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ON THE ROBUSTNESS OF HYPOTHESIS TESTING BASED ON FULLY MODIFIED VECTOR AUTOREGRESSION WHEN SOME ROOTS ARE ALMOST ONE

Published online by Cambridge University Press:  10 February 2004

Heikki Kauppi
Heikki Kauppi
Affiliation:
University of Helsinki
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Abstract

This paper proves that the fully modified vector autoregression (FM-VAR) estimator has second-order bias effects when some roots are local to unity. These bias effects are shown to result in potentially severe size distortions in FM-VAR testing when the hypothesis involves near unit root variables. In addition, the paper reveals that with the FM-VAR method near unit roots become estimated as exact unit roots with convergence speed faster than the order of the sample size. Also this result implies problems for FM-VAR testing, as such “hyperconsistent” estimates give rise to degenerate limit distributions under the null hypothesis.I am grateful to Pentti Saikkonen, Jim Stock, Markku Lanne, Jukka Nyblom, and three referees for very helpful comments on earlier drafts. This paper is a part of the research program of the Research Unit on Economic Structures and Growth (RUESG) at the Department of Economics at the University of Helsinki. Financial support from the ASLA Fulbright, the Yrjö Jahnsson Foundation, and the Finnish Cultural Foundation is gratefully acknowledged. The usual disclaimer applies.

Type
Research Article
Information
Econometric Theory , Volume 20 , Issue 2 , April 2004 , pp. 341 - 359
Copyright
© 2004 Cambridge University Press

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References

REFERENCES

Elliott, G. (1998) On the robustness of cointegration methods when regressors almost have unit roots. Econometrica 66, 149–158.Google Scholar
Freeman, J., D. Houser, P.M. Kellstedt, & J.T. Williams (1998) Long-memoried processes, unit roots, and causal inference in political science. American Journal of Political Science 42, 1289–1327.Google Scholar
Johansen, S. (1991) Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models. Econometrica 59, 1551–1580.Google Scholar
Park, J.Y. & P.C.B. Phillips (1988) Statistical inference in regressions with integrated processes, part 1. Econometric Theory 4, 468–497.Google Scholar
Phillips, P.C.B. (1991) Spectral regression for cointegrated time series. In W. Barnett, J. Powell, & G. Tauchen (eds.), Nonparametric and Semiparametric Methods in Econometrics and Statistics, pp. 413–435. Cambridge University Press.
Phillips, P.C.B. (1995) Fully modified least squares and vector autoregression. Econometrica 63, 1023–1078.Google Scholar
Phillips, P.C.B. & B.E. Hansen (1990) Statistical inference in instrumental variables regression with I(1) processes. Review of Economic Studies 57, 99–125.CrossRefGoogle Scholar
Quintos, C.E. (1998) Fully modified vector autoregressive inference in partially nonstationary models. Journal of the American Statistical Association 93, 783–795.Google Scholar
Saikkonen, P. & H. Lütkepohl (1999) Local power of likelihood ratio tests for the cointegrating rank of a VAR process. Econometric Theory 15, 50–78.Google Scholar
Toda, H.Y. & T. Yamamoto (1995) Statistical inference in vector autoregressions with possibly integrated processes. Journal of Econometrics 66, 225–250.Google Scholar
Yamada, H. & H.Y. Toda (1997) A note on hypothesis testing based on the fully modified vector autoregression. Economics Letters 56, 27–39.Google Scholar
Yamada, H. & H.Y. Toda (1998) Inference in possibly integrated vector autoregressive models: Some finite sample evidence. Journal of Econometrics 86, 55–95.Google Scholar