Maximum Simulated Likelihood Estimation of Consumer Demand Systems with Binding Non-Negativity Constraints

This paper proposes a maximum simulated likelihood estimator (MSLE) for demand systems with many binding non-negative constraints. Our study shows that the econo-metric implementation of the MSLE avoids high-dimensional integration. We have demonstrated the feasibility of the maximum simulated likelihood (MSL) approach for the linear expenditure system (LES) with non-negativity constraints. The results of a seven-goods demand system are presented. Direct simulation methods as in some simulation methods of moments and simulated pseudo-likelihood methods that require 1 the simulation of demand quantities subject to non-negativity constraints for each consumer in the sample are computationally expensive. The MSL approach avoids solving for simulated demand quantities since the likelihood function is conditional on observed demand quantities. In the MSL approach, only the likelihood function needs to be simulated.