Non-homothetic housing demand and geographic worker sorting

Housing expenditure shares decline with income. A household's income determines its sensitivity to housing costs and drives its location decision. Has spatial skill sorting increased because low income individuals are avoiding increasingly expensive regions? I augment a standard quantitative spatial model with flexible non-homothetic preferences to estimate the effect of the national increase in the relative supply of high skilled workers that has put upward pressure on housing costs in skill-intensive cities. My model explains 10% of the increase in average house prices in Germany from 2007 to 2017 and 11% of the regional differences in house price increases. One third of the effects is due to an increase in spatial skill sorting driven by differences in housing expenditure shares. The observed degree of skill sorting was not significantly different from the optimal allocation in 2007 while skill sorting was larger than optimal in 2017.