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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
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  1. 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.
  2. 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.
  3. 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.
  4. Fabio Canova & Evi Pappa, 2007. "Price Differentials in Monetary Unions: The Role of Fiscal Shocks," Economic Journal, Royal Economic Society, vol. 117(520), pages 713-737, 04.
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  7. 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.
  8. Hyungsik Roger Moon & Frank Schorfheide & Eleonara Granziera & Mihye Lee, 2011. "Inference for VARs identified with sign restrictions," Working Papers 11-20, Federal Reserve Bank of Philadelphia.
  9. Uhlig, Harald, 1999. "What are the Effects of Monetary Policy on Output? Results from an Agnostic Identification Procedure," CEPR Discussion Papers 2137, C.E.P.R. Discussion Papers.
  10. Luca Gambetti & Evi Pappa & Fabio Canova, 2008. "The Structural Dynamics of U.S. Output and Inflation: What Explains the Changes?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 40(2-3), pages 369-388, 03.
  11. 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.
  12. Juan F. Rubio-Ramírez & Daniel F.Waggoner & Tao Zha, 2008. "Structural vector autoregressions: theory of identification and algorithms for inference," Working Paper 2008-18, Federal Reserve Bank of Atlanta.
  13. 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.
  14. Lutz Kilian & Daniel P. Murphy, 2012. "Why Agnostic Sign Restrictions Are Not Enough: Understanding The Dynamics Of Oil Market Var Models," Journal of the European Economic Association, European Economic Association, vol. 10(5), pages 1166-1188, October.
  15. 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.
  16. Kilian, Lutz, 2006. "Not All Oil Price Shocks Are Alike: Disentangling Demand and Supply Shocks in the Crude Oil Market," CEPR Discussion Papers 5994, C.E.P.R. Discussion Papers.
  17. Christopher A. Sims & Tao Zha, 1995. "Error bands for impulse responses," Working Paper 95-6, Federal Reserve Bank of Atlanta.
  18. Peersman, Gert & Straub, Roland, 2004. "Technology shocks and robust sign restrictions in a euro area SVAR," Working Paper Series 0373, European Central Bank.
  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. repec:nys:sunysb:93-01 is not listed on IDEAS
  21. �scar Jordà, 2009. "Simultaneous Confidence Regions for Impulse Responses," The Review of Economics and Statistics, MIT Press, vol. 91(3), pages 629-647, August.
  22. 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.
  23. Christiane Baumeister & Gert Peersman, 2011. "The Role of Time-Varying Price Elasticities in Accounting for Volatility Changes in the Crude Oil Market," Working Papers 11-28, Bank of Canada.
  24. 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.).
  25. 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.
  26. 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.).
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