A bivariate ordered probit estimator with mixed effects

In this paper, we discuss the derivation and application of a bivariate ordered probit model with mixed effects. Our approach allows one to estimate the distribution of the effect (gamma) of an endogenous ordered variable on an ordered explanatory variable. By allowing gamma to vary over the population, our estimator offers a more flexible parametric setting to recover the causal effect of an endogenous variable in an ordered choice setting. We use Monte Carlo simulations to examine the performance of the maximum likelihood estimator of our system and apply this to a relevant example from the UK education literature.