODS
Estimating the loss of agricultural productivity in the
Amazon
Diana Weinhold *
De6elopment Studies Institute,London School of Economics,Houghton Street,London,WC2A2AE,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 on newly cleared land in the Brazilian Amazon. This estimated parameter has two advantages over conventional estimates. First, it is a general, average estimate that can be used in macro-scale economic analysis. Second, the estimate is derived from regional data accessible to economists rather than from remote scientific stations. In the first stage a model is estimated that tracks the transition of land use from period to period for each municipality, allowing the process to vary according to different characteristics of each municipality and time period. From this land use transition model the percentage of crop land in each municipality that is recently cleared, 5-years old, 10 years old or previously used for other purposes is calculated. These land vintage estimates are used with labor as inputs in a Cobb – Douglas production function which is estimated using GLS. The estimated elasticities are allowed to vary by relevant municipality characteristics and are then converted into a measure of productivity for each land vintage. It is shown that the productivity of land drops in the first 5-years after clearing land and stabilizes thereafter. Several economic 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 the Brazilian Amazon. The possibility of global cli-mactic change and the loss of biodiversity are
only two of the more serious consequences of the clearing of virgin forest. Although estimates of the extent of deforestation vary depending on the methodology of the study1, there is good evidence
1As of 1985 estimates of the total percentage of land cleared
ranged from 5% to 12% depending on whether land-based measures or satellite information was used (and how it was interpreted). 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)
Table 1
Literature values for decay rates of yields following land clearinga
(a)
Paddy Rice Ground-nuts Cassava
Crop Maize/Cassava
Zaire Zaire Zaire Ghana
Location Malaysia
kg/ha kg/ha kg/ha
Yields lb/acre
1750 2341 1363 45000
Year 1 X
Decay rate of yield 32% (b)
Maize Cattle
Crop Maize Yucca,pineapple,plantain
Honduras Venezuela Guatemala East Amazonia
Location
Decay rate of yield 26% 22% 30%
aSource: Robert Schneider (1995).
that after a decade of relatively slower rates of deforestation, clearing activity in the Amazon has shown a marked increase over the last 2 years. Generally, the cleared land is used for agricultural purposes, with land use following patterns dis-cussed below. Many scientists have argued that the economic benefits accruing from the agricul-tural output and associated activities will not compensate for the costs of deforestation.2 Other
researchers, however, have estimated that in some cases land clearing can provide a net benefit to the local economy.3 Given the sensitive nature (both
figuratively and literally) of this situation there is an acute need for policy makers to have accurate information about the economics of deforestation in order to make policy decisions with socially desirable outcomes. Although such policy advice is well beyond the scope of this paper, we attempt to contribute to the stock of relevant knowledge by providing an estimate of the mean rate at which agricultural productivity declines after land
clearing. The proposed methodology may be used for 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 scientific stations around the world. Schneider (1995) sum-marizes several of these studies and we reproduce his results here in Table 1 for convenience.
In general these studies are characterized by careful, controlled experiments focusing on partic-ular agricultural methods and crops over a period of 1 – 3 years.4 As can be observed, the rates of
land degradation range anywhere from 9 to 86% per year. Given the existence of these studies, one possible way to estimate a general average rate of land degradation for the Amazon would be to pool the results of these studies (one would either have to assume similar agricultural conditions across tropical countries or limit the analysis to studies from the Amazon) and conduct a meta-analysis. From an economist’s point of view there
2See, for example, Mahar (1989). 3See Andersen (1996).
4For another recent example of this type of study see
are several limitations associated with this ap-proach, however. The first obstacle is a practical one. Many of the relevant studies conducted at scientific stations in Bolivia, Peru, and Brazil (in Spanish and Portuguese) have never been pub-lished in the U.S.5 Second, since these studies use
very specific crop varieties and agricultural tech-nologies such a meta-analysis would require a careful pooling methodology and special technical knowledge. In addition, the rate of land degrada-tion thus calculated may or may not reflectactual rates of land degradation faced by common agri-culturists following normal patterns of land use in the Amazon.
This paper provides an alternative measure of the rate of agricultural productivity decline that can be estimated from less specific data that is more widely available. We do not intend the proposed methodology to serve as a substitute for careful field analysis, but rather as a complemen-tary form of analysis. As we shall discuss, our approach lacks the ability that field studies have to provide advice (on optimal cropping patterns, for example) on how to improve productivity. However it does have the advantage of being a more general, average measure that is relatively easier to compute.
The paper continues as follows. Section 2 pro-vides a very brief history of agricultural policy in the Amazon. Section 3 describes the data set and outlines the basic procedure to calculate the rate of degradation. Section 4 discusses some specific estimation and data issues and presents the main results. Finally, Section 5 summarizes the conclusions.
2. A brief economic history of agriculture in the Amazon
As documented in the literature6
it is generally accepted that the initial, primary causes of human incursions into the Brazilian Amazon were
gov-ernmental policies that encouraged settlement and land clearing. Although these policies began in 1958 with the opening of the Brasilia – Belem high-way, settlement and the consequent deforestation was minimal until the mid 1970s when the govern-ment embarked on a more aggressive pro-settle-ment program designed to increase population of the interior. Amazonian settlers cleared forest to gain title to the land, generally practicing small scale shifting agriculture or low-quality cattle ranching.7 Fiscal incentives insured that many
economic activities with low or even negative economic rates of return would be profitable, leading to excessive investment in clearing land. Road building on the part of the government and timber companies opened up new tracts of land to the agriculturists.
As the frontier moved further and further into the interior, a typical pattern of land use emerged. This began with land clearing by timber compa-nies, followed by the arrival of colonists attracted by the easy availability of cheap land. These early colonists generally practiced shifting cultivation, leaving the land fallow and moving on to clear new land after the land was exhausted (usually 3 – 4 years). As the frontier progressed outward, these early settlers found themselves surrounded by improved rural infrastructures or even urban centers with the value of their land correspond-ingly higher. At that point many colonists sold their plots to second-wave colonists, usually cattle ranchers or capital-intensive agricultural enter-prises. The first-wave colonists then moved on to the new frontier of newly cleared forest to begin the sequence anew, leaving the better-endowed second wave colonists to more intensively work the older lands (Andersen et al., 1996).
Considerable international pressure since 1992 has led to the removal or even reversal of many of the policies that had encouraged land clearing and settlement in the 1970s and 1980s (see Andersen et al., 1996). Indeed, deforestation slowed consider-ably between 1985 and 1994, although many ob-servers attribute this change more to the economic recession and hyperinflation than to changing
5The author has only indirectly heard of the existence of
these studies through informal conversations with scientists who have spent time in the Amazon region.
6See, for example, Mahar (1989), Schneider (1992) or
government policies (Moran, 1993). With a suc-cessful stabilization program now beginning to bear economic fruit in Brazil, figures for 1995 and 1996 reveal an alarming increase in deforestation rates.8
Indeed, currently 16 million people live and work in legal Amazonia, with over 1.4 million living in the city of Manaus (Andersen et al., 1996). The process of deforestation has, in a sense, taken on a life of its own responding to local and national economic forces of population growth, landlessness, and the need for producer and household goods, food and building supplies. Despite recent national ‘environmentally friendly’ legislation, further land clearing and local road building occurs due to these endogenous eco-nomic pressures. The co-movement of deforesta-tion and national economic performance underlines this point: the process of environmen-tal degradation may no longer respond primarily to changes in national land policy (although these are certainly important) but rather is part of the complex interaction of the local and national economies.
While it is beyond the scope of this paper to elucidate the complexities of this relationship, we do believe that a necessary ingredient of a dy-namic, macroeconomic model of the economics of deforestation is some aggregate parameter esti-mate of how crop land degrades over time. The methodology described below is presented as an alternative form to estimate this parameter.
3. Methodology
3.1. Description of the data
The data available for this study was derived largely 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 316 municipalities in the Brazilian Legal Amazonia. The data were cleaned, standardized and merged with data from other sources9 in a painstaking
exercise undertaken by Dr. Eustaquio Reis of the Institute of Applied Economic Research (IPEA) in Rio de Janeiro, without whose work this paper could not have been written.10 For each
munici-pality in each time period the variables11 that are
used for this analysis include total crop land, total planted pasture land, total fallow land, total labor force, value of total crop output, density of roads, population density, percentage land of high qual-ity soil, relative price of land, and finally, the state to which the municipality belongs. The variables and their definitions are reproduced for conve-nience in Table 2. Figs. 1 – 9 show the aggregate evolution from 1970 to 1985 of the percentage of
Table 2
Variable definitions
Total crop land in municipalityiin timet cropit
pastureit Total planted pasture land in municipalityiin
timet
fallowit Total fallow land in municipalityiin timet
laborit Total labor force in municipalityiin timet
Value of total crop output in municipalityiin
outputit
timet
roadit Density of roads in municipalityiin timet
denit Population density in municipalityiin timet
Percentage land of high quality soil in
munici-soilit
palityI
relprit Relative price of land in municipalityiin time
t
stateit The state to which municipalityibelongs
9Other variables in the original data set at IPEA covering
satellite deforestation measures and migration come from the population census and IBGE as well as some other govern-ment agencies. For this paper the data that was used were from the Agricultural Census, however.
10For an extensive discussion of the entire database see
Andersen et al. (1996).
11Some variables appear as logs of the described data in
later parts of the paper and are so noted.
8See Andersen et al. (1996) for 1995 figures. Statements on
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 the analysis.
3.2. O6er6iew of the proposed methodology
The purpose of this paper is to estimate the extent to which the value of crop output declines with time after forest has been cut and the land planted in crops. As described above, data is available in each period on the area of land used for crops and other agricultural activities in each municipality. However, in order to estimate the rate of land degradation directly we would have to know exactly what land was used for each activity, not just the share of the municipality
dedicated to each use. For example, if crop land increases from 20 to 25% between 1980 and 1985, we cannot know how much of the old crop land is still being used and how much is newly cleared or converted land. Thus it is necessary to estimate
Fig. 3. Amazonas. Fig. 5. Roraima.
land that was in crops in timet−1, land that was in pasture in timet−1, or land that was fallow in time t−1. Analogously both pasture and fallow land in time t must also come from these four sources, although the proportion from each source may vary. The land use model is thus:
cropit=b1Dclearit+b2cropit−1+b3pastureit−1
+b4fallowit−1 (1)
pastureit=f1Dclearit+f2cropit−1+f3pastureit−1
+f4fallowit−1 (2)
fallowit=h1Dclearit+h2cropit−1+h3pastureit−1
+h4fallowit−1 (3)
where bj, fj, and hjare parameters that indicate, at time t, what proportion of crop land, pasture land, and fallow land, respectively, come from source j, where jis 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 the model implies that bj+fj+hj=1 forj=1, 2, 3, 4. Eq. (1) holds in all time periods tso we can lag all variables by one period to obtain:
cropit−1=b1Dclearit−1+b2cropit−2
+b3pastureit−2+b4fallowi t−2 (4)
the pattern of land use and land vintage (i.e. to estimate the proportion of crop land that derives from newly cleared land, from old crop land, from pasture land or from fallow land) in each municipality in order to compute the rate of productivity decline.
This estimation is accomplished by first con-structing a land use transition model.12
We distin-guish between natural land which is defined as planted forest, virgin forest and natural pasture, andcleared landwhich is comprised of crop land, planted pasture and fallow land. As this is a closed 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 come from four possible sources: newly cleared land (i.e. land that was in a natural state in timet−1),
Fig. 4. Maranha˜o.
Fig. 6. Mato Grosso.
12This model was originally proposed by Clive Granger and
explored in Andersen and Granger (1995) for the Amazon.
Fig. 7. Amapa´. Fig. 9. Para´.
If we then substitute Eq. (4) into Eq. (1) it is then possible to expand the crop land Eq. (1)14 to get:
cropit=b1Dclearit
+b2(b1Dclearit−1+b2cropit−2
+b3pastureit−2+b4fallowit−2)
+b3pasturet−1+b4fallowit−1 (5)
We then collect terms and interpret the compo-nents of Eq. (5) as corresponding to different vintages of crop land in timet. For example, the first termb1Dclearit is defined as the area of crop land that comes from land that has been newly cleared during the current 5-year period (We note that since our data periodicity is every 5-years time ‘t’ actually corresponds in practice to a 5-year period. Thus timet−1 would correspond to the preceding 5-year period, and so on). We call thisNEWLAND. The second term,b2b1Dclearit−
1, corresponds to land that was newly cleared in the previous 5-year period (time t−1) and planted in crops at that time, and which has
remained in crop land to the present. Thus this land has been in crops for at least 5-years and we denote it5YRLAND. The third term isb22cropit−2
which is the current crop land area that was planted in crops in both the previous 5-year pe-riod and the 5-year pepe-riod before that. This land has been cultivated for at least 10 years and we thus denote it10YRLAND. We define the remain-der of the components of the expanded Eq. (5) in a similar fashion, with the definitions summarized in Table 3.
Thus the coefficient estimates from the crop land Eq. (1) in the land transition model defined above can be used to construct an estimate of the proportion of total crop land that comes from newly cleared land, NEWLAND, from land that was cleared in the previous 5-year period,
5YRLAND, from land that was cleared two 5-year periods ago, 10YRLAND, and from land that has had other uses in the previous time periods, CRPPAS, CRPFAL, PAS and FAL as described in Table 3. We refer to these categories as different6intagesof crop land. We then assume Cobb – Douglas agricultural production:
CROPOUTPUT=ALABORy1LAND j
yj
where A is a technological constant and the nj denote elasticities that give the percentage change in output that results from a unit percentage change in input j. Taking logs of both sides and defining 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+y8falit+oit (6) Fig. 8. Goia´s.
14It would, of course, be possible to expand out the last two
Table 3
Constructed land type (‘vintage’) definitions
Variable name
Term from Eq. Variable definition (5)
NEWLAND
b1Dclearit Land that has been newly cleared sometime during the current 5-year period and planted
in crops
b2b1Dclearit−1 5YRLAND Land that was newly cleared sometime during the previous 5-year period and been used
as crop land continuously since
10YRLAND
b22cropit−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 that
b2b3pastureit−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 that
b2b4fallowt−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 that
Land that was pasture during the previous 5-year period but has now been converted to
b3pasturet−1 PAS
crop land
Land that was left fallow during the previous 5-year period but has now been converted
b4fallowt−1 FAL
to crop land
The estimated coefficients from this regression,61 to67, give us an estimate of the percentage change in output for a 1% change in the corresponding land area. We can easily calculate the percentage change represented by an increase of a given area unit in one land category and the consequent change in output, which will give us an idea of the productivity of that land.
3.3. Estimation procedure for the land use transition model
As described in the previous subsection, the land use transition model has the theoretical property thatbj+fj+hj=1. Also, it is clear that theoretically all the coefficients should lie between zero and one since no less than 0% and no more than 100% of the land of a given type can be converted to crop land. When the basic model is estimated by a heteroskedasticity consistent gener-alized least squares procedure15
(henceforth sim-ply GLS) separately on each equation, the coefficients do indeed sum to one. Two problems emerge, however. First, Andersen and Granger (1995) show that the heterogeneity in the panel can lead to bias in the GLS estimates. Second, the summing up property is an artifact of the data,
and in the presence of heterogeneity comes at the cost of coefficient estimates that occasionally fall outside the [0, 1] bound. We will discuss the het-erogeneity problem first and then how it relates to the second problem of negative coefficient values. Land transition patterns could be expected to vary from municipality to municipality depending on any number of characteristics such as soil quality, population density, land type (savanna etc.), land area, and distance to nearby markets. In addition, the coefficients might be expected to change through time and from state to state. We thus try to control for these factors in the regres-sions. In addition to the above characteristics, we also control for the average price of land. Land prices serve as an excellent proxy for many unob-served (or imperfectly obunob-served) characteristics that impact the desirability of land, such as pres-ence of a rural infrastructure or economic proxim-ity to an urban center. In particular, Andersen et al. (1996) have found that land prices are very
Table 4
Productivity estimates of the value of additional crop output from a one hectacre increase of each given land vintagea
NEWLAND 5YRLAND 10YRLAND
993.42 919.76
Estimate 4955.26
41.18 103.06
St. Dev. 1832.9
aSample mean, 1671.60; sample SD, 1569.15. 15We use White’s Generalized
strongly correlated with subsidized credit and other fiscal incentives for the region. The data on land prices is in current prices so in order to avoid any biases from using a deflator, only relative prices in each year are used, so that each price represents that municipality’s share of total land prices for that year.
It is clearly necessary to take all of this infor-mation into account if meaningful estimates of land degradation are to be calculated. In addition, Andersen and Granger (1995) show that estimates will be biased if the heterogeneity is ignored. However, if we allow theb’s to vary according to different characteristics of the municipality, this multiplies the coefficients to be estimated and increases the probability of coefficient estimates falling outside the theoretical [0, 1] bound.16
This in turn may exacerbate a second problem, which is that the Cobb – Douglas production function that will be estimated must have only non-nega-tive inputs. However GLS on the land transition model does not put any constraints on the coeffi-cient estimates, leading in some cases to negative values.
Thus, although GLS yields the ‘summing up’ property referred to earlier, this is an artifact of the data construction and is achieved at the cost of coefficient estimates that occasionally lie out-side of the [0, 1] interval. While in theory coeffi-cients shouldn’t fall outside this interval, there could be measurement problems and actual cir-cumstances not controlled for in our simple model that could lead to negative GLS estimates. For example, the original census land use data is compiled from people who own agricultural
es-tablishments and report to the census taker how the land is used. In some cases the boundaries between the municipalities is not well defined, and agriculturists and census takers may attribute land to one municipality that actually lies in a neigh-boring municipality. This over-measuring of cleared land in one period may lead in subsequent periods to negative values for the change in cleared land for a particular municipality. This problem occurs most frequently where it would be expected: in the smaller municipalities. Negative values for the change in cleared land is a suffi-ciently common problem that simply eliminating all observations with this property can lead to severe sample selection bias in the estimates. We call this problem ‘shrinking’ and introduce a ‘shrinking’ dummy variable that interacts with the primary variables to allow the coefficients to vary between municipalities which display this prop-erty and those that do not. We thus allow both the land use coefficients and the elasticity esti-mates from the Cobb – Douglas production func-tion to vary according to whether or not a municipality exhibits ‘shrinking’ over time.
In sum, the estimation process thus entails us-ing GLS to estimate the initial land use transition system. Not truncating the coefficient estimates so as to enforce the [0, 1] bound actually accentuates the final results presented below. Therefore, to save space and in the interests of keeping the estimation consistent with the theory, only those results using truncated coefficients are presented in 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 as described in Table 3, and these are in turn used as inputs into a time- and municipality-varying Cobb – Douglas production function in which the elasticities are allowed to vary according to mu-nicipality specific characteristics. Thus we have:
outputit=a+y1itlaborit+y2itnewlandit
+y3it5yrlandit+y4it10yrlandit
+y5itcrppasit+y6itcrpfalit+y7itpasit
+y8itfalit+oit (7)
16Previous versions of this paper have used nonlinear least
squares to impose the restriction of the 0,1 bound on the coefficients. There were several problems associated with this method, however. The models were very difficult to estimate and often did not converge, leading to artificially restricted sets of explanatory variables. The estimates were also very sensitive to the choice of explanatory variables and often produced estimated betas with extremely bimodal distributions. A num-ber of trials were run in which betas estimated with GLS gave similar results to the betas estimated with nonlinear least squares with similar variables. However, by allowing for greater heterogeneity, more complex GLS estimation yields coefficients which are distributed with a unimodal bell shape.
17Primarily the untruncated productivity estimates differ in
Table 5
Land use regression results: dependent variable=crop land (1985)a,b
Tfor H0: Parameter
Variable Variable Parameter Tfor H0:
estimate
parameter =0 parameter =0
estimate
−1.589 CROPS8
DCLEAR −0.072620 0.571888 6.014***
0.506
CROPL1 0.127855 PASSAV 0.021368 3.828***
2.852*** PASSOI
0.170512 −0.029589
FALLOL1 −2.020***
0.015924
PASTUL1 0.739 PASDEN −0.000083341 −0.186
−0.066628
CLEARSAV −4.055*** PASARE −0.001302 −0.769
0.095 PAS5
0.003818 0.009524
CLEARSOI 2.571***
1.285
CLEARDEN 0.000869 PAS80 −0.011756 −2.518***
2.858*** PAS85
0.010913 −0.006182
CLEARARE −1.335
0.015403
CLEAR80 1.375 PASPR 1.697775 0.642
−0.033775
CLEAR85 −2.608*** PASSQ 17.702235 0.074
1.478 PASTURS2
7.112195 0.040851
CLEARPR 0.593
0.041 PASTURS3
CLEARSQ 15.281006 −0.095735 −1.983**
1.628*** PASTURS5
0.072107 0.000803
DCLEARS2 0.094
0.084827
DCLEARS3 2.901*** PASTURS6 −0.022572 −1.116
0.011887
DCLEARS5 0.664 PASTURS7 0.003730 0.317
0.127 PASTURS8
0.003950 −0.011261
DCLEARS6 −1.937**
1.386 FALSAV
DCLEARS7 0.028833 −0.018554 −0.795
3.962*** FALSOI
0.047039 0.040522
DCLEARS8 0.978
0.143347
CROPSAV 1.285 FALDEN −0.000540 −1.242
−0.197411
CROPSOI −1.451 FALARE −0.013747 −2.738***
−0.512 FAL5
−0.000796 −0.010793
CROPDEN −0.877
3.983*** FAL80
CROPARE 0.073664 0.028101 1.907**
−3.583*** FAL85
−0.204976 −0.059743
CROP5 −4.081***
−0.101815
CROP80 −1.325 FALPR 22.797138 3.621***
−0.051464
CROP85 −0.738 FALSQ −304.697179 −0.894
−1.906* FALLOWS2
−24.030320 0.008875
CROPPR 0.085
0.932 FALLOWS3 −0.017157 −0.485
CROPSQ 233.998902
−0.010 FALLOWS5
−0.003254 −0.016179
CROPS2 −0.641
0.294712
CROPS3 2.252** FALLOWS6 0.096211 0.979
0.260649
CROPS5 2.164** FALLOWS7 −0.031654 −1.271
0.359 FALLOWS8
0.161712 −0.093095
CROPS6 −3.837***
2.660** CROPS7 0.332501
aRegressionN, 945.
bR-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 each land type input by one hectacre and compare these yields across the different vintages of land. The difference between the yields on newly cleared land and land that has been in crops for longer periods will give us an estimate of the rate at which agricultural productivity is changing over time.
4. Results
4.1. Construction and estimation of the land use transition model
As discussed earlier we wish to allow the coeffi-cients to vary from municipality to municipality and over time depending on various characteris-tics of the location and land.
Table 6
Cobb–Douglas regression resultsa,b
Dependent variable=log(real crop output)
Parameter
Variable Tfor H0: Variable Parameter Tfor H0:
estimate
estimate parameter=0 parameter=0
23.950*** YR105
INTERCEPT 7.462146 −0.305727 −4.139***
−0.025811
LABSH −0.310 YR108 −0.160449 −2.383**
0.021742
NEWLAND 0.925 CRPPAS2 −0.197825 −0.777
0.204 CRPPAS5
0.005104 −0.066042
YR5LAND −1.340
−0.003567
YR5SH −0.179 CRPPAS7 0.019352 0.445
4.894** CRPPAS8
0.323511 0.126619
Y10LAND 2.199**
0.009743
YR10SH 0.125 CRPFAL2 0.124595 0.384
−0.021759
CRPFAL −0.478 CRPFAL3 0.179939 2.610***
0.889 CRPFAL5
0.031160 0.305736
CRPFSH 4.636***
0.186 CRPFAL6
PAS 0.007579 −0.183971 −1.017
−0.365 CRPFAL7
−0.012335 0.022055
PASSH 0.408
0.012004
CRPPAS 0.285 CRPFAL8 0.082920 1.558
0.038276
CRPSH 1.268 PAS2 0.142451 0.686
0.501 PAS5
0.011520 −0.033912
FAL −0.725
FALSH 0.027226 1.549 PAS7 −0.039818 −0.912
−0.383 PAS8
−0.029738 0.042607
NEW2 0.726
0.010081
NEW3 0.268 FAL2 0.078883 0.687
0.045140
NEW5 1.418 FAL3 −0.016650 −0.529
1.467 FAL5
0.109607 0.050125
NEW6 1.673
−0.053 FAL6
NEW7 −0.001562 0.488438 2.491***
2.286** FAL7
YR53 0.116 NEWSOI 0.049929 1.249
1.267 YR5SOI
0.041157 −0.028029
YR55 −0.705
−3.473***
YR56 −0.294741 YR10SOI 0.049763 0.489
0.716 CRPPSOI
0.020344 −0.212787
YR57 −2.166***
0.094037
YR58 2.902*** CRPFSOI −0.129868 −1.595
YR102 −0.060895 −0.428 PASSOI −0.031603 −0.349
−1.863* FALSOI 0.078401 1.564
−0.133088 YR103
aRegressionN, 629.
bR-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 the square of the relative price of land in that municipality.
GLS regression results from the land use tran-sition model are presented in Table 6. Variable names 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 denoted by soi, percentage of savanna land is sa6, log of
The estimatedb’s are in turn themselves used to construct the land categories described in Section 3. If the technique is accurate, the sum of all seven land categories ought to be close to the actual area of crop land in 1985. For both truncated and untruncatedb’s the percentage error between actual and predicted area of crop land is quite similar. The mean percentage error is−0.308 for the truncated b’s and −0.2216 for the untruncated b’s, with respective standard deviations 1.954 and 1.717. These seemingly high and variable percentage errors are almost completely determined by a very few outliers (most caused by large errors in the estima-tion ofCRPPAS andCRPFAL), however, as the corresponding medians are 0.038 and 0.068, respec-tively. If the worst offenders of these outliers are deleted, the mean errors fall dramatically. This is clearly illustrated in the case of the untruncatedb‘s, whose mean error, when the ten largest percentage error outliers are deleted, falls to −0.040 with a standard deviation of 0.735. At any rate, although some of these large outliers may lead to large errors in the estimates of productivity of CRPPAS and CRPFAL, they have very little impact on the estimated productivity ofNEWLAND,5YRLAND or 10YRLAND. The fundamental results on pro-ductivity reported below are extremely robust to the inclusion or exclusion of any of these outliers.
4.2. Estimation of the loss of crop producti6ity
The estimatedb’s are different for each munic-ipality and over time. These estimated coefficients are in turn used to estimate the land categories described in Section 3 for each municipality. Taking logs of both the land categories, labor and output a heteroskedasticity-consistent18GLS estimation of
a Cobb – Douglas production function (Eq. (7)) produces estimates of the relative elasticities for each land category.
As with the land transition model, it could be expected that productivity of various land types could vary across municipalities. For this reason the elasticity estimates are allowed to vary by soil type, state, and whether or not the municipality displays the measurement problem we call ‘shrinking’. In
addition each coefficient is allowed to vary over time to capture any general shift between sample periods. The relative price variable was not included in this regression due to the possibility of endogeneity between the value of crop output and land prices. For example, it could be the case that higher levels of agricultural output led to higher land prices rather than the reverse. If this is the case then including land prices on the right-hand side of the regression could induce bias in the coefficient estimates.
Table 6 presents the results of the Cobb – Douglas GLS regression of the log of crop output on the logs of the different land types, allowing the coefficients to vary according to the variables described above. Although the names of the variables seem a bit difficult, again in fact, they are simply a compound of the two variables compromising the interaction variable. The first part of the name corresponds to the land type, the second part to the interaction variable. Shrink is denoted by sh, percentage of good soil issoiand each state is represented by its corresponding number. The time shift dummy variable is represented by t85.
The final elasticities are calculated for each municipality in each time period using the estimated coefficients. Each of these elasticities is multiplied by (100/landj) which gives the percentage change in output produced by an increase of 1 area units of land in any given land categoryj. This percentage is then converted into an actual monetary change in output for the 1 area unit increase in crop land. These productivities are then averaged over all municipalities for each land category. In order to avoid letting a few outliers impact the mean exces-sively, each observation that falls outside of 2 SDs of the mean is deleted before averaging, leaving a mean that is closer to the median.19
The percentage change in output estimates are multiplied by the actual real output in each munic-ipality to give a monetary unit estimate of the increase in output for a 1 area unit increase in each type of land (i.e. marginal output). The main results are presented in Table 4 which focuses on
19Including the outliers essentially increases the productivity
estimates ofNEWLANDbut does not impact much the esti-mates of5YRLANDor10YRLAND.
the calculated productivity estimates (after delet-ing outliers as described above) forNEWLAND,
5YRLAND and 10YRLAND, and provides the sample 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$ (1985 prices);
increasing 5-year-old crop land area by one hectacre will increase output by an average of only 920 R$;
increasing 10-year-old crop land area by one hectacre will increase output by an average of about 1000 R$; it is important to note, how-ever, that this figure is not statistically different from the estimate of 920 R$ from increasing 5-year-old crop land.
The results imply a dramatic fall in productivity in the first 5-years after initial land clearing. The additional output from a 1 unit area increase in 5-year-old crop land is only 20% of the value of an additional unit of newly cleared land. Since the time span between periods is 5-years, these figures yield an annualized rate of just over 30% decline in agricultural productivity per year. This figure corresponds closely to the rates predicted by field research and to the general consensus of experts in the region of what the average rate of land degradation 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 cultivated first (i.e. the oldest land) was the best quality land settlers could find. In addition, the result could also be expected given the common land use patterns that prevailed at the time. Early colonists would clear land and practice low-capital shifting agriculture for a few years until the land was exhausted, then abandoning or selling the land to
better-endowed second-wave settlers who used more intensive agricultural practices to keep yields at sustainable levels.
5. Conclusions
This paper has presented an estimation proce-dure that uses data on areas of crop, pasture, and fallow from 1970, 1975, 1980, and 1985 and com-bines this with estimates of crop output value, the labor force and a variety of natural and demo-graphic municipality characteristics to calculate a general estimate of the average rate of decline of agricultural productivity that prevailed in the Amazon during the sample period. The procedure has two primary steps, and although data hetero-geneity may be a problem throughout both of these steps, it is shown that the estimated pattern and magnitude of land degradation does not vary much as the sample is restricted to only those observations without large outliers included in their construction. Measurement problems are also a serious concern with this data set. Never-theless, the actual money figures that are derived are within the neighborhood of sample averages and the calculated rate of land degradation is consistent with field research in this area. The results show strong evidence for a precipitous drop in productivity in the first 5-years after land has been cleared for crops, with an estimated fall of 30% per year in productivity. The productivity estimates increase slightly between 5-year-old crop land and 10-year-old crop land, although this increase is not statistically significant. The stabi-lization of productivity between 5 and 10 years may be explained by several observations. First, it is expected that the best land will be cultivated first. In addition, it has been noted that after the first few years a second wave of more permanent settlers move into the area and proceed to culti-vate the land more intensively and use more fertil-izer. Finally, land that has been continuously in cultivation for 10 years is most likely planted with perennial crops which do not deplete the soil as rapidly.
The estimates of the rate of land degradation presented in this paper differ in several ways from
20Readers should note that the reported standard deviations
the estimates derived from scientific field studies or case studies. A disadvantage of the estimates presented here is that they do not give an indica-tion of where the productivity frontier is, i.e. what agricultural productivity could be under ideal conditions. They cannot be used to derive what the optimal cropping patterns are, nor to compare the economic performance of different crops. Thus the proposed methodology is in no way meant as a substitute for careful field analysis.
On the other hand, the methodology proposed here has some advantages over field research as well. The average rates of land degradation thus calculated contain dynamic information from a much longer time period (15-years) and much larger area (Brazilian Legal Amazonia) than most field studies. Despite the extensive dynamic and spatial coverage, the models allow for the fact that land use patterns and methods of cultivation differ across space and have changed over time. Thus, to a much greater extent than is possible in a specific field study, the methodology outlined in this paper incorporates the actual distribution of agricultural activity that existed over the sample period in the Brazilian Amazon. The methodol-ogy produces estimates of the a6erage rate of agricultural productivity decline that prevailed over the sample period, given the pattern of crops and land use that existed, rather than the exact rate of land degradation for a particular crop, agricultural intensity and/or location.
Acknowledgements
The author acknowledges the partial support of NSF (Grant¯cSBR-930081). The much
appreci-ated support and advice of Eustaquio Ries, Clive W.J. Granger and Lykke Andersen, as well three anonymous referees, have all been invaluable. In addition, the author gratefully recognizes the helpful comments of participants of workshops at Indiana University, University of Houston, and Southern Methodist University and at the Econo-metric Society Meetings in Rio de Janeiro and the Southern Economic Association Meetings in Washington D.C. All errors are my own.
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