In this paper, persistent discrete data are modeled by Autoregressive Probit model and estimated by Composite Likelihood (CL) estimation. Autocorrelation in the latent variable results in an intractable likelihood function containing high dimensional integrals. CL approach offers a fast and reliable estimation compared to computationally demanding simulation methods. I provide consistency and asymptotic normality results of the CL estimator and use it to study the credit ratings. The ratings are modeled as imperfect measures of the latent and autocorrelated creditworthiness of firms explained by the balance sheet ratios and business cycle variables. The empirical results show evidence for rating assignment according to Through-the-cycle methodology, that is, the ratings do not respond to the short-term fluctuations in the financial situation of the firms. Moreover, I show that the ratings become more volatile over time, in particular after the crisis, as a reaction to the regulations and critics on credit rating agencies.
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