The role of commitment in bank runs Huberto M. Ennis Richmond Fed - PowerPoint PPT Presentation

Introduction A general framework Commitment No commitment Indirect mechanisms Reputation Conclusion The role of commitment in bank runs Huberto M. Ennis Richmond Fed Diamond-Dybvig 36 Conference - Wash U 29-30 March, 2019 • • • This presentation does not necessarily reflect the views of the Federal Reserve

Introduction A general framework Commitment No commitment Indirect mechanisms Reputation Conclusion Introduction Diamond and Dybvig’s (1983) model is considered one of the first “coherent explanation[s] of illiquid banking system portfolios” (Wallace, 1990) and the possibility of inefficient, panic-based bank runs Andolfatto, Nosal, Sultanum (2016) suggest that an important contribution of DD was offering “a prescription for how to prevent bank runs” → based on suspension of convertibility Wallace (1990) argues that (some form of) suspension was typical during banking crises in the U.S. before the introduction of deposit insurance in the 1930s however, in the canonical DD, suspension of convertibility is an off-equilibrium threat Ennis and Keister (2009) also show that DD suspensions can be non-credible threats In general, this suggests that lack of commitment may play a role in our understanding of bank runs

Introduction A general framework Commitment No commitment Indirect mechanisms Reputation Conclusion Are policymakers able to commit to their ex-ante strategies? Stern and Feldman (2004): “ Many of the existing pledges and policies meant to convince creditors that they will bear market losses when large banks fail are not credible ” In October 2008, bank regulators and the U.S. Treasury created the Transaction Account Guarantee (TAG) program, which insured all bank deposits in checking accounts above the $250,000 coverage already provided by the FDIC a maximum of over $800 billion on deposits were covered by the program Gruenberg (FDIC vice-chair at the time) “ this action being proposed today... is perhaps the most extraordinary ever taken by an FDIC Board ” i.e., not a component of a pre-set contingent plan During the 2001 crisis in Argentina: banking authority suspended payments to depositors court system intervened and mandated payment on a case-by-case basis — lots of them (Ennis and Keister, 2009) multiple government agencies can undermine commitment

Introduction A general framework Commitment No commitment Indirect mechanisms Reputation Conclusion Role of commitment in the economics of bank runs DD bank runs: outcomes of an incomplete information game the revelation principle has been used to simplify the analysis in some cases, off-equilibrium suspension of payments (convertibility) can produce uniqueness of equilibrium but, suspensions may not be credible Under lack of commitment → can recover multiplicity multiplicity implies that direct mechanisms cannot be applied without loss of generality Without relying on the revelation principle, studying implementation becomes a very complex matter may need to consider any and all possible mechanisms that one can come up with some recent work dealing with multiplicity of equilibria in DD-type environments proposed ingenious indirect mechanisms that produce good outcomes and uniqueness generally, those mechanisms rely on commitment

Introduction A general framework Commitment No commitment Indirect mechanisms Reputation Conclusion Outline for the talk Present a general framework Consider the case under commitment Consider the case under no-commitment Discuss indirect mechanisms Discuss reputation as a substitute for commitment Conclude

Introduction A general framework Commitment No commitment Indirect mechanisms Reputation Conclusion Contracting with imperfect commitment Follow the principal-agent framework of Bester and Strausz (2001) Consider a contracting problem between a principal and one or more agents the principal’s problem consists of selecting an allocation z = ( x , y ) the principal can commit to x but not to y each agent i ∈ I is privately informed about her type t i ∈ T i t ∈ T ≡ × i ∈ I T i has a prob. distribution p ( t ) ∈ P ( T ) after agent i observes her type t i , her conditional probability about other agents’ types is p ( t − i | t i ) the principal knows the distribution p ( t ) , but not t when agents’ types are t , the payoff of the principal is V ( x , y ; t ) and the payoff of each agent i is U i ( x , y ; t )

Introduction A general framework Commitment No commitment Indirect mechanisms Reputation Conclusion A mechanism or contract is a pair Γ = ( M , x ) : specifies for each agent i ∈ I a message space M i and a rule x : M → X where M ≡ × i ∈ I M i Γ induces a game between the principal and the agents after agent i learns her type, she chooses a message according to a reporting strategy q i : T i → Q ( M i ) where Q ( M i ) is the set of prob. distr. over M i the resulting m ∈ M determines x ( m ) ∈ X then the principal updates beliefs about agents’ types p : M → P ( T ) and chooses y ∈ F ( x ( m )) ⊂ Y → the decision on x may restrict the feasible choices for y the principal’s choice depends on t only through messages m consider the PBEs of this game agents anticipate the principal’s behavior y when choosing which message to send p obey Bayes’ rule on the support of agents’ reporting strategies

Introduction A general framework Commitment No commitment Indirect mechanisms Reputation Conclusion The vector ( q , p , y , x | M ) is incentive feasible if ( q , p , y ) is a PBE given the mechanism Γ ( M , x ) For a given M , the principal’s problem is to find ( q , p , y , x ) that maximizes his expected payoff subject to ( q , p , y ) being a PBE given x often, agents have the option to refuse to contract with the principal, captured with an individual-rationality constraint the principal’s overall problem includes the choice of an appropriate message set M note that Bester and Strausz, in the mechanism-design tradition, let the principal choose the PBE ( q , p , y ) The mechanism Γ = ( M , x ) is said to be a direct mechanism if M = T : in the game induced by Γ , each agent i simply announces some type in T i

Introduction A general framework Commitment No commitment Indirect mechanisms Reputation Conclusion The bank-run case The allocation z is: an investment decision (in some cases, non-trivial; e.g., Cooper and Ross, 1998 and Peck and Shell, 2010) a schedule of payments to depositors X and Y respect resource feasibility and sequential service Agent’s types are t = 0 (impatient) and t = 1 (patient) in some cases (e.g., Ennis and Keister 2016), agents are learning information as the game progresses agents’ (depositors) payoffs: u ( c 0 ) + tv ( c 1 ) principal’s (bank) payoff: under commitment, often assumed competition → max ex-ante expected utility of depositors (Andolfatto and Nosal (2008) consider a “self-interest” banker) without commitment, things are more complicated In general, we do not let the principal choose which PBE obtains. If there are multiple PBEs, then an equilibrium selection process (such as sunspots) is used

Introduction A general framework Commitment No commitment Indirect mechanisms Reputation Conclusion The commitment case When Z = X the Bester-Strausz framework reduces to the full commitment case note that the elements p and y are no longer relevant The revelation principle: When Z = X , if ( q , x | M ) is incentive feasible, then there is a direct mechanism Γ d = ( T , ˆ x ) and an incentive feasible ( ˆ x | M ) such that q , ˆ ( ˆ q , ˆ x | M ) and ( q , x | M ) are payoff-equivalent and ˆ q i ( t i ) = 1 for all t i ∈ T i in principle, this can greatly simplify the principal’s problem: choose M = T and restrict to allocation-functions z : T → X that satisfy incentive compatibility: E [ U i ( z ( t )) | t i ] ≥ E [ U i ( z ( ˜ t , t − i )) | t i ] for all ˜ t ∈ T i and all i note that IC takes as given truthful reporting by others the game induced by the mechanism may have multiple PBEs, making final payoff sensitive to equilibrium selection

Introduction A general framework Commitment No commitment Indirect mechanisms Reputation Conclusion Bank runs under commitment Original DD environment: I ⊂ R , a continuum of agents with independent types a version of the LLN holds ⇒ after p ( 0 ) withdrawals an extra withdrawal reveals a run threat of suspension makes this an off-equilibrium outcome aggregate uncertainty → suppose p ( 0 ) is a random variable suspension becomes costly → deriving the optimal mechanism is much harder De Nicol´ o (1996) uses a model with smooth preferences (depositors consume in both periods, with different marginal utilities for patient and impatient) and aggregate uncertainty all agents (naturally) report to the bank (early and late) exploit independence and the continuum of agents to infer the aggregate state at low cost commitment is crucial to induce uniqueness (off-equilibrium suspension and priority of claim with a backward induction argument – a predecessor of Green and Lin, 2003)