Title:      Endogeneity in Probit Response Models

Authors:    David Freedman, Jasjeet Sekhon

Entrydate:  2008-05-28 22:53:51

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

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 identifable;
these results appear to be new.

http://polmeth.wustl.edu/retrieve.php?id=747

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