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Exponent of Cross-sectional Dependence: Estimation and Inference

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Listed:
  • Natalia Bailey
  • George Kapetanios
  • M. Hashem Pesaran

Abstract

An important issue in the analysis of cross-sectional dependence which has received renewed interest in the past few years is the need for a better understanding of the extent and nature of such cross dependencies. In this paper we focus on measures of cross-sectional dependence and how such measures are related to the behaviour of the aggregates defined as cross-sectional averages. We endeavour to determine the rate at which the cross-sectional weighted average of a set of variables appropriately demeaned, tends to zero. One parameterisation sets the exponent of the cross-sectional dimension, N, being between 1/2 and 1. We refer to this as the exponent of cross-sectional dependence. We derive an estimator of this exponent from the estimated variance of the cross-sectional average of the variables under consideration. We propose bias corrected estimators, derive their asymptotic properties and consider a number of extensions. We include a detailed Monte Carlo study supporting the theoretical results. Finally, we undertake an empirical investigation of the exponent of cross-sectional dependence using the S&P 500 data-set, and a large number of macroeconomic variables across and within countries.

Suggested Citation

  • Natalia Bailey & George Kapetanios & M. Hashem Pesaran, 2012. "Exponent of Cross-sectional Dependence: Estimation and Inference," CESifo Working Paper Series 3722, CESifo.
  • Handle: RePEc:ces:ceswps:_3722
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    References listed on IDEAS

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    1. 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.
    2. Alessandro Rebucci & Ambrogio Cesa-Bianchi & M. Hashem Pesaran & TengTeng Xu, 2012. "China's Emergence in the World Economy and Business Cycles in Latin America," Economía Journal, The Latin American and Caribbean Economic Association - LACEA, vol. 0(Spring 20), pages 1-75, January.
    3. Stephen A. Ross, 2013. "The Arbitrage Theory of Capital Asset Pricing," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 1, pages 11-30, World Scientific Publishing Co. Pte. Ltd..
    4. M. Hashem Pesaran, 2006. "Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure," Econometrica, Econometric Society, vol. 74(4), pages 967-1012, July.
    5. Kapetanios, George, 2010. "A Testing Procedure for Determining the Number of Factors in Approximate Factor Models With Large Datasets," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(3), pages 397-409.
    6. Forni, Mario & Lippi, Marco, 2001. "The Generalized Dynamic Factor Model: Representation Theory," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1113-1141, December.
    7. Filippo di Mauro & L. Vanessa Smith & Stephane Dees & M. Hashem Pesaran, 2007. "Exploring the international linkages of the euro area: a global VAR analysis," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(1), pages 1-38.
    8. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    9. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
    10. Pesaran M.H. & Schuermann T. & Weiner S.M., 2004. "Modeling Regional Interdependencies Using a Global Error-Correcting Macroeconometric Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 129-162, April.
    11. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    12. Mario Forni & Marc Hallin & Marco Lippi & Lucrezia Reichlin, 2000. "The Generalized Dynamic-Factor Model: Identification And Estimation," The Review of Economics and Statistics, MIT Press, vol. 82(4), pages 540-554, November.
    13. Roll, Richard, 1977. "A critique of the asset pricing theory's tests Part I: On past and potential testability of the theory," Journal of Financial Economics, Elsevier, vol. 4(2), pages 129-176, March.
    14. Alexander Chudik & M. Hashem Pesaran & Elisa Tosetti, 2011. "Weak and strong cross‐section dependence and estimation of large panels," Econometrics Journal, Royal Economic Society, vol. 14(1), pages 45-90, February.
    15. Xavier Gabaix, 2011. "The Granular Origins of Aggregate Fluctuations," Econometrica, Econometric Society, vol. 79(3), pages 733-772, May.
    16. Alexei Onatski, 2009. "Testing Hypotheses About the Number of Factors in Large Factor Models," Econometrica, Econometric Society, vol. 77(5), pages 1447-1479, September.
    17. Eklund, Jana & Kapetanios, George & Price, Simon, 2010. "Forecasting in the presence of recent structural change," Bank of England working papers 406, Bank of England.
    18. Pesaran, M. Hashem & Yamagata, Takashi, 2012. "Testing CAPM with a Large Number of Assets," IZA Discussion Papers 6469, Institute of Labor Economics (IZA).
    19. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
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    More about this item

    Keywords

    cross correlations; cross-sectional dependence; cross-sectional averages; weak and strong factor models; Capital Asset Pricing Model;
    All these keywords.

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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