“Land Sparing” in a von Thünen Framework: Theory and Evidence from Brazil

1. Introduction

The Amazon Basin covers millions of square kilometers and hosts half of the world’s remaining tropical rainforests, around 60% of which is found in Brazil. Since the end of “passive protection” in the 1960s, the Brazilian Amazon has experienced deforestation and forest degradation, primarily along the “arc of deforestation” in the states of Rondônia, Mato Grosso, and Pará (Fearnside 2005; Rudel 2005), with critical implications for biodiversity and a range of ecosystem services (Asner et al. 2010; Gibson et al. 2011; Malhi et al. 2008). Underlying these trends is a transition from state-sponsored small-scale deforestation in the 1960s and 1970s to export-oriented industrial-scale deforestation in the 1980s and 1990s (Rudel, DeFries, et al. 2009). Despite a decline in deforestation rates between the 2000s and 2010s, due to, for example, improvements in law enforcement and the expansion of protected areas (Assunção, Gandour, and Rocha 2015; Nepstad et al. 2014), large areas of forest continue to be cleared, primarily for the cultivation of soybean and cattle ranching (e.g., Bowman et al. 2012).

Expanding cattle populations and pasture areas have been driven by a prolonged rise in domestic and international demand for milk and beef (Delgado 2003; Nepstad et al. 2014; Steiger 2006). The supply of Brazilian cattle rose from 147 million heads of cattle in 1980 to 200 million in 2008, with 80% of this increase occurring in the Brazilian Amazon (McAlpine et al. 2009). To counter the expansion of agricultural areas while continuing to meet the demand for food, agricultural intensification is often promoted as a means of reducing cultivated areas, concentrating production, and allowing some lands to be “spared” as natural habitats (e.g., Cohn et al. 2014; Nepstad et al. 2009; Phalan et al. 2011; Rudel, Schneider, et al. 2009).

In this paper, we evaluate the microscale evidence for such land sparing among rural households in the Amazon state of Rondônia, who, since the 1970s, have been resettled and allocated forest lots by Brazil’s National Institute of Colonization and Land Reform (INCRA). Given “frontier urbanization” and the establishment of almost 1,000 urban centers in the Brazilian Amazon over the past 50 years (Browder and Godfrey 1997),¹ we adopt the land rent framework as a starting point for our analysis. Originated by von Thünen in 1826, it posits that location and distance to markets determine rents (von Thünen 1966). Closer to market, farmers bear lower costs in getting their products to market, and since they make higher profits, rent is higher (Angelsen 2007; Chomitz et al. 2007).

With a focus on cattle production, we examine the extent to which patterns of land use and productivity at the household scale support a key insight of the land rent framework: factors that increase rent, for example, price rises reflecting growing demand for agricultural commodities, will also tend to increase agricultural intensity, with more intensive uses found closer to the central market (Angelsen 2007). In Section 2, we formalize this insight in a model of an agricultural household facing the decision of whether to adopt an intensive or extensive system of cattle production. The latter is assumed to require relatively more pastureland and labor and fewer capital inputs than the former. In the spirit of Chomitz and Gray (1996), distance to market is included as an additional cost, which is factored directly into input and output prices.

From the model, we hypothesize that the closer a household is to market, the more likely it will adopt land-sparing patterns of cattle production (characterized by higher rates of cattle intensification and lower rates of pasture expansion and deforestation) in response to rising demand for beef and milk, than one located farther away from market. Our hypothesis is put to the test using data collected from a sample of households with privately held lots. Described in Section 3, our data were sampled over three waves in the Ouro Preto do Oeste region of Rondônia between 2000 and 2009.

Rondônia experienced the most rapid land transformation of all Brazilian states between the 1980s and 2000s (Alves 2002), with its deforested area rising from 2% in 1977 to over 60% in 2005 (Caviglia-Harris et al. 2009). Underlying this transformation is the continued expansion of Rondônia’s cattle herd, from 1.7 million to 5.6 million heads of cattle between 1990 and 2000 (Barros et al. 2002). Similar to other parts of the Brazilian Amazon, most of Rondônia’s cattle herd is reared for beef, while the remainder is reared for milk production (McManus et al. 2016).²

Beef cattle production is found all over the Amazon, including frontier areas, and is perceived as being simpler, less risky, and easier to market than milk production (da Veiga et al. 2001). By contrast, milk production is often concentrated among smallholders located near urban centers, which reduces their reliance on roads for the transportation of milk during the wet season (Faminow 1998). In recent years, milk production has grown in popularity, increasing by 50% in Rondônia between 1996 and 2006, with farms increasingly engaged in dual-purpose cattle production (Soler, Verburg, and Alves 2014).

The growth of milk production is reflected in rising levels of milk production per hectare among smallholders in Rondônia, which is at least partially due to the intensification of pasture-based cattle production systems (Soler, Verburg, and Alves 2014). Indeed, since the 1990s there have been substantial increases in the productivity of cattle production (McManus et al. 2016). In 2006, the average pasture stocking rate in Rondônia was 1.76 animal units (1 AU is equivalent to 450 kg of live animal weight) per hectare, among the highest rates in the Legal Amazon and well above the average for Brazil as a whole, 0.91 AU/ha (Valentim and Andrade 2009).

The extent to which intensification—and land sparing—might constitute a viable strategy to increase the sustainability of beef and dairy production in the Amazon is thus an important question. In going some way to address it in our paper, we make a number of contributions to the literature. The decision of whether to intensify or extensify cattle production, which is adapted from the technology decision of Fernandez-Cornejo, Hendricks, and Mishra (2005), is formally incorporated into a von Thünen framework. Consistent with household deforestation models in the literature (e.g., van Soest et al. 2002), we treat cleared land as a variable input produced by labor, but also consider household location, different forest types, and capital as a separate input.

Our theoretical approach is similar to the model of Pendleton and Howe (2002), in which transaction costs—as a function of distance to market—affect net wages, net agricultural prices, and net prices of consumption goods. Also relevant is an explicit treatment of the trade-offs between forest clearance labor and off-farm wages, and how differences in the productivity (and clearance costs) of primary and secondary forest influence clearance rates. Since we focus on small-scale, commercial cattle production rather than shifting cultivation, we treat forest clearing as an input, and not as both an input and an investment. We also incorporate a positive incentive to keep forest standing in an extension of our model.

We apply a fixed effects estimator to our dataset. This approach, outlined in Section 4, enables us, first, to examine the data for patterns of land sparing at the microscale. The potential of cattle intensification to raise beef and milk productivity and reduce agricultural expansion into forest areas has long received attention from researchers and policy makers alike (see, e.g., Angelsen and Kaimowitz 2001). In Brazil, Martha, Alves, and Contini (2012) suggest that productivity gains made between 1996 and 2006 may have spared millions of hectares of Amazon forest. Yet, evidence for land-sparing patterns in Brazil is limited; indeed, at the microscale it is nonexistent. Barretto et al. (2013) show that pasture intensification between 1975 and 2006 correlates with a reduction in pasture area at the municipality scale in agriculturally consolidated areas of southern Brazil. In Amazon forest frontier areas, they find that intensification occurred alongside agricultural expansion, which is suggestive of a possible rebound effect (Angelsen 1999; Lambin and Meyfroidt 2011).³ This is countered by Vale (2014), who finds that the increase in cattle productivity is associated with less deforestation, again at the municipality scale.

Second, we test whether household location, and by extension von Thünen’s framework, has any conditional, causal impacts on household cattle production decisions. Whether and how von Thünen’s land use “zones” change over time has received less attention. Ahrends et al. (2010) estimate three theoretically consistent land use zones over time and space around Dar es Salaam, Tanzania. Although these should not be interpreted as perfect geometric patterns, they do accord with the basic predictions of the land rent framework. That said, their analysis is based solely on land use and biophysical data and the crude identification of local land uses. As such, what drove these observed land use patterns, for example, changes in input and output prices, cannot be empirically tested.

Empirical research on deforestation often uses distance to market as a measure of location (e.g., Pfaff 1999; Tachibana, Nguyen, and Otsuka 2001; and previous work that uses our dataset). Utilizing the first two waves, Caviglia-Harris (2005) finds significantly less deforestation and smaller cattle herds with increasing distance to market, but no effect on cattle stocking density. We extend the panel and, more crucially, account for household heterogeneity and municipality trends in our estimation framework. Caviglia-Harris and Harris (2011) investigate how settlement design affects land use using all four waves in a fixed effects framework. They find that higher milk prices decrease the rate of deforestation but increase the proportion of the plot deforested. The extent to which this effect might be conditional on location is neglected, as are beef prices, household forest endowments, and a distinction between primary and secondary forest.

In general, empirical analyses of tropical deforestation that differentiate between primary and secondary forest are rare. Combining these, as is typical in the literature, overlooks important differences with respect to the dynamics of deforestation and the relative ecological values of different forest types (Vincent 2016). Our results, presented in Section 5, provide some empirical support to the land-sparing hypothesis while demonstrating important differences depending on forest type as well as the commodity under consideration and households’ initial forest endowment. We discuss their implications for public policy, in Section 6.

2. Land Rent Framework

We present a model of a rural household engaged in cattle production. When resettled in the 1970s onward, households in our setting initially converted forest to crops before purchasing cattle and converting cropland to pasture. Increasingly, households moved toward the direct conversion of forest to pasture (Caviglia-Harris et al. 2014). Therefore, we focus on the transition from forest to pasture. Formally, we develop a Chayanovian model of the agricultural household with an explicit technology decision adapted from Fernandez-Cornejo, Hendricks, and Mishra (2005). Full details are shown in Appendix A. Here, we summarize the model and start by assuming that there are markets for outputs, capital inputs, and labor.⁴ Our utility function is continuously differentiable, concave, additively separable, and depends on the level of household consumption (Y) and leisure (l): U(Y,l).⁵ The household’s objective is to maximize its utility subject to four constraints.

First, an income constraint in which the expenditure on consumables, p_yY, is equal to total revenues.⁶ Total revenues consist of (1) farm profits, which are derived from selling Q units of output, for example, beef or milk, at a market price net of transport costs (p_q – td),⁷ net of the costs of purchasing X units of capital inputs, each purchased at a unit price of (w_x + td); and (2) off-farm earnings, where the household receives a net off-farm wage of (w_m – td) for each unit of time spent in off-farm labor, M. We assume that transport costs, t, vary linearly with distance, d.

The second constraint is a technology constraint. Each possible technology is defined by the use of three inputs, namely, variable capital inputs denoted X (e.g., high-yield grass and legume cultivars, fertilizers applied to rotationally grazed pastures to increase forage harvest efficiency, and improved animal breeding and nutrition techniques) (Latawiec et al. 2014), purchased at a unit price of (w_x + td), general on-farm labor, L_g, and pastureland, P. There are two possible technological choices, either enabling an extensive, τ₁, or intensive cattle production system, τ₂. While we do not have data for the technologies adopted in our setting, the intensive technology is assumed to use more of the capital input and less pastureland than the extensive technology. Thus, the levels of all of the inputs utilized depend on the technology chosen. In terms of the labor intensity of general labor (the labor intensity of the technology, net of labor required for clearing forest), the effects are ambiguous and depend on the technology adopted (Latawiec et al. 2014). As such, we assume that the increases in general labor are equivalent across the two technologies.⁸

The third constraint relates to the conversion of forest into new pastureland. Since households in our sample own lots that neither expand nor contract over time, we assume a fixed land area. Thus, the expansion of pasture is limited by the extent of a household’s lot, as well as its initial endowment of forest. When the entire lot area has been converted to pasture, the household can adopt a technology only if it requires no additional pastureland.⁹ If forest remains in the lot, an expansion of pastureland is possible through the use of labor to clear primary (L_f1), secondary (L_f2), or both types of forest. We assume that clearing primary forest is more costly than clearing secondary forest, which is captured by the greater amount of time needed to clear a given area of primary forest,¹⁰ and that the household obtains no rent from keeping any of its forest standing.¹¹ Finally, the household can leave pasture fallow and allow for forest regrowth (secondary forest). This does not require physical labor but instead the allocation of a nonzero amount of household labor, Lc₂ for planning and decision-making, for example, to decide when and where to leave land fallow (see Perz and Walker 2002).

As shown in Appendix A, the first three constraints can be combined in the full income constraint. In the final constraint, we impose that the total time endowment of the household be allocated among general on-farm labor, land-clearing labor, land-conversion labor, off-farm labor, and leisure. After writing the Lagrangian and deriving the first-order conditions, it is profitable for a household to engage in extensive cattle production, τ₁, when [1]

Thus, it is profitable to engage in extensive agriculture (τ₁ > 0) if the increase in revenues net of transport costs, (p_q – td)∂Q/∂τ₁, exceed the costs of doing so. These costs include (1) additional capital inputs, which comprise unit input costs net of transport costs (w_x + td) multiplied by the increase in the units of the capital input required by the technology, ∂X / ∂τ₁; and, (2) the costs associated with the additional labor required by the technology. If the household works off-farm, each unit of additional labor is compared to the market wage net of transport costs. Similarly, for the adoption of the intensive system, τ₂, [2]

Under the assumption that a unit of intensification leads to the same increase in output as a unit of extensification (∂Q/∂τ₁ = ∂Q/∂τ₂),¹² the technology adopted will depend on relative costs. If participating in a labor market, the household’s value of its labor is driven by the net off-farm wage, which is decreasing with distance.¹³ With increasing distance from market, net off-farm wages are lower while capital inputs are more costly. Thus, households located farther away from market are more likely to adopt the extensive rather than intensive technology, utilizing a greater quantity of the cheaper input (labor) and a smaller quantity of the more expensive input (capital). Formally, the condition for the adoption of the extensive technology (assuming that the gains exceed zero for at least one of the two systems) is given by [3]

Since μ/λ is decreasing in distance to market and (w_x + td) is increasing in distance, the greater the distance to market, d, the more likely that this condition will be satisfied, all else equal.

From the model, we hypothesize that a rise in beef or milk prices is, ceteris paribus, more likely to lead to patterns of land sparing the closer a lot is to market. In other words, the closer a lot is to market, we expect to observe a higher likelihood of intensive technology adoption and a lower likelihood of extensive technology adoption: each extra unit of intensive technology adopted by the household (instead of extensive technology) will lead to a lower rate of pasture expansion (since by assumption ∂P / ∂τ₁ > ∂P / ∂τ₂), and the sparing of (∂P / ∂τ₁ - ∂P / ∂τ₂) units of forest.¹⁴

Therefore, the model predicts that in lots closer to market, increases in the price of beef and milk are more likely to determine higher rates of cattle intensification and lower rates of pasture expansion and deforestation than in lots farther away from market. Regardless of location, primary forest is expected to be deforested at lower rates than secondary forest.

3. Dataset

Described in detail by Caviglia-Harris et al. (2009), our dataset draws upon a sample of rural households, originally resettled landless migrants, from six municipalities in the Ouro Preto do Oeste region of Rondônia. All households in our dataset have privately owned lots and none moved during the sample period. Land uses are tracked using both self-reported land use data and GIS estimates of land uses from satellite data.¹⁵ Pasture is defined as land utilized for rearing cattle. Primary forest is mature forest that has not been previously cleared by households, while secondary forest is former primary forest that has been cleared for agricultural purposes before being left fallow and allowed to regenerate.¹⁶ Additional self-reported data include sources of income, assets, and prices received.

The household survey was conducted over four waves (1996, 2000, 2005, and 2009), and sample size differs from year to year.¹⁷ In 2005, the original sample of 196 households, surveyed in 1996 and 2000, was expanded by 117 households.¹⁸ Another 200 households were added in 2009. Since data for beef prices were not collected in 1996, we focus our analysis on the data gathered in 2000, 2005, and 2009. Details of how we created our dataset are contained in Appendix B.

The town of Ouro Preto do Oeste is used as the measure of “distance to market” in all previous studies that utilize our data (e.g., Sills and Caviglia-Harris 2008). Home to around 25,000 to 30,000 people, the town is also selected as our measure of distance to market. Although we have data for distance from each lot to Ouro Preto do Oeste, we do not know the lots’ exact locations nor do we observe the locations of beef and dairy processing facilities. Yet, Ouro Preto do Oeste is the main urban center in the region, the third largest in Rondônia after the state capital Porto Velho and Ji Paraná, and a likely source of local demand. For robustness, two alternative measures of distance to market are also examined (and reported in Section 5): the distance from the lot to Ji Paraná, and since each municipality has at least one urban center, the distance from the lot to the closest urban center.¹⁹

From Table 1, we first observe that the average household in the sample is approximately 40 km away from Ouro Preto do Oeste, a distance that ranges from 5 to 82 km. Second, the three largest sources of income, in descending order, are milk, beef, and perennial crops. Third, households own relatively small lots (on average, 68 ha). In most cases, the majority of land has already been converted into pasture. A nonnegligible proportion, about 23%, remains under forest cover.

Between 2000 and 2009, the average price of milk (per liter) and beef (per steer) increased in real terms by 21% and 34%, respectively.²⁰ The time trends of prices and all of the other variables discussed in the remainder of this section, along with their spatial patterns with respect to distance from Ouro Preto do Oeste, can be seen graphically in Appendix B.

Land area under pasture and the number of cattle in the lot increased substantially over the sample period. This increase in cattle numbers is mostly driven by expansion of the nondairy cattle herd. Indeed, on average, nondairy herds are larger than dairy herds by a factor of four. The majority of sampled households engage in dual-purpose cattle production, owning both nondairy and dairy cattle.²¹ Households living farther away from market tend to allocate smaller proportions of land to pasture and own smaller numbers of cattle.

Cattle stocking density, defined as the total number of each cattle type (dairy, nondairy) per hectare of total lot area net of primary forest, increased over time, particularly for nondairy cattle. Nondairy cattle have a more than threefold higher stocking density than dairy cattle. For both types, average cattle stocking density declines in lots located farther away from market.

There was a consistent trend of deforestation throughout our sample period, which led to the average proportion of land under primary forest declining among households. By contrast, the average proportion of land under secondary forest appears to be relatively stable over time. This is consistent with patterns of secondary forest succession in the Brazilian Amazon, when land used in the past for cultivating annual and perennial crops is fallowed (Caviglia-Harris et al. 2014). In lots located farther away from the center of Ouro Preto do Oeste, there is a clear pattern of greater forest cover.

4. Methodology and Estimation

To test the hypothesis derived in Section 2, we estimate the following fixed effects model: [4]

Equation [4] models the dependent variable Y—cattle stocking density (dairy, nondairy), proportion of land under pasture, and proportion of land under forest cover (primary, secondary)—for household i at time t, first as a function of our variables of interest. Thus, we estimate the coefficients on the price of commodity c (milk, beef)²² in municipality m at time t(φp_cmt) and its interaction with distance to market (δp_cmt × dist_i). Next, we include year fixed effects μ_t, which control for common shocks affecting all households in a given year, such as weather or policy shocks, followed by a municipality-specific linear time trend (Ω_mt), which accounts for common trends across households in a municipality.

Common trends include the development of local infrastructure (e.g., road improvements), local economic growth, market integration, and the development of agricultural institutions. Our time trends also capture the fact that different municipalities have been settled at different points in time and, hence, have different deforestation trends at any given point in time.²³ We then add a set of time-varying household-specific controls X_it, including household size, years of education (household heads), and an asset index that controls for household wealth. Finally, household fixed effects (α_i) are included to address time-invariant household-level heterogeneity, like slope and soil quality.²⁴

When estimating equation [4], proportions are chosen over levels mainly due to the former being less sensitive to outliers than the latter. Regression results using levels remain very similar, however (see Section 5). Consistent with our land-sparing hypothesis, following a rise in milk or beef prices we expect to observe higher, positive rates of cattle intensification in household lots closer to market than in lots farther away from market, in other words, a positive sign on the coefficient φ and a negative sign on the coefficient. We expect the proportion of land under pasture to decline, an effect that is predicted to be less pronounced in lots farther away from market, that is, a negative sign on φ and a positive sign on. For forest cover, we expect to observe an increase in the proportion of land under forest, an effect to be less pronounced in lots farther away from market, that is, a positive sign on φ and a negative sign on. A steeper decline in secondary forest is expected in contrast to primary forest. We now discuss a number of remaining methodological issues regarding the estimation of equation [4].

First, we adopt a fixed effects framework because it allows us to control for household fixed effects, which are likely to be important in our setting to capture, for instance, (unobserved) preferences for deforestation as well as conversion costs. However, it is arguably not the best way to model proportions since it has the potential to predict values outside the possible bounds of the variable (i.e., values below zero or above one). To ensure that our main results are not a by-product of our methodological choice, we rerun our regressions (in Section 5) using a generalized linear model (GLM) model with a logistic link, as suggested by Papke and Wooldridge (1996). This estimator is able to handle proportional data, which includes zeros, ones, as well as intermediate values (Baum 2008). However, the GLM estimator does not allow for the inclusion of fixed effects.

Second, it is highly unlikely that the error terms of different land uses are uncorrelated, since conversion to one land use generally comes at the expense of another land use. While we do not directly observe the proportions of pasture generated from each of primary and secondary forest, modeling the proportions separately may not be ideal. A seemingly unrelated regressions (SUR) framework could be utilized to model such land use changes. Baum (2006) suggests that the asymptotic properties of SUR rely on having the number of time periods larger than the number of households. In our case, the number of households is much larger than the number of observations per household, and hence, a SUR framework is inappropriate.

Third, our model hypothesis and empirical strategy are based on the underlying assumption of a land use transition of forest to pasture, thus neglecting crop production. At 11%, the average proportion of the lot cultivated for crops is relatively small (see Table 1) and varies little over time. To further support our assumed land use transition, and qualify whether crop production ought to be included as an intermediate stage, in Section 5 we estimate equation [4] for the proportion of the lot under crop cultivation. Thus, as a kind of placebo test we do not expect beef or milk prices, nor their interactions with distance to market, to have any effect on the proportion of the lot under crop cultivation.

Fourth, household-level price data for beef and milk are arguably unlikely to be exogenous, since some farmers may be, for example, better at negotiating the selling price or simply have better connections that allow for more favorable selling conditions. We thus calculate average beef and milk prices at the municipality scale based on prices received by households in each year. A relatively large number of households report the prices of beef and milk received, which are unlikely to affect the average prices received in a given municipality.²⁵ This also allows us to have a good proxy for households that did not report prices received. A disadvantage of using municipality-level average prices is that it precludes the use of municipality-year fixed effects. Our municipality-specific linear time trends arguably attenuate such concerns by capturing common trends at the local scale. To attenuate concerns about the endogeneity of local prices, we rerun our regressions using international prices for beef and milk, in Brazilian reais, from price indices based on FAOSTAT (FAO 2017) milk and cattle producer price data (see Section 5). Note, however, that these regressions exclude year fixed effects and the variation declines. Also, missing data in the FAOSTAT repository necessitated changing the sample to include the 1996 wave and to exclude the 2009 wave.

A fifth issue relates to the potential endogeneity of distance to market, which implies that households may not be randomly allocated across space. Such sorting might occur, for example, when better-capitalized households choose to locate close to market. Thus, they may differ substantially from one another in a number of ways, for example, in terms of forest cover. This has been discussed in the literature, for example, in the identification of the returns to schooling using distance to school (Carneiro, Lokshin, and Umapathi 2017). In our setting, however, distance to market can be treated as exogenous, since the location of lots was determined by INCRA’s settlement plans (see Caviglia-Harris 2005).

Sixth, we have an unbalanced panel, and hence, our results may be partly driven by the fact that households added to the sample at different points in time may differ from one another. To provide assurance that our results are not driven by the inclusion of households added to the sample in 2005 (selection bias), we rerun the regressions as a robustness check for a subsample that excludes these households (see Section 5). Since households added to the sample in 2009 are observed only once, the use of a fixed effects estimator implies that they are excluded from the sample altogether. Our unbalanced sample also contains missing observations due to household attrition (i.e., households leaving the sample). An advantage of using a fixed effects estimator in such a context is that it attenuates potential sample selection issues by allowing this attrition to be correlated with α_i.

Finally, with the inclusion of trends, fixed effects, and so on, there is a large degree of parameterization in our model. An alternative way of taking care of unobserved heterogeneity in panel data without a random effects estimator is to use a first differences estimator, which reduces the number of estimated parameters. To ensure that our results are not driven by the choice of estimator, we thus rerun our regressions in first differences (see Section 5).

5. Results

Table 2 summarizes our main results. Starting with the results for cattle stocking densities (columns 1 and 2), higher milk prices are associated with an increase in cattle stocking density, an effect that is significant (at the 5% level) in the case of nondairy cattle.²⁶ Since households who own dairy cattle also tend to own nondairy cattle, it is possible that investments in one cattle type are influenced by price changes that affect the other type. The coefficient of the interaction term between milk price and distance to market is negative, and while this result is also consistent with our predictions, the effect is statistically insignificant. Beef prices similarly display a positive coefficient and a negative interaction with distance, although both of these effects are again insignificant.

From column 3 in Table 2, we first observe a positive direct effect of milk price on the proportion of land under pasture, an effect that becomes less pronounced (i.e., the interaction term is negative) with increasing distance from market. Both of these results are statistically insignificant. More in line with theory, we observe a negative yet insignificant direct effect of higher beef prices on pasture. The coefficient of the interaction between beef prices and distance to market is positive and significant (5% level). This implies that rising beef prices drive a significant increase in land under pasture in lots located farther away from market relative to those closer to market.

Results for secondary forest in Table 2 (column 4) suggest a positive yet insignificant coefficient for milk price. Its interaction with distance is, however, positive and significant (5% level). Higher prices of milk are thus associated with higher proportions of land in secondary forest, and this effect is significantly stronger in lots located farther away from market. This pattern is not consistent with theory and, since it is significant, is discussed further below. For beef, we estimate a negative and highly significant (1% level) coefficient for beef prices; its interaction with distance is negative and insignificant (Table 2, column 4). Thus, an increase in beef prices significantly and negatively affects the proportion of land under secondary forest cover regardless of the location of the household’s lot. That said, the rate of deforestation is larger in lots located farther away from market, a pattern more in line with our expectations than that for milk prices.

With respect to primary forest (Table 2, column 5), we observe, as expected, the prices of milk and beef both exhibit positive (but insignificant) coefficients. We also find their respective interactions with distance to market are negative and significant (10% level). This implies that increases in the prices of milk and beef drive a significant decline in land under primary forest cover in lots farther away from market in contrast to those closer to market. Finally, we find that regardless of household location, primary forest is deforested at lower rates than secondary forest, although this pattern holds only for beef prices.

Following the estimation of the regressions shown in Table 2, we obtain the corresponding marginal effects of beef and milk prices at varying distances to market. These are rescaled in order to allow for a more straightforward interpretation of results.²⁷ The results are summarized in Table 3 (and shown graphically in Appendix C).

A one-cent increase in milk prices is associated with a significant (5% level) increase in stocking density of nondairy cattle. This effect, at around 0.24 heads of cattle per hectare 6 km from market, declines with increasing distance to market. A similar increase in milk prices drives similar patterns with respect to Similarly, an estimated coefficient of –0.04 for beef implies that a one-unit (100 reais) increase in beef price leads to a 0.04 (4 percentage point) decrease in the dependent variable. dairy cattle, although the impacts are statistically insignificant. The marginal effects of milk price on pasture though insignificant are positive and declining with greater distance to market. For secondary forest, the marginal effect of milk prices becomes more positive in lots farther away from market, an effect that becomes significant (10% level) at distances greater than 40 km from market. For primary forest, a positive but insignificant marginal effect becomes negative though remains insignificant with increasing distance from market.

The marginal effects of an increase in beef prices on stocking density are generally insignificant. From Table 3, we observe a negative though insignificant effect of beef prices on pasture and a less pronounced effect the farther away the lot is from market. After a certain distance, 40 km from market, the predicted effect is positive, although it remains insignificant. Beef prices drive a significant loss of secondary forest, with the marginal effect becoming more negative in lots located farther from market: a 10 reais increase in the price of beef leads to an estimated reduction of 1.3 percentage points in secondary forest in lots located 6 km from market, and a reduction of 1.8 percentage points in lots located 80 km away. Similar to milk prices, we find that an increase in beef prices is associated with more primary forest in lots located closer to market, a positive effect that declines and becomes negative with distance. Although insignificant, these patterns are consistent with theory.

The effects of milk and beef prices on secondary forest clearly differ. Milk prices have a positive marginal effect on secondary forest irrespective of the distance to market, and this effect is larger the farther away the lot is located from market. Beef prices, by contrast, have a negative marginal effect throughout, an effect that becomes more negative with distance to market. Different production systems for milk and beef may help explain these seemingly conflicting results. Dairy systems are likely to be smaller in scale and more land intensive than those systems that mainly or only focus on beef production (see Cohn et al. 2011). Thus, when households switch from rearing beef cattle to dairy cattle, we speculate that this may allow for the conversion of pasture into secondary forest. From Table 2, we observe a statistically insignificant impact of higher milk prices on pasture, regardless of household location. By contrast, consistent with patterns of extensification, higher beef prices in Table 2 are associated with the expansion of pasture area and a decline in both primary and secondary forest in lots farther away from market.

In sum, we find evidence that patterns of cattle production at the household scale are conditional on distance to market, and that these, to some extent, are consistent with land sparing. Yet, more secondary and less primary forest is found closer to market. Thus, households’ forest “endowments” might be driving the effect of location in observed patterns. We explore this possibility further after testing for the robustness of our main results in the following subsection.

Robustness Checks

We undertake a number of checks for, respectively, cattle stocking density (dairy, nondairy), pasture, secondary forest, and primary forest. For cattle stocking density, we conduct seven robustness checks where we use the distance to the closest urban center (instead of the distance to Ouro Preto do Oeste); use the distance to Ji Paraná (again instead of the distance to Ouro Preto do Oeste); omit households added in 2005 (No 2005); estimate the equation using logs (Logs); use the first lag of prices (l.prices); address price endogeneity concerns by using national-level producer prices instead of municipality-average prices (Int.prices); and use first differences (FD) instead of a fixed effects estimator. For the three land uses, we conduct two additional robustness checks, in which we use levels instead of logs (Levels), and adopt a GLM (log-link) instead of a fixed effects estimator. We summarize the results here; tables containing detailed results for all robustness checks and for all of our dependent variables are presented in Appendix D.

For cattle stocking densities, the predicted effects are mostly insignificant except for the response of nondairy cattle to milk prices. This is shown to be positive and significant in four out of seven specifications. Most specifications for pasture suggest a positive effect of milk prices and a negative interaction term. Four out of nine specifications show a negative direct effect of beef prices on pasture, while eight out of nine specifications indicate a positive and significant coefficient for the interaction of distance and beef prices. Thus, we find support for the result that an increase in beef prices reduces pasture closer to market and increases it farther away.

The direct effect of milk prices on secondary forest is ambiguous, since three specifications suggest a negative effect and six indicate a positive effect. The interaction between milk prices and distance is positive in eight of the nine specifications. This effect is also significant in five. For the effect of beef prices on secondary forest, almost all specifications indicate a negative coefficient, which is significant in six cases. In addition, we estimate a negative interaction between beef prices and distance in most specifications, and a significant effect in three. These results provide some support for the result that an increase in beef prices leads to a loss in secondary forest cover and that this effect is more pronounced farther away from market.

All estimates show a positive direct effect of milk prices on primary forest, and this coefficient is significant in three specifications. Seven out of nine specifications indicate a negative interaction between milk prices and distance. This is also significant in four specifications. We find a similar pattern for beef prices in the majority of specifications. The one notable exception is the specification using international prices, which suggests a negative and significant direct effect but maintains a negative (though insignificant) interaction with distance. Thus, all but one specification suggest higher deforestation (or a lower amount of sparing) farther away from market.

Finally, we estimate equation [4] for the proportion of the lot under crop cultivation to check that the land use transition of forest to pasture does not involve crop production as an intermediate stage. From Appendix Table D6, we find that as expected, neither prices nor their interactions with distance to market have any statistically significant effects on the proportion of the lot under crop cultivation.

Further Results: Endowment Effects

We investigate the extent to which the initial endowment of forest plays a role in our main results. With high initial forest cover, households may be more likely to extensify rather than intensify regardless of location. Initial forest cover is primary forest cover in 2000 or in the first year for which we have data for the household. We split the sample into above- (“high”) and below-median (“low”) initial primary forest, with the median estimated as 15.3% of the total lot. Based on this sample split, we test for differences in outcomes. Table 4 shows the results.

In Table 4 (columns 1–4), we first observe a positive effect of higher milk prices on both types of cattle stocking density. Yet, contingent on forest endowment, none of these effects are significant. From column 5, an increase in milk prices leads to a significant increase in pasture among high-endowment households, an effect that becomes significantly less pronounced with increasing distance to market. More consistent with the land-sparing hypothesis is the opposite pattern we observe among low-endowment households (column 6). Our main result of a negative direct effect of beef prices on pasture that becomes positive and significant in lots located farther away from market is concentrated among high-endowment households (column 5).

The effect of higher milk prices driving significantly higher proportions of land under secondary forest in lots located farther away from market is also found among high-endowment households (column 7). In columns 7 and 8, we observe a negative impact of rising beef prices on secondary forest, which occurs not only irrespective of location but also regardless of forest endowment. This effect is much larger among high-endowment households. Both of the interaction terms for, respectively, low- and high-endowment households are small in magnitude, and neither is significant.

For primary forest, the significant and positive effect of an increase in milk prices is found among low-endowment households, an effect that is less pronounced with distance to market (column 10). Rising beef prices have a positive and significant effect on primary forest among high-endowment households, an effect that is also significantly less pronounced with distance to market (column 9).

6. Discussion and Policy Implications

Brazil has a long history of tropical deforestation, although recent trends suggest that the rate of deforestation has slowed. Nepstad et al. (2014) argue that for Brazil to maintain progress in reducing deforestation in the Amazon, one of the steps it must take is the stabilization and intensification of cattle production. Against expectations, Vale (2014) argues that this trend has already begun. However, there is a dearth of research exploring the intensification-deforestation nexus and patterns of land sparing at the micro scale, which is at least partly due to the paucity of available data at this level of aggregation.

Our results suggest some empirical support for land sparing in a von Thünen framework. Land use and productivity patterns differ depending on whether we consider primary or secondary forest, milk or beef prices, and initial household forest endowments. We find evidence that rising prices drive significant increases in pasture area and declines in primary forest in lots located farther away from market relative to those closer to market. Given the relative abundance of secondary vis-à-vis primary forest in lots located closer to market, it is perhaps unsurprising that in these lots we observe more deforestation (or less sparing) of secondary forest compared to primary forest. This could help explain why the coefficients of both beef and milk prices are positive in lots closer to market with respect to their effects on primary forest, which is suggestive of land sparing. Even when accounting for forest endowments, similar land-sparing patterns persist.

Higher beef prices have a negative impact on secondary forest, with a more negative effect found in lots farther away from market. Less in line with theory is the more pronounced, positive effect of milk prices on secondary forest in lots found farther away from market. Yet, both of these results are consistent with our results for pasture: milk prices have a statistically insignificant effect while beef prices have a significant impact in lots located farther from market. We speculate that since milk production requires less land for cattle than beef production, more land is converted from pasture to secondary forest when households switch from rearing beef to dairy cattle.

We acknowledge that our simple model is unlikely to fully capture the complex dynamics of deforestation and afforestation. Modeling the substitution between beef and milk production and showing how this relates to forest dynamics requires a different theoretical framework and, as such, is left for future work. Empirically, our measure of cattle stocking density cannot account for the land intensity of production: the majority of our sampled households own both cattle types, and we cannot distinguish between pasture utilized for dairy cattle and that used for beef cattle. Thus, it is perhaps unsurprising that the estimated coefficients of cattle stocking density are noisy and, for the most part, insignificant. The fit of our regressions improves when analyzing land use changes.

Research on tropical deforestation using longitudinal data at the household scale is critical for improving the design of policies to capture forest externalities such as climate and hydrological services and biodiversity. Since 1970, around one million landless migrants have been resettled by INCRA among 1,900 settlements (Schneider and Peres 2015). Such smallholders are responsible for only around 12% of all deforestation in the Brazilian Amazon, yet against a backdrop of falling deforestation rates and expanding cattle herds, smallholder deforestation rates rose by 68% between 2005 and 2011 (Godar et al. 2014). While our household sample may not be representative of the whole Amazon, we argue that it is representative of its forest frontier areas. This sample is also, to our knowledge, the best available microlevel panel dataset in a tropical forest setting, one that includes both socioeconomic survey and satellite data collected in multiple waves over a decade. From our results, we derive a number of implications for public policy at the household scale, with respect to resettlement, agricultural development, and forest conservation.

Resettlement policies have been implemented in a similar manner across the Brazilian Amazon. In our setting, land use patterns follow roads and are akin to so-called fishbone patterns. These are characteristic of the orthogonal settlement design, the commonest one employed by INCRA (Caviglia-Harris and Harris 2011). Given the rise of hundreds of new small towns in resettled areas that once formed part of the forest-agricultural frontier, there is now a surfeit of agricultural-forest mosaic lands. While such lands would command a higher price in contrast to more pristine forest areas, assigning households to these rather than to lots at the frontier might help prevent the “legal deforestation” that is likely to occur in the latter, more forest-rich lots. Our estimated marginal effects could enable the identification of possible zones in which deforestation and extensification are least likely to occur and, hence, where new settlements could potentially be located.

Our results suggest an endowment effect whereby households in lots with relatively large remaining areas of forest tend to be far more responsive to price changes than households with less forest. Conceptually, this is perhaps an obvious point, but it does imply that policy makers aiming to intensify cattle production should focus on households still owning proportionally larger areas of forest rather than those with relatively little forest remaining on their lots. Relatedly, policy makers keen to incentivize and nudge households into more sustainable patterns of cattle ranching in the Amazon could also focus on cattle reared for milk production, which appear to have greater potential for land-sparing effects than cattle reared for beef. Thus, agricultural policies could channel extension activities, credit, and technical support toward the development of dairy herds and associated infrastructure and institutions, rather than toward nondairy herds.

Policies geared toward protecting primary forest should target households farther away from market. This is perhaps pertinent given that lots located close to market may even be sparing forest, with or without the intensification of cattle production. Thus, deforestation baselines established at a more aggregate scale, for example, for state-level REDD+ initiatives, are likely to be overestimating rates of deforestation in areas close to urban centers. Our results could help design more precise deforestation baselines, not only according to distance to market but also according to forest type, in order to help evaluate the impact of such initiatives as they are rolled out.

Preventing legal deforestation on smallholder lots could be achieved by positive incentives created through a market for environmental reserve quotas (cotas de reserva ambiental; CRAs), which is presently being implemented by federal and state governments (Soares-Filho et al. 2014). Yet, in the revised Forest Code, approved in 2012, lots that had reduced their legal reserve below the 80% forest threshold before 2008 are subject to an amnesty clause that precludes the need to purchase CRAs. This amnesty applies to households in our setting. Recently resettled households, in other Amazon settings, still have to meet the 80% requirement. They could come into compliance either by restoring their forests to cover their legal reserve deficit or by compensating for their deficit by purchasing CRAs from lots with a legal reserve surplus (Cai et al. 2016). Such purchases could be made via a payment for ecosystem services (PES) scheme, which is incorporated in an extension of our model (see Appendix A). The result is intuitive in that it leads to fewer incentives to adopt any technology if it involves the conversion of forest into pasture. Yet, a PES is theoretically more likely to incentivize the adoption of an intensive rather than an extensive technology, and the higher the level of the payment the more effective this incentive is likely to be.

Finally, our empirical results could be used not only to establish baselines for deforestation trends and as a means of monitoring compliance with the revised Forest Code over time and space, but also as a way of identifying households that pose the greatest (legal) deforestation risk, for example, those living farther away from market with predominantly nondairy cattle herds. Such households could be targeted for PES and/or intensification strategies. Future theoretical and empirical work could closely examine the relationshipbetween incentives for forest conservation and intensification.