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Bootstrapping Impulse Responses of Structural Vector Autoregressive Models Identified through GARCH

Author

Listed:
  • Helmut Lütkepohl
  • Thore Schlaak
Abstract
Different bootstrap methods and estimation techniques for inference for structural vector autoregressive (SVAR) models identified by conditional heteroskedasticity are reviewed and compared in a Monte Carlo study. The model is a SVAR model with generalized autoregressive conditional heteroskedastic (GARCH) innovations. The bootstrap methods considered are a wild bootstrap, a moving blocks bootstrap and a GARCH residual based bootstrap. Estimation is done by Gaussian maximum likelihood, a simplified procedure based on univariate GARCH estimations and a method that does not re-estimate the GARCH parameters in each bootstrap replication. It is found that the computationally most efficient method is competitive with the computationally more demanding methods and often leads to the smallest confidence sets without sacrificing coverage precision. An empirical model for assessing monetary policy in the U.S. is considered as an example. It is found that the different inference methods for impulse responses lead to qualitatively very similar results.

Suggested Citation

  • Helmut Lütkepohl & Thore Schlaak, 2018. "Bootstrapping Impulse Responses of Structural Vector Autoregressive Models Identified through GARCH," Discussion Papers of DIW Berlin 1750, DIW Berlin, German Institute for Economic Research.
    • Handle: RePEc:diw:diwwpp:dp1750
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    1. Roberto Rigobon & Brian Sack, 2003. "Measuring The Reaction of Monetary Policy to the Stock Market," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 118(2), pages 639-669.
    2. Peter Boswijk, H. & van der Weide, Roy, 2011. "Method of moments estimation of GO-GARCH models," Journal of Econometrics, Elsevier, vol. 163(1), pages 118-126, July.
    3. Lütkepohl, Helmut & Milunovich, George, 2016. "Testing for identification in SVAR-GARCH models," Journal of Economic Dynamics and Control, Elsevier, vol. 73(C), pages 241-258.
    4. Giuseppe Cavaliere & Rasmus Søndergaard Pedersen & Anders Rahbek, 2018. "The Fixed Volatility Bootstrap for a Class of Arch(q) Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(6), pages 920-941, November.
    5. Herwartz, Helmut & Lütkepohl, Helmut, 2014. "Structural vector autoregressions with Markov switching: Combining conventional with statistical identification of shocks," Journal of Econometrics, Elsevier, vol. 183(1), pages 104-116.
    6. Netsunajev, Aleksei, 2013. "Reaction to technology shocks in Markov-switching structural VARs: Identification via heteroskedasticity," Journal of Macroeconomics, Elsevier, vol. 36(C), pages 51-62.
    7. Stefan Bruder, 2018. "Inference for structural impulse responses in SVAR-GARCH models," ECON - Working Papers 281, Department of Economics - University of Zurich.
    8. Roy van der Weide, 2002. "GO-GARCH: a multivariate generalized orthogonal GARCH model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 549-564.
    9. Markku Lanne & Helmut Lütkepohl, 2008. "Identifying Monetary Policy Shocks via Changes in Volatility," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 40(6), pages 1131-1149, September.
    10. Ronald L. Cooper, 1972. "The Predictive Performance of Quarterly Econometric Models of the United States," NBER Chapters, in: Econometric Models of Cyclical Behavior, Volumes 1 and 2, pages 813-947, National Bureau of Economic Research, Inc.
    11. Weide, R. van der, 2002. "Generalized Orthogonal GARCH. A Multivariate GARCH model," CeNDEF Working Papers 02-02, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    12. Goncalves, Silvia & Kilian, Lutz, 2004. "Bootstrapping autoregressions with conditional heteroskedasticity of unknown form," Journal of Econometrics, Elsevier, vol. 123(1), pages 89-120, November.
    13. Kilian,Lutz & Lütkepohl,Helmut, 2018. "Structural Vector Autoregressive Analysis," Cambridge Books, Cambridge University Press, number 9781107196575, January.
    14. Brüggemann, Ralf & Jentsch, Carsten & Trenkler, Carsten, 2016. "Inference in VARs with conditional heteroskedasticity of unknown form," Journal of Econometrics, Elsevier, vol. 191(1), pages 69-85.
    15. Silvia Goncalves & Lutz Kilian, 2007. "Asymptotic and Bootstrap Inference for AR(∞) Processes with Conditional Heteroskedasticity," Econometric Reviews, Taylor & Francis Journals, vol. 26(6), pages 609-641.
    16. Lütkepohl, Helmut & Staszewska-Bystrova, Anna & Winker, Peter, 2015. "Comparison of methods for constructing joint confidence bands for impulse response functions," International Journal of Forecasting, Elsevier, vol. 31(3), pages 782-798.
    17. Lütkepohl, Helmut & Schlaak, Thore, 2018. "Choosing Between Different Time-Varying Volatility Models for Structural Vector Autoregressive Analysis," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, issue 4, pages 715-735.
    18. 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.
    19. Lanne, Markku & Saikkonen, Pentti, 2007. "A Multivariate Generalized Orthogonal Factor GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 61-75, January.
    20. Lutz Kilian, 1998. "Small-Sample Confidence Intervals For Impulse Response Functions," The Review of Economics and Statistics, MIT Press, vol. 80(2), pages 218-230, May.
    21. Simon Gilchrist & Egon Zakrajsek, 2012. "Credit Spreads and Business Cycle Fluctuations," American Economic Review, American Economic Association, vol. 102(4), pages 1692-1720, June.
    22. Michael T. Belongia & Peter N. Ireland, 2015. "Interest Rates and Money in the Measurement of Monetary Policy," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 255-269, April.
    23. Lütkepohl, Helmut & Netšunajev, Aleksei, 2017. "Structural vector autoregressions with smooth transition in variances," Journal of Economic Dynamics and Control, Elsevier, vol. 84(C), pages 43-57.
    24. Jeong, Minsoo, 2017. "Residual-Based Garch Bootstrap And Second Order Asymptotic Refinement," Econometric Theory, Cambridge University Press, vol. 33(3), pages 779-790, June.
    25. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
    26. Normandin, Michel & Phaneuf, Louis, 2004. "Monetary policy shocks:: Testing identification conditions under time-varying conditional volatility," Journal of Monetary Economics, Elsevier, vol. 51(6), pages 1217-1243, September.
    27. He, Changli & Teräsvirta, Timo, 1999. "FOURTH MOMENT STRUCTURE OF THE GARCH(p,q) PROCESS," Econometric Theory, Cambridge University Press, vol. 15(6), pages 824-846, December.
    28. Roberto Rigobon, 2003. "Identification Through Heteroskedasticity," The Review of Economics and Statistics, MIT Press, vol. 85(4), pages 777-792, November.
    29. Milunovich George & Yang Minxian, 2013. "On Identifying Structural VAR Models via ARCH Effects," Journal of Time Series Econometrics, De Gruyter, vol. 5(2), pages 117-131, May.
    30. Helmut Lütkepohl & Anna Staszewska-Bystrova & Peter Winker, 2015. "Confidence Bands for Impulse Responses: Bonferroni vs. Wald," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 77(6), pages 800-821, December.
    31. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
    32. Lutz Kilian, 1999. "Finite-Sample Properties of Percentile and Percentile-t Bootstrap Confidence Intervals for Impulse Responses," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 652-660, November.
    33. Dario Caldara & Edward Herbst, 2019. "Monetary Policy, Real Activity, and Credit Spreads: Evidence from Bayesian Proxy SVARs," American Economic Journal: Macroeconomics, American Economic Association, vol. 11(1), pages 157-192, January.
    34. Nelson, Charles R, 1972. "The Prediction Performance of the FRB-MIT-PENN Model of the U.S. Economy," American Economic Review, American Economic Association, vol. 62(5), pages 902-917, December.
    35. Bouakez, Hafedh & Normandin, Michel, 2010. "Fluctuations in the foreign exchange market: How important are monetary policy shocks?," Journal of International Economics, Elsevier, vol. 81(1), pages 139-153, May.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Boer, Lukas & Lütkepohl, Helmut, 2021. "Qualitative versus quantitative external information for proxy vector autoregressive analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 127(C).
    2. Martin Bruns & Helmut Luetkepohl, 2023. "Have the Effects of Shocks to Oil Price Expectations Changed? Evidence from Heteroskedastic Proxy Vector Autoregressions," University of East Anglia School of Economics Working Paper Series 2023-03, School of Economics, University of East Anglia, Norwich, UK..
    3. Thore Schlaak & Malte Rieth & Maximilian Podstawski, 2023. "Monetary policy, external instruments, and heteroskedasticity," Quantitative Economics, Econometric Society, vol. 14(1), pages 161-200, January.
    4. Jinan Liu & Sajjadur Rahman & Apostolos Serletis, 2021. "Cryptocurrency shocks," Manchester School, University of Manchester, vol. 89(2), pages 190-202, March.
    5. Martin Bruns & Helmut Lütkepohl, 2023. "An Alternative Bootstrap for Proxy Vector Autoregressions," Computational Economics, Springer;Society for Computational Economics, vol. 62(4), pages 1857-1882, December.
    6. Helmut Lütkepohl & Thore Schlaak, 2022. "Heteroscedastic Proxy Vector Autoregressions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(3), pages 1268-1281, June.
    7. Hattori, Masazumi & Shim, Ilhyock & Sugihara, Yoshihiko, 2021. "Cross-stock market spillovers through variance risk premiums and equity flows," Journal of International Money and Finance, Elsevier, vol. 119(C).

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    More about this item

    Keywords

    Structural vector autoregression; conditional heteroskedasticity; GARCH; identification via heteroskedasticity;
    All these keywords.

    JEL classification:

    • 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

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