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GMM Estimation of Autoregressive Roots Near Unity with Panel Data

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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}, slower than /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.

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File URL: http://cowles.econ.yale.edu/P/cd/d13b/d1390.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1390.

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Length: 62 pages
Date of creation: Jan 2003
Date of revision:
Handle: RePEc:cwl:cwldpp:1390

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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Keywords: Bias; boundary point asymptotics; GMM estimation; local to unity; moment conditions; nuisance parameters; panel data; pooled regression; projected score;

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References

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Citations

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Cited by:
  1. 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.
  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 for Research in Economics, Yale University.
  3. 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).
  4. 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.
  5. Michael Jansson & Marcelo J. Moreira, 2004. "Optimal Inference in Regression Models with Nearly Integrated Regressors," NBER Technical Working Papers 0303, National Bureau of Economic Research, Inc.
  6. 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 for Research in Economics, Yale University, revised Jun 2004.
  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. 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.
  10. 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.).

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