Aggregate Productivity with Discrete Choice

This paper quantifies aggregate productivity in general equilibrium economies where agents with heterogeneous preferences make discrete choices between locations and occupations. We show how the conventional tools of welfare economics, like cost-benefit analysis, can be extended to these settings. Following Debreu (1951), we measure the change in aggregate productivity as the maximum reduction in total factor productivity such that it is possible to make every household at least indifferent to their status quo allocation. Aggregate productivity rises if primary factors can be saved while keeping every household at least indifferent. We characterize this measure of efficiency in terms of compensated supply and demand curves. We show that, to a first-order approximation, the elasticity of aggregate productivity to productivity shocks is given by sales shares (regardless of preferences and technologies). We also provide second-order approximations in terms of elasticities of uncompensated supply and demand curves. We contrast our approach with some popular alternative measures of aggregate efficiency and welfare: real GDP, the cross-sectional average of utilities, and the sum of compensating variations, and show that these alternative measures have serious flaws.