Risk-Adjusted Policy Learning and the Social Cost of Uncertainty: Theory and Evidence from CAP evaluation

Abstract: This paper develops a risk-adjusted alternative to standard optimal policy learning (OPL) for observational data by importing Roy's (1952) safety-first principle into the treatment assignment problem. We formalize a welfare functional that maximizes the probability that outcomes exceed a socially required threshold and show that the associated pointwise optimal rule ranks treatments by the ratio of conditional means to conditional standard deviations. We implement the framework using microdata from the Italian Farm Accountancy Data Network to evaluate the allocation of subsidies under the EU Common Agricultural Policy. Empirically, risk-adjusted optimal policies systematically dominate the realized allocation across specifications, while risk aversion lowers overall welfare relative to the risk-neutral benchmark, making transparent the social cost of insurance against uncertainty. The results illustrate how safety-first OPL provides an implementable, interpretable tool for risk-sensitive policy design, quantifying the efficiency-insurance trade-off that policymakers face when outcomes are volatile.