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Identification and normalization in Markov switching models of "business cycles"

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Penelope A. Smith
Peter M. Summers

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Abstract

Recent work by Hamilton, Waggoner and Zha (2004) has demonstrated the importance of identification and normalization in econometric models. In this paper, we use the popular class of two-state Markov switching models to illustrate the consequences of alternative identification schemes for empirical analysis of business cycles. A defining feature of (classical) recessions is that economic activity declines on average. Somewhat surprisingly however, this property has been ignored in most published work that uses Markov switching models to study business cycles. We demonstrate that this matters: inferences from Markov switching models can be dramatically affected by whether or not average growth in the 'low state' is required to be negative, rather than simply below trend. Although such a restriction may not be appropriate in all applications, the difference is crucial if one wants to draw conclusions about 'recessions' based on the estimated model parameters.

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Paper provided by Federal Reserve Bank of Kansas City in its series Research Working Paper with number RWP 04-09.

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Date of creation: 2004
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Handle: RePEc:fip:fedkrw:rwp04-09

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Keywords: Business cycles ; Recessions;

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Phillips, Kerk L., 1991. "A two-country model of stochastic output with changes in regime," Journal of International Economics, Elsevier, vol. 31(1-2), pages 121-142, August. [Downloadable!] (restricted)
  2. Waggoner, Daniel F. & Zha, Tao, 2003. "Likelihood preserving normalization in multiple equation models," Journal of Econometrics, Elsevier, vol. 114(2), pages 329-347, June. [Downloadable!] (restricted)
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  3. Albert, James H & Chib, Siddhartha, 1993. "Bayes Inference via Gibbs Sampling of Autoregressive Time Series Subject to Markov Mean and Variance Shifts," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 1-15, January.
  4. Goodwin, Thomas H, 1993. "Business-Cycle Analysis with a Markov-Switching Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(3), pages 331-39, July.
  5. Filardo, Andrew J. & Gordon, Stephen F., 1998. "Business cycle durations," Journal of Econometrics, Elsevier, vol. 85(1), pages 99-123, July. [Downloadable!] (restricted)
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  6. Christopher A. Sims & Tao Zha, 1999. "Error Bands for Impulse Responses," Econometrica, Econometric Society, vol. 67(5), pages 1113-1156, September.
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  7. Michael P. Clements & Hans-Martin Krolzig, 1998. "A comparison of the forecast performance of Markov-switching and threshold autoregressive models of US GNP," Econometrics Journal, Royal Economic Society, vol. 1(Conferenc), pages C47-C75.
  8. Harding, Don & Pagan, Adrian, 2002. "Dissecting the cycle: a methodological investigation," Journal of Monetary Economics, Elsevier, vol. 49(2), pages 365-381, March. [Downloadable!] (restricted)
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  9. Filardo, Andrew J, 1994. "Business-Cycle Phases and Their Transitional Dynamics," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 299-308, July.
  10. Scott S. L., 2002. "Bayesian Methods for Hidden Markov Models: Recursive Computing in the 21st Century," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 337-351, March. [Downloadable!] (restricted)
  11. James D. Hamilton & Daniel F. Waggoner & Tao Zha, 2004. "Normalization in econometrics," Working Paper 2004-13, Federal Reserve Bank of Atlanta. [Downloadable!]
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  12. Koop, Gary & Potter, Simon M., 1998. "Bayes factors and nonlinearity: Evidence from economic time series1," Journal of Econometrics, Elsevier, vol. 88(2), pages 251-281, November. [Downloadable!] (restricted)
  13. Penelope A. Smith & Peter M. Summers, 2002. "Regime Switches in GDP Growth and Volatility: Some International Evidence and Implications for Modelling Business Cycles," Melbourne Institute Working Paper Series wp2002n21, Melbourne Institute of Applied Economic and Social Research, The University of Melbourne. [Downloadable!]
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  1. Peter M. Summers & Penelope A. Smith, 2005. "How well do Markov switching models describe actual business cycles? The case of synchronization," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(2), pages 253-274. [Downloadable!]
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