It seems to me that the elephant in the room here are the peer effects.
By regressing on household identity, you capture how parents’ efforts to control kids’ peer groups influence outcomes. This was discussed (briefly) in the book, towards the beginning (~page30-40?)
By regressing on household identity, you capture how parents’ efforts to control kids’ peer groups influence outcomes. This was discussed (briefly) in the book, towards the beginning (~page30-40?)