Should interaction terms be estimated using xtreg (FE/RE) when the baseline model uses fixed/random effects, or is pooled OLS sufficient?

[Man Khanh Chau]

Hi everyone, In many tutorials and YouTube videos on moderation/interaction effects, people estimate the model with interaction terms using simple regress (pooled OLS), like:
reg y c.x1##c.x2
or with centering for probing simple slopes.

However, in my own analysis, the baseline model (without interaction) is a panel data model using fixed effects or random effects, for example:
xtreg y x1 x2 controls, fe
(or re).

My question is:
When I add an interaction term to test moderation, should I keep the same estimator (xtreg ..., fe or re) like this:
xtreg y c.x1##c.x2 controls, fe
or is it acceptable/common to switch to pooled OLS (regress) just for the interaction model?

I understand that if the data has panel structure and unobserved time-invariant heterogeneity is important (that's why I used FE/RE originally), then dropping FE/RE when adding the interaction might introduce bias similar to the baseline model. But I've seen some papers/tutorials stick with pooled OLS even for interactions in panel settings.
Is it standard practice to use xtreg (FE/RE) consistently for interaction models in panel data? Are there any specific considerations that I should be aware of?

And one additional question:
In my panel data model, the baseline model (without interaction) has 3 independent variables, for example:
xtreg y x1 x2 x3 controls, fe

When I add an interaction term between only two of them (say x1 and x2), do I still need to keep the third variable (x3) in the model? Like this:
xtreg y c.x1##c.x2 x3 controls, fe

Or is it okay to drop x3 when testing the interaction?
Thanks in advance for any advice or references!
Best regards,

[Manh Hoang Ba]

Ignoring individual effects (reg + without any dummies) is a potentially risky specification regarding endogenous variables. I'm not sure which guide you've seen on analyzing interaction variables using only reg without any dummies, but I believe such guidelines are imprudent and unreliable.
Interaction variables are essentially just independent variables added to the baseline model. They play a role in discovering the mechanisms of the effects of explanatory variables, so you can absolutely use the specification from the baseline model for mechanism analysis. Furthermore, robust inference should be used.

That is:
xtreg y c.x1##c.x2 x3 i.timevar, fe vce(cluster panelvar)
or with reg command
reg y c.x1##c.x2 x3 i.panelvar i.timevar, vce(cluster panelvar)

[Man Khanh Chau]

Ignoring individual effects (reg + without any dummies) is a potentially risky specification regarding endogenous variables. I'm not sure which guide you've seen on analyzing interaction variables using only reg without any dummies, but I believe such guidelines are imprudent and unreliable.
Interaction variables are essentially just independent variables added to the baseline model. They play a role in discovering the mechanisms of the effects of explanatory variables, so you can absolutely use the specification from the baseline model for mechanism analysis. Furthermore, robust inference should be used.

That is:
xtreg y c.x1##c.x2 x3 i.timevar, fe vce(cluster panelvar)
or with reg command
reg y c.x1##c.x2 x3 i.panelvar i.timevar, vce(cluster panelvar)

Thank you! Just to confirm: even when the interaction is between two time-varying variables, I should still use the same FE as baseline? And should I center the variables inside xtreg, fe?

[Manh Hoang Ba]

Happy Tet Holliday,
As mentioned, x1*x2 is an explanatory variable, so you just need to treat it like the other explanatory variables (x1, x2, x3) without doing anything extra.
If you try to center x1 and x2, the parameters (and consequently the coefficient estimates) of x1 and x2 will change. You can use mathematical transformations on the regression equation to see this clearly.

[Man Khanh Chau]

Happy Tet Holliday,
As mentioned, x1*x2 is an explanatory variable, so you just need to treat it like the other explanatory variables (x1, x2, x3) without doing anything extra.
If you try to center x1 and x2, the parameters (and consequently the coefficient estimates) of x1 and x2 will change. You can use mathematical transformations on the regression equation to see this clearly.

Happy Lunar New Year 2026! Hope you have a successful year!

I need your help with one more question

When testing moderation with two-way interactions, should I add only one interaction first (e.g., c.x1##c.x2 x3), or add all three interactions at once (c.x1##c.x2 c.x1##c.x3 c.x2##c.x3)? Because as I know, adding too many interaction terms in a regression model can cause multicollinearity, difficult interpretability, and lower statistical power.

Thanks in advance!

[Manh Hoang Ba]

I believe that adding interaction variables should serve to answer the research question, and if that's the case, then they should be included in the model. But as you mentioned, multicollinearity can be a nuisance, but not always. In panel data, multicollinearity is usually not a problem, and we can check by calculating VIFs for a specific model to assess its impact on the results.

[Carlo Lazzaro]

Man:
as an aside to Manh's helpful advice, I do not recall any econometric textbook recommending to switch from panel data regression to pooled OLS for interactions.
In addition, the mean conditional effects of the interacted terms should also be included.
The only exception that I know is -xtdidregress-.
Eventually, I concur with Manh's last recommendation to use cluster-robust standard errors instead of their default counterparts.

[Man Khanh Chau]

Thank you Mr. Manh Hoang Ba and Mr.Carlo Lazzaro for very helpful and detailed guidance!! I really appreciate that

[Riski Amalia]

If you don't mind can i know What's name of yutub that teach of panel data with interaction ?

[Carlo Lazzaro]

Riski:
you may want to take a look at https://www.stata.com/links/video-tutorials/ and https://www.stata.com/training/webin...lrm.slides.pdf.