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A residual-based cointegration test for near unit root variables

  • Erik Hjalmarsson
  • Par Osterholm

Methods of inference based on a unit root assumption in the data are typically not robust to even small deviations from this assumption. In this paper, we propose robust procedures for a residual-based test of cointegration when the data are generated by a near unit root process. A Bonferroni method is used to address the uncertainty regarding the exact degree of persistence in the process. We thus provide a method for valid inference in multivariate near unit root processes where standard cointegration tests may be subject to substantial size distortions and standard OLS inference may lead to spurious results. Empirical illustrations are given by: (i) a re-examination of the Fisher hypothesis, and (ii) a test of the validity of the cointegrating relationship between aggregate consumption, asset holdings, and labor income, which has attracted a great deal of attention in the recent finance literature.

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Paper provided by Board of Governors of the Federal Reserve System (U.S.) in its series International Finance Discussion Papers with number 907.

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Date of creation: 2007
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Handle: RePEc:fip:fedgif:907
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  1. Peter C.B. Phillips, 1986. "Regression Theory for Near-Integrated Time Series," Cowles Foundation Discussion Papers 781R, Cowles Foundation for Research in Economics, Yale University, revised Jan 1987.
  2. Wallace, Myles S & Warner, John T, 1993. "The Fisher Effect and the Term Structure of Interest Rates: Tests of Cointegration," The Review of Economics and Statistics, MIT Press, vol. 75(2), pages 320-24, May.
  3. repec:cup:etheor:v:10:y:1994:i:1:p:95-115 is not listed on IDEAS
  4. Mishkin, Frederic S., 1992. "Is the Fisher effect for real? : A reexamination of the relationship between inflation and interest rates," Journal of Monetary Economics, Elsevier, vol. 30(2), pages 195-215, November.
  5. Wright, Jonathan H, 2000. "Confidence Sets for Cointegrating Coefficients Based on Stationarity Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(2), pages 211-22, April.
  6. Russell Cooper & Joao Ejarque, 1994. "Financial Intermediation and Aggregate Fluctuations: A Quantative Analysis," NBER Working Papers 4819, National Bureau of Economic Research, Inc.
  7. Shin, Yongcheol, 1994. "A Residual-Based Test of the Null of Cointegration Against the Alternative of No Cointegration," Econometric Theory, Cambridge University Press, vol. 10(01), pages 91-115, March.
  8. Evans, Martin D D & Lewis, Karen K, 1995. " Do Expected Shifts in Inflation Affect Estimates of the Long-Run Fisher Relation?," Journal of Finance, American Finance Association, vol. 50(1), pages 225-53, March.
  9. Campbell, John & Yogo, Motohiro, 2006. "Efficient tests of stock return predictability," Scholarly Articles 3122601, Harvard University Department of Economics.
  10. James H. Stock, 1991. "Confidence Intervals for the Largest Autoresgressive Root in U.S. Macroeconomic Time Series," NBER Technical Working Papers 0105, National Bureau of Economic Research, Inc.
  11. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-80, November.
  12. Michael Jansson & Marcelo J. Moreira, 2006. "Optimal Inference in Regression Models with Nearly Integrated Regressors," Econometrica, Econometric Society, vol. 74(3), pages 681-714, 05.
  13. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  14. Miguel Casares, 2007. "The New Keynesian Model and the Euro Area Business Cycle," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 69(2), pages 209-244, 04.
  15. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-36, July.
  16. Peter C.B. Phillips & Sam Ouliaris, 1987. "Asymptotic Properties of Residual Based Tests for Cointegration," Cowles Foundation Discussion Papers 847R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1988.
  17. Sydney Ludvigson & Martin Lettau, 1999. "Consumption, aggregate wealth and expected stock returns," Staff Reports 77, Federal Reserve Bank of New York.
  18. Graham Elliott, 1998. "On the Robustness of Cointegration Methods when Regressors Almost Have Unit Roots," Econometrica, Econometric Society, vol. 66(1), pages 149-158, January.
  19. Gali, J., 1992. "Variability of Durable and Nondurable Consumption: Evidence for Six O.E.C.D. Countries," Papers 92-06, Columbia - Graduate School of Business.
  20. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
  21. Wu, Jhy-Lin & Chen, Show-Lin, 2001. " Mean Reversion of Interest Rates in the Eurocurrency Market," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 63(4), pages 459-73, September.
  22. Crowder, William J & Hoffman, Dennis L, 1996. "The Long-Run Relationship between Nominal Interest Rates and Inflation: The Fisher Equation Revisited," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 28(1), pages 102-18, February.
  23. Culver, Sarah E & Papell, David H, 1997. "Is There a Unit Root in the Inflation Rate? Evidence from Sequential Break and Panel Data Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(4), pages 435-44, July-Aug..
  24. Erik Hjalmarsson & Par Osterholm, 2007. "Testing for cointegration using the Johansen methodology when variables are near-integrated," International Finance Discussion Papers 915, Board of Governors of the Federal Reserve System (U.S.).
  25. repec:cup:macdyn:v:4:y:2000:i:4:p:423-47 is not listed on IDEAS
  26. Diebold, Francis X & Senhadji, Abdelhak S, 1996. "The Uncertain Unit Root in Real GNP: Comment," American Economic Review, American Economic Association, vol. 86(5), pages 1291-98, December.
  27. Hall, Robert E, 1978. "Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence," Journal of Political Economy, University of Chicago Press, vol. 86(6), pages 971-87, December.
  28. repec:cup:etheor:v:11:y:1995:i:5:p:1131-47 is not listed on IDEAS
  29. Wu, Yangru & Zhang, Hua, 1996. "Mean Reversion in Interest Rates: New Evidence from a Panel of OECD Countries," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 28(4), pages 604-21, November.
  30. Leybourne, S J & McCabe, B P M, 1994. "A Simple Test for Cointegration," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 56(1), pages 97-103, February.
  31. Cavanagh, Christopher L. & Elliott, Graham & Stock, James H., 1995. "Inference in Models with Nearly Integrated Regressors," Econometric Theory, Cambridge University Press, vol. 11(05), pages 1131-1147, October.
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