Nonparametric Measurement of Long-Run Growth in Consumer Welfare

How should we measure long-run changes in consumer welfare? This paper proposes a nonparametric approach with arbitrary observable preference heterogeneity, e.g. when expenditure shares vary with income. Our approach only requires data on the consumption baskets of a cross-section of consumers facing a common set of prices. We take nominal expenditures under a constant set of prices as our money-metric for real consumption (welfare), and we derive a consistent measure of its growth in terms of a correction to the conventional quantity indices. Our correction accounts for the cross-sectional dependence of price indices on consumer income and any obserable source of preference heterogeneity. We use nonparametric methods to approximate these corrections and provide bounds on the resulting approximation errors that hold under arbitrary underlying preferences. Applying our methodology to the measurement of growth in real consumption per capita in the United States, we find a sizable correction to standard measures of growth in the postwar era–a period of fast growth combined with substantial inflation gaps across income groups