Moment Estimation of the Probit Model with an Endogenous Continuous Regressor

15 Pages Posted: 28 May 2020

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: March 2017

Abstract

We propose a generalized method of moments (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 neighbour (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 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.

Suggested Citation

Kawaguchi, Daiji and Matsushita, Yukitoshi and Naito, Hisahiro, Moment Estimation of the Probit Model with an Endogenous Continuous Regressor (March 2017). The Japanese Economic Review, Vol. 68, Issue 1, pp. 48-62, 2017, Available at SSRN: https://ssrn.com/abstract=3607421 or http://dx.doi.org/10.1111/jere.12091

Daiji Kawaguchi (Contact Author)

University of Tokyo - Graduate School of Economics ( email )

Tokyo
Japan

Yukitoshi Matsushita

Tokyo Institute of Technology ( email )

Japan

Hisahiro Naito

University of Tsukuba ( email )

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

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