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

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References

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  1. Hiro Y. Toda & Peter C.B. Phillips, 1991. "Vector Autoregression and Causality," Cowles Foundation Discussion Papers 977, Cowles Foundation for Research in Economics, Yale University.
  2. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
  3. 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.
  4. Robert B. Litterman & Laurence M. Weiss, 1984. "Money, real interest rates, and output: a reinterpretation of postwar U.S. data," Staff Report 89, Federal Reserve Bank of Minneapolis.
  5. Christopher A. Sims, 1980. "Comparison of Interwar and Postwar Business Cycles: Monetarism Reconsidered," NBER Working Papers 0430, National Bureau of Economic Research, Inc.
  6. Peter C.B. Phillips, 1987. "Multiple Regression with Integrated Time Series," Cowles Foundation Discussion Papers 852, Cowles Foundation for Research in Economics, Yale University.
  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. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
  9. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
  10. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
  11. 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.
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Cited by:
  1. 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.
  2. 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.

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