Welfare and Output with Income Effects and Taste Shocks

We characterize how welfare responds to changes in budget set and technology 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 changes in welfare in response to a shock only requires knowledge of expenditure shares and elasticities of substitution, and given these statistics does not require knowledge of income elasticities or taste shocks. We also characterize the gap between changes in welfare and changes in chained indices. We apply our results to long-run and short-run phenomena. In the long-run, we show that structural transformation, if caused by income effects, is roughly twice as important for welfare than what is implied by standard measures of Baumol’s cost disease. In the short-run, we show that when firms’ demand shocks are correlated with their supply shocks, industry-level price and output indices are biased, and this bias does not disappear in the aggregate. Finally, using the Covid-19 crisis we illustrate the differences between partial and general equilibrium notions of welfare, and we show that real consumption and real GDP are unreliable metrics for measuring welfare or production.