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

#### numerator

##### New Member
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

#### kiton

##### Member
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.