Endogenous variables in non-linear models with mixed effects: Inconsistence under perfect identification conditions?

This paper examines the consequences of introducing a normally distributed effect into a system where the dependent variable is ordered and the explanatory variable is ordered and endogenous. Using simulation techniques we show that a naive bivariate ordered probit estimator which fails to take a mixed effect into account will result in inconsistent estimates even when identification conditions are optimal. Our results suggest this finding only applies to non-linear endogenous systems.