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We analyze demand settings where heterogeneous consumers maximize utility for product attributes subject to a nonlinear budget constraint. We develop nonparametric methods for welfare-analysis of interventions that change the constraint. Two new findings are Roy's identity for smooth, nonlinear budgets, which yields a Partial Differential Equation system, and a Slutsky-like symmetry condition for demand. Under scalar unobserved heterogeneity and single-crossing preferences, the coefficient functions in the PDEs are nonparametrically identified, and under symmetry, lead to path-independent, money-metric welfare. We illustrate our methods with welfare evaluation of a hypothetical change in relationship between property rent and neighborhood school-quality using British microdata.

The econometric literature on treatment-effects typically takes functionals of outcome-distributions as `social welfare' and ignores program-impacts on unobserved utilities. We show how to incorporate aggregate utility within econometric program-evaluation and optimal treatment-targeting for a heterogenous population. In the practically important setting of discrete-choice, under unrestricted preference-heterogeneity and income-effects, the indirect-utility distribution becomes a closed-form functional of average demand. This enables nonparametric cost-benefit analysis of policy-interventions and their optimal targeting based on planners' redistributional preferences. For ordered/continuous choice, utility-distributions can be bounded. Our methods are illustrated with Indian survey-data on private-tuition, where income-paths of usage-maximizing subsidies differ significantly from welfare-maximizing ones., Comment: 30 pages, 1 table, 3 figures

Many real-life settings of consumer-choice involve social interactions, causing targeted policies to have spillover-effects. This paper develops novel empirical tools for analyzing demand and welfare-effects of policy-interventions in binary choice settings with social interactions. Examples include subsidies for health-product adoption and vouchers for attending a high-achieving school. We establish the connection between econometrics of large games and Brock-Durlauf-type interaction models, under both I.I.D. and spatially correlated unobservables. We develop new convergence results for associated beliefs and estimates of preference-parameters under increasing-domain spatial asymptotics. Next, we show that even with fully parametric specifications and unique equilibrium, choice data, that are sufficient for counterfactual demand-prediction under interactions, are insufficient for welfare-calculations. This is because distinct underlying mechanisms producing the same interaction coefficient can imply different welfare-effects and deadweight-loss from a policy-intervention. Standard index-restrictions imply distribution-free bounds on welfare. We illustrate our results using experimental data on mosquito-net adoption in rural Kenya.

McFadden's random-utility model of multinomial choice has long been the workhorse of applied research. We establish shape-restrictions under which multinomial choice-probability functions can be rationalized via random-utility models with nonparametric unobserved heterogeneity and general income-effects. When combined with an additional restriction, the above conditions are equivalent to the canonical Additive Random Utility Model. The sufficiency-proof is constructive, and facilitates nonparametric identification of preference-distributions without requiring identification-at-infinity type arguments. A corollary shows that Slutsky-symmetry, a key condition for previous rationalizability results, is equivalent to absence of income-effects. Our results imply theory-consistent nonparametric bounds for choice-probabilities on counterfactual budget-sets. They also apply to widely used random-coefficient models, upon conditioning on observable choice characteristics. The theory of partial differential equations plays a key role in our analysis.

An important goal of empirical demand analysis is choice and welfare prediction on counterfactual budget sets arising from potential policy-interventions. Such predictions are more credible when made without arbitrary functional-form/distributional assumptions, and instead based solely on economic rationality, i.e. that choice is consistent with utility maximization by a heterogeneous population. This paper investigates nonparametric economic rationality in the empirically important context of binary choice. We show that under general unobserved heterogeneity, economic rationality is equivalent to a pair of Slutsky-like shape-restrictions on choice-probability functions. The forms of these restrictions differ from Slutsky-inequalities for continuous goods. Unlike McFadden-Richter's stochastic revealed preference, our shape-restrictions (a) are global, i.e. their forms do not depend on which and how many budget-sets are observed, (b) are closed-form, hence easy to impose on parametric/semi/non-parametric models in practical applications, and (c) provide computationally simple, theory-consistent bounds on demand and welfare predictions on counterfactual budget-sets.