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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 investigate what statistical properties drive risk-taking in a large set of observational panel data on online poker games (n=4,450,585). Each observation refers to a choice between a safe 'insurance' option and a binary lottery of winning or losing the game. Our setting offers a real-world choice situation with substantial incentives where probability distributions are simple, transparent, and known to the individuals. We find that individuals reveal a strong and robust preference for skewness. The effect of skewness is most pronounced among experienced and losing players but remains highly significant for winning players, in contrast to the variance effect.