Explaining the significant levels change when adding interaction variables?

[Phuc Nguyen]

Today, when running the regression, I found something quite complicated

Where Y1, Y2, Y3 are different dependent variables. pt_original is pt retrieved from this equation

Dependent_variables= pt + Independent_variables + fixed effects + error term

And pt along with developedpt is from this regression

Dependent_variables= pt + developed_dummy*pt + Independent_variables + fixed effects + error term

pt is a variable of interest in a Differentce-in-Difference setting.
where developed_dummy equalling to 1 if this observation is in developed countries.

So, in this Table, what I can conclude so far is:

0.00786: the law does not affect Y1 in developed countries differently compared to developing countries.

0.827*** : Laws' effect in developed countries is higher by 0.8270.827 relative to developing countries. The total effect of this law on Y2 in developed countries is 0.827−1.122=−0.2950.827−1.122=−0.295.

I hope the explanation above is correct.

My focus now is on another aspect of the results.

1> For Y1, pt becomes significant after controlling for developed_dummy * pt . So, what can I conclude about this phenomenon?

2> For Y3, coefficients of pt become negative significant and of developedpt becomes positive significant, what I can conclude about this phenomenon as well?
3> For Y4, coefficients of pt become positive significant when it was negative significant, what I can conclude about this phenomenon?

[Richard Williams]

First off, your equations don't seem to include developed_dummy as a separate variable. When you have interaction terms you usually want to include the variables used to compute the interaction.

Second, the meaning and interpretation of the main effects changes once interaction terms are added to the model. You shouldn't make a big deal about a main effect becoming significant or insignificant or even changing signs once an interaction is added to the model.

For a discussion, see

https://www3.nd.edu/~rwilliam/stats2/l53.pdf

[Phuc Nguyen]

First off, your equations don't seem to include developed_dummy as a separate variable. When you have interaction terms you usually want to include the variables used to compute the interaction.

Hi Richard Williams, thank you for your dedicated explanation. I am wondering about the quoted part. if my understand is correct, do you mean that I should run this regression

Dependent_variables= pt + developed_dummy*pt + developed_dummy + Independent_variables + fixed effects + error term

rather than
Dependent_variables= pt + developed_dummy*pt + Independent_variables + fixed effects + error term

Thanks in advance.

[Richard Williams]

Yes, run the regression that has both of the main effects and the interaction term computed from them.

[Bert Lloyd]

Prof. Richard Williams , is there a formal citation you recommend for centering, as discussed in the lecture notes you linked? I have read a few offhand, informal references to a saying attributed to John Tukey to "estimate centercepts, not intercepts" but don't know if there is a paper one should cite. And thank you for the link to your very clear and helpful notes.

[Richard Williams]

I certainly didn't invent centering! Although the handout did help me to understand it better. You could cite my handout, but a more impressive source would be Aiken and West:

https://smile.amazon.com/AIKEN-REGRE...-no-redirect=1