The wrong shape of insurance? What cross-sectional distributions tell us about models of consumption-smoothing

This paper shows how two standard models of consumption risk-sharing - self-insurance through borrowing and saving and limited commitment to insurance contracts - replicate similarly well the standard, second-moment measures of insurance observed in US micro-data. A non-parametric analysis, however, reveals strongly contrasting and counterfactual joint distributions of consumption, income and wealth. Method of moments estimation shows how measurement error in consumption eliminates excessive skewness and concentration of consumption growth. Moreover, counterfactual non-linearities disappear at high estimated risk-aversion under self-insurance, but are a robust feature of limited commitment. Its "shape of insurance" thus argues strongly in favour of the self-insurance model.