Can you use difference in difference with a single group of individuals? So I am looking at inheritances and how these could effect the labour supply choices of individuals. I have a variable where people state if they expect an inheritance or not. Now, I want to see if in time period 2 if individuals that did not expect an inheritance, but received one, change their labour supply in comparison to those that did not receive an inheritance or gift.
So my starting group would consist of the same group of people, those that did not expect any inheritance and then they are split in time period two. Is it possible to use diff in diff with this method? If not what alternative could I use?
 A: Welcome!
If you want to employ the "classical" difference-in-differences (DD) approach you need two groups and at least two time periods. If I understand you correctly, the “treatment” group would consist of individuals receiving a reward/inheritance of some sort; the control group would consist of individuals not receiving a reward/inheritance. If you are incorporating this into a regression framework, treated individuals are indexed with a value of 1; untreated individuals are indexed with a value of 0.
Next, you need to observe the same individuals in both groups before and after this event. Put differently, you observe the “inheritance-receiving” group (i.e., treatment group) before and after treatment, and the “inheritance-denying” group (i.e., control group) before and after treatment (pardon my naming convention). This is achieved by dummy coding the post-treatment period (i.e., time period two in your case) in both groups. In other words, this is a pre-post dummy that "turns on" in $t_{2}$ in the treatment group and the control group. Interacting these two variables gives you the standard DD estimator.
The only part that confuses me is your comment that your “starting group would consist of the same group of people.” In the pre-period (i.e., $t_{1}$, before the split as you indicate), you should demarcate two groups: a group of individuals that never receive an inheritance, and a group of individuals that are bequeathed some inheritance/gift.
In sum, this could work. If you have serial observations of individuals before the treatment you should assess for common trends in the outcome (i.e., trends over time in hours worked at a given rate). Ideally, you want trends in both groups to move in tandem prior to the treatment. This might not be practical in your setting, though.
Do all individuals receive the treatment at the same time? This is the only thing that could affect your DD set up. If different individuals receive treatment at different times, then you need a different modeling approach.
