Margins command and interaction term

[Lukas Lang]

Hi,

I am estimating a simple regression with interactions Y=a+bX+cZ+dXZ+error using the following command:

regress Y c.X##c.Z, robust

Then, I estimate the marginal effects of X and Z using the following command:

margins, dydx(X Z)

After that, I compute the marignal effects simply using the following commands:

regress Y X Z, robust
margins, dydx(X Z)

The problem is that the estimated marginal effect of X is much larger in the regression without interaction term compared to the regression with the interaction term, while the marginal effect of Z is almost identical in the regression with and without interaction term.

Would you reckon why that may be the case? How can the interaction term change the marginal effect on X so much while the marginal effect on Z is almost unchanged?

Thanks

Lukas

[William Lisowski]

Clyde Schechter frequently discusses the interpretation of coefficients and margins in models with interaction terms. Perhaps you will find these recent discussions helpful.

https://www.statalist.org/forums/for...raction-effect

https://www.statalist.org/forums/for...ction-variable

[Lukas Lang]

Thank you William for your reply. The posts that you highlight are helpful. However, I am still uncertain about the potentially correct terminology to use, so I would appreciate your further help on this.

My understanding from reading the posts is that the marginal effects estimated, as showed in post #1, from the interaction and the non-interaction regression cannot be compared. Thus, there is no reason to expect such marginal effects to be similar.

The marginal effect from the non-interaction regression complies with the traditional definition of marginal effect, while the marginal effect from the interaction regression is rather an average of marginal effects of say X across the infinite values of Z (since both X and Z are continuous variables).

So, my question is: would I be correct in saying that what I get from the margins command after the interaction regression is an average marginal effect rather than a marginal effect?

Thanks again,

Lukas

[Clyde Schechter]

Yes, the output of -margins, dydx(X Z)- after -regress Y c.X##c.Z- consists of the average marginal effects of X and Z on Y. More specifically, you have the average marginal effect of X, averaged over the distribution of Z, and the average marginal effect of Z, averaged over the distribution of X.

[Lukas Lang]

Thank you for your help!

Lukas