The pairwise correlation of the ratio of self-reported to sub-plot crop cut production estimates from MAPS I to MAPS II is 0.002, not statistically distinguishable from zero. Confidence in the consistency of self-reported measurement error in crop production is further degraded by the lack of predictive power from year to year. Table 5 presents the results of simple OLS regression of MAPS II yields on MAPS I yields, using both sub-plot crop cut production (columns 1, 2, and 3) and self-reported production (columns 4, 5, and 6).

When relying on the objective measure of production in the numerator, MAPS I yield is a significant predictor of MAPS II yields, particularly in the sample in which both plots were from the same parcel. This reflects farmer ability, the quality of the land, agricultural practices employed, etc. Conversely, self-reported production-based yields in MAPS I are not a statistically significant predictor of yields in MAPS II. The correlation of self-reported yields between MAPS I and II on the parcel panel sample is only 0.012, while the correlation between sub-plot crop cutting yields is 0.226. The inconsistency of measurement error in self-reported production estimates observed in Figure 6 and Table 5 severely limits the potential for utilizing a “corrected” self-reported production data in productivity analysis.

If the over-estimation of maize yields based on farmer-reported maize production were uniform across the distribution of plot sizes, it would have no influence on the observed relationship between land productivity and plot area. Rather, the differences in the plot area coefficients suggest that there is a systematic bias in farmer-reported maize production. To address whether the deviation between crop cutting and farmer estimates varies across the distribution of plot areas, Figure 7 presents the mean deviation in yields (as measured by self-reported yield minus cropcutting yield) by GPS-based plot area quintile for MAPS I and MAPS II. A clear downward trend exists, in which farmers more greatly over-estimate yields on smaller plots, with the degree of over-estimation decreasing with plot area. This systematic bias would have direct consequences on the IR.

This trend is consistent with evidence on the systematic nature of measurement error in farmer self-reported estimates of plot area _._ Carletto et al. (2013, 2015, Forthcoming) find that farmers overestimate plot areas relative to GPS-based area measurements more significantly on smaller plots, while only slightly overestimating (or underestimating) the area of larger plots. The collection of both GPS-based area measurement and farmer self-reported area in MAPS I and II allows for analysis of the relationship between the measurement error in self-reported crop production and plot area. As expected, the degree of measurement error observed in these two variables is significantly and positively correlated, with a correlation coefficient of 0.437 and 0.535 in MAPS I and II, respectively.<sup>35</sup>

> 35 The pairwise correlation coefficient of the ratio of self-reported to sub-plot crop cut based production to the ratio of self-reported to GPS-based plot area measurement is reported. In MAPS II, plots which were subject to full-plot crop cutting are excluded.

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