Sorting models at the national scale have been used to estimate the economic value of nonmarket amenities such as air quality and climate. This class of models typically uses a set of Metropolitan Statistical Area (MSAs) as the objects of choice and explains households' residency in an MSA as a function of wages, housing rents, local amenities, and household characteristics. By observing tradeoffs between amenities and wages and rents (i.e. the net income for a household in a location) across the landscape, it is possible to infer the marginal willingness to pay for an amenity based on Tiebout logic.

We investigate this spatial equilibrium approach to valuation when migration flows are observed. To exploit our observation of both the origin and destination of moves, we propose a static model that begins with a moving household observed at its origin MSA. We assume a conditional utility maximization framework whereby given its origin, a household selects the MSA that maximizes its utility. Using both aggregate- and household-level data environments, we find that the inclusion of migration flows in a spatial equilibrium model generates a gravity-type equation that identifies the marginal willingness to pay for an local amenities in a novel
fashion.