Endogeneity in Probit Response Models

13 Pages Posted: 29 May 2008 Last revised: 4 Aug 2008

Date Written: May 29, 2008

Abstract

In this paper, we look at conventional methods for removing endogeneity bias in regression models, including the linear model and the probit model. The usual Heckman two-step procedure should not be used in the probit model: from a theoretical perspective, this procedure is unsatisfactory, and likelihood methods are superior. However, serious numerical problems occur when standard software packages try to maximize the biprobit likelihood function, even if the number of covariates is small. The log likelihood surface may be nearly flat, or may have saddle points with one small positive eigenvalue and several large negative eigenvalues. We draw conclusions for statistical practice. Finally, we describe the conditions under which parameters in the model are identifiable; these results appear to be new.

Keywords: Bivariate probit, sample selection, identification, indefinite Hessian, optimization

JEL Classification: C30, C35

Suggested Citation

Freedman, David A. and Sekhon, Jasjeet S., Endogeneity in Probit Response Models (May 29, 2008). Available at SSRN: https://ssrn.com/abstract=1138489 or http://dx.doi.org/10.2139/ssrn.1138489

David A. Freedman

University of California, Berkeley ( email )

Department of Statistics
Berkeley, CA 94720
United States
510-642-2781 (Phone)

Jasjeet S. Sekhon (Contact Author)

UC Berkeley ( email )

310 Barrows Hall
Berkeley, CA 94720
United States

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