Bootstrapping Structural VARs: Avoiding a Potential Bias in Confidence Intervals for Impulse Response Functions

Phillips, Kerk L. and Spencer, David E. (2010): Bootstrapping Structural VARs: Avoiding a Potential Bias in Confidence Intervals for Impulse Response Functions. Published in: Journal of Macroeconomics , Vol. 33, No. 4 (2011): pp. 582-594.

Abstract

Constructing bootstrap confidence intervals for impulse response functions (IRFs) from structural vector autoregression (SVAR) models has become standard practice in empirical macroeconomic research. The accuracy of such confidence intervals can deteriorate severely, however, if the bootstrap IRFs are biased. We document an apparently common source of bias in the estimation of the VAR error covariance matrix which can be easily reduced by a scale adjustment. This bias is generally unrecognized because it only affects the bootstrap estimates of the error variance, not the original OLS estimates. Nevertheless, as we illustrate here, analytically, with sampling experiments, and in an example from the literature, the bootstrap error variance bias can have significant distorting effects on bootstrap IRF confidence intervals. We also show that scale-adjusted bootstrap confidence intervals can be expected to exhibit improved coverage accuracy.

• Item Type: MPRA Paper
• Language: English
• Keywords: impulse response function; structural VAR; bias; bootstrap
• Subjects: C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C32 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models; E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles > E32 - Business Fluctuations ; Cycles; E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles > E37 - Forecasting and Simulation: Models and Applications

References

Berkowitz, J., Kilian, L., 2000. Recent developments in bootstrapping time series. Econometric Reviews 19, 1-48.

Blanchard, O., Quah, D., 1989. The dynamic effects of aggregate demand and supply disturbances. American Economic Review 79, 655-673.

Christiano, L. J., Eichenbaum, M., Evans, C. L., 1999. Monetary policy shocks: What have we learned and to what end?, in: Taylor, J.B., Woodford, M., (Eds.) The Handbook of Macroeconomics, vol. 1. North Holland, Amsterdam, pp. 65-148.

Christiano, L. J., Eichebaum, M., Vigfusson, R., 2006. Assessing structural VARs. NBER Macroeconomics Annual 21, 1-72.

Davidson, R., MacKinnon, J. G., 1993. Estimation and inference in econometrics. Oxford University Press, New York.

Efron, B., Tibshirani, R. J., 1993. An introduction to the bootstrap. Chapman & Hall, New York.

Freedman, D. A., Peters, S. C., 1984. Bootstrapping a regression equation: Some empirical results. Journal of the American Statistical Association 79, 97-206.

Galí, J., 1999. Technology, employment, and the business cycle: Do technology shocks explain aggregate fluctuations? American Economic Review 89, 249-271.

Kilian, L., Chang, P., 2000. How accurate are confidence intervals for impulse responses in large VAR models? Economics Letters 69, 299-307.

Inoue, A., Kilian, L., 2002. Bootstrapping smooth functions of slope parameters and innovation variances in VAR(∞) models. International Economic Review 43, 309-331.

Peters, S. C., Freedman, D. A., 1984. Some notes on the bootstrap in regression problems. Journal of Business and Economics Statistics 2, 406-409.

Runkle, D. E., 1987. Vector autoregression and reality. Journal of Business and Economics Statistics 5, 437-442.

Sims, C. A., Zha, T., 1999. Error bands for impulse responses. Econometrica 67, 1113-1155.

Stine, R. A., 1987. Estimating properties of autoregressive forecasts. Journal of the American Statistical Association 82, 1072-1078.