In TWFE DiD with a 3-way interaction (policy × treated × continuous), which terms are omitted/dropped under firm & year fixed effects?

[Pranshu Tripathi]

Dear Stata Members,

I am estimating a panel-data Difference-in-Differences model with two-way fixed effects (firm and year).

• treated is time-invariant (treated and control group)
• post varies only by year (pre policy (say 2010-2013) and after policy (2014-2020)
• X is time variant & continuous

Which components of

i.post##i.treated##c.X

are identified and kept, and which are dropped due to collinearity?

Specifically, which of the following are omitted under TWFE (other than the main treated and post dummies)?

• X
• post × treated
• post × X
• treated × X
• post × treated × X

Thanks and Regards

[Jeff Wooldridge]

If X doesn’t change over time then X and treated x X drop out. If X does vary over time all terms will remain.

[Pranshu Tripathi]

Thanks Mr. Woolridge