Diff-in-Diff using -xtreg- & -reghdfe-

[Stephen Ch]

Consider a panel data where -gvkey- is the panel identifier and -fyear- is the time variable in the panel.

Suppose the following treatment occurs at the industry level

gen assignment=0
replace assignment =1 if (industry == 101 | industry == 102)
g period = 0
replace period = 1 if fyear >= 2020
g treatment = period * assignment


g two_before =.
replace two_before=1 if fyear==2018
replace two_before=1 if fyear==2019
replace two_before=1 if fyear==2020
gen D_before = sum(two_before), by (gvkey)
g two_after =.
replace two_before=1 if fyear==2021
replace two_before=1 if fyear==2022
replace two_before=1 if fyear==2023
gen D_after = sum(two_after), by (gvkey)

The policy change occurred in 2020.

gen period = 0
replace period = 1 if fyear>=2020

I test the following three diff-in-diff using -reghdfe- and -xtreg-:

Specification #1:

reghdge y i.treatment i.fyear if ( fyear>=2018 & fyear<=2022) & (industry == 101 | industry == 102) & D_before>=2 & D_after>=2, absorb(gvkey) cluster(gvkey)

Specification #2:

reghdfe y i.treatment i.fyear, absorb(gvkey fyear) cluster (gvkey)

Specification #3:

xtreg y i.treatment i.fyear, fe vce(cluster gvkey)

My questions:

(1) How are these three specifications different?

(2) I am getting similar coefficients for #2 and 3 but completely different coefficient for #1. Why is this the case?

(3) Which is the correct diff-in-diff specification?

[Carlo Lazzaro]

Stephen:
(1) and (2): Specifications #2 and #3 are equivalent, while the first one -absorb()- the -panelvar- only + many -if- qualifiers that I do not folllow;
(3): to make DID works, you should have: treatment (yes/no) groups; time of a given event (before/after). That said, why not considering -help didregress-?
See also Joshua Angrist's tutorial on DID at https://www.youtube.com/watch?v=eiffOVbYvNc

[Stephen Ch]

Hi Carlo,

Thanks for the reply.

I suspect #1 is a wrong specification for DID.

Yes, I have read the manual for the commands -xtdidregress- or -didregress-.

I believe #2 and 3 would be identical to the following -xtdidregress- command, would you agree:

 xtdidregress (y) (treatment), group(gvkey) time(fyear)

Stephen:
(1) and (2): Specifications #2 and #3 are equivalent, while the first one -absorb()- the -panelvar- only + many -if- qualifiers that I do not folllow;
(3): to make DID works, you should have: treatment (yes/no) groups; time of a given event (before/after). That said, why not considering -help didregress-?
See also Joshua Angrist's tutorial on DID at https://www.youtube.com/watch?v=eiffOVbYvNc

[Carlo Lazzaro]

Stephen:
Have you tried them out?

[Stephen Ch]

Carlo,

Yes, the -xtdidreg- results are same as the ones in -reghdfe- and -xtreg, fe-!

But it seems to have time-varying treatment assignment issues, which doesn't make sense to me given the identification strategy I have.

Stephen:
Have you tried them out?