In equilibrium, rent ~ monthly carrying costs (mortgage, property tax, insurance, HOA fee, less typical mortgage interest deduction ) On the way down, house prices are likely to overshoot.
Assume 20% down payment for upscale/move-up houses and 5% down payment for low-end houses. During the boom new homebuyers used to put zero down, but today zero-down loans are less common. Very few potential new homebuyers have enough cash to put 20% down on a house in SoCal.
Richest people will occupy most attractive houses. In many areas there are fewer houses than households. In this situation poorest households have no choice but to rent.
Some parts of the country are more attractive than others. People living in attractive areas choose to spend larger fractions of their incomes on housing rather than to leave (the “sunshine tax”). In an attractive area, both house prices and rents will be higher in proportion to income than in an unattractive area. The list of attractive parts of the country includes Hawaii and most of coastal California (from Napa and Sonoma to Santa Barbara to San Diego). Inland areas are generally unattractive, with a few exceptions.