The most extreme events, such as economic crises, are rare but often have a great impact. It is difficult to precisely determine the likelihood of such events because the sample is small.
Modeling and estimating persistent discrete data can be challenging. In this paper, we use an autoregressive panel probit model where the autocorrelation in the discrete variable is driven by the autocorrelation in the latent variable. In such a non-linear model, the autocorrelation in an unobserved variable results in an intractable likelihood containing high-dimensional integrals.