The formalization of the idea that area differences in wages and rents compensate people and businesses for differences in desirable local amenities is attributable to Jennifer Roback (1982). This important formalization built on Sherwin Rosen's (1974) seminal analysis of markets for bundled characteristics. An important difference between the two models is the use of a representative consumer (and firm) in Roback's model, (1) as opposed to a focus on heterogeneity in preference and cost functions among firms and people in the earlier Rosen paper. Roback (1982) also assumes for simplicity that moving costs are well approximated by zero. The addition of migration costs and heterogeneity was not seen as a major problem, as all the results of the model should still hold for the marginal migrant, defined as a person with zero migration costs. (2)
In this paper, we loosen these two assumptions simultaneously, and show the change modifies the interpretation of inter-city differences in wages and rents considerably. Intuitively, the presence of heterogeneous moving costs implies that at any combination of rents and wages, some people and businesses will be willing to locate in a city given its amenity level. (3) Thus, imposing locational equilibrium does not determine equilibrium rents or wages. Two additional conditions must be imposed to close the model: labor market equilibrium and housing market equilibrium. For the local labor market to be in equilibrium, an appropriate number of residents and businesses must wish to locate in a city. For any given amenity level, there are a set of points in rent-wage-population space that will satisfy local labor market equilibrium. However, this set of points includes a continuum of possible rents, populations, and wages. We show that for any given amenity level, rents--and thus wages and population--are actually set by the local supply of housing. We then proceed to confirm the existence of this housing supply effect using two different data sets.
This paper thus makes two significant contributions. First, it derives a housing supply effect on local housing values in an open city model, showing that this effect depends upon the heterogeneity of local attachments (moving costs) and not on the level of these costs. There has been a substantial literature debating the importance of such factors of late, including Glaeser and Gyourko (2005), Glaeser, Gyourko, and Saks (2005, 2006), Mayer et al. (2006), and Saiz (2008) emphasizing the importance of area housing supply while Aura and Davidoff (2008), Davidoff (2010), and Van Nieuwerburgh and Weill (2009) (4) downplay its importance. This paper shows that the importance of housing supply is a direct consequence of people's idiosyncratic attachment to their home cities, and provides additional empirical support for the effect's existence.
A second contribution of the paper is that it shows how the importance of housing supply and other housing market factors in the presence of heterogeneous costs to migration substantially changes the interpretation of inter-area price differences and their correlation with local characteristics. This undermines the use of such correlations as "market price" weights in measuring local attractiveness. For instance, we show that in such a context, amenities that restrict housing supply will appear more "valuable" than amenities that do not. Thus, in traditional Quality of Life (QOL) indices, areas with amenities that restrict supply (such as coasts, steep mountains, national parks, etc.) will appear more attractive than areas with amenities that do not (such as climate and cultural amenities). This implies that the widespread interpretation of such price differences as compensating is misguided.
The rest of the paper is organized as follows. Section II outlines the Rosen-Roback model and its core results. Section III incorporates heterogeneous moving costs, and shows that the results change substantially. …