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 sources
9
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 variables
11
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 municipality i in time t crop
it
pasture
it
Total planted pasture land in municipality i in time t
fallow
it
Total fallow land in municipality i in time t labor
it
Total labor force in municipality i in time t Value of total crop output in municipality i in
output
it
time t road
it
Density of roads in municipality i in time t den
it
Population density in municipality i in time t Percentage land of high quality soil in munici-
soil
it
pality I relpr
it
Relative price of land in municipality i in time t
state
it
The state to which municipality i belongs
9
Other 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.
10
For an extensive discussion of the entire database see Andersen et al. 1996.
11
Some variables appear as logs of the described data in later parts of the paper and are so noted.
8
See Andersen et al. 1996 for 1995 figures. Statements on 1996 deforestation rates are based on newly released statistics
from 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 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. 2. Acre.
Fig. 3. Amazonas. Fig. 5. Roraima.
land that was in crops in time t − 1, land that was in pasture in time t − 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:
crop
it
= b
1
Dclear
it
+ b
2
crop
it − 1
+ b
3
pasture
it − 1
+ b
4
fallow
it − 1
1 pasture
it
= f
1
Dclear
it
+ f
2
crop
it − 1
+ f
3
pasture
it − 1
+ f
4
fallow
it − 1
2 fallow
it
= h
1
Dclear
it
+ h
2
crop
it − 1
+ h
3
pasture
it − 1
+ h
4
fallow
it − 1
3 where b
j
, f
j
, and h
j
are parameters that indicate, at time t, what proportion of crop land, pasture
land, and fallow land, respectively, come from source 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 the
model implies that b
j
+ f
j
+ h
j
= 1 for j = 1, 2, 3,
4. Eq. 1 holds in all time periods t so we can lag all variables by one period to obtain:
crop
it − 1
= b
1
Dclear
it − 1
+ b
2
crop
it − 2
+ b
3
pasture
it − 2
+ b
4
fallow
i 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, and cleared land which 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 land
13
Dclear, can be constructed as:
clear
it
= crop
it
+ pasture
it
+ fallow
it
Dclear
it
= clear
it
− clear
it − 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 time t − 1,
Fig. 4. Maranha˜o.
Fig. 6. Mato Grosso.
12
This model was originally proposed by Clive Granger and explored 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 then possible to expand the crop land Eq. 1
14
to get: crop
it
= b
1
Dclear
it
+ b
2
b
1
Dclear
it − 1
+ b
2
crop
it − 2
+ b
3
pasture
it − 2
+ b
4
fallow
it − 2
+ b
3
pasture
t − 1
+ b
4
fallow
it − 1
5 We then collect terms and interpret the compo-
nents of Eq. 5 as corresponding to different vintages of crop land in time t. For example, the
first term b
1
Dclear
it
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 time t − 1 would correspond to
the preceding 5-year period, and so on. We call this NEWLAND. The second term, b
2
b
1
Dclear
it −
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 it
5
YRLAND. The third term is b
2 2
crop
it − 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 period before that. This land has been cultivated for at least 10 years and we
thus denote it
10
YRLAND. 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,
5
YRLAND, from land that was cleared two 5- year periods ago,
10
YRLAND, 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 different 6intages of crop land. We then assume Cobb – Douglas agricultural production:
CROPOUTPUT = ALABOR
y
1
LAND
j y
j
where A is a technological constant and the n
j
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:
output
it
= a + y
1
labor
it
+ y
2
newland
it
+ y
3
5yrland
it
+ y
4
10yrland
it
+ y
5
crppas
it
+ y
6
crpfal
it
+ y
7
pas
it
+ y
8
fal
it
+ o
it
6
Fig. 8. Goia´s.
14
It would, of course, be possible to expand out the last two equations as well, which would enable us to estimate the
dynamics of pasture productivity from data on cattle herd. However, this is not necessary for the task at hand.
Table 3 Constructed land type ‘vintage’ definitions
Variable name Term from Eq.
Variable definition 5
NEWLAND b
1
Dclear
it
Land that has been newly cleared sometime during the current 5-year period and planted in crops
b
2
b
1
Dclear
it−1
Land that was newly cleared sometime during the previous 5-year period and been used
5
YRLAND as crop land continuously since
10
YRLAND b
2 2
crop
it−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
b
2
b
3
pasture
it−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 b
2
b
4
fallow
t−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
b
3
pasture
t−1
PAS crop land
Land that was left fallow during the previous 5-year period but has now been converted b
4
fallow
t−1
FAL to crop land
The estimated coefficients from this regression, 6
1
to 6
7
, 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 that b
j
+ f
j
+ h
j
= 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 procedure
15
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 observed 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 vintage
a
NEWLAND
5
YRLAND
10
YRLAND 993.42
919.76 Estimate
4955.26 41.18
103.06 St. 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 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 the b’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:
output
it
= a + y
1it
labor
it
+ y
2it
newland
it
+ y
3it
5yrland
it
+ y
4it
10yrland
it
+ y
5it
crppas
it
+ y
6it
crpfal
it
+ y
7it
pas
it
+ y
8it
fal
it
+ o
it
7
16
Previous 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.
17
Primarily the untruncated productivity estimates differ in that the productivity of NEWLAND is considerable higher.
Table 5 Land use regression results: dependent variable = crop land 1985
a,b
T for H0: Parameter
Variable Variable
Parameter T for H0:
estimate parameter = 0
parameter = 0 estimate
− 1.589
CROPS8 DCLEAR
0.571888 −
0.072620 6.014
0.506 CROPL1
PASSAV 0.127855
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
PAS80 0.000869
− 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 −
0.095735 15.281006
− 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 −
0.018554 0.028833
− 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 0.028101
0.073664 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
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 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.
Thus each coefficient in the model is defined as varying by year, state, share of savanna land,
Table 6 Cobb–Douglas regression results
a,b
Dependent variable = logreal crop output Parameter
Variable T for H0:
Variable Parameter
T for H0: estimate
estimate parameter = 0
parameter = 0 23.950
YR105 INTERCEPT
− 0.305727
7.462146 −
4.139 −
0.025811 T85
− 0.331
YR106 −
0.276502 −
1.263 13.414
YR107 0.687467
− 0.062654
LLABOR −
0.958 −
0.018486 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
− 0.183971
0.007579 −
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 0.488438
− 0.001562
2.491 2.286
FAL7 0.082432
− 0.021756
NEW8 −
0.875 −
0.016530 YR52
− 0.356
FAL8 −
0.090620 −
2.653 0.003639
YR53 0.116
NEWSOI 0.049929
1.249 1.267
YR5SOI 0.041157
− 0.028029
YR55 −
0.705 −
3.473 YR56
YR10SOI −
0.294741 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
− 0.428
− 0.060895
PASSOI −
0.031603 −
0.349 −
1.863 FALSOI
0.078401 1.564
− 0.133088
YR103
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 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 area of the municipality is are, population den-
sity is den, relative prices are denoted by pr and the square of relative prices is sq. Each state is
denoted by its corresponding number, and time shifts are clearly named by the year. The model
explains about 94 of the variation in crop land although since there is no intercept in the
model due care must be exercised in interpreting the R-squared statistics. These coefficient esti-
mates are then used to calculate the land use transition b’s for each municipality in each sam-
ple period.
The estimated b’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 untruncated b’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 of CRPPAS and CRPFAL, 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 untruncated b‘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 of NEWLAND,
5
YRLAND or
10
YRLAND. 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 estimated b’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-consistent
18
GLS 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 is soi and each state is represented by its corresponding number. The time shift dummy
variable is represented by t
85
. The final elasticities are calculated for each
municipality in each time period using the estimated coefficients. Each of these elasticities is multiplied
by 100land
j
which gives the percentage change in output produced by an increase of 1 area units of
land in any given land category j. 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
19
Including the outliers essentially increases the productivity estimates of NEWLAND but does not impact much the esti-
mates of
5
YRLAND or
10
YRLAND.
18
White’s heteroskedasticity consistent methodology.
the calculated productivity estimates after delet- ing outliers as described above for NEWLAND,
5
YRLAND and
10
YRLAND, 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
