The first stage of the overall research program of Nelson and Kim was to develop a classical approach to making inferences of state-space models with Markov-switching and their applications. With the algorithm for approximate maximum likelihood estimation developed by Kim (1994), a broad class of models becomes operational that could not be handled before. The resulting model and the algorithm have been applied by principal investigators to various topics in macroeconomics and finance. (Kim and Nelson (1998), Kim and M. Kim (1996).)
The second stage of the program made Bayesian Gibbs sampling operational for the state-space model with Markov switching, building upon ideas in Albert and Chib (1993) and Carter and Kohn (1994). The methods were applied to: modeling business cycle asymmetry and comovement; testing business cycle duration dependence in a multivariate context (Kim and Nelson, 1998); and to modeling long-run U.S./U.K. real exchange rate. (Engel and Kim, 1998).
The third stage of the program was devoted to writing a book in order to introduce to a wider audience of researchers in economics and finance recent advances in the estimation of state-space models in which switching between regimes occurs stochastically according to a Markov process. The book, titled State-Space Models with Regime-Switching: Classical and Gibbs-Sampling Approaches with Applications, (Kim and Nelson, 1998), is forthcoming from the MIT Press.
While estimation of the models with Markov-switching has been well developed in the literature in both the classical and the Bayesian perspectives and their applications are abundant, there apparently seems to be a lag in the literature in the development of procedures for hypothesis testing. Thus, in this fourth stage of the research program, the investigators are designing various hypothesis tests within Markov-switching models. The current stage of the program consists of three related projects. First, they develop a test for structural change at an unknown changepoint in the hyperparameters of Markov-switching models that are otherwise assumed fixed. As an application, Nelson adn Kim test whether the U.S. economy has become more stable. In the second project, they develop a test of Markov-switching within a univariate framework. In the third project, they further extend the second project to develop a test of Markov-switching within a multivariate framework of a dynamic factor model. Tests of Markov-switching within both univariate and multivariate frameworks are based on the posterior probabilities of the model indicator parameters. The second and third projects test whether asymmetry is an important feature of the business cycle.
