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 that is valid under arbitrary preferences that depend on observable consumer characteristics, 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. Using nominal expenditures under a constant set of prices as our money-metric for real consumption (welfare), we derive a consistent measure of its growth in terms of a correction to the conventional measures based on price index formulas. Our correction ac-counts for the cross-sectional dependence of the measured price indices on consumer income and other characteristics. We use nonparametric methods to approximate these corrections and provide bounds on the resulting approximation errors. Applying the approach to the measurement of growth in US real consumption per capita, we find a sizable correction to the standard measures of growth in the post-war era, a period of fast growth combined with substantial inflation gaps across income groups.