Fixed effects with interaction with a time-variant variable and a year dummy

[Mizuki Kawabata]

Hello,

I have panel data with large N and short T, only two years of time (year = 2000, 2010). I estimated the following fixed-effects model (in my actual model, I have other explanatory variables). X1 is a time-varying variable (e.g. log of income).

xtreg Y c.X1##i.year, fe
margins, dydx(X1)
margins if year==2000, dydx(X1)
margins if year==2010, dydx(X1)

The second command line calculates the average marginal effect of X1 for total period (2000-2010). The third line calculates the average marginal effect of X1 in 2000. The fourth line calculates the average marginal effect of X1 in 2010. I included the interaction between X1 and the year dummy to examine whether the effect of X1 change over time. Is this understanding fine?

Wooldridge (2016, p. 437, Example 14.2) uses a similar approach, but his example uses interactions between a “time-invariant” variable (education) and year dummies. (He explains that “we can include interactions of educ with year dummies to test whether the return to education was constant over this time period.” Can we do this with interactions between a “time-variant” variable (e.g., log of income) and a year dummy (or year dummies)? Does doing so make sense?

Thank you for your kind assistance in advance.

[Jeff Wooldridge]

Yes, it's fine. You can interact any two variables you want. In your case, you can estimate the effect in any year because you can include X1 by itself. In the example you cite, educ gets removed and so we can only see whether the coefficient on educ has changed over time.

JW

[Mizuki Kawabata]

Dear Jeff,

Thank you very much for your prompt reply!
Your information is of great help.

Mizuki

[Irene Wong]

Yes, it's fine. You can interact any two variables you want. In your case, you can estimate the effect in any year because you can include X1 by itself. In the example you cite, educ gets removed and so we can only see whether the coefficient on educ has changed over time.

JW

Dr. Wooldridge, do you have a textbook or source that we can cite to justify the practice of interacting time dummies and variables that change over time?