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Weak and strong cross‐section dependence and estimation of large panels

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  • Alexander Chudik
  • M. Hashem Pesaran
  • Elisa Tosetti

Abstract

This paper introduces the concepts of time-specific weak and strong cross section dependence. A double-indexed process is said to be cross sectionally weakly dependent at a given point in time, t, if its weighted average along the cross section dimension (N) converges to its expectation in quadratic mean, as N is increased without bounds for all weights that satisfy certain ‘granularity’ conditions. Relationship with the notions of weak and strong common factors is investigated and an application to the estimation of panel data models with an infinite number of weak factors and a finite number of strong factors is also considered. The paper concludes with a set of Monte Carlo experiments where the small sample properties of estimators based on principal components and CCE estimators are investigated and compared under various assumptions on the nature of the unobserved common effects.

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File URL: http://hdl.handle.net/10.1111/j.1368-423X.2010.00330.x
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Article provided by Royal Economic Society in its journal The Econometrics Journal.

Volume (Year): 14 (2011)
Issue (Month): 1 (February)
Pages: C45-C90

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Handle: RePEc:ect:emjrnl:v:14:y:2011:i:1:p:c45-c90
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Find related papers by JEL classification:
  • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
  • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
  • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models

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  1. George Kapetanios & M. Hashem Pesaran & Takashi Yamagata, 2006. "Panels with Nonstationary Multifactor Error Structures," CESifo Working Paper Series 1788, CESifo Group Munich.
  2. Forni, Mario & Lippi, Marco, 2000. "The Generalized Dynamic Factor Model: Representation Theory," CEPR Discussion Papers 2509, C.E.P.R. Discussion Papers.
  3. Chamberlain, Gary, 1983. "Funds, Factors, and Diversification in Arbitrage Pricing Models," Econometrica, Econometric Society, vol. 51(5), pages 1305-23, September.
  4. Chudik , A. & Pesaran, M.H., 2007. "Infinite Dimensional VARs and Factor Models," Cambridge Working Papers in Economics 0757, Faculty of Economics, University of Cambridge.
  5. Kapetanios, George & Marcellino, Massimiliano, 2010. "Factor-GMM estimation with large sets of possibly weak instruments," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2655-2675, November.
  6. 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.
  7. 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.
  8. Gregory, Allan W. & Head, Allen C., 1999. "Common and country-specific fluctuations in productivity, investment, and the current account," Journal of Monetary Economics, Elsevier, vol. 44(3), pages 423-451, December.
  9. Ingersoll, Jonathan E, Jr, 1984. " Some Results in the Theory of Arbitrage Pricing," Journal of Finance, American Finance Association, vol. 39(4), pages 1021-39, September.
  10. Jerry Coakley & Ana-Maria Fuertes & Ron Smith, 2004. "Unobserved Heterogeneity in Panel Time Series Models," Birkbeck Working Papers in Economics and Finance 0403, Birkbeck, Department of Economics, Mathematics & Statistics.
  11. Stock, James H & Watson, Mark W, 2002. "Macroeconomic Forecasting Using Diffusion Indexes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 147-62, April.
  12. Pesaran, M.H., 2003. "A Simple Panel Unit Root Test in the Presence of Cross Section Dependence," Cambridge Working Papers in Economics 0346, Faculty of Economics, University of Cambridge.
  13. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
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