Federal Reserve Bank of Minneapolis Research Department Sta ¤ Report November 2009 Bailouts , Time Inconsistency and Optimal Regulation

We make three points. First, ex ante e¢ cient contracts often require ex post ine¢ ciency. Second, the time inconsistency problem for the government is more severe than for private agents because re sale e¤ects give governments stronger incentives to renegotiate contracts than private agents. Third, given that the government cannot commit itself to not bailing out rms ex post, ex ante regulation of rms is desirable. Chari, and Kehoe thank the National Science Foundation for nancial support. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System. Recent experience has shown that governments can, will, and perhaps should intervene during nancial crises. Such interventions typically occur because governments seek to minimize the spillover e¤ects of bankruptcy and liquidation upon the broader economy. Such interventions during nancial crises alter the incentives for rms and nancial intermediaries ex ante. In this paper we ask how optimal regulation should be designed to maximize ex ante welfare taking into account the temptation for the government to intervene ex post. The theme that we explore in this paper is that, by altering private contracts, the prospect of bailouts reduces ex ante welfare. We view the prescription that governments should refrain from bailing out potentially bankrupt rms as unrealistic in practice. Benevolent governments simply do not have the power to commit themselves to such a prescription. A pragmatic approach to policy dictates that we take as given the incentives of governments to undertake bailouts and design ex ante regulation to minimize the ex ante costs of these ex post bailouts. In thinking about bailouts by governments, a central question is why would the government nd it optimal to bail out rms ex post. We argue that confronted with an ex post situation in which many rms are about to undergo costly bankruptcies, a benevolent government has a strong incentive to bail out rms. These ex post bailouts, however, may distort the ex ante incentives of managers and rms and reduce ex ante welfare. In such a situation, a government with commitment would commit itself not to undertake bailouts. If the government lacks such commitment, it will bail out rms ex post and the expectation of such bailouts will reduce ex ante welfare. In this sense, the government has a time inconsistency problem in bailout policy. We show that this time inconsistency problem creates a role for ex ante regulation. Such regulation can reduce the temptation of governments to bail out rms ex post and thereby raise ex ante welfare. In analyzing the incentives of benevolent governments to intervene and prevent costly bankruptcies ex post, the obvious question arises, why would rms ex ante enter into contracts which impose ex post costs? More generally, why would rms design contracts that feature ex post ine¢ cient outcomes? Here we develop a model in which the optimal contract between a rm and a manager speci es bankruptcy when outcomes are bad in order to provide proper incentives to managers to engage in e¤ort. Bankruptcy is costly in two ways: it reduces the output of the rm and it imposes nonpecuniary costs on the manager. We think of these nonpecuniary costs as arising both from stigma-like e¤ects on the managers career as well as loss of private bene ts from operating the rm. In the model the optimal contract is ex post ine¢ cient in the sense that, once the manager has exerted e¤ort, bankruptcy imposes costs on the owners of the rm and the manager. While these ex post ine¢ ciencies create a time inconsistency problem for the government by giving it an incentive to bailout rms ex post, they also create a time inconsistency problem for private agents by giving them an incentive to avoid costly bankruptcy by renegotiating their contracts ex post. Analyzing these incentives requires modeling the bene ts and costs of both renegotiation and bailouts. The bene ts are the reduction in costly bankruptcies. We assume that the costs arise from changes in the beliefs of private agents about future outcomes. In particular, if a rm ever agrees to renegotiate, private agents will believe that rm will always renegotiate in the future. Expectations of such renegotiations constrain future contracts and thereby reduce future welfare. Likewise, if a government ever bails out rms, private agents believe that the government will always bailout rms in the future. Expectations of such bailouts constrain future contracts and reduce future welfare. 2 In an environment without commitment, private agents and governments balance these bene ts and costs in designing their interventions. For the private agents, this balance implies that ex ante optimal contracts must satisfy a private sustainability constraint. For the government, this balance implies that ex ante optimal contracts must, in equilibrium, satisfy a sustainability to bailouts constraint. The parallel way we have modeled bene ts and costs for governments and private agents leads us to ask, Given that a contract has already been designed to be privately sustainable, why would it not be sustainable to bailouts? When deciding whether to renegotiate a given contract, the private agents involved in that contract consider the bene ts from eliminating bankruptcy of their rm at given prices. When the government decides to bail out rms, it takes into account the private bene ts per rm in the same way that private agents do, but, in addition, it also takes into account the bene ts to other rms from its intervention. These bene ts arise because by bailing out rms the government can reduce the aggregate amount of assets sold in the market place and thereby raise the prices of these assets. The idea is that bankruptcy is socially costly because it forces rms to sell their assets and these re sales reduce the value of assets in otherwise healthy rms. Bailouts help reduce re sales and the resulting negative price e¤ects that give rise to the social cost. Since governments take into account re sale e¤ects and private agents do not, the sustainability to bailouts constraint is tighter than the private sustainability constraint. Thus, a contract that is privately sustainable is not necessarily sustainable to bailouts. In this sense, the time inconsistency problem is for the government is more severe than it is for private agents. The greater severity of the time inconsistency problem for the government implies that the equilibrium in an economy with bailouts has lower welfare than in an economy without 3 bailouts. It also implies that ex-ante regulation can be desirable. Such regulation must be designed so that ex-post the government does not have an incentive to engage in bailouts. The incentive to bail out rms is large when the aggregate amount of assets in bankrupt rms is large. We show that the optimal ex-ante regulation is to impose a cap on quantity of assets used by each manager and a cap on the probability of bankruptcy. This cap on assets limits the size of individual rms and thus can be interpreted as a regulation that prevents rms from becoming too big. We refer to this regulation as a too-big-to-fail-cap. The cap on the probability of bankruptcy can be implemented by a cap on the debt to value ratio of the rm. The reason is that this ratio is an increasing function of the probability of bankruptcy so that a cap on the probability of bankruptcy is equivalent to a cap on the debt to value ratio. 1. A simple economy We begin with a simple static version of our benchmark economy. We use this version to show that, in order to provide incentives, optimal contracts often require ex post ine¢ ciency, in the sense that ex post all agents can bene t by altering the terms of the contract. This feature of the model makes optimal contracts time inconsistent, in the sense that optimal contracts without commitment di¤er from those with commitment, and, in particular, give lower welfare. Consider a model in which decisions are made at two stages: a rst stage, called the beginning of the period, and a second stage called the end of the period. There are two types of agents, called lenders and managers both of whom are risk neutral and consume at the end of the period. There is a measure 1 of managers and a measure 1 of lenders.