for labor with the use of CC yields, these results suggest that if we suspect a high degree of correlation between the measurement error of labor with the true value of labor, it may be better to estimate the yield-input relationship using a predicted measure of CC yields that does not include SR yields among the list of predictors. On the other hand, if _λ_ is not high (as it seems to be the case with quantity of seeds per hectare), it is better to include SR yields among the list of predictors for CC yields. In any case, it is always better to use the ML yields rather than SR yields. Finally, the right panel of Figure 4 shows the results from the alternative regressions of ML yields which are computed with ML-based imputed measures of CC harvest that are in turn standardized by plot area (as opposed to imputing ML yields directly). We can see that the coefficients associated with the key inputs are not estimated correctly - especially for plot area. This confirms that deriving ML-based imputed CC yields, as opposed to CC harvests, is the most appropriate.

To further confirm that the use of ML yields de-biases the estimation of the relationships between yields and inputs, we estimate regression, as presented in Table 3, using the test sample and both SR and ML yields. The results are presented in Table 9. First, inputs do not correlate with overestimation of ML(SR,W) as much as they do with SR. In fact, none of the coefficients are significant. And although the coefficient for quantity of seeds per hectare was positive but not significant under the use of SR yields in the test sample, it is now reversed and is no longer significant. Second, the adjusted _R_<sup>2</sup> decreases considerably which indicates that the covariates are associated to a lesser extent with the difference in values between CC and ML yields.

# **4.2.4 Application on the nationally representative survey**

To assess the external validity of our findings thus far, we replicate the analysis with data from the Enquˆete de Conjoncture Int ́egr ́ee (EACI 2017)<sup>16</sup> a nationally-representative multi-topic household survey, spanning both rural and urban areas of Mali and with detail questionnaire modules on smallholder agricultural activities. The households were interviewed by semi-resident enumerators in three visits, following a fieldwork protocol that was similar to that of ERIVaS. All major crops, including sorghum, were subject to crop cutting during the EACI fieldwork, and the size of the randomly-placed crop cut sub-plot on sorghum plots specifically was 5m x 5m (opposed to 8m x 8m in ERIVaS). One of the objectives of EACI is to derive national- and regional-level estimates of total crop production and yields. On yield measurement, plots, rather than households, are the primarily units of analysis, with direct implications on the sampling of plots for crop cutting purposes. Specifically, in each sampled EACI enumeration area, a complete listing of plots was conducted, and the listed plots were organized into separate subsets in accordance with the cultivated crop (or crop combinations, in the case of intercropped plots). A third of plots were then selected at random from each subset. This means that households with more plots had a greater probability of having a plot selected for crop cutting. In the end, we have farmer self-reported production data for about 24,000 plots of which 7,800 were subject

> 16The EACI 2017 is also the Mali LSMS-ISA 2017. It was built upon the Agricultural Conjuncture Survey which is implemented yearly by the Statistical Unit of the Ministry of Agriculture. For the 2017 edition, living conditions modules were added on a subsample as part of the Mali LSMS-ISA project.

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