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Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure

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  • M. Hashem Pesaran

Abstract

This paper presents a new approach to estimation and inference in panel data models with a multifactor error structure where the unobserved common factors are (possibly) correlated with exogenously given individual-specific regressors, and the factor loadings differ over the cross section units. The basic idea behind the proposed estimation procedure is to filter the individual-specific regressors by means of (weighted) cross-section aggregates such that asymptotically as the cross-section dimension (N) tends to infinity the differential effects of unobserved common factors are eliminated. The estimation procedure has the advantage that it can be computed by OLS applied to an auxiliary regression where the observed regressors are augmented by (weighted) cross sectional averages of the dependent variable and the individual specific regressors. Two different but related problems are addressed: one that concerns the coefficients of the individual-specific regressors, and the other that focusses on the mean of the individual coefficients assumed random. In both cases appropriate estimators, referred to as common correlated effects (CCE) estimators, are proposed and their asymptotic distribution as N ¨ ‡, with T (the time-series dimension) fixed or as N and T¨ ‡ (jointly) are derived under different regularity conditions. One important feature of the proposed CCE mean group (CCEMG) estimator is its invariance to the (unknown but fixed) number of unobserved common factors as N and T¨ ‡ (jointly). The small sample properties of the various pooled estimators are investigated by Monte Carlo experiments that confirm the theoretical derivations and show that the pooled estimators have generally satisfactory small sample properties even for relatively small values of N and T.

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Bibliographic Info

Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 1331.

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Date of creation: 2004
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Handle: RePEc:ces:ceswps:_1331

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Keywords: cross section dependence; large panels; common correlated effects; heterogeneity; estimation and inference;

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References

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  1. Pesaran, M.H. & Weiner, S.M., 2001. "Modelling Regional Interdependencies Using a Global Error-Correcting Macroeconometric Model," Cambridge Working Papers in Economics, Faculty of Economics, University of Cambridge 0119, Faculty of Economics, University of Cambridge.
  2. Forni, Mario & Lippi, Marco, 1997. "Aggregation and the Microfoundations of Dynamic Macroeconomics," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780198288008, October.
  3. James H. Stock & Mark W. Watson, 1998. "Diffusion Indexes," NBER Working Papers 6702, National Bureau of Economic Research, Inc.
  4. Michael Binder & Cheng Hsiao & M. Hashem Pesaran, 2000. "Estimation and Inference In Short Panel Vector Autoregressions with Unit Roots And Cointegration," CESifo Working Paper Series 374, CESifo Group Munich.
  5. M. Hashem Pesaran, 2004. "General Diagnostic Tests for Cross Section Dependence in Panels," CESifo Working Paper Series 1229, CESifo Group Munich.
  6. Mario Forni & Lucrezia Reichlin, 1998. "Let's get real: a factor analytical approach to disaggregated business cycle dynamics," ULB Institutional Repository 2013/10147, ULB -- Universite Libre de Bruxelles.
  7. M. Hashem Pesaran, 2007. "A simple panel unit root test in the presence of cross-section dependence," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 22(2), pages 265-312.
  8. Jushan Bai & Serena Ng, 2000. "Determining the Number of Factors in Approximate Factor Models," Econometric Society World Congress 2000 Contributed Papers, Econometric Society 1504, Econometric Society.
  9. Kajal Lahiri, 2005. "Analysis of Panel Data," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, Agricultural and Applied Economics Association, vol. 87(4), pages 1093-1095.
  10. Lee, K.C. & Pesaran, M.H., 1992. "The Role of Sectoral Interactions in Wage Determination in the UK Economy," Cambridge Working Papers in Economics, Faculty of Economics, University of Cambridge 9214, Faculty of Economics, University of Cambridge.
  11. Pesaran, M.H. & Smith, R., 1992. "Estimating Long-Run Relationships From Dynamic Heterogeneous Panels," Cambridge Working Papers in Economics, Faculty of Economics, University of Cambridge 9215, Faculty of Economics, University of Cambridge.
  12. Peter C. B. Phillips & Donggyu Sul, 2003. "Dynamic panel estimation and homogeneity testing under cross section dependence *," Econometrics Journal, Royal Economic Society, Royal Economic Society, vol. 6(1), pages 217-259, 06.
  13. Hsiao, C. & Pesaran, M. H. & Tahmiscioglu, A. K., 1998. "Bayes Estimation of Short-run Coefficients in Dynamic Panel Data Models," Cambridge Working Papers in Economics, Faculty of Economics, University of Cambridge 9804, Faculty of Economics, University of Cambridge.
  14. Holtz-Eakin, Douglas & Newey, Whitney & Rosen, Harvey S, 1988. "Estimating Vector Autoregressions with Panel Data," Econometrica, Econometric Society, Econometric Society, vol. 56(6), pages 1371-95, November.
  15. Donald Robertson & James Symons, 2000. "Factor Residuals in SUR Regressions: Estimating Panels Allowing for Cross Sectional Correlation," CEP Discussion Papers, Centre for Economic Performance, LSE dp0473, Centre for Economic Performance, LSE.
  16. Swamy, P A V B, 1970. "Efficient Inference in a Random Coefficient Regression Model," Econometrica, Econometric Society, Econometric Society, vol. 38(2), pages 311-23, March.
  17. Ahn, Seung Chan & Hoon Lee, Young & Schmidt, Peter, 2001. "GMM estimation of linear panel data models with time-varying individual effects," Journal of Econometrics, Elsevier, Elsevier, vol. 101(2), pages 219-255, April.
  18. Timothy G. Conley & Bill Dupor, 2003. "A Spatial Analysis of Sectoral Complementarity," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 111(2), pages 311-352, April.
  19. 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, International Conferences on Panel Data B5-3, International Conferences on Panel Data.
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