Paper detail

A Theory of the Saving Rate of the Rich

Empirical evidence suggests that the rich have higher propensity to save than do the poor. While this observation may appear to contradict the homotheticity of preferences, we theoretically show that that is not the case. Specifically, we consider an income fluctuation problem with homothetic preferences and general shocks and prove that consumption functions are asymptotically linear, with an exact analytical characterization of asymptotic marginal propensities to consume (MPC). We provide necessary and sufficient conditions for the asymptotic MPCs to be zero. We calibrate a model with standard constant relative risk aversion utility and show that zero asymptotic MPCs are empirically plausible, implying that our mechanism has the potential to accommodate a large saving rate of the rich and high wealth inequality (small Pareto exponent) as observed in the data.