Exponent of Cross-sectional Dependence for Residuals

TY - JOUR

T1 - Exponent of Cross-sectional Dependence for Residuals

AU - Bailey, Natalia

AU - Kapetanios, George

AU - Pesaran, M. Hashem

PY - 2019/9/1

Y1 - 2019/9/1

N2 - 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.

AB - 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.

KW - C21

KW - C32

KW - CAPM and Fama-French factors

KW - Cross-sectional averages

KW - Cross-sectional dependence

KW - Pair-wise correlations

KW - Weak and strong factor models

UR - http://www.scopus.com/inward/record.url?scp=85066628244&partnerID=8YFLogxK

U2 - 10.1007/s13571-019-00196-9

DO - 10.1007/s13571-019-00196-9

M3 - Article

AN - SCOPUS:85066628244

SN - 0976-8386

VL - 81

SP - 46

EP - 102

JO - Sankhya B

JF - Sankhya B

ER -