Quantifying the cost of risk in consumption

Fixing a risky intertemporal, interagent consumption profile, its total cost is the total willingness to pay for smoothing everyone’s consumption. It decomposes into a micro cost that captures the inefficiency in the cross-sectional distribution of total consumption, risky as it is, and a macro cost that captures the additional benefit of eliminating the risk in total consumption, once efficiently redistributed. We consider the risk that a household experiences income mobility and the consequent consumption mobility. U.S. panel data estimates a consumption profile for which we compute the costs. The total cost is 9-18% of total initial consumption for CRRA parameters 1.25-3.5. Of this, 80- 90% is the micro cost and only 10-20% is the macro cost. The magnitude of these results, and in particular the relative importance of the micro cost, is in line with previous empirical evidence. Motivated by this evidence we develop the theory of micro cost. Moreover, because the micro cost does not admit a closed form, for general preferences, we lay out an approximation method.