Policy discussions of the future of small farms, for example, emphasize the role of small farms in agricultural development in part because of their superior efficiency . This argument leans heavily on the inverse farm size – productivity relationship, but requires that small farms be more efficient with their use of all resources and not just land. Whereas a farm size – land productivity relationship does not provide clarity on this issue, a farm size – total factor productivity relationship does. In this light, we argue that the inverse relationship literature needs to shift its focus from land productivity to total factor productivity. In fact, empirical studies assessing the productivity – farm size relationship in the developed world, such as Garcia et al. , Alvarez and Arias , and Rasmussen , almost exclusively use measures of technical efficiency or total factor productivity. Similarly, the literature estimating national level agricultural productivity is clear in its use of total factor productivity as a preferred measure . We illustrate the importance of productivity measures with new empirical evidence on the farm size – productivity relationship across regions of Brazil from 1985 to 2006 . Our evidence is only suggestive because we are unable to correct for potential issues of measurement error in farm size, output, and inputs that have been identified in recent literature. However, this period in Brazil provides an excellent case study because it includes regions with relatively advanced agricultural sectors, those characterized by more traditional agricultural production, and others experiencing rapid agricultural transformation, allowing us to assess the farm size – productivity relationship and its dynamics at different stages of agricultural development. Using a pseudo-panel of farms aggregated at the municipality by farm size level, square black flower bucket we show that estimating the farm size – productivity relationship using land productivity is potentially misleading.

While we always identify an inverse relationship using land productivity, we find disparate results when using total factor productivity. In the modern agricultural regions of Brazil, we find a direct relationship between farm size and total factor productivity, and in the rapidly transforming region of the Center-West we identify dynamics that suggest the inverse relationship is disappearing over time. The analysis highlights that the relationship between total factor productivity and farm size has evolved with modernization, shedding some light on the issues raised by Mill over 150 years ago. The remainder of this paper is organized as follows. In Section 2 we seek to clarify the common measures, their relationships, and their advantages and limitations in empirical work. Section 3 presents the empirical exercise, generating new evidence on the relationship between size and productivity in several macro regions of Brazil. In Section 4 we summarize and conclude with policy implications.Farm size may be related to a broad range of economic outcomes, such as employment, poverty, inequality, food security, efficiency and growth. While these are important issues connected to the role of farm size in development, here, as with most of the literature on the inverse relationship , we focus specifically on the concept of productivity. The following discussion seeks to clarify the relationships between the various productivity measures most commonly used in the literature, allowing us to draw conclusions on the impact that choice of measure may have on finding an IR and the potential implications for policy.The relationship captured by is unconditional in the sense that it is the simple bivariate relationship between land productivity and farm size. Using land productivity as a measure is inherently limited—as would be any partial measure of productivity—whenever there is more than one factor of production.

If use of other factors vary systematically with farm size, the IR between land productivity and farm size may simply reflect more input intensive practices of small farms. Higher land productivity may reflect overuse of fertilizer, for example, which would not necessarily reflect any underlying productivity advantage of small farms. In such situations, estimates of the farm size – land productivity relationship introduces omitted variable bias into estimates of the underlying farm size – productivity relationship. From this perspective, a focus on the relationship between land productivity and the size of farms may be misplaced. Similarly, analysis using different partial productivity measures may result in conflicting policy recommendations. Indeed, Sen’s seminal contribution revealed precisely this type of systematic relationship between the intensity of labor use and farm size, leading to his formal exposition of the dual labor market hypothesis . Figure 1.2 illustrates the problem in the case of Brazil. While there is an inverse relationship between land productivity and farm size, there is a direct relationship between labor productivity and size. Analysis of the farm size and productivity relationship using labor productivity suggests that larger farms are more productive than are their smaller counterparts. Policy recommendations from the two partial measures of productivity would differ, underscoring the need for a comprehensive measure of productivity when identifying any relationship with farm size.We now provide an example using data on Brazilian agriculture. The intention here is not to explain the relationship between farm size and productivity by controlling for its potential determinants. Rather, we seek to use a regional analysis within Brazil to highlight how the choice of measure influences the observed relationship and how these patterns can change across stages of agricultural development. Our evidence is only suggestive because we are unable to correct for the measurement issues in farm size, outputs, and inputs that recent literature has focused on. We discuss this further below. The results provide an important counterpoint to much of the literature that has focused on countries in Africa and Asia where the overwhelming majority of farms have less than 2 hectares . Mean and median farm size in Brazil, in contrast, were around 65 and 10 hectares in 2006. The data come from the 1985, 1995/1996, and 2006 rounds of the Brazilian agricultural census. For confidentiality reasons, we constructed a pseudo-panel in which all farms in the census are aggregated into five farm size classes within each municipality of Brazil.9 Aggregation requires that we assume homogeneity within each observation . We call these “representative-farms,” as they reflect the average behavior of a given farm size in a given municipality. The pseudo-panel approach has been used recently to study agricultural productivity growth by Key and Rada et al. . Antmann and McKenzie demonstrate that, in the context of mobility studies, pseudo-panels can be used to consistently estimate parameters of interest. The averaging within cells in each period reduces the influence of individual-level measurement error, and the fact that it is not a true panel of farms makes it less vulnerable to non-random attrition. They show the approach is also robust to some forms of non-classical measurement error. We begin with 47,365 representative farms for all of Brazil across the three survey years. Due to concern about the comparability of a small number of extremely large observations, square black flower bucket wholesale we remove all representative farms in the Northeast and South over 4,000 ha and all of those over 5,000 ha in the North, Southeast, and Center-West. We then identify land productivity outliers taking into account the IR shown in Figure 1.1 and potential non-linearities. Thus, rather than trim the tails of the unconditional land productivity distribution, we use a quadratic specification to regress land productivity on farm size with municipal fixed effects and survey year dummy variables.

From this regression we identify and remove outliers, defined as all representative farms with residuals greater than four standard deviations from their size specific predicted values. Together, the data cleaning exercises remove 1.8% of the initial sample. The Census data were gathered by the Brazilian Institute of Geography and Statistics through end of season in-person farmer interviews based on recall. Output is measured as the real value of total agricultural production, deflated to 2006 with a price index developed from the data in Gasques et al. . Farm size is measured in hectares , and unlike in many African and Asian countries the overwhelming majority of farms operate a single plot. Additional factors of production used in the production function are family labor, purchased inputs including hired labor, and an index of capital. The number of male, female, and child family members working on each farm are used to develop a family labor index measured in adult male equivalents. The index assigns weights of 1.0 to men, 0.75 to women and 0.5 to children under 14. In 2006 around two thirds of family labor was provided by men, and over 90% of working family members were 14 years or older. The real value of purchased inputs, including expenditure on fertilizer, seeds, hired labor, fuel, energy, soil amendments, and other items, are deflated with the same price index used for output. A proxy for the total capital stock is calculated as a quantity index comprised of machine, animal, and tree capital stock sub-indices following Moreira et al. and Butzer et al. . The machine capital stock index values tractors of five horsepower classes, trucks, harvesters and other agricultural equipment using a constant set of sale prices drawn from the Instituto de Economia Agrícola in São Paulo. The stock of animal capital is measured in cattle equivalents of the nine most important animal stocks and aggregated with a set of time invariant relative prices . The stock of tree capital is measured as the present discounted value of expected future profits for thirteen different tree crops, using region-specific estimates of expected profits. The subindices are aggregated using region-specific weights estimated by regressing output on the three capital stock sub-indices in the base year 1985.13 Additionally, we control for unexpected shocks in rainfall and temperature to each municipality in each survey year utilizing data described in Wilmott and Matsuura . These quarterly shocks are measured as standardized deviations from 25-year moving averages ending in the year prior to each Census. The data are transformed into categorical variables capturing extremely low, below average, average, above average, and extremely high values relative to the historical municipal average. Weather shocks between -1 and 1 standard deviations are treated as normal weather years and are the reference category, with extremely high and extremely low values occurring at more than ±1.645 standard deviations. The data used are drawn from a nation-wide decennial census and are potentially subject to multiple sources of measurement error. The literature on measurement error and its implications for the IR has grown rapidly in recent years. Of greatest concern are non-classical types of measurement error that are correlated with farm size. Carletto et al. , Carletto et al. , Abay et al. and Dillon et al. examine measurement error in self-reported farm size relative to more accurate approaches to measuring land . They demonstrate clearly that farmers report area with error, that this error varies systematically with farm size, and that whereas small farms tend to overestimate farm size, large farms tend to underestimate their size. The implications for the IR literature are mixed, as Carletto et al. and Abay et al. find that the IR becomes stronger when measurement error in farm size is the sole correction made, but Carletto et al. and Dillon et al. both find that correcting for such measurement error partially mitigates the IR in some of their data but has no statistically significant impact elsewhere. Similarly, several recent papers have explored the implications of non-classical measurement error in output. Desiere and Jolliffe , Gourlay et al. , and Lobell et al. show non-classical measurement error in self-reported output when compared to “crop cuts” as the gold standard measure. Importantly, small farms overreport output more so than larger farms in their data. Conditional on GPS land measurement, the IR disappears in these papers when they utilize the more objective measure of output. Abay et al. explore measurement error in both farm size and output, and concur that in their data the IR disappears when land is measured objectively and then crop cuts are used to correct for measurement error in production. However, they caution that the IR strengthens when land is self-reported and measurement error in output alone is corrected. Lastly, measurement error in the use of inputs such as labor is potentially an issue. Relative to weekly surveys conducted in-person or by phone, end of season surveys of labor usage can contain substantial errors .