The paper introduces a general methodological approach for the estimation of constrained optimisation models in agricultural supply analysis. It is based on optimality conditions of the desired programming model and shows a conceptual advantage compared with Positive Mathematical Programming in the context of well-posed estimation problems. Moreover, it closes the empirical and methodological gap between programming models and duality-based models with explicit allocation of fixed factors. Monte Carlo simulations are performed with a maximum entropy estimator to evaluate the functionality of the approach as well as the impact of empirically relevant prior information with small samples. Copyright 2003, Oxford University Press.