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Exponent of Cross-sectional Dependence: Estimation and Inference

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  • 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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    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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