A P Theory of Government Debt and Taxes

An optimal tax and government borrowing plan in a setting with tax distortions (Barro, 1979) locally pin down the marginal cost of servicing government debt, called marginal p. An option to default determines the government’s debt capacity and its optimal state-contingent risk management policies make its debt risk-free. Optimal debt-GDP ratio dynamics are driven not only by three widely discussed forces, 1.) a primary deficit, 2.) interest payments, and 3.) GDP growth, but also by 4.) hedging costs. Hedging fundamentally alters debt transition dynamics and equilibrium debt-capacity, which are at the center of the recent 'r-g' and debt sustainability discussions. We calibrate our model and make comparative dynamic quantitative statements about the debt-GDP ratio transition dynamics, equilibrium debt capacity, and how long it will take the US to attain debt capacity.