Panel data with Time-Invariant Variables / Dummy

[Wulan Lika]

I am conducting a panel data regression using 4 independent variables and 1 time-invariant variable.

Based on the Chow test, Hausman test, and LM test, the best model selected is the Fixed Effects Model (FEM).

However, when I estimate the FEM in Stata, the time-invariant variable is omitted due to collinearity, so its effect cannot be interpreted.

From my understanding, this occurs because in FEM, variables that do not change over time are fully captured by the fixed effects, making them perfectly collinear and therefore automatically dropped by Stata.

My questions are:

1. If I still want to estimate the effect of the time-invariant variable, what method or approach would be appropriate?
2. If I want to estimate the effect of the time-invariant variable, is it acceptable to directly use the Random Effects Model (REM), even though the Hausman test suggests FEM? Are there any references that support the use of REM in this situation?
   
   Thank you in advance and best regards
   Wulan

[Andrew Musau]

Your conclusion on the collinearity mechanism is correct - fixed effects absorb all time-invariant variables, so they are dropped. If you want to estimate that effect, consider Correlated Random Effects (CRE, not standard RE), which lets you keep time-invariant variables while controlling for correlation with unit effects. It essentially gives you the “best of both worlds.”

Using plain RE despite the Hausman test is generally not appropriate, but CRE is specifically designed for this situation (see https://www.stata.com/new-in-stata/c...effects-model/).

[Wulan Lika]

Andrew Musau Thank you for sharing the link.
However, I’m still unclear about when exactly CRE should be used in practice.

My questions:

1. If the Hausman test suggests that Fixed Effects is the preferred model, does that automatically justify switching to CRE instead of FE when we have time-invariant variables?
2. Is CRE considered a replacement for FE in this situation, or is it more of an extension used only for specific research purposes (e.g., when time-invariant variables are of interest)?
3. Is it acceptable to report CRE results as the main model even if the standard model selection tests (Chow/Hausman) originally pointed to FE?

Thank you in advance for your clarification.

[Andrew Musau]

Please take the time to read the contents of the link carefully. All of these questions are addressed there. Also note that you should not use the Hausman test to justify choosing fixed effects (FE). The FE estimator is consistent regardless of whether the random effects assumption holds. Finally, if you cluster your standard errors (which you should do when the number of clusters is sufficiently large), Stata's hausman command is not valid when a robust vce() is specified.

[Carlo Lazzaro]

Wulan:
as an aside the Andrew's helpful recommendation, when you impose non-default standard errors. you should switch from -hausman- to the community-contributed module -xtoverid-, that tests if -re- is the way to go.
Being glorious but a bit old-styled, -xtoverid- does no support -fvvarlist- notation (see -xi- prefix as a workaround).