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Published online by Cambridge University Press:  05 March 2019

Guillaume Chevillon*
ESSEC Business School
Sophocles Mavroeidis
University of Oxford
Zhaoguo Zhan
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:
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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.

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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.



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