Heterogenous treatment effect with difference-in-differences

[Nicolas Orgeira]

Hi,

I am working with a panel data with two periods (dummy variable time, which is equal to 1 after the intervention) and two groups (dummy variable treatment, which is equal to 1 for the group that received the intervention). To estimate the effect of the treatment overall, I ran a DID regression:

regress `outcomevar' i.time##i.treatment covariates

I would like to estimate the heterogenous treatment effect, between men and women for example. I was wondering which method would be econometrically valid. Should I run a Difference-in-difference-in-difference:

regress `outcomevar' i.time##i.treatment##i.gender covariates

or first run the regression for female respondents, then again for male respondents

regress `outcomevar' i.time##i.treatment covariates if gender==1
regress `outcomevar' i.time##i.treatment covariates if gender==0

Thank you

[Dimitriy V. Masterov]

Cross-psted on CV.

[Clyde Schechter]

In general, the three-way interaction is preferred. You need, however, to decide whether the effects of the covariates also differ by gender. If so, they, too, need to be interacted with gender.

The preference for the three-way interaction arises from a few different perspectives:

1. You better preserve the statistical power of your sample.
2. It is more conducive to the estimation of predictive margins and marginal effects.

[Nicolas Orgeira]

Hi Clyde,

Thank you for your answer. I will use the three-way interaction.

I have a follow-up question - the treatment effect of male respondents (gender=0) is the interaction coefficient of 1.time##1.treatment (DID), and the effect on female respondents is 1.time##1.treatment +1.time##1.treatment##1.gender (or DID+DIDID). Do you know if there is a way to automatically export the cofficient for female treatment effect? Also, in terms of interpretation, I guess that if the DIDID coefficient is not significant, it would mean that there is no statistical difference between the male and female treatment effects. But if it is significant, how would I know the significance level of the female treatment effect?

Thank you again

[Samsun Naher]

foreach var in HI_general PC DC Flu_shot Flu_spray Smoke Drink Quit Activity bmi Obese vgood_health {
diff `var', t( Treat ) p( ACA ) cov(female less_HS HS more_HS married english less_FPL FPL_1_2 FPL_2_plus HT AS DB AL) robust cluster(age)

I have run this difference-in-differences model. Now I would like to examine the heterogeneity by sex and education. How can I write the codes? Please, someone, help me. Thanks in advance.

[Maxence Morlet]

Dear Clyde Schechter,

Thank you for your informative post on this thread.

Suppose OP runs the following equation:

 
 regress `outcomevar' i.time##i.treatment##i.gender covariates

And then use marginsplot to plot the diff-in-diff treatment effect heterogeneity across genders. Would the following code be correct and obtain the diff in diff treatment effect for men and women?

margins, dydx(1.time#1.treatment) at(gender=(0 1))
marginsplot, recastci(rarea) xscale(range(0 1)) xlabel(0 1)  xdimension(gender) plotopts(msymbol(none)) yline(0) title("") ytitle("Average Marginal Effect", size(Medium)) xtitle("Gender")  ciopts(color(%50) lpat(line)) legend(off)