[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/tin/wpaper/20140145.html
   My bibliography  Save this paper

Vector Autoregressions with parsimoniously Time Varying Parameters and an Application to Monetary Policy

Author

Listed:
  • Laurent Callot

    (VU University Amsterdam, the Netherlands)

  • Johannes Tang Kristensen

    (University of Southern Denmark, Denmark)

Abstract
This paper studies vector autoregressive models with parsimoniously time-varying parameters. The parameters are assumed to follow parsimonious random walks, where parsimony stems from the assumption that increments to the parameters have a non-zero probability of being exactly equal to zero. We estimate the sparse and high-dimensional vector of changes to the parameters with the Lasso and the adaptive Lasso. The parsimonious random walk allows the parameters to be modelled non parametrically, so that our model can accommodate constant parameters, an unknown number of structural breaks, or parameters varying randomly. We characterize the finite sample properties of the Lasso by deriving upper bounds on the estimation and prediction errors that are valid with high probability, and provide asymptotic conditions under which these bounds tend to zero with probability tending to one. We also provide conditions under which the adaptive Lasso is able to achieve perfectmodel selection. We investigate by simulations the properties of the Lasso and the adaptive Lasso in settings where the parameters are stable, experience structural breaks, or follow a parsimonious random walk. We use our model to investigate the monetary policy response to inflation and business cycle fluctuations in the US by estimating a parsimoniously time varying parameter Taylor rule. We document substantial changes in the policy response of the Fed in the 1970s and 1980s, and since 2007, but also document the stability of this response in the rest of the sample.

Suggested Citation

  • Laurent Callot & Johannes Tang Kristensen, 2014. "Vector Autoregressions with parsimoniously Time Varying Parameters and an Application to Monetary Policy," Tinbergen Institute Discussion Papers 14-145/III, Tinbergen Institute, revised 09 Apr 2015.
    • Handle: RePEc:tin:wpaper:20140145
    as

    Download full text from publisher

    File URL: https://papers.tinbergen.nl/14145.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Alexandre Belloni & Victor Chernozhukov, 2011. "High Dimensional Sparse Econometric Models: An Introduction," Papers 1106.5242, arXiv.org, revised Sep 2011.
    2. Peter R. Hansen & Asger Lunde & James M. Nason, 2011. "The Model Confidence Set," Econometrica, Econometric Society, vol. 79(2), pages 453-497, March.
    3. Kock, Anders Bredahl, 2016. "Consistent And Conservative Model Selection With The Adaptive Lasso In Stationary And Nonstationary Autoregressions," Econometric Theory, Cambridge University Press, vol. 32(1), pages 243-259, February.
    4. Rajiv Lal & David Bell, 2003. "The Impact of Frequent Shopper Programs in Grocery Retailing," Quantitative Marketing and Economics (QME), Springer, vol. 1(2), pages 179-202, June.
    5. Zhongjun Qu & Pierre Perron, 2007. "Estimating and Testing Structural Changes in Multivariate Regressions," Econometrica, Econometric Society, vol. 75(2), pages 459-502, March.
    6. Deaton,Angus & Muellbauer,John, 1980. "Economics and Consumer Behavior," Cambridge Books, Cambridge University Press, number 9780521296762, September.
    7. Hausman, Jerry & Hall, Bronwyn H & Griliches, Zvi, 1984. "Econometric Models for Count Data with an Application to the Patents-R&D Relationship," Econometrica, Econometric Society, vol. 52(4), pages 909-938, July.
    8. Jushan Bai, 1997. "Estimation Of A Change Point In Multiple Regression Models," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 551-563, November.
    9. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    10. Qian, Junhui & Su, Liangjun, 2014. "Structural change estimation in time series regressions with endogenous variables," Economics Letters, Elsevier, vol. 125(3), pages 415-421.
    11. Hausman, Jerry A. & Leonard, Gregory K. & McFadden, Daniel, 1995. "A utility-consistent, combined discrete choice and count data model Assessing recreational use losses due to natural resource damage," Journal of Public Economics, Elsevier, vol. 56(1), pages 1-30, January.
    12. Giorgio E. Primiceri, 2005. "Time Varying Structural Vector Autoregressions and Monetary Policy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(3), pages 821-852.
    13. Koop, Gary & Korobilis, Dimitris, 2013. "Large time-varying parameter VARs," Journal of Econometrics, Elsevier, vol. 177(2), pages 185-198.
    14. Jushan Bai, 2000. "Vector Autoregressive Models with Structural Changes in Regression Coefficients and in Variance-Covariance Matrices," Annals of Economics and Finance, Society for AEF, vol. 1(2), pages 303-339, November.
    15. Drew Creal & Siem Jan Koopman & André Lucas, 2013. "Generalized Autoregressive Score Models With Applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(5), pages 777-795, August.
    16. Klemperer, Paul D, 1987. "Entry Deterrence in Markets with Consumer Switching Costs," Economic Journal, Royal Economic Society, vol. 97(388a), pages 99-117, Supplemen.
    17. Kock, Anders Bredahl & Callot, Laurent, 2015. "Oracle inequalities for high dimensional vector autoregressions," Journal of Econometrics, Elsevier, vol. 186(2), pages 325-344.
    18. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    19. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    20. Mara Lederman, 2007. "Do enhancements to loyalty programs affect demand? The impact of international frequent flyer partnerships on domestic airline demand," RAND Journal of Economics, RAND Corporation, vol. 38(4), pages 1134-1158, December.
    21. Severin Borenstein, 1989. "Hubs and High Fares: Dominance and Market Power in the U.S. Airline Industry," RAND Journal of Economics, The RAND Corporation, vol. 20(3), pages 344-365, Autumn.
    22. Leonardo J. Basso & Matthew T. Clements & Thomas W. Ross, 2009. "Moral Hazard and Customer Loyalty Programs," American Economic Journal: Microeconomics, American Economic Association, vol. 1(1), pages 101-123, February.
    23. Jan Rouwendal & Jaap Boter, 2009. "Assessing the value of museums with a combined discrete choice/count data model," Applied Economics, Taylor & Francis Journals, vol. 41(11), pages 1417-1436.
    24. Ran Kivetz & Oleg Urminsky & Yuhuang Zheng, 2006. "The Goal-Gradient Hypothesis Resurrected: Purchase Acceleration, Illusionary Goal Progress, and Customer Retention," Natural Field Experiments 00658, The Field Experiments Website.
    25. Paul Klemperer, 1987. "Markets with Consumer Switching Costs," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 102(2), pages 375-394.
    26. Jean Boivin & Marc P. Giannoni, 2006. "Has Monetary Policy Become More Effective?," The Review of Economics and Statistics, MIT Press, vol. 88(3), pages 445-462, August.
    27. Mara Lederman, 2008. "Are Frequent‐Flyer Programs a Cause of the “Hub Premium”?," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 17(1), pages 35-66, March.
    28. Ngai Hang Chan & Chun Yip Yau & Rong-Mao Zhang, 2014. "Group LASSO for Structural Break Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 590-599, June.
    29. Steven A. Morrison & Clifford Winston, 1989. "Enhancing the Performance of the Deregulated Air Transportation System," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 20(1989 Micr), pages 61-123.
    30. Paul Klemperer, 1987. "The Competitiveness of Markets with Switching Costs," RAND Journal of Economics, The RAND Corporation, vol. 18(1), pages 138-150, Spring.
    31. Taylor, John B., 1993. "Discretion versus policy rules in practice," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 39(1), pages 195-214, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Laurent Callot & Johannes Tang Kristensen, 2016. "Regularized Estimation of Structural Instability in Factor Models: The US Macroeconomy and the Great Moderation," Advances in Econometrics, in: Dynamic Factor Models, volume 35, pages 437-479, Emerald Group Publishing Limited.
    2. Gary Koop & Dimitris Korobilis, 2023. "Bayesian Dynamic Variable Selection In High Dimensions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 64(3), pages 1047-1074, August.
    3. Arnaud Dufays & Zhuo Li & Jeroen V.K. Rombouts & Yong Song, 2021. "Sparse change‐point VAR models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(6), pages 703-727, September.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Christiaan Behrens & Nathalie McCaughey, 2015. "Loyalty Programs and Consumer Behaviour: The Impact of FFPs on Consumer Surplus," Tinbergen Institute Discussion Papers 15-048/VIII, Tinbergen Institute.
    2. A. Yeşim Orhun & Tong Guo & Andreas Hagemann, 2022. "Reaching for Gold: Frequent-Flyer Status Incentives and Moral Hazard," Marketing Science, INFORMS, vol. 41(3), pages 548-574, May.
    3. Federico Rossi & Pradeep K. Chintagunta, 2023. "Consumer Loyalty Programs and Retail Prices: Evidence from Gasoline Markets," Marketing Science, INFORMS, vol. 42(4), pages 794-818, July.
    4. Bet, Germán, 2021. "Product specification under a threat of entry: Evidence from Airlines’ departure times," International Journal of Industrial Organization, Elsevier, vol. 75(C).
    5. Rossi, Barbara, 2013. "Advances in Forecasting under Instability," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 1203-1324, Elsevier.
    6. Alessandro Casini & Pierre Perron, 2018. "Structural Breaks in Time Series," Boston University - Department of Economics - Working Papers Series WP2019-02, Boston University - Department of Economics.
    7. Florez-Acosta, Jorge, 2021. "Do preferences for private labels respond to supermarket loyalty programs?," Journal of Economic Behavior & Organization, Elsevier, vol. 188(C), pages 183-208.
    8. Henri Bussink & Bas ter Weel, 2022. "Costs and benefits of an Individual Learning Account (ILA): A simulation analysis for the Netherlands," Tinbergen Institute Discussion Papers 22-077/V, Tinbergen Institute.
    9. Qian, Junhui & Su, Liangjun, 2016. "Shrinkage estimation of common breaks in panel data models via adaptive group fused Lasso," Journal of Econometrics, Elsevier, vol. 191(1), pages 86-109.
    10. Mahua Barari & Srikanta Kundu, 2019. "The Role of the Federal Reserve in the U.S. Housing Crisis: A VAR Analysis with Endogenous Structural Breaks," JRFM, MDPI, vol. 12(3), pages 1-20, July.
    11. Karsten Schweikert, 2022. "Oracle Efficient Estimation of Structural Breaks in Cointegrating Regressions," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(1), pages 83-104, January.
    12. Mara Lederman, 2007. "Do enhancements to loyalty programs affect demand? The impact of international frequent flyer partnerships on domestic airline demand," RAND Journal of Economics, RAND Corporation, vol. 38(4), pages 1134-1158, December.
    13. Karsten Schweikert, 2020. "Oracle Efficient Estimation of Structural Breaks in Cointegrating Regressions," Papers 2001.07949, arXiv.org, revised Apr 2021.
    14. Gayle, Philip G. & Wu, Chi-Yin, 2013. "A re-examination of incumbents’ response to the threat of entry: Evidence from the airline industry," Economics of Transportation, Elsevier, vol. 2(4), pages 119-130.
    15. Alastair R. Hall & Denise R. Osborn & Nikolaos Sakkas, 2017. "The asymptotic behaviour of the residual sum of squares in models with multiple break points," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 667-698, October.
    16. Davide Delle Monache & Ivan Petrella, 2014. "Adaptive Models and Heavy Tails," Working Papers 720, Queen Mary University of London, School of Economics and Finance.
    17. Duan, Jiangtao & Bai, Jushan & Han, Xu, 2023. "Quasi-maximum likelihood estimation of break point in high-dimensional factor models," Journal of Econometrics, Elsevier, vol. 233(1), pages 209-236.
    18. Baltagi, Badi H. & Feng, Qu & Kao, Chihwa, 2016. "Estimation of heterogeneous panels with structural breaks," Journal of Econometrics, Elsevier, vol. 191(1), pages 176-195.
    19. Kurozumi, Eiji & Tuvaandorj, Purevdorj, 2011. "Model selection criteria in multivariate models with multiple structural changes," Journal of Econometrics, Elsevier, vol. 164(2), pages 218-238, October.
    20. Oka, Tatsushi & Perron, Pierre, 2018. "Testing for common breaks in a multiple equations system," Journal of Econometrics, Elsevier, vol. 204(1), pages 66-85.

    More about this item

    Keywords

    Parsimony; time varying parameters; VAR; structural break; Lasso;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: 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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:tin:wpaper:20140145. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Tinbergen Office +31 (0)10-4088900 (email available below). General contact details of provider: https://edirc.repec.org/data/tinbenl.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.