and large plots (Table 7) and use sensitivity checks to rule out that the IR is driven by differences in crop-cut procedures between the waves, or by influential outliers (Table 8).

Column 1 of Table 3 considers the standard IR regression which includes household fixed effects and plot characteristics.<sup>15</sup> We are able to control for a fairly large set of observable plot characteristics including factors such as: slope, elevation, potential wetness index, distance between plot and dwelling, title status of plot, whether pure stand, irrigated, and several controls for fertilizer type. The household fixed-effects model provides a way to control for all timeinvariant household attributes that might be confounding factors affecting the association between yields and plot size. This specification indicates that yields decrease by 40 percent if plot size doubles, which is more strongly negative than indicated by the bivariate association noted earlier. It also suggests that the IR not only holds in Ethiopia but is stronger there than in many other Sub-Saharan African countries (Larson et al., 2014).<sup>16</sup> Column 2 replaces household fixed effects with parcel fixed effects, thereby identifying the IR through variation in plot size within a parcel, both within and across waves. We interpret parcel fixed effects as controls for unobserved plot characteristics, such as soil quality, that are unlikely to change substantially within a parcel. Including parcel fixed effects again does not weaken the IR, showing that differences in soil characteristics between small and large plots do not explain the relationship. The final specification (column 3) includes enumeration area fixed effects and additional controls for household characteristics. The set of household controls is limited to age, gender, literacy of household head and an asset index to proxy wealth. We find no change in the IR when considering this specification. While we view this specification as somewhat less informative than the (geographically much more refined) parcel fixed-effects estimation, we 15 We also estimate the IR with household-wave fixed effects to address the potential concern that the IR is resulting from shadow prices faced by the household that are changing over the waves in a way that differentially affects productivity across plot size. Across several different samples and specifications, using household-wave fixed effects did not change the findings. For example, in Table 3, column (1) the IR for self-reports is -0.397 with household fixed effects, when controlling for household-wave fixed effects, the IR is essentially the same at -0.401. When restricting the sample to only those plots where we have both crop cuts and self-reports, the IR for self-reports with household fixed effects is -0.287 while the IR with household-wave fixed effects is -0.291. Finally, when estimating the IR for crop cuts with household fixed effects, the coefficient on plot size is 0.119 and the same coefficient when estimated with household-wave fixed effects is 0.118. All the coefficients reported here are statistically significant at the 1% level.

16 Using a different data source from Ethiopia (Ethiopian Rural Household Survey) based on a purposeful (not probabilistic) sample design from 15 woredas (i.e. districts) from 2004 and 2009, Savastano and Scandizzo (forthcoming) examine heterogeneity in the relationship at different points on the conditional yield distribution. They interpret their analysis as showing both non-linearities in land size - productivity relationship and heterogeneity in these nonlinearities at different points on the conditional yield distribution.

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