Welfare and Output with Income Effects and Demand Instability

We provide a non-parametric characterization of how welfare responds to changes in budget and production possibility sets when preferences are non-homothetic or subject to shocks, in both partial and general equilibrium. We generalize Hulten's theorem, which is the basis for constructing aggregate quantities, to this context. We identify a new bias in measures of real consumption. This bias depends on the covariance of price changes and expenditure changes due to income effects or preference shocks. 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, we show that correlated supply and demand shifters make real GDP and aggregate TFP unreliable metrics for measuring production and productivity, and illustrate this using the Covid-19 crisis