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Optimal Estimation of Cointegrated Systems with Irrelevant Instruments

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Abstract

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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Bibliographic Info

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

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Keywords: Asymptotic efficiency; Cointegrated system; Instrumental variables; Irrelevant instrument; Karhunen-Loeve representation; Long memory; Optimal estimation; Orthonormal basis; Trend basis; Trend likelihood;

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References

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  1. Peter C.B. Phillips & Mico Loretan, 1989. "Estimating Long Run Economic Equilibria," Cowles Foundation Discussion Papers 928, Cowles Foundation for Research in Economics, Yale University.
  2. 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.
  3. Oliver Linton, 1993. "Second Order Approximation in the Partially Linear Regression Model," Cowles Foundation Discussion Papers 1065, Cowles Foundation for Research in Economics, Yale University.
  4. 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.
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  24. Peter C.B. Phillips, 1985. "Understanding Spurious Regressions in Econometrics," Cowles Foundation Discussion Papers 757, Cowles Foundation for Research in Economics, Yale University.
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Cited by:
  1. Tanaka, Katsuto, 2011. "Linear Nonstationary Models : A Review of the Work of Professor P.C.B. Phillips," Discussion Papers 2011-05, Graduate School of Economics, Hitotsubashi University.
  2. Gunnar Bårdsen & Niels Haldrup, 2006. "A Gaussian IV estimator of cointegrating relations," Economics Working Papers 2006-03, School of Economics and Management, University of Aarhus.

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