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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.

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  • $\begingroup$ I would have thought you needed to include time in your model unless you have a strong reason not to. $\endgroup$
    – mdewey
    Commented Jan 25, 2017 at 18:24

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My answer is purely on the basis of what you have written as really your intention to study : which is checking if gender effects or is correlated with the growth in the y variable over time. A simple regression possible to run for this is:

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

Here the interaction term gives you the differential growth rate of Y variable for G = 1. Say G = 1 means female and male otherwise. G is a dummy here. This seems to be more informative. Hope this helps.

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