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Identification and inference in moments based analysis of linear dynamic panel data models


  • Maurice J.G. Bun
  • Frank Kleibergen


We show that Dif(ference), see Arellano and Bond (1991), Lev(el), see Arellano and Bover (1995) and Blundell and Bond (1998), or the N(on-)L(inear) moment conditions of Ahn and Schmidt (1995) do not identify the parameters of a first-order autoregressive panel data model when the autoregressive parameter is equal to one. Combinations of the Dif and Lev, resulting in Sys(tem), moment conditions and the Dif and NL, resulting in A(hn-)S(chmidt), moment conditions identify the parameters when there are four or more time periods. The behaviour of one step and two step GMM estimators, however, remains non-standard. We therefore use size correct GMM statistics, like, the GMM-AR, GMM-LM or KLM statistic, to conduct inference. We compare their worst case large sample distributions with the power envelope to determine the optimal statistic. The power envelope involves a quartic root convergence rate which further indicates the non-standard identification issues. The worst case large sample distribution of the KLM statistic coincides with the power envelope whilst the one of the GMM-LM statistic only does so when there are four time periods. It shows that the KLM statistic is efficient both when the autoregressive parameter is one or less than one. The power envelopes for the AS and Sys moment conditons are identical so assuming mean stationarity does not help for identification.

Suggested Citation

  • Maurice J.G. Bun & Frank Kleibergen, 2013. "Identification and inference in moments based analysis of linear dynamic panel data models," UvA-Econometrics Working Papers 13-07, Universiteit van Amsterdam, Dept. of Econometrics.
  • Handle: RePEc:ame:wpaper:1307

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    References listed on IDEAS

    1. Stephen Bond & Frank Windmeijer, 2005. "Reliable Inference For Gmm Estimators? Finite Sample Properties Of Alternative Test Procedures In Linear Panel Data Models," Econometric Reviews, Taylor & Francis Journals, vol. 24(1), pages 1-37.
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    7. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September.
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    Cited by:

    1. Enrique Sentana, 2015. "Finite Underidentification," Working Papers wp2015_1508, CEMFI.
    2. Tue Gorgens & Chirok Han & Sen Xue, 2016. "Asymptotic distributions of the quadratic GMM estimator in linear dynamic panel data models," ANU Working Papers in Economics and Econometrics 2016-635, Australian National University, College of Business and Economics, School of Economics.
    3. Chudik, Alexander & Pesaran, M. Hashem, 2017. "A Bias-Corrected Method of Moments Approach to Estimation of Dynamic Short-T Panels," Globalization and Monetary Policy Institute Working Paper 327, Federal Reserve Bank of Dallas.
    4. Yoonseok Lee & Mehmet Caner & Xu Han, 2015. "Adaptive Elastic Net GMM Estimation with Many Invalid Moment Conditions: Simultaneous Model and Moment Selection," Center for Policy Research Working Papers 177, Center for Policy Research, Maxwell School, Syracuse University.
    5. Tue Gorgens & Chirok Han & Sen Xue, 2016. "Moment restrictions and identification in linear dynamic panel data models," ANU Working Papers in Economics and Econometrics 2016-633, Australian National University, College of Business and Economics, School of Economics.

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