That’s the title of a new working paper my brilliant student Ling Yao (she is on the market this year, and she will make a great hire for anyone looking for someone working on agricultural economics, labor economics, agribusiness, applied econometrics, or a combination thereof) and I put the finishing touch to this past weekend.
Here is the abstract, with what strikes me as the most exciting things about this paper in boldface font:
An inverse unconditional relationship between farm or plot size (e.g., hectares) and productivity (e.g., kilograms per hectare) is often observed in low- and middle-income countries that appears to be at odds with economic theory. The traditional approach to studying the inverse relationship regresses yield (i.e., output divided by size) on size as well as control variables, testing the null hypothesis that the coefficient on size is zero. We first show that in many circumstances, the relevant null hypothesis is misspecified because the estimand cannot be zero. Moreover, because size appears on both sides of the equation—indirectly on the left-hand side as denominator, and directly on the right-hand side as a measure of size—inherent issues arise with the identification of the relationship between size and productivity. Specifically, any unobserved production factor, even if independent from size, will introduce bias in the estimated coefficient. We next highlight persistent methodological flaws and contradictions in the literature on the inverse size–productivity relationship, discussing how better controls and more precise measurements are unlikely to ensure unbiased estimates. We further identify the stringent requirements that need to be satisfied to correctly estimate the relationship. Finally, we conduct a meta-analysis of the literature on the inverse relationship, discussing the evolution of empirical specifications and documenting evidence of publication bias in favor of negative and significant estimates of the relationship between size and productivity.
Ars longa, vita brevis. This paper is the fruit of several years of thinking. I remember working on early analytical derivations during the summer of 2018, trying to overcome jetlag while in Tokyo to teach a short course at Waseda University. This paper is also a contribution to a literature that is both old and new. Next year will mark the hundredth anniversary of A.V. Chayanov documenting the existence of an unconditional inverse relationship between farm size and productivity in Russia. But as we document in our meta-analysis, the number of studies on the inverse relationship has practically exploded since 2010. And over the last 100 years, the inverse relationship has captivated the attention of many researchers, including that of a Nobel laureate.
