Optimal Universal and Categorical Benefits with Classification Errors and Imperfect Enforcement

We determine he optimal combination of a universal benefit, B, and categorical benefit, C, for an economy in which individuals differ in both their ability to work - modelled as an exogenous zero quantity constraint on labour supply - and, conditional on being able to work, their productivity at work. C is targeted at those unable to work, and is conditioned in two dimensions: ex-ante an individual must be unable to work and be awarded the benefit, whilst ex-post a recipient must not subsequently work. However, the ex-ante conditionality may be imperfectly enforced due to Type I (false rejection) and Type II (false award) classification errors, whilst, in addition, the ex-post conditionality may be imperfectly enforced. If there are no classification errors - and thus no enforcement issues - it is always optimal to set C>0, whilst B=0 only if the benefit budget is sufficiently small. However, when classification errors occur, B=0 only if there are no Type I errors and the benefit budget is sufficiently small, while the conditions under which C>0 depend on the enforcement of the ex-post conditionality. We consider two discrete alternatives. Under No Enforcement C>0 only if the test administering C has some discriminatory power. In addition, social welfare is decreasing in the propensity to make each type error. However, under Full Enforcement C>0 for all levels of discriminatory power. Furthermore, whilst social welfare is decreasing in the propensity to make Type I errors, there are certain conditions under which it is increasing in the propensity to make Type II errors. This implies that there may be conditions under which it would be welfare enhancing to lower the chosen eligibility threshold - support the suggestion by Goodin (1985) to "err on the side of kindness".