Accident Risk, Limited Liability and Dynamic Moral Hazard∗

A firm is subject to accident risk, which the manager can mitigate by exerting effort. An agency problem arises because effort is unobservable and the manager has limited liability. The occurrence of accidents is modelled as a Poisson process, whose intensity is controlled by the manager. We use martingale techniques to formulate the manager’s incentive compatibility constraints and to study the optimal contract. The latter is characterized by a differential equation with delay. The manager receives cash transfers only if no accident occurs during a sufficiently long period of time, while the firm is downsized if accidents are too frequent. This can be implemented by cash reserves, along with insurance, financial, and compensation contracts. The insurance contract involves a deductible and a bonus-penalty system. The financial contract consists of bonds that pay constant coupons until the firm enters financial distress. Covenants request that the firm be downsized when its liquidity ratio falls below a threshold. The manager’s compensation policy promises incentive wages when the accumulated performance of the firm is high enough. Our theoretical analysis also delivers new empirical implications about the dynamics of insurance premia and credit yield spreads.