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

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Author Info
Barbara Rossi (Duke)
Elena Pesavento (Emory)

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

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Find related papers by JEL classification:
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
F40 - International Economics - - Macroeconomic Aspects of International Trade and Finance - - - General

References listed on IDEAS
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  1. Stock, James H., 1991. "Confidence intervals for the largest autoregressive root in U.S. macroeconomic time series," Journal of Monetary Economics, Elsevier, vol. 28(3), pages 435-459, December. [Downloadable!] (restricted)
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  2. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January. [Downloadable!] (restricted)
  3. Elliott, Graham & Jansson, Michael, 2003. "Testing for unit roots with stationary covariates," Journal of Econometrics, Elsevier, vol. 115(1), pages 75-89, July. [Downloadable!] (restricted)
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  4. Clarida, Richard & Galí, Jordi, 1994. "Sources of Real Exchange Rate Fluctuations: How Important are Nominal Shocks?," CEPR Discussion Papers 951, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  5. Kilian, Lutz, 2001. "Impulse Response Analysis in Vector Autoregressions with Unknown Lag Order," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 20(3), pages 161-79, April.
  6. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-36, July. [Downloadable!] (restricted)
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  7. Blanchard, Olivier Jean & Quah, Danny, 1989. "The Dynamic Effects of Aggregate Demand and Supply Disturbances," American Economic Review, American Economic Association, vol. 79(4), pages 655-73, September. [Downloadable!] (restricted)
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  8. M. Hashem Pesaran & Til Schuermann & Scott M. Weiner, 2002. "Modeling Regional Interdependencies Using a Global Error-Correcting Macroeconometric Model," Center for Financial Institutions Working Papers 01-38, Wharton School Center for Financial Institutions, University of Pennsylvania. [Downloadable!]
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  9. Nikolay Gospodinov, 2004. "Asymptotic confidence intervals for impulse responses of near-integrated processes," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 505-527, December. [Downloadable!] (restricted)
  10. Lutz Kilian, 1998. "Confidence intervals for impulse responses under departures from normality," Econometric Reviews, Taylor and Francis Journals, vol. 17(1), pages 1-29. [Downloadable!] (restricted)
  11. Ventzislav Ivanov & Lutz Kilian, 2005. "A Practitioner's Guide to Lag Order Selection For VAR Impulse Response Analysis," Studies in Nonlinear Dynamics & Econometrics, Berkeley Electronic Press, vol. 9(1), pages 1219-1219. [Downloadable!] (restricted)
  12. Koop, Gary & Pesaran, M. Hashem & Potter, Simon M., 1996. "Impulse response analysis in nonlinear multivariate models," Journal of Econometrics, Elsevier, vol. 74(1), pages 119-147, September. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. 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. [Downloadable!]
  2. Elena Pesavento, 2006. "Near-Optimal Unit Root Tests with Stationary Covariates with Better Finite Sample Size," Economics Working Papers ECO2006/18, European University Institute. [Downloadable!]
    Other versions:
  3. Elena Pesavento & Barbara Rossi, 2003. "Do Technology Shocks Drive Hours Up or Down? A Little Evidence From an Agnostic Procedure," Emory Economics 0326, Department of Economics, Emory University (Atlanta). [Downloadable!]
    Other versions:
  4. Kilian, Lutz & Kim, Yun Jung, 2009. "Do Local Projections Solve the Bias Problem in Impulse Response Inference?," CEPR Discussion Papers 7266, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
  5. Barbara Rossi & Elena Pesavento, 2004. "Do Technology Shocks Drive Hours Up or Down?," Econometric Society 2004 North American Summer Meetings 96, Econometric Society. [Downloadable!]
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