Identification of unobserved distribution factors and preferences in the collective household model

Abstract

This paper develops a non-parametric collective random utility model with a continuous choice of consumption and sharing. We allow for a heterogeneous population by introducing unobserved distribution factors and preferences that are non-separable in the stochastic household choice system. We provide necessary and sufficient conditions for invertibility with respect to the vector of unobserved heterogeneity. Further, we show non-parametric identification of each individual’s idiosyncratic preferences and Pareto weights from the distribution of observed choices. Based on this result we develop a non-parametric two-step estimation procedure and estimate individual counterfactuals in a collective labour supply model for households with children using the LISS panel.