  Threshold policies are targeting mechanisms that assign treatments based on
whether an observable characteristic exceeds a certain threshold. They are
widespread across multiple domains, such as welfare programs, taxation, and
clinical medicine. This paper addresses the problem of designing threshold
policies using experimental data, when the goal is to maximize the population
welfare. First, I characterize the regret (a measure of policy optimality) of
the Empirical Welfare Maximizer (EWM) policy, popular in the literature. Next,
I introduce the Smoothed Welfare Maximizer (SWM) policy, which improves the
EWM's regret convergence rate under an additional smoothness condition. The two
policies are compared studying how differently their regrets depend on the
population distribution, and investigating their finite sample performances
through Monte Carlo simulations. In many contexts, the welfare guaranteed by
the novel SWM policy is larger than with the EWM. An empirical illustration
demonstrates how the treatment recommendation of the two policies may in
practice notably differ.
