Can mortality risk explain the consumption hump?

A lifecycle consumption profile with a hump of roughly the same relative size and peak location as empirical consumption profiles can be obtained in a general equilibrium model where mortality risk is the only active mechanism that can account for the hump. Moreover, the key preference parameter, the elasticity of intertemporal substitution, is close to that estimated in a buffer-stock saving model by Gourinchas and Parker [Gourinchas, Pierre-Olivier, Parker, Jonathan A., 2002. Consumption over the life cycle. Econometrica 70, 47-89], where borrowing constraints primarily account for the consumption hump. Since borrowing is virtually eliminated in the model with mortality risk, mortality supplants the borrowing constraint as the explanation for the hump with these parameters. If a pay-as-you-go Social Security system is also incorporated in the model, mortality risk can no longer account for the observed properties of the hump. However, the set of intertemporal elasticities for which mortality risk disables the borrowing constraint in the neighborhood of peak consumption extends to any value greater than 1/3.