Estimating Hedonic Equilibrium for Metropolitan Housing Markets with Multiple Household Types

This paper provides a new estimation and solution method for a generalized class of sorting hedonic models based on discrete approximations of the distribution of housing quality. Our approach incorporates heterogeneity in preferences and treats quality as latent. Additionally, a housing market is taken as a whole metropolitan area, aggregating aggregating owners and renters and imposing equilibrium restrictions between rental prices and asset values. This model is flexible to different utility specifications and does not require a priori imposed functional forms on the income and value distributions. Finally, the obtained hedonic prices allow us to construct more refined price indices that measure change across time and metropolitan areas. In a first application, we use clustering techniques to learn categorization of households into types using data on age and number of children, and use the preference estimates to contrast preferences for overall quality in each type. The estimated preferences can be used to estimate compensating variations arising from the difference in quality and price across metropolitan areas for each type. Finally, we also consider the presence of children to define household types. We obtain the robust result that households without children have stronger preferences for housing quality conditional on income, which supports the view that children presence further raises the relative desired levels of non-housing consumption.