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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. 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.
  2. G. Kapetanios & M. Hashem Pesaran & T. Yamagata, 2010. "Panels with nonstationary multifactor error structures," Post-Print hal-00768190, HAL.
  3. Chudik, Alexander & Pesaran, Hashem, 2009. "Infinite-dimensional VARs and factor models," Working Paper Series 0998, European Central Bank.
  4. Forni, Mario & Reichlin, Lucrezia, 1998. "Let's Get Real: A Factor Analytical Approach to Disaggregated Business Cycle Dynamics," Review of Economic Studies, Wiley Blackwell, vol. 65(3), pages 453-73, July.
  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. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
  7. Forni, Mario & Lippi, Marco, 2001. "The Generalized Dynamic Factor Model: Representation Theory," Econometric Theory, Cambridge University Press, vol. 17(06), pages 1113-1141, December.
  8. Allan W. Gregory & Allen C. Head, 1996. "Common and Country-specific Fluctuations in Productivity, Investment, and the Current Account," Working Papers 931, Queen's University, Department of Economics.
  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, 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. 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.
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