Costly Increases in Public Debt when r < g

This paper quantifies the costs of a permanent increase in debt to GDP. We employ a deterministic, overlapping generations model with two assets and no risk of default. The two assets are public debt and private (productive) capital. We assume that the return on private capital equals the interest rate on public debt plus an exogenously given spread. Employing a analytical version of the model we show an example in which a permanent rise in the public debt ratio leads to a significant reduction in steady-state GDP even as r<g. Following McGrattan and Prescott (2017) we consider a calibrated model of the US economy including a rich set of features of national accounts, fixed assets, distribution of household incomes and demographics. The intuition (and even the orders of magnitude) from the simple analytical model carries over to this richer environment: the increase in the debt ratio, from 60 to 120 percent of GDP, is associated with a reduction in the capital stock of about 15 percent and a reduction in steady state GDP of about 8 percent