The Role of Staple Food Prices in Deforestation: Evidence from Cambodia  

Proposition 1 (Separable Model)

If the price of the staple food P_s increases:

• 1A. The total relative area allocated to staples dρ_s/dP_s and other land use dρ_o/dP_s will increase, respectively, if and only if the respective own-price and cross-price elasticities, η_ρsPs and η_ρoPs, are individually positive.

• 1B. The total land allocation dT/dP_s will increase if and only if the price elasticity of the staple to total cultivated area, η_{T Ps}, is positive.

Proposition 1 shows that a staple food price shock can increase land devoted to staples or other uses, increase the relative share of either land use, and increase total allocation to productive use.

Proposition 2 (Nonseparable Model)

If the price of the staple food P_s increases:

• 2A. The total relative area allocated to staples dρ_s/dP_s will increase if and only if the household is (1) a staple net buyer and staples and other land use are complements in production costs, or (2) a staple net buyer (net seller), staple and other land use are substitutes in production costs, and other-area-weighted second-order profit effects of other land use are greater than (less than) staple-area-weighted second-order cross-input cost effects.

• 2B. The total relative area allocated to other land use dρ_o/dP_s will increase if and only if the household is (1) a staple net seller and staples and other land use are substitutes in production, or (2) a staple net buyer, staple and other land use are complements in production costs, and other-area-weighted second-order profit effects of other land use are less than staple-area-weighted second-order cross-input cost effects.

• 2C. The total amount of land allocated to staples and other land use dT/dP_s will increase if and only if the household is (1) a staple net buyer and staples and other land use are complements in production, or (2) a staple net buyer (net seller), staple and other land use are substitutes in production costs, and other land use second-order profit effects are greater than (less than) second-order cross-input cost effects.

Proposition 2 shows that, under nonseparability, the household’s state as a net buyer or net seller in the staple is a determining factor in land use and that a staple price shock can increase nonstaple land use, the relative share of either land use, and the total amount of land in agriculture.

These propositions offer useful and intuitive insights. For example, if a household is a net buyer of the staple, increases in the price will increase the opportunity cost of nonproductive land. Once the land becomes valuable enough to overcome the cost of conversion, it may be used for staple production to reduce reliance on purchases or for cash crops to increase the availability of income to purchase the now more costly staple. The choice of crop will be based on the suitability of the land for each crop and the net revenue that could be generated. For this reason, a crop grown on deforested land may not be a good indicator of the impetus for deforestation.

We test these propositions in aggregate and at the household level. As will be shown in equation [5], a household’s net staple position is also encapsulated in the NBR, which adds further value to studying this short-run welfare measure as part of our household-level analysis.

Data Sources

Summary Statistics: Deforestation and Rice Prices

Figure 1 shows total deforestation trends in Cambodia disaggregated by land tenure (ELC and non-ELC land) between 2001 and 2018. We observe that total deforestation outside of ELCs greatly exceeded deforestation inside of ELCs. ELC and non-ELC deforestation also seem to have followed distinct time paths. These differences suggest varying mechanisms for the high deforestation levels in Cambodia over this period. Appendix B provides spatial maps of these deforestation trends for districts with local price data and a map of Cambodia showing the locations of ELCs overlain by districts and the location of Cambodia’s deep seaport at Sihanoukville (see Appendix Figures B2–B4).

Trends for our shift variable (a U.S.-based average international rice price) and local rice prices are captured in Figure 2. A strong correspondence is readily apparent between the international price trends and local prices. Figure 2 (top) shows that the price of rice more than doubled in 2008, followed by a steep decline in 2009 and subsequent tempered increases through 2014 that were well above the pre-2008 average. Figure 2 (bottom) shows the distribution of low-quality rice unit values along with the variance of the distribution. Appendix Figure B5 presents a similar figure for wet season paddy prices.

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Figure 2

Top, U.S.-Based Average International Rice Price; bottom, Low-Quality Rice Unit Value Distribution (n = 497,129)

Sources: Author’s calculations; Cambodia Socioeconomic Survey (CSES) consumption diary data; Cambodia National Institute of Statistics consumer price index data; FAO (2020).

Note: Centiles above 99% or below 1% are assigned to the mean; the CSES was not implemented in 2005–2006, and the consumption diary was not implemented in 2012–2013.

We use the local price distributions to construct district-level rice price observations for tests of aggregate impacts on deforestation. In Appendix B, we provide spatial maps of these price series reflecting where local price data are available for these series by year. We also show CSES and FAO price data for cash crops, fuelwood, and charcoal for comparison (Appendix Figures B6–B9).

Summary statistics for variables in our deforestation specifications are in Appendix Tables B1 and B2. District-level reduced-form models use balanced panels. In our district-level specifications for 2SLS estimation, panels are slightly unbalanced, with around 77% of the sampled districts being observed for at least four years. Models focused on low-quality rice unit values comprise a six-year panel, and models focused on wet season paddy prices have an eight-year panel.

Summary Statistics: Household Characteristics and Land Allocation

Household-level summary statistics appear in Appendix Table D1. This table differentiates variation by the full sample (n = 45,969), nonagricultural, and agricultural subsamples; sample sizes vary somewhat by covariate due to data availability or applicability.¹⁵ We highlight some important variation across households here.

Most of the sample (65%) has land for producing crops. Nonagricultural households fare better in terms of education (6.2 vs. 4.3 years for heads of households), time collecting fuelwood (1.5 vs. 4.5 hours per week), dietary diversity (10.6 vs. 9.5), and vulnerability (0.77 weeks starving vs. 1.08). All households spend about 80% of their monthly budget on food, and although the mean agricultural household is a rice net seller (across years), agricultural households spend more on rice (10% vs. 28% of the food budget).

On average, agricultural households grow 1.4 crops and have just under two plots on less than 2 ha of land; most (60%) do not have irrigated rice plots. Mean rice area allocation is 78% and 36% for wet and dry seasons, respectively; mean cash crop allocation is 9% and 18% in wet and dry seasons, respectively. These allocations imply that households are maximizing wet season rice—a logical strategy given limited irrigation access.

Figure 3 shows boxplots of rice and cash crop allocations by year and season. Figure 4 shows annual boxplots of the sum of seasonal cash crop and rice allocations and boxplots of total annual allocations. Within-season sums of rice (r) and cash crops (cc) for the dry season (d) and wet season (w) are defined as T_d=A_r,d+A_cc,d and T_w=A_r,w+A_cc,w. Total annual allocations are defined as T_dw=T_d+T_w. Each set of boxplots features period-specific means plotted over each boxplot and horizontal lines reflecting respective means for the first period observed.

Figures 3 and 4 show important stylized facts. First, allocations declined between 2003 and 2008, as exhibited by movements in averages, medians, and interquartile ranges, but allocations began to increase after 2008. By 2013, allocations regain or exceed their baseline means. Second, Figure 3 shows that cash crop allocations have fluctuated more than rice. This is consistent with the idea that households consistently prioritize rice allocations for their own consumption and that preshock rice allocations may have already been maximized. For analysis of these measures, we retain only households with total land holdings that are not extreme outliers and instances where cash crop area shares or within-season allocations do not exceed one.¹⁶ Summary statistics and regression results do not substantively change if outliers are retained.

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Figure 3

Wet and Dry Season Area Shares for Rice and Cash Crops Sources: Author’s calculations; CSES agricultural production module data from 2004, 2007–2013. Note: Distributions are assessed conditional on growing a crop in a given season.

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Figure 4

Sums of Rice and Cash Crops Shares: top, Within-Season Sum; bottom, Sum across Seasons

Sources: Author’s calculations; CSES agricultural production module data from 2004, 2007–2013.

Note: The range of the y-axis on the bottom graph is truncated to enable discernment of the tightly packed variation around one.

Econometric Models: Aggregate Deforestation Effects

In Section 3, our theoretical framework established direct and indirect pathways for staple food price shocks to impact deforestation. Now we test for the presence of aggregate impacts to deforestation in Cambodia from the rice price shock circa 2008. We use a reduced-form model and a 2SLS model. The value of the reduced form in this setting is twofold. First, the reduced form is well established as a valid means to approximate causal impacts (Chernozhukov and Hansen 2008; Angrist and Pischke 2009), and it is well established in the shift-share instrument setting (Goldsmith-Pinkham, Sorkin, and Swift 2020). Second, because the reduced form only requires values of the instrument, this approach allows us to construct a disaggregated balanced panel for the entire country using data between 2001 and 2018. Our reduced-form panel fixed effects model is given by

1

where D_{l, j, t+1} is deforestation (km²), with subscripts l indicating administrative unit, j indicating land tenure, and t time period; Z_{l, t} is an instrument for rice prices; is a vector of control variables; ℒ_ℓ and 𝒯_t represent unit and time fixed effects, respectively; μ_{l, j, t+1} is an error term; and α₁ and α are coefficients to be estimated. For X, we include a vector of seasonal weather controls, a shift-share instrument for rubber price, and deforestation in period t originating in land tenure j⁻ to account for potential spillover effects. Thus, if we are examining deforestation outside ELCs, we control for prior deforestation inside of ELCs and vice versa.

In equation [1], we are interested in α₁, which represents the impact of the rice price shock. Econometric theory dictates that α₁ is proportional to the causal effect of interest via indirect least squares (Chernozhukov and Hansen 2008; Angrist and Pischke 2009). Specifically, the indirect least squares estimate for an endogenous variable of interest in the second-stage equation can be written as α₁ divided by the coefficient on the instrument in the first-stage equation. Thus, in equation [1] the sign and significance of α₁ are of primary interest because magnitude is relative.

The lag structure in equation [1] reflects the fact that deforestation is a labor-intensive activity that requires time to implement in conjunction with the annual agricultural calendar and is less likely to occur contemporaneously with a local price shock. Our preferred reduced-form specification is at the district level because this provides consistency with the available panels for our 2SLS estimation. Land tenure differences j are used to differentiate ELC and non-ELC land use. This disaggregation allows construction of two dependent variables and separate tests of whether the rice price shock had different impacts on deforestation depending on the dominant agents present.

Our 2SLS model uses an instrumental variable (IV) panel fixed effects estimator. This model uses local prices with strongly balanced panels over a shorter time horizon than the reduced-form model owing to random sampling and time span of the CSES.¹⁷ The two-stage approach has important strengths. First, we can match local price data with local deforestation in an uncommonly precise manner. Second, data from the CSES allow construction of local price means and standard deviations and separate tests of whether impacts from price levels or variance were more consequential. Third, the CSES provides sufficient data to conduct tests with consumer- and producer-based price series. We estimate the following equations:

2

3

which represent the first- and second-stage equations, respectively. P_{l, t} represents rice price variation in unit l at time t (mean or standard deviation), and is the predicted price variation from equation [2] . δ₁, δ, β₁, and β are coefficients to be estimated; u_{l, t} and ε_{l, j, t+1} are error terms; and all other variables are as previously defined. We seek to identify β₁, the marginal effect of rice prices on deforestation. The lag structure in the second stage uses the same logic applied to equation [1] . We benefit from having local observations of price variation. Our shift-share instrument produces plausibly exogenous variation in prices. Our preferred specifications are at the district level because this matches our reduced-form models and maximizes panel balance. We target elasticity interpretations for β₁ and use the inverse hyperbolic sine (IHS) transformation for this purpose (Bellemare and Wichman 2020).¹⁸

We are concerned primarily with endogeneity between rice prices and aggregate deforestation. Simultaneity is not a concern because rice prices are realized prior to our outcomes. Classical measurement error is possible and may lead to attenuated parameters. The potential for nonclassical measurement error with remotely sensed binary outcomes has received recent attention. Because our analysis is not at the pixel level, concerns and potential solutions raised by Alix-Garcia and Millimet (2023) and Garcia and Heilmayr (2024) are not directly applicable. Omitted variables are another concern, particularly other prices and covariates that might impact deforestation.

To address endogeneity, we apply a shift-share instrument, defined as Z_{l, t}=w_l⋅s_t, where s_t (shift) is the mean of a U.S.-based average international rice price in t, and w_l (share) represents time-invariant linear (Euclidean) distances from administrative unit l centroids to Cambodia’s deep seaport. Distances are not a traditional “share” measure, as has been common in the labor-focused shift-share literature (e.g., Goldsmith-Pinkham, Sorkin, and Swift 2020). However, distances can capture cross-sectional exposure to shocks and are intuitive for exposure to price shocks because distance-induced transaction costs are likely to mediate price shock exposure. Distances have also been used as instruments in diverse settings, including studies of immigration and working conditions (Peri 2012; Tanaka 2020).

Recent shift-share IV literature points out that one ideally has exogenous shifts and shares because this ensures that the exclusion restriction is satisfied. In our case, this means that 𝔼(w_ls_tε_{l, j, t+1})=0. Asymptotic arguments have been developed for when identification will hold if either shifts or shares, but not both, are endogenous. Goldsmith-Pinkham, Sorkin, and Swift (2020) focus on exogenous shares, and Borusyak, Hull, and Jaravel (2022) focus on exogenous shifts. We contend that both our shift and share are likely exogenous: Euclidean distances from administrative unit boundaries cannot be changed, which reduces the potential for distances to be endogenous, and Cambodia is almost certainly a price taker on international rice markets (Pandey and Humnanth 2010). In robustness tests, we show how our results change with alternative share measures, including the aforementioned rice suitability measures from FAO GAEZ, road distances to Cambodia’s deep seaport, and interactions of these variables. We also conduct randomization tests discussed by Christian and Barrett (2023) to guard against spurious time series correlations in shift-share IV panel settings.

Reduced-Form Tests of Rice Price Shock Impacts on Deforestation

In Table 1, we present coefficients representing the reduced-form estimates of the impact of rice prices on deforestation resulting from estimation of equation [1] with district-level data and district-level clustered standard errors. The top panel of Table 1 shows estimated impacts on deforestation outside of Cambodia’s ELCs; the bottom panel shows corresponding estimates for deforestation inside ELCs. The sequence of specifications showcases how point estimates change with additional controls, district fixed effects, district-specific trends, and year fixed effects. Appendix Tables C1.1 and C1.2 provide full output for the specifications in Table 1, an alternate version of Table 1 with multiway clustered standard errors (Appendix Table C1.3), a table with commune-level reduced-form results (n = 27,557; see Appendix Table C1.4), and results estimated on the subset of districts with positive ELC land area (Appendix Tables C1.5 and C1.6).¹⁹ We showcase district-level results here to be consistent with our 2SLS models.

Reduced-form coefficients on the rice price IV are proportional to the causal effect of the rice price shock on deforestation. Therefore, the sign and significance are of primary importance as magnitude is relative (see Section 6 for details). At an intuitive level, the coefficient on the rice price IV reflects the sign of the causal effect of rice price on deforestation.²⁰ When deforestation outside of ELCs is the dependent variable, the coefficient for the rice price IV is positive, stable, and statistically significant at 1%. When deforestation inside of ELCs is the dependent variable, the coefficient for the rice price IV is inconsistent in sign, magnitude, and significance. This evidence implies that the price shock caused an increase in deforestation outside of ELCs.

Additional results in Appendix C1 strengthen the evidence for these findings. First, we see that our results remain significant at the 1% level for non-ELC deforestation with multiway clustered standard errors that address arbitrary spatial correlation within provinces and arbitrary serial correlation within districts and provinces (Appendix Table C1.3).²¹ Second, we see that commune-level results are qualitatively the same with logical adjustments in magnitude since communes are smaller (Appendix Table C1.4). We also observe that the rubber price IV is positive and significant only when deforestation inside ELCs is the dependent variable. Finally, we see that our results focused on deforestation inside ELCs are not attenuated because of the large number of zeros for districts that do not have any ELCs (Appendix Tables C1.5 and C1.6). These findings show that rice price shock impacts on deforestation were concentrated outside of ELCs, where most of Cambodia’s deforestation took place and where smallholder land use is dominant.

Robustness Checks

We discuss several common robustness tests here to examine the strength of our 2SLS results: estimation with alternative price series, share measures, and standard errors; estimation leaving out one or more districts; and permutation tests that randomly reassign the endogenous variable of interest. Respective tables and figures are in Appendix C3.

An analysis of alternative share measures has been recommended to assess potential spurious correlation or share endogeneity concerns (Goldsmith-Pinkham, Sorkin, and Swift 2020; Borusyak, Hull, and Jaravel 2022; Christian and Barrett 2023). We use the same estimation procedures used to produce results in Table 2 for mean low-quality rice unit values and wet season paddy price series using alternative shares interacted with the same U.S.-based international rice price series as our shift. For comparison, we include results with our share measure using linear distances to the deep seaport and alternative shares, including baseline (1960–1990) average rice suitability (FAO/IIASA 2010), road distances (km) to Cambodia’s deep seaport, and the interaction of average rice suitability and Euclidean distances to Cambodia’s deep seaport. Appendix Tables C3.1 and C3.3 give respective results, and Appendix Tables C3.2 and C3.4 show alternative versions of this output with multiway clustered standard errors. The three columns in each table mirror the specifications captured in columns (2)–(4) in Table 2. These results are consistent with the results in Table 2. Notably, we observe more stable and statistically significant elasticity point estimates that are less sensitive to the rubber price IV when road distances to the deep seaport are used as a share and when wet season paddy prices are employed. Intuitively, the greater variation in road distances and larger number of observations in the wet season paddy series yields stronger results. Among positive and statistically significant elasticity estimates in these tables, the mean elasticity estimate is 1.9.

Bootstrap-like procedures, including estimation after leaving one (or more) districts out and permutation tests, have been suggested in the shift-share and general IV literature to guard against overleveraged data or spurious time series correlation (Young 2022; Christian and Barrett 2023). Our benchmark estimations are the specification in column (3) of Table 2 for deforestation outside of ELCs. For tests leaving one (or more) districts out, we calculate kernel densities and mean statistics from distributions of statistics of interest that result when one district is dropped, two random districts are dropped (n = 1,000), and four random districts are dropped (n = 1,000). We study second-stage coefficients reflecting the rice price elasticity of deforestation, the respective p-value of the second-stage coefficient, and the first-stage F-statistics on our shift-share instrument. Resulting distributions are centered on our observed statistics, though with more dispersion due to losses in degrees of freedom from dropped districts. These tests show that our data are not overleveraged or a function of spurious correlation (see Appendix Figure C3.1).

For permutation tests, we randomly reassign realizations of the endogenous variable (n = 1,000) and estimate our benchmark model (i.e., Table 2, column (3)). Random reassignment should break a genuine relationship between the instrument and endogenous variable. We conduct randomization without replacement within year, between year t and t + 1, and across all years. Kernel densities are constructed along with mean statistics from each distribution to compare with observed statistics. We study second-stage coefficients reflecting the rice price elasticity of deforestation, respective t-statistics for the second-stage coefficient, first-stage F-statistics on our shift-share instrument, t-statistics on the instrument in the first stage, and DWH test statistics. The results further reinforce our findings. High correlation in prices in cross section produces densities for randomization within year that are somewhat close to observed statistics but not uniformly so. As randomization expands across time, deviation from observed statistics increases (see Appendix Figure C3.2).

Econometric Models: Household-Level Mechanisms

In Section 6, we present various results pointing to statistically significant impacts on deforestation from the rice price shock in Cambodia. Our findings indicate that respective impacts were concentrated in areas outside of ELCs, where smallholder land use is dominant. However, these aggregate findings do not provide a clear understanding of underlying mechanisms. We address this limitation by studying channels suggested by our theoretical framework in Section 3 using contemporaneous household data. We begin our household-level analysis with reduced-form estimation studying relationships between land allocation, local deforestation, and the rice price shock. Proper interpretation requires us to test the separation hypothesis, which we accomplish by adapting the test from Benjamin (1992) focused on household labor endowment. In our nonseparable model, a staple production constraint in part induces nonseparability; therefore, we also test for interactive effects between a rice production constraint and the price shock. A clear rice production constraint in Cambodia is irrigation access. Our reduced-form equation takes the form:

4

where A_{i, c, s, l, t} is a land allocation share for household i, crop c, season s, location l, in year t; Z_{l, t} is a commune-level shift-share instrument (for added precision); (Z_{l, t}*I_{i, l, t}) is an interaction term between the price shock (i.e., instrument Z), and I_{i, l, t}, a dummy variable equal to one if a household has no plots with irrigated rice; is commune-level non-ELC and ELC deforestation in t − 2; is a vector of household covariates selected to avoid “bad controls” when placed in regressions with recall-based land allocation measures (Angrist and Pischke 2009);²⁵ captures commune-level seasonal weather controls; ℒ_ℓ and 𝒯_t capture location and time fixed effects; η_{i, c, s, l, t} is an error term; and γ₁, γ₂, γ₃, γ₄, and ω are coefficients to be estimated. We study allocations across the dry and wet seasons for rice, cash crops (see Section 5), and summations of these shares within and across seasons to measure land allocation intensity (i.e., in analogous fashion to land allocation in our theoretical framework).

The reduced-form effect of the rice price shock is captured in γ₁ and in γ₂, which captures the interactive effect between the price shock and the aforementioned irrigation-based rice production constraint. The relationship between household land use and local deforestation in t − 2 is captured by γ₃, which accounts for added post-deforestation preparation time before land can be put into agriculture. We do not use a 2SLS model because of the recall-based nature of CSES production data. Specifically, the realization of agricultural production data places it in the past to realizations of household-level rice price data. This renders household-level prices used to construct local price series for equations [2] and [3] inappropriate regressors in equation [4].²⁶

Our main test of the separation hypothesis is based on elements of γ₄ reflecting household labor endowment, specifically household size, and male share of household above 15 years old. Our test adapts the separation test from Benjamin (1992). Applications of this test commonly regress measures of household labor endowment on household labor input decisions; however, the principle underlying the test is quite general in terms of the hypothesized relationship between labor markets and input decisions (Dillon and Barrett 2017; Dillon, Brummund, and Mwabu 2019). We therefore exploit the fact that land allocation behavior is an outcome that is also a production input with important relationships to labor. Hence, under separation, household labor endowment should have no relationship to land allocation decisions.²⁷

Note that outcomes A_{i, c, s, l, t} in equation [4] reflect a fractional data-generating process. By construction, A_{i, c, s, l, t}∈[0,1] for rice and cash crops, and mass at both boundaries is possible: one can opt out of planting a crop (share of zero) or plant all land available to a crop (share of one). An exception is sums of shares across and within seasons, which can exceed one. Thus, for several household land allocation outcomes, equation [4] is a linear approximation to a nonlinear fractional data-generating process that can potentially worsen with significant mass at the boundaries (Ramalho, Ramalho, and Murteira 2011). Appendix Figure D1 shows pooled histograms indicating presence of mass at the boundaries. There are several options for estimation, but some have significant problems, especially with repeated cross-sections.²⁸ We argue that the reduced-form model in equation [4] is our best alternative, though it comes with limitations. The Monte Carlo analysis in Ramalho, Ramalho, and Murteira (2011) indicates that a linear model can correctly estimate signs, but magnitudes of partial effects are more difficult to estimate accurately. Therefore, with equation [4], we seek to estimate signs of the marginal effects of interest, and we view magnitudes with caution.

Finally, we study the distribution of a well-established measure of welfare impacts from a price change developed by Deaton (1989), the NBR. Headey and Martin (2016) point out that it is challenging to measure the NBR precisely, and it is important to note that it is a short-run welfare measure (Barrett 2008). Even so, the NBR offers a unique opportunity to glean information about how welfare impacts of the rice price shock may relate to land use behavior. We use the following from Deaton (1989):

5

where NBR_{i, m, t} is the NBR for household i, in month m, and year t. By construction, the NBR is bounded between −1 and 1. Negative (positive) values indicate net-buyer (net-seller) status and net-negative (net-positive) welfare impacts. We focus our analysis on agricultural households. A limitation we face is that monthly rice income cannot be separated from monthly agricultural income; therefore, our measurements understate net buyers because it is certain that total monthly agricultural income is greater or equal to total monthly rice income. To mitigate this issue, we set monthly agricultural income to zero for households who report not growing rice in the prior agricultural year.

The focus of our NBR analysis is on distributions, particularly on how distributions vary conditional on having plots with irrigated rice.²⁹ This focus relates to our theoretical study of nonseparable households and our study of γ₂ in equation [4] since production constraints may induce nonseparability and a higher likelihood of being a rice net buyer. Under nonseparability, net-buyer status is a prominent condition that partly produces positive expansion in nonstaple crops and total land allocation intensity in response to a staple price shock (see proposition 2).

Household Land Allocation: Separability, Local Deforestation and Irrigation Access, and the Rice Price Shock

Here we present results for our study of household-level mechanisms suggested by our theoretical framework that might account for our aggregate deforestation findings. Table 3 presents a selection of results for tests of the separation hypothesis. Table 4 presents a selection of results testing for a relationship between land allocation, recent local deforestation, and lack of access to plots that can be irrigated to produce rice. Table 5 shows results for tests of a relationship between land allocation and the rice price shock in the reduced form, both conditional and unconditional on not having plots that can be irrigated to produce rice. Full results for each of these sets of tests, for each land allocation measure, are in Appendix Tables E1–E7. Recall that we are focused on the sign and statistical significance of coefficients of interest owing to the difficulties inherent with fractional data and repeated cross-sections (see earlier model discussion for equation [4] ). In Tables 3–5, the sample size in columns (3) and (4) is smaller because we drop observations where communes were observed once so that commune fixed effects can be applied.³⁰

In Table 3, we highlight estimated coefficients and statistical significance for male share of household above 15 years old, where the dependent variables are total wet season allocation, total dry season allocation, and the sum of total wet and dry season allocations. Appendix E shows similar results for other labor endowment measures and dependent variables. Overall, we find statistically significant relationships between labor endowment measures and land allocation and thus reject separation between consumption and production. The implication is that our nonseparable model is consistent with the data. According to our theoretical framework, a household’s net position in rice (net buyer vs. net seller) may have influenced household land use responses to the rice price shock. This finding highlights the potential importance of rice production constraints and the relevance of studying the NBR.

Table 4 shows estimated coefficients and statistical significance for commune-level deforestation originating outside of ELCs in t − 2 and a dummy variable indicating that a household does not have plots that can be irrigated to produce rice. The dependent variables are wet season cash crop allocation, dry season cash crop allocation, and the sum of total wet and dry season allocations. The corresponding results for all land allocation measures that we study, including results for deforestation from inside ELCs in t − 2, are shown in Appendix E.

Results in Table 4 show evidence for positive and statistically significant relationships between recent deforestation outside of ELCs and lack of access to irrigation to produce rice. The interpretation for deforestation results is an association that is consistent with our aggregate deforestation results: expansion in agricultural production has a positive and statistically significant relationship with recent local deforestation outside of ELCs. Alternative lag structures with deforestation (e.g., t − 1) show similar results. Notably, as is apparent in Appendix E, the positive association we find with deforestation outside of ELCs is most apparent with cash crop allocations and the sum of total land use allocations across seasons. Conversely, we find evidence of mostly negative relationships between land allocation measures and deforestation originating inside of ELCs.

The strong positive relationships shown between lack of access to irrigation to produce rice and agricultural expansion, particularly for cash crops, is notable and intuitive. For example, if a household is maximized in wet season rice allocation, and supplementary irrigation is not possible, increased cash crop allocation might be a next best land use alternative, particularly amid a price shock to rice. In Appendix E, we can see further intuitive relationships with this rice production constraint: a negative and statistically significant relationship with dry season rice allocation and a positive but insignificant relationship with wet season rice. The latter relationship is consistent with households preferentially maximizing rice in the wet season, in spite of any constraints, as suggested by summary data shown in Figure 3.

Table 5 presents results for the same dependent variables in Table 4 (wet and dry season cash crops and the sum of total wet and dry season allocations). All corresponding results are again in Appendix E. Here the focus is on coefficients for the interaction between our rice shift-share instrument and our dummy variable for not having plots to irrigate rice and coefficients for the shift-share instrument itself.

There are intuitive and counterintuitive elements to our findings regarding reduced-form rice price shock impacts. Counterintuitively, in Table 5 and in Appendix E, our findings for the coefficient on the shift-share instrument indicate negative relationships, even with wet season rice, though the sign and statistical significance are somewhat inconsistent across land use measures. There are several possible reasons for this. One perspective we find compelling is that this reflects nonseparability. For example, since rice consumption is omitted here, and it is relevant to rice production under nonseparability, related omitted factors may induce bias on the instrument (see discussion of counterintuitive reduced-form signs in Kennedy 2005 and An, Williams, and Zhao 2016). The more intuitive findings, considering the preceding results, are the coefficients in Table 5 for the interaction between the rice price shift-share instrument and the dummy for not having plots to irrigate rice. Here we see that conditional on not being able to produce irrigated rice, the reduced-form effect of the rice price shock is positive for cash crops and total allocation and negative for rice (see Appendix E).

Even with the limitations of these findings, a consistent narrative is evident. First, we find that the dominant type of deforestation in our study period (that originating outside of ELCs) is associated with increased household agricultural expansion, particularly for cash crops. This is consistent with the mechanism suggested by our theoretical framework and intuitive since smallholder agriculture is dominant outside of ELCs. Second, although we do not uncover a definitive smoking gun for the rice price shock in the conventional sense at the household level (e.g., positive staple supply expansion), we do find intuitive evidence for expansion into cash crops conditional on facing an irrigation-based rice production constraint. Although unconventional, expansion into cash crops amid a rice price shock is not difficult to conceptualize if one is already constrained in being able to increase staple land allocation. As we reject separability and also model nonseparability partly with a staple production constraint, this is consistent with our theoretical framework. To shed further light on these household-level findings we turn to the NBR.

Welfare Impacts from the Price Shock

According to our theoretical framework, nonseparability implies that staple consumption plays a role in the land use response to a staple food price shock. Analyzing the NBR can therefore shed light on mechanisms for land use response because it is a short-run welfare measure that also reflects the relative mass of rice net buyers versus net sellers. Figure 5 shows monthly distributions of the NBR for agricultural households between 2007 and 2011, denoted by season and conditional on not having irrigated rice plots.³¹ Negative (positive) values of the NBR correspond to net buyers (net sellers) and net-negative (net-positive) welfare impacts from a price change. Nonparametric densities that pool monthly observations are in Appendix E.

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Figure 5

Monthly Distribution of Approximate Net-Benefit Ratios for Agricultural Households: top, Conditional on Not Having Plots with Irrigated Rice; bottom, Conditional on Having Plots with Irrigated Rice

Sources: Author’s calculations; CSES consumption, income, and production module data from 2007–2011.

Note: Negative (positive) values denote net buyers (net sellers); the y-axis is set within the [−1, 1] theoretical support of the net-benefit ratio to better render the observed variation.

Several important findings are apparent in Figure 5. First, we see that the predominance of mass between net-buyer and net-seller status is dynamic. This can be seen in both the tails and the average trend lines, which shows evidence of net-seller status rising on average in the dry season and net-buyer status increasing in the wet season. This conforms with the observation that the lean season coincides with the wet season. Because we do not have a clear measure of monthly rice income, our measure understates the prevalence of net buyers. Therefore, the true distribution will be shifted toward the negative side of the y-axis. With this perspective in mind, our analysis suggests that net buyers were likely predominant in our period of study. This finding is consistent with research by Sophal (2011). This implies net-negative welfare impacts from the rice price shock but also heterogeneous land use choice regimes.

Second, we see clear evidence that households are more likely to be net buyers when they do not have irrigated rice plots. This is notable because it lends further depth and consistency to the findings in Table 5, which show that conditional on not having irrigated rice plots (an effective rice production constraint), the rice price shock caused increases in cash crop production and total allocation, rather than expansions in rice production. Figure 5 provides evidence that households facing production constraints are more likely to be net buyers. Together, these findings are consistent with positive cross-price impacts predicted by our nonseparable model when the household is a net buyer in the staple and there are complementarities between staple and nonstaple land use (see Section 3; proposition 2).

Our study of land allocation response and the NBR offers a compelling perspective. The picture that emerges is not one of a predominant scenario where profit-maximizing net sellers in rice were deforesting in pursuit of profit from the large increase in rice prices, although such actors may well have been present. Rather, most deforestation in this setting seems to be associated with agricultural expansion—carried out by a predominantly nonseparable, staple net-buyer population that faces staple production constraints—as an adaptation to negative welfare impacts from the rice price shock.