Leah Bevis is a PhD candidate at Cornell’s Dyson School, and beginning as an assistant professor at Ohio State University in the fall.
It has long been observed—in Africa, Latin America, Europe, and Asia—that smaller farms produce more per acre than larger farms, all else held constant. This is odd; within a functioning market system high marginal productivity farmers should purchase or rent inputs from low marginal productivity farmers, until the marginal returns to all factors equalizes across farms. The fact that land appears to be systematically more productive for smaller farmers has generated decades of speculation and academic research, from Chayanov’s 1921 observations on peasant farmers in Russia, to Sen’s work on smallholder farmers in India, and Kagin and coauthors’ recent JDS article on Mexican farmers.
Remarkably, with almost 100 years of investigation into the topic, no consensus has been reached on the mechanism driving this inverse relationship. In a new working paper we’ll present at the Midwest Development Conference, Christopher Barrett and I examine a new mechanism that appears to completely explain the inverse relationship in data from Uganda. We find that higher marginal productivity around the edges of plots—the “edge effect”—drives smaller plots to be more productive than larger plots. We also present suggestive evidence for a behavioral mechanism driving this effect: farmers investing greater quantities of labor around the highly visible, highly accessible plot edges.
Resolution of the inverse size productivity puzzle has long been complicated by the fact that few datasets are well suited to provide well-identified estimates of the inverse relationship. We estimate the inverse size productivity relationship for the very first time, to our knowledge, with plot fixed effects. Having plot-level data from both 2003 and 2013, we match plots over time using GPS coordinates. So while each plot has changed slightly over the decade in terms of the crops produced, productivity, management practices, inputs, and the precise size and shape, plot fixed effects allow us to control for time invariant characteristics such as a plot’s position on the landscape, distance from houses or roads, slope, etc.
We first show that the inverse relationship actually exists at the plot level, rather than the household level. Household-specific shadow prices cannot, therefore, drive the relationship. Confirming results by Carletto, Savastano and Zezza (2013), we also show that the relationship is stronger when plot size is measured with GPS rather than estimated by farmers; i.e., measurement error is not the culprit. We also control for plot-level soil fertility and a host of other time-varying characteristics, and the inverse relationship is not mitigated. (Barrett, Bellemare and Hou (2010) similarly find the inverse relationship impervious to soil fertility.) So, none of the traditionally considered mechanisms explain the inverse relationship.
Instead, we 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.
The next question, of course, is that of mechanism — why are plot edges more productive than plot interiors? We find no evidence for biophysical mechanisms (e.g., differences in sunlight, water, and nutrients), but given data constraints we cannot rule them out either.
We can, however, investigate a behavioral mechanism, that of farmer labor inputs. We find that labor intensity rises with perimeter-area ratio, just as productivity does. It seems, therefore, that farmers are more likely to invest greater resources in the edges of their plots for reasons related to spatial awareness or accessibility. (We also provide additional evidence that purely behavioral mechanisms—farmer’s misperception of plot size—can influence plot productivity.)
While we cannot speak to the external validity of our findings, these results (full paper here) suggest that a behavioral mechanism, namely farmers’ increased attention to and investment in the edges of plots, may explain much or all of the inverse size productivity ratio in many contexts.