Credit Booms, Financial Crises and MacroprudentialPolicy

Mark Gertler, Nobuhiro Kiyotaki, Andrea Prestipino

December 2018

What We Do

I We develop a model of banking panics in which:

1. Banking crises are usually preceded by credit booms

2. Credit booms often do not result in crises, i.e. good booms

I We study Macroprudential regulation in this model:

I How does Macroprudential policy weigh the benefits of preventing acrisis against the costs of stopping a good boom?

I What are the effects of macroprudential policy and the features ofoptimal regulation?

I Unintended consequences of regulation; Countercyclical buffers

Banking Crises in the Data (Schularick and Taylor)

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Credit Growth at time t-2 (" from Mean)

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Cre

dit G

row

th a

t tim

e t-

1 ( "

from

Mea

n)

No Crisis at time tCrisis at time t

Framework

I Endowment economy version of GKP (2018)

I Focus on how beliefs driven fluctuations can reproduce key empiricalproperties of banking crises in the data:

I Boom bust cycles in credit

I Unpredictability of crises

I Macroprudential regulation

Model Overview

I Capital is fixed Kt = K = 1 (normalized to unity)

I(Kbt

)intermediated by banks;

(Kht

)directly held by households :

1 = Kht + Kbt

I Households direct finance entails a quadratic deadweight loss

α

2

(Kht

)2

I Resource constraint is:

Yt = Zt −α

2

(Kht

)2= Ct

where Zt is an exogenous productivity shock

Marginal Rates of Return on Capital

Qt ≡ price of capital

I Intermediated capital

Rbt+1 =Zt+1+Qt+1

Qt

I Directly held

Rht+1 =1

1+αKhtQt

Rbt+1

i.e. increasing marginal cost of direct finance

Household and Bank Intermediation

���������

������ ��� ��� ����� � � ��

Qt Kt

Nt

Dt

HOUSEHOLDSCAPITAL

����������� �������������! �"����#�$��%

NO BANK RUN EQUILIBRIUM

Qt Kt

K

BANK RUN EQUILIBRIUM

HOUSEHOLDSQ*t K

CAPITAL

K

h

b

Bankers

I Objective

Vt = EtΛt,t+1[(1− σ)nt+1 + σVt+1]

I Net worth nt accumulated via retained earnings - no new equityissues

nt+1 = Rbt+1Qtk

bt − Rtdt if no run

= 0 if run

I Balance sheetQtk

bt = dt + nt

Deposit Contract

Rt ≡ deposit rate; Rt+1 ≡ return on depositspt ≡ run probability; xt+1 < 1 ≡ recovery rate

I Deposit contract: (One period)

Rt+1 =

{Rt with prob. 1− ptxt+1Rt with prob. pt

Limits to Bank Arbitrage

I Moral Hazard Problem:

I After banker borrows funds at t, it may divert fraction θ of assets forpersonal use.

I If bank does not honor its debt, creditors can

I recover the residual funds andI shut the bank down.

I ⇒ Incentive constraint (IC)

θQtkbt ≤ Vt

Solution

I Can show Vt = ψtnt with ψt ≥ 1 and independent of nt

I Combine with IC → endogenous capital requirement :

κt ≡nt

Qtkbt≥ θψt

I Note:

I ψt countercyclical→ market capital requirements relaxed in bad timesI nt ≤ 0⇒ bank cannot operate (key for run equilbria)

Bank Runs

I Self-fulfilling ”bank run” equilibrium (i.e. rollover crisis) possible if:

I A depositor believes that if other households do not roll over theirdeposits, the depositor will lose money by rolling over.

I Condition met iff banks’ net worth nt goes to zero during a run

I nt = 0 → banks cannot operate

Conditions for Bank Run Equilibrium (BRE)

I Run equilibrium exists at t + 1 if

(Q∗t+1 + Zt+1

)Kbt < Dt R̄t (1)

where Q∗t+1 ≡ is the liquidation price:

Q∗t = Et{Λt,t+1(Zt+1 + Qt+1} − αKht

evaluated at Kht = 1

I ιt+1 ≡ sunpot variable; if ιt+1 = 1 depositors panic when runpossible

I Run occurs if (i) equation (1) is satisfied and (ii) ιt+1 = 1

Run Probability pt

I Assume sunspot occurs with probability κ.I → The time t probability of a run at t + 1 is

pt = Pr t{Zt+1 < ZRt+1} · κ

I ZRt+1 is the threshold value below which a run is possible

Q∗t+1(ZRt+1

)+ ZRt+1 =

Dt R̄t

Kbt

→ Higher leverage ratios Dt R̄tKbt

increase run probability

Run Equilibrium

0 1

No Run-Equilibrium Possible

Run-Equilibrium Possible

Negative Productivity Shock

B

A

Dt R̄t

Kb

Qt∗+1

(ZRt+1

)+ ZRt+1

Run Equilibrium

0 1

No Run-Equilibrium Possible

Run-Equilibrium Possible

Higher Leverage Ratio

BA

Dt R̄t

Kb

Qt∗+1

(ZRt+1

)+ ZRt+1

Run After a Negative 2 std Shock

0 10 20 30 40 50 60-2.5

-2

-1.5

-1

-0.5

0

% "

from

SS

Productivity

0 10 20 30 40 50 600

1

2

3

4

5

6

Leve

l (pc

t)

Run Probability

0 10 20 30 40 50 60-100

-80

-60

-40

-20

0

% "

from

SS

Bank Net Worth

0 10 20 30 40 50 60

Quarters

-100

-80

-60

-40

-20

0

% "

from

SS

Bank Intermadiation

0 10 20 30 40 50 60

Quarters

200

220

240

260

280

300

Leve

l Ann

ual B

asis

Poi

nts

Excess Return: ER b-Rfree (10 years)

0 10 20 30 40 50 60

Quarters

-8

-6

-4

-2

0

% "

from

SS

Output

Sunspot No Sunspot

Run after a sequence of bad shocks

Boom leading to the bust: news driven optimism

I Productivity:

Zt+1 = ρZt + �t+1

I Normally, E{�t+1} = 0

I Occasionally, bankers receive news about future productivity

I If news at t, bankers learn that unusually large realization �tB of size

B > 0 will happen at tB ∈ {t + 1, ..., t + T} with prob. PB0 < 1

I Pr t{tB = t + i} is a truncated Normal (discrete approx.)

I Agents update Pr t+i and PBt+i by observing �t+i

I Prob. at t + i of shock at t + i + 1 is Pr t{tB = t + i + 1} · PBt+i

Beliefs Driven Credit Boom

t=1

t=5.5

t=11

0.15

0.3

Prior cond. prob. of shock happening at time t

t=1

t=5.5

t=11

0

0.2

0.4

0.6

0.8

1Beliefs Evolution

PBt

Pr tftb = t + 1g

t=1

t=5.5

t=11

0

0.5

1

1.5

2

% "

from

SS

Productivity

Zt

EtZ

t+4

t=1

t=5.5

t=11

-0.5

0

0.5

1

% "

from

SS

Output

t=1

t=5.5

t=11

0

5

10

15

20

% "

from

SS

Credit: Q " Kb

t=1

t=5.5

t=11

0.1

0.2

0.3

Leve

l

Prob. of being in crisis zone: Pr { Zt+1

Boom Leading to a bust

0 10 20 30 40 50 60-3

-2

-1

0

1

2

% "

from

SS

Expected Productivity

0 10 20 30 40 50 60-3

-2

-1

0

1

2

% "

from

SS

Realized Productivity

Zt

ZRt+1

0 10 20 30 40 50 60-100

-50

0

50

% "

from

SS

Bank Intermediation

0 10 20 30 40 50 600

5

10

Leve

l (pc

t)

Run Probability (if no boom)

0 10 20 30 40 50 60-100

-50

0

50 %

" fr

om S

S

Bank Net Worth

0 10 20 30 40 50 60-10

-5

0

5

% "

from

SS

Output

0 10 20 30 40 50 60

Quarters

-100

-50

0

50

% "

from

SS

Capital Ratio: 5

0 10 20 30 40 50 60

Quarters

-15

-10

-5

0

5

% "

from

SS

Asset Price

0 10 20 30 40 50 60

Quarters

150

200

250

300

Leve

l Ann

ual B

asis

Poi

nts Excess Return: ER

b-Rfree (10 yrs)

Sunspot observed No Sunspot observed

Run After Credit Boom

False Alarms

0 10 20 30 40 50 60-3

-2

-1

0

1

2

% "

from

SS

Expected Productivity

0 10 20 30 40 50 60-3

-2

-1

0

1

2

% "

from

SS

Realized Productivity

Zt

ZRt+1

0 10 20 30 40 50 600

5

10

15

20

% "

from

SS

Bank Intermediation

0 10 20 30 40 50 600

5

10

Leve

l (pc

t)

Run Probability (if no boom)

0 10 20 30 40 50 60-10

0

10

20

30 %

" fr

om S

S

Bank Net Worth

0 10 20 30 40 50 600

0.5

1

% "

from

SS

Output

0 10 20 30 40 50 60

Quarters

-5

0

5

10

% "

from

SS

Capital Ratio: 5

0 10 20 30 40 50 60

Quarters

-1

0

1

2

3

% "

from

SS

Asset Price

0 10 20 30 40 50 60

Quarters

190

200

210

220

Leve

l Ann

ual B

asis

Poi

nts Excess Return: ER

b-Rfree (10 yrs)

Boom Happens No Sunspot is Observed

False Alarms

Unpredictability of Crises: Data and Model

-1.5 -1 -0.5 0 0.5 1 1.5

Log " of Credit from trend at t-2

-1.5

-1

-0.5

0

0.5

1

1.5

Log "

of C

redi

t fro

m tr

end

at t-

1

No Crisis at tCrisis at time t

-1.5 -1 -0.5 0 0.5 1 1.5

% " of Credit from mean at year t-2

-1.5

-1

-0.5

0

0.5

1

1.5

% "

of C

redi

t fro

m m

ean

at y

ear

t-1

No Crisis at tCrisis at time t

Regulation

I Macroprudential regulator sets time varying capital requirement κ̄t

I Equilibrium capital ratios are

κt = max {κ̄t , κmt }

where κmt =θψt

are the market imposed capital ratios

I We restrict policy to be deteremined by simple rule

κ̄t =

{κ̄ if Nt ≥ N̄0 if Nt < N̄

I We look for(κ̄, N̄

)that maximize welfare

Regulation

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

Bank Net Worth

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Capital Ratio

Unregulated Equilbrium

Regulation

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

Bank Net Worth

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Capital Ratio

Unregulated EquilbriumCapital Requirement

Regulation

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

Bank Net Worth

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Capital Ratio

Unregulated EquilbriumCapital RequirementRegulated Equilibrium

Avoiding a Run with Regulation

0 10 20 30 40 50 60-3

-2

-1

0

1

2

% "

from

SS

Expected Productivity

0 10 20 30 40 50 60-3

-2

-1

0

1

2

% "

from

SS

Realized Productivity

Zt

ZRt+1

(Unregulated)

0 10 20 30 40 50 60-100

-80

-60

-40

-20

0

20

% "

from

SS

Capital Ratio: 5

0 10 20 30 40 50 60

Quarters

-100

-80

-60

-40

-20

0

20

% "

from

SS

Bank Intermediation

0 10 20 30 40 50 60

Quarters

0

2

4

6

8

Leve

l (pc

t)

Run Probability

0 10 20 30 40 50 60

Quarters

-8

-6

-4

-2

0

2

% "

from

SS

Output

Regulated Unregulated

Avoiding Runs with Macro Pru

Responding to False Alarms: No Sunspot Observed

0 10 20 30 40 50 60-3

-2

-1

0

1

2

% "

from

SS

Expected Productivity

0 10 20 30 40 50 60-3

-2

-1

0

1

2

% "

from

SS

Realized Productivity

Zt

ZRt+1

(Unregulated)

0 10 20 30 40 50 60-100

-80

-60

-40

-20

0

20

% "

from

SS

Capital Ratio: 5

0 10 20 30 40 50 60

Quarters

-100

-80

-60

-40

-20

0

20

% "

from

SS

Bank Intermediation

0 10 20 30 40 50 60

Quarters

0

2

4

6

8

Leve

l (pc

t)

Run Probability

0 10 20 30 40 50 60

Quarters

-8

-6

-4

-2

0

2

% "

from

SS

Output

Regulated Unregulated

Run After Credit Boom

Effect of Regulation

Unregulated Economy��� = 0; �N = 0

� Optimal Regulation��� = :13; �N = :85 �NDESS

� Fixed Capital Requirements��� = :13; �N = 0

�Run Frequency :8 pct :45 pct :3 pct

AVG Output Cond. No Run(� from Decentralized Economy)

0 �:4 pct �1:7 pct

AVG Output(� from Decentralized Economy)

0 :1 pct �:9 pct

Welfare Gain(� Permanent Consumption)

0 :16 pct �1:16 pct

1

Recovery From a Run

0 10 20 30 40 50 60

Quarters

-16

-14

-12

-10

-8

-6

-4

-2

0

% "

from

SS

Asset Price

0 10 20 30 40 50 60

Quarters

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

% "

from

SS

Net Worth

0 10 20 30 40 50 60

Quarters

-7

-6

-5

-4

-3

-2

-1

0

% "

from

SS

Output

Regulated Fixed Unregulated Regulated Countercyclical

Recovery from a run: Forgiveness VS No Forgiveness

Conclusion

I Develop model of banking panics that captures boom-bust cyclesand unpredictability of runs

I Study macroprudential policy

I Future work

I Ex-post intervention

I Regulated and Unregulated Banks

I Multiple assets