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Econometric Inference in the Vicinity of Unity

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Author Info

  • Peter C.B.Phillips

    (Yale University, University of Auckland,University of York & Singapore Management University)

  • Tassos Magdalinos

    (University of Nottingham, UK)

Abstract

Present econometric methodology of inference in cointegrating regression is extended to mildly integrated time series of the type introduced by Magdalinos and Phillips (2007, 2009). It is well known that conventional approaches to estimating cointegrat- ing regressions fail to produce even asymptotically valid inference procedures when the regressors are nearly integrated, and substantial size distortions can occur in econometric testing. The new framework developed here enables a general approach to inference that resolves this difficulty and is robust to the persistence character- istics of the regressors, making it suitable for general practical application. Mildly integrated instruments are employed, one using system regressors and internally gen- erated instruments, the other using external instruments. These new IV techniques eliminate the endogeneity problems of conventional cointegration methods with near integrated regressors and robustify inference to uncertainty over the precise nature of the integration in the system. The use of mildly integrated instruments also provides a mechanism for linking the conventional treatment of endogeneity in simultaneous equations with the econometric methodology for cointegrated systems. The methods are easily implemented, widely applicable and help to alleviate practical concerns about the use of cointegration methodology when roots are in the vicinity of unity rather than precisely at unity.

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Bibliographic Info

Paper provided by Sim Kee Boon Institute for Financial Economics in its series Working Papers with number CoFie-06-2009.

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Length: 37 Pages
Date of creation: Apr 2009
Date of revision:
Publication status: Published in SMU-SKBI CoFie Working Paper
Handle: RePEc:skb:wpaper:cofie-06-2009

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Keywords: Central limit theory; Cointegration; Endogeneity bias; Instrumentation; Mild integration; Mixed normality; Robustness; Simultaneity.;

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References

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  1. Peter C.B. Phillips & Tassos Magdalinos, 2004. "Limit Theory for Moderate Deviations from a Unit Root," Cowles Foundation Discussion Papers 1471, Cowles Foundation for Research in Economics, Yale University.
  2. Stock, James H, 1987. "Asymptotic Properties of Least Squares Estimators of Cointegrating Vectors," Econometrica, Econometric Society, vol. 55(5), pages 1035-56, September.
  3. James H. Stock & Mark W. Watson, 1991. "A simple estimator of cointegrating vectors in higher order integrated systems," Working Paper Series, Macroeconomic Issues 91-3, Federal Reserve Bank of Chicago.
  4. 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.
  5. Abadir,Karim M. & Magnus,Jan R., 2005. "Matrix Algebra," Cambridge Books, Cambridge University Press, number 9780521537469, April.
  6. 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.
  7. 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.
  8. Magdalinos, Tassos & Phillips, Peter C.B., 2009. "Limit Theory For Cointegrated Systems With Moderately Integrated And Moderately Explosive Regressors," Econometric Theory, Cambridge University Press, vol. 25(02), pages 482-526, April.
  9. Phillips, Peter C B & Hansen, Bruce E, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," Review of Economic Studies, Wiley Blackwell, vol. 57(1), pages 99-125, January.
  10. 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.
  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. Saikkonen, Pentti, 1991. "Asymptotically Efficient Estimation of Cointegration Regressions," Econometric Theory, Cambridge University Press, vol. 7(01), pages 1-21, March.
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Citations

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Cited by:
  1. Phillips, Peter C.B., 2014. "Optimal estimation of cointegrated systems with irrelevant instruments," Journal of Econometrics, Elsevier, vol. 178(P2), pages 210-224.
  2. Ioannis Kasparis & Elena Andreou & Peter C. B. Phillips, 2012. "Nonparametric Predictive Regression," University of Cyprus Working Papers in Economics 14-2012, University of Cyprus Department of Economics.
  3. Phillips, Peter C.B. & Lee, Ji Hyung, 2013. "Predictive regression under various degrees of persistence and robust long-horizon regression," Journal of Econometrics, Elsevier, vol. 177(2), pages 250-264.
  4. Peter C.B. Phillips, 2012. "On Confidence Intervals for Autoregressive Roots and Predictive Regression," Cowles Foundation Discussion Papers 1879, Cowles Foundation for Research in Economics, Yale University.

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