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  • Fixed Effects with Differences-in-Differences

    Dear all,

    I am writing my master’s thesis and to conduct my analysis, I use register data/panel data. I have data on a large number of individuals before and after a reform. Thus, I want to do a fixed effects with DiD analysis. What I want to estimate the effect of a parental leave reform on wage.
    I want to analyze three years prior to the reform and ten years after the reform was implemented.
    I created a reform dummy (called reform), denoting the individuals who had their first child before and after the reform.
    Further, I created a time dummy (called time) equal to one after the reform and 0 before and the code is as follows:

    xtreg DepVar i.reform##i.time controls, fe robust

    However I am concerned if I could just use the original years (hence 1995, 1996 1997, 1998, etc.) in the interaction term such as

    xtreg DepVar i.year i.year##i.reform, fe robust


    I would really appreciate if someone could help me on this one and to clarify which one is the right one to use given my intention with the analysis.
    Thanks a lot.
    Best,
    Kamilla

  • #2
    Hi Kamilla,

    If you are looking to do a dif-in-dif then your first specification is correct. The double hashtag notation tells Stata to run something of form:
    Code:
    Y = a + bReform + cTime + dReform*Time + eControls + u
    In other words, you are controlling for the reform (individuals affected), time (before/after) and an interaction. The coefficient d will be the one of interest (i.e. the coefficient on the interaction term).

    In your second specification, I believe i.year is superfluous given your double hashtag notation. I don't believe this is suitable for your research, but you could of course create a dummy variable called affected (for instance) which equals 0 if before the reform and 1 if after the reform and an individual is affected by the reform. You can then run a sort of two-way fixed effects (controlling for time and also individual fixed effects - in which case you should also cluster over these:
    Code:
    xtreg depvar i.year i.individual_id i.affected controls, fe cluster(individual_id)
    Best,
    Rhys

    Comment


    • #3
      Hi Rhys,

      Thank you very much for your reply.

      If I choose the first specification, is it then possible to interpret the how the wage changes in for example 1 year after the reform, 2 years after the reform etc.? What I would like to do is to sort of follow the wage after the reform, which I find hard to interpret this way.

      Best,
      Kamilla

      Comment


      • #4
        Hi Kamilla,

        I hadn't realised you wanted to follow the trajectory of change. If that is the case then you are correct that the first specification would not achieve that. However, I do not believe that the second specification would do that either (I don't think what you are after would be captured solely by the time dummies). Instead, you may well want to do some kind of event study or include an interaction of the treatment on the year variable to plot the trajectory.

        Best,
        Rhys

        Comment


        • #5
          Thank you again, Rhys.
          Would it be correct to include an interaction of the treatment on the year variable in the first specification:
          Code:
          xtreg DepVar i.reform##i.time i.reform*i.year controls, fe robust

          Comment


          • #6
            It seems reasonable to me, however I am not sure what exactly is done in the literature and whether there are any robustness issues etc. Maybe have a look into event studies and see what formulation they use.

            Best,
            Rhys

            Comment

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