Exponent of Cross-sectional Dependence for Residuals

Natalia Bailey*, George Kapetanios, M. Hashem Pesaran

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)


In this paper, we focus on estimating the degree of cross-sectional dependence in the error terms of a classical panel data regression model. For this purpose we propose an estimator of the exponent of cross-sectional dependence denoted by α, which is based on the number of non-zero pair-wise cross correlations of these errors. We prove that our estimator, α~ , is consistent and derive the rate at which it approaches its true value. We also propose a resampling procedure for the construction of confidence bounds around the estimator of α. We evaluate the finite sample properties of the proposed estimator by use of a Monte Carlo simulation study. The numerical results are encouraging and supportive of the theoretical findings. Finally, we undertake an empirical investigation of α for the errors of the CAPM model and its Fama-French extensions using 10-year rolling samples from S&P 500 securities over the period Sept 1989 - May 2018.

Original languageEnglish
Pages (from-to)46-102
Number of pages57
JournalSankhya B
Early online date30 May 2019
Publication statusPublished - 1 Sept 2019


  • C21
  • C32
  • CAPM and Fama-French factors
  • Cross-sectional averages
  • Cross-sectional dependence
  • Pair-wise correlations
  • Weak and strong factor models


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