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The Spurious Effect of Unit Roots on Exogeneity Tests in Vector Autoregressions: An Analytical Study

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Abstract

This paper analyzes whether inclusion of a statistically independent random walk in a vector autoregression can result in spurious inference. The problem was raised originally by Ohanian (1988). In a Monte Carlo simulation based on the VAR's estimated by Sims (1980b, 1982), Ohanian found that block exogeneity of the genuine variables with respect to an artificially generated random walk variable was rejected too often. In the present paper we attempt a full analytical study of this problem. It can be shown that if the genuine variables are nonstationary, the Wald statistic for testing the block exogeneity hypothesis does not have the usual asymptotic chi-square distribution. This result is consistent with Ohanian's finding. Furthermore, the derived asymptotic distribution is free of nuisance parameters so that we can unambiguously determine the effect of including the random walk. Interestingly, it can also be shown that if the genuine variables of the model are stationary, the asymptotic distribution is still chi-square in spite of the inclusion of the random walk.

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File URL: http://cowles.econ.yale.edu/P/cd/d09b/d0978.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 978.

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Length: 30 pages
Date of creation: May 1991
Date of revision:
Publication status: Published in Oxford Economic Papers (1993), 59: 229-255
Handle: RePEc:cwl:cwldpp:978

Note: CFP 854.
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

Related research

Keywords: Random walk; exogeneity; vector autoregressions; unit roots; Wald tests;

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References

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  1. Peter C.B. Phillips, 1985. "Understanding Spurious Regressions in Econometrics," Cowles Foundation Discussion Papers 757, Cowles Foundation for Research in Economics, Yale University.
  2. Toda, Hiro Y & Phillips, Peter C B, 1993. "Vector Autoregressions and Causality," Econometrica, Econometric Society, vol. 61(6), pages 1367-93, November.
  3. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
  4. Park, Joon Y. & Phillips, Peter C.B., 1989. "Statistical Inference in Regressions with Integrated Processes: Part 2," Econometric Theory, Cambridge University Press, vol. 5(01), pages 95-131, April.
  5. Litterman, Robert B & Weiss, Laurence M, 1985. "Money, Real Interest Rates, and Output: A Reinterpretation of Postwar U.S. Data," Econometrica, Econometric Society, vol. 53(1), pages 129-56, January.
  6. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
  7. Ohanian, Lee E., 1988. "The spurious effects of unit roots on vector autoregressions : A Monte Carlo study," Journal of Econometrics, Elsevier, vol. 39(3), pages 251-266, November.
  8. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
  9. Peter C.B. Phillips, 1987. "Multiple Regression with Integrated Time Series," Cowles Foundation Discussion Papers 852, Cowles Foundation for Research in Economics, Yale University.
  10. Sims, Christopher A & Stock, James H & Watson, Mark W, 1990. "Inference in Linear Time Series Models with Some Unit Roots," Econometrica, Econometric Society, vol. 58(1), pages 113-44, January.
  11. Sims, Christopher A, 1980. "Comparison of Interwar and Postwar Business Cycles: Monetarism Reconsidered," American Economic Review, American Economic Association, vol. 70(2), pages 250-57, May.
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Cited by:
  1. Robert K. Kaufmann & David I. Stern, 2004. "A Statistical Evaluation of Atmosphere-Ocean General Circulation Models: Complexity vs. Simplicity," Rensselaer Working Papers in Economics 0411, Rensselaer Polytechnic Institute, Department of Economics.
  2. Peter C.B. Phillips, 1991. "The Long-Run Australian Consumption Function Reexamined: An Empirical Exercise in Bayesian Influence," Cowles Foundation Discussion Papers 1000, Cowles Foundation for Research in Economics, Yale University.

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