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Inference for Impulse Responses

  • Oscar Jorda

    (Department of Economics, University of California Davis)

Poor identification of individual impulse response coefficients does not necessarily mean that an impulse response is imprecisely estimated. This paper introduces a three-pronged approach on how to communicate uncertainty of impulse response estimates: (1) withWald tests of joint significance; (2) with conditional t-tests of individual marginal coefficient significance; and (3) with fan charts based on the percentiles of the joint Wald statistics. The paper also shows how to anchor the impulse response analysis with a priori economic restrictions that can be formally tested and used to tighten structural identification. These methods are universal and do not depend on how the impulse responses are estimated. An empirical application illustrates the techniques in practice.

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Paper provided by University of California, Davis, Department of Economics in its series Working Papers with number 77.

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Length: 40
Date of creation: 07 Jun 2007
Date of revision:
Handle: RePEc:cda:wpaper:07-7
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  1. Gali, J., 1996. "Technology, Employment, and the Business Cycle: Do Technology Shocks Explain Aggregate Fluctuations?," Working Papers 96-28, C.V. Starr Center for Applied Economics, New York University.
  2. Olivier Jean Blanchard & Danny Quah, 1988. "The Dynamic Effects of Aggregate Demand and Supply Disturbance," Working papers 497, Massachusetts Institute of Technology (MIT), Department of Economics.
  3. Leeper, Eric M. & Zha, Tao, 2003. "Modest policy interventions," Journal of Monetary Economics, Elsevier, vol. 50(8), pages 1673-1700, November.
  4. Selva Demiralp & Kevin D. Hoover, 2003. "Searching for the Causal Structure of a Vector Autoregression," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 65(s1), pages 745-767, December.
  5. 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.
  6. James H. Stock & Mark W. Watson, 2001. "Vector Autoregressions," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 101-115, Fall.
  7. 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.
  8. 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.
  9. Kuersteiner, Guido M., 2001. "Optimal instrumental variables estimation for ARMA models," Journal of Econometrics, Elsevier, vol. 104(2), pages 359-405, September.
  10. Kuersteiner, Guido M., 2002. "Efficient Iv Estimation For Autoregressive Models With Conditional Heteroskedasticity," Econometric Theory, Cambridge University Press, vol. 18(03), pages 547-583, June.
  11. Lewis, Richard & Reinsel, Gregory C., 1985. "Prediction of multivariate time series by autoregressive model fitting," Journal of Multivariate Analysis, Elsevier, vol. 16(3), pages 393-411, June.
  12. Òscar Jordà, 2005. "Estimation and Inference of Impulse Responses by Local Projections," American Economic Review, American Economic Association, vol. 95(1), pages 161-182, March.
  13. Lütkepohl, Helmut & Poskitt, D.S., 1991. "Estimating Orthogonal Impulse Responses via Vector Autoregressive Models," Econometric Theory, Cambridge University Press, vol. 7(04), pages 487-496, December.
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