Two-way fixed effect (FE) estimator: Are individual-specific and time-specific effects identifiable?

[River Huang]

Dear All, Suppose that I am interested in the estimates of company- and year-specific effects (dummy variables) in the following standard panel data:

webuse grunfeld, clear
tab company, gen(company)
tab year, gen(year)
reg invest mvalue kstock company2-company10 year2-year20, robust
reg invest mvalue kstock company1-company9 year1-year19, robust

I wonder if ALL the estimates of company and year dummies are unidentifiable? Thanks.

[Jared Greathouse]

Maybe it's possible, but there are really strong parametric assumptions we'd need to make to ID the individual effect. That's why we work in averages, assuming I've understood the question well

[River Huang]

Dear Jared, Thanks for your reply. I just wonder if "ALL" FEs are identifiable because they are obviously perfectly correlated (individual, year, and possibly constant).

[FernandoRios]

Hi RIver,
I think it depends on the true question.
1) can you estimate a value for each dummy associated to companies and years?
In principle no, because of the dummy variable trap. However, under some conditions (for example that the sum of all coefficients are 0, or that the weighted sum is 0) it is possible to get a value for each coefficient.
Incidentally, that is kind of how reghdfe works to produce the FE estimates (when requested).
2) Are these coefficients identifying the underlying unobserved effects that are fixed across companies and years.
No, what the fixed effects capture is the "fixed" company and year fixed effects plus the "average" effect of all other factors that are fixed across time or fixed across companies (but not necessarily the company fixed effect).

HTH

[River Huang]

Dear FernandoRios, Thanks for these helpful explanations.