Assuming an interest only mortgage: if mortgage rates are 10% then Bob can bid somewhere around $500k for a house, but if mortgage rates are 4% then Bob can bid somewhere around $1250k. But fundamentally the same 10 people get the 10 houses, and the same other 10 people miss out.
If we add in principal, taxes and maintenance: over a 30 year period Bob pays the same amount because Bob has bid the house price up to what he could only just afford. The amount Bob can only just afford is fixed by Bob’s income, so the amount Bob can afford is the constraint on what the lowest house price becomes due to his bidding.
That result is because the median buyer had to bid as much as they could afford, so house prices are caused by mortgage costs. The other 10 that got houses were bidding against each other, so they also pay as much as they can afford. Interest rates change the mixture of payments, but they don’t make those 10 houses more or less affordable.
If rates double in the long term then house prices should halve in the long term. In the short term with higher mortgage rates, most people stay in the home they have with the mortgage they have, and fewer houses transact.
Is there a housing shortage? Firstly most people are living somewhere, so perhaps there is already enough housing? Alternatively most people want a better place than where they are living, so there can never be enough housing? There are many places in the first world where there is enough housing, so the least wanted house will sell for $0. Yet high demand areas can perhaps never have enough housing? If New York doubled it’s housing tomorrow, how long before it would be back to the same prices?
A higher interest rate environment could possibly help the less well off, because they can save for a bigger deposit quicker?
All the different dynamics require some deeper analysis to determine what is actually happening. There is a lot of misinformation and common wild misunderstandings about how the market dynamics actually affect us.
I will add two real world observations.
Firstly, only a single digit percentage of homes are sold each year, so houses price expectations are set by a relatively small number of house purchases. A few years ago in Christchurch, New Zealand, auctions changed from nobody bidding on most houses to crazy crazy bidding. The economy didn’t really change, so there was a herd problem with housing prices. Certainly the economy didn’t get better by 30%, but house prices changed that much.
Secondly, an anecdote that mortgages drive house prices: I bought a house in Christchurch for less than half price of the equivalent house up the road. In 2010 we had a severe earthquake in Christchurch, which left many houses uninsurable. Some homes were perfectly safe (could be rented) but were uninsurable for technical policy reasons. Genreally you can’t get a mortgage on an uninsurable house, so in Christchurch we could see the situation where two equivalent houses would go for wildly different prices, because house prices are mostly driven by mortgages. The rental yield on my property would theoretically be high so investors should have bid on it, but they didn’t: maybe because small investors had already spent their money buying houses, and maybe corporate investors felt it was a risky market due to earthquake risk?