substantially in effect creating a steeper estimate. Further, the constant (α) increases to 1.25. The results then suggest that bias remains positive up until 2 acres—or equivalently, that controlling for rounding, plots under 2 acres tend to be over reported.

The inclusion of household fixed effects leads to a decline in the land-bias relationship suggesting household factors matter to a degree. Note also that there are changes in the magnitude of the rounding coefficients indicating that rounding is partially linked to household factors. Separate analysis using household variables rather than fixed effects (available from the authors) shows that a number of factors including head education and gender are significant predictors of bias, but, as the fixed effect results show, the systematic bias remains. Looking at the fourth specification, the entry of plot characteristics has limited effect on the overall relationship. Only land tenure is linked to bias and topography does not seem to matter. The results for the inclusion of household and plot factors are important since they suggests that the use of household and plot control variables in regressions assessing agricultural relationships is insufficient to deal with the potential bias in self-reported areas.<sup>10</sup> The last two columns repeat the analysis of the final specification but limiting the sample to observations where the GPS measure is less than 1 acre and then more than 5 acres. The reason for including these specifications is to check the sensitivity of the results to different parts of the distribution. This is particularly important given the potential issues with using GPS measures for smaller land holdings. The results for the observations under 1 acre show an insignificant linear term but a negative and significant squared term for land area. Combined with the result for the constant term (α), we again observe over reporting by farmers for very small plots and a shift towards under reporting with movement towards 1 acre. The results for the observations greater than 5 acres show a larger linear term on the GPS measure when combined with the constant, indicating that on average larger plots are under reported. These tests confirm the widespread over reporting by farmers.

Table 4 repeats the analysis using the fourth specification for each of the individual countries included in the metadata. The country-level results confirm those found in the metadata. Constant terms are between 0.54 and 3.005 (although not always significant) and bias is significant and declining with GPS plot area with linear estimates between -0.405 and -0.755. Estimates on the rounding variables also confirm that rounding plays a significant role in the level of bias.

The analysis of GPS and self-reported plot areas establish systematic and significant discrepancy between the two land measurement approaches. Results indicate that while small plots may be over reported by farmers, larger farmers tend to under report their holdings. These results hold even controlling for other factors including rounding, household factors and plot characteristics. These exist across the countries studied and are likely to hold true in other locations. Overall they suggest that land measurement error is non-classical. The results mirror those of Escobal and Laszlo (2008) who found the same result when comparing self-reported and GPS measured distances to market.

The deviation in land area measurement across methodologies found in these countries could serve to either unravel or reinforce commonly trusted agricultural relationships. The implications of using readily available yet imprecise self-reported land area measurements are explored below through an analysis of the inverse productivity relationship.

> 10 To ensure metadata results were not driven solely by Malawi, the country with the largest share of plots, additional metadata analysis was conducted excluding Malawi. Results showed consistent trends (full results available from the authors).

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