Movers and stayers in the farming sector: accounting for unobserved heterogeneity in structural change

This article compares the respective performance of the mover-stayer model (MSM) and the Markov chain model (MCM) to investigate whether accounting for unobserved heterogeneity in the rate of movements of farms across size categories improves the representation of the transition process. The MCM has become a popular tool in agricultural economics research to describe how farms experience structural change and to study the impact of the various drivers of this process, including public support. Even though some studies have accounted for heterogeneity across farms by letting transition probabilities depend on covariates depicting characteristics of farms and/or farmers, only observed heterogeneity has been considered so far. Assuming that structural change may also relate to unobserved characteristics of farms and/or farmers, we present an implementation of the MSM which considers a mixture of two types of farms: the `stayers' who always remain in their initial size category and the `movers' who follow a first-order Markovian process. This modeling framework relaxes the assumption of homogeneity in the transition process which the basis of the usual MCM. Then, we explain how to estimate the model using likelihood maximization and the expectation-maximization (EM) algorithm. An empirical application to a panel of French farms over 2000-2013 shows that the MSM outperforms the MCM in recovering the underlying year-on-year transition process as well as in deriving the longrun transition matrix and predicting the future distribution of farm sizes