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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
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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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  1. Phillips, Peter C.B., 2005. "Hac Estimation By Automated Regression," Econometric Theory, Cambridge University Press, vol. 21(01), pages 116-142, February.
  2. 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.
  3. Phillips, Peter C B & Hansen, Bruce E, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 57(1), pages 99-125, January.
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  25. 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.
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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 BÃ¥rdsen & Niels Haldrup, 2006. "A Gaussian IV estimator of cointegrating relations," Economics Working Papers, School of Economics and Management, University of Aarhus 2006-03, School of Economics and Management, University of Aarhus.

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