Including additional interaction fixed effects in a two way fixed effect model

[Austin Yi]

Hi Statalist,

I just joined the community and I would like to ask a question that I couldn’t solve for my analysis.

I try to use a two way fixed effect model to see the effect of some policy on revenues of restaurants.

I have data on restaurants of different cuisines for Feb and Mar. I control for date fixed effects and cuisine fixed effects, the code is:

regress Revenue i.date i.cuisine i.cuisine#post, robust

However, I found there is a within week cyclical trend for some cuisines, so I want to control for the interaction fixed effects for (Monday to Sunday) x (cuisines), So I run

regress Revenue i.date i.cuisine i.cuisine#post i.weekday#i.cuisine, robust

however, my i.weekday#i.cuisine were all dropped because of multicollinearity, which makes sense after I pondered for a bit. So my question is, how should I control for the weekday fixed effects in this two way fixed effect model? Thanks!

[William Lisowski]

If you list your weekday interaction first, then Stata will judge some of the date indicators collinear rather than all of the weekday indicators. And to interpret your results, you should include the main effects for your interactions. So try

regress Revenue i.cuisine##i.post i.weekday##i.cuisine i.date , robust

Also, you should specify i.post if it is an indicator variable, or c.post if it is a continuous measure. I guessed it was an indicator variable.

[Austin Yi]

If you list your weekday interaction first, then Stata will judge some of the date indicators collinear rather than all of the weekday indicators. And to interpret your results, you should include the main effects for your interactions. So try

regress Revenue i.cuisine##i.post i.weekday##i.cuisine i.date , robust

Also, you should specify i.post if it is an indicator variable, or c.post if it is a continuous measure. I guessed it was an indicator variable.

Thanks for replying. After I tried, most of them still dropped out, and the cyclical weekday trend for some cuisine group is still there. I wonder if there is another way to account got the weekday trend?

[George Ford]

With restaurants, it seems to me that i.date is unnecessary. Day of the week seems more important.

This might tell you if there's a pattern in the date.

regress Revenue i.cuisine##i.post i.weekday##i.cuisine, robust
predict efit, resid
scatter efit date