The authors propose an estimation procedure dealing with multivariate selection and dynamics in land choice and unobserved heterogeneity in structural and crop selection equations. The method is applied to a multi-output profit function with multiple corner solutions and farm-level panel data. Estimation results reveal that the single selection rule associated with the Tobit procedure is rejected in favor of our multivariate selection treatment. Inconsistent estimates are expected with the Tobit procedure, or if farmer fixed effects are omitted, which can have important consequences for policy recommendations, as illustrated in an evaluation of nitrogen runoff elasticities with respect to economic variables.