# **1 Introduction**

Small farms (with fewer than 2 ha) represent 84% of the estimated 570 million farms worldwide (Lowder et al., 2016). In view of the prevalence of smallholder farming across the developing world and the linkages between agricultural and welfare outcomes, one of the targets of the Sustainable Development Goal of Ending Hunger has been identified as doubling the agricultural productivity and incomes of small-scale food producers. One measure of agricultural productivity is crop yield, which is the amount of crop production harvested per unit of cultivated land. Increasing crop yields has been a long-standing goal of African governments and is key to feeding a growing global population while managing natural resources efficiently (Lobell et al., 2009; van Ittersum et al., 2013; Zhang et al., 2016).

Despite the seemingly simple formula for computing crop yields, and its frequent use in agricultural economics research, obtaining accurate measures of crop yields is underlined by a host of challenges in low- and middle-income countries, mainly due to reliance on household and farm surveys and measurement errors in self-reported information on crop production and cultivated area. Research has demonstrated the effects of these measurement errors on our understanding of the inverse-scale productivity relationship (IR) in agriculture – i.e. the finding that the productivity measures, including crop yields, are, on average, higher on smaller farms and plots vis-`a-vis their larger counterparts.

The first strand of research has focused on the denominator in the formula for crop yields: cultivated land area, and has documented systematic discrepancies between GPS-based and self-reported plot areas (Carletto et al., 2013; Carletto et al., 2015; Kilic et al., 2017). The cross-country comparable finding across these studies is that on average, farmers tend to over-report plot areas, and more so at the lower end of the plot area distribution. As a result of using GPS-based plot area measures, as opposed to their self-reported counterparts, research has shown that the IR, though weakened, remained statistically significant.

The second strand of research has focused on the numerator in the formula for crop yields: total crop production, which, in low- and middle-income countries, has traditionally been based on self-reported survey data. There are, however, several complications in eliciting accurate self-reported information on crop production, including (i) potential recall biases, in part as a function of when data are collected vis-`a-vis the harvest period (Wollburg et al., 2021), (ii) inclination to round off numbers (as shown by Gourlay et al. (2019) for crop production and by Carletto et al. (2015) for land area), and (iii) reliance on non standard measurement units, such as bunches and carts, and gaps in the availability and quality of conversion factors that are required to express non-standard measurement units in kilogram-equivalent terms and that are ideally differentiated for different conditions in which crop harvest may be reported by farmers (Oseni et al., 2017). Researchers have demonstrated that self-reported crop yields are subject to non-classical measurement errors, and are over-estimated on smaller plots, in comparison to objective measured yields based on crop cutting, i.e. the gold standard, albeit resource- and supervision-intensive, approach to crop yield estimation based on weighing the harvest of a randomly selected sub-section of a farmer’s plot. The key cross-country finding of interest is that at the plot-level the IR is strong and statistically significant when self-reported crop yields are used, and that the IR ceases to exist when crop cutting yields are used instead (Desiere and Jolliffe, 2018 and Abay et al., 2019 for Ethiopia; Gourlay 2