A Model of Optimal Corporate Bailouts - Faculty of Business and ...

1.1 Sequential StructureThe model has three discrete time periods, t ∈ {0, 1, 2}, with no inter-temporal discounting,and three participants: a firm, a manager, and the government. The sequence is as follows:Time 0:• The government announces a bailout policy g, T 1 , T 2 , F G , the terms of whichare described below.Time 1: • The firm decides whether to invest in a project with initial cost, I 1 > 0.Time 2:• The project can be a “success,” yielding a gross payoff R > 0, or a “failure,” yieldinggross payoff 0.• The probability of success depends on managerial effort. We assume the probabilityof success is the manager’s effort level e 1 . Thus, the project fails with probability(1 − e 1 ). 5• If the project succeeds, the firm must pay the manager a contingent wage of w 1 ≥ 0and the government a tax of T 1 ≥ 0. 6 The game then ends.• If the project fails, the game transitions to time 2, described next.Effort should not be taken literally here. It is a modeling device to characterize a conflictof interest between managers and owners that needs to be remedied by paying a successcontingentwage. The conflict could equally well be a desire to build empires or not toperform unpleasant tasks (such as fighting bureaucracy or unions).• The government may readjust the remaining components of policy that are notyet sunk, g, T 2 , F G . This is tantamount to assuming that the government cannotcommit itself to a time-inconsistent policy.• The firm has a real option of either abandoning the project or “restarting” it for anadditional investment of I 2 > 0. If the firm restarts, the firm can dismiss or keep themanager, F F = {FIRE, RETAIN}.• If the firm restarts, it may use a government-provided cash subsidy (or “bailout”)of g ≥ 0, which effectively underwrites a portion of the reinvestment costs. Inaddition, if the firm accepts the subsidy g, and it has not already fired the manager,the government can force dismissal of the manager, F G = {FIRE, RETAIN}.5 At the cost of tractability, one could introduce alternative algebraic specifications translating effort into successprobability. That said, because “effort” has no natural measuring unit, we lose little or no generality from ourcurrent setup, which uses convex effort costs and basic parameter restrictions (c > (R + S)) to bound 0 ≤ e 1 ≤ 1.6 As is customary in this literature, we do not allow the manager to purchase the firm and thus circumventthe main incentive problem. The nonnegativity of wages is the functional equivalent of limited liability for themanager. It is easy to introduce private managerial benefits if the project succeeds. In contrast to wages, privatebenefits are obtained even without managerial effort. Like wages, they accrue only upon success. The conclusionsof our model remain unaltered, because the benefits simply serve to reduce the wage that the firm needs to paymanagers.8