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We develop a framework for difference-in-differences designs with staggered treatment adoption and heterogeneous causal effects. We show that conventional regression-based estimators fail to provide unbiased estimates of relevant estimands absent strong restrictions on treatment-effect homogeneity. We then derive the efficient estimator addressing this challenge, which takes an intuitive "imputation" form when treatment-effect heterogeneity is unrestricted. We characterize the asymptotic behaviour of the estimator, propose tools for inference, and develop tests for identifying assumptions. Our method applies with time-varying controls, in triple-difference designs, and with certain non-binary treatments. We show the practical relevance of our results in a simulation study and an application. Studying the consumption response to tax rebates in the U.S. we find that the notional marginal propensity to consume is between 8 and 11% in the first quarter—about half as large as benchmark estimates used to calibrate macroeconomic models—and predominantly occurs in the first month after the rebate. [ABSTRACT FROM AUTHOR]

How should we measure changes in consumer welfare given observed data on prices and expenditures? This article proposes a nonparametric approach that holds under arbitrary preferences that may depend on observable consumer characteristics, for example, when expenditure shares vary with income. Using total expenditures under a constant set of prices as our money metric for real consumption (welfare), we derive a principled measure of real consumption growth featuring a correction term relative to conventional measures. We show that the correction can be nonparametrically estimated with an algorithm leveraging the observed, cross-sectional relationship between household-level price indices and household characteristics such as income. We demonstrate the accuracy of our algorithm in simulations. Applying our approach to data from the United States, we find that the magnitude of the correction can be large because of the combination of fast growth and lower inflation for income-elastic products. Setting reference prices in 2019, we find that (i) the uncorrected measure underestimates average real consumption per household in 1955 by 11.5%, and (ii) the correction reduces the annual growth rate from 1955 to 2019 by 18 basis points, which is larger than the well-known "expenditure-switching bias" over the same time horizon. [ABSTRACT FROM AUTHOR]