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Error Bands for Impulse Responses

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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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File URL: http://cowles.econ.yale.edu/P/cd/d10b/d1085.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1085.

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Length: 42 pages
Date of creation: Nov 1994
Date of revision:
Publication status: Published in Econometrica (1999), 67(5): 1113-1156
Handle: RePEc:cwl:cwldpp:1085

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  1. Christopher A. Sims & Harald Uhlig, 1988. "Understanding unit rooters: a helicopter tour," Discussion Paper / Institute for Empirical Macroeconomics 4, Federal Reserve Bank of Minneapolis.
  2. David B. Gordon & Eric M. Leeper, 1993. "The dynamic impacts of monetary policy: an exercise in tentative identification," Working Paper 93-5, Federal Reserve Bank of Atlanta.
  3. David E. Runkle, 1987. "Vector autoregressions and reality," Staff Report 107, Federal Reserve Bank of Minneapolis.
  4. Phillips, P C B, 1991. "To Criticize the Critics: An Objective Bayesian Analysis of Stochastic Trends," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(4), pages 333-64, Oct.-Dec..
  5. 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.
  6. repec:nys:sunysb:93-01 is not listed on IDEAS
  7. 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.
  8. 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.
  9. Poterba, James M & Rotemberg, Julio J & Summers, Lawrence H, 1986. "A Tax-Based Test for Nominal Rigidities," American Economic Review, American Economic Association, vol. 76(4), pages 659-75, September.
  10. 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.
  11. Christopher A. Sims, 1986. "Are forecasting models usable for policy analysis?," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Win, pages 2-16.
  12. 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..
  13. Runkle, David E, 1987. "Vector Autoregressions and Reality," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(4), pages 437-42, October.
  14. 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.
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