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  • Difference-in-difference with interactions

    Hi,

    I'm trying to estimate a straight forward Difference-in-Difference model to find the impact of a treatment (targeting 50 out of 100 schools) on student maths scores in grade 7. I have baseline pre-treatment data for both groups and end-line data for both groups. So a simple school level fixed effects model with clustered standard errors would be:

    reg maths_score i.treated##i.y2016 male income i.school_id, cluster(school_id)

    where treated=1 if the school was treated, y2016=1 if end-line year, male is a gender dummy and income is a continuous variable. When estimated both male and income are significant at the 1% level.

    But what I really want to know is whether the coefficient on treated and income are significantly different for males versus females. Will the following help me achieve this?

    reg y i.treated##i.year##i.male c.income##i.male i.school_id, cluster(school_id)

    I ask as fully interacting the model with the gender variable gives me a result where male and all the new interaction terms become non-significant. Income alone remains significant. I'm struggling to interpret why/how male lost significance while male#income is not significant either. Any insights much appreciated.




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