BIROn - Birkbeck Institutional Research Online

    A Bayesian analysis of linear regression models with highly collinear regressors

    Pesaran, M.H. and Smith, Ron P. (2018) A Bayesian analysis of linear regression models with highly collinear regressors. Econometrics and Statistics 11 , pp. 1-21. ISSN 2452-3062.

    [img]
    Preview
    Text
    PS high collinearity 6 October 2018.pdf - Author's Accepted Manuscript
    Available under License Creative Commons Attribution Non-commercial No Derivatives.

    Download (322kB) | Preview

    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.

    Metadata

    Item Type: Article
    Keyword(s) / Subject(s): Bayesian identification, Multicollinear regressions, Weakly identified regression coefficients, Highly collinear regressors
    School: Birkbeck Faculties and Schools > Faculty of Business and Law > Birkbeck Business School
    Research Centres and Institutes: Innovation Management Research, Birkbeck Centre for
    Depositing User: Ron Smith
    Date Deposited: 26 Oct 2018 08:48
    Last Modified: 02 Aug 2023 17:45
    URI: https://eprints.bbk.ac.uk/id/eprint/24824

    Statistics

    Activity Overview
    6 month trend
    312Downloads
    6 month trend
    336Hits

    Additional statistics are available via IRStats2.

    Archive Staff Only (login required)

    Edit/View Item Edit/View Item