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Error bands for impulse responses

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Author Info

  • Christopher A. Sims
  • Tao Zha

Abstract

We examine the theory and behavior in practice of Bayesian and bootstrap methods for generating error bands on impulse responses in dynamic linear models. The Bayesian intervals have a firmer theoretical foundation in small samples, are easier to compute, and are about as good in small samples by classical criteria as are the best bootstrap intervals. Bootstrap intervals based directly on the simulated small-sample distribution of an estimator, without bias correction, perform very badly. We show that a method that has been used to extend to the overidentified case standard algorithms for Bayesian intervals in reduced form models is incorrect, and we show how to obtain correct Bayesian intervals for this case.

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Bibliographic Info

Paper provided by Federal Reserve Bank of Atlanta in its series Working Paper with number 95-6.

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Date of creation: 1995
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Publication status: Published in Econometrica, September 1999
Handle: RePEc:fip:fedawp:95-6

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Keywords: Econometric models;

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References

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  1. 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.
  2. Sims, Christopher A & Uhlig, Harald, 1991. "Understanding Unit Rooters: A Helicopter Tour," Econometrica, Econometric Society, vol. 59(6), pages 1591-99, November.
  3. Runkle, David E, 1987. "Vector Autoregressions and Reality," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(4), pages 437-42, October.
  4. Sims, Christopher A & Stock, James H & Watson, Mark W, 1990. "Inference in Linear Time Series Models with Some Unit Roots," Econometrica, Econometric Society, vol. 58(1), pages 113-44, January.
  5. repec:nys:sunysb:93-01 is not listed on IDEAS
  6. David B. Gordon & Eric M. Leeper, 1992. "The dynamic impacts of monetary policy: an exercise in tentative identification," Working Paper 92-13, Federal Reserve Bank of Atlanta.
  7. Kloek, Tuen & van Dijk, Herman K, 1978. "Bayesian Estimates of Equation System Parameters: An Application of Integration by Monte Carlo," Econometrica, Econometric Society, vol. 46(1), pages 1-19, January.
  8. James M. Poterba & Julio J. Rotemberg & Lawrence H. Summers, 1987. "A Tax-Based Test for Nominal Rigidities," NBER Working Papers 1627, National Bureau of Economic Research, Inc.
  9. Lastrapes, William D & Selgin, George A, 1994. "Buffer-Stock Money: Interpreting Short-Run Dynamics Using Long-Run Restrictions," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 26(1), pages 34-54, February.
  10. 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.
  11. David E. Runkle, 1987. "Vector autoregressions and reality," Staff Report 107, Federal Reserve Bank of Minneapolis.
  12. Christopher A. Sims, 1986. "Are forecasting models usable for policy analysis?," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Win, pages 2-16.
  13. Peter C.B. Phillips, 1990. "To Criticize the Critics: An Objective Bayesian Analysis of Stochastic Trends," Cowles Foundation Discussion Papers 950, Cowles Foundation for Research in Economics, Yale University.
  14. Koop, G, 1992. "Aggregate Shocks and Macroeconomic Fluctuations: A Bayesian Approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(4), pages 395-411, Oct.-Dec..
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