In Act 1, neighborhood kid Bert asks Joe to arrest another boy for saying a bad word. Joe has given out that he has a jail in his basement. It's all fun and games until Kate comes in, angry, and tells them to cut it out.
Keller: …What happened was that when I got home from the penitentiary the kids got very interested in me. You know kids. I was [laughs] the expert on the jail situation. And as time passed they got it confused and… I ended up a detective [laughs].
Mother: Except that they didn't get it confused. [To Ann] He hands out police badges from the Post Toasties box. (1.438-439)
We start to understand that this jail game is one of the ways Joe has charmed the community into turning a blind eye to his crime.