  Subsidies are commonly used to encourage behaviors that can lead to short- or
long-term benefits. Typical examples include subsidized job training programs
and provisions of preventive health products, in which both behavioral
responses and associated gains can exhibit heterogeneity. This study uses the
marginal treatment effect (MTE) framework to study personalized assignments of
subsidies based on individual characteristics. First, we derive the optimality
condition for a welfare-maximizing subsidy rule by showing that the welfare can
be represented as a function of the MTE. Next, we show that subsidies generally
result in better welfare than directly mandating the encouraged behavior
because subsidy rules implicitly target individuals through unobserved
heterogeneity in the behavioral response. When there is positive selection,
that is, when individuals with higher returns are more likely to select the
encouraged behavior, the optimal subsidy rule achieves the first-best welfare,
which is the optimal welfare if a policy-maker can observe individuals' private
information. We then provide methods to (partially) identify the optimal
subsidy rule when the MTE is identified and unidentified. Particularly,
positive selection allows for the point identification of the optimal subsidy
rule even when the MTE curve is not. As an empirical application, we study the
optimal wage subsidy using the experimental data from the Jordan New
Opportunities for Women pilot study.
