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

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  • Maurice J.G. Bun
  • Frank Kleibergen

Abstract

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.

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Bibliographic Info

Paper provided by Universiteit van Amsterdam, Dept. of Econometrics in its series UvA-Econometrics Working Papers with number 13-07.

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Date of creation: 20 Jun 2013
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Handle: RePEc:ame:wpaper:1307

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Postal: Dept. of Econometrics, Universiteit van Amsterdam, Valckenierstraat 65, NL - 1018 XE Amsterdam, The Netherlands
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Web page: http://www.ase.uva.nl/uva-econometrics
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  1. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
  2. Frank Kleibergen, 2001. "Testing Parameters in GMM without Assuming that they are identified," Tinbergen Institute Discussion Papers 01-067/4, Tinbergen Institute.
  3. Blundell, R. & Bond, S., 1995. "Initial Conditions and Moment Restrictions in Dynamic Panel Data Models," Economics Papers 104, Economics Group, Nuffield College, University of Oxford.
  4. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-80, November.
  5. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
  6. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  7. M Arellano & O Bover, 1990. "Another Look at the Instrumental Variable Estimation of Error-Components Models," CEP Discussion Papers dp0007, Centre for Economic Performance, LSE.
  8. Javier Alvarez & Manuel Arellano, 2004. "Robust Likelihood Estimation Of Dynamic Panel Data Models," Working Papers wp2004_0421, CEMFI.
  9. Frank Kleibergen, 2000. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Tinbergen Institute Discussion Papers 00-055/4, Tinbergen Institute.
  10. 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.
  11. Kruiniger, Hugo, 2009. "Gmm Estimation And Inference In Dynamic Panel Data Models With Persistent Data," Econometric Theory, Cambridge University Press, vol. 25(05), pages 1348-1391, October.
  12. Steve Bond & CĂ©line Nauges & Frank Windmeijer, 2005. "Unit roots: identification and testing in micro panels," CeMMAP working papers CWP07/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  13. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-38, May.
  14. Donald W. K. Andrews & Marcelo J. Moreira & James H. Stock, 2006. "Optimal Two-Sided Invariant Similar Tests for Instrumental Variables Regression," Econometrica, Econometric Society, vol. 74(3), pages 715-752, 05.
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