Two-Stage Estimation of Nonrecursive Choice Models

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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.

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