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Estimation of Autoregressive Roots near Unity using Panel Data

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  • Moon, Hyungsik R.
  • Phillips, Peter C.B.

Abstract

Time series data are often well modelled by using the device of an autoregressive root that is local to unity. Unfortunately, the localizing parameter (c) is not consistently estimable using existing time series econometric techniques and the lack of a consistent estimator complicates inference. This paper develops procedures for the estimation of a common localizing parameter using panel data. Pooling information across individuals in a panel aids the identification and estimation of the localising parameter and leads to consistent estimation in simple panel models. However, in the important case of models with concomitant deterministic trends, it is shown that pooled panel estimators of the localising parameter are asymptotically biased. Some techniques are developed to overcome this difficulty and consistent estimators of c in the region c
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Suggested Citation

  • Moon, Hyungsik R. & Phillips, Peter C.B., 1999. "Estimation of Autoregressive Roots near Unity using Panel Data," University of California at Santa Barbara, Economics Working Paper Series qt7fd8x80m, Department of Economics, UC Santa Barbara.
  • Handle: RePEc:cdl:ucsbec:qt7fd8x80m
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    1. Moon, Hyungsik R. & Phillips, Peter C.B., 2000. "Estimation Of Autoregressive Roots Near Unity Using Panel Data," Econometric Theory, Cambridge University Press, vol. 16(06), pages 927-997, December.
    2. Peter C. B. Phillips & Hyungsik R. Moon, 1999. "Linear Regression Limit Theory for Nonstationary Panel Data," Econometrica, Econometric Society, vol. 67(5), pages 1057-1112, September.
    3. Eugene Canjels & Mark W. Watson, 1997. "Estimating Deterministic Trends In The Presence Of Serially Correlated Errors," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 184-200, May.
    4. Uhlig, Harald, 1994. "On Jeffreys Prior when Using the Exact Likelihood Function," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 633-644, August.
    5. Elliott, Graham, 1999. "Efficient Tests for a Unit Root When the Initial Observation Is Drawn from Its Unconditional Distribution," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(3), pages 767-783, August.
    6. Phillips, Peter C.B. & Moon, Hyungsik Roger & Xiao, Zhijie, 2001. "How To Estimate Autoregressive Roots Near Unity," Econometric Theory, Cambridge University Press, vol. 17(01), pages 29-69, February.
    7. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    8. Xiao, Zhijie & Phillips, Peter C.B., 1999. "Efficient Detrending In Cointegrating Regression," Econometric Theory, Cambridge University Press, vol. 15(04), pages 519-548, August.
    9. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    10. Perron, Pierre & Rodriguez, Gabriel, 2003. "GLS detrending, efficient unit root tests and structural change," Journal of Econometrics, Elsevier, vol. 115(1), pages 1-27, July.
    11. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
    12. Peter Phillips & Hyungsik Moon, 2000. "Nonstationary panel data analysis: an overview of some recent developments," Econometric Reviews, Taylor & Francis Journals, vol. 19(3), pages 263-286.
    13. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    14. Peter C.B. Phillips & Chin Chin Lee, 1996. "Efficiency Gains from Quasi-Differencing Under Nonstationarity," Cowles Foundation Discussion Papers 1134, Cowles Foundation for Research in Economics, Yale University.
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    18. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    19. Stock, James H., 1991. "Confidence intervals for the largest autoregressive root in U.S. macroeconomic time series," Journal of Monetary Economics, Elsevier, vol. 28(3), pages 435-459, December.
    20. Cavanagh, Christopher L. & Elliott, Graham & Stock, James H., 1995. "Inference in Models with Nearly Integrated Regressors," Econometric Theory, Cambridge University Press, vol. 11(05), pages 1131-1147, October.
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    Cited by:

    1. Moon, Hyungsik R. & Phillips, Peter C.B., 2000. "Estimation Of Autoregressive Roots Near Unity Using Panel Data," Econometric Theory, Cambridge University Press, vol. 16(06), pages 927-997, December.
    2. Moon, H.R.Hyungsik Roger & Perron, Benoit, 2004. "Testing for a unit root in panels with dynamic factors," Journal of Econometrics, Elsevier, vol. 122(1), pages 81-126, September.
    3. Hyungsik Roger Moon & Peter C. B. Phillips, 2004. "GMM Estimation of Autoregressive Roots Near Unity with Panel Data," Econometrica, Econometric Society, vol. 72(2), pages 467-522, March.
    4. Westerlund, Joakim & Larsson, Rolf, 2015. "New tools for understanding the local asymptotic power of panel unit root tests," Journal of Econometrics, Elsevier, vol. 188(1), pages 59-93.
    5. Moon, Hyungsik R & Phillips, Peter C B, 1999. " Maximum Likelihood Estimation in Panels with Incidental Trends," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 61(0), pages 711-747, Special I.
    6. McMillan, David G., 2013. "Consumption and stock prices: Evidence from a small international panel," Journal of Macroeconomics, Elsevier, vol. 36(C), pages 76-88.
    7. Phillips, Peter C. B. & Park, Joon Y. & Chang, Yoosoon, 2004. "Nonlinear instrumental variable estimation of an autoregression," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 219-246.
    8. Hjalmarsson, Erik, 2005. "Predictive regressions with panel data," Working Papers in Economics 160, University of Gothenburg, Department of Economics.
    9. Bai, Jushan & Kao, Chihwa & Ng, Serena, 2009. "Panel cointegration with global stochastic trends," Journal of Econometrics, Elsevier, vol. 149(1), pages 82-99, April.
    10. Pástor, Ľuboš & Stambaugh, Robert F. & Taylor, Lucian A., 2015. "Scale and skill in active management," Journal of Financial Economics, Elsevier, vol. 116(1), pages 23-45.
    11. Phillips, Peter C.B. & Sul, Donggyu, 2007. "Bias in dynamic panel estimation with fixed effects, incidental trends and cross section dependence," Journal of Econometrics, Elsevier, vol. 137(1), pages 162-188, March.
    12. Choi, Yongok & Jacewitz, Stefan & Park, Joon Y., 2016. "A reexamination of stock return predictability," Journal of Econometrics, Elsevier, vol. 192(1), pages 168-189.
    13. Hayakawa, Kazuhiko, 2016. "Improved GMM estimation of panel VAR models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 240-264.
    14. Kruiniger, Hugo, 2009. "Gmm Estimation And Inference In Dynamic Panel Data Models With Persistent Data," Econometric Theory, Cambridge University Press, vol. 25(05), pages 1348-1391, October.
    15. Arthur Grimes & Andrew Aitken, 2010. "Housing Supply, Land Costs and Price Adjustment," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 38(2), pages 325-353.
    16. Hjalmarsson, Erik, 2008. "The Stambaugh bias in panel predictive regressions," Finance Research Letters, Elsevier, vol. 5(1), pages 47-58, March.
    17. Peter Phillips & Hyungsik Moon, 2000. "Nonstationary panel data analysis: an overview of some recent developments," Econometric Reviews, Taylor & Francis Journals, vol. 19(3), pages 263-286.
    18. Phillips, Peter C.B. & Moon, Hyungsik Roger & Xiao, Zhijie, 2001. "How To Estimate Autoregressive Roots Near Unity," Econometric Theory, Cambridge University Press, vol. 17(01), pages 29-69, February.
    19. Jamie Emerson & Chihwa Kao, 2000. "Testing for Structural Change of a Time Trend Regression in Panel Data," Center for Policy Research Working Papers 15, Center for Policy Research, Maxwell School, Syracuse University.
    20. Michael Jansson & Marcelo J. Moreira, 2006. "Optimal Inference in Regression Models with Nearly Integrated Regressors," Econometrica, Econometric Society, vol. 74(3), pages 681-714, May.
    21. Di Iorio, Francesca & Fachin, Stefano, 2010. "A Panel Cointegration study of the long-run relationship between Savings and Investments in the OECD economies, 1970-2007," MPRA Paper 25873, University Library of Munich, Germany.
    22. Erik Hjalmarsson, 2005. "Estimation of average local-to-unity roots in heterogenous panels," International Finance Discussion Papers 852, Board of Governors of the Federal Reserve System (U.S.).
    23. Hjalmarsson, Erik, 2010. "Predicting Global Stock Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 45(01), pages 49-80, February.
    24. Chihwa Kao & Long Liu, 2007. "Consistent Estimation with Weak Instruments in Panel Data," Center for Policy Research Working Papers 95, Center for Policy Research, Maxwell School, Syracuse University.
    25. Westerlund, Joakim, 2015. "The effect of recursive detrending on panel unit root tests," Journal of Econometrics, Elsevier, vol. 185(2), pages 453-467.

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    Keywords

    Estimation of Autoregressive Roots near Unity using Panel Data;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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