GPS and self-reported areas are significantly different in the pooled data as well as in Malawi and Niger.

Since a key potential component of the error in self-reported land area is rounding, as a first look at the source of mismeasurement Figure 1 provides histograms of the self-reported land data (left hand side) compared to the GPS data (right hand side) including all plots with 5 acres or less. The difference is striking. On both graphs there is clustering on the low end of the scale, which is to be expected given that at least 40% of plots in each country are less than 2 acres. In the selfreported areas, however, there is clear heaping on whole numbers as well as intermediate rounding, especially on the lower end on the quarter, half and three-quarter acre marks. In Malawi, farmers had the option of reporting in acres, hectares or square meters but 99.7% chose to report in acres. In Uganda and Tanzania, acres were the only option, which could lead to rounding on the part of farmers or enumerators. In Niger, square meters were the only available unit and therefore the heaping is not centered on the same acre proportions. While the GPS histograms are markedly smoother, the existence of spikes in Malawi and Tanzania GPS figures suggest there is still some rounding of GPS-measured areas because of survey design and technology.<sup>8</sup> To assess whether rounding is the source of the trends noted in Table 2, Figure 2 reports the distribution of GPS measures relative to “rounded” self-reported areas for the metadata.<sup>9</sup> For areas such as 0.5 acres, 1 acre, 2 acres and similar higher common rounding values, we check to see the distribution of GPS measures. Near perfect reporting of self-reported measures would lead to (i) a narrow distribution of GPS measures around the self-reported acre value, and (ii) symmetry in the distribution around the self-reported value indicating an equal level of under and over reporting.

Looking at the figures, the distributions for lower estimates appear to include a range of GPS values and the distributions are generally asymmetric. For example, the self-reported 0.5 acre measure has GPS values that primarily range from very small levels up to 1 acre but the distribution appears largely symmetric and in fact 50% under report, 46% over report and 4% are almost exact. Similar results are found for those rounding to 1 acre with a primary range between 0 and 2 acres but largely symmetric. However, for measures rounded at slightly higher amounts (2, 3, 4 and 5 acres) more systematic over reporting is found with nearly two-thirds of households providing estimates over the GPS measure. Generally, the distributions of GPS values display a heavier left tail and wider distribution with increasing self-reported plot size, suggesting that over reporting is more prevalent and self-reported precision declines as the self-reported figure increases. For even higher measures, there are too few observations to create clear distributions but the pattern remains the same with more over reporting of land size than under reporting relative to the GPS measure. In general, rounding appears to induce more over reporting.

# _Regression analysis of bias_

To analyze the range of factors that may influence differences in land areas as measured by GPS units and farmer estimates, following Escobal and Laszlo (2008) we turn to regression analysis. Using plot-level data, we estimate the following equation:

> 8 In Malawi, the interviewer manual instructs enumerators to record only two digits to the right of the decimal and the questionnaire itself only provides this much space—thus, the ten small spikes seen in Malawi’s GPS histogram between 0 and 1 acre. In Uganda, similar instructions led the enumerators to record two spaces to the right of the decimal.

> 9 Self-reported areas are considered rounded if they are equal to the following: in meters – 1000, 5000, 10,000, 20,000, 30,000, 40,000, 50,000, 100,000, 200,000 or 500,000; in acres – 0.25, 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 10, 15, 20, 25, 30, 40, 50, 100 or 300; or, in hectares – 0.5, 1, 2 or 5.

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