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

• ne 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

• r 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 ti ∈ Ti t ∈ T ≡ ×i∈I Ti has a prob. distribution p(t) ∈ P(T) after agent i observes her type ti, her conditional probability about other agents’ types is p(t−i | ti) 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 Ui(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 Mi and a rule x : M → X where M ≡ ×i∈IMi

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 qi : Ti → Q(Mi) where Q(Mi) is the set of prob. distr. over Mi 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

• ften, 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 Ti

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(c0) + tv(c1) 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

• btains. 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 Γd = (T, ˆ x) and an incentive feasible (ˆ q, ˆ x | M) such that (ˆ q, ˆ x | M) and (q, x | M) are payoff-equivalent and ˆ qi(ti) = 1 for all ti ∈ Ti

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[Ui(z(t)) | ti] ≥ E[Ui(z(˜ t, t−i)) | ti] for all ˜ t ∈ Ti 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´

• (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)

Introduction A general framework Commitment No commitment Indirect mechanisms Reputation Conclusion

Peck and Shell (2003) also study aggregate uncertainty with an explicit sequential service constraint

they study more general preferences for agents than DD and various specification of sequential service

agents and the bank only observe withdrawals (leading eg.) agents do not know their place in line

they show that the constrained-optimal mechanism is consistent with multiple equilibria and runs

high marginal utility of impatient agents can make IC constraints bind

commitment plays a role when IC constraints are binding

under full lack of commitment, the Peck-Shell allocation is not a best response in the simultaneous-move game between agents and the bank with imperfect (partial) commitment, if the bank can set the early withdrawal payouts before agents move, but not the late withdrawal payouts, then the Peck-Shell allocation is an equilibrium

Introduction A general framework Commitment No commitment Indirect mechanisms Reputation Conclusion

Imperfect commitment With imperfect commitment, the procedure of the standard revelation principle is no longer applicable

a contract Γ = (M, x) may support an outcome that cannot be replicated by a direct mechanism Γd = (T, ˆ x) Bester and Strausz (2001) show that a version of the revelation principle holds when there is only one agent

the argument, however, does not extend to multiple agents (Bester and Strausz (2000))

it becomes “unclear” how to characterize the set of implementable allocations

• ne alternative (in some cases) is to find a mechanism that

implements the first-best

Introduction A general framework Commitment No commitment Indirect mechanisms Reputation Conclusion

Bank runs under no commitment Ennis and Keister (2010) follow DD in assuming I ⊂ R: a continuum of agents with independent types

• nly withdrawals observed

after p(0) withdrawals → run revealed

at that point in a run (ex-post), immediate suspension is not

• ptimal

some impatient agents still need to withdraw making extra payments depletes resources, reducing the payoff from waiting and validating the run

the optimal “direct” mechanism under imperfect commitment admits a run equilibrium (when prob. of run is small enough)

whether other more general mechanisms could rule out multiplicity has not yet been studied

In a similar environment, Keister (2016) and Mitkov (2017) study bank runs and bailouts under lack of commitment

Introduction A general framework Commitment No commitment Indirect mechanisms Reputation Conclusion

Green and Lin (2003): I is finite with independent types

a natural setting to study aggregate uncertainty together with an explicit specification of sequential service

all agents report to the bank (not just those withdrawing) agents know their place in line (with enough accuracy)

the optimal mechanism (respecting sequential service) is incentive compatible and delivers a unique equilibrium

does not rely on commitment (recursive solution)

Ennis and Keister (2009): with correlated types, multiplicity and runs can be recovered

the ability to commit to specific patterns of late payments could matter again to deal with multiplicity

Introduction A general framework Commitment No commitment Indirect mechanisms Reputation Conclusion

Dealing with multiplicity – Indirect mechanisms Two reasons limiting the generality of direct mechanisms

(1) multiplicity of PBE (2) lack of commitment with multiple agents

lack of commitment also can bring multiplicity back

Some work dealing with (1) using indirect mechanisms

Cavalcanti and Monteiro (2016)

agents have the option to “segregate” some investment and leave it at the bank an agent that withdraws and “segregates” investment, revealing a run, triggers a sharp suspension of payments

Andolfatto, Nosal, and Sultanum (2017)

introduce a third report (aside from patient and impatient) with payoffs such that reporting impatient for a patient agent is dominated by this third option a report of the third option triggers full suspension

These indirect mechanisms rely (heavily) on commitment, which limits applicability in dealing with (2)

Introduction A general framework Commitment No commitment Indirect mechanisms Reputation Conclusion

Dynamic games and reputation A possible alternative to directly assuming commitment is to introduce reputational concerns There are two approaches to reputations in the repeated games literature (Mailath and Samuelson, 2006)

Sustainable plans: an equilibrium of the repeated game can involve actions along the equilibrium path which are not Nash equilibrium of the stage game

no fundamental changes to the game except for repetition usually not aimed (effective) at reducing multiplicity

The adverse selection approach: players are uncertain about a key aspect of their opponent → a small probability of facing a “commitment type”

this changes the original (stage) game

Both approaches rely on discount factors close to unity

unlikely during periods of general financial distress

• r, maybe crises are (partly) triggered by high discount rates

undermining reputation-induced credibility

Introduction A general framework Commitment No commitment Indirect mechanisms Reputation Conclusion

Conclusion The degree of commitment to contracts can matter for the economics of bank runs Some form of imperfect (partial) commitment may strike the right balance

full commitment permits “extreme” arrangements, such as priority-of-claims or, even, segregation of assets full lack of commitment can sharply reduce the role of banking but, placing some limits on the ability to commit seems reasonable in many cases (eg., full suspensions)

⇒ important to be explicit about commitment assumptions On the technical front, imperfect commitment comes with complications

no revelation principle can bring back multiplicity limits the set of indirect mechanisms to considered

Introduction A general framework Commitment No commitment Indirect mechanisms Reputation Conclusion

Closing thought A philosophical divide (at the extremes)

Are we trying to provide a coherent explanation for the possibility of inefficient (self-fullfiling) runs? → imperfect commitment may help Or, are we trying to assert that inefficient runs are not an accurate description of reality by portraying them as theoretical impossibilities? → indirect mechanisms and reputations may help