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Inference on Impulse Response Functions in Structural VAR Models

  • Atsushi Inoue
  • Lutz Kilian

Skepticism toward traditional identifying assumptions based on exclusion restrictions has led to a surge in the use of structural VAR models in which structural shocks are identified by restricting the sign of the responses of selected macroeconomic aggregates to these shocks. Researchers commonly report the vector of pointwise posterior medians of the impulse responses as a measure of central tendency of the estimated response functions, along with pointwise 68 percent posterior error bands. It can be shown that this approach cannot be used to characterize the central tendency of the structural impulse response functions. We propose an alternative method of summarizing the evidence from sign-identified VAR models designed to enhance their practical usefulness. Our objective is to characterize the most likely admissible model(s) within the set of structural VAR models that satisfy the sign restrictions. We show how the set of most likely structural response functions can be computed from the posterior mode of the joint distribution of admissible models both in the fully identified and in the partially identified case, and we propose a highest-posterior density credible set that characterizes the joint uncertainty about this set. Our approach can also be used to resolve the long-standing problem of how to conduct joint inference on sets of structural impulse response functions in exactly identified VAR models. We illustrate the differences between our approach and the traditional approach for the analysis of the effects of monetary policy shocks and of the effects of oil demand and oil supply shocks.

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File URL: http://hdl.handle.net/10097/56548
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File URL: http://ir.library.tohoku.ac.jp/re/bitstream/10097/56548/1/terg307.pdf
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Paper provided by Graduate School of Economics and Management, Tohoku University in its series TERG Discussion Papers with number 307.

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Length: 27 pages
Date of creation: Jul 2013
Date of revision:
Handle: RePEc:toh:tergaa:307
Contact details of provider: Postal: Kawauchi, Aoba-ku, Sendai 980-8476
Web page: http://www.econ.tohoku.ac.jp/econ/english/index.html
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  1. Almuth Scholl & Harald Uhlig, 2005. "New Evidence on the Puzzles. Results from Agnostic Identification on Monetary Policy and Exchange Rates," SFB 649 Discussion Papers SFB649DP2005-037, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  2. Dedola, Luca & Neri, Stefano, 2004. "What Does A Technology Shock Do? A VAR Analysis with Model-based Sign Restrictions," CEPR Discussion Papers 4537, C.E.P.R. Discussion Papers.
  3. Ren�e Fry & Adrian Pagan, 2011. "Sign Restrictions in Structural Vector Autoregressions: A Critical Review," Journal of Economic Literature, American Economic Association, vol. 49(4), pages 938-60, December.
  4. Juan F. Rubio-Ram�rez & Daniel F. Waggoner & Tao Zha, 2010. "Structural Vector Autoregressions: Theory of Identification and Algorithms for Inference," Review of Economic Studies, Oxford University Press, vol. 77(2), pages 665-696.
  5. Faust, Jon, 1998. "The robustness of identified VAR conclusions about money," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 49(1), pages 207-244, December.
  6. Uhlig, Harald, 2005. "What are the effects of monetary policy on output? Results from an agnostic identification procedure," Journal of Monetary Economics, Elsevier, vol. 52(2), pages 381-419, March.
  7. Lutz Kilian, 2009. "Not All Oil Price Shocks Are Alike: Disentangling Demand and Supply Shocks in the Crude Oil Market," American Economic Review, American Economic Association, vol. 99(3), pages 1053-69, June.
  8. Granziera, Eleonora & Lee, Mihye & Moon, Hyungsik Roger & Schorfheide, Frank, 2011. "Inference for VARs Identified with Sign Restrictions," CEPR Discussion Papers 8432, C.E.P.R. Discussion Papers.
  9. Dario Caldara & Christophe Kamps, 2012. "The analytics of SVARs: a unified framework to measure fiscal multipliers," Finance and Economics Discussion Series 2012-20, Board of Governors of the Federal Reserve System (U.S.).
  10. Andrew Mountford & Harald Uhlig, 2005. "What are the Effects of Fiscal Policy Shocks?," SFB 649 Discussion Papers SFB649DP2005-039, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  11. Canova, Fabio & Nicolo, Gianni De, 2002. "Monetary disturbances matter for business fluctuations in the G-7," Journal of Monetary Economics, Elsevier, vol. 49(6), pages 1131-1159, September.
  12. Mittnik, Stefan & Zadrozny, Peter A, 1993. "Asymptotic Distributions of Impulse Responses, Step Responses, and Variance Decompositions of Estimated Linear Dynamic Models," Econometrica, Econometric Society, vol. 61(4), pages 857-70, July.
  13. Kilian, Lutz & Murphy, Daniel P, 2009. "Why Agnostic Sign Restrictions Are Not Enough: Understanding the Dynamics of Oil Market VAR Models," CEPR Discussion Papers 7471, C.E.P.R. Discussion Papers.
  14. C. Baumeister & G. Peersman & -, 2010. "Sources of the Volatility Puzzle in the Crude Oil Market," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 10/634, Ghent University, Faculty of Economics and Business Administration.
  15. Shigeru Fujita, 2011. "Dynamics of worker flows and vacancies: evidence from the sign restriction approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(1), pages 89-121, January/F.
  16. Christiane Baumeister & Gert Peersman, 2013. "The Role Of Time‐Varying Price Elasticities In Accounting For Volatility Changes In The Crude Oil Market," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(7), pages 1087-1109, November.
  17. Gert Peersman & Roland Straub, 2009. "Technology Shocks And Robust Sign Restrictions In A Euro Area Svar," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 50(3), pages 727-750, 08.
  18. Jon Faust, 1998. "The robustness of identified VAR conclusions about money," International Finance Discussion Papers 610, Board of Governors of the Federal Reserve System (U.S.).
  19. Lutkepohl, Helmut, 1990. "Asymptotic Distributions of Impulse Response Functions and Forecast Error Variance Decompositions of Vector Autoregressive Models," The Review of Economics and Statistics, MIT Press, vol. 72(1), pages 116-25, February.
  20. Evi Pappa, 2009. "The Effects Of Fiscal Shocks On Employment And The Real Wage," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 50(1), pages 217-244, 02.
  21. Francesco Lippi & Andrea Nobili, 2009. "Oil and the macroeconomy: a quantitative structural analysis," Temi di discussione (Economic working papers) 704, Bank of Italy, Economic Research and International Relations Area.
  22. Fabio Canova & Evi Pappa, 2003. "Price differentials in monetary unions: The role of fiscal shocks," Economics Working Papers 923, Department of Economics and Business, Universitat Pompeu Fabra, revised Jun 2005.
  23. Christopher A. Sims & Tao Zha, 1995. "Error bands for impulse responses," Working Paper 95-6, Federal Reserve Bank of Atlanta.
  24. �scar Jordà, 2009. "Simultaneous Confidence Regions for Impulse Responses," The Review of Economics and Statistics, MIT Press, vol. 91(3), pages 629-647, August.
  25. repec:nys:sunysb:93-01 is not listed on IDEAS
  26. Canova, Fabio & Gambetti, Luca & Pappa, Evi, 2006. "The Structural Dynamics of US Output and Inflation: What Explains the Changes?," CEPR Discussion Papers 5879, C.E.P.R. Discussion Papers.
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