Consumption inequality across heterogeneous families

This paper studies the transmission of wage shocks into consumption across families that exhibit unobserved preference heterogeneity. Heterogeneity and preferences over consumption and family labor supply are nonparametric. I show that any moment of the joint distribution of policy-relevant wage elasticities of consumption and labor supply is identified separately from the distributions of incomes and outcomes. I decompose consumption inequality into components pertaining to wage inequality, preference heterogeneity and heterogeneity in wealth, and I show that preference heterogeneity always increases consumption inequality. To illustrate these points empirically, I fit second and third moments of consumption, earnings and wages in the PSID. I find that: (i) the distributions of permanent and transitory wage shocks exhibit strong negative skewness; (ii) there is substantial heterogeneity in consumption elasticities but not in elasticities of labor supply; (iii) consumption is on average fully insured against transitory shocks but tracks permanent shocks much more closely than previously found; moreover, there is substantial heterogeneity in the response of consumption to such shocks involving both the magnitude and the sign of the response; (iv) preference heterogeneity accounts for up to 58\% of consumption inequality in the US since 1999. Seen together, these results suggest that preference heterogeneity has substantial implications for consumption inequality and partial insurance.