Composite Likelihood Estimation of an Autoregressive Panel Ordered Probit Model with Random Effects

Modeling and estimating autocorrelated discrete data can be challenging. In this paper, we use an autoregressive panel ordered probit model where the serial correlation in the discrete variable is driven by the autocorrelation in the latent variable. In such a nonlinear model, the presence of a lagged latent variable results in an intractable likelihood containing high-dimensional integrals. To tackle this problem, we use composite likelihoods that involve a much lower order of integration. However, parameter identification might potentially become problematic since the information employed in lower dimensional distributions may not be rich enough for identification. Therefore, we characterize types of composite likelihoods that are valid for this model and study conditions under which the parameters can be identified. Moreover, we provide consistency and asymptotic normality results for two different composite likelihood estimators and conduct Monte Carlo studies to assess their finite-sample performances. Finally, we apply our method to analyze corporate bond ratings.