Simulated Maximum Likelihood Estimation of the Linear Expenditure System with Binding Non-Negativity Constraints

Chihwa Kao

Lung-fei Lee
and   Mark M. Pitt

This paper discusses issues on the estimation of consumer demand equations subject to binding non-negative constraints. We propose computationally feasible specifications and a simulated maximum likelihood (SML) method for demand systems. Our study shows that the econometric implementation of the SML estimates can avoid high-dimensional integration problems. As contrary to the simulation method of moments and simulated pseudo-likelihood methods that require the simulation of demand quantities subject to non-negativity constraints for consumers in the sample, the SML approach requires only simulation of the likelihood function. The SML approach avoids solving for simulated demand quantities because the likelihood function is conditional on observed demand quantities.

We have applied SML approach for the linear expenditure system (LES) with non-negativity constraints. The results of a seven-goods demand system are presented. The results provide empirical evidence on the importance of taking into account possible cross equation correlations in disturbances.

Key Words: Simulated likelihood; Linear expenditure system; Non-negativity constraints; Multivariate censored variables; Nonlinear simultaneous equations.
JEL Classification Numbers: C15, C34, D12.