Two-Stage Estimation of Non-Recursive Choice Models

Questions of causation are important issues in empirical research on political behavior. Most of the discussion of the econometric problems associated with multi-equation models with reciprocal causation has focused on models with continuous dependent variables (e.g. Markus and Converse 1979; Page and Jones 1979). Since many models of political behavior involve discrete or dichotomous dependent variables, this paper turns to two techniques which can be employed to estimate reciprocal relationships between dichotomous and continuous dependent variables. One technique which I call two-stage probit least squares (2SPLS) is very similar to familiar two-stage instrumental variable techniques. The second technique, called two-stage conditional maximum likelihood (2SCML), may overcome problems associated with 2SPLS, but has not been used in the political science literature. First I show the properties of both techniques using Monte Carlo simulations. Then, I apply these techniques to an empirical example which focuses 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