Because we do not have more objective measures that could be used to correct the data, our results should only be considered suggestive. Second, the pseudo-panel approach based on cohort averages should reduce the influence of classical measurement error, and may even help diminish some of the non-classical measurement error. In the case of land measurement, for example, the evidence from Africa suggests that the largest errors happen for the smallest of farms , with the sign of the bias flipping from positive to negative somewhere between 0.75 ha and 2.0 ha . Since our smallest farm size class is 0-5 ha, over- and under-estimation in this group may partially cancel. Third, while the literature suggests that the largest errors occur on the smallest of farms, it has little to say about measurement error for the larger farms included in our study. In the case of measurement error in output, for example, ninety five percent of parcels in the Ethiopian sample used by Desiere and Jolliffe were smaller than 1 ha, and mean plot size in the Ugandan sample used by Gourlay et al. is under 0.18 ha. What happens to measurement error in area and output as we move from farms of 10 to 100 to 1000 ha is an open question, and the IR in land productivity continues out this far in our data. Fourth, any sources of measurement error that are correlated with size, but constant over time, dutch bucket for tomatoes would not explain how the farm size – productivity gradient changes over time.

This is an important aspect of our empirical analysis. Finally, Abay et al. provide a unifying framework for thinking about data with multiple sources of non-classical measurement error. In this case, they show that the “signs and magnitude of resulting biases in estimates of a key parameter are analytically ambiguous.” Thus, any attempt to correct for some, but not all, sources of measurement error could “prove inferior to a `second best’ approach that uses multiple variables measured with error” . In light of this discussion, we remain agnostic on measurement error and make no attempt to correct for it, reiterating that our results are only suggestive. By focusing on a regional analysis we are able to examine the relationship between farm size and productivity in light of each region’s characteristics and stage of development. The five macro-regions of Brazil differ in both the type of predominant agricultural activities and the degree of modernization. They include the Amazon rainforest in the North, a large semi-arid region in the Northeast, a highly mechanized and commercial agriculture in the Southeast, a predominance of family farms in the South, and the Cerrado of the Center-West where grains have rapidly expanded and agriculture has modernized in recent decades. We restrict attention to the North, CenterWest, and Southeast, three macro-regions that capture sufficient regional variation in Brazilian agriculture to illustrate our argument. 16 Descriptive statistics for output and input intensities for these regions in 2006 are shown in Table A.2.2 of the appendix.

Differences in input intensities reflect the heterogeneity in agricultural production across regions. The more traditional agricultural region in the North relies more heavily on family labor, whereas the mechanized Southeast and Center-West use capital and purchased inputs more intensively. We also observe that the intensities of capital and labor decline with farm size, whereas the intensity of purchased inputs declines through the first three or four size classes, and then inverts. This was not the case in 1985. The use of purchased inputs on farms in the 500- ha class has grown more rapidly than in all the other size classes during this period. Figure 1.3 shows the unconditional relationship between land productivity and farm size class for the three regions under study. Despite considerable regional heterogeneity in their agricultural activities and agrarian structures, each region mirrors the country as a whole in displaying a strong inverse relationship between land productivity and farm size. There is no evidence of it disappearing during this period. The estimated coefficients from region-specific estimates of equation are shown in Table A.3.1 of the appendix, which generate the TFP estimates presented in Figures 1.4 through 1.6. Recall from Section 1.2 that these relationships potentially include the influence of deviations from constant returns to scale.17 In the North , we estimate an inverse relationship between farm size and TFP. It is not, however, a linear relationship, but rather an emerging U-shaped inverse relationship with farms over 500 ha becoming more productive than medium-sized farms. The significance tests in Table 1.1 confirm this, showing that while the productivity of farms between 20 ha and500 ha is statistically less than the smallest farms in all periods, the largest farms are not statistically different from the smallest farms after the first period. Thus, while a strong negative relationship would be found in this region when using land productivity, a Ushaped relationship begins to emerge when TFP is used and linearity is not imposed.

The Center-West demonstrates a more dynamic pattern. Table 1.1 shows that the farm size – TFP relationship in the Center-West in 1985 looked very similar to the inverse relationship in the North. However, by 2006 the inverse relationship had disappeared in the Center-West, with the TFP of all farm sizes being statistically indistinguishable from that of the smallest farms. The point estimates show that the largest farms in the Center-West were 46% less productive than the smallest farms in 1985, yet by 2006 they were 8% more productive, albeit statistically insignificantly so. Once again, a U-shape begins to emerge, driven by rapid growth of the productivity of larger farms. Increased use of purchased inputs played an important role in this transformation, as they grew roughly three to four times as fast on farms over 500 ha than on farms in the middle three size classes. This is the clearest case of a strong inverse relationship becoming reversed over the 21 year period. Using land productivity to measure the farm size – productivity relationship in a rapidly modernizing agricultural region such as the Center-West would completely miss this transformation. The Southeast, in contrast, shows a positive non-linear relationship between farm size and TFP. The relationship was statistically flat in 1985, although the point estimates show that even in 1985 the largest farms were 25% more productive than the smallest. Rapidly rising TFP at the upper end of the farm size distribution makes the relationship more positive over time, and by 2006 the largest farms were 48% more productive than the smallest, and statistically so. Once again, the relationship appears non-linear. This contrasts sharply with the persistent IR found in the Southeast when using land productivity as a measure. In comparison to much of the development literature surrounding the IR, the Brazilian data used here represent a very heterogeneous group of farms and span a much greater range of farm sizes. A more accurate comparison group to the international literature might be farms less than 100 ha, blueberry grow pot which indeed make up approximately 90% of all Brazilian farms. Even when restricting our analysis to this subset of farms, the use of land productivity would still show a marked inverse relationship while the use of TFP would reveal a negative relationship that has disappeared in the more modernizing regions. Perhaps more importantly, inclusion of the largest farm size class reveals that these farms have notably higher productivity in the more modern regions, and it is only when TFP is used that this becomes apparent. These are commercial farms that are unlikely to be included in most household surveys in developing countries, but they are present in the Agricultural Census data used here. The regional analysis of Brazil provides insight into how the farm size – productivity relationship that was discussed in Section 1.2 can evolve with the modernization of agriculture. In the least developed regions of the country, the North and Northeast, the inverse relationship persists through the 100-500 ha size class regardless of the productivity measure used, and it is only with TFP that an emerging U-shape begins to appear. In the Center-West, where farms over 500 ha operated 80% of the land and accounted for around 75% of output in 2006, modernization of agriculture in this period converted an initially strong negative TFP relationship into one that was statistically flat by the end of the period. And in the Southeast, the most modern region of the country, the use of TFP reveals that the largest farms had higher productivity than all other size classes as early as 1985, but that this only became statistically significant in 2006.

While it is beyond the scope of this paper to explain the causes of these changes, we note that conditions and from Section 1.2 provide insight. The use of modern inputs and technology appears to have successfully inverted the size – TFP relationship. Future research should seek to address whether these changes are due to increasing returns to scale above a certain size, diminishing importance of market failures, measurement error or other factors.We have sought to address an important weakness of the development economics literature on the inverse relationship between farm size and productivity. We argued that a variety of productivity measures are used when estimating this relationship, that the choice of measure matters for its identification and interpretation, and that total factor productivity is, in most cases, the preferred and most informative measure for policy. Furthermore, we argued that a commonly used measure – land productivity – is problematic and potentially misleading when used in modernizing agricultural contexts or when assessing a full range of farm sizes. Where comprehensive measures of productivity are more relevant and of interest, a focus on land productivity introduces omitted variable bias by not controlling for the intensity with which other inputs are used. Our conceptual discussion provides a framework for assessing the implications of the choice of productivity measure. Theoretically, it is clear that an inverse relationship between land productivity and farm size is neither necessary nor sufficient for an inverse relationship to exist between farm size and TFP. How much does this critique matter? We conduct an empirical analysis at the regional level in Brazil using a pseudo-panel from 1985 to 2006 to contrast the land productivity – farm size relationship with the TFP – farm size relationship. While the analysis is only suggestive due to potential bias stemming from non-classical measurement error or endogeneity of inputs, the results indicate that the choice of productivity measure matters greatly. As in many developing country contexts, there exists an inverse relationship between land productivity and farm size for Brazil, and within each of its macro-regions in every period. In contrast, the TFP and farm size relationship varies across time and space. The regional analysis of the TFP and farm size relationship shows 1) land productivity is not always an appropriate proxy for TFP; 2) the relationship is dynamic, changing with agricultural modernization; 3) the relationship is non-linear, often characterized by a U-shape; and 4) the very largest farms, such as those with more than 500 ha, are important to consider when assessing any relationship between farm size and productivity. From a policy perspective, our findings have important implications for the debate about the future of small farms in developing countries. When using TFP, we see that superior productivity of small farms in traditional agricultural contexts is fully consistent with emergent productivity advantages for larger commercial farms in modernizing agricultural sectors. As economies develop, superior productivity may not continue to provide a valid argument for the importance and future of small farms, as we expect larger farms to play a more important role in driving national-level agricultural productivity growth. As such, it is increasingly unlikely that redistributive land reform could positively impact both equity and efficiency. However, this does not imply that small farms will, nor should, disappear. We expect them to remain important for generating livelihoods for rural households, providing food security, and contributing to the development of rural economies. Total factor productivity gains among small farmers will also continue to be essential for poverty alleviation.