Running Primary Deficits Forever in a Dynamically Efficient Economy: Feasibility and Optimality

Government debt can be rolled over forever without primary surpluses in some stochastic economies, including some economies that are dynamically efficient. In an overlapping-generations model with constant growth rate, g, of labor-augmenting productivity, and with shocks to the durability of capital, we show that along a balanced growth path, the maximum sustainable ratio of bonds to capital is attained when the riskfree interest rate, rf , equals g. Furthermore, this maximal ratio maximizes utility per capita along a balanced growth path and ensures that the economy is dynamically efficient. ∗We thank Andrew Atkeson, Alan Auerbach, Laurence Ball, Gadi Barlevy, Olivier Blanchard, Itamar Drechsler, Joao Gomes, Lars Hansen, Richard Kihlstrom, Narayana Kocherlakota, Dirk Krueger, Greg Mankiw, Tom Sargent, Lawrence Summers, Richard Zeckhauser and seminar participants at Chicago Booth, Columbia, Harvard, UCLA, UT Austin, Wharton, and the Cowles Summer Conference in Macroeconomics for helpful comments and discussions. A previous version of this paper was circulated with the title “Optimal Rollover of Government Bonds in Dynamically Efficient Economies”. What is the maximum amount (possibly zero) of bonds that a government can rollover forever without running primary budget surpluses? If the government can rollover a positive amount of bonds forever, what is the optimal amount of bonds to rollover? Blanchard’s presidential address to the American Economic Association spurred renewed scholarly interest in these questions. Only a year later, global events brought these issues into the public realm as governments around the world ran huge deficits to deal with the catastrophic economic consequences of the covid-19 pandemic. In the absence of uncertainty, the ability of the government to rollover bonds forever is determined by the “r vs g” comparison, as it is colloquially known, where r is the net rate of return on all assets, including government bonds, and g is the growth rate of the capital stock. Specifically, if and only if r < g along a balanced growth path in a competitive economy, government bonds can be rolled over forever and will shrink as a share of the economy over time. Also, if and only if r < g, the economy suffers from a dynamically inefficient overaccumulation of capital. That is, government bonds can be rolled over forever if and only if the economy is dynamically inefficient. In the presence of uncertainty, the link between dynamic inefficiency and the feasibility of rolling over government bonds forever is more nuanced. Put simply, the rate of return on capital is the rate of return relevant for assessing dynamic efficiency, but the riskfree interest rate is the rate of return relevant for assessing whether the government can rollover its bonds forever. Uncertainty breaks the equality of these two rates of return. As we will show, in some dynamically efficient competitive economies with a constant growth rate g ≥ 0, it is possible for the riskfree interest rate, rf , to be less than g, which makes permanent rollover of government bonds feasible. This possibility of permanently rolling over debt in an efficient economy does not exist in deterministic, dynamically efficient, competitive economies. Our principal findings in this paper result from both positive and normative analyses of sustainable levels of the ratio of government bonds to the capital stock, which we define as levels of this ratio that permit government bonds to be rolled over forever without any primary surpluses. In our positive analysis, we find that if rf < g along a balanced growth path without government bonds (which can be the case in some dynamically efficient economies,