Mixture models for U.S. agricultural land and its growth rate

Farm size distributions are central to empirical research, agricultural policy, and farm management. Yet, a clear consensus on the appropriate parametric distribution for farm sizes remains elusive, leading applied work to rely on ad hoc modeling choices. To address this gap, we analyze U.S. county-level agricultural land sizes and their growth rates from 1997 to 2017 using rigorous parametric density estimation techniques. Our results show that the parametric distributions conventionally used in the literature do not provide plausible fits across the full support of the data. Among standard probability distributions not previously considered, the Burr family performs reasonably well for farm sizes, though only for select years and specific measures of agricultural land. In contrast, several mixture distributions – 3-, 4-, and 5-component normal mixtures for farm sizes, and 4- and 5-component normal mixtures as well as 2- and 3-component Student's t mixtures for growth rates – can plausibly characterize the empirical distributions across time and across different types of agricultural land. Given this evidence, policies and discussions concerning farm size and structure may need to be refined and refocused.