"Never reason from a price change." This is a very useful dictum, coined by Scott Sumner, that tells people to ask why a price change happened before they conclude it will have a given set of effects. Typically, a fall in house prices makes houses more affordable; therefore if interest rates go up and house prices fall, houses are more affordable, right? Wrong.

Think why house prices are falling. House prices are falling because the demand for houses is falling. The demand for houses is falling because higher (market) interest rates mean that for any given mortgage loan, the monthly mortgage servicing cost is higher, and the total you pay over the course of a loan is higher. Any given house price is less affordable for a prospective homebuyer. Can housing be more affordable because it's less affordable?

Yes, prices fall when interest rates rise, or, more specifically, when expected market real interest rates for the next forty years or so rise. But they fall precisely because these higher rates make mortgage loans more expensive and thus make housing at any given price less affordable. It falls to the point where it is about as affordable as before in terms of expected total repayment compared to expected earnings and wealth.

The case is slightly different with crime, graffiti, pollution or other disamenities. They do make specific houses cheaper, through reducing demand for them. But it doesn't improve the affordability of any given quality of flat or house. It just makes them all worse, which makes them cheaper, like if you decreed that four of the slices of a pack of bread had to come mouldy.

Land value tax advocates claim that a land value tax makes housing more affordable. But house prices rapidly adjust to take account of amenities, transport links, and expected taxes that the property owner will pay. These "capitalise in" so to speak. If you add £50,000 of expected taxes to a property (or, precisely, a net present value of that) its price will go down about that much. But it doesn't make the house more affordable! You pay £50,000 less for the house and £50,000 more in tax. No change. Once again, reasoning from the price change leads us astray.

What could make housing more affordable? Rent controls do work in the narrow sense of making rents cheaper. But without incredibly clever rules and micromanagement they're likely to have lots of side costs that end up frustrating the original goal: reduced quality, long waiting lists, rationing by other mechanisms than money, even lower construction, fewer new rental units, and switching units away from rental. Subsidies like housing benefit can work, but where housing supply is highly restricted, they bid up rents, going into landlord pockets. Help to Buy is an even worse version of this. They help those who get subsidies, but cost those who don't, as well as those paying.

Social housing can make housing cheaper. But where is the price reduction coming from? Either it's a subsidy from the government, and has all the problems of housing benefit, but is even stickier—once you've got a sweet deal you won't move. Or it's coming through steamrollering regulations and restrictions that stop private builders—well why not just let them do it? It's not a magic bullet, but a special way of applying other bullets. If council tenants in central London could, many of them would sublet their apartment, live further out, and pocket the difference. We can cut out the middleman by giving benefits in cash, not in kind.

All these clever solutions are dancing around the only thing that will dent affordability without costly side-effects, picking favoured groups, handing out to landlord, or devastating quality: increasing supply. If we regulated cars like housing there would be a cottage industry of commentators telling us that car banking was the cause of high car prices, or that an oligopoly of only 15 car companies caused them, or that we had a brick shortage. But these are actually outcomes of our system, not causes.

Flatten out the housing supply curve and when housing vacancies get low, prices get high, and rents become unaffordable you see builders fill the gap until these fall to the point they can’t profit. It’s happened before and could happen again.