A computationally fast estimator for semiparametric multinomial choice model

Abstract

In this article, based on cyclical monotonicity moment inequalities implied by the random utility choice model, we propose a computationally fast estimator for semiparametric multinomial choice models. The term semiparametric refers to the fact that we do not specify a particular functional form for the error term in the random utility function. The proposed estimators are consistent. Comparing with the estimators developed by the cyclic monotonicity method, simulations show the estimators we proposed have great advantages on the running time.

Keywords:

• Discrete choice models
• fixed effect
• individual heterogeneity
• semiparametric

Acknowledgment

The authors thank the anonymous referee and the editor for their useful comments and suggestions on an earlier version of this manuscript which resulted in this improved version.

Notes

1 Equation (11) also implies that $E[({\mathit{\beta }}^{\prime }△{\mathit{X}}_i\ast △{\mathit{Y}}_i)\ast g({\mathit{X}}_{i1},{\mathit{X}}_{i2})]\ge 0$ for $g(·)$ being any positive function of $({\mathit{X}}_{i1},{\mathit{X}}_{i2}),$ and we thank the reviewer for pointing out this result.