relationship, but the estimates again diverge with self-reported areas indicating a significantly stronger relationship than GPS.

The inclusion of appropriate control variables in both sets of regressions (Tables 6 and 7) appears to create greater divergence between the two land area measures. First, this suggests that self-reported area is more responsive to the inclusion of these controls indicating this land measure is capturing characteristics of the land operator in addition to the land area. This is consistent with the earlier analysis which showed household- and plot-level factors are significant determinants of bias. It is also consistent with the presence of land measurement error, which is expected to lead to biased estimates (Bound, Brown and Mathiowetz, 2001). Second, it suggests that the inclusion of controls in assessing the inverse productivity relationship may lead to an overestimate of the true relation. At minimum, it indicates that control variables do not help overcome the inherent bias generated by using self-reported land areas.

Of course, as noted earlier in the paper, GPS units potentially underestimate land areas for smaller plots (less than 0.5 hectares or 1.24 acres). If that is the case, the overestimate of the inverse productivity relationship might reflect under reporting of smaller plots by GPS rather than over reporting of self-reported areas. To check this possibility, the two equations are first re-estimated using land area dummies to see if the relationship is greater at lower levels (suggesting this is driving the results). The results (available from the authors) indicate that on the contrary, the differences are greater at larger land areas. Second, the equations are estimated separately for farms under 1 acre and those over 5 acres to see if the estimates vary depending on the observations used. The results (reported in the last columns of Tables 6 and 7) appear consistent and suggest selfreporting of land areas overestimates the inverse productivity relationship at all land sizes.

Finally, Table 8 presents the results for the four individual countries included in the metadata using the final specification. For the individual countries, a few differences emerge from the metadata analysis. First, all estimates suggest an inverse productivity relationship although when using self-reported areas for value of output (equation 3) for Niger, the results are not significant, raising the possibility that self-reported areas include sufficient error to falsely reject the hypothesis of an inverse productivity relationship. In the value of output per acre model, however, the results for Niger are consistent in that the inverse productivity relationship is stronger with farmer selfreported areas. Second, while Malawi and Uganda have trends consistent with what is found in the metadata, the Tanzania results imply that the self-reported land area estimates suggest a weaker inverse productivity relationship compared to using GPS.

# **4. Conclusions**

The objectives of this paper are to compare the use of GPS devices to traditional self-reporting of plot land area and to determine the implications of using a GPS-based system for the analysis of agricultural relationships. Particularly, we compare GPS land measurement to self-reported land area in estimating the inverse farm-size productivity relationship. Meeting these objectives is possible because of recently collected LSMS-ISA data which includes GPS and self-reported land areas along with detailed agricultural information from four countries in Sub-Saharan Africa.

The analysis indicates that there is a systematic discrepancy between GPS and self-reported plot areas. The data indicate that small plot areas are generally over reported by farmers while larger plot areas are generally under reported. Given the majority of plots in Sub-Saharan Africa are small, over reporting in this critical area of the land distribution appears to dominate. Of course, in other contexts where the land distribution differs, underreporting may dominate. The source of misreporting seems to be related to rounding as well as a number of household factors. While these factors play an important role in the misreporting, systematic discrepancies between the two 12