When Is (Performance-Sensitive) Debt Optimal?

Existing theories of debt consider a single contractible performance measure ("output"). In reality, many other performance signals are also available. It may seem that debt is no longer optimal; for example, if the signals are sufficiently positive, the agent should receive a payment even if output is low. This paper shows that debt remains the optimal contract under additional signals -- they only affect the face value of debt, but not the form of the contract. We show how the face value should depend on other signals, providing a theory of performance-sensitive debt.