The models all use community fixed effects and, for simplicity, have farm size entering linearly.The estimated coefficients from models 1 – 5 are largely consistent. They indicate a strong inverse relationship between farm size and frontier TFP and that the frontier is increasing over time, reflecting positive technical change. The coefficients on inputs are positive and stable across specifications, with family labor and purchased intermediate inputs being significant. The variance of the inefficiency term 2 is roughly double the size of the variance of the noise 2 in all models, and lambda – the ratio of the two variances – indicates that estimation of a stochastic frontier is appropriate with the MxFLS data. The models indicate an inverse relationship between farm size and productivity at the technological frontier of the same order of magnitude as the farm size-TFP relationship estimated in the preceding analysis of the average production function. The coefficients on survey year dummies in Table 2.12 are all positive and significant, u plangting gutter indicating that the frontier is increasing over time. Thus, in contrast to the results from the average production function analysis where evidence of declining average TFP over time was found, here we find evidence of positive technical change at the frontier.
The interaction between farm size and the survey year dummies in model 5 identifies a positive and significant relationship between farm size and technical change, suggesting that technical change has been biased towards larger farms and that the inverse relationship along the frontier became less steep over time.Models 1 through 4 show that, while the variance of the inefficiency distribution increased over time, there is no relationship between farm size and inefficiency. The inclusion of interactions between farm size and survey year dummy variables in model 5, however, reveals a more nuanced dynamic relationship between farm size and technical inefficiency. Larger farms were indeed more efficient than smaller farms in 2002 but inefficiency is increasing faster for larger farms. These differential changes in inefficiency across the farm size distribution have caused the farm size – inefficiency relationship to disappear in the latter waves of the MxFLS.20 Model 5 reveals that rising technical inefficiency has accompanied technological change, suggesting that the majority of farms have been unable to keep up with the TFP growth of the most productive farms. This is particularly true for larger farms, who have experienced faster growth in both frontier productivity and technical inefficiency. Having secondary or college education reduces the variance of the one-sided inefficiency term when education is included in the inefficiency equation. When education of the household head is included in the frontier specifications but not in the explanation of inefficiency , having secondary education or a college education is positively associated with higher levels of productivity among frontier producers.
When education is included in both the frontier and inefficiency equations , almost none of the education dummies are significant as the model appears to struggle to identify the separate relationships with education. In models not shown here, we estimate a stochastic frontier including the household controls from Table 2.8 as explanatory variables of the inefficiency term. In addition to educational attainment of the household head, technical inefficiency is lower among Procampo participants and higher among farms practicing monocropping. When interacted with farm size, none of the interaction terms are statistically significant, suggesting that they do not fundamentally change the relationships observed in Table 2.12. The analysis of Mexican data reveals an inverse and time-invariant relationship between farm size and TFP. Underlying this IR is a negative relationship between farm size and frontier productivity that has diminished over time and a positive relationship between farm size and technical efficiency that disappeared over the sample period. This evidence suggests that, in the wake of NAFTA era reforms, the IR is weakening for the most productive farms along the production frontier but that this change is not widespread. Although frontier productivity is increasing most rapidly for larger farms, the higher growth of inefficiency for large farms leaves the farm size – TFP relationship unchanged over the period.
The evolving relationships between farm size and frontier productivity and technical efficiency cast doubt on the ability to exploit the existing inverse relationship between farm size and TFP to generate productivity gains. These results are complemented by previous work on the farm size – productivity relationship in Brazil. Whereas the Brazilian experience suggests a dynamic farm size –TFP relationship, with an inverse relationship in traditional agriculture becoming flat and potentially positive with modernization, we observe no such dynamics in the Mexican sample. The relationship observed in the MxFLS is time invariant and persistently negative, contrasting with the emerging U-shaped relationship observed in the modernizing regions of Brazil. It is quite similar, however, to the more traditional agricultural regions in Brazil that display a persistent inverse relationship between farm size and TFP. The lack of corporate-run commercial farms is one limitation of using the MxFLS data, inhibiting analysis of the farm size-productivity relationship across all sectors of Mexican agriculture. This is especially true in light of findings that, in Brazil, larger commercial farms exhibit distinct advantages in achieving productivity growth . The frontier analysis using MxFLS data finds that technical change has been biased towards larger farms, weakening the farm size – productivity relationship at the frontier. This indicates that if inefficiency had not increased, the average inverse relationship between farm size and productivity would have weakened with modernization of the agricultural sector. This analysis indicates the potential for larger farms to be the key drivers of future productivity growth in Mexico. Policies geared towards smaller family farms may not have large returns in terms of increasing overall agricultural productivity, but they are likely very important for poverty reduction. Even if small farms generate an increasingly smaller share of agricultural output, they are likely here to stay because of their roles in generating livelihoods for rural households. Increasing their productivity remains an important component of facilitating poverty reduction in rural areas. These findings are largely consistent with earlier empirical work by Kagin et al. , who estimate both an average production function and a stochastic production frontier using a different panel of Mexican family farms. They find that both technical change and technical inefficiency increased over time and, as with the current analysis, planting gutter their fixed effects estimates show inverse relationships between farm size and both TFP and frontier productivity. Similarly, they find that smaller farms are more efficient than larger farms. In addition to highlighting the non-linearity in the farm size – TFP relationship, we provide evidence of a more nuanced and dynamic relationship between farm size and technical inefficiency and between farm size and productivity at the frontier. Larger farms have both more rapidly growing frontier productivity and technical inefficiency than their smaller counterparts, and these considerations are important for effective policy. We find evidence of declining average TFP over the period of analysis for the MxFLS sample of family farms. This appears to be driven by increasing average technical inefficiency offsetting the positive technical change and expansion of the productivity frontier. The largest farms in the sample and their relatively rapidly growing technical inefficiency are an important factor here, indicating a growing advantage for some large farms in harnessing more modern agricultural practices that has not been widespread enough to translate into sector-wide average TFP growth. Policies enabling broader inclusion in the benefits from technical change would both increase average TFP and likely further diminish the IR. Whereas policies promoting technical change are more relevant for smaller farms, policies improving technical efficiency, such as extension services, are exceptionally important for larger farms.
The growing technical inefficiency observed in Mexico indicates the potential for policies designed to promote and support the adoption and efficient use of best practices to achieve gains in agricultural productivity. The finding of declining average TFP over time is a curious result, running counter to both the body of long-run country-level analyses and the micro-level analysis of Kagin et al. over similar time periods. One important caveat is the MxFLS sample does not include corporate run commercial farms as do national-level studies such as an agricultural census. To the extent that such farms have more effectively harnessed the gains from technological change, as with larger family farms on the frontier, the potentially heightened productivity of such large farms is not included in the current evaluation of the farm size – TFP relationship in Mexican agriculture or growth in average TFP over time. This has important policy implications for the development impacts of agriculture productivity gains – if these gains are experienced primarily by corporate-run commercial farms and not by family-run farms, the potential impacts on poverty and broader rural economic development will not be fully realized. Productivity gains for smaller family farms not only reduce poverty directly but are also likely to contribute more to local development because of how they interact with the local economy. To be most effective, policy directed at spurring development and poverty reduction through agricultural productivity gains should be inclusive of smaller family farms. The lack of commercial farms does not, however, reconcile this finding with that of Kagin et al. , who find rising average TFP over a similar period in a different sample of rural households. One difference is the MxFLS includes more larger family farms, and these farms are experiencing the most rapid increase in technical inefficiency. The inclusion of more large family farms may be the source of this result. One possible explanation of the finding of declining average TFP over the first decade of the 21st century is that the productivity of Mexican family farms has declined in the wake of the NAFTA era reforms. This interpretation is consistent with claims that NAFTA era reforms were insufficient for generating positive change in Mexico’s agricultural sector, and that these reforms may have been detrimental to some segments of Mexican agriculture. Participation in Procampo and increased education are found to be positively correlated with the agricultural productivity of Mexican family farms, whereas the practices of monocropping and operating as a subsistence farm are found to be negatively correlated with TFP. We are tentative in drawing stronger conclusions about the causal impact of these variables, as they are likely endogenous. However, the frontier analysis suggests how these controls relate to productivity. Education appears to increase the efficiency with which inputs are used on family farms, and monocropping is found to be an inefficient use of inputs. In this light, farmer education – particularly in methods such as intercropping – is expected to increase technical efficiency on family farms. Procampois primarily an income support program it is unclear how participation would affect agricultural productivity. On the one hand, participation may relax income constraints and allow for adopting more productive methods because payments are distributed prior to planting season. This would suggest an emphasis on improving access to credit to improve the efficiency of Mexico’s family farms. On the other hand, the historical production requirements of Procampo participation may mean that participants are simply more experienced producers. Policies to ensure that farms have the necessary documentation could potentially help provide farms with the opportunity to keep abreast of technical change, as documented property rights are an important condition for accessing credit and thus facilitating adoption. This is especially true for ejido farms transitioning into participation with private credit and land markets. Nevertheless, we find no correlation here between agricultural TFP and property right documentation, access to credit, or ejido status, as we would have expected. Working with a sample of family farms from the Mexican Family Life Survey , we document a persistent inverse relationship between farm size and land productivity over the period 2002 to 2009. Similarly, when estimating an average production function we find a time-invariant inverse relationship between farm size andTFP, driven by the relatively high productivity of the smallest farms relative to those in the middle, and relatively low productivity of the largest farms. This is complemented by a stochastic frontier analysis, allowing for estimation of the relationship between farm size and frontier productivity and between farm size and technical inefficiency.