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Dynamic Probabilities of Restrictions in State Space Models: An Application to the Phillips Curve

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  • Koop, Gary
  • Leon-Gonzalez, Roberto
  • Strachan, Rodney W.

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.
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Suggested Citation

  • Koop, Gary & Leon-Gonzalez, Roberto & Strachan, Rodney W., 2010. "Dynamic Probabilities of Restrictions in State Space Models: An Application to the Phillips Curve," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(3), pages 370-379.
  • Handle: RePEc:bes:jnlbes:v:28:i:3:y:2010:p:370-379
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    References listed on IDEAS

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    7. Thomas Sargent & Noah Williams & Tao Zha, 2006. "Shocks and Government Beliefs: The Rise and Fall of American Inflation," American Economic Review, American Economic Association, vol. 96(4), pages 1193-1224, September.
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    Citations

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    Cited by:

    1. Joshua C.C. Chan, 2015. "Specification tests for time-varying parameter models with stochastic volatility," CAMA Working Papers 2015-42, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    2. repec:taf:jnlbes:v:35:y:2017:i:1:p:17-28 is not listed on IDEAS
    3. Y'erali Gandica & Marco Valerio Geraci & Sophie B'ereau & Jean-Yves Gnabo, 2017. "Fragmentation, integration and macroprudential surveillance of the US financial industry: Insights from network science," Papers 1707.00296, arXiv.org, revised Jan 2018.
    4. 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.
    5. Eric Eisenstat & Rodney W. Strachan, 2016. "Modelling Inflation Volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(5), pages 805-820, August.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Qian, Hang, 2015. "Inequality Constrained State Space Models," MPRA Paper 66447, University Library of Munich, Germany.
    14. Marco Valerio Geraci & Jean-Yves Gnabo, 2015. "Measuring interconnectedness between financial institutions with Bayesian time-varying vector autoregressions," Working Papers ECARES 2015-51, ULB -- Universite Libre de Bruxelles.
    15. 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.

    More about this item

    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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