Panel data model for time variant Y with time invariant X?

What is the appropriate panel data model when you have time dependent Y, but the X's are time-invariant (apart from the implicit time variable itself of course)?

My desired model is analogous to the following - my Y is income (which varies over time), but I want to see how growth in income is affected by gender (which is time-invariant). Thus, I have a model like:

Yit = ait + bit*gender + errors

Random effects seems to allow time-invariant X's, but doesn't quite seem appropriate and is not working in Stata either.

• I would have thought you needed to include time in your model unless you have a strong reason not to. – mdewey Jan 25 '17 at 18:24

$log(Y_{it}) = \alpha + \beta_{0} t + \beta_{1} t*G + \varepsilon_{it}$