Prisoner’s dilemma game justification for state housing

I’ve been thinking about potential justifications for building a stock of state housing when we have no issues of credit constraints.

Say we have a bunch of people walking around wanting to buy two goods – housing services and non-housing goods and services.  People will, on average, allocate their spending such that the marginal benefit of an extra unit of housing services is equal to the marginal benefit of non-housing services.  This will lead to the appropriate level of housing services being provided, and it is all gravy.

But then say that the benefit of a housing service is actually a function of the quality of the housing service other people are receiving.  So if your neighbour/co-worker builds a big sexy house, you feel you need a bigger house to keep up.  The “marginal benefit” from housing services is higher, so you swap some non-housing goods and services for housing services (building a bigger house) – however, the marginal benefit is only higher because the other persons bigger house imposed a cost on you (making you feel inferior, or reduced the quality of the signal your house was providing regarding how well off you are).  As a result, house sizes are an arms race.

This view of consumption stems from back with people like Veblen, has been written about widely (and are used in modern macro-models), and in recent times has been reiterated by Rogoff and Shiller when discussing issues such as the “housing bubble” in the US.  A common term for this is of course “keeping up with the Joneses”.  An economics term for these sorts of goods is positional goods.

In so far as we see growing house size, and increasing borrowing to fund it, as a type of arms race based on this “positional good” logic we could well end up in a situation where we have “too few” houses that are “too big”.  We cannot rule out that this is in fact a contributor to high house prices and the limited stock of housing in Auckland, in addition to the zoning laws and high cost of subdividing.

Now when looking at this in terms of policy we can say this is really a standard prisoner’s dilemma.  Private value is only being created due to the larger housing being “relative better than” the current  – not because the house itself is bigger.  In that case, each individual sees building a bigger house as a dominant strategy – as if the other people don’t, they feel superior, if the other people involved do they don’t feel inferior.  As a result, everyone builds big houses, even though everyone would be better off with smaller houses and higher non-housing consumption (note this additional point).

Here, state houses may be a mechanism for trying to deal with that – by building a series of similar, smaller, houses at a lower cost.

This is the kicker though – to some people this argument sounds compelling.  To others it sounds horrible, as they genuinely get direct value from a larger house, and the fact that different houses on the street look different.  To buy the PD argument we have to make the case that:

1. Much of the increase in house size and the variation between houses is due solely to “trying to out do other people”, and not due to actually valuing the additional housing services.
2. That there are significant enough transaction costs within a community that prevent household near each other “negotiating” about this externality.
3. That the “externality” itself is large enough to warrant attention.

And even with all that it is not necessarily policy relevant – as if people simply decide to overconsume housing, and lower their own welfare significantly, then we should really be asking why there isn’t more inter-community co-operation rather than arbitrarily throwing money at them.

A more compelling version of this argument would rely on the ideas Robert Frank – where the bidding up of house prices and size is occuring among those who are well off, and is having a negative impact on those with low incomes by also increasing the cost of their housing services!  This is the very issue that everyone is concerned about.  And yet, the data suggests that spending on housing service among the lowest declines relative to income has been declining and relative to incomes those in the lowest declines are spending about the same proportion of their consumer spending on housing …

There are no doubt some things going on in the housing market – but I’m not sure we can use the idea of positional goods to justify building a series of homogenous state houses in of itself.