EM algorithms for ordered probit models with endogenous regressors

We propose an EM algorithm to estimate ordered probit models with endogenous regressors. The proposed algorithm has a number of computational advantages in comparison to direct numerical maximization of the (limited information) log-likelihood function. First, the sequence of conditional M(aximization)-steps can all be computed analytically. Second, the algorithm updates the model parameters so that positive definiteness of the covariance matrix and monotonicity of cutpoints are naturally satisfied. Third, the variance parameters normalized for identification can be activated to accelerate convergence of the algorithm. The algorithm can be applied to models with dummy endogenous, continuous endogenous or latent endogenous regressors. A small Monte Carlo simulation experiment examines the finite sample performance of the proposed algorithms.