Exponent of Cross-sectional Dependence for Residuals
- PDF / 11,320,691 Bytes
- 57 Pages / 439.37 x 666.142 pts Page_size
- 30 Downloads / 187 Views
Exponent of Cross-sectional Dependence for Residuals Natalia Bailey Monash University, Clayton, Australia
George Kapetanios King’s College London, London, UK
M. Hashem Pesaran University of Southern California, Los Angeles, USA Trinity College, Cambridge, UK
Abstract 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. AMS (2000) subject classification. C21, C32. Keywords and phrases. Pair-wise correlations, Cross-sectional dependence, Cross-sectional averages, Weak and strong factor models, CAPM and FamaFrench factors
1 Introduction Interest in the analysis of cross-sectional dependence applied to households, firms, markets, regional and national economies has become prominent Electronic supplementary material The online version of this article (https://doi.org/10.1007/s13571-019-00196-9) contains supplementary material, which is available to authorized users.
2
N. Bailey et al.
over the past decade, especially so in the aftermath of the latest financial crisis given its effects on the global economy. Researchers in many fields have turned to network theory, spatial and factor models to obtain a better understanding of the extent and nature of such cross dependencies. There are many issues to be considered: how to test for the presence of cross-sectional dependence, how to measure the degree of cross-sectional dependence, how to model cross-sectional dependence, and how to carry out counterfactual exercises under alternative network formations or market inter-connections. Many of these topics are the subject of ongoing research. In this paper we focus on measuring cross-sectional dependence. Bailey, Kapetanios and Pesaran (2016, BKP hereafter) give a thorough account of the rationale and motivation behind the need for determining the extent of cross-sectional dependence, be it in finance, micro or macroeconomics. They focus on the asymptotic behaviour of the variance of the cross section average of the observations on a double array of random variables, say xit , indexed by i = 1, 2, . . . , N and t = 1, 2, . . . , T , over space and time. In particular, they analyse the rate at which this variance tends to zero and show that it depends on
Data Loading...
