Dear all,

This is a question not directly about stata application. I notice there are many topics about the Mundlak (or Chamberlain) device. Virtually all of them are projecting the unobserved heterogeneity onto the regressors (means of regressors across time) such that c_i=\bar x_i +e. This may help to identify the effect of time-invariant variables in the model.

I wonder if it's possible to project the unobserved heterogeneity (with a time subscript) onto the cross-sectional averages such that c_t=\bar x_t+e. If so it could help identify the effect of aggregate shock.

I cannot see anything contradictory for a relatively long panel. However, I cannot find such practice in the literature. Wonder if anyone have seen this type of examples. Please advise if this is simply wrong.

Thanks.