Welfare Analysis with Discrete Choice in General Equilibrium

Discrete-choice general-equilibrium models capture rich heterogeneity in where people live and work, but this heterogeneity complicates the aggregation of welfare gains and losses. We measure aggregate economic surplus by the fraction of endowments that can be saved after a change while keeping every household as well off as before. This is a general-equilibrium counterpart to cost-benefit analysis that allows prices, wages, and choices to adjust as winners compensate losers. It requires neither utility cardinalizations nor Pareto weights. Under perfect competition, the first-order welfare elasticity with respect to a producer’s productivity equals its sales relative to GDP, regardless of the distribution of preferences and technologies. Beyond first order, we provide exact characterizations using supply and demand functions and second-order approximations using observable income and expenditure shares and supply and demand elasticities. We compare this measure with commonly-used alternative measures of aggregate welfare like real GDP, the sum of compensating variations, and average utility. Using a version of the Allen and Arkolakis (2014) spatial model, we show that welfare estimates and policy prescriptions based on average-utility vary erratically across observationally equivalent cardinal representations of the same ordinal preferences. Our welfare measure is invariant to these arbitrary assumptions.