Measuring Welfare by Matching Households across Time

The money metric utility function is an essential tool for calculating welfare-relevant growth and inflation. We show how to recover it from repeated cross-sectional data without making parametric assumptions about preferences. We do this by solving the following recursive problem. Given compensated demand, we construct money metric utility by integration. Given money metric utility, we construct compensated demand by matching households over time whose money metric utility value is the same. We illustrate our method using household consumption survey data from the United Kingdom from 1974 to 2017 and find that real consumption calculated using official aggregate inflation statistics overstates money metric utility in 1974 pounds for the poorest households by around half a percent per year and understates it by around a third of a percentage point per year for the richest households. We extend our method to allow for missing or mismeasured prices, assuming preferences are separable between goods with well-measured prices and the rest. We discuss how our results change if the prices of some service sectors are mismeasured.