The allocation of benefits under uncertainty: a decision-theoretic framework

We consider the problem of targeting benefits when the incomes of families are not accurately observable by the public authorities. By income uncertainty it is meant that the decision-maker cannot ascertain an applicant's income, but that he can assign probabilities with respect to the level of his resources. A decision-theoretic framework is used in order to analyze the decision to grant a benefit of fixed size. The derived decision rule consists of balancing the expected social cost of denying assistance to a person in need (type-I error) against that of granting a benefit to a non-poor (type-II error). Thus, when the cost of type-I errors are on the rise, or those of type-II errors fall, it becomes more desirable socially to increase population coverage of the benefit programme. Empirical illustrations are provided using a sample from the PSID.