A Look Inside the Box: Combining Aggregate and Marginal Distributions to Identify Joint Distributions

This paper proposes a method for estimating the joint distribution of two or more variables when only their marginal distributions and the distribution of their aggregates are observed. Nonparametric identification is achieved by modelling dependence using a latent common-factor structure. Multiple examples are given of data settings where multivariate samples from the joint distribution of interest are not readily available, but some aggregate measures are observed. In the application, intra-household distributions are recovered by combining individual-level and household-level survey data. I show that, for individuals living in couple relationships, personal cash-management practices are significantly influenced by the partner's use of cash and stored-value cards. This finding implies that, for some methods of payment at least, ignoring the partner's impact might lead to spurious regression results due to an omitted variable bias.