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.

中文翻译：

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通过跨时间匹配家庭来衡量福利

货币度量效用函数是计算与福利相关的增长和通货膨胀的重要工具。我们展示了如何从重复的横截面数据中恢复它，而不对偏好做出参数假设。我们通过解决以下递归问题来做到这一点。给定补偿需求，我们通过积分构建货币度量效用。给定货币度量效用，我们通过随着时间的推移匹配货币度量效用值相同的家庭来构建补偿需求。我们使用 1974 年至 2017 年英国家庭消费调查数据来说明我们的方法，发现使用官方总通胀统计数据计算的实际消费高估了 1974 年最贫困家庭的货币计量效用约 0.5%，并低估了它最富有的家庭每年增加约三分之一个百分点。我们扩展了我们的方法，允许价格缺失或错误衡量，假设价格准确的商品和其他商品之间的偏好是可区分的。我们讨论如果某些服务部门的价格被错误衡量，我们的结果将如何变化。