Welfare rankings of income distributions: A rôle for the variance and some insights for tax reform

When generalized Lorenz curves cross, it is not possible to rank the underlying income distributions by the unanimous preference of all additively separable symmetric inequality-averse social welfare functions. But in many cases, unanimous preference results in terms of inequality-aversion are nevertheless available. When generalized Lorenz curves cross once, variance is decisive in determining a robust welfare ranking, and can provide a rationale for choosing equity over efficiency where these two desiderata conflict. Welfare recommendations for certain types of income tax reform are implied, including cases of yield-increasing redistribution.This paper has benefitted considerably from the perceptive comments of an anonymous referee. Valentino Dardanoni gratefully acknowledges financial assistance from the Banco di Sicilia and the Ente Luigi Einaudi of Rome.