Household expenditures, wages, rents

New evidence from the 1980, 1990, and 2000 Decennial Census of Housing indicates that expenditure shares on housing are constant over time and across US metropolitan statistical areas (MSA). Consistent with this observation, we consider a model in which identical households with Cobb–Douglas preferences for housing and non-housing consumption choose a location and locations differ with respect to income earned by their residents. The model predicts that the relative price of housing of any two MSAs disproportionately reflects differences in incomes of those MSAs and is independent of housing supply in each MSA. According to the predictions of our calibrated model, the dispersion of rental prices across low- and high-wage MSAs should be larger than we observe: High-wage MSAs like San Francisco are puzzlingly inexpensive relative to low-wage MSAs like Pittsburgh.