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  • "Exponent of Cross-sectional Dependence for Residuals", by Natalia Bailey, George Kapetanios and M. Hashem Pesaran, forthcoming in Sankhya B. The Indian Journal of Statistics, April 2019

    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, ã, is consistent and derive the rate at which ã, approaches its true value. 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.
    JEL Classifications: C21, C32
    Key Words: Pair-wise correlations, Cross-sectional dependence, Cross-sectional averages, Weak and strong factor models. CAPM and Fama-French Factors.
    Full Text: http://www.econ.cam.ac.uk/people-files/emeritus/mhp1/fp19/BKP_res_paper_4_Apr_2019.pdf
     

  • "A Bayesian Analysis of Linear Regression Models with Highly Collinear Regressors", by M. Hashem Pesaran and Ron P. Smith, forthcoming in Econometrics and Statistics, October 2018

    Abstract: Exact collinearity between regressors makes their individual coefficients not identified. But, given an informative prior, their Bayesian posterior means are well defined. Just as exact collinearity causes non-identification of the parameters, high collinearity can be viewed as weak identification of the parameters, which is represented, in line with the weak instrument literature, by the correlation matrix being of full rank for a finite sample size T, but converging to a rank deficient matrix as T goes to infinity. The asymptotic behaviour of the posterior mean and precision of the parameters of a linear regression model are examined in the cases of exactly and highly collinear regressors. In both cases the posterior mean remains sensitive to the choice of prior means even if the sample size is sufficiently large, and that the precision rises at a slower rate than the sample size. In the highly collinear case, the posterior means converge to normally distributed random variables whose mean and variance depend on the prior means and prior precisions. The distribution degenerates to fixed points for either exact collinearity or strong identification. The analysis also suggests a diagnostic statistic for the highly collinear case. Monte Carlo simulations and an empirical example are used to illustrate the main …findings.
    JEL Classifications: C11, C18
    Key Words: Bayesian identi…cation, multicollinear regressions, weakly identi…ed regression coefficients, highly collinear regressors.
    Full Text: http://www.econ.cam.ac.uk/emeritus/mhp1/fp18/PS_high_collinearity_6_October_2018.pdf

    Note: A previous version of the paper was distributed as CESifo Working Paper 6785 under the title of "Posterior Means and Precisions of the Coefficients in Linear Models with Highly Collinear Regressors"