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GMM Estimation of Short Dynamic Panel Data Models With Error Cross-Sectional Dependence

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  • Sarafidis, Vasilis

Abstract

This paper considers the issue of GMM estimation of a short dynamic panel data model when the errors are correlated across individuals. We focus particularly on the conditions required in the cross-sectional dimension of the error process for the dynamic panel GMM estimator to remain consistent. To this end, we demonstrate that cross-sectional independence (or uncorrelatedness) is not necessary - rather, it suffices that, if there is such correlation in the errors, this is weak. We define a stochastic scalar sequence to be cross-sectionally weakly correlated at any given point in time if the sequence of the covariances of the observations across individuals i and j at time t, given the conditioning set of all time-invariant characteristics of individuals i and j, converges absolutely as N grows large. Spatial dependence satisfies this condition but factor structure dependence does not. Consequently, the dynamic panel GMM estimator is consistent only in the first case. Under cross-sectionally weakly correlated errors, an additional, non-redundant, set of moment conditions becomes relevant for each i - specifically, instruments with respect to the individual(s) which unit i is correlated with. We demonstrate that these moment conditions remain valid when the errors are subject to both weak and strong correlations, in which situation the standard moment conditions with respect to individual i itself are invalidated - meaning that the dynamic panel GMM estimator is inconsistent. Simulated experiments show that the resulting method of moments estimators largely outperform the conventional ones in terms of both median bias and root median square error.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 25176.

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Date of creation: Jan 2009
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Handle: RePEc:pra:mprapa:25176

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Related research

Keywords: Dynamic panel data; spatial dependence; factor structure dependence; Generalised Method of Moments;

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References

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  1. Badi H. Baltagi & Georges Bresson & Alain Pirotte, 2006. "Panel Unit Root Tests and Spatial Dependence," Center for Policy Research Working Papers 88, Center for Policy Research, Maxwell School, Syracuse University.
  2. Sarafidis, Vasilis & Yamagata, Takashi & Robertson, Donald, 2009. "A test of cross section dependence for a linear dynamic panel model with regressors," Journal of Econometrics, Elsevier, vol. 148(2), pages 149-161, February.
  3. Arellano, Manuel, 1993. "On the testing of correlated effects with panel data," Journal of Econometrics, Elsevier, vol. 59(1-2), pages 87-97, September.
  4. Blundell, Richard & Bond, Stephen, 1998. "Initial conditions and moment restrictions in dynamic panel data models," Journal of Econometrics, Elsevier, vol. 87(1), pages 115-143, August.
  5. Bover, Olympia & Watson, Nadine, 2001. "Are there Economies of Scale in the Demand for Money by Firms? Some Panel Data Estimates," CEPR Discussion Papers 2818, C.E.P.R. Discussion Papers.
  6. Pesaran, M. Hashem & Tosetti, Elisa, 2007. "Large Panels with Common Factors and Spatial Correlations," IZA Discussion Papers 3032, Institute for the Study of Labor (IZA).
  7. 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.
  8. Breusch, Trevor & Qian, Hailong & Schmidt, Peter & Wyhowski, Donald, 1999. "Redundancy of moment conditions," Journal of Econometrics, Elsevier, vol. 91(1), pages 89-111, July.
  9. M. Hashem Pesaran, 2004. "Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure," CESifo Working Paper Series 1331, CESifo Group Munich.
  10. Arellano, Manuel & Bover, Olympia, 1995. "Another look at the instrumental variable estimation of error-components models," Journal of Econometrics, Elsevier, vol. 68(1), pages 29-51, July.
  11. 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.
  12. Kiviet, Jan F., 1995. "On bias, inconsistency, and efficiency of various estimators in dynamic panel data models," Journal of Econometrics, Elsevier, vol. 68(1), pages 53-78, July.
  13. Conley, T. G., 1999. "GMM estimation with cross sectional dependence," Journal of Econometrics, Elsevier, vol. 92(1), pages 1-45, September.
  14. Jerry Coakley & Ana-Maria Fuertes & Ron Smith, 2002. "A Principal Components Approach to Cross-Section Dependence in Panels," 10th International Conference on Panel Data, Berlin, July 5-6, 2002 B5-3, International Conferences on Panel Data.
  15. Donald Robertson & James Symons, 2000. "Factor Residuals in SUR Regressions: Estimating Panels Allowing for Cross Sectional Correlation," CEP Discussion Papers dp0473, Centre for Economic Performance, LSE.
  16. Kapoor, Mudit & Kelejian, Harry H. & Prucha, Ingmar R., 2007. "Panel data models with spatially correlated error components," Journal of Econometrics, Elsevier, vol. 140(1), pages 97-130, September.
  17. Goldberger, Arthur S, 1972. "Structural Equation Methods in the Social Sciences," Econometrica, Econometric Society, vol. 40(6), pages 979-1001, November.
  18. 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.
  19. F Stetzer, 1982. "Specifying weights in spatial forecasting models: the results of some experiments," Environment and Planning A, Pion Ltd, London, vol. 14(5), pages 571-584, May.
  20. Vasilis Sarafidis & Donald Robertson, 2009. "On the impact of error cross-sectional dependence in short dynamic panel estimation," Econometrics Journal, Royal Economic Society, vol. 12(1), pages 62-81, 03.
  21. 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, Wiley Blackwell, vol. 58(2), pages 277-97, April.
  22. Lee, Lung-fei, 2007. "GMM and 2SLS estimation of mixed regressive, spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 137(2), pages 489-514, April.
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Citations

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Cited by:
  1. Vasilis Sarafidis & Tom Wansbeek, 2012. "Cross-Sectional Dependence in Panel Data Analysis," Econometric Reviews, Taylor & Francis Journals, vol. 31(5), pages 483-531, September.
  2. Bin Peng & Giovanni Forchini, 2012. "Consistent Estimation of Panel Data Models with a Multi-factor Error Structure," School of Economics Discussion Papers 0112, School of Economics, University of Surrey.
  3. Ertur, C. & Musolesi, A., 2013. "Weak and strong cross-sectional dependence: a panel data analysis of international technology diffusion," Working Papers 2013-09, Grenoble Applied Economics Laboratory (GAEL).
  4. Bin Peng & Giovanni Forchini, 2014. "Consistent Estimation of Panel Data Models with a Multifactor Error Structure when the Cross Section Dimension is Large," Working Paper Series 20, Economics Discipline Group, UTS Business School, University of Technology, Sydney.
  5. Maurice J.G. Bun & Sarafidis, V., 2013. "Dynamic Panel Data Models," UvA-Econometrics Working Papers 13-01, Universiteit van Amsterdam, Dept. of Econometrics.

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