COHERENCY AND REGULARITY OF DEMAND SYSTEMS WITH EQUALITY AND INEQUALITY CONSTRAINTS

In neoclassical structural models dealing with rationing, comer solutions, or nonlinear budget constraints, utility theory is more crucial than in traditional demand systems. If in these models negativity of the Slutsky matrix is violated, the models will in general not be coherent, in the sense that endogenous variables are not unambiguously determined. We show that not imposing coherency may yield inconsistent estimators. A general framework is sketched which allows for the analysis of the relation between coherency, regularity of preferences, and the stochastic specification of the model. We discuss sufficient conditions for regularity which can be imposed in estimation.