I had to find this paper.
It is "Linking Residents to Opportunity: Gentrification and Public Housing" and I'm a little less excited having read it. I'm thinking it is a NYC thing. For one, public housing in NYC doesn't change, whereas in DC what was once public housing can change into private or mixed use housing or transform. So DC public housing residents cannot necessarily feel comfortable that their housing will remain as a neighborhood changes. The second thing are improved schools. But in DC a little under half of DC students go to charter schools which do not necessarily reflect home addresses. So once again, it might be more of a NYC thing.
So how is it that the public housing residents in gentrifying NYC neighborhoods have more income and less unemployment? Craziest thing, the income gains come through paid employment. And they are probably not from jobs in the neighborhood. New businesses were not seen by pubic residents as sources for job opportunity. I know a popular question in DC is what do you do, which sometimes leads to where does one work? For the middle class hipsters and oldsters a lot of time whatever it is, it's not in walking distance. Biking distance maybe. So maybe public housing residents decided not to wait around for the jobs to come to them, seeing their gentrifying neighbors leave the neighborhood on a regular enough basis for work.