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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.

Suggested Citation

  • Peter C. B. Phillips, 2006. "Optimal Estimation of Cointegrated Systems with Irrelevant Instruments," Cowles Foundation Discussion Papers 1547, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1547
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    3. Zongwu Cai & Haiqiang Chen & Xiaosai Liao, 2020. "A New Robust Inference for Predictive Quantile Regression," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202002, University of Kansas, Department of Economics, revised Feb 2020.
    4. Lightwood, James & Glantz, Stanton, 2011. "Effect of the Arizona tobacco control program on cigarette consumption and healthcare expenditures," Social Science & Medicine, Elsevier, vol. 72(2), pages 166-172, January.
    5. 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.
    6. James Lightwood & Stanton A Glantz, 2013. "The Effect of the California Tobacco Control Program on Smoking Prevalence, Cigarette Consumption, and Healthcare Costs: 1989–2008," PLOS ONE, Public Library of Science, vol. 8(2), pages 1-11, February.
    7. Gunnar Bårdsen & Niels Haldrup, 2006. "A Gaussian IV estimator of cointegrating relations," Economics Working Papers 2006-03, Department of Economics and Business Economics, Aarhus University.
    8. Peter C. B. Phillips & Xiaohu Wang & Yonghui Zhang, 2019. "HAR Testing for Spurious Regression in Trend," Econometrics, MDPI, Open Access Journal, vol. 7(4), pages 1-28, December.
    9. Jungbin Hwang & Gonzalo Valdés, 2020. "Low Frequency Cointegrating Regression in the Presence of Local to Unity Regressors and Unknown Form of Serial Dependence," Working papers 2020-03, University of Connecticut, Department of Economics, revised Aug 2020.
    10. Phillips, Peter C.B. & Leirvik, Thomas & Storelvmo, Trude, 2020. "Econometric estimates of Earth’s transient climate sensitivity," Journal of Econometrics, Elsevier, vol. 214(1), pages 6-32.
    11. Chen, Zhihong & Xia, Huizhu, 2020. "Trend instrumental variable regression with an application to the US New Keynesian Phillips Curve," Economic Modelling, Elsevier, vol. 93(C), pages 595-604.
    12. Igor Kheifets & Peter C.B. Phillips, 2019. "Fully Modified Least Squares for Multicointegrated Systems," Cowles Foundation Discussion Papers 2210, Cowles Foundation for Research in Economics, Yale University.

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    More about this item

    Keywords

    Asymptotic efficiency; Cointegrated system; Instrumental variables; Irrelevant instrument; Karhunen-Loeve representation; Long memory; Optimal estimation; Orthonormal basis; Trend basis; Trend likelihood;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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