Measuring growth in consumer welfare with income-dependent preferences

How should we measure changes in consumer welfare given observed data on prices and expenditures? This paper proposes a nonparametric approach that holds under arbitrary preferences that may depend on observable consumer characteristics, e.g., when expenditure shares vary with income. Using total expenditures under a constant set of prices as our money-metric for real consumption (welfare), we derive a principled measure of real consumption growth featuring a correction term relative to conventional measures. We show that the correction can be nonparametrically estimated with an algorithm leveraging the observed, cross-sectional relationship between household-level price indices and household characteristics such as income. We demonstrate the accuracy of our algorithm in simulations. Applying our approach to data from the United States, we find that the magnitude of the correction can be large due to the combination of fast growth and lower inflation for income-elastic products. Setting reference prices in 2019, we find that (i) aggregate real consumption per household in 1955 is underestimated by 11.5% by the uncorrected measure, and (ii) the correction reduces the annual growth rate from 1955 to 2019 by 18 basis points, which is larger than the well-known "expenditure switching bias" over the same time horizon.