Difference-in-differences, two way fixed effects model

[Olivier Van Coppenolle]

Hello everyone,

For my master’s thesis, me and my thesis partner are conducting a DiD research on how an exposed debt to the UK in 2016 has affected bank’s performance (in our analysis we are looking at ROA), looking at the debt of 2016 in particular for the treatment variable because the thesis has to have a link to Brexit. For this we are looking at the event window of 2013 until 2019. And we are using the following variables in our basic regression:

ROA= dependent variable
TREATED = which is the treatment variable that is 0 if the bank had no debt to the UK in 2016 and 1 if it did.
POST= which is the POST BREXIT variable that is 1 when the year is 2016 or after and 0 if it is before.
DID = which is POST*TREATED, which is the interaction variable between the two.

For our research we opted it would be good enough to do the following:

 xtset BANK_ID YEAR

Whereas BANK_ID is the particular ID variable of each bank in our dataset. And YEAR is the time variable. And for the basic regression we would type in:

 xtreg ROA TREATED POST DID

Our thesis-promotor told us that we should use a two-way fixed effects regression, including the bank and year fixed effects, is this the actual case in the last stata command (the xtreg)? Or does this have to be done differently? And we do have some control variables that we can include in our model, but the promotor also tells us to have some fixed effects as control variables, if there are any suggestions on these, those would be welcome, as we do not have these yet in our model.

Thank you in advance,

Best regards, Olivier

[George Ford]

reghdfe ROA POST*TREATED , absorb(BANK_ID YEAR) cluster(BANK_ID)

[Jeff Wooldridge]

Olivier: As I show in this paper, without covariates and with a balanced panel, the two estimators are identical. If you only use time-constant controls (something often recommended so that you don't control for variables you shouldn't be controlling for after the intervention), they are also the same. They are different with an unbalanced panel, in which case TWFE has an advantage to being more robust. With time-varying covariates they are also different and you might want to use TWFE. However, fundamentally, they both require parallel trends and no anticipation.