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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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  • 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.
  • Handle: RePEc:cwl:cwldpp:1390
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    Cited by:

    1. 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.
    2. 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.
    3. Kajal Lahiri & Zhongwen Liang & Huaming Peng, 2017. "The Local Power of the IPS Test with Both Initial Conditions and Incidental Trends," CESifo Working Paper Series 6313, CESifo Group Munich.
    4. Hayakawa, Kazuhiko, 2016. "Improved GMM estimation of panel VAR models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 240-264.
    5. Gonçalves, Sílvia & Kaffo, Maximilien, 2015. "Bootstrap inference for linear dynamic panel data models with individual fixed effects," Journal of Econometrics, Elsevier, vol. 186(2), pages 407-426.
    6. Moon, Hyungsik Roger & Perron, Benoit & Phillips, Peter C.B., 2007. "Incidental trends and the power of panel unit root tests," Journal of Econometrics, Elsevier, vol. 141(2), pages 416-459, December.
    7. 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.
    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.
    9. 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.
    10. 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.
    11. Joakim Westerlund & Jörg Breitung, 2013. "Lessons from a Decade of IPS and LLC," Econometric Reviews, Taylor & Francis Journals, vol. 32(5-6), pages 547-591, August.
    12. Skrobotov, Anton & Turuntseva, Marina, 2017. "Testing the Hypothesis of a Unit Root for Independent Panels," Working Papers 021707, Russian Presidential Academy of National Economy and Public Administration.
    13. Zhongwen Liang, 2017. "A Unified Approach on the Local Power of Panel Unit Root Tests," Papers 1710.02944, arXiv.org.
    14. 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.
    15. Peter C.B. Phillips & Chirok Han, 2014. "True Limit Distributions of the Anderson-Hsiao IV Estimators in Panel Autoregression," Cowles Foundation Discussion Papers 1963, Cowles Foundation for Research in Economics, Yale University.
    16. Bai, Jushan & Kao, Chihwa & Ng, Serena, 2009. "Panel cointegration with global stochastic trends," Journal of Econometrics, Elsevier, vol. 149(1), pages 82-99, April.
    17. Phillips, Peter C.B. & Han, Chirok, 2015. "The true limit distributions of the Anderson–Hsiao IV estimators in panel autoregression," Economics Letters, Elsevier, vol. 127(C), pages 89-92.
    18. 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.).
    19. 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

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

    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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