Dealing with corner solutions in multi-crop micro-econometric models: an endogenous regime approach with regime fixed costs

Corner solution problems are pervasive in micro-econometric acreage choice models because farmers rarely produce the same crop set in a considered sample. These crop choice problems raise significant modelling issues. The main aim of this paper is to propose an endogenous regime switching model specifically designed for empirically modeling acreage choices with corner solutions. Contrary to models based on censored regression systems that have been used until now, this model is fully coherent from a micro-economic point of view. It also includes regime fixed costs accounting for unobserved costs which only depend on the set of crops grown simultaneously. We illustrate the empirical tractability of this model by estimating an endogenous regime switching multi-crop model for a panel dataset of French farmers. The estimated model considers yield supply, input demand and acreage share models for 7 crops and considers 8 production regimes. It also accounts for unobserved heterogeneity in farmers' behaviors through the specification of random parameters. We assume that most model – intercept and slope – parameters are farmer specific and estimate their distribution across the farmers' population represented by our sample. We compute the Maximum Likelihood estimator of the parameter vector of our model by relying on a specifically designed Stochastic Approximate Expectation–Maximization algorithm. Our results show that farmers' production acreage choice mechanisms strongly depend on the production regime in which this choice takes place and that regime changes underlie a large part of the acreage changes of minor crops.