Fixed Effects

Dear All,

I have the following model

Investment_it=a + b*X_it + c*Treatment_i + d*After_t + e*Treatment_i*After_t + Industry f.e. + error (1)

where "i" is an index for firm, "t" is an index for quarter. "After "is a dummy after 2007. "Treatment" is a dummy for the

treated firms and 0 for the control/untreated firms.

Now the variable "Treatment_i" is endogenous and I use 2SLS with an instrumental variable Z_it.

1st stage is:

Treatment_i=a + b* X_it + Z_it + industry f.e. + error (2)

and using then predicted Treatment_i, I re-estimate (1) . In 2SLS the set of explanatory variables in (2) must be same as

those in (1). My question is that do I need to use the "After" in (2) since it also shows up in (1)? Thing is that "After" is like

a time fixed effects and Treatment_i is time invariant in (2). Any feedback is greatly appreciated. thanks!