Interaction in manual DID

[Eve Alexander]

Hello,

Im running a DID model( over two waves of a longitudinal survey) where the code that I use is;

reg  `y' i.treatment##i.post  $controls i.PERSONID , cl(PSUID)

Suppose I wanted to find the effect for various age cohort separately, which is generated using the following code,

recode agecohort(15/22=1) (23/29=2) (30/36=3) (37/43=4) (43/50=5) , gen(cbin)

the data is like this,

[CODE]----------------------- copy starting from the next line -----------------------

* Example generated by -dataex-. To install: ssc install dataex
clear
input float(agecohort cbin)
45 5
33 3
26 2
19 1
36 3
40 4
27 2
40 4
26 2
36 3
32 3
28 2
49 5
29 2
28 2
34 3

Should I run the code like this?

reg  `y' i.treatment##i.post  $controls i.PERSONID if cbin==1 , cl

or this

reg  `y' i.treatment##i.post##i.cbin  $controls i.PERSONID , cl

But if I do the latter, the coefficient in stata will not show for the cbin==1.

Please clarify what the difference is between the two.

Or third option is I define my treatment in a way that it is in cbin==1 ,2,3 respectively and do

reg  `y' i.treatment##i.post  $controls i.PERSONID , cl(PSUID)

separately for the differently defined treatments.

which one is the right way to go about it?

[Andrew Musau]

There is no need to define the two variables "treatment" and "post" separately. Just create a treated indicator (=1 if an individual in a survey wave is treated and zero otherwise). Then you can use the margins command to get all levels. In the regression, the level that is not estimated is referred to as the base or reference category and needs to be omitted as it combined with the included levels are collinear with the constant term.

gen treated=treatment & post
*TREATMENT EFFECTS ACROSS COHORTS
regress outcome i.treated##i.cbin $controls i.PERSONID i.WAVE, cluster(PERSONID)

*MARGINS
 margins treated#cbin

Please clarify what the difference is between the two.

Clearly, in one case you are restricting the sample to one cohort and in the other, you are using the full sample and including interactions to identify the cohort effects. You would need to combine estimated results if you pursue the subsample analyses and wish to run tests of cross-model hypotheses. See, e.g., the discussion in the documentation on suest.

help suest

[Eve Alexander]

The post variable that I use is the survey wave indicator.
post==1 (if wave2) and post==0 (ifwave1).

Maybe I'll try to describe my research question.
Im trying to use the exogenous variation of a household members death across two waves as treatment.

so treatment=death of household member

So I did i.treatment##i.post so that my treatment variable would mean death in wave two.
Since i.treatment##i.post already regresses i.post , that's why I didn't add i.wave separately.

Is this method right?

[Andrew Musau]

So I did i.treatment##i.post so that my treatment variable would mean death in wave two.

So the suggestion in #2 is to create a treated indicator instead of specifying it as an interaction between 2 variables. In this way, you avoid triple interactions once you further interact the treated variable with the cohort indicators.

gen treated= 1.treatment#1.post

Since i.treatment##i.post already regresses i.post , that's why I didn't add i.wave separately.

Now, no need to cause confusion by calling the wave indicator something else. I suggest

gen wave2=1.post
regress outcome i.treated##i.cbin $controls i.PERSONID i.wave2, cluster(PERSONID)
margins treated#cbin

[Eve Alexander]

Thank you for your time and help.