Interaction term with individual in FE

[Julia Raciniewska]

Hello!

I have a following question: I want to estimate the impact of increased use of computers by employees on their employment. I have panel data for 11 industries and 11 time periods. My question is whether it would not be a mistake for me to include an interaction term with my individual term (industry) as I want to see in which industry this effect has been larger or smaller?
That is:
xtset industry time
xtreg employment computer_use c.using_computer#i.industry degree, fe

In addition, if I get a result that coefficient of computer use is -0.2 but insignificant, while the coefficient on interaction term of computer use and industry==1 is -0.1 and significant, does it mean that the overall impact of computer use in industry 1 on employment is -0.3?
Or does it matter that coefficient of computer use on its own was insignificant?

Thank you very much!

[Clyde Schechter]

If there is reason to believe that the relationship between computer_use and employment differs across industries, then including an interaction term in the model to represent that is appropriate. Why do you fear it wouldn't be? Am I missing something?

Regarding the interpretation, the statistical significance of the computer use term is irrelevant to the calculation you made about impact of computer use in industry 1. In industry 0, the effect of computer use is -0.2, and in industry 1 it is -0.2 + (-0.1) = -0.3.

I will spare you my long rant about this topic (one of my pet peeves) but whatever little use statistical significance may have in interpreting this kind of model (and, personally, I don't believe it actually has any --https://www.nature.com/articles/d41586-019-00857-9) it is, by any sane reckoning, 100% useless in the calculation of the effects at the various levels of industry. You shouldn't even look at those p-values: at best they will confuse you, at worst they will lead you to make terrible mistakes.

[Julia Raciniewska]

Clyde Schechter Thank you very much for this advice, Sir. This article has a very interesting point, I will definitely refer to that, thank you for providing me with this.

I also wanted to ask about one additional aspect. As Hausman test suggested I have a correlation between error terms and my regressor, therefore I am using a fixed effects model. However, I thought that actually computer_use (% of employees using a computer) could be endogenous in the sense that the price of the computer could be a good instrument for that.
I have searched in a variety of articles but cannot find an answer to my (potentially stupid) question: if I am using a fixed effect model, does it exclude the option of instrumental variables? Isn't fixed effects already controlling for endogeneity and I should not worry about IV ?

[Clyde Schechter]

I see. I didn't consider the possibility of endogeneity, and I don't see that you raised it in #1.

I'm really not sure what to think about that. And I do not work with instrumental variables, so I can't really advise you.

[Dario Maimone Ansaldo Patti]

I would say that fixed effects control for heterogeneity in your sample coming from mixing different groups in your dataset rather than controlling for endogeneity. The presence of fixed effects do not exclude the IV procedure. In fact you can use an IV - fe model.

You have three possibilities:

1) using xtivreg
2) using xtivreg2 (which is preferable in my view, since it provides additional statistics)
3) ivreg2h with fe option, if you do not have a specific set of instruments to use (see Lewbel, 2012) but still you want to use an IV approach.