εi measures the difference between the area measures for plot _i_ (SRi − GPSi) and can be viewed as an estimate of _bias_ associated with self-reporting land areas. Measuring in this manner makes it possible to assess the factors that determine the difference between measures.

With no other controls, α would simply represent the mean difference between the two measures. If α is not significantly different from zero or very small it would suggest that the measures are similar. Adding a measure of the GPS area controls for bias by GPS reported area. If the coefficient β is not significantly different from zero, it suggests that there is no systematic difference between self-reported and GPS-measured land area and the direction of overall bias would depend solely on α. If the coefficient is significant and negative, it suggests that as land size increases farmers systematically move towards under reporting land areas while if it is significant and positive it suggests that farmers move towards systematically over reporting land areas. Whether they are under or over reported on average for a given land area would depend on both the value of α and the value of β. Of course, a nonlinear relationship between GPS area and bias might exist and this is explored. If neither α nor β are significantly different from zero it would suggest that self-reported land measures are reasonable substitutes for GPS measures.

Including additional controls provides an assessment of whether other hypothesized factors may influence bias. Further, the inclusion of additional variables may drive out the results on GPS land area (β) or general mean differences (α)—that is, make them insignificantly different from zero— and suggest that while there are differences in farmer estimates and GPS measures, these can be controlled for in any analysis of agricultural relationships. Xi′ is then a vector of control variables that are likely to influence self-reporting including those previously hypothesized to influence bias such as factors linked to intentional or unintentional misreporting, rounding, and topography. Since local units were not used in the included countries, this should not be a factor and is not considered. Finally, μi is the error term.

Plot-level data are used in the analysis since this is the point of measure and it is this bias that we are interested in understanding. The equation is estimated for the metadata and then the individual country data. The analysis of the metadata takes a stepwise approach. First, the relationship between bias and GPS-measured land area is considered since this is the key relationship of interest as it forms the basis for understanding if self-reported areas are systematically different from GPS measures. Next, a series of rounding dummies are included first to see if these are important in bias and second to see whether this explains part of the relationship between GPS area and bias. Third, household fixed effects are added to the regression to determine the role household factors play in bias. Since household fixed effects require multiple plots per household, the estimates in this table only include plots in households with multiple plots (15,724 observations). Fourth, plot level factors are added to establish if topography or other plot level factors play a role. Robust standard errors have been used in all estimations to control for heteroskedasticity.

Table 3 reports the results of the four steps with mean values of variables reported in the first column. The results of the first specification show that bias in reporting is declining with plot GPS land area indicating that bias is relatively greater for small land sizes. While the squared term is negative, it is relatively small in the range of interest creating a near linear relationship. With a constant (α) equivalent to half an acre and a point estimate on the linear term of -0.3, what this means is that self-reported areas are larger than GPS areas for very small plots but that bias tends to decline beyond this, reflecting the systematic differences found in Table 2. Above half an acre, farmers tend to systematically under report land areas.

Adding in the rounding variables in the second specification, the importance of rounding is clearly shown as all categories of rounding are found to be significant and contribute to bias. Note that with the rounding variables included, the relationship between bias and GPS strengthens 8