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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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Bibliographic Info

Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 2689.

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Date of creation: 2009
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Handle: RePEc:ces:ceswps:_2689

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Keywords: panels; strong and weak cross section dependence; weak and strong factors;

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References

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  1. Alexander Chudik & M. Hashem Pesaran, 2007. "Infinite Dimensional VARs and Factor Models," CESifo Working Paper Series 2176, CESifo Group Munich.
  2. 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.
  3. George Kapetanios & M. Hashem Pesaran & Takashi Yamagata, 2006. "Panels with Nonstationary Multifactor Error Structures," CESifo Working Paper Series 1788, CESifo Group Munich.
  4. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
  5. 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.
  6. 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.
  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., vol. 22(2), pages 265-312.
  8. 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.
  9. Forni, Mario & Lippi, Marco, 2001. "The Generalized Dynamic Factor Model: Representation Theory," Econometric Theory, Cambridge University Press, vol. 17(06), pages 1113-1141, December.
  10. 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.
  11. Chamberlain, Gary, 1983. "Funds, Factors, and Diversification in Arbitrage Pricing Models," Econometrica, Econometric Society, vol. 51(5), pages 1305-23, September.
  12. 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.
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