Is an individual firm-level fixed effect necessary in the model?

[Chul-Kyoo Jung]

Hi, I want to design a two-way fixed effects model on whether industrial policy affected firms' profitability.
I have a model options in my consideration as follows:

Every firm belongs to either large enterprise (LE) or small and medium sized enterprises (SME), which are represented by a binary variable (0,1).
And also each firm also belongs to a certain industry among several industries such as manufacturing, service, etc. Then the model goes:

Y_fit = a_f + b_i + c_t + beta₁ x TREAT_fit + beta₂ x Var2_fit + e_it where Y_fit is the profitability of individual firm that belongs to a certain industry and a_f, b_i, c_t are firm-level, industry-level, year fixed effects.

I included an individual firm level fixed effect to control for unobserved heterogeneous firm characteristics but I did not for LE and SME because I assume there is a parallel trend between LE and SME.
My first question is whether individual firm-level fixed effect (a_f) in this case is necessary and my model can be justified without dummy variable for LE and SME.

I would appreciate it if anyone could give me a small tip. Thanks.

[Carlo Lazzaro]

Chul-Kyoo:
it may seem you're planning to go -xtreg,fe-.
If that were the case, you should -xtset- you data with -panelid- (firms, in your case) and -timevar-, first.
Adding -i.timevar- is also highly recommended for -fe- specification.
As far as fim size is concerned, if it is time-invariant it will be wiped out from the -fe- machinery by default.
As an aside, you might be also interested in the community-contributed module -reghdfe-.

[Chul-Kyoo Jung]

Carlo Lazzaro thanks Carlo, do you suggest the following? Please let me know if I am missing something:

xtset firmid year
xtreg DepVar TREAT Var2 i.firm i.year, re vce(robust)

rather than

xtset firmid year
xtreg DepVar TREAT Var2 i.industry i.year, re vce(robust)

?

And if it is the case, I am also wondering why I don't need i.industry in the model.

[Carlo Lazzaro]

Chul-Kyoo:
your second code is the way to go.
If you go -re- instead of -fe- -i.industry- even though time-invariant makes sense, as a coefficient will be calculated.

[Chul-Kyoo Jung]

Carlo Lazzaro , my mistake. It should be with -fe- not -re-.
In case with -fe-, then should I go with the following? I feel still missing something here.

xtset firmid year
xtreg DepVar TREAT Var2 i.firmid i.year, fe vce(robust)

I don't understand why i.industry (industry fixed effect) does not fit with -fe-. Thanks.

[Carlo Lazzaro]

Chul-Kyoo:
as expected, due to demeaning, the -fe- estimator wipes out all time-invariant variables. Therefore, if -i.industry- is a time- invariant predictor because, as it is often the case, firms do not change industry as time goes by, Stata will not give back any coefficient for -i.industry- (and rightfully so).

[Chul-Kyoo Jung]

Carlo Lazzaro thanks so much!