Exponent of Cross-sectional Dependence for Residuals

Springer Science and Business Media LLC - Tập 81 - Trang 46-102 - 2019
Natalia Bailey1, George Kapetanios2, M. Hashem Pesaran3,4
1Monash University, Clayton, Australia
2King's College London, London, UK
3University of Southern California, Los Angeles, USA
4Trinity College, Cambridge, UK

Tóm tắt

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$, \tilde {\alpha }$, 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.

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