Government Guarantees and Financial Stability · Government Guarantees and Financial Stability 4 /...

Government Guarantees and Financial Stability

F. Allen ‡ E. Carletti † I. Goldstein ‡ A. Leonello ‡

†Bocconi University and CEPR

‡University of Pennsylvania

Government Guarantees and Financial Stability 1 / 21

Introduction

Government guarantees to financial institutions are common all overthe world and take different forms

Deposit insurance or implicit guarantees for a bailout

The recent crisis has renewed the debate on their desirability:

They help preventing the occurrence and the consequences of panics(Diamond and Dybvig (1983))But, they introduce moral hazard, encouraging banks to take excessiverisksOverall effect is unclear


What we do in the paper

We present a model to analyze the trade-off involved in the choice ofthe level of government guarantees

What is needed:

Endogenize the probability of a run on banks to see how it is affectedby banks’risk choices and government guaranteesEndogenize banks’risk choices to see how they are affected bygovernment guarantees, taking into account investors’expected runbehavior

We put all these ingredients together and derive some surprisingresults on different guarantee schemes

Existing models —e.g., Boot and Greenbaum (1993), Cooper and Ross(2002), and Keister (2014) —don’t have all these ingredients


Starting point: Diamond and Dybvig (DD, 1983)

Banks provide risk sharing against early liquidity needs to depositors,thus improving investors’welfare

But, the deposit contracts expose banks to the risk of a run asdepositors may panic out of self-fulfilling beliefs

Deposit insurance eliminates runs and restores full effi ciency

It solves depositors’coordination failure without entailing anydisbursement for the government

However, reality is much more complex

Even with deposit insurance, runs might still occur due to adeterioration in the banks’fundamentalsGiven this, should the government protect depositors only againstilliquidity due to coordination failures or also against bank insolvency?


Our framework

We build on Goldstein and Pauzner (2005), where

depositors’withdrawal decisions are uniquely determined using theglobal-game methodologythe run probability depends on the banking contract (i.e., amountpromised to early withdrawers), and the bank decides on it taking intoaccount its effect on the probability of a run

We add a government to this model to study how the government’sguarantees policy interacts with the banking contract and theprobability of a run


Decentralized economy

Two period model, where banks raise deposits from risk-averseconsumers and invest in risky projects

At the interim date, each depositor receives an imperfect signalregarding the fundamentals and decides when to withdraw

Runs occur when the fundamentals are below a unique threshold andcan be

panic-based runs (out of self fulfilling beliefs), orfundamental-based runs (when fundamentals are low enough)

Two ineffi ciencies: ineffi cient fundamental runs and too little risksharing to depositors


Introducing government guarantees

Main scope is to reduce the probability of runs by guaranteeingdepositors a minimum repayment

We consider two different guarantee schemes:1 Against panics only : Depositors are guaranteed if the bank’s project issuccessful irrespective of what the other depositors do (as in DD)

2 Against runs and bank failures: Depositors are guaranteed irrespectiveof what the others do and irrespective of the bank’s available resourcesso that they are protected against both illiquidity and insolvency


Guarantees against panics only

As in DD, this scheme prevents panic runs (but not fundamentalruns) without entailing any disbursement

Unlike DD, in response banks offer a greater rate to earlywithdrawing depositors

This improves risk sharing but it also increases the probability offundamental-based runs and possibly overall instability (consistentwith evidence in Demirguc-Kunt and Detragiache, 1998)

First effect dominates so that welfare is higher than in thedecentralized solution, but no full effi ciency


Guarantees against runs and bank failures

Probability of both types of runs runs is reduced but runs still occur,leading to actual disbursements for the government

Given this, there is now an ineffi ciency

Banks internalize the effect of their choices on the probability of a runbut not on the cost to provide the guaranteeThere is a wedge between the deposit rate set by banks and the onethe government would like to set

Interestingly, banks set too high deposit rates and thus take toomuch risk (typical moral hazard) or too low

It depends on whether the government pays more to depositors at thefinal date when the bank fails or when there is a run and the bank isilliquid

Despite this, this scheme may lead to higher welfare than previousone as it reduces runs much more


The basic model I

Three date (t = 0, 1, 2) economy with a continuum [0, 1] of banksand consumers

Banks raise one unit of funds from depositors in exchange for ademandable deposit contract and invest in a risky project

The project returns 1 if liquidated at date 1 and R̃ at date 2 with

R̃ ={R > 1 w. p. p(θ)0 w. p. (1− p(θ))

with θ ∼ U [0, 1], p′(θ) > 0 and Eθ [p(θ)]R > 1. For simplicity,p(θ) = θ


The basic model II

Consumers are risk-averse (RRA > 1 for any c ≥ 1) and endowedwith 1 unit each at date 0

At date 0 they deposit at the bank in exchange for a deposit contract(c1, c̃2)

Consumers are ex ante identical but each has probability λ ofsuffering a liquidity shock and having to consume at date 1(uncertainty is resolved at the beginning of date 1)

Consumers derive utility both from consuming at date 1 or 2 andfrom enjoying a public good g

U (c, g) = u(c) + v(g)

with u′(c) > 0, v ′(g) > 0, u′′(c) < 0, v ′′(g) < 0, u(0) = v(0) = 0

Banking sector is competitive


Depositors’information

At the beginning of date 1, each depositor receives a private signal xiregarding the fundamental of the economy θ of the form

xi = θ + εi ,

with εi ∼ U [−ε,+ε] being i.i.d. across agents. Most of the time, ε isvery close to 0

Based on the signal, depositors update their beliefs about thefundamental θ and the actions of the other depositors

Early depositors always withdraw at date 1Late depositors withdraw at date 1 if they receive a low enough signal

The bank satisfies early withdrawal demands by liquidating itsinvestments. If proceeds are not enough, depositors receive a pro-ratashare


The decentralized solution: Depositors’withdrawals

Lower dominance Intermediate Upper dominance| | |

late θ(c1) late θ∗(c1) θ(c1)depositors depositors no latewithdraw withdraw depositoras low θ because of withdraws

− fundamental θ and n − no runsruns − panics

where θ(c1) is the solution to

u(c1) = p(θ)u(1− λc11− λ

R)

and θ∗(c1) to ∫ 1c1

n=λp(θ∗)u(

1− nc11− n R) =

∫ 1c1

n=λu(c1) +

∫ 1

n= 1c1

u(1n)

Both thresholds θ(c1) and θ∗(c1) increase with c1, which measures bank risk taking


The decentralized solution: The bank’s choice

Given depositors’withdrawal decisions, at date 0 each bank choosesc1 to maximize:∫ θ∗(c1)

0u (1) dθ +

∫ 1

θ∗(c1)

[λu(c1) + (1− λ)θu

(1− λc11− λ

R)]dθ

+v(g)

The optimal cD1 > 1 trades off better risk sharing with higher

probability of runs(

∂θ∗(c1)c1

> 0)

Two ineffi ciencies:

Banks offer less risk sharing in anticipation of the runRuns lead to ineffi cient liquidation of bank investment for θ∈ (θ(1), θ∗(c1))


Government guarantees against panics only

Depositors are guaranteed to receive c = 1−λc11−λ R when the bank’s

project is successful at date 2, irrespective of how many depositorshave withdrawn at date 1

Panic runs are eliminated but fundamental runs remain for θ∈ [0, θ(c1)]Bank chooses c1 to maximize∫ θ(c1)

0u(1)dθ +

∫ 1

θ(c1)

[λu(c1) + (1− λ)θu

(1− λc11− λ

R)]dθ

+∫ 1

0v(g)dθ

Result: cDD1 > cD1 . Thus, θ(cDD1 ) > θ(cD1 ) and possiblyθ(cDD1 ) > θ∗(cD1 )

Note: No distortion in the choice of cDD1 as the guarantee entails nodisbursement for the government


Government guarantees against runs and bank failure I

Depositors are guaranteed to receive c > 1 whenever their bank isunable to repay them the promised repayments

Runs occur now for θ < θ∗(c1, c), with∂θ∗(c1,c )

∂c1> 0 and ∂θ∗(c1,c )

∂c < 0

Bank chooses c1 to maximize∫ θ∗

0u(c)dθ +

∫ 1

θ∗[λu(c1) + (1− λ)(θu

(1− λc11− λ

R)+

+ (1− θ) u (c))]dθ + E [v (g , c∗1 , c)]

where θ∗ = θ∗(c1, c), and

E [.] =∫ θ∗

0v (g − c + 1) dθ+

∫ 1

θ∗[θv(g) + (1− θ)v (g − (1− λ)c)] dθ

Result: c IN1 > cD1 with dc IN1dc > 0


Government guarantees against runs and bank failure II

Both types of runs occur still and deposit insurance entails now adisbursement, thus introducing an ineffi ciency

The bank takes E [v (g , c∗1 , c)] as given when choosing c1, differentlyfrom what a planner would do

Result: c IN1 < cSP1 if

[θ∗(c1, c)v(g) + (1− θ∗(c1, c))v(g − (1− λ)c)− v(g − c + 1)] < 0

and c IN1 > cSP1 otherwise

There is not always moral hazard! it depends on whether it is morecostly to guarantee all depositors in the case of runs or (only) thelate ones against bank failure


Comparing government guarantees: An example

Consider

u(c) + v(g) =(c + f )1−σ

1− σ− (f )

1−σ

1− σ+(g + f )1−σ

1− σ− (f )

1−σ

1− σ,

σ = 3; R = 5; λ = 0.3, f = 4 and g = 1.5


A numerical Example

Table 2 : g = 1.5 [θθ∗

] [c1c2

]c

[E [u (c1, c2, c)]E [v(g , c)]

][SW (c1, c2, g , c)]

Decentralized Economy0.4514360.463162

1.00764.98372

00.01392020.0147211

0.0286413

Guarantees against panic runs0.488273

θ1.107624.7694

1−λc11−λ R

0.0139450.147211

0.028666

Guarantees against runsand bank failure

0.05762630.0790303

1.153974.67006

1.0550.01638070.0123515

0.0287322

Social Planner0.1701410.331056

1.4111444.11878

1.127020.0161830.013117

0.0293

Comparing government guarantees: An example

1 Both guarantees improve upon the decentralized solution2 Guarantee against panics only: It removes panics but leads to morecrises because cDD1 > cD1

3 Guarantee against panics and bank failure: Both runs still occur butcrises are much less likely despite the higher c1 (c IN1 >c

DD1 > cD1 )

4 Broader guarantee scheme achieves higher level social welfare


Conclusions

Government guarantees present a complicated trade-off andunderstanding it requires endogenizing banks’choices and depositors’behavior in response to government intervention

A scheme resembling the one in DD removes panics and does notentail any disbursement for the government, but it may increase bankinstability

A scheme protecting against runs and bank failures is more effectivein reducing the likelihood of runs and may be welfare superior

Although it is ineffi cient in terms of the deposit contract and theamount of guarantee chosen by the government

Possible extensions: no commitment, feedback loop of governmentbudget for financial stability, etc.


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