How to Handle Time-Invariant Dummy Variables in Fixed Effects Model

[Wulan Lika]

Hello, I would like to ask a question.
I am currently conducting research on income distribution using panel data. My model consists of four independent variables and one dummy variable that is time-invariant.

The issue I am facing is that, based on the Hausman test, the Fixed Effects Model (FEM) is the preferred model. However, when I estimate the model using FEM, the time-invariant dummy variable is omitted, so I am unable to analyze it, even though this variable is important for my research.

My question is:
How can I address this issue so that the time-invariant dummy variable can still be analyzed while using an appropriate estimation approach (given that the Hausman test suggests FEM)?

Thank you very much,
Wulan

[Maarten Buis]

You can estimate a correlated random effects model, and the effects of time changing variables will be fixed effects estimates, but the effects of time constant variables will be random effect estimates. There is nothing you can do to change that. A fixed effects estimate uses only variation within an individual, if there is no variation within an individual then you cannot get a fixed effects estimate.

[Erik Ruzek]

Agreed with Maarten. The only thing you can do is look at interactions between the time invariant variable and cluster dummies, which means that you do not get an average slope associated with the time-invariant variable, only conditional slopes based on the clusters:

reg outcome time_varying_variables time_invariant##i.cluster

[Wulan Lika]

Thank you Maarten Buis and Erik Ruzek
So, if I understand correctly, one possible solution to this issue is to use the Correlated Random Effects (CRE) approach.

I would also like to ask, if my model does not show any signs of heteroskedasticity or autocorrelation, would it still be recommended to use robust (e.g., clustered) standard errors -xtreg, cre vce(cluster id)-, or would conventional standard errors be sufficient?

Thank you again for your guidance!

Best wishes,

Wulan

[Erik Ruzek]

Wulan - the use of robust standard errors is de facto for many Stata users. Should it be? That's another question, and many, many papers and blog posts have been dedicated to this. I suggest you consult those. E.g., this recent one by Uri Simonson.