So I am testing a policy which was introduced in a country trying to incentivise people to stay employed at older ages (beyond the retirement age of 65). As such, they introduced a bonus where people who work a year longer beyond 65 receive a higher pension a year later. I want to know if this policy incentivised more people to work beyond 65 after the policy introduction in 2004.

I am using a logit model with the binary variable showing status as (Employed/Retired) as my dependent variable. I have health and financial characteristics of the individuals as independent variables.

How can I test the policy's effect? Have one dummy variable showing whether an individual is over 65 or not, one dummy variable that shows 1 for the years the policy was active, and finally an interaction of these two (lets call it PA) (this coefficient will show the real policy effect significance), and a bunch of control variables.

And then to check whether the effect of the policy is different men and women, should I split the sample into men first and then run the regression, then take the sample of only women and then run the regression? Alternatively, keep the model as specified above and just add a dummy variable for "female = 1, male = 0) and then another one that is a cross of gender dummy variable and policy dummy variable?