NCEE#
NATIONAL CENTER FOR
ENVIRONMENTAL ECONOMICS
Forest Fallow Ecosystem Services: Evidence from the Eastern
Amazon
Heather Klemick
Working Paper Series
Working Paper # 08-05
May, 2008
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U.S. Environmental Protection Agency
National Center for Environmental Economics
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Forest Fallow Ecosystem Services: Evidence from the Eastern
Amazon
Heather Klemick
NCEE Working Paper Series
Working Paper # 08-05
May, 2008
DISCLAIMER
The views expressed in this paper are those of the author(s) and do not necessarily represent
those of the U.S. Environmental Protection Agency. In addition, although the research described
in this paper may have been funded entirely or in part by the U.S. Evironmental Protection
Agency, it has not been subjected to the Agency's required peer and policy review. No official
Agency endorsement should be inferred.
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Forest Fallow Ecosystem Services: Evidence from the Eastern Amazon
Heather Klemick
National Center for Environmental Economics
US Environmental Protection Agency
1200 Pennsylvania Ave, NW (1809T)
Washington, DC 10460
klemick.heather@epamail.epa.gov
202-566-2522 (phone)
202-566-2338 (fax)
This research was supported in part by the Bundesministerium fur Bildung und
Forschung (BMBF) and the Brazilian National Council for Research (CNPq). I thank
Ramon Lopez, Erik Lichtenberg, Maureen Cropper, Howard Leathers, and Marc Nerlove
for their comments and suggestions.
Subject categories: forests (25), sustainable agriculture (39), environment and
development (49)
Key words: forest, farms, fallow, ecosystem services, land use, spatial econometrics,
externalities, Brazil
May 28, 2008
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Abstract
With tropical deforestation a major contributor to greenhouse gas emissions and
biodiversity loss, the land-use decisions of small-scale farmers at the forest margins have
important implications for the global environment. Farmers' incentives for maintaining
forest fallow in a shifting cultivation agricultural system depend upon the market and
non-market services it provides to them. This study estimates the value of those services,
including hydrological externalities that may affect other farms downstream.
The analysis uses cross-sectional farm-level survey data from the Zona Bragantina in the
Eastern Brazilian Amazon to assess the value of forest fallow to farmers and test whether
it provides local externalities. I estimate production functions for crops and forest
products to determine the contributions of on-farm and off-farm forest fallow to income
from these two activities. Instrumental variables and spatial econometric approaches help
address issues of endogeneity and variation in unobservable factors over space. I use
geographic information on the location of farms to obtain data on external forest fallow
and to model the hydrological externality as an upstream-to-downstream process.
The results indicate that fallow does contribute significantly to productivity both on-farm
and downstream, boosting income from both crops and forest products. In addition, most
farms appear to allocate sufficient land to fallow, accounting for both the value of
hydrological spillovers and the opportunity cost of land left out of cultivation. These
results suggest that farming communities may have some self-interest in preserving forest
cover locally—a finding that may bolster policy efforts aimed at conserving tropical
forests.
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Introduction
With tropical deforestation a major contributor to greenhouse gas emissions and
biodiversity loss, the land-use decisions of small-scale farmers at the forest margins have
important implications for the global environment. In some tropical forested areas, such
as the Zona Bragantina in the Eastern Brazilian Amazon, farmers practice a shifting
cultivation, or slash-and-burn, system that maintains large amounts of land under forest
fallow. Farmers' incentives for maintaining forest fallow depend upon the market and
non-market services it provides to them. This study estimates the value of fallow
ecosystem services in shifting cultivation, including hydrological externalities that may
affect other farms downstream.
Where land is abundant and other inputs are scarce, long fallow periods can be a
cost-effective way to restore land for future agricultural uses. Secondary forest fallow
provides on-site benefits to farmers, such as soil regeneration, erosion prevention, weed
control, and harvestable products. It also provides off-site services, supplying some of
the same public goods as mature forests. These services are not only global in scale but
may also be local, such as hydrological regulation that moderates the flow of water in the
soil. Understanding the magnitude of secondary forests' contribution to agricultural
productivity will be increasingly important as population and economic pressures spur
many of the estimated 300 million1 shifting cultivators world-wide to shorten fallow
periods, adopt new technologies, and intensify cultivation. Valuing the net benefits of
forest cover to local populations could help justify conservation efforts with global
importance (Chomitz and Kumari 1998).
1 Current estimates of the number of shifting cultivators are hard to come by. The 300-million figure was
given by Sanchez (1996) and Brady (1996).
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Economic studies accurately estimating the value of forest ecosystem services are
sparse, and results from hydrologic studies have been ambiguous as to the effects of
reforestation on water yields (Bruijnzeel 2004). The Millennium Ecosystem Assessment
(2005) has identified lack of information about the value of non-market ecosystem
services—particularly regulating services such as hydrological functions—as a major
knowledge gap hampering informed decision-making on ecosystem management.
This paper takes up this challenge by quantifying the returns to fallowing in
agricultural production. The analysis uses cross-sectional farm survey data from the
Zona Bragantina to assess the value of forest fallow to farmers and test whether it
provides economically significant local externalities that may justify forest conservation
from a local perspective. Private land tenure in the study region allows me to disentangle
the on-farm and externality effects. I estimate production functions for crops and forest
products to determine the contributions of on-farm and off-farm forest fallow to income
from these two activities. Instrumental variables and spatial econometric approaches help
address issues of endogeneity and variation in unobservable factors over space. I use
geographic information on the location of farms to obtain farm-level data on external
forest fallow and to model the hydrological externality as an upstream-to-downstream
process, allowing for identification in the presence of spatial correlation.
Fallow as a production input in shifting cultivation
In many contexts world-wide, fallow is a common property resource prone to
overexploitation in the absence of community controls (Lopez 1993, 1997). Even under
private land tenure, inefficiencies could arise if fallow biomass provides local positive
externalities in addition to on-site ecosystem services. Correcting these inefficiencies can
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boost downstream farm income while providing incidental carbon sequestration services.
Thus, whether fallow biomass provides economically significant local externalities is an
empirical question with important implications for tropical forest policy.
Fallowing restores plots for future cultivation by drawing soil nutrients and water
to the surface, raising soil pH, minimizing surface erosion, and suppressing weeds
(Nepstad et al. 2001; Holscher et al. 1997; Altieri 1995; Sanchez et al. 1982; de Rouw
1995; Staver 1991).2 Root systems remain intact after manual land clearing, fostering
rapid vegetative regeneration during initial fallow years. Forest cover also plays an
important role in the hydrological cycle. Tree cover lessens peak flows and surface
runoff due to increased soil infiltration capacity and evapotranspiration of soil water
(Hamilton and King 1983, Bruijnzeel 2004), which may benefit agricultural activities by
reducing floods and waterlogging.
While few studies have estimated the value of fallow biomass and forest cover in
agricultural production, some have found that it provides economically important
services. Lopez (1993, 1997) showed that village-level fallow biomass (capturing both
on-farm soil quality and external hydrological benefits) contributed significantly to
agricultural profitability in Ghana and Cote d'lvoire. Research in Ruteng National Park,
Indonesia, found that off-farm forest cover provided beneficial hydrological services (in
this case, drought mitigation) to small-scale agricultural production (Pattanayak and
Kramer 2001; Pattanayak and Butry 2005).
2 Secondary forest root systems also provide below-ground carbon storage comparable to that of mature
forests (Sommer et al. 2000), although converting land to shifting cultivation entails a loss of above-ground
carbon stocks. In addition, forest stands can affect nearby farms' productivity through crop pollination
(Ricketts et al. 2004, Kremen et al. 2004) and tree seed availability (Tucker et al. 1998). I do not
concentrate on these services here.
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Study region and data
The Zona Bragantina offers a compelling case study as a region with over one
hundred years of agricultural settlement where shifting cultivation persists as the
principal means of livelihood. Despite integration into regional markets through railways
and roads, perennial cash-crop agro-processing, and government programs to encourage
agricultural intensification, shifting cultivation dominates other land-use practices in the
region. Figure 1 presents a map of the region.
Most households in Bragantina are considered smallholders by Brazilian
standards, with landholdings under 100 hectares. Family labor and manual land clearing
predominate, though hired labor and mechanized equipment are also used for labor-
intensive tasks like land preparation, weeding, and harvesting. A typical one to two year
cropping sequence includes maize, upland rice, and cowpea, with cassava grown as the
final crop while fallow vegetation reestablishes (Holscher et al. 1997). These annual
crops are used for home consumption and sale to regional markets. Since the mid
twentieth century, smallholders have also branched into perennials like black pepper,
passion fruit, oranges, and coconut, as well as ranching.
While virtually all virgin forest in Bragantina has been cleared over the decades,
roughly 75% of the land area remains under secondary forest (Kato et al. 1999). Soil is
relatively homogenous in the region, though rainfall does decrease along a gradient from
west to east (Borner 2005). The climate is humid, receiving an average rainfall of 2400-
2700 mm annually. The region faces major challenges in improving agricultural
productivity due to poor quality Oxisol, Spodosol, and Ultisol soils vulnerable to acidity
and aluminum toxicity (Tucker et al. 1998; Holscher et al. 1997). Experiments varying
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fertilizer treatments in the Zona Bragantina identified phosphorus and nitrogen as major
limiting factors in crop production and fallow biomass growth (Gehring et al. 1999).
Data for the study were collected as part of the SHIFT (Studies on Human Impact
on Forests and Floodplains in the Tropics) project, an initiative to study tropical
livelihoods and ecosystem dynamics in Brazil. Three municipios out of the 14 that
comprise the Bragantina were chosen for study to capture regional variation in distance to
commercial centers, agricultural intensification, and rainfall (Mendoza 2004). In late
2002, 271 households in 22 villages were randomly selected and surveyed. The survey
gathered farm production, land use, and demographic data for the 2001-2002 growing
season. Table 1 presents the mean values for selected household-level characteristics.
Comprehensive farm-level data on forest fallow for the entire Zona Bragantina
would be ideal to estimate the off-site flow of benefits and their spatial scale, but are
unavailable. I make use of the household survey data on land use among the sampled
farms as one solution. As an additional approach to address this gap, I turn to GIS
(geographic information systems) data on forest cover, using the MODIS Vegetation
Continuous Fields (VCF) to construct an alternative measure of external fallow. The
VCF data consist of 25 hectare resolution pixels created using 40 day composite satellite
images from March 2001-March 2002 (Hansen et al. 2006).3 Each pixel represents
percent canopy cover, defined as the amount of sunlight blocked by tree canopies over
five meters high. Figure 2 shows 2001-02 tree canopy cover for the Zona Bragantina.
3 The 2001-02 VCF data provide the closest available estimates of forest cover during the 2001-2002
cropping season. Twenty-five hectare pixels are a sufficiently fine measure of tree cover relative to the size
of landholdings among the surveyed farmers, as the median farm size is also 25 hectares. The percent
canopy cover approximates both the area and density of forest cover, since the share of land with five-
meter tree cover is likely to be highly correlated with vegetation density.
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I also use GIS flow direction data from the US Geological Survey to determine
where farms lie along a gradient from upstream to downstream in relation to one another.
According to a flow direction map for the region (Figure 3), farms cluster into 11 groups
defined by a common drainage area and flow direction. Each cluster includes at least one
sampled community. Within each group, I assume each observation affects farms
downstream and is affected by farms upstream. The US Geological Survey also provides
slope data for the region at 1-km resolution.
Crop production function estimation
My approach to valuing the services provided by on-farm and off-site forest
fallow involves estimating production functions for two primary activities in the Zona
Bragantina: crop production and forest product harvesting.4 The surveyed farmers
produced a total of 50 annual and perennial crops, with cassava, maize, beans, and black
pepper among the most common. Collecting forest products made a modest contribution
to income relative to cropping but was practiced by over two-thirds of the surveyed
farms. The production function estimations allow me to measure the contribution of on-
and off-farm fallow to these activities and test for positive fallow externalities in each. I
also calculate the contribution of fallow resources to total farm income by aggregating
the respective contributions of fallow to crops and forest products.
The dependent variable in the crop production function is the log of crop output
value, with different commodities aggregated using average output prices in the region.
Although farms reserved some crops for home consumption, market prices provide
appropriate values for these commodities since 97% of sampled farmers sold at least
4 Ranching and livestock products make up the remainder of agricultural activities, though they are less
common in the Zona Bragantina than either cropping or forest product collection.
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some of their produce. I employ a Cobb-Douglas specification for cropping technology.
Output is modeled as a function of cultivated land area, family and hired labor, fertilizer,
on-farm fallow area, and off-farm (upstream) fallow area.5
The crop value equation can be represented as follows
Inyt =Po +px In / + P2WX In F + & In Xt + j34Ht + st
sj = AW2s + uj
where y; represents the ith farm's crop value. The farm's fallow area is represented by f,,
while F is a vector of all farms' fallow area. Cultivated land area, family and hired labor,
and fertilizer are represented by X;, a vector of conventional inputs.
The error term is given by 8;, which includes a component that varies over space
and a white noise term, u,. A spatial error model accounts for the fact that unobserved
factors may influence farmers' and their neighbors' land use decisions in similar ways,
allowing for efficient estimation of the parameters. The strength of the spatial correlation
among the disturbances is represented by X.
Spatial weighting matrices for off-farm fallow and the error term are represented
by Wi and W2, respectively. Wi is a row-normalized matrix that gives equal weight to
neighbors upstream of each farm to capture the hydrological externalities of local forest
fallow.6 Wi In F thus represents a weighted average of off-farm fallow area upstream of
each observation.7 I also refer to this term as a spatial lag of the fallow variable.8
5 Because farm products are marketed goods, valuation of the fallow ecological services using a production
function approach is straightforward and does not depend on detailed knowledge of the ecological
mechanisms at work (Maler 1991).
6 Estimation results do not qualitatively differ when upstream neighbors are weighted by inverse distance.
7 Although row normalization is not appropriate in all spatial analyses, normalizing by the number of
sampled farms in each farm's neighborhood is important in this case to avoid inferring that farms with
more sampled neighbors have higher levels of nearby forest cover.
8 Following the convention used by Anselin (1988) and others, I use the term spatial lag to mean a
weighted sum of neighboring or contiguous values of the variable of interest, somewhat analogous to the
concept of temporally-lagged variables in time-series analysis.
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W2 is a matrix of inverse distances between all sampled farms, reflecting
correlation in unobserved factors expected to decline with distance, such as weather
shocks. W2 is not row normalized, as row normalization would imply that more isolated
farms are affected by their neighbors' disturbances as much as farms with many
neighbors in close proximity. The uniqueness of the two spatial weighting matrices is
thus justified conceptually, and it allows for identification of the spatial autoregressive
parameters.9 However, if spatial correlation among the disturbances or other non-
stochastic factors follows the same pattern as the hypothesized hydrological externality,
then these effects cannot be disentangled without further parameter restrictions.
I include household and farm characteristics in the vector H, to control for
observable aspects of management ability and land quality. The household head's
schooling years, use of extension services, and land ownership help control for farmer
management skills. A binary variable for perennial crop production controls for the
higher prices perennial crops command in regional markets relative to annual crops.10
Land quality indicators include farmer-reported dummy variables for black clay and
charcoal-enriched soil ("massape" and "preto," both favorable types) and poor soil
("araca") and GIS data on slope, which indicates the farm's vulnerability to erosion.
While soil is fairly homogenous throughout the region and land is not steeply sloped,
these variables help account for micro-level agroecological variation. The equation also
9 As shown by Anselin 1988 (pp. 84-85), spatial lag and spatial error parameters are generally not identified
without nonlinear restrictions when the two weighting matrices are the same.
10 In a preliminary attempt to control for the potential endogeneity of producing perennial crops, I estimated
a treatment effects model. I could not reject they hypothesis that the crop output and perennial production
equations are independent (p = 0.86-0.88, depending on the measure of off-farm fallow used), so I treat
perennial production as exogenous in the regressions that follow. Perennial crops can be grown in soil
conditions found throughout the Zona Bragantina. However, farmers with facing higher rainfall, better
access to extension services, and those less averse to price risks are more likely to produce perennials.
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includes municipality dummies. Table 2 reports the mean values for the variables used in
the production function estimation.
The primary parameters of interest are the coefficients of on-farm fallow and
external fallow. These coefficients give the output elasticities of on-farm and external
fallow, indicating the contribution of these fixed environmental factors to crop
production. I tackle the hypothesis that local forest cover provides positive externalities
to downstream farms by testing whether the coefficient of the spatially-weighted
upstream forest fallow variable is significantly greater than zero.
Fallow variable definitions
I use area under fallow during the cropping season as a proxy for fallow biomass.
While fallow area does not directly measure biomass or capture the dynamic aspects of
fallowing, larger fallow relative to cultivated area allows for more forest recovery time
and higher peak biomass density.11 The two alternative measures of off-farm fallow are
1) the average area under forest fallow upstream of each farm, indicated by the household
survey data and using the spatial weighting matrix Wi to define which farms are
considered neighbors,12 and 2) percent canopy cover upstream of each farm, given by the
VCF data.13 Both approaches define the externality at the farm level, allowing for more
11 When fallow management is in steady state equilibrium, fallow area has a direct relationship with
biomass volume, though the relationship is still positive when the system is out of equilibrium (Lopez
1993). The steady state assumption is plausible in the conditions of the Zona Bragantina, where agronomic
practices have been in place and minimal migration has occurred for the past several decades, unlike much
of the Brazilian Amazon. Lopez (1997) also found similar output elasticities of fallow using biomass
volume and fallow area as alternative measures in Ghana.
12 Those farms furthest upstream within a locality are assumed to affect all downstream farms; however,
they have no neighbors among the sampled farms and so are excluded from the final crop value equation
testing for externalities.
13The GIS data give upstream forest cover for all farms for which I have GIS coordinates. GIS coordinates
are missing for 10 farms in the sample, which are excluded from the analysis. I cannot extract upstream
forest cover within each drainage area individually for each farm using the GIS data, so I instead extract a
wedge-shaped neighborhood upstream of each farm with a radius of 3 km. As expected, the survey- and
GIS-derived variables are positively and significantly correlated (rho = 0.36).
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variation in the off-farm upstream forest cover variable compared to other studies that
define the forest externality at the village or sub-watershed level (e.g., Lopez 1993, 1997;
Pattanayak and Kramer 2001; Pattanayak and Butry 2005).
Figure 4 illustrates the geographic structure of the relationship. Land use on farm
1 affects all farms downstream, but I have no information on land use upstream of farm 1.
Meanwhile, farm 8 is affected by land use on farms 1-7 in its position as the farthest
observation downstream. Table 3 summarizes the fallow variables and indicates the
proportion of farms without on-farm or upstream fallow.
Endogeneity and identification strategy
Potential endogeneity of the fallow variables is a concern in obtaining consistent
parameter estimates, particularly if poor soil quality spurs farmers to allocate more land
to fallow while depressing yields. This effect could bias the on-farm fallow coefficient
downward. Measurement error of the fallow variables, which proxy for but do not
exactly measure fallow biomass, may cause attenuation bias, further lowering the
elasticity estimates (Greene 2000). In addition, differing measurement error between the
on-farm fallow area and off-farm GIS canopy cover variable may also be a source of bias
due to the different data sources used to construct them. The GIS canopy cover data
indicates fallow biomass density as well as area, while the on-farm fallow variable only
incorporates fallow area. Thus, the coefficient of on-farm fallow may be biased
downward and the coefficient of GIS canopy cover upward if external canopy cover is
correlated with on-farm biomass density. However, the survey-reported data on off-farm
fallow area avoids this source of bias. The error term in the production equation thus
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encompasses not only white noise, but also measurement error, agroecological
conditions, farmer intentions, and other factors unaccounted for in the data.14
With these drawbacks in mind, I employ several strategies in an effort to
consistently estimate the parameters of interest. As discussed above, I include several
observed indicators of land quality and management ability. Modeling spatial correlation
in the error terms based on distance between farms helps control for unobserved patterns
in agroclimatic factors and farmer knowledge over space.15 I also use an instrumental
variables (IV) estimator to address potential omitted variables and measurement error
issues. Finally, the likely downward bias on the on-farm fallow coefficient suggests that a
least-squares estimate can be interpreted as a lower bound of the elasticity.
I use the log of farm size, forest product prices, and binary variables indicating
ownership of firewood and gas stoves to instrument for on-farm fallow. Farm size affects
the amount of land available for fallowing and so is likely to be a strong predictor of
fallow area. In addition, farm size has no direct effect on crop output because cultivated
land area, clearly a crucial factor of production, is included directly in the production
function, making total farm area unrelated to crop value and hence a valid instrument. I
expect forest product prices and firewood stove ownership to be positively correlated
with on-farm fallow since fallow land typically serves as a source of forest products for
sale or home consumption, with firewood the most common product. Conversely, gas
14 In addition, the coefficients of cultivated area, labor, fertilizer, and on-farm fallow may be biased upward
if the farmer chooses input and output levels simultaneously. Off-farm fallow is less vulnerable to
simultaneity problems since the farmer does not determine fallow levels on neighboring farms, though it
may still be affected by climatic shocks experienced by all farms within a neighborhood.
15 Mardia and Marshall (1984) show that the maximum likelihood estimator of the spatial error model is
consistent if the domain or observation area of the data increases as the sample size increases (domain
asymptotics). The consistency of the maximum likelihood estimator has not been shown when the sample
size increases under a fixed domain, causing an increase in the density of observations within the given
region (infill asymptotics) (Cressie 1993). Therefore, consistency of the spatial errors estimators discussed
in this paper applies only under increasing domain asymptotics.
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stove ownership could negatively affect on-farm fallow by decreasing the household's
dependence on firewood fuel. Forest product price is a good instrument because it is
unlikely to be correlated with unobservable factors affecting crop output mix and yields
despite its impact on the marginal returns to fallow area. Firewood and gas stove
ownership have similar advantages as instruments unless farmers invest in stoves based
on their planned allocation of land to fallow.
To instrument for off-farm fallow, I use the spatially-lagged values of the on-farm
fallow instruments and of other household-level variables included in the crop production
equation. Thus, the instruments include the spatial lags of the log of farm size, forest
product prices, firewood and gas stove ownership, and other household and
agroecological characteristics expected to affect crop production. The spatially-lagged
values of farm and household characteristics affect neighbors' land allocation decisions
and hence off-farm fallow but are uncorrected with the residual of own-farm output
because own-farm characteristics are controlled for directly in the production function.16
I do not use the spatially-lagged values of conventional inputs or the perennial production
indicator due to concerns about the potential endogeneity of these variables. I use the
same spatial weighting matrix to construct the instrumental variables as that used to
construct the lagged fallow variables to ensure that neighbors' fallow area is regressed on
the characteristics of these same neighbors.
First-stage regressions for the on- and off-farm fallow variables are presented in
the appendix (table Al). The instruments are strong predictors of on- and off-farm
161 also tested the exogeneity of all inputs jointly, including cultivated area, labor, and fertilizer. I added
the log of family size and the share of males age 16-65 as instruments in this regression. I could not reject
exogeneity of all inputs jointly (p = 0.76-0.96, depending on the off-farm fallow variable). Thus, I focus on
controlling for endogeneity of the fallow variables only.
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fallow, as indicated by R-squared statistics of 0.68-0.91.17 While the IV estimates are
consistent, a Hausman test could not reject exogeneity of the on- and off-farm fallow
variables, whether using the survey or GIS measures of off-farm fallow (p= 0.40-0.88).
Thus, the least squares estimates of the elasticities of on- and off-farm fallow are both
consistent and more efficient than the IV estimates.
Treatment of non-essential inputs
Use of the Cobb-Douglas specification implies that all inputs are used in positive
quantities. However, some farmers in the sample use no fertilizer, hired labor, or fallow
land, and a few have no survey-reported upstream fallow area (tables 2 and 3). I do not
employ the widely-used strategy of adding a small shifter to the inputs before taking logs
because parameter estimates tend to be highly sensitive to the value of the shifter
(Soloaga 2000). Instead, I deal with non-essential inputs according to the approach
outlined by Battese (1997), adding dummy variables to indicate non-use of each input.18
These dummy variables function as different intercepts for the farmers who do not use
each of the inputs (including the on- and off-farm fallow variables). While non-use of
fallow or conventional inputs, or location downstream of land with no fallow cover,
might be indicative of a different production system than that used by most farmers, data
17The Sargan test for overidentification indicates that the instrumental variables as a group are uncorrelated
with the residuals of the output equations (p = 0.89-0.95, depending on the upstream fallow variable). In
addition, none of the instruments were significant at conventional levels when included one-by-one in the
IV estimation of crop value. Although these IV validity tests have low power, they support the assertion
that the instruments are uncorrelated with crop value.
18 Battese represents a two-input Cobb-Douglas production technology using two equations, assuming that
one input, xl, is used by all firms, and a second input, x2, is used by only some firms:
In y = bO + b 1 *ln xl + b2*ln x2 + u, for all farms with x2>0
In y = aO + b 1 *ln xl + u, for all farms with x2=0
The two equations can be pooled to write
lny = bO + (a0-b0)*D +bl*lnxl +b2*ln z + u
where D is a dummy variable indicating non-use of x2 and z = max(D,x2). This strategy assumes a
constant parameter b 1 and error u across both equations.
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are insufficient to estimate separate production functions for these individuals. In
addition, ten farms produce no outputs during the season and are excluded from the crop
production regression.
Results
Table 4 presents four sets of estimates of the crop production function. The first
two columns report estimates from the spatial error model (SEM) (1) and from the spatial
error model with instrumental variables (SEM-IV) (2) using survey-reported off-farm
fallow area to represent upstream fallow. The last two columns show SEM (3) and SEM-
IV (4) estimates with the GIS canopy cover variable as an alternative measure of
upstream fallow. As stated above, the fallow variables can be considered exogenous, so
all four sets of elasticity estimates are consistent. All models have a satisfactory fit, as
indicated by R-squared statistics of 0.56-0.60, and the coefficients largely have the
expected signs across the different models. The spatial error correlation coefficient is not
significantly different from zero in any of the specifications, indicating that unobserved
variables varying with distance between farms have no systematic effect on crop output
once inputs and observed farmer and soil characteristics are controlled for.
Comparisons among the four models reveal that on-farm and upstream fallow are
both important factors of crop production in the Zona Bragantina. The elasticity of on-
farm fallow is positive across all models and significantly different from zero in two of
the four models, varying from 0.09-0.18. These estimates suggest that own-fallow land
makes a substantial contribution to crop output, close to that of hired labor or fertilizer.
In addition, the non-IV coefficient estimates (0.09-0.10) from models (1) and (3)
represent a lower bound on elasticity due to the potential for downward bias caused by
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omitted soil quality variables and measurement error, though formal tests could not reject
exogeneity of on-farm fallow.
The elasticity estimates are similar in magnitude to those from other econometric
and agronomic studies. For instance, Lopez (1993, 1997) finds the village-level fallow
biomass factor share to vary between 0.15 and 0.2 in Ghana and Cote d'lvoire. Mendoza
(2004) uses the same data set as this study to estimate the contribution of fallow length to
cassava profits, finding an output elasticity of 0.22. An Altamira, Para, field study finds
the elasticity of maize yields with respect to fallow age to be 0.33 (Silva-Forsberg et al.
1997). An agronomic study from Bragantina showed rice yields to improve by 10-44%
as fallow age increased from four to ten years, corresponding to a fallow elasticity of
0.07-0.29, with the lower elasticities found on fields to which fertilizer was applied (Kato
et al. 1999). The wide use of fertilizer by sampled farms may help explain why the
elasticities estimated here fall in the lower range of previous studies.
The estimated elasticity of off-farm fallow in crop production is positive across
three of the four estimates, providing evidence that upstream forest fallow improves
productivity for downstream farms. The actual elasticity estimate varies considerably
based on the estimator used. Models (1) and (2), which use survey-reported fallow area
as the measure of upstream fallow, show a significant and positive elasticity of 0.37-0.38.
In model (3), which employs the GIS canopy cover variable to measure off-site fallow,
the elasticity jumps to 0.66. This high coefficient could result from off-farm canopy
cover proxying for on-farm biomass density, which is not completely reflected by the on-
farm fallow area variable. The SEM-IV estimate of upstream canopy cover in model (4)
17
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drops to 0.23, which is closer in magnitude to the elasticities from models (1) and (2),
though not significantly different from zero.
The large magnitude of the upstream fallow elasticity estimate, which surpasses
the on-farm fallow elasticity, is surprising. Potential explanations include downward bias
of the on-farm fallow coefficient, discussed above, and the possibility that non-stochastic
factors correlated with forest cover other than hydrological externalities affect
downstream crop production. While the hydrological externality effect cannot be isolated
if other factors lead to a correlation between off-farm land use and on-farm output, the
positive and significant coefficient provides support for the hypothesis that farms benefit
from forest cover upstream. In addition, the magnitude of the upstream fallow effect
estimated in models (1), (2), and (4) is similar to the results from the Ruteng National
Park, Indonesia, study, where a 10% increase in soil moisture due to afforestation was
associated with a 2-3% boost in farm profits (Pattanayak and Butry 2005).
As an additional verification that forest cover provides hydrological externalities,
I also estimate all four specifications of the crop production function including
downstream forest cover as an additional regressor. If forest cover provides positive
hydrological externalities, then upstream forest cover will affect crop production but
downstream forest cover will not. The appendix (table A2) presents the results of these
regressions. Across all four models, downstream forest cover has no significant effect on
crop value, in contrast to the elasticity of upstream forest cover. In fact, the coefficient
on downstream forest cover is negative. These findings support the contention that forest
cover improves crop output by regulating floods and soil moisture, and that other
potential non-hydrological services such as crop pollination do not drive the results.
18
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Elasticity estimates for the conventional inputs are largely positive and
significantly different from zero across all four specifications (table 4). Cultivated area
makes the most substantial contribution to crop output, with an elasticity of 0.41-0.44.
Hired labor and fertilizer are also important, supplying 17-19% and 15-17% of crop
output, respectively. Production of perennial crops raises output value considerably.
Agroecological variables are also important—black clay and charcoal-enriched soils
boost output, while poor soils and steeper slopes dampen it, though only the effect of
charcoal-enriched soil is statistically significant. The household head's schooling, use of
extension services, and ownership of the farm have no significant effect on output value,
which could result if differences in management ability are reflected in input quantities
rather than farmer characteristics. Models (3) and (4) indicate that farms in Castanhal
municipality garner higher crop revenues than those from Igarape A<;u or Bragan9a.
Farms with no family labor, on-farm fallow, or upstream fallow area produce higher crop
values, as indicated by the coefficients of the dummy variables for non-use of each input.
Resampling and robustness analysis
I carry out a number of robustness checks to ensure that the estimated elasticities
of on- and off-farm fallow are stable across different sub-samples of farmers. When
farms in the lowest and highest tenth percentiles of on-farm and upstream fallow area are
excluded from the regression, the coefficient for on-farm fallow varies between 0.08-
0.11. Upstream fallow area is less robust, though still high in magnitude, ranging from
0.20-0.51. The elasticity of GIS canopy cover varies from 0.55-0.67 and is significantly
different from zero in both sub-groups, indicating that the estimates are stable.
19
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Coefficient estimates are similar when each observation is dropped one-by-one in
a leave-one-out cross-validation procedure (LOOCV; see, e.g., Stone 1974, Geisser
1975). The elasticity estimates fall within a similar range as those estimated when
dropping the top and bottom tenth percentiles: 0.07-0.12 for on-farm fallow, 0.30-0.43
for upstream survey-reported fallow area, and 0.60-0.70 for upstream GIS canopy cover.
Averaging the results of the LOOCV gives elasticities of 0.10, 0.37, and 0.66 for on-farm
fallow, upstream fallow area, and upstream canopy cover, all very close to the SEM
estimates reported in table 4. Finally, the bootstrap bias estimates of on- and off-farm
fallow elasiticities from the four models calculated using 500 replications indicate that
the finite sample biases are small relative to the sizes of the parameter estimates (table 5).
Forest product harvesting function
I now turn to forest product harvesting, an important use of fallow land beyond
the ecosystem services it provides in crop production. Sixty-nine percent of farmers in
the sample collect products from their fallow land. The most common products are wood
and charcoal, used primarily for cooking fuel, though farmers also gather honey and
forest fruits. Most of the produce is reserved for home consumption, with only one
farmer selling the entire harvest. Twenty-six percent of harvesters both consume and sell
some of their products. Forest products tend to be overshadowed by cropping,
comprising 14% of the income from farm activities on average among sampled farmers.
Some studies argue that forest product harvesting represents an important risk mitigation
or "natural insurance" strategy for small-scale farmers (Pattanayak and Sills 2001,
Hedden-Dunkhorst et al. 2003). Research from the Amazon indicates that forest product
20
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harvesting can contribute substantially to shifting cultivators' incomes, though virgin
forest may yield more lucrative products than secondary forest (Smith et al. 1999).
I estimate an equation to measure the value of fallow in harvested forest products.
The dependent variable is the log of forest product value. Although most products are
reserved for home consumption, I aggregate over different commodities using farmer-
reported market prices in the absence of alternative weights.
The logs of on-farm and upstream fallow land are the primary regressors of
interest. On-farm fallow land proxies for fallow biomass, which is the source of the
harvested commodities. Upstream forest fallow may facilitate easier harvesting and more
abundant products by moderating floods and soil moisture. I again use the two
alternative measures of off-farm fallow biomass derived from survey and GIS data. The
equation can be written as
\nqi =a0+al In/ +a2Wl InF + a3 InHt +st
sj =AW2s + uj
Here, q, represents the value of forest product harvests. On- and off-farm fallow
are again given by f, and F, respectively, while Wi represents the same row-normalized
spatial weighting matrix as that used in the crop production function, giving all upstream
neighbors equal importance. Use of the same weighting matrix is appropriate if the
externalities provided to forest products are similar to those relevant in crop production.
Household characteristics expected to affect output value are included in the vector H,.
The disturbance, 8;, is again comprised of a component that varies systematically over
space with inverse distance, XW28, and white noise, u;. I also use Battese's (1997)
approach, discussed above, adding dummy variables to indicate observations with no
fallow on their own farms and no fallow upstream.
21
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I cannot estimate a structural production function due to missing input data,
namely harvesting labor. To proxy for collecting labor availability, I include the log of
household size and the agricultural wage rate. I also include black clay, charcoal-
enriched, and poor soil type indicators and slope to control for land quality. I add
variables indicating ownership of firewood and gas stoves, as cooking fuel is an
important commodity for home consumption. I also include three indicators of
household wealth—car ownership, television ownership, and electricity use—to examine
whether low-income households are more likely to collect forest products. Other control
variables include forest product prices,19 the household head's education level, ownership
of the farm, and municipality dummies.
Treatment of censoring in forest product harvests
Because only 69% of farms harvest forest products, the econometric model must
account for censoring to consistently estimate the parameters of interest. Factors
affecting demand for forest products, such as market prices, opportunity cost of labor,
and land quality, may have different impacts on the decision to harvest and the amount of
output conditional on participation. The two-part hurdle model allows for different effects
across the two processes.20 Because the same set of variables affects both the binary
19 In the absence of data on market prices for the harvested commodities, I use village medians of farmer-
reported forest product prices as regressors to avoid bias due to common measurement error and quality
effects by including farmer-reported prices directly on both sides of the equation. Use of unit value cluster
means outperforms other proxies for market prices in estimating price elasticities in a study using
Vietnamese data (Niimi 2005). I use village medians to minimize the influence of outliers.
201 test the Tobit restriction against the two-part Cragg hurdle model, which nests the Tobit, to determine
whether the coefficients vary across the two processes (Fin and Schmidt 1984). The explanatory variables
do differ in magnitude, and in some cases even sign, across the probit and non-limit regression models.
Indeed, a likelihood ratio test rejects equality of the coefficients across the two equations for all four model
specifications (p = 0.00). Results of these regressions are available upon request I use the hurdle model
estimates in the remainder of my analysis. I employ the two-part probit-least squares model rather than the
Cragg approach to facilitate estimation using spatially-correlated errors and instrumental variables.
However, the significance and magnitudes of the coefficients are very similar across the Cragg and probit-
least squares models, indicating that the hurdle model is robust across the two specifications.
22
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choice and conditional outcome, the lack of valid exclusion restrictions makes the
Heckman selection model infeasible to implement. A hurdle model of forest product
harvesting with spatially correlated error terms in both equations can be written as
A = r0 + n ln / + r2Wi In F + y3Hi + £, D = {0,1}
In qt =/?0 +A ln / + P2WX ln F + P3H1 + si if I), = 1
sl =A2W2s + vt
where D denotes a dummy variable indicating participation in harvesting forest products.
The selection equation is estimated using a probit model, while the conditional outcome
equation can be estimated by ordinary least squares regression on the non-limit
observations (Wooldridge 2001, p. 536).
Identification and instrumental variables
Similar to the omitted variable problem raised in the crop production function,
poor land quality could lead farmers to allocate more land to fallow but reap lower yields
of forest products, biasing the on-farm fallow coefficient downward. Measurement error
may also lead to attenuation bias on the fallow coefficients since fallow biomass is
proxied by fallow area or canopy cover. The elasticity of GIS off-farm canopy cover
may also be overestimated and the elasticity of on-farm fallow area underestimated if
canopy cover is correlated with on-farm fallow biomass density. Simultaneity between
fallow area and forest product output may bias the coefficient of on-farm fallow upwards
as well, though it is less likely to affect the coefficient of off-farm fallow.
I employ similar approaches as those used in the crop production estimation to
address concerns about endogeneity. Control variables on land quality and farmer
characteristics are included directly in both the probit and non-limit regressions models.
23
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Spatially correlated errors are included in both to reflect unobserved factors that vary
between farms with distance.
I again use the log of farm size as an instrument for on-farm fallow. Total farm
size determines the land available for allocation to fallow. However, beyond its effect on
the size of fallow land, farm area should have no direct effect on forest product harvests.
Forest product prices and firewood and gas stove ownership, used as instruments for
fallow in the crop production function, are not valid exclusion restrictions and are
included in the forest products equation. I employ spatially-lagged values of farm size
and several other household-level exogenous variables from the forest products equation
as instruments for off-farm fallow.
The instruments explain much of the variation in on-farm fallow area, upstream
fallow area, and canopy cover, as seen in first-stage equations with R-squared statistics of
0.74, 0.90, and 0.65, respectively (table A3 of the appendix). Overidentification tests
confirm that the instruments are uncorrected with forest product harvesting decisions and
output value.21 Smith-Blundell tests indicate that on- and off-farm fallow can be
considered exogenous to the forest product harvesting decision in model (1) but not in
model (3). In addition, the fallow variables are not exogeneous to the value of forest
products conditional on harvesting, according to Hausman test results (p = 0.04-0.09).
Therefore, the SEM-IV estimates of the probit and non-limit regressions are consistent,
while the regular SEM-probit and non-limit regression estimates are not.
21 The instruments are also uncorrelated with the outcome variables individually, as shown by including
each in the outcome equations. Certain lagged household characteristics, including education, farm
ownership, electricity use, and slope were not used as instruments because they were found to be correlated
with the forest product harvesting decision or conditional value.
24
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Results
Tables 6 and 7 show the results of the forest product harvesting participation and
outcome equations, respectively. Columns (1) and (2) of table 6 report SEM probit and
SEM-IV probit coefficient estimates using survey-derived off-farm fallow area. Columns
(3) and (4) instead use GIS canopy cover. Table 7 follows the same pattern, with
columns (1) and (2) giving non-limit SEM and SEM-IV estimates using survey-reported
upstream fallow area, and columns (3) and (4) using GIS canopy cover. The spatial
correlation coefficient of the probit equation error term is positive and significant across
all four models, indicating that unobservable factors do have similar effects on neighbors'
harvesting decisions. The error terms are not significantly spatially correlated in the non-
limit regressions, however.
While I use separate probit and non-limit regression models to estimate the
parameters of the hurdle model, the combined effect or unconditional elasticity of the
fallow variables are the main parameters of interest from the model of forest product
harvesting.22 The non-limit regression equations estimate the conditional elasticity
directly, since product value and fallow are expressed in log form. I calculate the
probability elasticities using the coefficients from the probit models, using
0) (p(yz)
d\nf ^ O(^)
where yi is the coefficient of the log of on-farm fallow from the probit equation, and yz is
the linear prediction.
22
McDonald and Moffitt (1980) derive the decomposition of the effects of the participation decision and
the value of the outcome conditional on participation in the Tobit context, showing that
E(y | x) = Pr(y > 0 | x) • E(y \ y > 0, x) ¦ Log differentiating this expression reveals that the unconditional
elasticity is simply the sum of the probability elasticity and the conditional elasticity.
25
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Table 8 reports the probability, conditional, and unconditional elasticities of on-
and off-farm fallow in forest product harvesting. The unconditional output elasticity of
on-farm fallow is positive across all four models, varying from 0.22 to 0.49. However, it
is higher in magnitude and significantly different from zero only in models (2) and (4),
when the IV approach addresses the endogeneity of on- and off-farm fallow. This
finding indicates that omitted variables and measurement error bias the estimates of the
probability and conditional elasticities downward. These results confirm that on-farm
fallow makes an important contribution to the value of forest products, as expected. In
fact, the elasticities derived from the SEM-IV estimates suggest that on-farm fallow
contributes close to 50% of the value of forest products.
The estimates of the unconditional elasticity of off-farm fallow are also all
positive, spanning 0.76-0.89. Similar to the results from the crop production function, the
elasticity of upstream fallow area is significantly greater than zero in models (1), (2), and
(3). The SEM-IV estimate (model (4)) is not significantly different from zero. These
results suggest that farms located downstream of neighbors with higher levels of forest
fallow garner higher incomes from forest products, even accounting for positive spatial
correlation in omitted variables affecting neighbors' harvesting decisions.23 The net
effect is positive and statistically significant for three out of four estimates. Thus, these
findings provide some support the hypothesis that upstream forest fallow provides
231 also investigate whether fallow externalities only arise from upstream forest cover by estimating the
probit and non-limit regressions including downstream fallow. I find that downstream fallow has no
significant effect on the probability of harvesting forest products, and the coefficient is actually negative
across all four models. The results from the conditional outcome equation are less conclusive—Models (2)
and (3) show downstream fallow to have a positive, though not significant, effect on harvest value. Thus, I
cannot confirm whether the positive effects of off-farm fallow on forest product harvests are strictly
hydrological, flowing from upstream to downstream, or whether insect pollinators, tree seed availability, or
other potential forest ecosystem services may play a role. These results are available upon request.
26
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positive externalities not only in crop production but also in forest product harvests,
thought the results are less conclusive than those from the crop production function.
Turning to the other explanatory variables in the hurdle model of forest product
harvesting, labor availability is important in the decision to collect forest products, as
indicated by the positive and significant coefficient of the log of household size and the
negative and significant coefficient of the wage rate in the probit equation. Ownership of
a gas stove is negatively associated with harvesting forest products, as expected given
these farms' decreased reliance on firewood as a cooking fuel. Farms that do not own a
car or use electricity are more likely to collect forest products, implying that low-income
farmers rely more heavily on forest products than do better-off households. However, car
and television ownership have the opposite effect on the conditional value of forest
products, suggesting that wealthier households reap greater value from this activity when
they choose to participate. Families with a more educated household head also earn
higher revenues from harvesting. Land quality affects harvests as well: favorable black
clay soils and less steeply-sloped land increase the conditional value of harvested
products. Farmers located in Castanhal and Igarape A<;u are more likely to collect forest
products than those in Bragan9a. In addition, households' whose upstream neighbors
maintain no fallow area are significantly less likely to harvest any forest products Village
median forest product prices, firewood stove ownership, and farm ownership do not have
significant effects on the probability of harvesting or on conditional harvest value.
Resampling and robustness analysis
I carry out similar tests of robustness to those used in the crop production section
to investigate whether the results hold across different sub-groups of farmers. Excluding
27
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farms from the top and bottom tenth percentiles of on-farm fallow from the probit and
non-limit regressions, I find that the results are largely stable. On-farm fallow has a
positive and significant effect on the probability of harvesting across the different sub-
samples, though it has no significant effect on the conditional value of the harvest. The
effect of upstream fallow area is somewhat less robust across different groups—farms
with more fallow upstream experience a much larger impact on the probability of
harvesting, but find less of an effect on the conditional harvest value. Upstream canopy
cover has a consistent effect on the probability of harvesting across different sub-
samples, but farms with less upstream canopy cover reap greater benefits in terms of
harvest value.
Using the leave-one-out cross-validation procedure, the total elasticity estimates
do vary quite a bit, ranging from 0.09-0.20 for on-farm fallow, 0.52-0.78 for upstream
fallow area, and 0.64-0.89 for upstream canopy cover, with means of 0.13-0.16, 0.70, and
0.77, respectively. Thus, while total elasticity estimates for forest product harvests with
respect to on-farm and upstream fallow are positive across different sub-samples of
farmers, they are more variable than those from the crop production function.
Total on- and off-farm fallow elasticities
To better understand the economic significance of forest fallow services in farm
activities, I calculate the total farm output elasticity of on- and off-farm fallow using the
results from all four models of the crop and forest product estimations. The total output
elasticities of on- and off-farm fallow account for their respective contributions to both
crop and forest product income, which vary by farm with the share of income from each
activity.
28
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The mean elasticity of on-farm fallow ranges from 0.11-0.22, depending on the
estimates used, but is significantly different from zero in all four specifications (table 9).
This positive mean elasticity underscores the importance of forest fallow to farms in the
Zona Bragantina in providing both consumable products and ecological support services.
In addition, the mean output elasticity of upstream fallow is significantly different
from zero in three of the four sets of estimates, spanning 0.29-0.68. The effect of off-
farm fallow on farm revenue appears to be important both statistically and in magnitude.
As in the results from the crop production function alone, I cannot rule out whether the
high magnitude of the off-farm effect is in part driven by other factors that lead upstream
land use to be correlated with downstream farm income. However, the positive and
significant effect of upstream but not downstream forest cover on crop value does
provide support for the hypothesis that hydrological externalities contribute to
agricultural income.
These findings support the hypothesis that upstream forest fallow provides flows
of economically significant ecological services to farms in the Zona Bragantina. They
suggest that off-site hydrological regulation may be important even in low and
moderately sloped regions with porous soils. These hydrological support services may
justify continued allocation of significant amounts of land to forest fallow in the future,
even if farms increasingly substitute chemical fertilizer for fallow-based soil nutrients.
Land allocation efficiency
While fallow provides important ecological services in shifting cultivation, it can
be a costly investment when the opportunity costs of land and labor are considered. Land
must remain out of cultivation for years at a time to ensure sustainability, and land
29
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clearing requires large investments of labor. The total returns to fallowing thus depend
on the relative contributions of fallow and cultivated land to farm income once all costs
are considered.
The estimated income elasticities of cultivated area, on-farm fallow, and upstream
fallow can be used to determine whether farmers allocate land between cultivation and
fallow efficiently. Farmers manage land efficiently from a social perspective if they
balance the marginal contribution of cultivated area to crop income with the marginal
value of the lost fallow services to on-farm and downstream crop production and forest
product harvesting. Klemick (2008) derived the expression for efficient land allocation
from an optimal control model of shifting cultivation. This measure, termed the social
income elasticity of cultivated land, represents the impact of a 1% increase in cultivated
area on agricultural profits earned on the farm itself and on farms affected downstream.24
Using this expression, Klemick calculated whether each farmer allocated the optimal
amount of land to fallow using the estimated parameters from the crop and forest product
equations presented in model (1).
Efficient allocation of land between cultivation and fallow implies that the social
income elasticity of cultivated land is equal to zero. If the elasticity is significantly
greater (less) than zero at the 1% level, the farm is considered to be over-(under-)
24 The social income elasticity of cultivated land is written as
r
i crop
8 = —
SOC I
71
f
X
:—C
V1
y crop J
7r { r ¦
( \1L Ye ^ + p r'f°r +y \ (e rJ rJ )1
[r + x'/X' J 0 Jr - x' ^ X' - x' t (XJ - xJ) K P f°r,J
and depends on the amount of land under cultivation (x) and fallow (X - x), crop and forest product
income (rcrop, rfor), total farm profits (71),and marginal land-clearing costs (c), factors that vary across all
farms in the sample. It also depends on the elasticities of crop output with respect to cultivated area (Cx),
on-farm fallow (e0), and upstream fallow (e20), and on the elasticity of forest product harvests with respect
to on-farm fallow (§3) and upstream fallow (c3 l). which can be approximated by the parameters from the
equations estimated in this article. The rate of interest is given by r. The variance of this expression can be
estimated using the variance-covariance matrices from the crop and forest product equations.
30
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fallowing. I follow the same procedure here to test whether sampled farmers managed
land efficiently, allocated too much land to fallow, or allocated too little according to
each of the four sets of parameter estimates.
Table 10 presents the results on land allocation efficiency, assuming that farmers
face a 10% interest rate.25 The results suggest that most sampled farmers did indeed
allocate land between cultivation and fallow efficiently—74-88% of them, depending on
the elasticity estimates used. While some farmers devoted too much (1-17%) or too little
(2-12%) land to fallow, by and large, most farmers managed land optimally. These
results contrast those of Lopez (1993, 1997), who found that farmers in Ghana and Cote
d'lvoire holding fallow in common property cleared excessive amounts of fallow for
cultivation relative to the social optimum, indicating that private property ownership may
improve the efficiency of land management.
Summary and conclusions
This study adds to the growing body of literature quantifying the value of forest
resources for human livelihoods, specifically agriculture. Such knowledge is essential for
policy-makers involved in land-use planning and economic development in forested areas
where poverty remains widespread.
Fallow makes an important contribution to farm income in semi-commercial,
smallholder agriculture in the Zona Bragantina, a region with similar agroecological
conditions and a somewhat more developed infrastructure than other frontier regions in
Brazil. Fallowing provides ecological services to farmers by improving land quality and
25 As discussed in Klemick (2008) and Lopez (1997), the interest rate is a key parameter because it
determines how heavily farmers discount the future value of the fallow biomass stock. In the absence of
data on interest rates facing sampled farmers, I assume a 10% interest rate to capture a balance between the
subsidized credit programs and market interest rates available to farmers in the region.
31
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serving as a source of harvestable products. The econometric analysis indicates that
fallow provides valuable hydrological services to downstream farmers as well. The
results also suggest that farmers allocated land between cultivation and fallow efficiently,
even accounting for the value of these downstream services.
These findings imply that farming communities may have some self-interest in
preserving forest cover locally, even if transition to permanent cultivation becomes more
attractive in the future. Knowledge of the local benefits of forest fallow may bolster
efforts aimed at conserving tropical forests as a strategy to mitigate greenhouse gas
emissions and biodiversity loss. Conversely, policies encouraging farmers to transition
from slash-and-burn to permanent cultivation may have unintended consequences due to
the loss of local hydrological services.
32
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References
Anselin, Luc, 1988. Spatial Econometrics: Methods and Models. Dordecht, The
Netherlands: Kluwer Academic Publishers.
Altieri, Miguel. 1995. Agroecology: the Science of Sustainable Agriculture. Boulder, CO:
Westview Press.
Battese, George. 1997. "A note on the estimation of Cobb-Douglas production functions
when some explanatory variables have zero values." Journal of Agricultural Economics
48: 250-252.
Brady, N.C. 1996. "Alternatives to slash and burn: a global imperative." Agriculture,
Ecosystems and Environment 58: 3-11.
Bruijnzeel, L.A. 2004. "Hydrological functions of tropical forests: not seeing the soil for
the trees?" Agriculture, Ecosystems and Environment 104: 185-228.
Chomitz, Kenneth M. and Kanta Kumari. 1998. "The domestic benefits of tropical
forests: a critical review." World Bank Research Observer 13 (1): 13-35.
Cragg, J. "Some statistical models for limited dependent variables with application to the
demand for durable goods." Econometrica 39: 829-844.
Cressie, Noel. 1993. Statistics for spatial data. New York: J. Wiley.
de Rouw, Anneke. 1995. "The fallow period as a week-break in shifting cultivation
(tropical wet forests) " Agriculture, Ecosystems and Environment 54: 31-43.
Fin, T. and P. Schmidt. 1984. "A test of the tobit specification against and alternative
suggested by Cragg." Review of Economics and Statistics 66: 174-177.
Gehring, Christoph, Manfred Denich, Milton Kanashiro, and Paul Vlek. 1999. "Response
of secondary vegetation in Eastern Amazonia to relaxed nutrient availability constraints."
Biogeochemistry 45: 223-241.
Geisser, Seymour. 1975. "The predictive sample reuse method with applications."
Journal of the American Statistical Association 70(350): 320-328.
Greene, William. 2000. Econometric analysis, fourth edition. Upper Saddle River, NJ:
Prentice-Hall, Inc.
Hamilton, Lawrence S. and Peter N. King. 1983. Tropical Forested Watersheds. Boulder,
CO: Westview Press.
33
-------
Hansen, M., R. DeFries, J.R. Townshend, M. Carroll, C. Dimiceli, and R. Sohlberg,
2006. Vegetation Continuous Fields MOD44B, 2001 Percent Tree Cover, Collection 4,
University of Maryland, College Park, Maryland, 2001.
Hedden-Dunkhorst, B., M. Denich, K. Vielhauer, F. Romualdo de Sousa Filho, T. D. de
Abreau Sa, T. Hurtienne, F. de Assis Costa, A. Mendoza-Escalante, and J. Borner. 2003.
"Forest-based fallow systems as a safety net for smallholders in the Eastern Amazon."
Paper presented at the International Conference on Rural Livelihoods, Forests and
Biodiversity, Bonn, Germany, 19-23 May 2003.
Holscher, D., B. Ludwig, R.F. Moller, and H. Folster. 1997. "Dynamic of soil chemical
parameters in shifting cultivation agriculture in the Eastern Amazon." Agriculture,
Ecosystems and Environment 66: 153-163.
Kato, M.S.A., O.R. Kato, M. Denich, and P.L.G. Vlek. 1999. "Fire-free alternatives to
slash-and-burn for shifting cultivation in the eastern Amazon region: the role of
fertilizers." Field Crops Research 62: 225-237.
Klemick, H. 2008. "Do Liquidity Constraints Help Preserve Tropical Forests? Evidence
from the Eastern Amazon." Selected Paper prepared for presentation at the American
Agricultural Economics Association Annual Meeting, Orlando, FL, July 27-29, 2008.
Kremen, Claire, Neal Williams, Robert Bugg, John Fay and Robin Thorp. 2004. "The
area requirements of an ecosystem service: crop pollination by native bee communities in
California." Ecology Letters 7: 1109-1119.
LeSage, James. 1998. "Spatial Econometrics." [Available at www, spatial-
econometrics, com]
Lopez, R. 1993. "Resource Degradation, Community Controls and Agricultural
Productivity in Tropical Areas." Working Paper No. 93-08, AREC, University of
Maryland.
Lopez, R. 1997. "Environmental Externalities in Traditional Agriculture and the Impact
of Trace Liberalization: the Case of Ghana." Journal of Development Economics 53: 17-
39.
Maler, Karl-Goran. 1991. "Measuring environmental damage: the production function
approach." Valuing environmental benefits in developing countries, proceedings of a
seminar, Feb. 1990, Michigan State University.
Mardia, K.V. and R.J. Marshall. 1984. "Maximum Likelihood Estimation of Models for
Residual Covariance in Spatial Regression." Biometrika 71(1): 135-146.
McDonald, John and Robert Moffitt. 1980. "The uses of Tobit analysis." Review of
Economics and Statistics 62: 318-321.
34
-------
Mendoza-Escalante, Arisbe. 2004. "Analysis of smallholder agricultural production in the
Eastern Amazon: empirical evidence and policy perspectives for the Bragantina region."
PhD diss., ZEF, University of Bonn.
Millennium Ecosystem Assessment. 2005. Ecosystems and Human Well-being:
Synthesis. Washington, DC: Island Press.
Nepstad, Daniel, Paulo Moutinho, and Daniel Markewitz. 2001. "The recovery of
biomass, nutrient stocks, and deep soil functions in secondary forests." In The
Biogeochemistry of the Amazon Basin. Micheal McClain et al., eds. New York: Oxford
University Press.
Niimi, Yoko. 2005. "An analysis of household responses to price shocks in Vietnam: can
unit values substitute for market prices?" PRUS Working Paper no. 30.
Pattanayak, Subhrendu and David Butry. 2005. "Spatial complementary of forests and
farms: accounting for ecosystem services." American Journal of Agricultural Economics
87(4): 995-1008.
Pattanayak, Subhrendu and Randall A. Kramer. 2001. "Worth of watersheds: a producer
surplus approach for valuing drought mitigation in Eastern Indonesia." Environment and
Development Economics 6: 123-146.
Pattanayak, Subhrendu and Erin O. Sills. 2001. "Do tropical forests provide natural
insurance? The microeconomics of non-timber forest product collection in the Brazilian
Amazon." 77(4): 595-612.
Ricketts, Taylor, Gretchen Daily, Paul Erlich, and Charles Michener. 2004. "Economic
value of tropical forests to coffee production."
Sanchez, Pedro, Dale Brandy, J. Hugo Villachica, and John Nicholaides. 1982. "Amazon
basin soils: management for continuous crop production." Science 216: 821-827.
Sanchez, Pedro. 1996. "Introduction." Agriculture, Ecosystems and Environment 58: 1-2.
Silva-Forsberg, Maria Clara and Philip M. Fearnside. 1997. "Brazilian Amazonian
caboclo agriculture: effect of fallow period on maize yield." Forest ecology and
management 97:283-291.
Smith, Joyotee, Petra van de Kop, Keneth Reategui, Ignacio Lmbardi, Cesar Sabogal, and
Armando Diaz. 1999. Dynamics of secondary forests in slash-and-burn farming:
interactions among land use types in the Peruvian Amazon. Agriculture, Ecosystems and
Environment 76: 85-98.
35
-------
Soloaga, Isidro. 2000. Production and factors allocation in farm households." PhD diss.,
Agricultural and Resource Economics Department, University of Maryland.
Sommer, Rolf, Manfred Denich, and Paul L.G. Vlek. 2000. "Carbon storage and root
penetration in deep soils under small-farmer land-use systems in the Eastern Amazon
region, Brazil." Plant and Soil 219: 231-241.
Staver, C. 1991. "The role of weeds in the productivity of Amazonian bush fallow
agriculture." Experimental Agriculture 27: 287-304.
Stone, M. 1974. "Cross-validatory choice and assessment of statistical predictions."
Journal of the Royal Statistical Society. Series B (Methodological) 36(2): 111-147.
Tucker, Joanna M., Eduardo S. Brondizio and Emilio Moran. 1998. "Rates of forest
regrowth in Eastern Amazonia: a comparison of Altamira and Bragantina Regions, Para
State, Brazil." Interciencia 23 (2): 64-73.
U.S. Geological Survey, National Center for Earth Resources Observation & Science
(EROS). HYDROlk South America. [AccesedNov. 16, 2005
http://edc.usgs.gov/products/elevation/gtopo30/hydro/sa fd.htmll
Wooldridge, Jeffrey. 2001. Econometric Analysis of Cross Section and Panel Data.
Cambridge, MA: The MIT Press.
36
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Figure 1 Municipios in the Zona Bragantina
Atlantic Ocean
Mara jo
iraccm.
Zona Bragantina
jmingo
Source: http://pt-uf.pt-dlr.de/Shift/english/map/envl01.htm. Accessed Nov. 28, 2005
Figure 2 Tree canopy cover in the Zona Bragantina, March 2001-March 2002
Households
Water
Forest cover
High: 100
Low: 0
Legend
60 Kilometers
37
-------
Figure 3 Flow direction in the Zona Bragantina
0 15 30 60 Kilometers
I—I—I—I—I—I—I—I—I
Figure 4 Flow direction of hypothesized hydro logical externalities
Upstream
Downstream
38
-------
Table 1 Household characteristics
Mean
(Standard deviation)
Observations
Farm size (ha)
40.73
271
(47.97)
Household size (members)
6.18
271
(2.78)
Own farmland (legal title)
0.65
271
1 = yes, 0 = no
(0.48)
Household head education (years)
3.77
271
(2.91)
Use extension services
0.24
271
1 = yes, 0 = no
(0.43)
Own car
0.09
271
1 = yes, 0 = no
(0.28)
Own television
0.60
271
1 = yes, 0 = no
(0.49)
Use electricity
0.62
271
1 = yes, 0 = no
(0.49)
Own firewood stove
0.85
271
1 = yes, 0 = no
(0.36)
Own gas stove
0.84
271
1 = yes, 0 = no
(0.37)
Village-level annual price index
0.81
271
($B/kg)
(0.23)
Village-level perennial price index
3.26
271
($B/kg)
(1.81)
Forest product price ($B/kg)26
6.57
187
(14.76)
Agricultural wage rate ($B/day)
8.26
271
(1.38)
261 impute forest product prices for households that do not collect forest products using village averages.
39
-------
Table 2 Production function variables
Mean
Observations
(Standard deviation)
Crop output value ($B)
5118.27
261
(11972.62)
Cultivated area (ha)
3.75
270
(4.64)
Family labor (person-days)
112.47
271
(97.42)
No family labor used
0.02
271
1 = yes, 0 = no
(0.15)
Hired labor (person-days)
52.94
271
(75.36)
No hired labor used
0.17
271
1 = yes, 0 = no
(0.37)
Fertilizer (kg NPK)
389.90
271
(1525.69)
No fertilizer used
0.29
271
1 = yes, 0 = no
(0.46)
Slope (degrees)
2.65
261
(2.54)
Black clay (massape) soil
0.10
271
1 = yes, 0 = no
(0.30)
Charcoal enriched (preta) soil
0.10
271
1 = yes, 0 = no
(0.31)
Poor (arisca) soil
0.06
271
1 = yes, 0 = no
(0.24)
Table 3 Fallow variables
Mean
Observations
(Standard deviation)
On-farm fallow area (ha)
22.60
271
(28.97)
No on-farm fallow land
0.14
271
1 = yes, 0 = no
(0.35)
Off-farm (upstream) average fallow
24.54
236
area - survey data (ha/upstream
(19.62)
neighbor)
No upstream fallow area
0.03
236
1 = yes, 0 = no
(0.16)
Off-farm (upstream) canopy cover -
24.61
261
GIS data, 3 km radius (% area)
(9.08)
No upstream canopy cover
0
261
1 = yes, 0 = no
(0.00)
40
-------
Table 4 Crop production function estimation
SEM27
SEM-IV
SEM
SEM-IV
(1)
(2)
(3)
(4)
Log on-farm fallow area
0.098*
0.125
0.093
0.177**
[0.058]
[0.078]
[0.058]
[0.090]
Log off-farm fallow - upstream
0.366**
0.378**
survey fallow area
[0.158]
[0.184]
Log off-farm fallow - 3 km
0.655***
0.231
upstream GIS canopy cover
[0.231]
[0.403]
Log cultivated area
q 424***
0.405***
0.438***
0.434***
[0.099]
[0.101]
[0.094]
[0.096]
Log family labor
0.128
0.126
0.062
0.074
[0.093]
[0.094]
[0.088]
[0.090]
Log hired labor
0.175***
0.172***
q 294***
q 272***
[0.065]
[0.066]
[0.061]
[0.063]
Log chemical fertilizer
0.146***
0.146***
q 274***
0.159***
[0.055]
[0.056]
[0.056]
[0.058]
Perennial producer (binary)
q 921***
q 924***
0.826***
0.830***
[0.177]
[0.178]
[0.165]
[0.167]
Use extension services (binary)
0.262
0.27
0.205
0.206
[0.177]
[0.178]
[0.164]
[0.166]
Household head schooling years
-0.018
-0.018
-0.02
-0.02
[0.025]
[0.025]
[0.024]
[0.024]
Farm owner (binary)
0.07
0.07
-0.045
-0.018
[0.157]
[0.158]
[0.148]
[0.151]
Black clay soil (binary)
0.221
0.227
0.193
0.179
[0.236]
[0.238]
[0.233]
[0.236]
Charcoal-enriched soil (binary)
0.373*
0.381*
0.363*
0.414*
[0.215]
[0.216]
[0.215]
[0.221]
Poor soil (binary)
-0.122
-0.125
0.213
0.106
[0.309]
[0.310]
[0.283]
[0.298]
Slope
-0.011
-0.013
-0.021
-0.012
[0.027]
[0.027]
[0.027]
[0.028]
Castanhal municipality (binary)
0.25
0.251
0.634***
0.456*
[0.228]
[0.229]
[0.234]
[0.273]
Igarape A<;u municipality (binary)
0.281
0.277
0.304
0.244
[0.229]
[0.233]
[0.214]
[0.220]
No on-farm fallow (binary)
0.429
0.495
0.515**
0.676**
[0.285]
[0.323]
[0.261]
[0.312]
No upstream fallow area (binary)
1.102*
[0.602]
1.131*
[0.657]
No family labor (binary)
1.260*
1.243*
0.898
0.901
[0.651]
[0.653]
[0.641]
[0.649]
No hired labor (binary)
0.018
0.013
0.173
0.066
27 All regressions estimated in Stata 8 unless otherwise noted
41
-------
[0.284]
[0.285]
[0.269]
[0.278]
No fertilizer (binary)
0.174
0.157
0.325
0.275
[0.308]
[0.312]
[0.299]
[0.305]
Constant
3.343***
3.202***
2.500***
3.720***
[0.732]
[0.758]
[0.952]
[1.419]
Spatial error correlation coefficient
-0.033
-0.055
-0.016
-0.021
ft)
[0.138]
[0.142]
[0.156]
[0.30]
Observations
228
228
251
251
R-squared
0.60
0.60
0.57
0.56
Log likelihood
-313.83
-314.36
-347.77
-350.80
Standard errors in brackets
* significant at 10%; ** significant at 5%; *** significant at 1°/
-o
Table 5 Bootstrap bias estimates for crop production function parameters, 500 replications
Model (1)
Model (2)
Model (3)
Model (4)
On-farm fallow
-0.004
-0.005
-0.004
-0.008
Upstream fallow area
0.003
0.003
Upstream canopy cover (3km
-0.005
-0.041
radius)
42
-------
Table 6 Forest product harvesting: participation equation
SEM28
SEM-IV
SEM
SEM-IV
Probit (1)
probit (2)
Probit (3)
probit (4)
Log on-farm fallow area
0.281***
0.370***
0.395***
0.473***
[0.110]
[0.146]
[0.117]
[0.198]
Log off-farm fallow - upstream
0.430
0.425
survey fallow area
[0.278]
[0.302]
Log off-farm fallow - 3 km
0.591
1.754**
upstream GIS canopy cover
[0.491]
[0.980]
Forest product price (village
-0.224790
-0.181
0.164
0.185*
median)
0.182062
[0.168]
[0.143]
[0.138]
Log household size
0.965***
0.962***
0.834***
0.896***
[0.300]
[0.260]
[0.310]
[0.313]
Agricultural wage rate
-0.245***
-0.234***
-0.230**
-0.237**
[0.010]
[0.095]
[0.100]
[0.104]
Household head schooling years
0.051
0.061*
0.034
0.041
[0.047]
[0.043]
[0.051]
[0.052]
Farm owner (binary)
0.303
0.274
-0.066
-0.080
[0.294]
[0.275]
[0.315]
[0.320]
Own car (binary)
-0.975***
-0.936***
-0.946**
-0.852**
[0.403]
[0.397]
[0.473]
[0.480]
Own television (binary)
0.047
-0.015
-0.064
0.022
[0.314]
[0.320]
[0.362]
[0.365]
Use electricity (binary)
-0.841***
-0 744***
-0.723**
-0.755**
[0.335]
[0.316]
[0.390]
[0.377]
Own firewood stove (binary)
0.293
0.326
0.474*
0.332
[0.329]
[0.319]
[0.384]
[0.428]
Own gas stove (binary)
-1 498***
-1 478***
-1.075**
-0 994***
[0.552]
[0.553]
[0.508]
[0.563]
Black clay soil (binary)
0.851*
0.858*
0.799*
0.654*
[0.534]
[0.550]
[0.599]
[0.549]
Charcoal-enriched soil (binary)
0.197
0.185
0.101
0.073
[0.396]
[0.394]
[0.447]
[0.482]
Poor soil (binary)
-0.381
-0.311
-0.343
-0.075
[0.602]
[0.609]
[0.692]
[0.064]
Slope
-0.008
-0.020
-0.047
-0.075
[0.054]
[0.053]
[0.057]
[0.0064]
Castanhal municipality (binary)
0.742**
0.685**
0.821**
1.330**
[0.404]
[0.423]
[0.503]
[0.690]
Igarape A<;u municipality
\ 497***
1 401***
0.918**
1.023**
(binary)
[0.479]
[0.509]
[0.501]
[0.564]
No on-farm fallow area (binary)
0.248
0.581
0.149
0.635
[0.483]
[0.592]
[0.548]
[0.711]
No upstream fallow area (binary)
-2.858**
-3.018**
28
Spatial errors probit model estimated using Gibbs sampler algorithm in Matlab (LeSage 1998).
43
-------
[1.441]
[1.384]
Constant
0.936
0.364
-1.674
-5.860**
[1.568]
[1.667]
[1.911]
[3.043]
Spatial error correlation
0.535***
0.545***
0.345***
0.341***
coefficient (k)
[0.245]
[0.234]
[0.239]
[0.250]
Observations
236
236
261
261
McFadden R-squared
0.30
0.29
0.66
0.26
Standard errors in brackets
* significant at 10%; ** significant at 5%; *** significant at 1%
Table 7 Forest product harvesting: conditional outcome equation
SEM
SEM-IV
SEM
SEM-IV
(1)
(2)
(3)
(4)
Log on-farm fallow area
0.065
0.283**
0.025
0.269*
[0.107]
[0.139]
[0.111]
[0.163]
Log off-farm fallow - upstream
0.549**
0.548*
survey fallow area
[0.278]
[0.322]
Log off-farm fallow - 3 km
0.598
-0.002
upstream GIS canopy cover
[0.411]
[0.781]
Forest product price (village
0.037
0.116
0.158
0.202
median)
[0.187]
[0.191]
[0.175]
[0.178]
Log household size
0.087
0.113
0.209
0.234
[0.265]
[0.264]
[0.260]
[0.259]
Agricultural wage rate
0.027
0.01
-0.02
-0.031
[0.100]
[0.098]
[0.088]
[0.088]
Household head schooling years
0.03
0.041
0.07
0.082*
[0.047]
[0.047]
[0.046]
[0.046]
Farm owner (binary)
-0.191
-0.201
-0.334
-0.264
[0.267]
[0.264]
[0.270]
[0.270]
Own car (binary)
1.215**
1.217**
1.130**
1.109**
[0.525]
[0.517]
[0.512]
[0.511]
Own television (binary)
0.631**
0.652**
0.666**
0.664**
[0.274]
[0.271]
[0.271]
[0.271]
Use electricity (binary)
-1.078***
-1.102***
-1.021***
-1.090***
[0.270]
[0.268]
[0.270]
[0.275]
Own firewood stove (binary)
0.406
0.386
0.284
0.412
[0.378]
[0.373]
[0.392]
[0.402]
Own gas stove (binary)
-0.017
-0.088
0.119
0.023
[0.308]
[0.305]
[0.304]
[0.310]
Black clay soil (binary)
0.963**
0.968**
0.753*
0.783*
[0.413]
[0.408]
[0.401]
[0.400]
Charcoal-enriched soil (binary)
-0.124
-0.079
-0.444
-0.355
[0.386]
[0.382]
[0.393]
[0.398]
Poor soil (binary)
0.44
0.522
0.671
0.581
[0.537]
[0.534]
[0.525]
[0.540]
Slope
-0.064
-0.084*
-0.076
-0.074
-------
[0.048]
[0.049]
[0.047]
[0.051]
Castanhal municipality (binary)
0.647
0.625
0.672
0.408
[0.442]
[0.446]
[0.467]
[0.542]
Igarape A911 municipality
0.235
0.136
-0.072
-0.23
(binary)
[0.462]
[0.481]
[0.404]
[0.418]
No on-farm fallow area (binary)
-0.178
0.352
-0.112
0.57
[0.563]
[0.604]
[0.557]
[0.616]
No upstream fallow area (binary)
0.401
0.007
[1.633]
[1.655]
Constant
2.942
2.116
2.177
3.388
[1.908]
[2.003]
[1.976]
[2.824]
Spatial error correlation
0.153
0.176
0.075
0.087
coefficient (k)
[0.186]
[0.197]
[0.198]
[0.175]
Observations
167
167
184
184
R-squared
0.19
0.20
0.17
0.18
Log likelihood
-293.23
-291.62
-330.65
-330.17
Standard errors in brackets
* significant at 10%; ** significant at 5%; *** significant at 1%
45
-------
Table 8 Forest product harvesting elasticities
SEM
SEM-IV
SEM
SEM-IV
(1)
(2)
(3)
(4)
Log on-farm
Probability elasticity
0.14**
q 29***
q 29***
0.23**
fallow area
(0.06)
(0.07)
(0.06)
(0.09)
Conditional elasticity
0.06
0.28**
0.03
0.27*
(0.11)
(0.14)
(0.11)
(0.16)
Unconditional elasticity
0.21
q 47***
0.22
0.49**
(0.13)
(0.17)
(0.13)
(0.20)
Log upstream
Probability elasticity
0.22
0.22
fallow -
(0.14)
(0.16)
survey fallow
Conditional elasticity
0.55*
0.55*
area
Unconditional elasticity
(0.28)
0.77**
(0.34)
(0.32)
0.76*
(0.38)
Log upstream
Probability elasticity
0.29
0.84*
off-farm
(0.24)
(0.47)
fallow - GIS
Conditional elasticity
0.60
-0.002
canopy cover
(0.41)
(0.78)
(3 km radius)
Unconditional elasticity
0.89*
(0.51)
0.84
(0.99)
Standard errors of the probability elasticities were calculated using the delta method.
* significant at 10%; ** significant at 5%; *** significant at 1%
Table 9 Total output elasticities of on- and off-farm fallow
SEM
SEM-IV
SEM
SEM-IV
(1)
(2)
(3)
(4)
Total output elasticity of on-farm
0.11*
0.17**
0.11*
0.22**
fallow (sample mean)
(0.06)
(0.08)
(0.06)
(0.10)
Total output elasticity of upstream
0.42**
0.43**
fallow area (sample mean)
(0.16)
(0.19)
Total output elasticity of upstream
0.68***
0.29
canopy cover (sample mean)
(0.24)
(0.44)
Note: sample means of standard errors given in parentheses were calculated using the
estimated standard errors from the previous analyses.
Table 10 Land allocation efficiency of sampled farms, assuming 10% interest rate
Model (1) Model (2) Model (3) Model (4)
Optimal fallow 85% 88% 74% 88%
Over-fallow 4% 1% 17% 10%
Under-fallow 12% 10% 9% 2%
46
-------
Appendix
Table Al. First stage OLS regressions for on- and off-farm fallow used in crop
production equations
Model 2 Model 4
Log of
Log of
Log of
Log of
fallow
upstream
fallow
upstream
area
fallow area -
survey data
area
canopy cover -
GIS data, 3 km
radius
Log cultivated area
-0.038
-0.012
-0.006
-0.005
[0.087]
[0.025]
[0.080]
[0.023]
Log family labor
-0.175**
0.02
-0.086
-0.007
[0.083]
[0.023]
[0.075]
[0.022]
Log hired labor
0.002
-0.027*
0
-0.001
[0.056]
[0.016]
[0.051]
[0.014]
Log chemical fertilizer
0.023
-0.021
0.027
-0.022
[0.052]
[0.015]
[0.046]
[0.014]
Perennial producer
-0.053
-0 117***
-0.09
-0.024
(binary)
[0.154]
[0.043]
[0.143]
[0.041]
Use extension services
-0.031
0.035
-0.038
0.033
(binary)
[0.156]
[0.044]
[0.141]
[0.040]
Household head's
-0.006
0.001
-0.004
0.006
schooling years
[0.023]
[0.006]
[0.021]
[0.006]
Farm owner (binary)
0.133
-0.032
0.147
0.049
[0.134]
[0.038]
[0.123]
[0.035]
Black clay soil (binary)
-0.246
-0.122**
-0.186
0.019
[0.217]
[0.061]
[0.203]
[0.062]
Charcoal-enriched soil
-0.022
-0.034
-0.053
0.019
(binary)
[0.183]
[0.052]
[0.181]
[0.053]
Poor soil (binary)
0.061
-0.069
-0.017
-0.04
[0.283]
[0.080]
[0.255]
[0.073]
Slope
0.074**
0.025**
0.039
0.006
[0.036]
[0.010]
[0.035]
[0.010]
No on-farm fallow
-1.884***
0.021
-1.840***
-0.014
(binary)
[0.213]
[0.060]
[0.187]
[0.053]
No family labor (binary)
-0.808
0.215
-0.177
0.03
[0.571]
[0.161]
[0.539]
[0.155]
No hired labor (binary)
-0.016
-0.152**
0.041
-0.058
[0.242]
[0.068]
[0.219]
[0.063]
No fertilizer (binary)
0.106
-0.069
0.141
-0.047
[0.280]
[0.079]
[0.242]
[0.072]
No upstream fallow
1.177**
-1 423***
(binary)
[0.491]
[0.139]
Log of farm size
0.856***
-0.032*
0.743***
0.019
[0.063]
[0.018]
[0.058]
[0.017]
0.005
0
0.008**
-0.001
47
-------
Forest product prices
0.005
0
0.008**
-0.001
(farm-level)
[0.004]
[0.001]
[0.004]
[0.002]
Own firewood stove
-0.133
-0.005
-0.067
0.132***
(binary)
[0.169]
[0.048]
[0.160]
[0.046]
Own gas stove (binary)
-0.048
-0.016
0.002
-0.041
[0.170]
[0.048]
[0.160]
[0.046]
Log of farm size -
-0.058
0.512***
-0.102
0.058***
upstream weighted ave.
[0.143]
[0.040]
[0.078]
[0.022]
Forest product price -
-0.016
0.016**
-0.010***
0.001
upstream weighted ave.
[0.025]
[0.007]
[0.004]
[0.002]
Own firewood stove -
0.422
0.432***
0.325
0.452***
upstream weighted ave.
[0.538]
[0.152]
[0.343]
[0.097]
Own gas stove -
-0.035
-0.483***
-0.097
0.151*
upstream weighted ave.
[0.568]
[0.160]
[0.276]
[0.078]
Use extension service -
-0.495
0.085
-0.244
-0.295***
upstream weighted ave.
[0.381]
[0.108]
[0.269]
[0.077]
Household head
-0.04
-0.012
-0.165
0.024
schooling - upstream
[0.079]
[0.022]
[0.151]
[0.044]
weighted ave.
Farm owner - upstream
0.2
-0.119
0.036
0.149**
weighted average
[0.408]
[0.115]
[0.242]
[0.071]
Black clay soil -
-0.536
-1.161***
-0.167
-0.111
upstream weighted ave.
[0.658]
[0.186]
[0.314]
[0.089]
Charcoal-enriched soil -
-0.326
-0.159
-0.336
-0.185**
upstream weighted ave.
[0.602]
[0.170]
[0.278]
[0.081]
Poor soil - upstream
0.132
-0.026
-0.166
-0.316***
weighted ave.
[0.540]
[0.153]
[0.401]
[0.115]
Slope - upstream
-0.041
-0.012
-0.032
0.017
weighted ave.
[0.043]
[0.012]
[0.040]
[0.011]
Castanhal municipality
0.243
-0.175*
0.096
-0.311***
[0.328]
[0.093]
[0.228]
[0.065]
Igarape A<;u municipality
0.044
-0.253**
0.222
-0.145**
[0.365]
[0.103]
[0.217]
[0.062]
Constant
0.602
\ 934***
0.909
2.468***
[0.810]
[0.229]
[0.657]
[0.188]
Observations
R-squared
Standard errors in brackets
235
0.75
235
0.91
270
0.74
260
0.68
* significant at 10%; ** significant at 5%; *** significant at 1%
48
-------
Table A2. Crop production function estimation including downstream forest fallow
SEM
SEM-IV
SEM
SEM-IV
(1)
(2)
(3)
(4)
Log on-farm fallow area
0.107*
0.174**
0.091
0.164*
[0.058]
[0.079]
[0.059]
[0.089]
Log off-farm fallow - upstream
0.373**
0.403**
survey fallow area
[0.157]
[0.178]
Log off-farm fallow - 3 km
0.740***
0.435
upstream GIS canopy cover
[0.285]
[0.605]
Log off-farm fallow - downstream
-0.15
-0.302**
survey fallow area
[0.098]
[0.140]
Log off-farm fallow - 3 km
-0.297
-0.172
downstream GIS canopy cover
[0.592]
[1.085]
Log cultivated area
0.423***
0.395***
0.446***
0.435***
[0.099]
[0.099]
[0.096]
[0.101]
Log family labor
0.132
0.136
0.06
0.069
[0.093]
[0.093]
[0.088]
[0.090]
Log hired labor
0.166**
0.168***
q 294***
0.180***
[0.065]
[0.065]
[0.061]
[0.063]
Log chemical fertilizer
0.145***
q 247***
0.168***
0.161***
[0.055]
[0.055]
[0.057]
[0.059]
Perennial producer (binary)
0.896***
0.907***
0.835***
0.834***
[0.176]
[0.176]
[0.166]
[0.169]
Use extension services (binary)
0.236
0.242
0.21
0.212
[0.177]
[0.177]
[0.164]
[0.168]
Household head schooling years
-0.018
-0.019
-0.018
-0.019
[0.025]
[0.025]
[0.024]
[0.025]
Farm owner (binary)
0.092
0.112
-0.048
-0.028
[0.157]
[0.157]
[0.148]
[0.152]
Black clay soil (binary)
0.201
0.146
0.168
0.183
[0.236]
[0.237]
[0.238]
[0.251]
Charcoal-enriched soil (binary)
0.342
0.316
0.35
0.393*
[0.215]
[0.216]
[0.216]
[0.227]
Poor soil (binary)
-0.184
-0.198
0.201
0.139
[0.310]
[0.309]
[0.284]
[0.294]
Slope
-0.013
-0.019
-0.022
-0.017
[0.027]
[0.027]
[0.027]
[0.029]
Castanhal municipality (binary)
0.238
0.152
0.613***
0.516**
[0.228]
[0.231]
[0.237]
[0.263]
Igarape A<;u municipality (binary)
0.234
0.13
0.3
0.261
[0.230]
[0.238]
[0.214]
[0.219]
No on-farm fallow (binary)
0.451
0.632*
0.507*
0.668**
[0.284]
[0.323]
[0.261]
[0.312]
No upstream fallow area (binary)
1.247**
[0.606]
1.387**
[0.654]
No family labor (binary)
1.269**
1.259*
0.894
0.89
-------
[0.648]
[0.645]
[0.640]
[0.648]
No hired labor (binary)
-0.033
-0.001
0.174
0.115
[0.284]
[0.282]
[0.269]
[0.279]
No fertilizer (binary)
0.195
0.183
0.318
0.284
[0.307]
[0.308]
[0.299]
[0.303]
Constant
3.787***
3.968***
3.285*
3.671
[0.805]
[0.851]
[1.849]
[2.630]
Spatial error correlation coefficient
-0.026
-0.045
-0.014
-0.018
ft)
[0.129]
[0.125]
[0.138]
[0.131]
Observations
228
228
251
251
R-squared
0.60
0.60
0.57
0.56
Log likelihood
-312.65
-311.87
-347.64
-350.48
Standard errors in brackets
* significant at 10%; ** significant at 5%; *** significant at 1%
Table A3. First stage OLS regressions for on- and off-farm fallow used in forest product
equations
Model 2 Model 4
Log of off-
Log of
Log of off-farm
Log of
farm
fallow
upstream
fallow area
upstream
area
canopy cover -
fallow area -
GIS data, 3 km
survey data
radius
Forest product price
-0.083
0.042*
-0 171***
0.011
(village median)
[0.082]
[0.023]
[0.054]
[0.016]
Log of household size
-0.099
0.043
-0.092
-0.013
[0.122]
[0.035]
[0.110]
[0.034]
Wage rate
-0.031
-0.021
-0.012
0.005
[0.046]
[0.013]
[0.040]
[0.012]
Household head's
-0.003
0.007
-0.007
0.003
schooling years
[0.021]
[0.006]
[0.020]
[0.006]
Farm owner (binary)
0.116
-0.059
0.094
0.045
[0.130]
[0.037]
[0.117]
[0.035]
Car owner (binary)
-0.22
-0.114*
-0.241
-0.113*
[0.223]
[0.063]
[0.202]
[0.060]
Television owner
0.098
0.016
0.108
-0.005
(binary)
[0.145]
[0.041]
[0.132]
[0.040]
Use electricity (binary)
-0.092
-0.022
-0.053
0.005
[0.145]
[0.041]
[0.135]
[0.041]
Own firewood stove
-0.218
-0.01
-0.151
0.129***
(binary)
[0.166]
[0.047]
[0.155]
[0.046]
Own gas stove (binary)
-0.08
-0.013
-0.068
-0.012
[0.169]
[0.048]
[0.160]
[0.049]
Black clay soil (binary)
-0.27
-0.075
-0.289
0.002
[0.217]
[0.061]
[0.198]
[0.060]
0.025
-0.056
0.046
0.054
-------
Charcoal-enriched soil
0.025
-0.056
0.046
0.054
(binary)
[0.189]
[0.053]
[0.180]
[0.054]
Poor soil (binary)
0.082
0.006
-0.045
-0.084
[0.276]
[0.078]
[0.245]
[0.073]
Slope
0.047*
0.014**
0.038*
0.013*
[0.025]
[0.007]
[0.023]
[0.007]
No on-farm fallow
-1 995***
-0.004
-2.046***
-0.035
(binary)
[0.202]
[0.057]
[0.182]
[0.054]
No upstream fallow
0.748
-1.280***
(binary)
[0.601]
[0.170]
Log of farm size
0 sis***
-0.033**
0.745***
0.032**
[0.058]
[0.016]
[0.052]
[0.016]
Log of farm size -
-0.091
0.550***
-0.042
0.088***
upstream weighted ave.
[0.141]
[0.040]
[0.079]
[0.024]
Log of household size -
0.129
0.027
-0.058
-0.049*
upstream weighted ave.
[0.422]
[0.119]
[0.087]
[0.026]
Wage rate - upstream
0.051
0.033
0.11
-0.049
weighted ave.
[0.141]
[0.040]
[0.240]
[0.072]
Car owner (binary) -
-0.069
-0.548**
-0.29
-0.299**
upstream weighted ave.
[0.872]
[0.246]
[0.414]
[0.123]
Television owner
0.159
-0.205*
0.13
-0.003
(binary) - upstream
[0.386]
[0.109]
[0.230]
[0.069]
weighted aver.
Own firewood stove -
0.663
0.05
0.457
0.450***
upstream weighted ave.
[0.613]
[0.173]
[0.314]
[0.094]
Own gas stove -
-0.531
-0.339*
-0.353
0.157**
upstream weighted ave.
[0.612]
[0.173]
[0.252]
[0.075]
Black clay soil -
-0.284
-1 127***
-0.085
-0.155
upstream weighted ave.
[0.624]
[0.176]
[0.316]
[0.094]
Charcoal-enriched soil -
-0.368
-0.223
-0.264
-0.07
upstream weighted ave.
[0.592]
[0.167]
[0.283]
[0.084]
Poor soil - upstream
0.197
0.003
0.297
-0.443***
weighted average
[0.459]
[0.129]
[0.379]
[0.115]
Castanhal municipality
0.233
-0.210*
0.406*
-0.313***
[0.387]
[0.109]
[0.227]
[0.068]
Igarape A<;u municipality
0.054
-0.277**
0.322
-0.107*
[0.393]
[0.111]
[0.211]
[0.063]
Constant
0.304
1 594***
1.485
2 734***
[1.393]
[0.393]
[0.957]
[0.284]
Observations
236
236
271
261
R-squared
0.74
0.90
0.74
0.65
Standard errors in brackets
* significant at 10%; ** significant at 5%
; *** significant at 1%
51
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