partial insurance of parental investments against permanent income shocks, but the magnitude of the estimated responses is … small. We cannot reject the hypothesis full insurance against temporary shocks. Another interpretation of our findings is … that there is very little insurance available, but the fact that skill is a non-separable function of parental investments …

provide a novel decomposition of labor income tax formulas into a redistribution and an insurance component. The latter is … capital tax is non-zero and trades off redistribution and insurance against savings distortions. Our quantitative results … reveal that the insurance component contributes significantly to optimal labor tax rates and provides an informative lower …