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On the asymptotic distribution of the quadratic GMM estimator of a dynamic panel data model under a unit root

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  • Gørgens, Tue
  • Han, Chirok
  • Xue, Sen

Abstract

This paper considers the GMM estimator, αˆ, of the autoregressive parameter in linear dynamic panel data models with fixed effects when the data-generating process has a unit root. Previous literature has established that the limit distribution of n1∕4(αˆ−1) is degenerate and nondegenerate each with probability 1/2. We sharpen this result by showing that the limit distribution of n1∕2(αˆ−1) is nondegenerate when n1∕4(αˆ−1) converges in probability to 0, and we characterize the limit distribution which is nonstandard.

Suggested Citation

  • Gørgens, Tue & Han, Chirok & Xue, Sen, 2020. "On the asymptotic distribution of the quadratic GMM estimator of a dynamic panel data model under a unit root," Economics Letters, Elsevier, vol. 197(C).
    • Handle: RePEc:eee:ecolet:v:197:y:2020:i:c:s0165176520303657
    DOI: 10.1016/j.econlet.2020.109605
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    References listed on IDEAS

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    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. Alvarez, Javier & Arellano, Manuel, 2022. "Robust likelihood estimation of dynamic panel data models," Journal of Econometrics, Elsevier, vol. 226(1), pages 21-61.
    3. Han, Chirok & Kim, Hyoungjong, 2014. "The role of constant instruments in dynamic panel estimation," Economics Letters, Elsevier, vol. 124(3), pages 500-503.
    4. Sargan, J D, 1983. "Identification and Lack of Identification," Econometrica, Econometric Society, vol. 51(6), pages 1605-1633, November.
    5. Ahn, Seung C. & Schmidt, Peter, 1995. "Efficient estimation of models for dynamic panel data," Journal of Econometrics, Elsevier, vol. 68(1), pages 5-27, July.
    6. Kruiniger, Hugo, 2013. "Quasi ML estimation of the panel AR(1) model with arbitrary initial conditions," Journal of Econometrics, Elsevier, vol. 173(2), pages 175-188.
    7. Tue Gørgens & Chirok Han & Sen Xue, 2019. "Moment Restrictions and Identification in Linear Dynamic Panel Data Models," Annals of Economics and Statistics, GENES, issue 134, pages 149-176.
    8. Manuel Arellano & Stephen Bond, 1991. "Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(2), pages 277-297.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Dynamic panel data models; Fixed effects; Generalized method of moments; Quadratic moment restrictions; Nonstandard limiting distributions;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables

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