Difference between Wooldridge extended TWFE & Sun & Abraham

[fadi martinos]

Friends at Statalist,

Walking into the more serious part of my paper, I am wondering whether I should use the Wooldridge extendend TWFE or the Sun & Abraham estimator. I am trying to understand the difference here between both approaches. To my best understanding, the Wooldridge ETWFE esimtator uses covariates with more flexibility and "relaxes?," the parallel trend assumption compared to Sun & Abraham. - Any further elaboration would be much appreciated.

PS: I promise I went through the FAQs (all of them), and this is a late-resort question after reading both papers very carefully.

Thank you & happy holidays!

Fadi

[Jeff Wooldridge]

Hi Fadi. Glad you asked this. After teaching this material for a while, I think I've sorted things out. I just finished a revision of my paper where I introduced ETWFE and now I discuss its relationship to Sun and Abraham. I'll post the new version at SSRN later today.

You are correct that my approach handles covariates more flexibly. But there is another important difference: Sun and Abraham is what's known as a "leads and lags" estimator because it estimates the pre-treatment effects as well as actual treatment effects. ETWFE uses all of the implications of parallel trends. What I've been able to show is that, if you want to do flexible Sun and Abraham, then use Callaway and Sant'Anna with regression and the long2 option. Without controls and the long2 option, SA and CS are identical. With covariates, CA is what you get by adding a full set of interactions of the covariates with the pre-treatment indicators. In other words, take my ETWFE estimation and add interactions of the form dg*fs*x where dg are the treatment cohort indicators, fs are time dummies, and x are controls.

Some times the leads and lags approach will be less biased if parallel trends is violated, sometimes it will be more biased. But with the leads and lags you get the typical event study plot so that you can visually study the conditional PT assumption. Plus, leads and lags can be more efficient than ETWFE if there is strong serial correlation.

Something I hope Stata adds is the "long2" option that is available in csdid. Currently, xthdidregress ra does not allow the usual event study estimation where the period just before the intervention occurs is the reference period.

Here's how to do flexible Sun and Abraham (leads and lags), which is CS with the regression option. You have to created the first_treat variable:

csdid y x1 ... xK, ivar(id) time(year) gvar(first_treat) method(reg) long2
estat event

If you drop the controls, you will reproduce Sun and Abraham. You'll get the same treatment effects using

 xthdidregress ra (y x1 ... xK) (treat), group(id)

where "treat" is the time-varying treatment indicator. But the pre-treatment effects will differ because they follow the original CS suggestion.

ETWFE is gotten by

 xthdidregress twfe (y x1 ... xK) (treat), group(id)

[FernandoRios]

Added point here
you could also use jwdid instead of Csdid.
mid you add the option never, it produces the sun Abraham estimator.
thua command aims to follow prof Wooldridge ideas regarding etwfe estimator

[Jeff Wooldridge]

Thanks Fernando! I'd forgotten that.

[Jeff Wooldridge]

It's too bad that Stata didn't incorporate the "never" option in xthdidregress twfe. The controlg(never) option doesn't change the estimates (and so, in particular, does not give the usual weighted event study plot).

[FernandoRios]

I mentioned that to them couple of times. So I’m thinking they will incorporate it at some point

[fadi martinos]

Added point here
you could also use jwdid instead of Csdid.
mid you add the option never, it produces the sun Abraham estimator.
thua command aims to follow prof Wooldridge ideas regarding etwfe estimator

Does this mean that the other difference is Sun and Abraham only use never treated as controls?

[fadi martinos]

Hi Fadi. Glad you asked this. After teaching this material for a while, I think I've sorted things out. I just finished a revision of my paper where I introduced ETWFE and now I discuss its relationship to Sun and Abraham. I'll post the new version at SSRN later today.

You are correct that my approach handles covariates more flexibly. But there is another important difference: Sun and Abraham is what's known as a "leads and lags" estimator because it estimates the pre-treatment effects as well as actual treatment effects. ETWFE uses all of the implications of parallel trends. What I've been able to show is that, if you want to do flexible Sun and Abraham, then use Callaway and Sant'Anna with regression and the long2 option. Without controls and the long2 option, SA and CS are identical. With covariates, CA is what you get by adding a full set of interactions of the covariates with the pre-treatment indicators. In other words, take my ETWFE estimation and add interactions of the form dg*fs*x where dg are the treatment cohort indicators, fs are time dummies, and x are controls.

Some times the leads and lags approach will be less biased if parallel trends is violated, sometimes it will be more biased. But with the leads and lags you get the typical event study plot so that you can visually study the conditional PT assumption. Plus, leads and lags can be more efficient than ETWFE if there is strong serial correlation.

Something I hope Stata adds is the "long2" option that is available in csdid. Currently, xthdidregress ra does not allow the usual event study estimation where the period just before the intervention occurs is the reference period.

Here's how to do flexible Sun and Abraham (leads and lags), which is CS with the regression option. You have to created the first_treat variable:

csdid y x1 ... xK, ivar(id) time(year) gvar(first_treat) method(reg) long2
estat event

If you drop the controls, you will reproduce Sun and Abraham. You'll get the same treatment effects using

 xthdidregress ra (y x1 ... xK) (treat), group(id)

where "treat" is the time-varying treatment indicator. But the pre-treatment effects will differ because they follow the original CS suggestion.

ETWFE is gotten by

 xthdidregress twfe (y x1 ... xK) (treat), group(id)

Professor Wooldridge, thank you for the clarification!

[Jeff Wooldridge]

Does this mean that the other difference is Sun and Abraham only use never treated as controls?

Correct. Without controls, it is equivalent to the CS estimator, which uses "long" differences across time, where the control group is the NT group. By contrast, it can be shown that, for any cohort/time pair, the ETWFE estimator can be obtained by using all control observations at time t and the treated cohort g as the treated group. Already treated observations are, of course, not used. So ETWFE uses the not-yet-treated observations while CS uses the NYT units. When csdid uses the NYT group, no information on units already treated is used. ETWFE uses all untreated observations: even if a unit has been treated at time t, all of it's observations before it was treated are used in effectively constructing the control.

[fadi martinos]

Correct. Without controls, it is equivalent to the CS estimator, which uses "long" differences across time, where the control group is the NT group. By contrast, it can be shown that, for any cohort/time pair, the ETWFE estimator can be obtained by using all control observations at time t and the treated cohort g as the treated group. Already treated observations are, of course, not used. So ETWFE uses the not-yet-treated observations while CS uses the NYT units. When csdid uses the NYT group, no information on units already treated is used. ETWFE uses all untreated observations: even if a unit has been treated at time t, all of it's observations before it was treated are used in effectively constructing the control.

The puzzle in my head is officially complete. Thank you Professor Wooldridge!