Kim-Nelson (1998) Business Cycle Turning Points, A New Coincident Index, and Tests of Duration Dependence Based on a Dynamic Factor Model with Regime Switching

Summary

Kim and Nelson (1998) synthesize the Stock-Watson (1989, 1991) linear dynamic factor model with Hamilton's (1989) Markov-switching model in a fully Bayesian framework estimated via multimove Gibbs sampling. Applied to four monthly U.S. coincident indicators (1960–1995), the combined model generates a new composite coincident index that closely tracks the NBER business cycle chronology and substantially outperforms the univariate model in identifying turning points. The paper also develops a Bayesian variable-selection test for business cycle duration dependence, finding robust positive duration dependence in recessions but weak and prior-sensitive evidence for booms.

Key Claims

• Both comovement among indicators and regime switching are empirically important features of the business cycle; the multivariate model identifies NBER turning points far more precisely than a univariate Markov-switching model of a single indicator.
• The model-based coincident index correlates 0.9825 with the Department of Commerce (DOC) index in first differences but shows sharper declines during recessions; posterior regime probabilities are robust to whether tight or diffuse priors on transition probabilities are used.
• Recessions exhibit positive duration dependence — posterior probabilities of no duration dependence range from 0.014 to 0.187 across prior configurations, providing strong evidence beyond the prior; results for booms are weak and prior-sensitive.
• Multimove Gibbs sampling (Carter-Kohn 1994; Shephard 1994) is approximation-free for non-Gaussian nonlinear state-space models, while maximum-likelihood requires approximations to the Kalman filter that are difficult to assess.
• Joint inference on the factor path, regime path, and parameters is feasible by exploiting the conditional linear-Gaussian structure of the model at each Gibbs step.

Concepts Introduced or Extended

• Markov-Switching Model (extends standard MS to multivariate dynamic factor structure; adds duration dependence)
• Gibbs Sampler (multimove application to non-Gaussian nonlinear state-space model)
• Variable Selection (Bayesian variable selection prior for duration dependence test)
• State-Space Representation (nonlinear, non-Gaussian; three latent vectors jointly sampled)

Entities Mentioned

• Chang-Jin Kim
• Charles R. Nelson

Quotes

"Recent advances in multimove Gibbs sampling methodology open the way to approximation-free inference in such non-Gaussian, nonlinear models."

"The answers to all three [questions] would appear to be yes." [Are both features of the business cycle empirically relevant? Is the new coincident index useful in practice? Does the data show evidence of duration dependence?]

My Take

The key methodological advance is recasting a previously intractable nonlinear state-space estimation problem as a three-block Gibbs sampler that exploits the conditional Gaussian structure. The duration dependence test is methodologically elegant — it reads posterior probabilities of point-mass indicators rather than computing p-values under a non-standard null distribution (a problem that plagues classical likelihood ratio tests when nuisance parameters vanish under the null). The finding of robust recession duration dependence but fragile boom duration dependence aligns with the broader business cycle asymmetry literature. The main limitation is scale: the model is estimated on 4 series and would become computationally demanding with a larger coincident indicator panel.