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Time-Varying Parameter Vector Autoregressions: Specification, Estimation, and an Application

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  • Thomas A. Lubik
  • Christian Matthes

Abstract

Time-varying parameter vector autoregressions (TVP-VARs) have become a popular tool to study the dynamics of macroeconomic time series. In this article, we discuss the specification and estimation of this class of models with a focus on implementability. We provide a step-by-step guide for researchers interested in utilizing this methodology in their own research. Specifically, we discuss how to use Bayesian Gibbs-sampling techniques to easily conduct inference.

Suggested Citation

  • Thomas A. Lubik & Christian Matthes, 2015. "Time-Varying Parameter Vector Autoregressions: Specification, Estimation, and an Application," Economic Quarterly, Federal Reserve Bank of Richmond, issue 4Q, pages 323-352.
    • Handle: RePEc:fip:fedreq:00040
    DOI: 10.21144/eq1010403
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    References listed on IDEAS

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    1. Fabio Canova & Fernando J. Pérez Forero, 2015. "Estimating overidentified, nonrecursive, time‐varying coefficients structural vector autoregressions," Quantitative Economics, Econometric Society, vol. 6(2), pages 359-384, July.
    2. Thomas A. Lubik & Frank Schorfheide, 2004. "Testing for Indeterminacy: An Application to U.S. Monetary Policy," American Economic Review, American Economic Association, vol. 94(1), pages 190-217, March.
    3. Christiano, Lawrence J. & Eichenbaum, Martin & Evans, Charles L., 1999. "Monetary policy shocks: What have we learned and to what end?," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.),Handbook of Macroeconomics, edition 1, volume 1, chapter 2, pages 65-148, Elsevier.
    4. Jouchi Nakajima, 2011. "Time-Varying Parameter VAR Model with Stochastic Volatility: An Overview of Methodology and Empirical Applications," Monetary and Economic Studies, Institute for Monetary and Economic Studies, Bank of Japan, vol. 29, pages 107-142, November.
    5. Fabio Canova & Filippo Ferroni & Christian Matthes, 2015. "Approximating Time Varying Structural Models With Time Invariant Structures," Working Paper 15-10, Federal Reserve Bank of Richmond, revised 23 Oct 2015.
    6. Thomas A. Lubik & Paolo Surico, 2010. "The Lucas critique and the stability of empirical models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(1), pages 177-194.
    7. Koop, Gary & Korobilis, Dimitris, 2010. "Bayesian Multivariate Time Series Methods for Empirical Macroeconomics," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(4), pages 267-358, July.
    8. Canova, Fabio & Gambetti, Luca, 2009. "Structural changes in the US economy: Is there a role for monetary policy?," Journal of Economic Dynamics and Control, Elsevier, vol. 33(2), pages 477-490, February.
    9. Luca Benati & Thomas A. Lubik, 2014. "Sales, Inventories And Real Interest Rates: A Century Of Stylized Facts," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(7), pages 1210-1222, November.
    10. Christopher A. Sims & Tao Zha, 2006. "Were There Regime Switches in U.S. Monetary Policy?," American Economic Review, American Economic Association, vol. 96(1), pages 54-81, March.
    11. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 361-393.
    12. Michael Connolly & Taeyoung Doh, 2012. "The state space representation and estimation of a time-varying parameter VAR with stochastic volatility," Research Working Paper RWP 12-04, Federal Reserve Bank of Kansas City.
    13. Pooyan Amir‐Ahmadi & Christian Matthes & Mu‐Chun Wang, 2016. "Drifts and volatilities under measurement error: Assessing monetary policy shocks over the last century," Quantitative Economics, Econometric Society, vol. 7(2), pages 591-611, July.
    14. Thomas A. Lubik & Christian Matthes & Andrew Owens, 2016. "Beveridge Curve Shifts and Time-Varying Parameter VARs," Economic Quarterly, Federal Reserve Bank of Richmond, issue 3Q, pages 197-226.
    15. Giorgio E. Primiceri, 2005. "Time Varying Structural Vector Autoregressions and Monetary Policy," Review of Economic Studies, Oxford University Press, vol. 72(3), pages 821-852.
    16. Marco Del Negro & Giorgio E. Primiceri, 2015. "Time Varying Structural Vector Autoregressions and Monetary Policy: A Corrigendum," Review of Economic Studies, Oxford University Press, vol. 82(4), pages 1342-1345.
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    Cited by:

    1. Jonathan Lecznar & Thomas A. Lubik, 2017. "Real Rates and Consumption Smoothing in a Low Interest Rate Environment: The Case of Japan," Working Paper 17-8, Federal Reserve Bank of Richmond, revised 18 May 2017.
    2. Auray, Stéphane & Eyquem, Aurélien, 2019. "Episodes of war and peace in an estimated open economy model," Journal of Economic Dynamics and Control, Elsevier, vol. 105(C), pages 203-249.
    3. Legrand, Romain, 2018. "Time-Varying Vector Autoregressions: Efficient Estimation, Random Inertia and Random Mean," MPRA Paper 88925, University Library of Munich, Germany.
    4. Josh Davis & Cristian Fuenzalida & Alan M. Taylor, 2019. "The Natural Rate Puzzle: Global Macro Trends and the Market-Implied r," NBER Working Papers 26560, National Bureau of Economic Research, Inc.
    5. Lombardi, Domenico & Siklos, Pierre L. & Xie, Xiangyou, 2018. "Monetary policy transmission in systemically important economies and China’s impact," Journal of Asian Economics, Elsevier, vol. 59(C), pages 61-79.
    6. Thomas A. Lubik & Christian Matthes & Andrew Owens, 2016. "Beveridge Curve Shifts and Time-Varying Parameter VARs," Economic Quarterly, Federal Reserve Bank of Richmond, issue 3Q, pages 197-226.
    7. Hess Chung & Etienne Gagnon & Taisuke Nakata & Matthias Paustian & Bernd Schlusche & James Trevino & Diego Vilan & Wei Zheng, 2019. "Monetary Policy Options at the Effective Lower Bound : Assessing the Federal Reserve's Current Policy Toolkit," Finance and Economics Discussion Series 2019-003, Board of Governors of the Federal Reserve System (U.S.).
    8. Krustev, Georgi & Casalis, André, 2020. "Cyclical drivers of euro area consumption: what can we learn from durable goods?," Working Paper Series 2386, European Central Bank.

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