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Error Bands for Impulse Responses

  • Christopher A. Sims
  • Tao Zha

We show how to correctly extend known methods for generating error bands in reduced form VAR's to overidentified models. We argue that the conventional pointwise bands common in the literature should be supplemented with measures of shape uncertainty, and we show how to generate such measures. We focus on bands that characterize the shape of the likelihood. Such bands are not classical confidence regions. We explain that classical confidence regions mix information about parameter location with information about model fit, and hence can be misleading as summaries of the implications of the data for the location of parameters.

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Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 67 (1999)
Issue (Month): 5 (September)
Pages: 1113-1156

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Handle: RePEc:ecm:emetrp:v:67:y:1999:i:5:p:1113-1156
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  1. 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.
  2. 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.
  3. David B. Gordon & Eric M. Leeper, 1992. "The dynamic impacts of monetary policy: an exercise in tentative identification," FRB Atlanta Working Paper 92-13, Federal Reserve Bank of Atlanta.
  4. 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.
  5. Christopher A. Sims, 1986. "Are forecasting models usable for policy analysis?," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Win, pages 2-16.
  6. 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.
  7. repec:nys:sunysb:93-01 is not listed on IDEAS
  8. David E. Runkle, 1987. "Vector autoregressions and reality," Staff Report 107, Federal Reserve Bank of Minneapolis.
  9. Christopher A. Sims & Harald Uhlig, 1988. "Understanding unit rooters: a helicopter tour," Discussion Paper / Institute for Empirical Macroeconomics 4, Federal Reserve Bank of Minneapolis.
  10. Runkle, David E, 1987. "Vector Autoregressions and Reality," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(4), pages 437-42, October.
  11. 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.
  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. 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.
  14. 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.
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