Aggregate Welfare with Discrete Choice Across Places and Jobs

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 proposes a TFP-equivalent welfare measure: the largest uniform reduction in factor productivity such that it is possible to keep every household at least as well off as in the status quo. This measures the resource surplus left after 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 producer i’s sales share, 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 can fall even when every household is better off; average utility depends on arbitrary cardinalizations of individual utility; and the sum of compensating variations can rise after pure redistributions because it holds general-equilibrium prices fixed during compensation. The measure avoids these problems while preserving the logic of cost-benefit analysis in general equilibrium.