Numerical methods for estimating linear econometric models

The estimation of the Seemingly Unrelated Regressions (SUR) model and its variants is a core area of econometrics. The purpose of this thesis is the investigation and development of efficient numerical and computational methods for solving large-scale SUR models. Specifically, its aim is twofold: firstly to continue past successful research into the design of numerically efficient methods for estimating the basic SUR model; secondly to extend these methods to variants and special cases of that model. The basic computational formulae for deriving the estimators of SUR models involve Kronecker products and direct sum of matrices that make the solution of the models computationally expensive even for modest sized models. Alternative numerical methods, which substantially reduce the computational burden of the estimation procedures, are proposed. Such methods successfully tackle the estimation of the basic SUR model, and that of SUR models derived from VAR(p) processes, SUR models with VAR disturbances, SUR models with unequal size observations and SUR models with orthogonal regressors. The proposed methods are based on orthogonal transformations, and thus, results to be numerically stable. Furthermore, they do not require the common assumption, which is usually made in most theoretical analyses, that the disturbance covariance matrix be non-singular.

Thèse de doctorat : Université de Neuchâtel : 2003 ; 1746