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  • Diff-in-diff regression design and estimates

    Hi all. I am pretty new to microeconometrics so be patient. I may ask questions that are stupid or obvious to many of you.

    I have a panel data dataset on US schools and need to estimate a diff-in-diff model from it. In particular, I am trying to estimate the effects of the passing of a bill in certain US states. My regression looks like this:

    y_{it} = α + γ_i + ω_t + β_t * D_ i + ϵ_{it}

    Where y_{it} is a maths score index, γ_i and ω_t are fixed effects for the school and the year, D_i is a dummy = 1 if the school has received benefits from the bill, and ϵ_{it} is a school-year error term. I have data from 2009 to 2018. The bill was passed in 2013. I am trying to estimate β_t, the treatment effect specific to year t, to see whether this bill has had a positive or negative effect on maths scores in schools that have received the treatment.

    My three questions are:
    1. Does it make sense to estimate β_t for years before 2013? If so, what does the β_t estimated for the periods before 2013 represent?
    2. Should I run the regression separately for each year or can I estimate everything at once?
    3. What does this regression look like on Stata? How would you include the command for fixed effects? Should I choose 2013 as my base (omitted) category? I was thinking of something like: reg y i.fixed_effects_school i.year + i.treat. Would that work?
    Thank you so much in advance, sorry again if this stuff is obvious!
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