This paper develops a framework for individualized treatment allocation in the presence of market equilibrium spillovers. Motivated by coupon programs widely used during the COVID-19 pandemic, the framework highlights when universal distribution is optimal, when targeted allocation dominates, and how the planner's targeting problem can be solved tractably. We show that the policymaker's welfare function is supermodular in treatment assignments under broad and interpretable conditions. Supermodularity implies that treatments are complements, so the welfare gain from treating one group is larger when others are also treated. This property both clarifies the trade-off between universal and targeted distribution and ensures computational feasibility, since maximizing a supermodular function can be solved in polynomial time using off-the-shelf algorithms. We also establish statistical guarantees that account for estimation uncertainty in the demand and supply equations. Finally, we illustrate our proposal in a coupon allocation problem calibrated with households expenditure data from Philippines.
(The full draft will be publicly available very soon!)
This paper studies debiased machine learning when nuisance parameters appear in indicator functions. An important example is maximized average welfare gain under optimal treatment assignment rules. For asymptotically valid inference for a parameter of interest, the current literature on debiased machine learning relies on Gateaux differentiability of the functions inside moment conditions, which does not hold when nuisance parameters appear in indicator functions. In this paper, we propose smoothing the indicator functions, and develop an asymptotic distribution theory for this class of models. The asymptotic behavior of the proposed estimator exhibits a trade-off between bias and variance due to smoothing. We study how a parameter which controls the degree of smoothing can be chosen optimally to minimize an upper bound of the asymptotic mean squared error. A Monte Carlo simulation supports the asymptotic distribution theory, and an empirical example illustrates the implementation of the method.