The bivariate probit model, maximum likelihood estimation, pseudo true parameters and partial identification

This paper examines the notion of “identification by functional form” for two equation triangular systems for binary endogenous variables by providing a bridge between the literature on the recursive bivariate probit model and that on partial identification. We evaluate the impact of functional form on the performance of (quasi) maximum likelihood estimators, and investigate the practical importance of available instruments in both cases of correct and incorrect distributional specification. Finally, we calculate average treatment effect bounds and demonstrate how properties of the estimators are explicable via a link between the notion of pseudo-true parameters and the concepts of partial identification.