$n^{1/6}$ n 1 / 6 , slower than $\sqrt{n}$ n , when the true localizing parameter is zero (i.e., when there is a panel unit root) and the deterministic trends in the panel are linear. These results, which rely on boundary point asymptotics, point to the continued difficulty of distinguishing unit roots from local alternatives, even when there is an infinity of additional data. Copyright The Econometric Society 2004.">

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GMM Estimation of Autoregressive Roots Near Unity with Panel Data

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Hyungsik Roger Moon
Peter C. B. Phillips

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Abstract

This paper investigates a generalized method of moments (GMM) approach to the estimation of autoregressive roots near unity with panel data and incidental deterministic trends. Such models arise in empirical econometric studies of firm size and in dynamic panel data modeling with weak instruments. The two moment conditions in the GMM approach are obtained by constructing bias corrections to the score functions under OLS and GLS detrending, respectively. It is shown that the moment condition under GLS detrending corresponds to taking the projected score on the Bhattacharya basis, linking the approach to recent work on projected score methods for models with infinite numbers of nuisance parameters (Waterman and Lindsay (1998)). Assuming that the localizing parameter takes a nonpositive value, we establish consistency of the GMM estimator and find its limiting distribution. A notable new finding is that the GMM estimator has convergence rate $n^{1/6}$ n 1 / 6 , slower than $\sqrt{n}$ n , when the true localizing parameter is zero (i.e., when there is a panel unit root) and the deterministic trends in the panel are linear. These results, which rely on boundary point asymptotics, point to the continued difficulty of distinguishing unit roots from local alternatives, even when there is an infinity of additional data. Copyright The Econometric Society 2004.

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File URL: http://hdl.handle.net/10.1111/j.1468-0262.2004.00498.x
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Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 72 (2004)
Issue (Month): 2 (03)
Pages: 467-522
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Handle: RePEc:ecm:emetrp:v:72:y:2004:i:2:p:467-522

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation, Yale University. [Downloadable!]
  2. McCloughan, Patrick, 1995. "Simulation of Concentration Development from Modified Gibrat Growth-Entry-Exit Processes," Journal of Industrial Economics, Blackwell Publishing, vol. 43(4), pages 405-33, December. [Downloadable!] (restricted)
  3. Peter C.B. Phillips, 1992. "Hyper-Consistent Estimation of a Unit Root in Time Series Regression," Cowles Foundation Discussion Papers 1040, Cowles Foundation, Yale University. [Downloadable!]
  4. Pesaran, M. Hashem & Smith, Ron, 1995. "Estimating long-run relationships from dynamic heterogeneous panels," Journal of Econometrics, Elsevier, vol. 68(1), pages 79-113, July. [Downloadable!] (restricted)
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  5. Arellano, M. & Honore, B., 2000. "Panel Data Models: Some Recent Developments," Papers 0016, Centro de Estudios Monetarios Y Financieros-.
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  6. Hyungsik Roger Moon & Peter C.B. Phillips, 2000. "GMM Estimation of Autoregressive Roots Near Unity with Panel Data," Cowles Foundation Discussion Papers 1274, Cowles Foundation, Yale University. [Downloadable!]
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  7. Quah, D., 1993. "Exploiting Cross Section Variation for Unit Root Inference in Dynamic Data," Papers 549, Stockholm - International Economic Studies.
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  8. Peter C.B. Phillips & Joon Y. Park, 1986. "Statistical Inference in Regressions with Integrated Processes: Part 2," Cowles Foundation Discussion Papers 819R, Cowles Foundation, Yale University, revised Feb 1987. [Downloadable!]
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  9. Evans, David S, 1987. "Tests of Alternative Theories of Firm Growth," Journal of Political Economy, University of Chicago Press, vol. 95(4), pages 657-74, August. [Downloadable!] (restricted)
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  10. 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. [Downloadable!]
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  11. Oh, Keun-Yeob, 1996. "Purchasing power parity and unit root tests using panel data," Journal of International Money and Finance, Elsevier, vol. 15(3), pages 405-418, June. [Downloadable!] (restricted)
  12. Hyungsik R. Moon & Peter C.B. Phillips, . "Maximum Likelihood Estimation in Panels with Incidental Trends," University of California Santa Barbara - Department of Economics 6-99, California Santa Barbara - Department of Economics. [Downloadable!]
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  13. Pedroni, Peter, 1999. " Critical Values for Cointegration Tests in Heterogeneous Panels with Multiple Regressors," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 61(0), pages 653-70, Special I. [Downloadable!] (restricted)
  14. Peter C.B. Phillips, 1986. "Towards a Unified Asymptotic Theory for Autoregression," Cowles Foundation Discussion Papers 782R, Cowles Foundation, Yale University, revised Aug 1986. [Downloadable!]
  15. Coakley, Jerry & Kulasi, Farida & Smith, Ron, 1996. "Current Account Solvency and the Feldstein-Horioka Puzzle," Economic Journal, Royal Economic Society, vol. 106(436), pages 620-27, May. [Downloadable!] (restricted)
  16. Peter C.B. Phillips & Hyungsik R. Moon, 1999. "Linear Regression Limit Theory for Nonstationary Panel Data," Cowles Foundation Discussion Papers 1222, Cowles Foundation, Yale University. [Downloadable!]
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  17. Jinyong Hahn & Guido Kuersteiner, 2002. "Asymptotically Unbiased Inference for a Dynamic Panel Model with Fixed Effects when Both "n" and "T" Are Large," Econometrica, Econometric Society, vol. 70(4), pages 1639-1657, July. [Downloadable!] (restricted)
  18. 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. [Downloadable!] (restricted)
  19. Peter C.B. Phillips & Chin Chin Lee, 1996. "Efficiency Gains from Quasi-Differencing Under Nonstationarity," Cowles Foundation Discussion Papers 1134, Cowles Foundation, Yale University. [Downloadable!]
  20. Bernard, Andrew B & Jones, Charles I, 1996. "Productivity across Industries and Countries: Time Series Theory and Evidence," The Review of Economics and Statistics, MIT Press, vol. 78(1), pages 135-46, February. [Downloadable!] (restricted)
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  21. Nickell, Stephen J, 1981. "Biases in Dynamic Models with Fixed Effects," Econometrica, Econometric Society, vol. 49(6), pages 1417-26, November. [Downloadable!] (restricted)
  22. Jinyong Hahn & Jerry Hausman & Guido Kuersteiner, 2005. "Bias Corrected Instrumental Variables Estimation for Dynamic Panel Models with Fixed E¤ects," Boston University - Department of Economics - Working Papers Series WP2005-024, Boston University - Department of Economics. [Downloadable!]
  23. Hugo Kruiniger, 2000. "GMM Estimation of Dynamic Panel Data Models with Persistent Data," Working Papers 428, Queen Mary, University of London, Department of Economics. [Downloadable!]
  24. MacDonald, Ronald, 1996. "Panel unit root tests and real exchange rates," Economics Letters, Elsevier, vol. 50(1), pages 7-11, January. [Downloadable!] (restricted)
  25. Donald W. K. Andrews, 1999. "Estimation When a Parameter Is on a Boundary," Econometrica, Econometric Society, vol. 67(6), pages 1341-1384, November.
  26. Jovanovic, Boyan, 1982. "Selection and the Evolution of Industry," Econometrica, Econometric Society, vol. 50(3), pages 649-70, May. [Downloadable!] (restricted)
  27. Phillips, Peter C B, 1995. "Fully Modified Least Squares and Vector Autoregression," Econometrica, Econometric Society, vol. 63(5), pages 1023-78, September. [Downloadable!] (restricted)
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  28. Maddala, G S & Wu, Shaowen, 1999. " A Comparative Study of Unit Root Tests with Panel Data and a New Simple Test," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 61(0), pages 631-52, Special I. [Downloadable!] (restricted)
  29. Andrew Levin & Chien-Fu Lin, 1993. "Unit Root Tests in Panel Data: New Results," University of California at San Diego, Economics Working Paper Series 93-56, Department of Economics, UC San Diego. [Downloadable!]
  30. Bronwyn H. Hall & Jacques Mairesse, 2000. "Univariate Panel Data Models and GMM Estimators: An Exploration Using Real and Simulated Data," Econometric Society World Congress 2000 Contributed Papers 1114, Econometric Society. [Downloadable!]
  31. Pasaran, M.H. & Im, K.S. & Shin, Y., 1995. "Testing for Unit Roots in Heterogeneous Panels," Cambridge Working Papers in Economics 9526, Faculty of Economics, University of Cambridge.
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Moon, H.R. & Perron, B., 2002. "Testing for a Unit Root in Panels with Dynamic Factors," Cahiers de recherche 18-2002, Centre interuniversitaire de recherche en économie quantitative, CIREQ. [Downloadable!]
    Other versions:
  2. Hyungsik Roger Moon & Peter C.B. Phillips, 2003. "GMM Estimation of Autoregressive Roots Near Unity with Panel Data," Cowles Foundation Discussion Papers 1390, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  3. Jinyong Hahn & Hyungsik Roger Moon, 2005. "Reducing Bias of MLE in a Dynamic Panel Model," IEPR Working Papers 05.36, Institute of Economic Policy Research (IEPR). [Downloadable!]
    Other versions:
  4. 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.). [Downloadable!]
  5. Jushan Bai & Chihwa Kao & Serena Ng, 2007. "Panel Cointegration with Global Stochastic Trends," Center for Policy Research Working Papers 90, Center for Policy Research, Maxwell School, Syracuse University. [Downloadable!]
  6. Hyungsik Roger Moon & Benoit Perron & Peter C.B. Phillips, 2005. "Incidental Trends and the Power of Panel Unit Root Tests," IEPR Working Papers 05.38, Institute of Economic Policy Research (IEPR). [Downloadable!]
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  7. Peter C.B. Phillips & Donggyu Sul, 2003. "Bias in Dynamic Panel Estimation with Fixed Effects, Incidental Trends and Cross Section Dependence," Cowles Foundation Discussion Papers 1438, Cowles Foundation, Yale University, revised Jun 2004. [Downloadable!]
    Other versions:
  8. Jinyong Hahn & Jerry Hausman & Guido Kuersteiner, 2005. "Bias Corrected Instrumental Variables Estimation for Dynamic Panel Models with Fixed E¤ects," Boston University - Department of Economics - Working Papers Series WP2005-024, Boston University - Department of Economics. [Downloadable!]
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