The farms in the sample that monocrop do so on the vast majority of their farm, not just on specific plots. In each survey year over half of the plots being monocropped are growing maize, with approximately 10% each growing beans and coffee. As shown in Table B.3.1 of Appendix B.3, there is no discernible difference in monocropping across farm sizes, although ejido farms are marginally more likely to employ monocropping than non-ejido farms. To account for potentially persistent negative productivity shocks we generate a dummy variables for whether the household suffered crop or livestock loss in either of the previous two years. The MxFLS asks households about their participation in a variety of government programs. The two most important programs are Progresa/Oportunidades and Procampo. Procampo is an income transfer program designed to support agricultural producers of staple crops. Progresa, later renamed Oportunidades, is a conditional cash transfer program designed to combat poverty and incentivize investments in children. Data limitations do not allow us complete information on participation in Progresa14 so we focus exclusively on participation in Procampo. Table B.3.1 in Appendix B.3 shows the share of farms participating in Procampo by year and farm size. With the exception of the largest farms, participation increases with farm size. In addition, nft system we consider participation in Alianza, a government-run program designed to aid farmers’ transition into crops for export.
While less than 3% of the sample participated in this program in any survey round, we consider participation in this program for its potentially important impact on farmers. Having access to credit is an important determinant of agricultural productivity, and the existence of credit constraints and differential access to credit is one theoretical source of a relationship between farm size and productivity. Table B.3.3 in Appendix B.3 shows “access to credit” by farm size, where a household is considered to have access if the household head knows where they can go to borrow or ask for a loan. This is a crude measure as it does not account for credit rationing and the likelihood that a household could succeed in obtaining a loan. A follow up question regarding the source of that credit allows us to identify if access is through a formal or an informal financial institution. There are no clear relationships between farm size and this measure of access to credit. We introduce an indicator variable to control for access to formal lines of credit.As with much of the literature, we begin the discussion of the farm size – productivity relationship using land productivity, measured as output per hectare. Figure 2.1 shows the non-parametric relationship between the log of farm size and the log of output per hectare in 2002, where output is measured using the Fisher quantity index. There is a clear inverse relationship between farm size and land productivity over the entire range of farm sizes, and while not shown here this relationship is strikingly consistent across the three survey waves. Land productivity falls rapidly up to approximately 1 ha, at which point the relationship levels before resuming a dramatic decline in land productivity after approximately 20 ha.As shown in chapter 1, an inverse relationship between farm size and land productivity is neither necessary nor sufficient for the existence of an inverse relationship between farm size and total factor productivity. For reference, the linear relationship between land productivity and farm size is estimated.
Farm size is inversely related to land productivity at the 1% level of significance, as shown in column 1 of Table 2.6, where we estimate the elasticity of land productivity with respect to farm size to be -0.82. We then estimate the average production function identified by equation assuming four alternate specifications of the farm size – productivity relationship that vary in their flexibility. These regressions measure output using the quantity index, weight observations by the expansion factors provided by MxFLS, use the preferred measure of the family labor index, employ community fixed effects, and cluster standard errors at the community level. Coefficients for the farm size variables, the primary variables of interest, are displayed in Table 2.6. Table 2.7 displays the coefficients for additional household controls, and technology coefficients are included as Table B.4.1 of Appendix B.4. The results indicate an inverse relationship between farm size and TFP, as shown by the negative and statistically significant coefficient on the linear Farm Size variable in model 2. In the sample, a 1% increase in farms size is associated with a 0.81% decrease in output per hectare, ceteris paribus. The farm size coefficient is slightly less negative than in model 1, but not statistically different, indicating that the relationships between farm size and land productivity and farm size and TFP are almost identical in this sample. Models 3 and 4 allow for a quadratic and cubic relationship between farm size and TFP, but the coefficients on the higher ordered terms are either not statistically significant or do not have a noticeable impact on the linear model. Model 5 captures some nonlinearity in the farm size – TFP relationship by using dummy variables for 7 farm size bins.The smallest of farms, those less than one half of a hectare, are significantly more productive than all other farms, while the largest, those greater than 20 hectares, are significantly less productive than all smaller farms.
Productivity between these two extremes, however, appears relatively stable. This closely mirrors the non-parametric relationships between farm size and land productivity shown in Figure 2.1, highlighting the need to assume a flexible functional form to fully understand the farm size – productivity relationship. The linear relationships identified in the parametric specifications 2 through 4 do not capture these subtleties. We see little change in the inverse relationship over time across all models, as none of the farm size and survey year interaction terms are statistically significant. The finding of a time invariant inverse relationship between farm size and productivity – when using both land productivity and TFP – suggests that the IR is alive and well in Mexico. There is, however, evidence for a decline in average productivity over time in this sample, as the 2009 dummy variable is negative and statistically significant. Results for the household explanatory variables, displayed in Table 2.7, show that monocropping and operating as a subsistence farm have a consistently negatively relationship with TFP. In contrast, participating in Procampo is positively associated with productivity . It is important to reiterate that these are potentially endogenous explanatory variables, hydroponic gutter and we should not interpret the coefficients as identifying causal relationships. Having more education is positively related to TFP, but with the exception of a college education these results are not consistently statistically significant at standard levels. Estimates of equation explore heterogeneity in the farm size – productivity relationship across different groups of Mexican family farms by interacting indicator variables for those groups with farm size. For simplicity, we assume the farm size – TFP relationship to be linear and time invariant. 17 Table 2.8 displays the results from interacting farm size with being located in the more commercially oriented agricultural region of Northern Mexico, participation in Procampo, practicing monocropping, operating as a subsistence farm, and whether or not the household head has any education beyond secondary school. Overall, the farm size – TFP relationship remains stable, as none of these additional interactions contribute to explaining the farm size – TFP relationship that we have identified. 18 In addition, we interact controls for farms having ejido status, various forms of property rights, and access to credit in Table 2.9. These are of special interest given the reforms of the ejido system and rural credit markets. Again, the IR is unaltered across these subgroups as these interactions are not statistically significant. The relationship between farm size and TFP is the same for ejido farms as for non-ejido farms, is the same regardless of how property rights are documented, and is the same whether or not farms have access to formal credit markets.The farm-size – TFP relationship is subjected to a series of robustness tests. We assume the farm size – TFP relationship is best captured by the linear and dummy variable models used above, as the quadratic and cubic models provide little additional information. Table 2.10 contains the results from the linear models and Table 2.11 from the dummy variable specification. First, model 1 introduces household-level fixed effects to control for timeinvariant, unobserved, household heterogeneity. The model omits time-invariant household controls, clusters standard errors at the household level, and provides a superior approach to addressing potential omitted variable biasrelative to the model with community level fixed effects. Second, model 2 tests the sensitivity of the relationship to decisions regarding the construction of the family labor index by using an alternative index of family labor described in Appendix B.2. Third, we test the impact of choice of weighting of the observations.
Whereas the core results apply the MxFLS weights designed to make the sample statistically representative of Mexican households in each survey year, model 3 shows results when we apply no weighting at all. We explore sensitivity to the use of weights because we are interested in Mexican agriculture, not rural Mexican households, and the treatment of the data reduces the sample size; therefore, it is not clear that these weights remain appropriate. Fourth, model 4 uses an alternative measure of the dependent variable – farm output. Whereas the core results uses the preferred approach of calculating a quantity index for each household , model 4 deflates the nominal value of production in each year for each household and uses the real value of output . Lastly, model 5 uses the real value of output as in model 4, but estimates the relationship over the repeated cross-sections. This final robustness check speaks to the potential for households to be selecting into or out of the unbalanced panel. Overall, these alternative treatments of the data generate qualitatively similar results to the core regressions in Table 2.6 for our primary variables of interest. This is true in terms of the coefficient signs and orders of magnitude. The exception is model 2 using the alternative index of family labor, for which the farm size coefficients are diminished in magnitude although negative and still statistically significant. The consistency across models is reassuring that treatment of the data is not driving the core results regarding the farm size – TFP relationship. In similar fashion, estimated coefficients on household explanatory variables are quite robust. The coefficients identifying farms engaged in monocropping and operating as subsistence farms remain negative and statistically significant in almost all of the robustness exercises, while the coefficients for participation in Procampo and college education remain positive and statistically significant. In results not shown here, we estimate the core models using crop production only in measuring output and the conclusions regarding the farm size – productivity relationship are robust to this dimension as well.Estimating a stochastic frontier complements analysis of the average production function by identifying productivity at the frontier and production inefficiencies. Together, these components determine average TFP identified with the average production function. In similar fashion, whereas the estimation of the average production function allows us to assess the relationship between farm size and average productivity, stochastic frontier analysis allows us to assess any relationships between farm size and productivity at the technical frontier and between farm size and technical inefficiency. The results of five specifications of the stochastic production frontier are shown in Table 2.12, with the top and bottom panels displaying the results from the frontier and variance of inefficiency equations, respectively. Model 1, the baseline model, has no additional household controls in either the frontier or the inefficiency equations . Model 2 includes dummy variables for the household head’s level of education in the frontier equation and includes a dummy variable for the household head being of indigenous ethnicity in the inefficiency equation. Model 3 alternatively assumes that education of the household head should be included as a control in the inefficiency equation but not the frontier equation. Model 4 assumes that education belongs in both equations. Model 5 includes education in the frontier equation only, adding interaction terms between farm size and the survey year dummies in both the frontier and the inefficiency equations.