The HPPANEL Procedure

Between Estimators

The between-groups estimator is the regression of the cross section means of $\mb{y}$ on the cross section means of $\tilde{\mb{X}}_{s}$. In other words, you fit the following regression:

\[ \bar{\mi{y}}_\mi {i \cdot } = \bar{\mi{\mb{x}}}_\mi {i \cdot }{\beta }^{BG} + \eta _\mi {i} \]

The between-time-periods estimator is the regression of the time means of $\mb{y} $ on the time means of $\tilde{\mb{X}}_{s}$. In other words, you fit the following regression:

\[ \bar{\mi{y}}_\mi {\cdot t} = \bar{\mi{\mb{x}}}_\mi {\cdot t}{\beta }^{BT} + \zeta _\mi {t} \]

In both cases, the error is assumed to be normally distributed with mean zero and a constant variance.