Conditional heteroskedasticity in qualitative response models of time series: a Gibbs sampling approach to the bank prime rate

Previous time series applications of qualitative response models have ignored features of the data, such as conditional heteroskedasticity, that are routinely addressed in time-series econometrics of financial data. This article addresses this issue by adding Markov-switching heteroskedasticity to a dynamic ordered probit model of discrete changes in the bank prime lending rate and estimation via the Gibbs sampler. The dynamic ordered probit model of Eichengreen, Watson and Grossman (1995) allows for serial autocorrelation in probit analysis of a time series, and the present article demonstrates the relative simplicity of estimating a dynamic ordered probit using the Gibbs sampler instead of the Eichengreen et al. maximum-likelihood procedure. In addition, the extension to regime-switching parameters and conditional heteroskedasticity is easy to implement under Gibbs sampling. The article compares tests of goodness of fit between dynamic ordered probit models of the prime rate that have constant variance and conditional heteroskedasticity.