Welfare and Output with Income Effects and Taste Shocks

Abstract

We characterize how welfare responds to changes in budget sets and technologies when preferences are non-homothetic or subject to shocks, in both partial and general equilibrium. We generalize Hulten’s theorem, the basis for constructing aggregate quantity indices, to this context. We show that calculating the response of welfare to a shock only requires knowledge of expenditure shares and elasticities of substitution and (given these elasticities) not of income elasticities and taste shocks. We also characterize the gap between welfare and chain-weighted indices. We apply our results to long- and short-run phenomena. In the long-run, we show that if structural transformation is caused by income effects or changes in tastes, rather than substitution effects, then Baumol’s cost disease is twice as important for welfare. In the short-run, we show that standard deflators understate welfare-relevant inflation because product-level demand shocks are positively correlated with price changes. Finally, using the Covid-19 recession we illustrate the differences between partial and general equilibrium notions of welfare, and show that real consumption and real GDP are unreliable metrics for measuring welfare or production.