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

Author

Listed:
  • 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 identified, holds. The probability that it holds fluctuates over time with most evidence in favor of the restriction occurring after 1990.

Suggested Citation

  • Gary Koop & Roberto Leon-Gonzalez & Rodney W. Strachan, 2008. "Dynamic probabilities of restrictions in state space models: An application to the Phillips curve," Working Paper series 26_08, Rimini Centre for Economic Analysis.
    • Handle: RePEc:rim:rimwps:26_08
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    References listed on IDEAS

    as
    1. 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.
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    Citations

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    Cited by:

    1. Joshua C.C. Chan & Gary Koop & Roberto Leon-Gonzalez & Rodney W. Strachan, 2012. "Time Varying Dimension Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(3), pages 358-367, January.
    2. Geraci, Marco Valerio & Gnabo, Jean-Yves, 2018. "Measuring Interconnectedness between Financial Institutions with Bayesian Time-Varying Vector Autoregressions," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 53(3), pages 1371-1390, June.
    3. Yerali Gandica & Marco Valerio Geraci & Sophie Béreau & Jean-Yves Gnabo, 2018. "Fragmentation, integration and macroprudential surveillance of the US financial industry: Insights from network science," PLOS ONE, Public Library of Science, vol. 13(4), pages 1-23, April.
    4. Baruník, Jozef & Ellington, Michael, 2024. "Persistence in financial connectedness and systemic risk," European Journal of Operational Research, Elsevier, vol. 314(1), pages 393-407.
    5. 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.
    6. 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.
    7. Joshua C. C. Chan, 2018. "Specification tests for time-varying parameter models with stochastic volatility," Econometric Reviews, Taylor & Francis Journals, vol. 37(8), pages 807-823, September.
    8. Eric Eisenstat & Rodney W. Strachan, 2016. "Modelling Inflation Volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(5), pages 805-820, August.
    9. Terence D. Agbeyegbe, 2023. "The Link Between Output Growth and Output Growth Volatility: Barbados," Annals of Data Science, Springer, vol. 10(3), pages 787-804, June.
    10. Joshua C. C. Chan, 2017. "The Stochastic Volatility in Mean Model With Time-Varying Parameters: An Application to Inflation Modeling," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 17-28, January.
    11. 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.
    12. Jansson, Walter, 2018. "Stock markets, banks and economic growth in the UK, 1850–1913," Financial History Review, Cambridge University Press, vol. 25(3), pages 263-296, December.
    13. Qian, Hang, 2015. "Inequality Constrained State Space Models," MPRA Paper 66447, University Library of Munich, Germany.
    14. Joshua C.C. Chan & Rodney W. Strachan, 2023. "Bayesian State Space Models In Macroeconometrics," Journal of Economic Surveys, Wiley Blackwell, vol. 37(1), pages 58-75, February.
    15. Nonejad Nima, 2016. "Particle Markov Chain Monte Carlo Techniques of Unobserved Component Time Series Models Using Ox," Journal of Time Series Econometrics, De Gruyter, vol. 8(1), pages 55-90, January.
    16. Han, Xiaoyi & Hsieh, Chih-Sheng & Lee, Lung-fei, 2017. "Estimation and model selection of higher-order spatial autoregressive model: An efficient Bayesian approach," Regional Science and Urban Economics, Elsevier, vol. 63(C), pages 97-120.
    17. Apergis, Nicholas, 2015. "Policy risks, technological risks and stock returns: New evidence from the US stock market," Economic Modelling, Elsevier, vol. 51(C), pages 359-365.
    18. Marco Valerio Geraci & Jean-Yves Gnabo, 2015. "Measuring Interconnectedness between Financial Institutions with Bayesian Time-Varying VARS," Working Papers ECARES ECARES 2015-51, ULB -- Universite Libre de Bruxelles.
    19. Grant, Angelia L., 2018. "The Great Recession and Okun's law," Economic Modelling, Elsevier, vol. 69(C), pages 291-300.

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    More about this item

    Keywords

    Bayesian; state space model; Savage-Dickey density ratio; time varying parameter model;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy

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