event study approach: coefficients different between 2 groups

[Sandra Bloem]

Hi there,

I am working with an event study approach to see if the effect of becoming a parent on earnings is different for men vs women. the year of the first child birth (when individual i becomes a first time parent) is event time t = 0 and the rest is indexed. I leave event dummy t=-1 out of the regression so that the other event time dummy variables measure the effect relative to right before the child birth. time window is t=-2 to t=5. to make dummy variables, event time is not set at t=-2 to t=5, but at t=1 to t=8. female = 1 for female and 0 for male. income is gross earnings.

I run the following regressions to estimate this:

clear all

program eventstudy
reg income ib2.eventtime i.age i.year, robust cluster(id)
predict income_p, xb

generate b = .
replace b = 0 if eventtime==2
generate se = .
replace se = 0 if eventtime==2

foreach i in 1 3 4 5 6 7 8 {
replace b = _b[`i'.eventtime'] if eventtime==`i'
replace se = _se[`i'.eventtime'] if eventtime==`i'
}

generate income_c = income_p - b
end

use "sampleddefinitive.dta"
runby eventstudy, by(female) verbose

collapse income income_p income_c b se, by(female eventtime)


generate gap = b/income_c
generate gapse = se/income_c
generate cilow = gap - 1.96*gapse
generate cihigh = gap + 1.96*gapse


reshape wide income income_p income_c b se gap gapse cilow cihigh, i(eventtime) j(female)

generate penalty = (b1-b2)/income_c2

The coefficients are eventually calculated for percentage effects, which is the variable gap. The penalty is the relative child penalty, i.e. the relative difference between men and women. I would like to know if there is a way to find out if the gaps are significantly different between men and women, so gap male in t=1 vs gap female in t=1, gap male in t=2 vs gap female in t=2. Is that possible to do with just the penalty variable? Or should I look at just the gap? Or is it only possible to find a statistical difference if you look at the coefficients of the regression, and then men vs women.

If the latter is the case, is it then best to use 1 regression and use interaction effects? If so, is this the correct regression and how do I test whether there is a difference?

regress income i.age i.year ib2.eventtime (ib2.eventtime i.age i.year)#i.female i.female, robust cluster(id)

If you want the data I will put a -dataex- code.

Thank you in advance

[Kailin Gao]

Curious about similar questions and waiting for replies! Thanks!

The question is how to examine differential effects in an event study, e.g. whether the event-study effect differs by gender in the above question.
Separately estimate event-study equations among different groups (maybe also test the difference between coefficients) or add interaction terms?

Thanks again.