Small farmers’ superior levels of output can thus be attributed to higher intensity of (family) labor, consistent with the notion that they maximize profits in the presence of market imperfections.

# **4.1 Production function estimates**

The top panel of table 3 reports parameter estimates from the Cobb-Douglas and translog specifications at household (columns 1-3) and plot (columns 4 and 5) level, respectively. We note that all conventional factors are significant and positive with elasticities of 0.31for land, 0.41 for labor, 0.9 or 0.14 for fertilizer, 0.05 or 0.10 for pesticides, and 0.12 for manure at holding level. We cannot reject constant returns to scale at holding level though there is some indication of increasing returns to scale (at 5% or 10% level of significance for translog and Cobb-Douglas functional forms, respectively) at plot level. Crop shocks (drought, flooding, damage due to pests or insects), are estimated to reduce output by 21 percentage points, and soil type with loam soils increasing output by some 20 points. Plot level regressions also point towards a negative impact of distance from the homestead; one minute of additional travel time estimated to reduce output by about 0.4 percentage points.

Estimates of technical efficiency from a stochastic frontier production function, plotted against holding size in appendix figure 3 together with a kernel-weighted local polynomial regression fitted through them, fail to support a systematic relationship between efficiency and size.<sup>17</sup> Also, household- and village-fixed effects from plot level regressions can be used to recover a measure of farmers’ ability as the difference between household- and village-level fixed effects. Plotting this variable and the regression fitted through it against cultivated area in appendix figure 4 points in the same direction.

Marginal products of male and female family labor together with market wages are displayed in the bottom of table 3. To check the plausibility of the results, appendix figures 5 and 6 plot mean values and 95% confidence intervals of estimated shadow wages for male and female casual and semi-skilled labor against four employment regimes, namely those who are (i) fully autarkic in labor markets; (ii) only work off-farm but do not hire in any labor; (iii) work in off-farm employment and hire in labor; and (iv) only employ others but do not work off-farm.<sup>18</sup> In all cases, and irrespective of gender, shadow wages for households who do not hire in (i.e., remain in autarky or hire out family labor for casual work) are significantly below those for households who hired in agricultural labor. Shadow wage rates for those employing workers are in most cases indistinguishable from the village wage rate. For semi-skilled offfarm work, the situation is similar except that estimated shadow wage rates for households who at the same time hire in and out labor are estimated to be above those for households working only on their own

> 17 Results from estimating the stochastic frontier production function with a truncated normal non-negative distribution component are available upon request from the authors.

> 18 For casual labor markets, 30% of sample households remained in autarky; 31% only hired out family labor; 8% hired out family labor and employed hired labor on-farm; and 31% only hired labor for farming. For semi-skilled labor, 56% remained in autarky, 5% only hired out family labor, 7% hired out and hired in agricultural labor, and 32% only hired in.

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