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Small sample confidence intervals for multivariate impulse response functions at long horizons

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  • Barbara Rossi (Duke)
  • Elena Pesavento (Emory)

Abstract

Existing methods for constructing confidence bands for multivariate impulse response functions depend on auxiliary assumptions on the order of integration of the variables. Thus, they may have poor coverage at long lead times when variables are highly persistent. Solutions that have been proposed in the literature may be computationally challenging. The goal of this paper is to propose a simple method for constructing confidence bands for impulse response functions that are robust to the presence of highly persistent processes. We do so by using alternative approximations based on local-to-unity asymptotic theory and by allowing the lead time of the impulse response function to be a fixed fraction of the sample size. Monte Carlo simulations, in which this method is compared with those existing in the literature, show that our method has good coverage properties. We also investigate the properties of the various methods in terms of the length of their confidence bands. Finally, we show, with empirical applications, that our method may provide different economic interpretations of the data. An example to the analysis of nominal versus real sources of fluctuations in real and nominal exchange rates is discussed

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Bibliographic Info

Paper provided by Econometric Society in its series Econometric Society 2004 North American Winter Meetings with number 364.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:nawm04:364

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Keywords: Local to unity asymptotics; persistence; impulse response functions; confidence bands;

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References

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  1. Richard Clarida & Jordi Gali, 1994. "Sources of Real Exchange Rate Fluctuations: How Important are Nominal Shocks?," NBER Working Papers 4658, National Bureau of Economic Research, Inc.
  2. Ivanov Ventzislav & Kilian Lutz, 2005. "A Practitioner's Guide to Lag Order Selection For VAR Impulse Response Analysis," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, De Gruyter, vol. 9(1), pages 1-36, March.
  3. Nikolay Gospodinov, 2004. "Asymptotic confidence intervals for impulse responses of near-integrated processes," Econometrics Journal, Royal Economic Society, Royal Economic Society, vol. 7(2), pages 505-527, December.
  4. Pesaran M.H. & Schuermann T. & Weiner S.M., 2004. "Modeling Regional Interdependencies Using a Global Error-Correcting Macroeconometric Model," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 22, pages 129-162, April.
  5. Andrews, Donald W K, 1993. "Exactly Median-Unbiased Estimation of First Order Autoregressive/Unit Root Models," Econometrica, Econometric Society, Econometric Society, vol. 61(1), pages 139-65, January.
  6. Graham Elliott & Thomas J. Rothenberg & James H. Stock, 1992. "Efficient Tests for an Autoregressive Unit Root," NBER Technical Working Papers 0130, National Bureau of Economic Research, Inc.
  7. Stock, James H., 1991. "Confidence intervals for the largest autoregressive root in U.S. macroeconomic time series," Journal of Monetary Economics, Elsevier, Elsevier, vol. 28(3), pages 435-459, December.
  8. Rossi, Barbara, 2005. "Confidence Intervals for Half-Life Deviations From Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 23, pages 432-442, October.
  9. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, Econometric Society, vol. 48(1), pages 1-48, January.
  10. Olivier Jean Blanchard & Danny Quah, 1988. "The Dynamic Effects of Aggregate Demand and Supply Disturbance," Working papers, Massachusetts Institute of Technology (MIT), Department of Economics 497, Massachusetts Institute of Technology (MIT), Department of Economics.
  11. Koop, Gary & Pesaran, M. Hashem & Potter, Simon M., 1996. "Impulse response analysis in nonlinear multivariate models," Journal of Econometrics, Elsevier, Elsevier, vol. 74(1), pages 119-147, September.
  12. Elliott, Graham & Jansson, Michael, 2003. "Testing for unit roots with stationary covariates," Journal of Econometrics, Elsevier, Elsevier, vol. 115(1), pages 75-89, July.
  13. Kilian, Lutz, 2001. "Impulse Response Analysis in Vector Autoregressions with Unknown Lag Order," Journal of Forecasting, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 20(3), pages 161-79, April.
  14. Lutz Kilian, 1998. "Confidence intervals for impulse responses under departures from normality," Econometric Reviews, Taylor & Francis Journals, Taylor & Francis Journals, vol. 17(1), pages 1-29.
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