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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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    References listed on IDEAS

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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. Phillips, P.C.B., 1989. "Partially Identified Econometric Models," Econometric Theory, Cambridge University Press, vol. 5(02), pages 181-240, August.
    3. Peter C. B. Phillips & Bruce E. Hansen, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," Review of Economic Studies, Oxford University Press, vol. 57(1), pages 99-125.
    4. Chirok Han & Peter C. B. Phillips, 2006. "GMM with Many Moment Conditions," Econometrica, Econometric Society, vol. 74(1), pages 147-192, January.
    5. repec:cup:etheor:v:11:y:1995:i:5:p:818-87 is not listed on IDEAS
    6. Peter C.B. Phillips, 1999. "Discrete Fourier Transforms of Fractional Processes," Cowles Foundation Discussion Papers 1243, Cowles Foundation for Research in Economics, Yale University.
    7. Peter C. B. Phillips & Mico Loretan, 1991. "Estimating Long-run Economic Equilibria," Review of Economic Studies, Oxford University Press, vol. 58(3), pages 407-436.
    8. Phillips, Peter C.B., 2005. "Challenges of trending time series econometrics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 68(5), pages 401-416.
    9. Phillips, Peter C. B., 2002. "New unit root asymptotics in the presence of deterministic trends," Journal of Econometrics, Elsevier, vol. 111(2), pages 323-353, December.
    10. Stock, James H & Watson, Mark W, 1993. "A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems," Econometrica, Econometric Society, vol. 61(4), pages 783-820, July.
    11. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    12. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    13. Liao, Zhipeng, 2013. "Adaptive Gmm Shrinkage Estimation With Consistent Moment Selection," Econometric Theory, Cambridge University Press, vol. 29(05), pages 857-904, October.
    14. P. M. Robinson & M. Gerolimetto, 2006. "Instrumental variables estimation of stationary and non-stationary cointegrating regressions," Econometrics Journal, Royal Economic Society, vol. 9(2), pages 291-306, July.
    15. John C. Chao & Norman R. Swanson, 2005. "Consistent Estimation with a Large Number of Weak Instruments," Econometrica, Econometric Society, vol. 73(5), pages 1673-1692, September.
    16. Linton, Oliver, 1995. "Second Order Approximation in the Partially Linear Regression Model," Econometrica, Econometric Society, vol. 63(5), pages 1079-1112, September.
    17. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    18. 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.
    19. repec:cup:etheor:v:7:y:1991:i:1:p:1-21 is not listed on IDEAS
    20. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March.
    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(01), 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(05), 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.
    26. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    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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    Citations

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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. Hwang, Jungbin & Sun, Yixiao, 2016. "Simple, Robust, and Accurate F and t Tests in Cointegrated Systems," University of California at San Diego, Economics Working Paper Series qt82k1x4rd, Department of Economics, UC San Diego.
    3. 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.
    4. 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.

    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;

    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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