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

constraints, and budgetary constraints. Each of these constraints warrants a brief discussionbefore we formally state the design problem.The first set of constraints concerns incentive compatibility: Both the manager’s and thefirm’s strategies (Σ m and Σ f , respectively) must be part of a Bayesian-perfect equilibrium,so that they choose strategies that maximize their expected payoffs—M( Σ|Ω ) and Π( Σ|Ω ),respectively, where M is managerial utility and Π is corporate profit—at every continuationgame, given their beliefs. 11 In addition, we require that the government’s strategy Σ G mustalso be part of a Bayesian perfect equilibrium. Given that the government is presumed tomaximize SV (·), this is functionally equivalent to assuming that the government has limitedability to commit and thus maximizes social welfare at each continuation stage. More formally,if Γ( SV (·), M(·), Π(·), Σ, Ω ) denotes the game established by our framework, and B( Γ ) denotesthe Bayesian perfect equilibria of Γ, incentive compatibility requires that Σ 1 , Σ 2 , Σ 3 ∈ B( Γ ).The second set of constraints concerns participation by the firm and the manager. Werequire that under the optimal bailout plan, the firm is still willing to invest, and the manager isstill willing to work for the firm. Thus, we require both parties to achieve expected payoffs thatexceed their reservation utilities (which we normalize at zero). Formally, individual rationalityrequires that both M ( Σ|Ω ) ≥ 0 and Π ( Σ|Ω ) ≥ 0.The third constraint concerns budgetary feasibility. Specifically, we require that the bailoutprogram achieves actuarial budget balance, so that the expected tax received by the government(through T 1 and T 2 ) can finance the expected bailout costs. 12 In effect, the actuarial budgetbalance requirement constitutes the government’s de facto participation constraint. Formally,actuarial budget balance requires thate 1·T 1 + 1 − e 1 · e2·T 2 − g ≥ 0 .The optimal bailout design problem can now be stated formally asmax SV ( Σ|Ω ) (3)〈Σ m ,Σ f ,Σ G〉subject to: (IC) : Σ m , Σ f , Σ G∈ B( Γ )(IR) : M( Σ|Ω ) ≥ 0; Π( Σ|Ω ) ≥ 0(BB) : e 1·T 1 + 1 − e 1 · e2·T 2 − g ≥ 0where (IC), (IR), and (BB) are the incentive, participation, and budget-balance constraints.11 For the exposition here, we slightly abused notation by not differentiating between the period-2 strategies/payoffsof the retained manager and those of her replacement (if the incumbent is fired). This is withoutloss of generality, because the incumbent and replacement cases are mutually exclusive, and because they faceidentical continuation payoffs / strategies as of period 2. That said, we are careful to distinguish in what followshow the retention of the incumbent affects her first period behavior.12 The assumption that the government actuarially balances its budget (instead of on a firm-by-firm basis) isnatural. The government regulates an entire population of firms and balance budgeting is a condition that holdsin the aggregate. Actuarial budget balancing is only the per-firm analog of an aggregate budget-balance condition.11