xtreg: Using monthly and yearly fixed effects versus date fixed effects

[Millis Liljedahl]

Hi all,

I currently have a panel data set with observations from January of 2014 to March of 2020. I was wondering if someone could explain why I am getting different regression results when I control for i.date (which is the year and month combined, 75 total) versus when I control for year and month separately (i.month and i.year together) when using xtreg?

[William Lisowski]

Because when you control for i.date you are fitting 75 parameters, and when you control for i.month and i.year you are fitting just 7+12=19 parameters. Different parameterization, different results.

Added: Crossed with #3, a far more comprehensive explanation.

[Clyde Schechter]

The two approaches are completely different.

When you use i.date, you are modeling a shock to the outcome that occurs independently every single month throughout the study period. In particular, the shock in, say, June 2015 is independent of the shock in June 2019 or June of any other year.

When you use i.month and i.year, you are modeling a very different series of shocks. First there is a shock that occurs separately and independently in every year. But the "monthly" shock is, in this model, a recurring shock. That is, the month-level shock in June 2015 is the same as the shock in June of every year; it is a recurring seasonal effect (where, in this case, the "season" is just one month long.)

Added: Crossed with #2.