Econometric mathematical programming: an application to the estimation of costs and risk preferences at farm level

This study belongs to the barely explored research strand of “Econometric Mathematical Programming” and presents a simultaneous estimation of the cost function and of the farmers’ risk attitude parameter in a programming model setup. Resource and policy constraints of the model are allowed to be not binding. We use crop shares as decision variables to avoid scale bias and we consider price and crop yield variances separately. The model is formulated as a bi‐level programming model and the empirical application concerns three unbalanced panels of specialized arable farms observed for at least three consecutive years in Northern Italy, in the Cologne‐Aachen area in Germany and in the Grandes‐Cultures area in France over the time period 1995–2007. We achieve a quite satisfactory fit in the estimation exercise and find own and cross price elasticities from sensitivity experiments in reasonable ranges. We also propose a novel approach to derive confidence intervals around parameter estimates for Econometric Mathematical Programming.