Mundlak (1978) proposed the addition of time averages to the usual panel equation in order to remove the fixed effects bias. We extend this Mundlak equation further by replacing the time-varying explanatory variables by the corresponding deviations from the averages over time, while keeping the time averages in the equation. It appears that regression on this extended equation provides simultaneously the within and in-between estimator, while the pooled data estimator is a weighted average of the within and in-between estimator. In Section 3 we introduce observed and unobserved fixed effects In Section 4 we demonstrate that in this extended setup Probit estimation on panel data sets does not pose a specific problem. The usual software will do. In Section 5 we give an empirical example.
panel data estimation techniques ordered probit fixed effects estimator within estimator pooled regression between estimator