Thinking about housing in terms of affordability causes a lot of confusion, I think. There is confusion about the difference between the affordability of using a home (rent) and the affordability of owning a home. There is confusion about the difference between real housing consumption (size, location, etc.) and nominal housing consumption (the rent check). And, I think there are two big reasons why affordability is not a coherent way to think about housing expenses, anyway.
1) Housing is largely a sunk cost. The homes we have were built in the past and they are what they are. Since the 1960s, Americans have spent about 18% of our personal consumption expenditures on housing with surprising regularity. Lacking a major shift in a number of political and cultural factors, we will continue to spend about 18% of our budgets on housing. It doesn't matter if those houses are 500 sq. ft., 2,000 sq. ft., with or without air conditioning, with thatched roofs or tile. We will spend 18% of our budgets on it. It is that affordable. The affordability, in the aggregate, is the one thing that doesn't change. Everything else changes to keep affordability where it is.
And, we certainly won't suddenly discover that we can't afford the homes we have built and have to leave some of them empty until we can afford to fill them. They are here, they are ours to use, and we will pay about 18% of our personal household spending for them.
2) Affordability is not what is keeping people from moving to cities with employment opportunities. It looks like affordability is the problem. If you lost your manufacturing job in Buffalo, and you're thinking of moving to New York City because there are more jobs there, you might decide not to move because it is too expensive. It is the affordability that is keeping you out. But, even here, the affordability problem is just the messenger. It is the rationing mechanism for a housing stock that is relatively fixed for political reasons.
In a market with free flowing capital, labor, and money, price has more meaning. But, in the Closed Access cities, there are limits to the flow of capital and labor. If you decide to move to New York City, the shift in demand isn't going to move across an upward sloping supply curve. Supply has a pretty hard cap on it.
So, it doesn't matter if Brooklyn apartments rent for $500, or $1,000, or $2,000, or $4,000. There isn't one for you. Fixing this by fixing affordability isn't going to move the supply curve. It's simply substituting non-monetary rationing mechanisms for the monetary one.
The housing bubble was a huge neon sign blinking to the country that this is the core problem of our time - that there is a structural problem here that is eating us alive. And, the consensus error of seeing the bubble as a demand or credit phenomenon has delayed the progress on this problem for a decade while we impose self-inflicted wounds on ourselves.