Explaining individual response using aggregated data

Empirical analysis of individual response behavior is sometimes limited due to the lack of explanatory variables at the individual level. In this paper we put forward a new approach to estimate the effects of covariates on individual response, where the covariates are unknown at the individual level but observed at some aggregated level. This situation may, for example, occur if the response variable is available at the household level but covariates only at the zip-code level. We describe the missing individual covariates by a latent variable model which matches the sample information at the aggregate level. Parameter estimates can be obtained using maximum likelihood or a Bayesian approach. We illustrate the approach estimating the effects of household characteristics on donating behavior to a Dutch charity. Donating behavior is observed at the household level, while the covariates are only observed at the zip-code level.