Hostname: page-component-76fb5796d-dfsvx Total loading time: 0 Render date: 2024-04-25T06:59:24.268Z Has data issue: false hasContentIssue false
  • English
  • Français

Endogeneity in Probit Response Models

Published online by Cambridge University Press:  04 January 2017

David A. Freedman  and
Jasjeet S. Sekhon
David A. Freedman
Affiliation:
Department of Statistics, University of California, Berkeley, CA 94720-3860. e-mail: freedman@stat.berkeley.edu
Jasjeet S. Sekhon*
Affiliation:
Department of Political Science, University of California, Berkeley, CA 94720-1950
*
e-mail: sekhon@berkeley.edu (corresponding author)
Get access Rights & Permissions [Opens in a new window]

Abstract

We look at conventional methods for removing endogeneity bias in regression models, including the linear model and the probit model. It is known that the usual Heckman two-step procedure should not be used in the probit model: from a theoretical perspective, it 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. We draw conclusions for statistical practice. Finally, we prove the conditions under which parameters in the model are identifiable. The conditions for identification are delicate; we believe these results are new.

Type
Research Article
Information
Political Analysis , Volume 18 , Issue 2 , Spring 2010 , pp. 138 - 150
Copyright
Copyright © The Author 2010. Published by Oxford University Press on behalf of the Society for Political Methodology 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Authors' note: Derek Briggs, Allan Dafoe, Thad Dunning, Joe Eaton, Eric Lawrence, Walter Mebane, Jim Powell, Rocío Titiunik, and Ed Vytlacil made helpful comments. Errors and omissions remain the responsibility of the authors.

References

Angrist, J. D. 2001. Estimation of limited-dependent variable models with binary endogenous regressors: simple strategies for empirical practice. Journal of Business and Economic Statistics 19: 2–28(with discussion).CrossRefGoogle Scholar
Bhattacharya, J., Goldman, D., and McCaffrey, D. 2006. Estimating probit models with self-selected treatments. Statistics in Medicine 25: 389–413.CrossRefGoogle ScholarPubMed
Briggs, D. C. 2004. Causal inference and the Heckman model. Journal of Educational and Behavioral Statistics 29: 397–420.CrossRefGoogle Scholar
Bushway, S., Johnson, B. D., and Slocum, L. A. 2007. Is the magic still there? The use of the Heckman two-step correction for selection bias in criminology. Journal of Quantitative Criminology 23: 151–78.CrossRefGoogle Scholar
Copas, J. B., and Li, H. G. 1997. Inference for non-random samples. Journal of the Royal Statistical Society, Series B 59: 55–77.CrossRefGoogle Scholar
Dunning, T., and Freedman, D. A. 2007. Modeling selection effects. In The handbook of social science methodology, eds. Turner, Steven and Outhwaite, William, 225–31. London: Sage.Google Scholar
Freedman, D. A. 2005. Statistical models: theory and practice. New York: Cambridge University Press.CrossRefGoogle Scholar
Freedman, D. A. 2007. How can the score test be inconsistent? The American Statistician 61: 291–95.CrossRefGoogle Scholar
Heckman, J.J. 1978. Dummy endogenous variables in a simultaneous equation system. Econometrica 46: 931–59.CrossRefGoogle Scholar
Heckman, J.J. 1979. Sample selection bias as a specification error. Econometrica 47: 153–61.CrossRefGoogle Scholar
Meng, C., and Schmidt, P. 1985. On the cost of partial observability in the bivariate probit model. International Economic Review 26: 71–85.CrossRefGoogle Scholar
Mills, J. P. 1926. Table of the ratio: area to boundary ordinate, for any portion of the normal curve. Biometrika 18: 395–400.CrossRefGoogle Scholar
Muthen, B. 1979. A structural probit model with latent variables. Journal of the American Statistical Association 74: 807–11.Google Scholar
Ono, H. 2007. Careers in foreign-owned firms in Japan. American Sociological Review 72: 267–90.CrossRefGoogle Scholar
Rao, C. R. 1973. Linear statistical inference. 2nd ed. New York: Wiley.Google Scholar
Rivers, D., and Vuong, Q. H. 1988. Limited information estimators and exogeneity tests for simultaneous probit models. Journal of Econometrics 39: 347–66.CrossRefGoogle Scholar
Sekhon, J. S., and Mebane, W. R. Jr. 1998. Genetic optimization using derivatives: theory and application to nonlinear models. Political Analysis 7: 189–213.CrossRefGoogle Scholar
Stata. 2005. Stata base reference manual. Stata Statistical Software. Release 9. Vol. 1. College Station, TX: StataCorp LP.Google Scholar
Tong, Y. L. 1980. Probability inequalities in multivariate distributions. New York: Academic Press.Google Scholar
Van de Ven, W. P. M. M., and Van Praag, B. M. S. 1981. The demand for deductibles in private health insurance: a probit model with sample selection. Journal of Econometrics 17: 229–52.Google Scholar
Winship, C., and Mare, R. D. 1992. Models for sample selection bias. Annual Review of Sociology 18: 327–50.CrossRefGoogle Scholar
Yee, T. W. 2007. The VGAM package. http://www.stat.auckland.ac.nz/y͂ee/VGAM Google Scholar