Chang-Jin Kim, Sources of Monetary Growth Uncertainty and Economic Activity: The Time- Varying-Parameter Model with Heteroskedastic Disturbances, The Review of Economics and Statistics, Vol. 75, No. 3 (Aug., 1993), pp. 483-492

In this paper, we relax the assumption of constant regime-specific mean growth rates in Hamilton's (1989) two-state Markov-switching model of the business cycle. We introduce a random walk hierarchy prior for each regime-specific mean growth rate and impose a cointegrating relationship between the mean growth rates in recessionary and expansionary periods. By applying the proposed model to postwar U.S. real GDP growth (1947:Q4–2011:Q3), we uncover the evolving nature of the regime-specific mean growth rates of real output in the U.S. business cycle. Additional features of the postwar U.S. business cycle that we uncover include a steady decline in the long-run mean growth rate of real output over the postwar sample and an asymmetric error-correction mechanism when the economy deviates from its long-run equilibrium.

We hope to answer three questions: Has there been a structural break in postwar U.S. real GDP growth towards stabilization? If so, when? What is the nature of this structural break?We employ a Bayesian approach to identify a structural break at an unknown changepoint in a Markov-switching model of the business cycle. Empirical results suggest a break in GDP growth toward stabilization, with the posterior mode of the break date at 1984:1. Furthermore, we find a narrowing gap between growth rates during recessions and booms that is at least as important as any decline in the volatility of shocks.

The synthesis of the dynamic factor model of Stock and Watson (1989) and the regime-switching model of Hamilton (1989) proposed by Diebold and Rudebusch (1996) potentially encompasses both features of the business cycle identified by Burns and Mitchell (1946): (1) comovement among economic variables through the cycle and (2) nonlinearity in its evolution. However, maximum-likelihood estimation has required approximation. Recent advances in multimove Gibbs sampling methodology open the way to approximation-free inference in such non-Gaussian, nonlinear models. This paper estimates the model for U.S. data and attempts to address three questions: Are both features of the business cycle empirically relevant? Might the implied new index of coincident indicators be a useful one in practice? Do the resulting estimates of regime switches show evidence of duration dependence? The answers to all three would appear to be yes.