Individual fixed effects in panel data

[Jason Cruso]

Hello Xperts,

I have the following panel data set (this is just a sample since I cannot use the real dataset for copyright reasons):

Id	year	age	treatment	prepost	salary	CapInc	OccId
1	1990	23	0	0	100	234	33
1	1991	24	0	0	212	23	33
1	1992	25	0	0	122	23	33
1	1993	26	0	1	345	23	33
1	1994	27	0	1	234	2	33
1	1995	28	0	1	11	45	33
2	1990	33	0	0	223	23	33
2	1991	34	0	0	678	9	22
2	1992	35	0	0	121	9	22
2	1993	36	0	1	33	9	22
2	1994	36	0	1	45	12	22
2	1995	38	0	1	67	0	22
2	1995	39	0	1	78	5	22
3	1990	56	1	0	23	3	11
3	1991	57	1	0	88	5	11
3	1992	58	1	0	99	7	11
3	1993	59	1	1	44	21	11
3	1994	60	1	1	11	23	11
3	1995	61	1	1	33	3453	11
4	1990	45	1	0	44	3	77
4	1991	46	1	0	12	454	77
4	1992	47	1	0	12	5	77
4	1993	48	1	1	34	45	77
4	1994	49	1	1	66	454	77
4	1995	50	1	1	777	56	77

I need to implement the following FE model (diff-in-diff) :

Wit = Ai+ Xit*Beta + Dit*Sigma + Ci*Xit*Beta + Ci*Dit*Sigma + Errorit

Ai = Individual fixed effects
Wit = Salary
Xit = contains observed time-varying characteristics of individuals
Ci = treatment variable
Dit = Dummy variable indicating the pre and post period

I have the following code implemented in stata:

 xtset id year

 xtreg salary i.treatment##i.prepost i.treatment##c.age i.treatment##c.CapInc, fe robust

Is my code correct?
I am wondering the Ai component of the model that needs to capture the individual fixed effects. Does my code capture the individual fixed effects?


Thanks a lot as usual for all your inputs.

Regards,

Jason

[Carlo Lazzaro]

Jason:
the fixed effect is actually captured by -panelid- included in -xtset-.
That said, so many interactions look problematic to understand and disseminate.

[Jason Cruso]

Thanks Calro!
The first interaction

xtreg salary i.treatment##i.prepost, fe

is the diff-in-diff estimator.

The rest of the interactions are the interaction of the treatment variable with each of the time variant control.
Hope that makes sense.

Just to continue, what if I also need to include the occupation id (OccId) fixed effect into my model?

Will the stata code by something like this (without controls)?

xtset OccId year
xtreg salary i.treatment##i.prepost, fe robust

Thanks as usual,

Jason

[Carlo Lazzaro]

Jason:
interactions make sense as long as they contribute to give a fair and true data generating process.
As far as your second question is concerned, your new code change the -paneid-.My guess is that this is not what you want. If you want to control for employment just add -i.Occid- (which probably is a categorical variable) in the right-hand side of -xtreg- keeping -id- as -panelid-.

[Jason Cruso]

Thanks Carlo.
This is what i understand from your comment.

xtset id year
xtreg salary i.treatment##i.prepost i.OccId, fe robust

This is the problem I have, and I would like to include it in the model. My theory suggests that an individual's salary is likely to be biased due to an occupation before the treatment year (i.e. 1992). Hence I would like to "take away" the 1992 occupation effects on the salary from 1993-1995. Hence the occupation is time invariant (thats why you see that the occupation id does not change).

Any suggestions how can I do this? Basically I would like to include occupation and individual FE in the same model. Something like:

Wit = Ai+ Bo + Xit*Beta + Dit*Sigma + Ci*Xit*Beta + Ci*Dit*Sigma + Errorit
Bo = occupation fixed effects.

Possible?
(Apologies if my question sound very basic, I am still getting my head around FE in a panel data)

Thanks again.

J

[Carlo Lazzaro]

Jason:
if you want to estimate more than one fixed effect, you may want to consider the community-contributed programme -reghdfe- (just type -search reghdfe- and follow the instructions to install it).

[Jason Cruso]

Ah ok! This is new to me. I will take a look.
Thanks a lot!

J

[Jason Cruso]

This is what I did:

reghdfe salary i.treatment##i.prepost, vce(robust) absorb(Id OccId)

This is to model my individual and occupation fixed effects in one model.

J

[Carlo Lazzaro]

Jason:
it looks reasonable.

[Jason Cruso]

Thanks a lot Carlo!

[Kelvin Hici]

Jason, if occupation does not change over time, then it is already absorbed by the individual fixed effects in your first regression (the one that uses xtreg). So you may not need to correct for it separately, unless it changes over the years, others it is captured by Ai

[Jason Cruso]

Thanks Kelvin for that point! I also realised that. When adding the additional occupation fixed effects, there is hardly any difference from my prior results when I use only individual FE!