Some finite sample results for a system of seemingly unrelated regression equations

Jinshan Liu and Qiang Xia

Communications in Statistics - Theory and Methods, 2022, vol. 51, issue 11, 3629-3644

Abstract: In this paper, we consider a system of seemingly unrelated regression equations: yi=Xiβi+εi,i=1,…,m,m≥2, with μ{X1}⊇⋯⊇μ{Xm}, where the symbol μ{Xi} denotes the linear space spanned by all the column vectors of matrix Xi,1≤i≤m. Some exact finite sample results of Zellner’s two-stage β-estimators are extended under multivariate normal and multivariate t distributions of the disturbances, respectively. It is found that when (n−p1−1)ρ(i)j2/(m−j+1)>1, the relevant information among {yj,…,ym} can increase the efficiency of the two-stage estimator of βi, and this efficiency increases with the sample size n, where ρ(i)j is the multiple correlation coefficient between yi and {yj,…,ym},j>i.

Date: 2022
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DOI: 10.1080/03610926.2020.1800738

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