"In markets with low regulation the supply of housing will accommodate most of the rise in demand and the prices will not change much. Every period elections are held to local governments. Residents vote for candidates, each with a proposed level of regulation, via probabilistic voting. The selected level of regulation will be determined by two competing sets of interests: those of renters and those of owners. Renters prefer less regulation because this decreases rents and house prices, thereby lowering the downpayment they need to pay in case they decide to buy. Owners prefer more regulation as it increases the value of their houses."
This paper's decision to assume regulation is a scalar value, and renters as being "obviously" against rent control and rules about building affordable housing stock renders the conclusion of correlation pretty dubious, let alone causation.
Property developers are largely the ones fighting for cutting building regulations, not renters. Including regulations against building a set number of affordable housing units.
Income and wealth inequality was primarily triggered by union busting, untaxing the rich and offshoring, not how many parking spaces you were obligated to build in Los Angeles.