Testing household-specific explanations for the inverse productivity relationship.

The inverse relationship between land productivity and farm size has puzzled economists for a long time. (1) Chayanov (1926) first documented that small farms produced more output per unit of land in Russia. The same result was found in India by Sen (1962), Bardhan (1973), and Rosenzweig and Binswanger (1993); and in Brazil, Pakistan, and Malaysia by Berry and Cline (1979). This inverse relationship is intriguing as there is a large body of literature that estimates constant returns to scale for agricultural production in different countries (e.g., Hayami and Ruttan 1970; Bardhan 1973; Berry and Cline 1979; Fulginiti and Perrin 1993). Moreover, in the absence of market failures, farmers would voluntarily subdivide their lands in order to increase productivity thereby eliminating the inverse relationship.

Understanding this empirical regularity has important policy implications. Land redistribution would increase the agricultural productivity if small plots were intrinsically more productive than large pieces of land. However, this would not be effective if the puzzle was just a spurious statistical result; and alternative policies would be required if the inverse relation were caused by market failures in the labor and credit markets.

Feder (1985) noted that a single market failure is typically insufficient to generate the inverse relationship. Under constant returns to scale, the explanations for the puzzle are likely to depend on market failures that simultaneously prevent land subdivision and distort the shadow price of some productive factors. Chayanov (1926), Sen (1962), Carter (1984), and Carter and Wiebe (1990) argue that peasant households apply family labor more intensively because the opportunity cost of their time is low. If imperfections in the labor market cause the peasant's shadow price of time to differ from the market wages, and if failures in the land-rental market prevent them from managing lands owned by others, then the peasant mode of production would generate an inverse relationship.

In an alternative vein, Bardhan (1973), Feder (1985), Eswaran and Kotwal (1986), and Taslim (1989) theorize that labor is subject to increasing marginal cost of supervision, thus the optimal land-to-labor ratio is higher for large landowners. This argument generates the inverse relation when the land market is imperfect.

Moreover, as noted by Srinivasan (1972), Rosenzweig and Binswanger (1993), and Barrett (1996), risk concerns could also generate the inverse relationship. Consider, for instance, a scenario in which incomplete insurance markets hinder full hedging against agrarian risks and failures in the land market prevent small farmers from increasing the cropped area. In this case, small farmers experience food-security stress and then overapply productive inputs on their lands.

Assuncao and Ghatak (2003) state that the heterogeneity of farmers skills, coupled with credit-market imperfections in an environment with constant returns to scale and no labor-market imperfection, is another explanation for the puzzle. In equilibrium, the occupational choice is such that high-skilled peasants end up cropping small farms because they have higher opportunity costs to become wage workers. In this context, there is a range in which small farms are profitable for skilled peasants and not profitable for unskilled peasants. Farmer self-selection would then generate the inverse relationship.

In this article, we empirically assess these theoretical explanations. Our main contribution is noticing that all of these theories depend on cross-household heterogeneity, and this should equally affect the lands cropped by the same household. We analyze a very special data set--from the International Crops Research Institute for Semi-Arid Tropics (ICRISAT)--which contains households cropping multiple plots in each season. This allows us to investigate the inverse relationship across different plots cropped simultaneously by the same household.

If the inverse relationship were due to either the peasant mode of production or increasing supervision costs, then the plot-level productivity should be related to the total area managed by the household in each period, rather than the area of each particular plot. Contrary to this prediction, we show that plot productivity is inversely related to plot area and unrelated to the total area managed by the household.

Furthermore, according to all previous explanations, the inverse relationship is due to unobserved features in the household. We assess the importance of those explanations by using regression models with fixed effects to estimate the inverse relationship. We first use household fixed effects in order to account for household characteristics that are fixed over time. We then explore the fact that households harvest multiple plots in each season and introduce dummy variables for households in each period (season of the year), which accounts for unobserved household characteristics that are not fixed over time. The results show that the magnitude of the inverse relationship remains statistically unchanged. This evidence does not make the case for explanations based on cross-household heterogeneity.

Naturally, some of those explanations could be coupled with intrahousehold issues to generate the inverse relation. For instance, members with different characteristics could be allocated to supervise cropping activities in different plots of each household. We show, however, that the inverse relationship holds with the same magnitude when we restrict the analysis to plots cropped by households with one single adult member. Other intrahousehold issues--such as heterogeneous supervision costs due to geographical distance and differences in the cropping pattern across plots of each household--are also analyzed in a section of robustness checking. The results do not support those possibilities.

Our article is related to the work by Lamb (2003), which explores the ICRISAT/VLS sample at the aggregate farm level. In contrast, we explore the plot-level data to investigate the inverse relation across plots simultaneously cropped by the same household. This strategy leads us to obtain more conclusive results on the lack of importance of household-based explanations for the puzzle.

By rejecting household-based explanations for the inverse productivity relationship, our findings favor the literature that explains the puzzle by unobserved heterogeneity across plots and lands (e.g., Bhalla 1988; Bhalla and Roy 1988; Benjamin 1995; Chen, Huffman, and Rozelle 2003; Lamb 2003; and Kimhi 2006). In our view, future attempts to understand the economic content of the inverse relationship should focus on plot-specific unobservables as opposed to market failures affecting productivity at the household level. The policy implications of this research agenda depend crucially on understanding which are the specific unobservables associated with size at the plot level and which are the market forces behind this association.

Data

We use data from the longitudinal Village-Level Studies (VLS) conducted by the International Crops Research Institute for Semi-Arid Tropics (ICRISAT), in India, from 1975 to 1984. Six villages were initially selected from different agroclimatic zones, namely Aurapalle and Dokur (in the state of Andhra Pradesh); Kanzara, Kinkheda, Shirapur, and Kalman (in the state of Maharashtra). In 1980, the villages of Boriya Becharji and Rampura (in the state of Gujarat) were also included in the study. Farmers were randomly selected in each of these villages and resident investigators recorded information about all plots cultivated by them in each season of the year. Note that although the database is collected at the plot level, the household is the primary sampling unit. Farmers who moved out of the village during the period of data collection were randomly replaced. Further details about the data collection method can be found in Jodha, Asokan, and Ryan (1977) and Singh, Binswanger, and Jodha (1985).

The main data source is the ICRISAT's PS files, which contain plot-level information on cropping activities such as output value, cropped area, value of different nonlabor and labor inputs, estimated per acre value of the plot, irrigation, soil type, cropping pattern, village, year, and season. An auxiliary schedule, the C files, which contain information on household characteristic, is also used to measure the number of adult members in each household.

The ownership status is varied among the surveyed plots. We focus on plots cropped by their owners in order to avoid concerns about incentive problems sometimes associated with farms managed by tenants. The qualitative results, however, remain unchanged when we include these plots in the analysis. (2)

Farmers typically manage many different plots simultaneously. On average, each household harvests 5.6 plots per period. In order to study the importance of monitoring activities, we construct a variable describing the total area managed by the household in that period--i.e., for each plot, this variable sums the area of all plots cropped under the responsibility of the same household in that particular year and season. When constructing this variable, we include the plots rented by each household because, even if farmers faced incentive problems in rented farms, they would still expend part of their time with these plots. All results remain identical if we exclude the rented area from this variable.