r Minus g

Long-term data show that the dynamic efficiency condition `r>g` holds when `g` is represented by the average growth rate of real GDP if `r` is the average real rate of return on equity, `E(r^e)`, but not if `r` is the risk-free rate, `r^f`. This pattern accords with a simple disaster-risk model calibrated to fit observed equity premia. If Ponzi (chain-letter) finance by private agents and the government are precluded, the equilibrium can feature `r^f≤E(g)`, a result that does not signal dynamic inefficiency. In contrast, `E(r^e)>E(g)` is required for dynamic efficiency, implied by the model, and consistent with the data. The model satisfies Ricardian Equivalence because, without Ponzi finance by the government, a rise in safe assets from increased public debt is matched by an increase in the safe (that is, certain) present value of liabilities associated with net taxes.