Change of sign of coefficients when an interaction is added

[Loic DUBOIS]

Hello everyone,

I'm posting this message on this forum because I need information to help interpret my results.

I am currently running regressions to show the impact of gender on financial performance and the moderating role of culture.

To do this, I'm running a fixed-effect regression as follows:
(I'm using regress and not xtreg because I think I have cross-sectional data)

regress TobinsQ_w gender institutionalcollectivism c.institutionalcollectivism#c.gender lnAGE lnboardsize indep CEOChairmanDuality lnmarketcap_w debtoasset_w Dummylegalsystem quota corruption GDPgrowth uncemployement popgrwoth i.Fesize i.Year i.sector, vce(robust)

As you can see, I include fixed effects by size (FEsize) by year (Year) and by sector (sector). Firstly, can you tell me if the syntax is correct?

Then here's my problem. When I don't include the interaction term I have positive and statistically significant coefficients for the "gender" variable and a negative coefficient for the "institutionalcollectivism" variable. However, as soon as I include the interaction term, my gender coefficient remains significant but has changed sign. (You can see the two regressions below).

Regression without the interaction term:



And regression with the interaction term:



My VIF test is good (except when I do it with the interaction, but I think that's normal since this variable is constructed in relation to two other variables).

Is this normal or are there any errors?

Thanks a lot in advance,

Loïc

[FernandoRios]

With interactions, you CANT just look at coefficients.
You either need to estimate marginal effects (avg or at means) or center your variables.

[Loic DUBOIS]

Hello Fernando,

Thank you very much for your comment.

I did take that into account and tried to estimate the marginal effects. So I ran my regression regress TobinsQ_w gender Performanceorientation c.Performanceorientation#c.gender lnAGE lnboardsize indep CEOChairmanDuality lnmarketcap_w debtoasset_w Dummylegalsystem quota corruption GDPgrowth uncemployement popgrwoth i.Fesize i.Year i.sector, vce(robust)

Then I estimated the marginals effect :

margins, dydx(gender Performanceorientation c.Performanceorientation#c.gender lnAGE lnboardsize indep CEOChairmanDuality lnmarketcap_w debtoasset_w Dummylegalsystem quota corruption GDPgrowth uncemployement popgrwoth) atmeans

I find the same coefficients and t and p values as in the regression. Is this normal?

Thanks in advance,

Loïc

[FernandoRios]

Si you did something wrong here
margins never accepts interactions within dydx
you have to only Ibclude variables in levels (originals) simply type dydx(*)
other than that
with Tobit there are many outcomes poaaible
make sure the one you get is the one you are interested in

[daniel klein]

I think it's a simple regress. Tobins_w appears to be a variable name. In a linear model, the coefficients are equivalent to the marginal effects.

I do not have the time right now to explain how interaction effects change the meaning of the coefficients for the lower-order terms. I have the time to ask you to make sure gender is really a continuous variable. I am aware of the 'non-binary' culture but even there gender is typically measured in categories rather than on a continuous scale. You probably want:

c.Performanceorientation##i.gender

[Loic DUBOIS]

Thank you for your answers,

I use a simple fixed-effect regression.
Concerning the gender variable, it is indeed a continuous variable (it characterizes the percentage of women on boards).

So if I understand correctly, given these elements, I can interpret my coefficients without centering my variables or using another method?

Thanks in advance,

[daniel klein]

So if I understand correctly, given these elements, I can interpret my coefficients without centering my variables or using another method?

Yes, if do so correctly. With an interaction, the coefficient of the lower-order term ("main-effect") of Performanceorientation refers to the subset with 0 females on the board. Likewise, the coefficient of the lower-order-term ("main-effect") of gender then refers to the subset with 0 Perfromanceorientation. Centering the variables usually makes 0, and thus these coefficients more interesting.