et al., 2013; Larson et al., 2014)<sup>2</sup> — which we refer to throughout the paper as self-reported yields. One reason why systematic measurement error in self-reported production has not yet been considered as an explanation for the IR is that the data requirements to test it are very demanding. Systematic measurement error can only be studied if there is a second, independent measurement of the same concept. In this study, we draw on two waves of data representative of rural Ethiopia which asked farmers to report production for all plots; these plots were also measured with GPS. In addition to the self-reported crop production, crop cuts were conducted on a limited number of randomly selected plots.

First used in the 1950s in India, the crop-cut method is now widely recommended by the Food and Agriculture Organization for accurate measurement of crop production (Fermont and Benson, 2011). This methodology estimates yields by first randomly sampling plots from a master listing, then identifying a random start point within each selected plot, delimiting from that point a small subplot (often a 4m x 4m square), and finally cutting and weighing the harvest from this subplot. Yields are then defined as the harvest in the subplot divided by the area of the subplot.

While crop cuts are often considered to be a gold standard for measuring crop production, this does not mean that they estimate yield without error. As one example, even though mechanical scales are much more precise than self-reports, they still entail rounding errors when reading the weight from the scale. As another example, because crop cutting entails randomly selecting a subplot from a larger plot, there is sampling error if yields within the plot are heterogeneous.

The main assumption in this paper is that whatever error there is in crop-cut estimates, whether from sampling or measurement, the error is independent of the size of the plot.<sup>3</sup> Given that the size of the subplot is fixed, regardless of the size of the entire plot, there is little reason

> 2 Most studies about the IR do not discuss how they measured yields, but all the studies cited above used self-reported production. As far as we know, no study has used crop cuts except the very recent study of Gourlay, Kilic, and Lobell (2017).

> 3 In this paper we emphasize that measurement error is likely to affect both crop cut and self-reported yield estimates, and while not a necessary condition for our findings, it strikes us as reasonable to assert that the magnitude of error in self-reports is expected to be much larger than that associated with crop cuts. One piece of evidence supporting this assertion is that the coefficient of variation in estimated maize yields from self-reports is about twice as large (in both waves) as the coefficient of variation when based on crop cuts. We also interpret findings from Gourlay, Kilic, and Lobell (2017, Table 2) as aligning with this view. They use as a benchmark production estimates from trained technicians harvesting an entire plot to compare estimates for these same plots when based on self-reports and crop cuts. The average crop cut estimate is within 10 percent of the benchmark, while the self-reported estimates are more than two and a half times greater than the actual harvest.

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