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K-state switching models with endogenous transition distributions

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  • Kaufmann Sylvia

Abstract

Two Bayesian sampling schemes are outlined to estimate a K-state Markov switching model with time-varying transition probabilities. The multinomial logit model for the transition probabilities is alternatively expressed as a random utility model and as a difference random utility model. The estimation uses data augmentation and both sampling schemes can be based on Gibbs sampling. Based on the model estimate, we are able to discriminate the model against a smooth transition model, in which the state probability may be influenced by a variable, but without depending on the past prevailing state. Formulating a definition allows to determine the relevant threshold level of the covariate influencing the transition distribution without resorting to the usual grid search. Identification issues are addressed with random permutation sampling. In terms of efficiency the extension to difference random utility in combination with random permutation sampling performs best. To illustrate the method, we estimate a two-pillar Phillips curve for the euro area, in which the inflation rate depends on the low-frequency components of M3 growth, real GDP growth and the change in the government bond yield, and on the highfrequency component of the output gap. Using recent data series, the effect of the low-frequency component of M3 growth depends on regimes determined by lagged credit growth.

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Bibliographic Info

Paper provided by Swiss National Bank in its series Working Papers with number 2011-13.

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Length: 48 pages
Date of creation: 2011
Date of revision:
Handle: RePEc:snb:snbwpa:2011-13

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Keywords: Bayesian analysis; credit; M3 growth; Markov switching; Phillips curve; permutation sampling; threshold level; time-varying probabilities;

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References

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  1. Andrew J. Filardo & Stephen F. Gordon, 1993. "Business cycle durations," Research Working Paper 93-11, Federal Reserve Bank of Kansas City.
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  12. Monica Billio & Roberto Casarin, 2010. "Bayesian Estimation of Stochastic-Transition Markov-Switching Models for Business Cycle Analysis," Working Papers 1002, University of Brescia, Department of Economics.
  13. Chib, Siddhartha, 1996. "Calculating posterior distributions and modal estimates in Markov mixture models," Journal of Econometrics, Elsevier, vol. 75(1), pages 79-97, November.
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