Appendix: the credit dynamics of house prices

This is an extract from an as yet unpublished paper undertaken with Paul Ormerod and Nyman Rickard.

Arguments over whether there is or is not a bubble in housing are endless and seemingly futile. Proponents of the bubble hypothesis point to various metrics when they exceed historic norms, such as house prices relative to rents or household income. Opponents argue that such divergences simply reflect the balance of the forces of supply and demand, or propose reasons why these price to income ratios should in fact rise over time. Bubble proponents slate the blame for the perceived bubble to the banking sector; opponents of the bubble hypothesis blame inflexible supply for any perceived deviation of prices from affordability metrics.

The current state of this debate is thus akin to the irresolvable question of “which came first: the chicken or the egg”? Given the importance of housing both socially and economically, this is an unsatisfactory state of affairs.

Clearly there are causal factors working in multiple directions: is it possible to disentangle them to work out what is the predominant factor, and thus determine whether housing is or is not in a bubble? In this paper we propose a causal analysis, and apply a well-known—if limited by its linear assumptions—statistical test to resolve this dispute.

14.1 The argument

We commence with an argument couched in terms of supply and demand. The supply of housing has two major components: the turnover of existing properties (whether for speculative, demographic or social reasons), and additions to the stock of properties by construction. We can therefore specify the physical flow of supply onto the market at a point in time as having one factor relating to the fraction of existing stock supplied to the market each year, and H S (A) another consisting of construction or the change in stock: H α(A) Q (A)

The market demand and supply factors thus have monetary forces on one side (change in mortgage debt and the house price level) and physical supply on the other, with numerous potential causal channels: rising mortgage debt might drive house prices; rising house prices might encourage people to take on mortgage debt; rigid supply meeting flexible demand may push house prices up; rising house prices might encourage more circulation of existing stock, and new construction, and so on.

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Stating the causal dynamics in an agnostic way, and dropping the time argument for notational simplicity, we start with the relation between demand and supply shown in equation (0.233):

Restating this in terms of the house price index yields:

We are interested in the change in house prices—which immediately suggests that one factor in the change in house prices is not the rate of change of mortgage debt, but its acceleration:

Expanding this out yields:

  A simplification makes this relation more tractable: we note that equation (0.234) suggests that can be substituted for � : H P d dt MSH d  d 2 d 

Equation (0.238) expresses the rate of change of house prices as a function of supply and demand, as participants in this debate all agree. However, what may be unexpected is that this relationship includes acceleration terms for both mortgage debt and housing supply. Substituting (0.231) into ((0.238) yields:

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This implies that for house prices to rise, the acceleration of mortgage debt must be positive, and greater (when deflated by the current monetary value of transactions on the housing market) than the supply-deflated sum of the rate of change of the physical housing stock times its turnover rate, plus the rate of change of new construction (and thus the acceleration of the housing stock).

We have revealed a potential relationship between the rate of change of house prices and the acceleration of mortgage debt: but which causes which? Do rising house prices cause people to decide to take on mortgage debt, or does accelerating mortgage debt cause house prices to rise?

If the former, then the supply “chicken” leads the demand “egg”, and those who argue that there is no bubble have a case. If there is a policy desire to reduce the rate of growth of house prices, then that policy must focus on the supply of housing. There is also no reason why sustained price rises cannot continue.

But if it is the latter, then the demand “egg” leads the supply “chicken”, and the argument that there is a debt-financed bubble driving house prices has legs: limits on the capacity of banks to create mortgages would impact upon house price growth. There is also a very good reason why house price rises must ultimately stop: they depend on the acceleration of mortgage debt being not merely permanently positive but substantially greater than zero, to counter the impact of the two supply factors. This is impossible, since nothing, not even mortgage debt, can accelerate forever.

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