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


  • M. Hashem Pesaran


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.

Suggested Citation

  • M. Hashem Pesaran, 2004. "Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure," CESifo Working Paper Series 1331, CESifo Group Munich.
  • Handle: RePEc:ces:ceswps:_1331

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    References listed on IDEAS

    1. Binder, Michael & Hsiao, Cheng & Pesaran, M. Hashem, 2005. "Estimation And Inference In Short Panel Vector Autoregressions With Unit Roots And Cointegration," Econometric Theory, Cambridge University Press, vol. 21(04), pages 795-837, August.
    2. 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 9804, Faculty of Economics, University of Cambridge.
    3. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    4. Holtz-Eakin, Douglas & Newey, Whitney & Rosen, Harvey S, 1989. "The Revenues-Expenditures Nexus: Evidence from Local Government Data," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 30(2), pages 415-429, May.
    5. Robertson, Donald & Symons, James, 2000. "Factor residuals in SUR regressions: estimating panels allowing for cross sectional correlation," LSE Research Online Documents on Economics 20163, London School of Economics and Political Science, LSE Library.
    6. Swamy, P A V B, 1970. "Efficient Inference in a Random Coefficient Regression Model," Econometrica, Econometric Society, vol. 38(2), pages 311-323, March.
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    8. 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., vol. 22(2), pages 265-312.
    9. Forni, Mario & Lippi, Marco, 1997. "Aggregation and the Microfoundations of Dynamic Macroeconomics," OUP Catalogue, Oxford University Press, number 9780198288008.
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    11. Peter C. B. Phillips & Donggyu Sul, 2003. "Dynamic panel estimation and homogeneity testing under cross section dependence *," Econometrics Journal, Royal Economic Society, vol. 6(1), pages 217-259, June.
    12. Kajal Lahiri, 2005. "Analysis of Panel Data," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 87(4), pages 1093-1095.
    13. Pesaran, M.H., 2004. "‘General Diagnostic Tests for Cross Section Dependence in Panels’," Cambridge Working Papers in Economics 0435, Faculty of Economics, University of Cambridge.
    14. Timothy G. Conley & Bill Dupor, 2003. "A Spatial Analysis of Sectoral Complementarity," Journal of Political Economy, University of Chicago Press, vol. 111(2), pages 311-352, April.
    15. James H. Stock & Mark W. Watson, 1998. "Diffusion Indexes," NBER Working Papers 6702, National Bureau of Economic Research, Inc.
    16. 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, vol. 101(2), pages 219-255, April.
    17. 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.
    18. Mario Forni & Lucrezia Reichlin, 1998. "Let's Get Real: A Factor Analytical Approach to Disaggregated Business Cycle Dynamics," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 453-473.
    19. Lee, Kevin C & Pesaran, M Hashem, 1993. "The Role of Sectoral Interactions in Wage Determination in the UK Economy," Economic Journal, Royal Economic Society, vol. 103(416), pages 21-55, January.
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    cross section dependence; large panels; common correlated effects; heterogeneity; estimation and inference;

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