## The Inverse Farm Size–Productivity Relationship: Asked and Answered?

The 2016 MidDev conference, which my colleague Paul Glewwe organizes here at the University of Minnesota every other year, is almost upon us.

One of the papers I am most looking forward to seeing presented at the conference is a new paper on the inverse farm size-productivity relationship by Leah Bevis and Chris Barrett, which Leah will be presenting on Saturday morning in an organized session on agriculture in developing countries.

Briefly, for those of you who may not be familiar with it, the inverse farm size-productivity relationship is the empirical regularity whereby smaller farms are on average more productive than larger farms in developing countries. (Here, note that “productivity” refers to the amount produced per unit of land–kilograms of rice per hectare, for example–and not the total amount harvested.)

The existence of that inverse relationship has preoccupied economists for almost 100 years now, and many have tried to explain how and why it arises. If there truly is an inverse relationship, then this is at odds with neoclassical economic theory, according to which we would expect low-productivity producers to sell or lease their plots to high-productivity producers.

Moreover, if there truly is an inverse relationship, then the obvious policy recommendation for anyone interested in improving food security is to break up larger farms into smaller ones.

Taking this argument to its extreme implies that one could feed the world from a handful of flower pots, which is probably why economists have a hard time accepting that the inverse relationship is actually a thing, and not a statistical artifact that is simply the result of unobserved heterogeneity. In our 2010 article on the inverse relationship, for example, my coauthors and I looked at whether the inclusion of precise soil quality measurements (i.e., indicators such as soil pH, carbon, nitrogen, and potassium, as well as the breakdown of each plot in terms of clay, silt, and sand) explained the inverse relationship in a sample of rice plots in Madagascar. It turns out that the omission of those precise measurements does not cause the apparent inverse relationship.

Enter Bevis and Barrett. In their new paper, they manage to “make the inverse relationship go away,” i.e., they find that elusive x-factor which looks like it might explain why we see an inverse relationship in the data. In this case, it looks as though the inverse relationship is cause by “edge effects,” whereby farmers work harder along the edges than they do in the middle of their plots (though biophysical effects, such as different levels of nutrients around the edges, cannot be ruled out).

Leah Bevis dedicated a post to the paper over at Economics that Really Matters:

[W]e propose and test a new mechanism: the edge effect. A vast agronomy literature documents the fact that sunlight, biodiversity, water, and other inputs may differ around the edges of a plot, making this section more productive than the interior of the plot. Additionally, the edge of a plot may be more visible or more accessible to a farmer, changing his or her awareness of and management of this space. Behavioral economics research illustrates that individuals change food consumption behavior based on information about portion size or based on visual cues about portion size. We hypothesize that farmers similarly change crop or soil management based on their awareness of plot size.

If plots are more productive around the edges, then smaller plots will be more productive as they will have a higher edge-to-interior ratio, as pictured to the right. Interested readers can see our full paper for the math; we control for this effect by controlling for the perimeter-area ratio. Once we control for this ratio, the inverse size productivity relationship disappears completely; in these Uganda data the inverse relationship is driven entirely by the edge effect, namely that plots are more productive around their perimeter.

If it holds up to reviewer scrutiny (and having read and commented on the paper, I see no reason why it would not), this is a very important finding, seeing as to how it might help resolve an old puzzle in development economics.