than 0.007 ha) where the relationship is very imprecisely estimated.<sup>12</sup> By contrast, profit net of family labor valued at market prices (the solid lines) remains virtually constant for all plot/holding sizes above 0.02 ha. If supported by parametric results, this would suggest no benefits from policies to promote consolidation. Gains from measures to prevent subdivision, if existent, would be of small size magnitude and at most affect the very smallest plots (note that 25.8% of plots are below 0.02 ha).

Plot level data in table 2 suggest that small plots are of higher quality (16% in the bottom vs. 8% in the top tercile are wetland and 8% vs. 3% in a valley), a conclusion supported by higher self-assessed land values of US$ 19,070 per hectare for the bottom vs. US$ 8,387 in the top plot size tercile.<sup>13</sup> The relationship between farm size, yield, and gross and shadow profits per hectare remains similar to what was found earlier, i.e., a negative relationship between plot-size and output value that disappears once net profit valuing family labor at market wages is considered.

# **3.2 Econometric approach**

To make inferences on scale of production and technical efficiency across farm size classes and appreciate households’ patterns of resource allocation to crop production, we estimate Cobb-Douglas and translog production functions at holding- and plot-levels. The general form of the translog production function with no restrictions on cross elasticities of substitution is (Berndt and Christensen 1973)<sup>14</sup> where _Yij_ is the total value of crop output (in logarithms) on plot _j_ cultivated by household _i_ ; _αi_ is a vector of household fixed effects; _Xijk_ or _Xijl_ are the logarithm of the quantities of variable inputs used (subscripts _k_ and _l_ stand for types of inputs including the number of labor days, quantity of chemical fertilizer, pesticides and manure used); _Zij_ is a vector of plot characteristics that may affect production, e.g., distance from homestead, years of possession, presence of irrigation or being located in wetland, soil type, topography, and incidence of crop shocks; _β_ , _γ_ , and _δ_ are vectors/matrix of parameters to be estimated; and εii a random error term. Fixed effects, _αi_ , at plot or (for household-level regressions) village level include time invariant unobserved factors affecting crop production at the relevant level. Computing the difference between village-level fixed effects and _αi_ will provide a measure of farmers’ ability or technical efficiency (Deininger and Jin 2008).

Value of crop output and all inputs are normalized by dividing them by their sample means. In the empirical estimation, we also include dummies for zero values of non-labor variable inputs (Battese 1997). Given

> 12 Note that, in light of the paucity of observations, these are not very precisely estimated.

> 13  Note that these values are very high by international standards, reflecting partly the lack of alternative assets.

> 14 We present the plot-level specification, noting that it is straightforward to translate this to the holding level where _j_ would index households in village _i_ , and plot-level variables are aggregated at household level using plot size as a weight, and _αi_ is a village-level fixed effect.

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