# **6 Concluding remarks**

This paper attempts to increase the reliability of assessments of yield-input relationships when yields based on self-reported survey data on crop production are subject to non-classical measurement errors. We show analytically and empirically that it is possible to construct imputed measures of objective crop cut yields, using a machine learning model and a sub-sample of plot observations with both crop cut and self-reported yield measures in a household survey. The imputed crop cut yields are shown to be less biased vis-`a-vis self-reported yields, and the errors in the imputed measures are uncorrelated with input use per hectare. As such, the regressions of imputed crop cut yields replicate the true relationships between yields and inputs that are estimated with observed crop cut yields. These conclusions are robust to whether we use the data from a small-scale methodology study conducted in southwestern Mali or a nationally-representative survey.

From a data collection point of view, these findings carry the implications that more objective methods of collecting crop production data need to be integrated in the protocol of household surveys. We rely on two household survey data sets from Mali with the rare characteristic of having both self-reported and crop cut data. The first data set from a methodological experiment enables us to empirically show that it is possible to combine self-reported yields data to judiciously predict crop cut yields and, thus build a measure of yields that appears to be fit for a correct assessment of the relationship between yields and inputs with a random sample representing one-third of the entire sample. The second data set, a nationally representative survey, enabled us to validate the approach but also served as a stark reminder that even when a data collection method is theoretically objective, execution is key to ensure that meaningful inference can be made based on it. Although these results are promising, further work considering other crops should be pursued to improve the machine learning predictions, evaluate the limit of the inferences that can be carried out using this approach, and better understand its potential bias reducing properties.

Finally, our analysis expands on the body of work related to non-classical measurement errors and its impact on agricultural policy analysis in a smallholder context. We show that measurement errors in self-reported yields are correlated with major factors of production in smallholder farming systems. On land; the factor that has been the focus of the recent literature regarding the study of the inverse scale-productivity relationship (Desiere and Jolliffe, 2018; Abay et al.,2019; Gourlay et al.,2019), our results corroborate the existing evidence that IR disappears and is even reversed when the relationship is assessed with crop cut yield as opposed to self-reported yields. We also examine the relationships between yields and seeds per hectare and yields and household labor per hectare. These relationships have serious implications for agricultural policy especially as it pertains to the question of agricultural intensification. A positive relationship between yields and quantity of seeds suggests that farmers could improve their yields by applying more seeds and thus would provide support for making seeds more accessible to farmers. A positive relationship between yield and household labor indicates that plot-level land productivity could be increased with more labor, suggesting that labor is not correctly allocated across households. But similar to what is observed in the case of plot area, we document that measurement errors in self-reported yields are correlated with the quantity of seeds and household 37