## The Inverse Farm Size–Productivity Relationship: “Proof” that Smallholders Can Feed the World?

I spent the last week in Montreal for the McGill Global Food Security Conference, where I had been asked to present some of the work I have been doing on food prices.

The conference was very interesting, and it allowed me to finally meet colleagues whom I only knew through their work, meet new colleagues, and interact with a number of students interested in food policy.

At some point, however, one of the presenters mentioned the inverse relationship between farm size (i.e., the amount of land a farmer cultivates) and productivity (i.e., the amount of output per unit of land a farmer can get, or that farmer’s yield), an empirical regularity in the developing world which constitutes an old puzzle in development economics and on which I have done some work a few years ago. The following figure is an example of such a relationship for rice farms in Madagascar — the y-axis measures the logarithm of a plot’s yield in kilograms of rice for one hundredth of a hectare, and the x-axis measures a plot’s size in hundredths of a hectare.

(Source: Barrett et al., 2010).

What that presenter said was that the existence of an inverse relationship between farm size and productivity is proof that smallholders can feed the world. Nothing, however, could be further from the truth.

Indeed, the inverse relationship between farm size (or plot size, since the inverse relationship has also been observed within farms) and productivity can be the result of three different things, none of which indicates that smaller farms should be relied upon for food security.

### Three Explanations for the Inverse Relationship

The first explanation for the inverse relationship has to do with market failures. In one of the earliest studies on the inverse relationship, for example, Sen (1966) posited that everything else equal, households whose farms were smaller simply had more labor per hectare than larger farms. Though the labor market can usually absorb surplus labor, high unemployment might push households whose farms are smaller to use more labor than is optimal on their farms, with the end result being that households whose farms are smaller will have higher yields.

The second explanation for the inverse relationship has to do with omitted variables. Most empirical researchers working on the inverse relationship do not have precise measures of soil quality (e.g., carbon, nitrogen, and potassium in the soil as well as soil pH). But since most people choose to cultivate good lands first and will tend to choose relatively worse lands as they increase the size of their farms, it is very likely that larger farms have lower soil quality on average. Once again, the end result is that larger farms appear less productive than smaller farms.

The third explanation for the inverse relationship has to do with measurement error. This happens when the size of a farmer’s landholdings is measured with error and that error is negatively correlated with the true size of a farmer’s landholdings. For example, if farmers consistently over-report the size of their landholdings (say, because land is a measure of prestige and political power, as in many developing countries), one would find a spurious inverse relationship between farm size and productivity.

In a 2010 World Development article on the inverse relationship, my coauthors and I had access to precise soil quality measurements for a sample of Malagasy farms. We found that those usually omitted soil quality measurements explain only a very small fraction of the observed inverse relationship and that market failures explain most (though not all) of it.

### Policy (Non)Implications

None of the explanations above mean that smallholders are in a better position to feed the world, and to claim otherwise is dangerous, as it leaves people with gravely mistaken beliefs about food security.

To see this, you only need to ask yourself whether you really believe that the key to improving food security and feeding the world lies in breaking up large farms into smaller ones.