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We extend the canonical income process with persistent and transitory risk to shock distributions with left-skewness and excess kurtosis, to which we refer as higher- order risk. We estimate our extended income process by GMM for household data from the United States. We find countercyclical variance and procyclical skewness of persistent shocks. All shock distributions are highly leptokurtic. The existing tax and transfer system reduces dispersion and left-skewness of shocks. We then show that in a standard incomplete-markets life-cycle model, first, higher-order risk has sizable welfare implications, which depend crucially on risk attitudes of households; second, higher-order risk matters quantitatively for the welfare costs of cyclical idiosyncratic risk; third, higher-order risk has non-trivial implications for the degree of self-insurance against both transitory and persistent shocks.
We extend the canonical income process with persistent and transitory risk to cyclical shock distributions with left-skewness and excess kurtosis. We estimate our income process by GMM for US household data. We find countercyclical variance and procyclical skewness of persistent shocks. All shock distributions are highly leptokurtic. The tax and transfer system reduces dispersion and left-skewness. We then show that in a standard incomplete-markets life-cycle model, first, higherorder risk has sizable welfare implications, which depend on risk attitudes; second, it matters quantitatively for the welfare costs of cyclical idiosyncratic risk; third, it has non-trivial implications for self-insurance against shocks.
We develop a novel empirical approach to identify the effectiveness of policies against a pandemic. The essence of our approach is the insight that epidemic dynamics are best tracked over stages, rather than over time. We use a normalization procedure that makes the pre-policy paths of the epidemic identical across regions. The procedure uncovers regional variation in the stage of the epidemic at the time of policy implementation. This variation delivers clean identification of the policy effect based on the epidemic path of a leading region that serves as a counterfactual for other regions. We apply our method to evaluate the effectiveness of the nationwide stay-home policy enacted in Spain against the Covid-19 pandemic. We find that the policy saved 15.9% of lives relative to the number of deaths that would have occurred had it not been for the policy intervention. Its effectiveness evolves with the epidemic and is larger when implemented at earlier stages.