That has to assume that most people would choose lower-paying jobs if the extra income presents. But I don't think it is necessarily true. It is also unlikely t

That has to assume that most people would choose lower-paying jobs if the extra income presents. But I don't think it is necessarily true. It is also unlikely that people would right away leave their current job if rents are on the rise, at least not until the net gain gets surpassed by the alternatives. The extra income probably gives the tenants more 'tolerance' to the rent increase and that is simply how subsidies interact with market.