What measure of r-g matters?
Robert Barro in this paper argues that long-term data show that the dynamic efficiency condition r>g holds when g is represented by the average growth rate of real GDP and when r is gauged by the average of the realized real rate of return on equity. The condition does not hold when r equals the average of the realized real rate of return on short-term government bills. He uses a simple representative agent model that features stochastic depreciation of capital, with the potential for disaster events in which large portions of capital are destroyed and finds that:
As long as Ponzi-type finance for private agents and the government are precluded, the equilibrium can feature a risk-free rate, rf, below the expected growth rate, E(g), and possibly close to zero. (The model assumes that there do not exist real assets that deliver a positive, safe real rate of return.) The result rf≤E(g) does not signal dynamic inefficiency. In contrast, the inequality E(re)>E(g) [where re is the expected return on equity] is required for dynamic efficiency, implied by the model, and consistent with the data. The model satisfies Ricardian Equivalence for public debt because, with Ponzi finance by the government excluded, a rise in safe assets from increased government bonds is matched by an increase in the safe (that is, certain) present value of liabilities associated with net taxes.
r Minus g*
Author: Robert J. Barro
From: Harvard University
r<g against the backdrop of very large debt
John Cochrane argues that r < g is like seignorage, allowing a small steady deficit. But r < g is irrelevant for the current high levels of US debt:
So what does r < g mean? r < g may shift the average surplus to a slight perpetual deficit, just as seigniorage allows a slight perpetual deficit. But any substantial variation in deficits about that average – business cycles, wars, infrastructure programs – must be met by a substantial period of above average surpluses, to bring back debt to GDP in a reasonable time. And r < g is by any reasonable measure far too small to make a dent in the US existing fiscal problem, let alone a “one-time” fiscal expansion that is really a multi-decade increase in permanent deficits.
r < g
Author: John H. Cochrane
From: Hoover Institution, Stanford University
