My topic is on the Affordable Care Act's Medicaid expansion which happened in America for different years for different states, and I am seeing how this affected violent crime rates through treating for alcohol abuse. I am doing so by looking at how this impacted different races violent crime rates in different states because different races have different alcohol abuse rates.
For my model, I am doing a generalised difference in difference using panel data. I have grouped together "race" and "state" to be "race-state" to be the individual level of the regression. So my "individuals" are for example: "Asians in NY" "Asians in California" "Native Americans in NY" etc. and the time component refers to the years, ranging from 2010 to 2019.
My regression is:
Y(rs)t = Ξ΄(BingeAlcoholRate(rs)π‘ π₯ Medicaidπ π‘) + c(rs)+ d(t)+ controls(rs)t + Ξ΅(rs)t
Where Medicaidπ π‘= {1 ππππππππ βππ ππππ πππππππππ‘ππ ππ π‘βππ ππππ‘πππ’πππ π π‘ππ‘π ππ‘ π‘πππ π‘, 0 ππ‘βπππ€ππ π
c(rs) refers to the unobserved race-state effects or the race-state fixed effects that are time invariant. Given that this is a difference-in-difference, do I still need this variable as surely these unobservable effects will disappear, and if I still do, how would I input this data; in particular if I would include, factors like state geography how should I input that data?
d(t) also refers to time effects that are common shocks to all units that vary through time. I am struggling to think of examples for this, could someone give me an idea of what would be included?
Also in my research I have found that no effect is exclusively time invariant for race-states or time variant but for all race-states, but vary in both to at least some degree; making them more suitable for controls. Is this common and how should I approach this?
A bit of a wordy question but than you for reading and all help is welcome!
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