
The between-groups estimator is the regression of the cross section means of
on the cross section means of
. In other words, you fit the following regression:
![\[ \bar{\mi{y}}_\mi {i \cdot } = \bar{\mi{\mb{x}}}_\mi {i \cdot }{\beta }^{BG} + \eta _\mi {i} \]](images/etsug_hppanel0126.png)
The between-time-periods estimator is the regression of the time means of
on the time means of
. In other words, you fit the following regression:
![\[ \bar{\mi{y}}_\mi {\cdot t} = \bar{\mi{\mb{x}}}_\mi {\cdot t}{\beta }^{BT} + \zeta _\mi {t} \]](images/etsug_hppanel0128.png)
In both cases, the error is assumed to be normally distributed with mean zero and a constant variance.