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Exponent of Cross-sectional Dependence: Estimation and Inference

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  • Bailey, N.
  • Kapetanios, G.
  • Pesaran, M. H.

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 this to be , for . Given the fashion in which it arises, we refer to as the exponent of cross-sectional dependence. We derive an estimator of 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 using the S&P 500 data-set, and a large number of macroeconomic variables across and within countries.

Suggested Citation

  • Bailey, N. & Kapetanios, G. & Pesaran, M. H., 2012. "Exponent of Cross-sectional Dependence: Estimation and Inference," Cambridge Working Papers in Economics 1206, Faculty of Economics, University of Cambridge.
  • Handle: RePEc:cam:camdae:1206
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    References listed on IDEAS

    as
    1. Alessandro Rebucci & Ambrogio Cesa-Bianchi & M. Hashem Pesaran & TengTeng Xu, 2012. "China's Emergence in the World Economy and Business Cycles in Latin America," ECONOMIA JOURNAL, THE LATIN AMERICAN AND CARIBBEAN ECONOMIC ASSOCIATION - LACEA, vol. 0(Spring 20), pages 1-75, January.
    2. Eklund, Jana & Kapetanios, George & Price, Simon, 2010. "Forecasting in the presence of recent structural change," Bank of England working papers 406, Bank of England.
    3. 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.
    4. Forni, Mario & Lippi, Marco, 2001. "The Generalized Dynamic Factor Model: Representation Theory," Econometric Theory, Cambridge University Press, vol. 17(06), pages 1113-1141, December.
    5. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
    6. Xavier Gabaix, 2011. "The Granular Origins of Aggregate Fluctuations," Econometrica, Econometric Society, vol. 79(3), pages 733-772, May.
    7. 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.
    8. Pesaran, M. Hashem & Yamagata, Takashi, 2012. "Testing CAPM with a Large Number of Assets," IZA Discussion Papers 6469, Institute for the Study of Labor (IZA).
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    More about this item

    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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