Official price indexes, such as the CPI, are imperfect indicators of inflation calculated using ad hoc price formulae different from the theoretically well-founded inflation indexes favored by economists. This paper provides the first estimate of how accurately the CPI informs us about “true” inflation. We use the largest price and quantity dataset ever employed in economics to build a Törnqvist inflation index for Japan between 1989 and 2010. Our comparison of this true inflation index with the CPI indicates that the CPI bias is not constant but depends on the level of inflation. We show the informativeness of the CPI rises with inflation. When measured inflation is low (less than 2.4% per year) the CPI is a poor predictor of true inflation even over 12-month periods. Outside this range, the CPI is a much better measure of inflation. We find that the U.S. PCE Deflator methodology is superior to the Japanese CPI methodology but still exhibits substantial measurement error and biases rendering it a problematic predictor of inflation in low inflation regimes as well.
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..