basic characteristics of the head of household; _D_ and _E_ are district and enumerator fixed effects, respectively; and ε is the error term.<sup>15</sup> The coefficient _β_ on _A_ is the parameter of interest while testing for the existence of the IR. A negative _β_ indicates the presence of the IR: the more negative the coefficient, the stronger the IR. We estimate Equation 1 separately with (i) the incomplete dataset using the observed GPS-based plot areas, and (ii) the complete dataset using the multiply-imputed GPS-based plot areas. In the latter case, the regression is estimated _m_ (i.e. 50) times with each of the _m_ complete datasets, and the coefficient estimates and associated standard errors are combined in accordance with the framework presented in Section 5.

The regression results are presented in Tables 6 and 7 for the UNPS 2009/10 and the TZNPS 2010/11, respectively.<sup>16, 17</sup> The results from the incomplete case analysis and the multiply-imputed complete case analysis are presented in Columns 1 and 2, respectively. The coefficient on the plot area is negative and statistically significant at the 1 percent level across all columns reported in Tables 6 and 7. However, with respect to the _β_ obtained under the incomplete case analysis, the _β_ associated with multiply-imputed GPS-based plot area is 33 percent and 9 percent higher in Uganda, and Tanzania, respectively, revealing how the selection bias introduced in the GPS-based plot area measurement process carries all the way to the analysis stage. It should also be noted that not only does working with the full sample have implications for the IR, the coefficients and standard errors of several other explanatory variables of interest are observed to change when the complete dataset 15 Plot value of agricultural output in Ugandan/Tanzanian Shillings (USH, TZS) is computed by (i) expressing crop-condition-non-standard measurement unit combinations in kilogram-equivalent terms and the reference crop condition, (ii) multiplying the kilogram-equivalent quantity of production for each crop on a given plot by the median crop sales value per kilogram at the enumeration area-level, and (iii) summing all imputed values of crop production on that plot. The median crop sales value per kilogram is computed at the enumeration area-level only if at least 10 unit sale values are available at that level of aggregation. Otherwise, the median crop unit sale value is computed at a higher level, in the order of parish, sub-county, county, district, and region in the case of Uganda, and in order of ward, district, and region in the case of Tanzania. Plot value of inputs in USH/TZS includes (i) expenditures on hired labor and (ii) the imputed values of nonlabor inputs, including organic fertilizer, inorganic fertilizer, pesticides/herbicides, based on median costs per kilogram computed at the enumeration area-level only if at least 10 unit cost observations are available for a specific class of non-labor input at that level of aggregation. Otherwise, the median unit costs are computed at a higher level, in the order of parish, sub-county, county, district, and region in the case of Uganda, and in the order of ward, district, and region in the case of Tanzania. Our results are robust to (i) using net revenue (i.e. gross value of output net of gross value of non-labor input) per acre as the dependent variable, and/or (ii) including enumeration area, as opposed to district, fixed effects in the imputation and analysis models.

16 Using the sample of plots with observed GPS-based areas, we also estimated Equation 1 using the farmerreported plot areas in both settings. Just as in Carletto et al. (2013), the resulting β is negative and its absolute value is lower than the β obtained by using the observed GPS-based plot areas. These results are available from the authors upon request, but are not reported as they are not the focus of this paper.

17 The combined MI results reported in Tables 6 and 7 are underlined by complex survey regressions that correctly take into account clustering and stratification in weighted regressions. The results are robust to not weighting our regressions.

17