Really

How does one compare the cost of renting and the cost of buying a house? There are many ways...

I'll argue that for owning, a significant "premium" over the cost of renting an equivalent place is reasonable and sustainable, when comparing monthly cashflow. Without even assuming any real appreciation. Only assuming that the price of real estate just keeps pace with inflation over the long term.

Assume that the cost of owning includes mortgage, property tax, and homeowner's association fees or maintenance.

From most conservative to least:

1. Compare monthly rent and monthly total payments for owning.
2. The above, plus take into account the income tax deduction on interest and property tax.
3. All of the above, plus discount principal portion of mortgage payments.
4. All of the above, plus include expected gain from the inflation of the home price.

An approximation for the cost of owning as a rate on home price is then:

c = (m+p)*(1-t) + h - i

m = mortgage interest rate
p = property tax rate
t = income tax rate to use for tax deduction
h = maintenance as a rate (including HOA, etc.)
i = inflation rate

Current estimates (actually being conservative):
m = 6.25% for fixed-rate
p = 1.25%
t = 0.3
h = 1%
i = 3%

c = 3.25%

I estimate that renters in the Bay Area are being charged somewhere just under 4% of current property prices. As long as the difference between total payment rates and inflation is less than the rental rate, it pays off to own. Barring huge disasters, of course. And weathering price volatility. It actually costs less to own... the difference being the return for the risk assumed by owners.

People in the Bay Area are so sophisticated that the market is so efficient....

I haven't yet figured out why, in regions where rental properties are immediately cashflow positive, that not more people get into the business of landlording. Maybe it's the weather.

Yeah, only about 0.1% or 0.01% of the population would agree with me on this analysis.