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 shift 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. In the absence of household heterogeneity, it nests the standard notions of aggregate TFP and consumption-equivalent welfare changes. It can also be interpreted as a general-equilibrium analogue of cost-benefit analysis, increasing whenever the gains to winners are more than sufficient to compensate the losers. We show how to port results that hold for aggregate TFP in representative agent settings, like Hulten’s theorem and Harberger triangles, to this setting. We characterize changes in aggregate productivity in terms of observables, including expenditures and price elasticities, and apply our measure to study the effects of productivity shocks, the costs of misallocation, and the impact of trade shocks, both with and without costly redistribution.