Debt-Maturity Management with Liquidity Costs

Abstract

We characterize the optimal debt-maturity management problem in the presence of liquidity costs. A government issues an arbitrary number of finite-maturity bonds and faces income and interest-rate risk, which can tempt it to default. Optimal issuances are spread out across maturities and are given by the ratio of a value gap over a liquidity coefficient that measures the price impact. The value gap is the proportional difference between the bond prices obtained by discounting with the international interest rates and with the domestic discount factor. This characterization allows us to quantify the contribution of different economic forces—impatience, yield-curve riding, expenditure smoothing, self-insurance, credit risk, and default incentives—in shaping the optimal debt maturity distribution. In an application, we estimate the liquidity coefficients using Spanish debt auction data and exploit the framework to evaluate Spanish debt management practices.