## Seemingly Unreleted Regression Model

The seemingly unrelated regression (SUR) model proposed by Zellner (1962) consists of the following N regression equations, each of which satisfies the assumptions of the standard regression model (Model 1):

y.-X/A+u,, 1=1,2______ ,N, (6.4.1)

where y, and u, are T-vectors, X, is a T X Kt matrix, and fit is a A, -vector. Let utt bethetthelementofthevectoru,-.Thenweassumethat(uu, Цц,. . . , uM)is an i. i.d. random vector with Eu„ = 0 and Cov (ий, Uj,) = a0. Defining у = (УЇ, У2. • • • ,У*)’> Р^іРиРг,- • • ,0’nY, u = (ui, u^,. . . ,ui,)’, and X = diag (Xj, X2,. . . , ХД we can write (6.4.1) as

у = Xfi + u. (6.4.2)

This is clearly a special case of Model 6, where the covariance matrix of u is given by

£uu’ = ft = 2 ® Iy, (6.4.3)

where 2 = {(Ту) and ® denotes the ...

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