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.
The first dummy indicating whether an individual is over 65 or not does not need to be defined the same was as a treatment group in a Difference-in-difference approach, right? (It does not need to fulfill parallel trend assumption, etc ...)
Question 2: If I want to see if females are incentivised more than men then is an interaction of a gender and the policy activation= PA enough to see this effect or is a 'conditional fixed effects model' more appropriate?