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Faculty of Economics

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Wu, R., Weeks, M.

A Semi-Parametric Bayesian Generalized Least Square Estimator


Abstract: Generalized Least Square (GLS) estimators have been vastly applied in empirical studies to improve the efficiency of estimation. However, parametric GLS still imposes certain assumptions on the form of the covariance matrix of the unobservable, and the efficiency gain of GLS in fact depends on these assumptions being correct. In this paper we propose a semi-parametric Bayesian GLS estimator to cope with such heterogeneity. A Dirichlet process prior is put on the distribution of the covariance matrices of the unobservables, leading to a model that could be interpreted as the mixture of a variable number of normal distributions. Our methods let the number of heterogeneous groups be data driven, and so is the group membership of each observation. The semi-parametric Bayesian Seemingly Unrelated Regression (SUR) for equation systems, as well as Random Effects Model (REM) and Correlated Random Effects Model (CREM) for panel data are then described as special cases of the GLS estimators. A series of simulation experiments is designed to explore the performance of our methods, and demonstrates that they provide more reliable inference than the parametric Bayesian GLS. We then apply our semi-parametric Bayesian SUR and REM/CREM methods to empirical examples.

Keywords: Bayesian semi-parametric, generalized lease square estimator, Dirichlet process, equation system, seemingly unrelated regression, panel data, random effects model, correlated random effects model.

JEL Codes: C30

Author links: Melvyn Weeks  


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