A new paper from Francois Ortalo-Magne and Morris Davis on Housing Expenditures and Wages

Morris reads my observations about rents in Greenwich Village, and sends me a paper that concludes:

We use micro data from the 1980, 1990, and 2000 DCH to document that the expenditure share on housing is remarkably constant across MSAs and over time. We study the equilibrium properties for housing rents of a simple model consistent with this observation. A key distinguishing feature of our general spatial equilibrium model, relative to many papers in the urban economics and local public finance literatures, is our use of Cobb-Douglas preferences. This assumption yields a constant housing expenditure share in equilibrium, consistent with the evidence we uncover. The same assumption has been used to explain the distribution of population across places(Eeckhout 2004) and to study the internal structure of cities (Lucas 2001 and Lucas and Rossi-Hansberg 2002).

Our multi-location model predicts that in the aggregate, the ratio of rental price-
per-unit to per-capita income is constant as long as the aggregate stock of housing
per capita is also constant. This is a common result of macroeconomic models when
households have Cobb-Douglas utility. We show that this result does not hold at the
MSA level; instead, rental prices disproportionately reflect income differentials. We
conclude that the intuition – commonly assumed by policy-makers and housing-market commentators – that local house price indexes should increase at the same rate as local per-capita income is incorrect whenever income growth differs across MSAs.