On Dual Approaches to Demand Systems Estimation in the Presence of Binding Quantity Constraints

TLDR: It is demonstrated that the more commonly used approach for treating binding non-negativity constraints is incompatible with economic theory and thus produces inconsistent estimates of price response, and a numerical integration approach is presented that facilitates direct maximum likelihood estimation for some problems.

Abstract: Binding quantity constraints, especially non-negativity constraints, appear frequently in micro-level data sets. Two dual approaches to demand systems estimation in the presence of binding non-negativity constraints are reviewed. It is demonstrated that, in a demand systems context, the more commonly used approach for treating binding non-negativity constraints is incompatible with economic theory and thus produces inconsistent estimates of price response. Furthermore, Monte Carlo experiments indicate that bias can be substantial even if limit observations comprise a relatively small portion of the sample. The alternative, a direct maximum likelihood estimation approach, has desirable properties; however, analytical and computational difficulties severely hamper application. The numerical integration approach, employed here for direct maximum likelihood estimation, is presented. It is believed that this integration approach facilitates direct maximum likelihood estimation for some problems. Nevertheless, the ability to estimate complex demand systems remains constrained.