# Mundlak Approach when panel data include time fixed effects

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 $$\bullet$$.