Are Poor Cities Cheap for Everyone? Non-Homotheticity and the Cost of Living Across U.S. Cities

Abstract

Standard cost-of-living indexes assume that preferences are homothetic, ignoring the well-established fact that tastes vary with income. This paper considers how assuming homotheticity biases our estimates of spatial price indexes for consumers at different income levels. I use Nielsen household-level purchase data in over 500 categories of food products to calculate micro-founded income- and city-specific price indexes that account for non-homotheticity, as well as city-specific price indexes that do not. I find that the income-specific cross-city price indexes vary widely across income groups. Grocery costs are 20 percent lower in a poor city relative to a wealthy city for a low-income household, but they are 20 percent higher in the poor city for a high-income household. The homothetic price indexes perform well in predicting the cross-city variation in prices for low- and middle-income households, but poorly for high-income households. These results suggest that using homothetic cost-of-living indexes understate the relative price level in poor locations for rich households.