Abstract
This article is concerned with the estimation problem of multicollinearity in two seemingly unrelated regression (SUR) equations with linear restrictions. We propose a restricted feasible SUR estimates of the regression coefficients of this model and compare with feasible generalized least squares (FGLS) estimator and the estimator proposed by Revankar (1974) in the matrix mean square error sense. The ideas in the article are evaluated using Monte Carlo simulation.
Highlights
The seemingly unrelated regression model, introduced by Zellner (1962) improves the estimation efficiency by combining several equations into a single equation
The object of the present paper is to consider the problem of multicollinearity and its statistical consequences for two seemingly unrelated regression (SUR) model when additional linear restrictions are assumed to hold
We investigate the efficiency of the restricted feasible SUR estimator of 1, as compared to the unrestricted estimator in Revankar (1974)
Summary
The seemingly unrelated regression model, introduced by Zellner (1962) improves the estimation efficiency by combining several equations into a single equation. Consider a system of two SUR equations yi Xi i i , i 1, 2 where yi is a T 1 vector of observations on the dependent variable, Xi is a T ni matrix of explanatory variables in the ith equation with rank ni , i is a ni 1 vector of unknown parameters, i is an T 1 vector of unobservable disturbances with. ˆGLS is the best linear unbiased estimator (BLUE) of in the SUR model. This estimate is not a feasible estimator of because in general is not known. Replacing the unknown by its unrestricted estimate S , yields the two-stage Aitken estimator of
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