Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-22T04:53:08.011Z Has data issue: false hasContentIssue false
  • English
  • Français

ROBUST INFERENCE IN STRUCTURAL VECTOR AUTOREGRESSIONS WITH LONG-RUN RESTRICTIONS

Published online by Cambridge University Press:  05 March 2019

Guillaume Chevillon ,
Sophocles Mavroeidis  and
Zhaoguo Zhan
Guillaume Chevillon*
Affiliation:
ESSEC Business School
Sophocles Mavroeidis
Affiliation:
University of Oxford
Zhaoguo Zhan
Affiliation:
Kennesaw State University
*
*Address correspondence to Guillaume Chevillon, ESSEC Business School, Department of Information Systems, Decision Sciences and Statistics, Ave. B. Hirsch, 95000 Cergy-Pontoise, France; e-mail: [email protected].
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Long-run restrictions are a very popular method for identifying structural vector autoregressions, but they suffer from weak identification when the data is very persistent, i.e., when the highest autoregressive roots are near unity. Near unit roots introduce additional nuisance parameters and make standard weak-instrument-robust methods of inference inapplicable. We develop a method of inference that is robust to both weak identification and strong persistence. The method is based on a combination of the Anderson-Rubin test with instruments derived by filtering potentially nonstationary variables to make them near stationary using the IVX instrumentation method of Magdalinos and Phillips (2009). We apply our method to obtain robust confidence bands on impulse responses in two leading applications in the literature.

Type
ARTICLES
Information
Econometric Theory , Volume 36 , Issue 1 , February 2020 , pp. 86 - 121
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
Copyright © Cambridge University Press 2019

Footnotes

We would like to thank Catherine Doz, Jean-Marie Dufour, Patrick Fève, TassosMagdalinos, Nour Meddahi, Adrian Pagan, the late Jean-Pierre Urbain, the Co-Editor Anna Mikusheva, the Editor Peter Phillips, two anonymous referees, and seminar participants at the Universities of Cambridge, Maastricht, Melbourne, Toulouse, as well as CREST and the European University Institute, the North American Winter Meeting of the Econometric Society, the NBER Summer Institute, the Barcelona GSE Summer Forum, the CRETE, IAAE and Oxmetrics Users conferences, the IWH-CIREQ Macroeconometrics Workshop in Halle, the 24th symposium of the SNDE for helpful comments and discussion. Mavroeidis acknowledges financial support from European Commission FP7 Marie Curie Fellowship CIG 293675, and European Research Council Consolidator Grant 647152. Zhan acknowledges the financial support from the National Natural Science Foundation of China, Project No. 71501104.

References

REFERENCES

Anderson, T.W. & Rubin, H. (1949) Estimation of the parameters of a single equation in a complete system of stochastic equations. Annals of Mathematical Statistics 20, 46–63.CrossRefGoogle Scholar
Andrews, D.W. & Cheng, X. (2012) Estimation and inference with weak, semi-strong, and strong identification. Econometrica 80 (5), 2153–2211.Google Scholar
Andrews, D.W., Cheng, X., & Guggenberger, P. (2011) Generic Results for Establishing the Asymptotic Size of Confidence Sets and Tests. Cowles Foundation Discussion Papers 1813, Cowles Foundation for Research in Economics, Yale University.CrossRefGoogle Scholar
Andrews, D.W.K. & Guggenberger, P. (2010) Applications of subsampling, hybrid, and size-correction methods. Journal of Econometrics 158(2), 285–305.CrossRefGoogle Scholar
Beveridge, S. & Nelson, C.R. (1981) A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the business cycle. Journal of Monetary Economics 7(2), 151–174.CrossRefGoogle Scholar
Blanchard, O.J. & Quah, D. (1989) The dynamic effects of aggregate demand and supply disturbances. American Economic Review 79(4), 655–673.Google Scholar
Chaudourne, J., Fève, P., & Guay, A. (2014) Understanding the effect of technology shocks in svars with long-run restrictions. Journal of Economic Dynamics and Control 41, 154–172.CrossRefGoogle Scholar
Christiano, L.J., Eichenbaum, M., & Vigfusson, R. (2003) What happens after a technology shock? International Finance Discussion Papers 768, Board of Governors of the Federal Reserve System (U.S.).CrossRefGoogle Scholar
Christiano, L.J., Eichenbaum, M., & Vigfusson, R. (2007) Assessing structural VARs. In Acemoglu, D., Rogoff, K. & Woodford, M., NBER Macroeconomics Annual 2006, vol. 21, pp. 1–106. MIT Press.Google Scholar
Dufour, J.-M. (1997) Some impossibility theorems in econometrics with applications to structural and dynamic models. Econometrica 65(6), 1365–1387.CrossRefGoogle Scholar
Dupaigne, M., Fève, P., & Matheron, J. (2007) Some analytics on bias in DSVARs. Economics Letters 97(1), 32–38.CrossRefGoogle Scholar
Fève, P. & Guay, A. (2009) The response of hours to a technology shock: A two-step structural var approach. Journal of Money, Credit and Banking 41(5), 987–1013.CrossRefGoogle Scholar
Fève, P. & Guay, A. (2010) Identification of technology shocks in structural vars. The Economic Journal 120(549), 1284–1318.CrossRefGoogle Scholar
Francis, N. & Ramey, V.A. (2005) Is the technology-driven real business cycle hypothesis dead? Shocks and aggregate fluctuations revisited. Journal of Monetary Economics 52(8), 1379–1399.CrossRefGoogle Scholar
Francis, N. & Ramey, V.A. (2009) Measures of per capita hours and their implications for the technology-hours debate. Journal of Money, Credit and Banking 41(6), 1071–1097.CrossRefGoogle Scholar
Fukac, M. & Pagan, A. (2006) Issues in adopting DSGE models for use in the policy process. CAMA Working Papers 2006–2010, Australian National University, Centre for Applied Macroeconomic Analysis.Google Scholar
Galí, J. (1999) Technology, employment, and the business cycle: Do technology shocks explain aggregate fluctuations? American Economic Review 89(1), 249–271.CrossRefGoogle Scholar
Gospodinov, N. (2010) Inference in nearly nonstationary SVAR models with long-run identifying restrictions. Journal of Business and Economic Statistics 28(1), 1–11.CrossRefGoogle Scholar
Gospodinov, N., Maynard, A., & Pesavento, E. (2011) Sensitivity of impulse responses to small low-frequency comovements: Reconciling the evidence on the effects of technology shocks. Journal of Business and Economic Statistics 29(4), 455–467.CrossRefGoogle Scholar
Hansen, B.E. (1999) The grid bootstrap and the autoregressive model. The Review of Economics and Statistics 81(4), 594–607.CrossRefGoogle Scholar
Horowitz, J.L. (2001) The bootstrap. Handbook of Econometrics 5, 3159–3228.CrossRefGoogle Scholar
Kilian, L. (1998) Small-sample confidence intervals for impulse response functions. Review of Economics and Statistics 80(2), 218–230.CrossRefGoogle Scholar
Kleibergen, F. & Mavroeidis, S. (2014) Identification issues in bayesian analysis of structural macroeconomic models with an application to the phillips curve. Journal of Applied Econometrics 29(7), 1183–1209.CrossRefGoogle Scholar
Kleibergen, F. & Zivot, E. (2003) Bayesian and classical approaches to instrumental variable regression. Journal of Econometrics 114(1), 29–72.CrossRefGoogle Scholar
Kostakis, A., Magdalinos, T., & Stamatogiannis, M.P. (2015) Robust econometric inference for stock return predictability. Review of Financial Studies 28(5), 1506–1553.CrossRefGoogle Scholar
Magdalinos, A. & Phillips, P.C.B. (2009) Econometric inference in the vicinity of unity. Working paper, Yale University, USA.Google Scholar
McCloskey, A. (2012) Bonferroni-Based Size-Correction for Nonstandard Testing Problems. Technical report, Brown University.CrossRefGoogle Scholar
Mikusheva, A. (2012) One-dimensional inference in autoregressive models with the potential presence of a unit root. Econometrica 80(1), 173–212.Google Scholar
Mittnik, S. & Zadrozny, P.A. (1993) Asymptotic distributions of impulse responses, step responses, and variance decompositions of estimated linear dynamic models. Econometrica 61(4), 857–870.CrossRefGoogle Scholar
Pagan, A.R. & Pesaran, M.H. (2008) Econometric analysis of structural systems with permanent and transitory shocks. Journal of Economic Dynamics and Control 32(10), 3376–3395.CrossRefGoogle Scholar
Pagan, A.R. & Robertson, J.C. (1998) Structural models of the liquidity effect. Review of Economics and Statistics 80(2), 202–217.CrossRefGoogle Scholar
Pesavento, E. & Rossi, B. (2005) Do technology shocks drive hours up or down? A little evidence from an agnostic procedure. Macroeconomic Dynamics 9(04), 478–488.CrossRefGoogle Scholar
Phillips, P.C., Park, J.Y., & Chang, Y. (2004) Nonlinear instrumental variable estimation of an autoregression. Journal of Econometrics 118(1), 219–246.CrossRefGoogle Scholar
Phillips, P.C.B. (2014) On confidence intervals for autoregressive roots and predictive regression. Econometrica 82(3), 1177–1195.Google Scholar
Ramey, V.A. (2016) Macroeconomic Shocks and Their Propagation. Technical report, National Bureau of Economic Research.CrossRefGoogle Scholar
Sims, C.A. (1980) Macroeconomics and reality. Econometrica 48(1), 1–48.CrossRefGoogle Scholar
Staiger, D. & Stock, J.H. (1997) Instrumental variables regression with weak instruments. Econometrica 65(3), 557–586.CrossRefGoogle Scholar
Stock, J.H. (1994) Unit roots, structural breaks and trends. In Engle, R.F. & McFadden, D. (eds.), Handbook of Econometrics, vol. 4, chapter 46, pp. 2739–2841. Elsevier.Google Scholar
Stock, J.H., Wright, J.H., & Yogo, M. (2002) A survey of weak instruments and weak identification in generalized method of moments. Journal of Business and Economic Statistics 20(4), 518–529.CrossRefGoogle Scholar
Wald, A. (1943) Tests of statistical hypotheses concerning several parameters when the number of observations is large. Transactions of the American Mathematical Society 54(3), 426–482.CrossRefGoogle Scholar
Supplementary material: PDF

Chevillon et al. supplementary material

Appendix

Download Chevillon et al. supplementary material(PDF)
PDF 586.1 KB