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  • What variation is being used?

    Hello,

    I have panel data, i.e., monthly data (12 months) on 5 states and 100+ cities in these states. The proportion of the female population (FEM_POP) in a city is one of the variables of interest to me. This variable does not vary over months.

    In my first model estimate, (xtreg 2sls), I use state-fixed effects. My understanding is that in this estimate, the FEM_POP coefficient represents: within-states, counties with a higher female population have higher intention to y variable.
    In another estimate, I include state-fixed effects and city-fixed effects (both). In this second estimate, what variation is being used for FEM_POP to get the coefficient? How would I interpret the coefficient? Also, my coefficient for this second estimate is in the direction opposite to that in the first estimate.

    Please help! Easy question, but I am unable to process and sign flip is making me flippant

    Best,
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