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  • Interaction of time-invariant variable in fixed effects model

    Hello everyone,

    I am currently running fixed effects model to see the relationship between program participation and child outcomes. There are two waves and the FE is at the individual level. I want to test whether this relationship varies by a child's poverty status in a prior wave and to do so, I added an interaction term of poverty status & program participation variable. But since this poverty status variable comes from a prior wave (say, wave 1 when FE model includes wave 2 and wave 3), I was not sure how I should interpret the coefficient on this interaction term.

    This is the code I used: xtreg y i.x1##i.x2 covariates i.year, fe (when x1 is program participation var and x2 is poverty status)

    First, is it correct to say that the poverty status is a time-invariant variable here? I am pretty positive it is, since it gets omitted in the model, but wanted to double check.

    Second, Is it correct to interpret the coefficient on the interaction term as how the relationship between program participation and child outcomes varies depending on a child's poverty status in a prior wave?

    And if the coefficient is positive and significant, can we say the program is more strongly related to child outcomes for children living in poverty in a prior wave compared to children who are not poor? I was confused whether I can make this comparison between children in poverty and those who are not, since the FE is a within-entity estimator.

    I'd highly appreciate if any of you can give me some help on this. Thank you in advance!!

  • #2
    Stephanie:
    as you might have already read in the FAQ, the best ways to help interested listers helping yourself are:
    1) posting what you typed and what Stata gave you back (too) via CODE delimiters (# toggle);
    2) share an excerpt/example of your dataset via -dataex-. Thanks.
    Kind regards,
    Carlo
    (Stata 19.0)

    Comment


    • #3
      Hello Carlo,

      Thank you for your note. I pasted my code below! The results show that the interaction term is significant and positive.

      Code:
      xtreg y i.x1##i.x2 covs i.year, fe
      (when x1 is an indicator of program participation (time-varying) and x2 is an indicator for poverty status (time-invariant))

      I could not share an excerpt of my dataset since it is a restricted data. But to provide a brief description, it is a longitudinal dataset with five waves but I'm using only two waves from them.

      If you have any suggestions on my question, it will be very helpful. Thanks.

      Comment


      • #4
        Stephanie:
        1) without seeing your data, it is difficult to say whether or not poverty status is a time-invariant predictor (if it does not change within panel, it is);
        2) as far as your second question is concerned, posting what Stata gave you back (ie, -xtreg- outcome table and results above it) would help enormously interested listers in replying positively. Thanks.
        Kind regards,
        Carlo
        (Stata 19.0)

        Comment


        • #5
          Stephanie: I think you mostly have correctly interpreted what it means to interact a time-invariant variable with the treatment effect. Your poverty variable is time-invariant. If the coefficient on the interaction is positive it does mean the program had a larger effect for children living in poverty.

          One thing to be aware of: you should add vce(cluster id) to obtain valid standard errors.

          Comment


          • #6
            Thank you so much for your help. That clarifies my question!

            Comment

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