On the identification of joint distributions using marginals and aggregates

Abstract

A data combination approach is proposed to identify variables’ joint distribution when only their marginals and the distribution of their sum are known. Nonparametric identification is achieved by modelling dependence using a latent common-factor structure. A variation of the well-known Lemma of Kotlarski (Kotlarski,1967) is established. Potential applications are proposed where aggregated data help identify within-household or longitudinal distributions in the absence of intra-household or panel data, respectively.