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Online Econometrics Textbook - Regression Extensions - Seemingly unrelated regression (SUR) - A dummy variable approach to pooling time series and cross-sectional data

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III.II.1 A dummy variable approach to pooling time series and cross-sectional data

We assume a special case of SUR where

Online Econometrics Textbook - Regression Extensions - Seemingly unrelated regression (SUR) - A dummy variable approach to pooling time series and cross-sectional data

(III.II.1-1)

and where the coefficients are the same for all equations, except for the intercepts.

Such a special model looks like

(III.II.1-2)

In matrix notation this can be written as

(III.II.1-3)

or

(III.II.1-4)

or

(III.II.1-5)

The GLS-BLUE is

(III.II.1-6)

while the parameter covariance matrix is equal to

(III.II.1-7)

whereas the unbiased estimator for the variance is

(III.II.1-8)

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