Moment Estimation of the Probit Model with an Endogenous Continuous Regressor

Japanese Economic Review, Forthcoming

38 Pages Posted: 4 Feb 2016

See all articles by Daiji Kawaguchi

Daiji Kawaguchi

University of Tokyo - Graduate School of Economics

Yukitoshi Matsushita

Tokyo Institute of Technology

Hisahiro Naito

University of Tsukuba

Date Written: December 2015

Abstract

We propose a GMM estimator with optimal instruments for a probit model that includes a continuous endogenous regressor. This GMM estimator incorporates the probit error and the heteroscedasticity of the error term in the first-stage equation in order to construct the optimal instruments. The estimator estimates the structural equation and the first-stage equation jointly and, based on this joint moment condition, is efficient within the class of GMM estimators. To estimate the heteroscedasticity of the error term of the first-stage equation, we use the k-nearest neighbor (k-nn) non-parametric estimation procedure. Our Monte Carlo simulation shows that in the presence of heteroscedasticity and endogeneity, our GMM estimator outperforms the two-stage conditional maximum likelihood (2SCML) estimator. Our results suggest that in the presence of heteroscedasticity in the first-stage equation, the proposed GMM estimator with optimal instruments is a useful option for researchers.

Keywords: Probit, Continuous endogenous regressor, Moment estimation

JEL Classification: C25

Suggested Citation

Kawaguchi, Daiji and Matsushita, Yukitoshi and Naito, Hisahiro, Moment Estimation of the Probit Model with an Endogenous Continuous Regressor (December 2015). Japanese Economic Review, Forthcoming, Available at SSRN: https://ssrn.com/abstract=2706994

Daiji Kawaguchi

University of Tokyo - Graduate School of Economics ( email )

Tokyo
Japan

Yukitoshi Matsushita

Tokyo Institute of Technology ( email )

Japan

Hisahiro Naito (Contact Author)

University of Tsukuba ( email )

Tennodai 1-1-1
Tsukuba City, Ibaraki Prefecture
Japan
81-29-853-7431 (Phone)

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