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An Estimator for Some Binary-Outcome Selection Models Without Exclusion Restrictions

Published online by Cambridge University Press:  04 January 2017

Anne E. Sartori
Anne E. Sartori*
Affiliation:
Department of Politics, Princeton University, Corwin Hall, Princeton, NJ 08544-1012. e-mail: asartori@princeton.edu
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Abstract

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This article provides a new maximum-likelihood estimator for selection models with dichotomous dependent variables when identical factors affect the selection equation and the equation of interest. Such situations arise naturally in game-theoretic models where selection is typically nonrandom and identical explanatory variables influence all decisions under investigation. When identical explanatory variables influence selection and a subsequent outcome of interest, the commonly used Heckman-type estimators identify from distributional assumptions about the residuals alone. When its own identifying assumption is reasonable, the new estimator allows the researcher to avoid the painful choice between identifying from distributional assumptions alone and adding a theoretically unjustified variable to the selection equation in a mistaken attempt to “boost” identification. The article uses Monte Carlo methods to compare the small-sample properties of the estimator with those of the Heckman-type estimator and ordinary probit.

Information

Type
Research Article
Information
Political Analysis , Volume 11 , Issue 2 , Spring 2003 , pp. 111 - 138
Copyright
Copyright © Political Methodology Section of the American Political Science Association 2003 

References

Achen, C. H. 1986. The Statistical Analysis of Quasi-Experiments. Berkeley: University of California Press.Google Scholar
Amemiya, T. 1985. Advanced Econometrics. Cambridge, MA: Harvard University Press.Google Scholar
Bellman, R. 1960. Introduction to Matrix Analysis. New York: McGraw-Hill.Google Scholar
Berinsky, A. 1999. “The Two Faces of Public Opinion.” American Journal of Political Science 43:1209–1230.Google Scholar
Boehmke, F. J. 2003. “Using Auxiliary Data to Estimate Selection Bias Models, with an Application to Interest Groups' Use of the Direct Initiative Process.” Political Analysis in press.Google Scholar
Brehm, J. 1993. The Phantom Respondents: Opinion Surveys and Political Representation. Ann Arbor: University of Michigan Press.Google Scholar
Dubin, J. A., and Rivers, D. 1990. “Selection Bias in Linear Regression, Logit and Probit Models.” In Modern Methods of Data Analysis, eds. Fox, J., and Long, J. S. Newbury Park, CA: Sage, pp. 410–443.Google Scholar
Greene, W. H. 1993. Econometric Analysis, 2nd ed. New York: Macmillan.Google Scholar
Heckman, J. J. 1974. “Shadow Prices, Market Wages, and Labor Supply.” Econometrica 42:679–694.Google Scholar
Heckman, J. J. 1976. “The Common Structure of Statistical Models of Truncation, Sample Selection, and Limited Dependent Variables and a Simple Estimator for Such Models.” The Annals of Economic and Social Measurement 5(4): 475–492.Google Scholar
Heckman, J. J. 1979. “Sample Selection Bias as a Specification Error.” Econometrica 47:153–161.Google Scholar
Huber, P. J. 1967. “The Behavior of Maximum-Likelihood Estimates under Nonstandard Conditions.” In Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1. eds. Le Cam, L. M., and Neyman, J. Berkeley: University of California Press, pp. 221–233.Google Scholar
King, G. 1990. Unifying Political Methodology. Cambridge: Cambridge University Press.Google Scholar
Lemke, D., and Reed, W. 2001. “War and Rivalry among Great Powers.” American Journal of Political Science 45:457–469.Google Scholar
Lewis, J. B., and Schultz, K. A. 2003. “Revealing Preferences: Empirical Modeling of a Crisis Bargaining with Incomplete Information.” Manuscript.Google Scholar
Maddala, G. 1999. Limited-dependent and Qualitative Variables in Econometrics. Cambridge: Cambridge University Press.Google Scholar
Mitchell, N. J., Hansen, W. L., and Jepsen, E. M. 1997. “The Determinants of Domestic and Foreign Corporate Political Activity.” The Journal of Politics 59:1096–1113.Google Scholar
Pakes, A., and Pollard, D. 1989. “Simulation and the Asymptotics of Optimization Estimators.” Econometrica 57:1027–1057.Google Scholar
Reed, W. 2000. “A Unified Statistical Model of Conflict Onset and Escalation.” American Journal of Political Science 44:84–93.Google Scholar
Sartori, A. E. 2002. “Enduring Facts about Enduring Rivals.” Presented at the Annual Meeting of the American Political Science Association, Boston.Google Scholar
Signorino, C. S. 1999. “Strategic Interaction and the Statistical Analysis of International Conflict.” American Political Science Review 92:279–297.Google Scholar
Signorino, C. S. 2002. “Strategy and Selection in International Relations.” International Interactions 28:93–115.Google Scholar
Simon, C. P., and Blume, L. 1994. Mathematics for Economists. New York: W. W. Norton.Google Scholar
Smith, A. 1998. “A Summary of Political Selection: The Effect of Strategic Choice on the Escalation of International Crises.” American Journal of Political Science 42:698–702.Google Scholar
Van de Ven, W. P., and Van Praag, B. 1981. “The Demand for Deductibles in Private Health Insurance.” Journal of Econometrics 17:229–252.Google Scholar