The bivariate probit model, maximum likelihood estimation, pseudo true parameters and partial identification
This paper presents an examination of the finite sample performance of likelihood based estimators derived from different functional forms. We evaluate the impact of functional form miss specification on the performance of the maximum likelihood estimator derived from the bivariate probit model. We also investigate the practical importance of available instruments in both cases of correct and incorrect distributional specifications. We analyze the finite sample properties of the endogenous dummy variable and covariate coefficient estimates, and the correlation coefficient estimates, and we examine the existence of possible "compensating effects" between the latter and estimates of parametric functions such as the predicted probabilities and the average treatment effect. Finally, we provide a bridge between the literature on the bivariate probit model and that on partial identification by demonstrating how the properties of likelihood based estimators are explicable via a link between the notion of pseudo true parameter values and the concepts of partial identification.
Journal of Econometrics