Would a universal basic income be eaten up by higher housing costs?

Earlier this week, I reviewed David Graeber's book Bullshit Jobs. In the conclusion to the book, Graeber discusses a universal basic income as a solution to the problem of bullshit jobs. However, one point in particular struck me:

One could make the argument UBI wouldn't work with a rent-based economy because, say, if most homes were rented, landlords would just double rents to grab the additional income.

That got me thinking back to the points raised in Robert Frank's book Falling Behind: How Rising Inequality Harms the Middle Class (which I have previously discussed here and here). I think Graeber has underestimated the importance of his point (which is buried in a footnote), and that it doesn't rely on a rent-based economy, since it would also apply to an economy where home ownership is more prevalent.

Frank argues that housing is a 'positional good', and that people are concerned about their relative status in terms of positional goods. For instance, a house in a good neighbourhood comes with low crime and access to better schools. People prefer to live in houses in the good neighbourhood rather than the worse neighbourhood, and so the value of houses in the good neighbourhood is bid upwards.

If you give one family a boost in income, they will use some of that extra income to buy or rent a house in a better neighbourhood. They will invest in the positional good in order to raise their relative status. However, if you give all families a boost to their incomes, all families would want to buy or rent a house in the better neighbourhood. Since there is a limited supply of such houses, all that would happen is that the rents (or house prices) in good neighbourhoods would be bid up to a higher level. There would be no change in relative status for any families, and the additional income would be captured by landlords in the form of higher rents, or by home sellers or developers in the form of higher house prices. Families that tried to opt out of this process would miss out on a house in a good neighbourhood and would end up living in a worse neighbourhood (so there is an incentive not to opt out).

It seems to me, then, that a large proportion (if not all) of a universal basic income would be eaten up by higher housing costs, with no net benefit to families. Aside from the general unaffordability of a universal basic income at a level that people could actually live on, this seems to be a very important problem with UBI proposals that I don't think has been addressed. At the least, it would be interesting to see whether some of the high-profile UBI pilot programmes in recent years have looked at housing costs.