Default risk premia on government bonds in a quantitative macroeconomic model

We develop a macroeconomic model where the government does not guarantee to repay debt. We ask whether movements in the prices of government bonds can be rationalized by lender's unwillingness to roll over debt when the outstanding debt level exceeds a government's repayment capacity. Default occurs if a worsening state of the economy leads to a build-up of debt that exceeds the government's ability to repay. Investors are unwilling to engage in a Ponzi game and withdraw lending in this case and thus force default at an endogenously determined fractional repayment rate. Interest rates on government bonds reflect expectations of this event. We analytically show that there exist two equilibrium bond prices. Our numerical analysis shows that, at moderate debt-to-gdp levels, default premia hardly emerge in the low risk equilibrium. High risk premia can either arise at high debt-to-gdp ratios, where even small changes in fundamentals lead to steeply rising interest rates, or as realizations of the high risk equilibrium.