Interaction vs. endogeneity

[Noha Ali]

Dear statalist members,
I have a technical question in statistics. if I would like to estimate a regression model y=x1+x2+x3+x4, and I hypothesize that x1 affect x2, is this an example of endogeneity or interaction.
Can this problem be solved by adding an interaction term x1*x2 or it has to be a 2 stage regression?

Thanks

[Carlo Lazzaro]

Noha:
I would interact x1 with x2 (see -fvvarlist-).

[Noha Ali]

Thanks Carlo, I will do that.

[Noha Ali]

Carlo:
what I mean in the question is that my study has the following equations:

variable (a)=variable(b)+ variable (c)+ variable (d)+ other variables (1)

variable(b)= variable (c)+variable (e)+ variable (f) (2)

variable (d)=variable (c) + variable (g) + variable (h) (3)

so what I mean is my independent variable b and d in equation (1) are dependent on c,
so I just need to confirm whether its valid to add interaction to equation (1) , I am sorry for repeating my question but I think my first question was not detailed,
Thanks

[Max Hoerl]

Adding an interaction term for variables b and c in a linear model would imply that the effect of b on a is moderated by c, meaning that the effect of b on a is different depending on the level of c. I don't think that is what you are looking for.

It seems to me that with your setup you should apply structural equation modeling (SEM). You should look into this type of models. In Stata you can apply them by using the gsem command.

[Noha Ali]

no actually I am looking at it as a moderator and, equation 2 and 3 are irrelevant to equation 1, but I have a debate with my supervisor on the soundness of presenting my equations as stated in #4, variable (c) is a regulatory standard (dummy variable whether the standard is applied or not) I hypothesis that it affects debt terms variable (a) and also I hypothesis that it affects accounting quality (variable(b)), so in equation ( 2) I test the effect of the regulatory standard on accounting quality.

[Max Hoerl]

If I understand you correctly, the model of equation 1 can be used to test of the hypothesis that debt terms differ by regulatory standard (while controlling for the other variables in the model).
And the model of equation 2 can be used to test the hypothesis that the accounting quality differs by regulatory standards (while controlling for the other variables in the model).

Adding an interaction term to the model of equation 1 would mean something different. The significance of the interaction effect would tell you whether the effect of accounting quality on debt terms would different depending on regulatory standards. This can be true even if the accounting quality does not on average differ between regulatory standards. For example it could be that two groups of cases (with regulatory standards and without regulatory standards) have the same average of accounting quality but in the first group the effect of accounting quality on debt terms can be positive and in the second group it can be negative. In this case you would have a significant interaction effect of (b) and (c) on (a) but no effect of (c) on (b).

So I would say that using an interaction term doesn't help in testing your hypotheses.