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Inference on Impulse Response Functions in Structural VAR Models

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  • Inoue, Atsushi
  • Kilian, Lutz

Abstract

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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Bibliographic Info

Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 8419.

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Date of creation: Jun 2011
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Handle: RePEc:cpr:ceprdp:8419

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Keywords: Credible Set; Impulse responses; Median; Mode; Sign restrictions; Simultaneous inference; Vector autoregression;

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References

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Citations

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Cited by:
  1. Kilian, Lutz, 2011. "Structural Vector Autoregressions," CEPR Discussion Papers 8515, C.E.P.R. Discussion Papers.
  2. Atsushi Inoue & Lutz Kilian, 2014. "Joint Confidence Sets for Structural Impulse Responses," Departmental Working Papers 1401, Southern Methodist University, Department of Economics.
  3. Ham, John C. & Woutersen, Tiemen, 2011. "Calculating Confidence Intervals for Continuous and Discontinuous Functions of Estimated Parameters," IZA Discussion Papers 5816, Institute for the Study of Labor (IZA).
  4. Gupta, Rangan & Modise, Mampho P., 2013. "Does the source of oil price shocks matter for South African stock returns? A structural VAR approach," Energy Economics, Elsevier, vol. 40(C), pages 825-831.
  5. Helmut Lütkepohl & Anna Staszewska-Bystrova & Peter Winker, 2014. "Confidence Bands for Impulse Responses: Bonferroni versus Wald," Discussion Papers of DIW Berlin 1354, DIW Berlin, German Institute for Economic Research.
  6. Benjamin Wong, 2013. "Inflation Dynamics and The Role of Oil Shocks: How Different Were the 1970s?," CAMA Working Papers 2013-59, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
  7. Chudik, Alexander & Pesaran, M. Hashem, 2014. "Theory and practice of GVAR modeling," Globalization and Monetary Policy Institute Working Paper 180, Federal Reserve Bank of Dallas.
  8. Keating, John W., 2013. "What do we learn from Blanchard and Quah decompositions of output if aggregate demand may not be long-run neutral?," Journal of Macroeconomics, Elsevier, vol. 38(PB), pages 203-217.
  9. Tachibana, Minoru, 2013. "How have inflation-targeting central banks responded to supply shocks?," Economics Letters, Elsevier, vol. 121(1), pages 1-3.

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