What would happen when, starting from a panel data model with group fixed effects and time fixed effects I apply the Mundlak approach?
This is the model:
$ y_{i,t} = c + \beta x_{i,t} + \alpha_i + \delta_2 B2_t + \delta_3 B3_t +....\delta_T BT_t +\epsilon_{i,t} $
where $B_t$ are time dummies (time fixed effects).
Should I also include the sample averages for each $B_t$ so that the equation becomes:
$ y_{i,t} = c + \beta x_{i,t} + \gamma \bar{x}_{i} + \delta_2 B2_t + \delta_3 B3_t +....\delta_T BT_t + \tilde{\delta}_2 \bar{B2} + \tilde{\delta}_3 \bar{B3} +....+\tilde{\delta}_T \bar{BT} +\nu_{i,t}$
wher $\bar{\bullet}$ denotes the sample average computed over each panel for variable $\bullet$.