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Optimal estimation of cointegrated systems with irrelevant instruments

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  • Phillips, Peter C.B.

Abstract

It has been known 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 both in terms of point and interval estimation, 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 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.

Suggested Citation

  • Phillips, Peter C.B., 2014. "Optimal estimation of cointegrated systems with irrelevant instruments," Journal of Econometrics, Elsevier, vol. 178(P2), pages 210-224.
  • Handle: RePEc:eee:econom:v:178:y:2014:i:p2:p:210-224
    DOI: 10.1016/j.jeconom.2013.08.022
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    as
    1. Phillips, Peter C.B., 2005. "Hac Estimation By Automated Regression," Econometric Theory, Cambridge University Press, vol. 21(1), pages 116-142, February.
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    21. Peter C.B. Phillips, 1988. "Spectral Regression for Cointegrated Time Series," Cowles Foundation Discussion Papers 872, Cowles Foundation for Research in Economics, Yale University.
    22. Peter C. B. Phillips, 1998. "New Tools for Understanding Spurious Regressions," Econometrica, Econometric Society, vol. 66(6), pages 1299-1326, November.
    23. Saikkonen, Pentti, 1991. "Asymptotically Efficient Estimation of Cointegration Regressions," Econometric Theory, Cambridge University Press, vol. 7(1), pages 1-21, March.
    24. Jeganathan, P., 1995. "Some Aspects of Asymptotic Theory with Applications to Time Series Models," Econometric Theory, Cambridge University Press, vol. 11(5), pages 818-887, October.
    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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    27. Phillips, Peter C.B., 2007. "Unit root log periodogram regression," Journal of Econometrics, Elsevier, vol. 138(1), pages 104-124, May.
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    Cited by:

    1. Liang, Chong & Schienle, Melanie, 2019. "Determination of vector error correction models in high dimensions," Journal of Econometrics, Elsevier, vol. 208(2), pages 418-441.
    2. 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.
    3. Peter C. B. Phillips & Zhentao Shi, 2021. "Boosting: Why You Can Use The Hp Filter," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 62(2), pages 521-570, May.
    4. Tanaka, Katsuto & 田中, 勝人, 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.
    5. 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.
    6. Kheifets, Igor L. & Phillips, Peter C.B., 2023. "Fully modified least squares cointegrating parameter estimation in multicointegrated systems," Journal of Econometrics, Elsevier, vol. 232(2), pages 300-319.
    7. Peter C. B. Phillips & Xiaohu Wang & Yonghui Zhang, 2019. "HAR Testing for Spurious Regression in Trend," Econometrics, MDPI, vol. 7(4), pages 1-28, December.
    8. 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.
    9. 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.
    10. Hwang, Jungbin & Sun, Yixiao, 2018. "SIMPLE, ROBUST, AND ACCURATE F AND t TESTS IN COINTEGRATED SYSTEMS," Econometric Theory, Cambridge University Press, vol. 34(5), pages 949-984, October.
    11. Peter C. B. Phillips & Sainan Jin, 2021. "Business Cycles, Trend Elimination, And The Hp Filter," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 62(2), pages 469-520, May.
    12. Torfinn Harding & Frederick Ploeg, 2013. "Official forecasts and management of oil windfalls," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 20(5), pages 827-866, October.
    13. Jan Mutl & Leopold Sögner, 2019. "Parameter estimation and inference with spatial lags and cointegration," Econometric Reviews, Taylor & Francis Journals, vol. 38(6), pages 597-635, July.
    14. Peter C.B. Phillips & Igor Kheifets, 2021. "On Multicointegration," Cowles Foundation Discussion Papers 2306, Cowles Foundation for Research in Economics, Yale University.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. Cai, Zongwu & Chen, Haiqiang & Liao, Xiaosai, 2023. "A new robust inference for predictive quantile regression," Journal of Econometrics, Elsevier, vol. 234(1), pages 227-250.

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    More about this item

    Keywords

    Asymptotic efficiency; Cointegrated system; Coverage probability; Instrumental variables; Irrelevant instrument; Karhunen–Loève representation; Optimal estimation; Orthonormal basis; Sieve estimation of stochastic processes; 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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