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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

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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Bibliographic Info

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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Cited by:
  1. Lubos Pastor & Robert F. Stambaugh & Lucian A. Taylor, 2014. "Scale and Skill in Active Management," Working Papers 2014-003, Becker Friedman Institute for Research In Economics.
  2. Hyungsik Roger Moon & Benoit Perron & Peter C.B. Phillips, 2003. "Incidental Trends and the Power of Panel Unit Root Tests," Cowles Foundation Discussion Papers 1435, Cowles Foundation for Research in Economics, Yale University.
  3. Hyungsik Roger Moon, 2000. "GMM Estimation of Autoregressive Roots Near Unity with Panel Data," Econometric Society World Congress 2000 Contributed Papers 0913, Econometric Society.
  4. Michael Jansson & Marcelo J. Moreira, 2006. "Optimal Inference in Regression Models with Nearly Integrated Regressors," Econometrica, Econometric Society, vol. 74(3), pages 681-714, 05.
  5. 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.
  6. Joakim Westerlund, . "Pooled Panel Unit Root Tests and the Effect of Past Initialization," Financial Econometics Series 2014_06, Deakin University, Faculty of Business and Law, School of Accounting, Economics and Finance.
  7. 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.
  8. 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.
  9. 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.).
  10. Bai, Jushan & Kao, Chihwa & Ng, Serena, 2009. "Panel cointegration with global stochastic trends," Journal of Econometrics, Elsevier, vol. 149(1), pages 82-99, April.
  11. Joakim Westerlund & J�rg Breitung, 2013. "Lessons from a Decade of IPS and LLC," Econometric Reviews, Taylor & Francis Journals, vol. 32(5-6), pages 547-591, August.

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