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Using GMM when testing for a unit root in panels where the time-series dimension is fixed

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Author Info
Edith Madsen (Institute of Economics, University of Copenhagen)
Abstract

In this paper we investigate GMM-based unit root inference in an autoregressive panel data model with individual-specific levels. We consider tests based on GMM estimators of the AR parameter and moment condition tests. The limiting distributions of the corresponding test statistics are derived when the AR parameter is unity and local-to-unity. This provides information about which statistics lead to valid test procedures. The performance of the valid tests in terms of their local power can then be compared. The results show that the GMM estimator of the AR parameter based on the Arellano-Bover type moment conditions, expressing that lagged differences are used as instruments for the equations in levels, can be used to detect a unit root. On the other hand, the widely used GMM estimator of the AR parameter based on the Arellano-Bond type moment conditions, expressing that lagged levels are used as instruments for the equations in first-differences, can not be used for this purpose. Instead a moment condition test of the hypothesis that the Arellano-Bond type moment conditions do not identify the AR parameter is valid as a unit root test. Finally, a simulation study demonstrates that the local power of the tests provides good approximations of their actual power in finite samples.

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Paper provided by University of Copenhagen. Department of Economics. Centre for Applied Microeconometrics in its series CAM Working Papers with number 2003-11.

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Length: 38 pages
Date of creation: Aug 2003
Date of revision:
Handle: RePEc:kud:kuieca:2003_11

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Related research
Keywords: dynamic panel data model; unit roots; GMM estimation; local alternatives; weak instruments;

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Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data

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  1. Arellano, Manuel & Bond, Stephen, 1991. "Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations," Review of Economic Studies, Blackwell Publishing, vol. 58(2), pages 277-97, April. [Downloadable!] (restricted)
  2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July. [Downloadable!] (restricted)
  3. Breitung, Jorg & Meyer, Wolfgang, 1994. "Testing for Unit Roots in Panel Data: Are Wages on Different Bargaining Levels Cointegrated?," Applied Economics, Taylor and Francis Journals, vol. 26(4), pages 353-61, April.
  4. Stephen Bond & Céline Nauges & Frank Windmeijer, 2002. "Unit Roots and Identification in Autoregressive Panel Data Models: A Comparison of Alternative Tests," 10th International Conference on Panel Data, Berlin, July 5-6, 2002 C5-4, International Conferences on Panel Data. [Downloadable!]
  5. Banerjee, Anindya, 1999. " Panel Data Unit Roots and Cointegration: An Overview," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 61(0), pages 607-29, Special I. [Downloadable!] (restricted)
  6. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
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  7. Richard Blundell & Steve Bond & Frank Windmeijer, 2000. "Estimation in dynamic panel data models: improving on the performance of the standard GMM estimator," IFS Working Papers W00/12, Institute for Fiscal Studies. [Downloadable!]
  8. Holtz-Eakin, Douglas & Newey, Whitney & Rosen, Harvey S, 1988. "Estimating Vector Autoregressions with Panel Data," Econometrica, Econometric Society, vol. 56(6), pages 1371-95, November. [Downloadable!] (restricted)
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  10. Harris, R. & Tzavalis, E., 1996. "Inference for Unit Roots in Dynamic Panels," Discussion Papers 96/04, University of Exeter, School of Business and Economics.
  11. Edith Madsen, 2003. "Unit root inference in panel data models where the time-series dimension is fixed: A comparison of different tests," CAM Working Papers 2003-13, University of Copenhagen. Department of Economics. Centre for Applied Microeconometrics. [Downloadable!]
  12. 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!]
  13. Harris, Richard D. F. & Tzavalis, Elias, 1999. "Inference for unit roots in dynamic panels where the time dimension is fixed," Journal of Econometrics, Elsevier, vol. 91(2), pages 201-226, August. [Downloadable!] (restricted)
  14. Badi H. Baltagi & Chihwa Kao, 2000. "Nonstationary Panels, Cointegration in Panels and Dynamic Panels: A Survey," Center for Policy Research Working Papers 16, Center for Policy Research, Maxwell School, Syracuse University. [Downloadable!]
  15. Manuel Arellano & Lars P. Hansen & Enrique Sentana, 2000. "Underidentification?," Econometric Society World Congress 2000 Contributed Papers 1824, Econometric Society. [Downloadable!]
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  16. Anderson, T. W. & Hsiao, Cheng., 1980. "Estimation of Dynamic Models with Error Components," Working Papers 336, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
  17. Baltagi, Badi H. & Boozer, Michael A., 1997. "Econometric Analysis of Panel Data," Econometric Theory, Cambridge University Press, vol. 13(05), pages 747-754, October. [Downloadable!]
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