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Optimal Estimation of Cointegrated Systems with Irrelevant Instruments

It has been know since Phillips and Hansen (1990) that cointegrated systems can be consistently estimated using stochastic trend instruments that are independent of the system variables. A similar phenomenon occurs with deterministically trending instruments. The present work shows that such “irrelevant” deterministic trend instruments may be systematically used to produce asymptotically efficient estimates of a cointegrated system. The approach is convenient in practice, involves only linear instrumental variables estimation, and is a straightforward one step procedure with no loss of degrees of freedom in estimation. Simulations reveal that the procedure works well in practice, having little finite sample bias and less finite sample dispersion than other popular cointegrating regression procedures such as reduced rank VAR regression, fully modified least squares, and dynamic OLS. The procedure is shown to be a form of maximum likelihood estimation where the likelihood is constructed for data projected onto the trending instruments. This “trend likelihood”” is related to the notion of the local Whittle likelihood but avoids frequency domain issues altogether. Correspondingly, the approach developed here has many potential applications beyond conventional cointegrating regression, such as the estimation of long memory and fractional cointegrating relationships.

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File URL: http://cowles.econ.yale.edu/P/cd/d15a/d1547.pdf
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Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1547.

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Length: 44 pages
Date of creation: Jan 2006
Date of revision:
Publication status: Published in Journal of Econometrics (January 2014), 178(2): 210-214
Handle: RePEc:cwl:cwldpp:1547
Note: CFP 1400
Contact details of provider: Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/

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Order Information: Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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  1. Peter C.B. Phillips, 1987. "Partially Identified Econometric Models," Cowles Foundation Discussion Papers 845R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1988.
  2. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  3. Peter C. B. Phillips, 1998. "New Tools for Understanding Spurious Regressions," Econometrica, Econometric Society, vol. 66(6), pages 1299-1326, November.
  4. Phillips, Peter C.B., 2005. "Challenges of trending time series econometrics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 68(5), pages 401-416.
  5. John C. Chao & Norman Rasmus Swanson, 2004. "Consistent Estimation with a Large Number of Weak Instruments," Yale School of Management Working Papers ysm374, Yale School of Management.
  6. 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.
  7. repec:cup:etheor:v:7:y:1991:i:1:p:1-21 is not listed on IDEAS
  8. Xiao, Zhijie & Phillips, Peter C. B., 2002. "Higher order approximations for Wald statistics in time series regressions with integrated processes," Journal of Econometrics, Elsevier, vol. 108(1), pages 157-198, May.
  9. Liao, Zhipeng, 2013. "Adaptive Gmm Shrinkage Estimation With Consistent Moment Selection," Econometric Theory, Cambridge University Press, vol. 29(05), pages 857-904, October.
  10. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March.
  11. Peter C.B. Phillips, 1999. "Unit Root Log Periodogram Regression," Cowles Foundation Discussion Papers 1244, Cowles Foundation for Research in Economics, Yale University.
  12. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
  13. Peter C.B. Phillips, 1985. "Understanding Spurious Regressions in Econometrics," Cowles Foundation Discussion Papers 757, Cowles Foundation for Research in Economics, Yale University.
  14. Linton, Oliver, 1995. "Second Order Approximation in the Partially Linear Regression Model," Econometrica, Econometric Society, vol. 63(5), pages 1079-1112, September.
  15. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501, March.
  16. repec:cup:cbooks:9780521385824 is not listed on IDEAS
  17. Peter C.B. Phillips, 1998. "New Unit Root Asymptotics in the Presence of Deterministic Trends," Cowles Foundation Discussion Papers 1196, Cowles Foundation for Research in Economics, Yale University.
  18. Saikkonen, Pentti, 1991. "Asymptotically Efficient Estimation of Cointegration Regressions," Econometric Theory, Cambridge University Press, vol. 7(01), pages 1-21, March.
  19. 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.
  20. repec:cup:etheor:v:11:y:1995:i:5:p:818-87 is not listed on IDEAS
  21. Peter C. B. Phillips & Chirok Han, 2004. "GMM with Many Moment Conditions," Econometric Society 2004 Far Eastern Meetings 525, Econometric Society.
  22. Phillips, Peter C.B., 2005. "Hac Estimation By Automated Regression," Econometric Theory, Cambridge University Press, vol. 21(01), pages 116-142, February.
  23. repec:cep:stiecm:/2006/500 is not listed on IDEAS
  24. Phillips, Peter C B & Loretan, Mico, 1991. "Estimating Long-run Economic Equilibria," Review of Economic Studies, Wiley Blackwell, vol. 58(3), pages 407-36, May.
  25. Peter C.B.Phillips & Tassos Magdalinos, 2009. "Econometric Inference in the Vicinity of Unity," Working Papers CoFie-06-2009, Sim Kee Boon Institute for Financial Economics.
  26. Xiao, Zhijie & Phillips, Peter C. B., 1998. "Higher-order approximations for frequency domain time series regression," Journal of Econometrics, Elsevier, vol. 86(2), pages 297-336, June.
  27. Jeganathan, P., 1995. "Some Aspects of Asymptotic Theory with Applications to Time Series Models," Econometric Theory, Cambridge University Press, vol. 11(05), pages 818-887, October.
  28. Peter C.B. Phillips, 1988. "Spectral Regression for Cointegrated Time Series," Cowles Foundation Discussion Papers 872, Cowles Foundation for Research in Economics, Yale University.
  29. Peter C.B. Phillips, 1999. "Discrete Fourier Transforms of Fractional Processes," Cowles Foundation Discussion Papers 1243, Cowles Foundation for Research in Economics, Yale University.
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