Interact time-invariant variable in a fixed effect model

[Tim Berg]

Hello everyone,

I have a Stata question and hope you can help.

I want to use fixed effect model but I want to test an interaction between female(1 if true) which is not changing across users(id). I wrote Stata code shown below and the results are shown after.

IS it correct to do such cross level interaction in a fixed effect model.

IF the interaction term is significant, how can I interpret the results?

Many thanks if anyone can help.

DV: wage IV: working experience, working weeks, and whether is a female.
xtset id t
xtreg lwage experience weeks i.female#c.experience, fe

[Clyde Schechter]

Yes, it is fine to do what you have done. It is not, using terminology carefully, a cross-level interaction, even though experience and female are defined at different levels. A cross-level interaction would be an interaction between id itself and experience.

The magnitude of the interaction term is your estimate of the difference between the lwage:experience slope among females and the lwage:experience slope among males. Confidence intervals and p-values for this are interpreted the same way as for any other variable.