Debt Sustainability in a Low Interest Rate World

Abstract

Conditions of secular stagnation—low output growth g and low interest rates r—have counteracting effects on the cost of servicing public debt, r − g. Using data for ad- vanced economies, we document that r is often less than g, but r − g exhibits substan- tial variability over the medium-term. We build a continuous-time model in which the debt-to-GDP ratio is stochastic and r < g on average. We analytically characterize the distribution of the debt-to-GDP ratio, showing how two candidate explanations for low interest rates, slower trend growth and higher output risk, can lower the debt- to-GDP ratio. When the primary surplus is bounded above, we characterize a fiscal limit, above which default occurs, and a debt tipping point, above which the pub- lic debt is on an unsustainable path, but default does not occur immediately. Slower trend growth and higher output risk can paradoxically improve debt sustainability. A conservative calibration suggests a fiscal limit for the US of 184 percent of GDP and a tipping point of 115 percent of GDP.