Hostname: page-component-76fb5796d-2lccl Total loading time: 0 Render date: 2024-04-25T11:36:03.228Z Has data issue: false hasContentIssue false
  • English
  • Français

Two-Stage Estimation of Nonrecursive Choice Models

Published online by Cambridge University Press:  04 January 2017

R. Michael Alvarez  and
Garrett Glasgow
R. Michael Alvarez
Affiliation:
California Institute of Technology
Garrett Glasgow
Affiliation:
California Institute of Technology
Get access Rights & Permissions [Opens in a new window]

Abstract

Questions of causation are important issues in empirical research on political behavior. Most of the discussion of the econometric problems associated with multiequation models with reciprocal causation has focused on models with continuous dependent variables (e.g., Markus and Converse 1979; Page and Jones 1979). Yet, many models of political behavior involve discrete or dichotomous dependent variables; this paper describes two techniques which can consistently estimate reciprocal relationships between dichotomous and continuous dependent variables. The first, two-stage probit least squares (2SPLS), is very similar to two-stage instrumental variable techniques. The second, two-stage conditional maximum likelihood (2SCML), may overcome problems associated with 2SPLS, but has not been used in the political science literature. We demonstrate the potential pitfalls of ignoring the problems of reciprocal causation in nonrecursive choice models and examine the properties of both techniques using Monte Carlo simulations: we find that 2SPLS slightly outperforms 2SCML in terms of bias but that 2SCML produces more accurate standard errors. However, the 2SCML model offers an explicit statistical test for endogeneity. The results from our simulations, and the statistical test for exogeneity, lead us to advocate the use of 2SCML for estimation of this class of causal models. We then apply both of these techniques to an empirical example focusing on the relationship between voter preferences in a presidential election and the voter's uncertainty about the policy positions taken by the candidates. This example demonstrates the importance of these techniques for political science research.

Type
Research Article
Information
Political Analysis , Volume 8 , Issue 2 , 16 December 1999 , pp. 147 - 165
Copyright
Copyright © 1999 by 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.)

References

Achen, C. H. 1986. The Statistical Analysis of Quasi-Experiments. Berkeley: University of California Press.CrossRefGoogle Scholar
Aldrich, J. H., and Nelson, F. D. 1984. Linear Probability, Logit, and Probit Models. Beverly Hills, CA: Sage.CrossRefGoogle Scholar
Aldrich, J. H., Niemi, R. G., Rabinowitz, G., and Rohde, D. W. 1982. “The Measurement of Public Opinion About Public Policy: A Report on Some New Issue Question Formats.” American Journal of Political Science 26: 391–414.Google Scholar
Alvarez, R. M. 1998. Information and Elections, Revised to Include the 1998 Presidential Election. Ann Arbor: University of Michigan Press.Google Scholar
Alvarez, R. M., and Butterfield, T. L. 1999a. “The Resurgence of Nativism in California? The Case of Proposition 187 and Illegal Immigration,” Manuscript. Pasadena: California Institute of Technology.Google Scholar
Alvarez, R. M., and Butterfield, T. L. 1999b. “The Revolution Against Affirmative Action in California: Politics, Economics and Proposition 209,” Manuscript. Pasadena: California Institute of Technology.Google Scholar
Alvarez, R. M., and Franklin, C. H. 1994. “Uncertainty and Political Perceptions.” Journal of Politics 56: 671–688.CrossRefGoogle Scholar
Amemiya, T. 1978. “The Estimation of a Simultaneous Equation Generalized Probit Model.” Econometrica 46: 1193–1205.CrossRefGoogle Scholar
Bartels, L. M. 1986. “Issue Voting Under Uncertainty: An Empirical Test.” American Journal of Political Science 30: 709–728.Google Scholar
Beck, N., and Katz, J. N. 1995. “What to Do (and Not to Do) With Time-Series Cross-Section Data.” American Political Science Review 89: 634–647.CrossRefGoogle Scholar
Brehm, J. 1993. The Phantom Respondents. Ann Arbor: University of Michigan Press.Google Scholar
Caldeira, G. A., and Wright, J. R. 1998. “Lobbying for Justice: Organized Interests, Supreme Court Nominations, and the United States Senate.” American Journal of Political Science 42: 499–523.Google Scholar
Campbell, J. E. 1983. “Ambiguity in the Issue Positions of Presidential Candidates: A Causal Analysis.” American Journal of Political Science 27: 284–293.Google Scholar
Downs, A. 1957. An Economic Theory of Democracy. New York: Harper and Row.Google Scholar
Enelow, J. M., and Hinich, M. J. 1984. The Spatial Theory of Voting. New York: Cambridge University Press.Google Scholar
Fiorina, M. P. 1981. Retrospective Voting in American National Elections. New Haven, CT: Yale University Press.Google Scholar
Fiske, S. T., and Pavelchak, M. A. 1986. “Category-Based versus Piecemeal-Based Affective Responses: Developments in Schema-Triggered Affect.” In The Handbook of Motivation and Cognition, Sorrentino, R. M. and Higgins, E. T., eds. New York: Guilford Press.Google Scholar
Franklin, C. H. 1991. “Eschewing Obfuscation? Campaigns and the Perceptions of U.S. Senate Incumbents.” American Political Science Review 85: 1193–1214.CrossRefGoogle Scholar
Franklin, C. H., and Jackson, J. E. 1983. “The Dynamics of Party Identification.” American Political Science Review 77: 957–973.Google Scholar
Graber, D. A. 1988. Processing the News. White Plains, NY: Longman.Google Scholar
Hanushek, E. A., and Jackson, J. E. 1977. Statistical Methods for Social Scientists. New York: Academic Press.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.” Annals of Economic and Social Measurement 5: 475–492.Google Scholar
Heckman, J. J. 1979. “Sample Selection Bias as a Specification Error.” Econometrica 47: 153–161.CrossRefGoogle Scholar
Jacobson, G. C., and Kernell, S. 1981. Strategy and Choice in Congressional Elections. New Haven, CT: Yale University Press.Google Scholar
King, G. 1989. Unifying Political Methodology. Cambridge: Cambridge University Press.Google Scholar
Lazarsfeld, P., Berelson, B., and Gaudet, H. 1944. The People's Choice. New York: Columbia University Press.Google Scholar
Maddala, G. S. 1983. Limited-Dependent and Qualitative Variables in Econometrics. Cambridge: Cambridge University Press.Google Scholar
Markus, G. B., and Converse, P. E. 1979. “A Dynamic Simultaneous Equation Model of Electoral Choice.” American Political Science Review 73: 1055–1070.Google Scholar
McCullagh, P., and Nelder, J. A. 1983. Generalized Linear Models, 2nd ed. London: Chapman and Hall.Google Scholar
Page, B. I., and Jones, C. 1979. “Reciprocal Effects of Policy Preferences, Party Loyalties and the Vote.” American Political Science Review 73: 1071–1089.Google Scholar
Patterson, T. C. 1980. The Mass Media Election. New York: Praeger.Google Scholar
Rahn, W. M. 1990. Perception and Evaluation of Political Candidates: A Social-Cognitive Perspective, Ph.D. dissertation. Minneapolis: University of Minnesota.Google Scholar
Rivers, D., and Vuong, Q. H. 1988. “Limited Information Estimators and Exogeneity Tests for Simultaneous Probit Models.” Journal of Econometrics 39: 347–366.Google Scholar
Schotz, J. T., and Lubell, M. 1998. “Trust and Taxpaying: Testing the Heuristic Approach to Collective Action.” American Journal of Political Science 42: 398–417.Google Scholar
Verba, S., and Nie, N. H. 1972. Participation in America. New York: Harper and Row.Google Scholar
Witcover, J. 1977. Marathon. New York: Viking Press.Google Scholar
Wolfinger, R. E., and Rosenstone, S. J. 1980. Who Votes? New Haven, CT: Yale University Press.Google Scholar