Moment Estimation of the Probit Model with an Endogenous Continuous Regressor

Daiji Kawaguchi, Yukitoshi Matsushita and Hisahiro Naito

Tsukuba Economics Working Papers from Faculty of Humanities and Social Sciences, University of Tsukuba

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.

Date: 2015-12
New Economics Papers: this item is included in nep-ecm
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Related works:
Journal Article: Moment Estimation of the Probit Model with an Endogenous Continuous Regressor (2017)
Journal Article: Moment Estimation of the Probit Model with an Endogenous Continuous Regressor (2017)
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