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

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  • Penelope A. Smith
  • Peter M. Summers

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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Bibliographic Info

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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References

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  1. 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.
  2. 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.
  3. Christopher A. Sims & Tao Zha, 1999. "Error Bands for Impulse Responses," Econometrica, Econometric Society, vol. 67(5), pages 1113-1156, September.
  4. James D. Hamilton & Daniel F. Waggoner & Tao Zha, 2007. "Normalization in Econometrics," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 221-252.
  5. Daniel F. Waggoner & Tao Zha, 2000. "Likelihood-preserving normalization in multiple equation models," Working Paper 2000-8, Federal Reserve Bank of Atlanta.
  6. Sylvia Kaufmann, 2000. "Measuring business cycles with a dynamic Markov switching factor model: an assessment using Bayesian simulation methods," Econometrics Journal, Royal Economic Society, vol. 3(1), pages 39-65.
  7. Andrew J. Filardo & Stephen F. Gordon, 1993. "Business cycle durations," Research Working Paper 93-11, Federal Reserve Bank of Kansas City.
  8. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-84, March.
  9. 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.
  10. 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.
  11. Harding, Don & Pagan, Adrian, 2002. "Dissecting the cycle: a methodological investigation," Journal of Monetary Economics, Elsevier, vol. 49(2), pages 365-381, March.
  12. Hamilton, James D, 1991. "A Quasi-Bayesian Approach to Estimating Parameters for Mixtures of Normal Distributions," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(1), pages 27-39, January.
  13. 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.
  14. Smith Penelope & Summers Peter M, 2009. "Regime Switches in GDP Growth and Volatility: Some International Evidence and Implications for Modeling Business Cycles," The B.E. Journal of Macroeconomics, De Gruyter, vol. 9(1), pages 1-19, September.
  15. 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.
  16. 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.
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Cited by:
  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.
  2. James D. Hamilton & Daniel F. Waggoner & Tao Zha, 2004. "Normalization in econometrics," Working Paper 2004-13, Federal Reserve Bank of Atlanta.

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