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Thread: Interaction between a time-varying and a time invariant variable? (Panel regression)

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    Interaction between a time-varying and a time invariant variable? (Panel regression)




    Hi everyone,

    I have got a question regarding the specification of interaction effects in panel regressions (fixed effects within estimators).

    I would like to know:

    Can I create an interaction-term between a time-varying and a time-invariant variable?

    Some background: My data is from a survey with repeated (T=5) measurements of the same behaviors (my time-varying variables). I want to study if a time-invariant personality trait interacts with a time-varying variable.

    Equation:

    (Yti-Yi_personMean) = (X1ti-X1i_personMean) + (X1X2ti-X1X2i_personMean) + (Eti-Ei_personMean)

    Y:= Dependent Variable
    X1:= Time-Varying Independent Variable
    X2:= Time-Invariant Independent Variable
    E:= Time-Variyng Error-Term
    The suffix "_personMean" referrs to the mean value of one person (i) across all panel waves (the within transformation).


    I know that the fixed effects within estimator wipes out all time-invariant variables. However, when I multiply a time-invariant variable (X2) with a time-varying variable (x1) (before applying the within transformation), I get a time-varying interaction-term (X1X2) between both variables.

    Can anyone please confirm or reject my reasoning?

    Thanks!
    numerator

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    Re: Interaction between a time-varying and a time invariant variable? (Panel regressi


    Hello numerator,

    FE "partials out" the time-invariant effect, not just "wipes it out". In my opinion, your logic on the time-variant interaction is plausible. Yet, note that without the main effect for the time-invariant predictor (i.e., the "wiped-out" one), the interpretation of the interaction becomes somewhat unclear.

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