Forecasting credit ratings with the varying-coefficient model

The dynamic ordered varying-coefficient probit model (DOVPM) is proposed as a model for studying credit ratings. It is constructed by replacing the constant coefficients of firm-specific predictors in the dynamic ordered probit model (DOPM) of Blume, Lim and MacKinlay (1998) with the smooth functions of macroeconomic variables. Thus, the proposed model allows the effects of firm-specific predictors on credit risk to change with macroeconomic dynamics as investigated by Pesaran, Schuermann, Treutler and Weiner in 2006. The unknown coefficient functions in DOVPM are estimated using a local maximum likelihood method. Real data examples for studying credit ratings are used to illustrate the proposed model. Our empirical results show that macroeconomic dynamics significantly affect the sensitivities of firm-specific predictors on credit ratings, and there are nonlinear relationships between them. Comparing the out-of-sample performance of DOPM and DOVPM using an expanding rolling window approach, our empirical results confirm that the advantages of DOVPM over DOPM are twofold. First, the out-of-sample firm-by-firm rating probabilities predicted by DOVPM are more accurate and robust. Second, the out-of-sample total error rates of the prediction rule based on DOVPM are not only of smaller magnitudes but also of lower volatility. Thus, the proposed DOVPM is a useful alternative for credit rating forecasting.