Abstract
We examine the finite-sample accuracy of impulse responses obtained using local projections (LP) and vector autoregressive (VAR) models. In view of the fact that impulse responses are differences between multistep predictors, we propose to assess the relative performance of impulse-response estimators using tests for equal predictive accuracy. In our Monte Carlo experiments, LP-based and VAR-based estimators are found to be equally accurate in large samples under a mean-squared-error risk function. VAR-based estimators tend to have an advantage over LP-based estimators in small and moderately sized samples, particularly at long horizons.
Acknowledgments
The authors thank Martin Gonzalez-Rozada, Constantino Hevia, Fabio Spagnolo and two anonymous referees for helpful comments and/or discussions. For the purpose of open access, the authors have applied a Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising.
References
Brugnolini, L. 2018. “About Local Projection Impulse Response Function Reliability.” CEIS Working Paper No. 440. University of Rome Tor Vergata.10.2139/ssrn.3229218Search in Google Scholar
Diebold, F. X., and R. S. Mariano. 1995. “Testing the Equality of Prediction Mean Squared Errors.” Journal of Business & Economic Statistics 13 (3): 253–63.10.1080/07350015.1995.10524599Search in Google Scholar
Harvey, D., S. Leybourne, and P. Newbold. 1997. “Testing the Equality of Prediction Mean Squared Errors.” International Journal of Forecasting 13 (2): 281–91. https://doi.org/10.1016/s0169-2070(96)00719-4.Search in Google Scholar
Herbst, E., and B. K. Johannsen. 2021. “Bias in Local Projections.” FEDS Working Paper No. 2020-010R1. Board of Governors of the Federal Reserve System.10.17016/feds.2020.010r1Search in Google Scholar
Jordà, O. 2005. “Estimation and Inference of Impulse Responses by Local Projections.” The American Economic Review 95 (1): 161–82. https://doi.org/10.1257/0002828053828518.Search in Google Scholar
Koop, G., H. M. Pesaran, and S. M. Potter. 1996. “Impulse Response Analysis in Nonlinear Multivariate Models.” Journal of Econometrics 74 (1): 119–47. https://doi.org/10.1016/0304-4076(95)01753-4.Search in Google Scholar
Li, D., M. Plagborg-Møller, and C. K. Wolf. 2024. “Local Projections vs. VARs: Lessons from Thousands of DGPs.” Journal of Econometrics 244 (2): 105722. https://doi.org/10.1016/j.jeconom.2024.105722.Search in Google Scholar
Plagborg-Møller, M., and C. K. Wolf. 2021. “Local Projections and VARs Estimate the Same Impulse Responses.” Econometrica 89 (2): 955–80.10.3982/ECTA17813Search in Google Scholar
Supplementary Material
This article contains supplementary material (https://doi.org/10.1515/snde-2024-0053).
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