Testing for significant differences between the betas of two FE model specifications without using an interaction term

[Diane Geelon]

Good morning all,

I am using 2-wave panel data and a standard fixed effects model to estimate the moderating impact of homeworking or not homeworking on the effect of covid-19 on a series of dependent variables (captured by the binary indicator variables wave and didwfh). I run the model twice for each outcome variable, first for non-homeworkers and then for homeworkers.

xtreg DV1 wave if didwfh==0, fe vce (cluster id)
xtreg DV1 wave if didwfh==1, fe vce (cluster id)

This tells me whether the impact of C19 on DV1 (beta1) is significant for a) non-homeworkers and b) homeworkers SEPARATELY

I now want to test whether the beta produced by specification 1 and the beta produced by specification 2 are significantly different i.e. whether the differential impact of C19 on homeworkers / nonhomeworkers is stat significant

Is there any way to do this using a post estimation command? My supervisors are not keen on me using an interaction model.

I have tried the following:

quietly xtreg DV1 wave if didwfh==0, fe vce (cluster id)
est sto DVnhw
quietly xtreg DV1 wave if didwfh==1, fe vce (cluster id)
est sto DVhw
ttest DVnhw == DVhw

but it just tells me that "variable DVnhw is not found"

Any ideas on how to do this? I can't think of anything else to try so any help would be greatly appreciated

Many thanks for taking the time to read this message,
Diane

[Maarten Buis]

Why do you not want to use interaction effects?

[Diane Geelon]

My supervisors are not keen on them. Say they are too difficult to interpret when using two binary variables. I currently have a table in my paper with two columns, one for the main effect (beta) of Covid on non-homeworkers and one for homeworkers. They have asked me to add a third column which estimates whether the difference between the two coefficients is significant

[Maarten Buis]

You implicitly included all interaction effects by estimating separate models. So any objection against interaction effects also applies in the same way to estimating separate models.