La programmation mathématique positive dans les modèles d'exploitation agricole. Principes et importance du calibrage

Abstract

Positive mathematical programming in agricultural economics. Principles and importance of calibrating. The modelling of agricultural producer behaviour using mathematical programming has a long tradition in agricultural economics. The linear mathematical programming approach has been prevalent in this field for a long time. But linear programming models, that are tightly constrained to reproduce agricultural producers' choices observed at the base period, are often unacceptable and also inappropriate under policy changes. Several researchers have alluded to this problem in the past and came up with several solutions such as incorporating risk or considering "flexibility" constraints. Furthermore, to solve this problem, new methodological developments also occurred, including Positive Mathematical Programming (PMP). PMP emerged more than ten years ago but its formal presentation is relatively recent. In this article, we first present the principles of PMP, using a simple example of an arable crop producer. It appears that the two main advantages of PMP are its perfect calibration to base period levels of endogenous variables and its derivation of smooth simulation results, both resulting from the incorporation of non linear terms in the objective function. Empirical implications of the standard PMP' s parameter calibration process are then discussed.