Aggregate Welfare with Discrete Choice

Discrete-choice general-equilibrium models are widely used to study how people sort across places, sectors, and jobs, but they lack a canonical aggregate welfare statistic. This paper characterizes a general equilibrium counterpart to cost-benefit analysis. We measure aggregate welfare by the largest uniform reduction in factor productivity such that everyone can be at least as well off as in the status quo. This quantifies total surplus left once winners compensate losers, allowing prices, wages, and choices to adjust in general equilibrium. We characterize this measure using compensated supply and demand functions. A main result is a version of Hulten’s theorem for discrete-choice economies: under perfect competition, the first-order welfare effect of a productivity shock to producer i is given by its sales relative to GDP, regardless of the distribution of preferences and technologies. Beyond first order, we provide approximations in terms of observable income and expenditure shares and uncompensated supply and demand elasticities. We compare this measure with common alternatives: real GDP ignores amenity value; average utility depends on arbitrary assumptions about how ordinal preferences are mapped into cardinal utils. In an application to the U.S. Interstate Highway System, we show that average-utility estimates and the optimal place-based policies they imply vary erratically across observationally equivalent representations of the same preferences, while our welfare measure is invariant to these arbitrary assumptions.