Aggregate Productivity with Heterogeneous Agents

We develop a welfare-based measure of aggregate productivity for economies with heterogeneous households. For any change in the economic environment, we define the associated change in aggregate productivity as the largest contraction in total factor-augmenting productivity that makes it feasible to leave every household at least as well off as under the status quo allocation. This construction maps arbitrary shocks to the economy into a TFP-equivalent change: aggregate productivity rises when the post-shock economy can make every household whole and still have resources left over, and falls when doing so requires additional resources. This measure provides a general-equilibrium analogue of cost-benefit analysis. Under standard representative-agent assumptions, it coincides with familiar measures such as real GDP, cost-benefit efficiency, and consumption-equivalent welfare. We show how to extend results that hold for welfare in representative-agent settings, including Hulten’s theorem, gains from trade formulas, and deadweight-loss triangles, to heterogeneous-agent economies. We characterize changes in aggregate productivity in terms of observables, including expenditures and price elasticities, and apply the measure to productivity shocks, misallocation, and trade shocks, both with and without costly redistribution.