Measuring Welfare by Matching Households across Time*.

The article focuses on developing a nonparametric method to recover money metric utility functions—key tools for measuring welfare-relevant economic growth and inflation—using repeated cross-sectional household data without imposing homotheticity or parametric assumptions on preferences. The approach solves a fixed-point integral equation by matching households over time who share the same money metric utility, enabling the construction of compensated budget shares and money metrics from observed uncompensated budget shares. Applied to UK household expenditure data from 1974 to 2017, the method reveals that real consumption deflated by aggregate inflation statistics overstates welfare for poorer households and understates it for richer ones. The methodology is extended to handle missing or mismeasured prices under a separability assumption, requiring knowledge of the compensated elasticity of substitution between observed and unobserved goods, and is empirically illustrated by adjusting for mismeasured service prices. This framework offers a data-driven, theoretically grounded alternative to standard price deflators and ad hoc income-group price indices, though it assumes stable preferences across households and common prices over time.