Endogenous Regressors in Nonlinear Probability Models: A Generalized Structural Equation Modeling Approach

Endogeneity of explanatory variables is a common problem in many areas of social sciences. Ironically, there seems to be a gap between being aware of the problem and knowing how best to handle it. The problem is exacerbated when the outcome variable of interest is categorical and thus non-linear probability models are involved. The study fills the gap by first distinguishing two main sources of endogeneity, including unmeasured confounders (＂latent factors＂) and measured but omitted causes (＂endogenous mediators＂), and then proposing an integrated approach to confront the two problems simultaneously. This strategy generalizes structural equation models to categorical outcome by including a shared latent factor between correlated error terms to tackle unobserved confounders, on the one hand, and extending mediation analysis to deal with potentially endogenous discrete mediators, on the other hand. For illustrative purpose, this proposed modeling strategy is presented with an example of heated debates in economic voting literature concerning the possible endogeneity of voters' economic perceptions.