Difference in difference with region and time fixed effect

[Alex Red Smith]

Hello all

I have a research about a policy change and here is a brief introduction.

So I have 10 mothly data of salaries before a policy changes and 12 monthly data after the policay change. (panel data at individual level) Only female got influced by the policy change :female as treatment group and males as control group.

I have this model specification and can someone please tell me if it is correct?

Y_ijt= α + β * Female_ijt *POST+ γ_j +Θ _t +error_{ijt
where Yijt} is individual i's salary in company j at month t;
female is a dummy,which is set to 1 if the individual is a female ;
Post is a dummy indicates that the time is after the policy change;
γj +Θ t are company fixed effects and time fixed effects.

Is the β here captures the causal influence? Or should I drop the POST?


Thank you all very much for your great help!

Alex

[Andrew Musau]

This will be fine if all females are in the treatment group. Essentially, what you want is to create an indicator variable equal to 1 if individual \(i\) in year \(t\) was subject to the treatment, and 0 otherwise.

Added: Because you are analyzing individuals, you should have the fixed effects at the individual level. Company fixed effects are accounted for by individual fixed effects (individuals are within companies), so I would estimate the following model instead

$$Y_{it} = \alpha + \beta*\text{treatment}_{it} +\gamma^{\prime}X_{it}+ \eta_{i}+\theta_{t} +e_{it}$$