The power-law distribution of agricultural land size*

Power-law distributions explain a variety of natural and man-made processes spanning various disciplines including economics and finance. This paper demonstrates that the distribution of agricultural land size in the United States is best described by a power-law distribution. Maximum likelihood estimation is carried out using county-level data of over 3000 observations gathered at five-year intervals by the USDA Census of Agriculture. Our analysis indicates that U.S. agricultural land size is heavy-tailed, that variance estimates generally do not converge, and that the top 5% of agricultural counties account for about 25% of agricultural land between 1997 and 2012. The goodness of fit of power-law distribution is evaluated using likelihood ratio tests and regression-based diagnostics. The power-law distribution of farm size has important implications for the design of more efficient regional and national agricultural policies as counties close to the mean account for little of the cumulative distribution of total agricultural land.