female headship, and age composition, not having affected use of labor for crop production in the preharvest stage and overall (columns 1 and 2). The relationship disappears for the second period (columns 3 and 4), pointing toward better functioning of agricultural labor markets. To formally check whether labor market imperfections were present in the first but not the second period, we test for coefficients on all demographic variables jointly being equal to zero. Results, reported in the bottom of Table 6, suggest that this null hypothesis can be rejected at 5% in the first but not the second period, supporting the notion that labor market functioning did improve over time.

Estimated coefficients on other variables are mostly consistent with expectations. Negative and significant coefficients on agricultural wage in all equations are consistent with downward sloping demand curves. The same is true for negative and significant coefficients (except in one case) on non-agricultural wages. Where they are significant, coefficients on fertilizer and bullock prices have the expected positive signs. Demand for pre-harvest farm labor increases in cropped area as well and the household head’s gender was a key determinant of labor demand in the early but not the later panel period.

Although results from estimating equation (5) allowed us to reject the hypothesis of labor market imperfections in 2008 for the total sample, we noted earlier that the negative relationship between farm size and productivity did not disappear entirely in the second period (see Figure 1 & Table 3). If this is a result of labor market imperfections, we should be able to document these empirically. Variation in nonagricultural labor demand across villages can provide a plausible cause of exogenous variation and to explore whether it may play a role, we split sample villages into three equally sized groups with high, medium, and low levels of nonfarm labor demand and we interacted household characteristics with – dummies for each group to test for heterogeneity along this dimension in the 1999 2008 panel.<sup>13</sup> Results shown in Table 7 are for specifications in which we interacted total household size (columns 1 and 2) and other demographic variables (columns 3 and 4) with indicator variables for high, medium and low levels of village level activity in non-agricultural labor markets. Estimated coefficients provide support for the hypothesis that low levels of non-agricultural labor demand are a key driver of observed labor market imperfections and most plausibly the inverse relationship between farm size and productivity. Although the interactions indicate that household size is insignificant in villages with more active non-agricultural labor demand, the coefficient on household size interacted with low level of non-farm labor market activity is highly significant for pre-harvest and total labor (columns 1 and 2). The result is robust to the addition of more indicators of household composition. In addition to one of these indicators (share of elderly male adults) being significant for the group with low level of nonagricultural labor market activity, results from

> 13The level of nonfarm labor demand is measured by the share of nonfarm work to total work in the village. Such information is not available in the 1982 survey so we only use the later panel for this analysis.

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