Binary outcomes and endogenous explanatory variables: tests and solutions with an application to the demand for...

Many demographic studies examine discrete outcomes, and researchers often suspect that some of the explanatory variables may be influenced by the same unobserved factors that determine the discrete outcome under examination. In linear models, the standard solution to this potential endogeneity bias is an estimator such as two-stage least squares. These methods have been extended to models with limited dependent variables, but there is little information on the performance of the methods in the types of data sets typically used in demographic research. This paper helps to fill this gap. It describes a simple analytic framework for estimating the effects of explanatory variables on discrete outcomes, which controls for the potential endogeneity of explanatory variables. It also discusses tests for exogeneity and joint determination of the outcomes and the explanatory variables. It summarizes the results of a Monte Carlo study of the performance of these techniques and uses these results to suggest how researchers should approach these problems in practice. We apply these methods to the examination of the impact of fertility intentions on contraceptive use, based on data from the 1988 Tunisia Demographic and Health Survey.