effect, which may make it uneconomical to apply every year). Second, for those plots on which FYM is applied, there is a great range of variation in the amount per acre. We thus experimented with various transformations of the dependent variable. Among those that can handle zero values, we found that a simple one, log(M + k), works reasonably well in terms of fi tting the data. Unfortunately, in the presence of zeros, there is no way to let k be a free parameter in the estimation, so the choice of k is largely arbitrary (we set it to 0.1).<sup>19</sup> In addition, the estimated coefficients are not invariant to the choice of k, which means that these coefficients cannot be used to compute, say, the implied percentage differential in FYM use on leased versus owned plots. Instead of making such quantitative statements, our focus, for now at least, is on hypothesis testing. For this purpose, the logarithmic transformation is perfectly adequate since the t-statistics are essentially invariant to the choice of k.<sup>20</sup> Our analysis controls for the following plot characteristics: area, location (inside/outside village), access to year-round or seasonal canal irrigation, access to groundwater of varying quality, topography, soil quality, and self-assessed plot value.<sup>21</sup> Details of these variables, means by tenancy status, and coefficient estimates for a particular speci fi cation are reported in appendix Table A.1. Note that we do not have data on the exact distance between the farmer’s house and the plot; we only know whether the plot is outside his village or not. This could be a concern, given that both the cost of manure application on a given plot and tenancy status might vary by distance to the homestead. However, in our sample, 92% of all cultivated plots are located within the village (93% of owned plots compared to 90% of leased plots). Given the size of most villages in Pakistan, the vast majority of plots are therefore, at most, only a kilometer or two from the farmer’s home.<sup>22</sup> Within this radius, transport cost differentials are likely to be minimal. More-

> 19 We choose k so that it is at least an order of magnitude less than the minimum value of the dependent variable. Maximum likelihood estimation of k would fail, since the log Jacobian of the transformation of y is − log(y + k). At y = 0, the optimization algorithm would always try to set k as close to zero as possible.

> 20 For example, the t-value for the leasing coefficient in row (3) of Table 4 is 5.91. The corresponding t-value is 5.92 when k = 0.01 and 5.93 when k = 0.001, even though the associated coefficients vary widely in magnitude.

> 21 Both owners and tenant cultivators are asked to report plot value in the survey. One might worry that these values partly re fl ect the extent of past manuring, although this seems quite unlikely given that the effects of FYM are far from permanent. In any event, the exclusion of this variable from the regressions has a negligible impact on the estimates of interest.

22 We can be more precise by examining data from the 1991 IFPRI survey, which did collect information on distance to plot (but not on whether the plot was outside the village). Virtually all of the households in this survey were included in the 2001 PRHS sample as part of a panel. Among the 914 plots recorded in the 1991 survey, mean distance between household and plot is only 600 meters (median 300 meters).

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