17 - Coherency and Maximum Likelihood Estimation in Demand Systems with Binding Inequality Constraints

Abstract

This chapter discusses the coherency and maximum likelihood estimation in demand systems with binding inequality constraints. In modeling microeconomic phenomena, economists usually assume - either out of habit, by lack of alternatives or out of conviction - that agents maximize or minimize something. If the restrictions implied by utility theory are not rejected by the data, the model may be used not only for investigating the behavioural effects of changes in exogenous variables, but also to study their welfare effects. The more recent microeconometric literature exhibits an increasing degree of complexity as a result of taking into account aspects such as non-linear or non-convex budget constraints, rationing, corner solutions and endogenous switching regimes. This chapter points out some potential problems that may arise in the empirical use of demand systems with inequality constraints. A first conclusion that can be drawn is that in the case of a model with corner solutions, non-linear budget constraints, rationing, etc. the model is likely to be incoherent for at least some parameter values and some range of exogenous variables. Coherency is guaranteed if the direct utility function is globally concave and the budget set is convex.