Economics 241B
Seemingly Unrelated Regressions
We begin our discussion of systems of equations with a system that is not
simultaneous in nature.
Consider two dependent variables that are considered
as a group because they bear a close conceptual relationship to one another.
Aside from this conceptual relationship, the two linear regression models have,
outwardly, no connection with one another.
Each equation models a di/erent
dependent variable and the regressors in each equation need not be the same.
The two equations are
Y
t;
1
=
X
0
t;
1
1
+
U
t;
1
(1)
Y
t;
2
=
X
0
t;
2
2
+
U
t;
2
:
(2)
Because the two equations appear unrelated, we would think of estimating them
separately. (And the system is referred to as a system of seemingly unrelated
regression (SUR) equations.)
Of course, if the two equations actually are un
related, then we should estimate them separately. But it may be the case that
there is a relation between the equations, brought forward by correlation between
the two error terms.
If the two error terms are correlated, then we can gain a
more e¢ cient estimator by estimating the two equations jointly, as was shown by
Zellner in 1962.
The intuition mirrors the intuition for a single equation with
serial correlation. If
U
t;
1
is correlated with
U
t;
2
, then knowledge of
U
t;
2
can help
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 Fall '08
 Staff
 Economics, Regression Analysis, Xt, seemingly unrelated regression

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