Aggregate Productivity with Heterogeneous Agents

We develop a TFP-equivalent measure of aggregate welfare gains and losses for economies with heterogeneous agents. Our measure is the largest scalar by which total factor productivity can be contracted while keeping every household at least indifferent to the status quo. This construction maps arbitrary shocks to the economy into an equivalent aggregate productivity 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. Hence, this measure provides a general-equilibrium analogue of total surplus in cost-benefit analysis. Under standard representative-agent assumptions, it coincides with familiar measures such as real GDP, the sum of compensating variations, 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 this measure in terms of observables, including expenditures and price elasticities, and apply it to study productivity shocks, misallocation from wedges, and trade shocks, both with and without costly redistribution.