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18 Seemingly Unrelated Regression

# 18 Seemingly Unrelated Regression - Economics 241B...

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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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18 Seemingly Unrelated Regression - Economics 241B...

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