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Dynamic probabilities of restrictions in state space models: An application to the Phillips curve

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Author Info

  • Gary Koop

    ()
    (University of Strathclyde, UK and The RImini Centre for Economic Analisys, Italy)

  • Roberto Leon-Gonzalez

    ()
    (National Graduate Institute for Policy Studies, Japan and The RImini Centre for Economic Analisys - Italy)

  • Rodney W. Strachan

    ()
    (University of Queensland, Australia and The RImini Centre for Economic Analisys - Italy)

Abstract

Empirical macroeconomists are increasingly using models (e.g. regressions or Vector Autoregressions) where the parameters vary over time. State space methods are frequently used to specify the evolution of parameters in such models. In any application, there are typically restrictions on the parameters that a researcher might be interested in. This motivates the question of how to calculate the probability that a restriction holds at a point in time without assuming the restriction holds at all (or any other) points in time. This paper develops methods to answer this question. In particular, the principle of the Savage-Dickey density ratio is used to obtain the time-varying posterior probabilities of restrictions. We use our methods in a macroeconomic application involving the Phillips curve. Macroeconomists are interested in whether the long-run Phillips curve is vertical. This is a restriction for which we can calculate the posterior probability using our methods. Using U.S. data, the probability that this restriction holds tends to be fairly high, but decreases slightly over time (apart from a slight peak in the late 1970s). We also calculate the probability that another restriction, that the NAIRU is not identied, holds. The probability that it holds ‡uctuates over time with most evidence in favor of the restriction occurring after 1990.

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Bibliographic Info

Paper provided by The Rimini Centre for Economic Analysis in its series Working Paper Series with number 26-08.

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Date of creation: Jan 2008
Date of revision: Jan 2008
Handle: RePEc:rim:rimwps:26-08

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Keywords: Bayesian; state space model; Savage-Dickey density ratio; time varying parameter model.;

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References

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  1. Martin Lettau & Sydney C. Ludvigson, 2004. "Understanding Trend and Cycle in Asset Values: Reevaluating the Wealth Effect on Consumption," American Economic Review, American Economic Association, vol. 94(1), pages 276-299, March.
  2. Timothy Cogley & Thomas J. Sargent, 2002. "Evolving Post-World War II U.S. Inflation Dynamics," NBER Chapters, in: NBER Macroeconomics Annual 2001, Volume 16, pages 331-388 National Bureau of Economic Research, Inc.
  3. Douglas Staiger & James H. Stock & Mark W. Watson, 1997. "The NAIRU, Unemployment and Monetary Policy," Journal of Economic Perspectives, American Economic Association, vol. 11(1), pages 33-49, Winter.
  4. Gary Koop & Simon M. Potter & Rodney W. Strachan, 2005. "Reexamining the consumption-wealth relationship: the role of model uncertainty," Staff Reports 202, Federal Reserve Bank of New York.
  5. Sylvia Fruhwirth-Schnatter, 2004. "Estimating marginal likelihoods for mixture and Markov switching models using bridge sampling techniques," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 143-167, 06.
  6. J. Durbin, 2002. "A simple and efficient simulation smoother for state space time series analysis," Biometrika, Biometrika Trust, vol. 89(3), pages 603-616, August.
  7. King, Robert G. & Plosser, Charles I. & Stock, James H. & Watson, Mark W., 1991. "Stochastic Trends and Economic Fluctuations," American Economic Review, American Economic Association, vol. 81(4), pages 819-40, September.
  8. King, Robert G. & Watson, Mark W., 1994. "The post-war U.S. phillips curve: a revisionist econometric history," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 41(1), pages 157-219, December.
  9. Timothy Cogley & Thomas Sargent, . "Drifts and Volatilities: Monetary Policies and Outcomes in the Post WWII US," Working Papers 2133503, Department of Economics, W. P. Carey School of Business, Arizona State University.
  10. Durbin, James & Koopman, Siem Jan, 2001. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, number 9780198523543, September.
  11. Thomas Sargent & Noah Williams & Tao Zha, 2004. "Shocks and Government Beliefs: The Rise and Fall of American Inflation," NBER Working Papers 10764, National Bureau of Economic Research, Inc.
  12. Gary Koop & Roberto Leon-Gonzalez & Rodney W. Strachan, 2008. "On the Evolution of Monetary Policy," Working Paper Series 24-08, The Rimini Centre for Economic Analysis, revised Jan 2008.
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Cited by:
  1. Koop, Gary & Tole, Lise, 2013. "Modeling the relationship between European carbon permits and certified emission reductions," Journal of Empirical Finance, Elsevier, vol. 24(C), pages 166-181.
  2. Joshua C.C. Chan & Gary Koop & Roberto Leon-Gonzalez & Rodney W. Strachan, 2010. "Time Varying Dimension Models," Working Paper Series 44_10, The Rimini Centre for Economic Analysis.
  3. Koop, Gary & Potter, Simon M., 2011. "Time varying VARs with inequality restrictions," Journal of Economic Dynamics and Control, Elsevier, vol. 35(7), pages 1126-1138, July.
  4. Benjamin Wong, 2013. "The Evolution of the U.S. Output-Inflation Tradeoff," CAMA Working Papers 2013-70, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.

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