forbearance and broken credit cycles

Tomohiro OtaBank of England

15th December 201315th Macro Conference at the University of Tokyo

* The views expressed in this presentation are mine and not necessarily those of the Bank of England.

Forbearance and Broken Credit Cycles

Forbearance and Broken Credit Cycle

Motivations: from crisis to post-crisis

•Low Productivity (except for US)• Unusual fall in the level of productivity after the crisis

•Property Price Puzzle (except for US etc)• Property price shows resilience after the crisis

•Slow Deleverage (except for US)• Especially in less-performing sectors such as real-estate

•Broken Credit Cycle• Especially in less-performing sectors such as real-estate

1. Introduction



•Broken credit cycle in Japan• Correlation of land price and GDP (1st order difference) was 0.49

from 1956 till 1991, but -0.15 from 1991 till 2005.• Looks like the correlation recovers after 2005

Mar-65 Mar-70 Mar-75 Mar-80 Mar-85 Mar-90 Mar-95 Mar-00 Mar-05 Mar-10-15%

-10%

-5%

0%

5%

10%

15%

20% land priceReal GDP (old)Real GDP (new)

Mar

ket c

rash

Bank

ing

cris

is

NPL

reso

lved

1. Introduction


Motivations: Can forbearance be an answer?

•Forbearance:• Banks do not liquidate less-performing borrowers by revising terms

of the contracts• Also called: Zombie lending, evergreening loans

•Why banks forbear• Liquidating bad borrowers need capital (or bankrupt)• Liquidation value could be higher in the future (gamble for

resurrection)

•Impacts to macroeconomy• Production capitals are wasted on the hand of ‘zombies’• Forbearance hinders new lending (and new investments)

• New entrants are especially penalised• But forbearance can also boost investment if the financial

accelerator of the economy is high

1. Introduction


Literature

• Forbearance (theory)• Kocherlakota and Shim (2007)• Caballero Hoshi and Kashyap (2008)• Philippon and Schnabl (2013)

• Forbearance (empirical)• Peek and Rosengren (2005)• Saita et. al. (2003)

• Relevant theories• Credit Cycles:

• Kiyotaki and Moore (1997)• Krishnamurthy (2003)• Korineck and Jeanne (2011)

• Optimal bubbles:• Martin and Ventura (2013)

1. Introduction


Overview

1. Introduction

2. Defining baseline model 1. Mechanism of leverage and de-leverage2. Financial accelerator and “crisis”

3. Modelling forbearance1. Impacts of forbearance2. Banks’ incentive and coalition

4. Policy discussions1. Welfare analysis (simplistic)2. Implementing efficient outcome

1. Introduction


Assumptions• 3 sets of players:

• Firms (atomless): better stochastic production technology at={aH, aL}• Banks (many, but finite): collect deposit to lend or invest directly• Dealers (atomless): with less profitable non-stochastic technology

Firms

Banks

2. Benchmark model

Dealers

Asset Market

(qt)

Loans Dt

Collateralland

LiquidateSeized collateral

Buy /sell kft Buy /sell kb

t

DepositorsWealth ωt


Timeline

• Land (K) is supplied by outsiders• Firms receive endowment ω0

• Banks receive endowed ‘capital’ W0

Firms and banks sell land to outsiders at q2

They consume all the wealth and die

2. Benchmark model

t = 0 t = 1 t = 2 t = 3

Land price q0 is determined


Firm’s problem

• Budget constraint

• Collateral constraint

• Demand function(constrained)

• Harvest (at t+1): firms obtain at+1 kft

at+1 = {aH, aL} with prob π and 1-π

• Bankruptcy: Firms cannot harvest any with Prob γ

• Updating wealth ωt+1:

2. Benchmark model


Firms’ problem: one more assumption

• Do firms realise all capital gains from their asset holding?

• Firms realise a fraction η of the capital gain

• Firms’ demand function and financial accelerator

2. Benchmark model


Dealers’ problem

• Dealers’ payoff function

• Dealers’ demand function (downward sloping)

• Market Clearing condition

2. Benchmark model


Banks’ problem

• Banks determine loan size Dt and repayment Rt to maximise their next period payoff

• Each bank lends to many firms• Banks make a take-it-or-leave-it offer to firms and take all excess profits

• Borrowing firms’ default risks are perfectly correlated:• i.e. with probability γ, a bank receives no repayment

2. Benchmark model


Equilibrium (when η is low)

ktf kt

b K

Firms’ unconstrained demand fn

Firms’ constrained demand fnqt

dealers’ demand fn (horizontally inverted)

(1 – h)Et[qt+1]

2. Benchmark model


Equilibrium with negative macro shock (at+1 = aL)

• When η is small: Unique equilibrium

ktf kt

b K

qt

(1 – h)Et[qt+1]

Negative macro shock

2. Benchmark model

aH

aL

qt

Timet=0 t=1 t=2 t=3

E0[q1]

aH

aL

aH

aL

E1[q2]

q0

Equilibrium Price (output) Dynamism


2. Benchmark model

Proposition: In the baseline model, the asset price qt follows a process with (nearly) zero drift.


Overview

1. Introduction

2. Defining baseline model 1. Mechanism of leverage and de-leverage2. Financial accelerator and “crisis”

3. Modelling forbearance1. Impacts of forbearance2. Banks’ incentive and coalition

4. Policy discussions1. Welfare analysis (simplistic)2. Implementing efficient outcome

1. Introduction


What happens to the ‘stricken’ banks under neg. shock

• Asset price plunge creates loan loss of the banks

• Banks with capital Wt below a regulatory threshold are penalised

• Banks can ‘make up’ their capitals if they can contain the plunge

• … but how?

3. Forbearance model


Forbearance: a basic structure

Survived firms

Banks

2. Benchmark model

Dealers

Asset Market

repayment

LiquidateSeized collateral

Buy /sell Buy /sell

Depositors

failed firms

Collateral

Liquidate a fraction (1 – θ) of seized

collateral


Forbearance: definitions

• Renegotiation of terms and conditions of loan contracts• LTV covenant breach• Interest / debt service breach• Maturity extension• Payment holiday

• Creating new loans to help borrowers service their debts• “snowballing loans” (Japan)

• Foreclosing borrowers, but not liquidating collateral assets• Spanish banks till 2011


Forbearance: assumptions

• Bad borrowers (fraction γ)’ productivity is fixed at zero throughout the periods• Ie they do not recover, nor deteriorate further

• The value of bad borrowers is measured by the value of their collateral (ie banks have to write off all negative equities)

• Banks can forbear only at t=1, and have to unwind at t=2

• Banks have a chance to collude (not to liquidate bad borrowers)


3. Forbearance


Forbearance: impact on price and investment

• bad borrowers stay at their land without producing any • … and squeeze total available production capital• Asset price should be pushed up in any equilibrium


k1f k1

b K

q1

θγk0f

q1 s.t. W1=W

aH

aL

qt

Time

t=0 t=1 t=2 t=3

q0

aH

aL

aL

E0[q1]

Equilibrium Price Dynamism



Pre-crisis crisis Post-crisis

aH

aL

kft

Time

t=0 t=1 t=2 t=3

kf0

aH

aL

aH

E0[kf1]

Equilibrium Investment Dynamism (when η is low)




Forbearance: impact on k1f

• Firms’ demand function:

• Higher land price lowers firms’ purchasing power directly• But the collateral value of land does not increase as the

unwinding of forbearance is expected• i.e. the ‘haircut’ of collateral land increases by forbearance• Higher land price increases firms’ wealth

• Total supply of land decreases to K – θγkf0 .

• θγkf0 is left unused



Forbearance (when η is high)• Forbearance could increase or decrease firms’ land holding k1

f

• Depend on parameters, particularly higher η• Difficult to solve analytically – numerical exercise needed

• Increase of k1f is not the sufficient condition of higher output


ktf kt

b K

qt


Forbearance: impact on k1f (new entrants)

• Firms’ demand function:

• Survived (incumbent) firms’ purchasing power is supported by the wealth effect to some extent• If we introduce new entrants with higher productivity

possessing ω0 at t=1, their land holding decreases further than the incumbents



Incentive of Forbearance

• Authorities monitor banks’ W1 and force banks to close if W1 < 0• Banks choose the fraction of zombie borrowers θ • Two symmetric equilibria:

• θ*=0• θ* such that W1=Wbar: minimum deviation by a bank triggers

default


k1f k1

b K

q1

θγk0f

q1 s.t. W1=W


Discouraging forbearance

• If W1 is increased by the government (capital injection), or the threshold Wbar is lowered, banks do not have to forbear

• But if the injection is insufficient it could rather incentivise forbearance


k1f k1

b K

q1

θγk0f

q1 s.t. W1=W


Provisioning and capitalisation: Japan and Spain

19921993

19941995

19961997

19981999

20002001

20022003

20042005

20062007

0

2

4

6

8

10

12

14

-9%

-8%

-7%

-6%

-5%

-4%

-3%

-2%

-1%

0%

public capital in-jection (LHS)

land price growth (RHS)

(JPY TLN) (YOY %)

2008Q1 2009Q1 2010Q1 2011Q1-12

-10

-8

-6

-4

-2

0

2

4

0

1

2

3

4

5

6

7

8

9

10

House Price Index (% YoY, LHS)

Capital Injection (€ BLN, RHS)

Deadline for new capital req.

4. Discussions


Policy implications

• Externalities to healthy banks and healthy firms• Forbearance reduces new lending from healthy banks to healthy

firms• Healthy banks’ capital accumulation would slow down

• Explains the international productivity gap • The US: de-leveraging till 2010• The UK: less de-leveraging in CRE sectors etc

4. Discussions


Directions for further works

• Social planner’s optimal θ (regulatory forbearance)• Bank failure is currently costless in this model

• Surviving banks replace loans without friction• Stricken banks do not internalise all negative effect on output

• Another incentive of forbearance• Expected price recovery in the future can lead to forbearance• Externality creates a dynamic inconsistency

• Endogenous interest rate

4. Discussions


Summary

• Banks do forbearance to avoid liquidating collateral assets in the middle of the plunge of asset price (= realising a larger loan losses).

• Higher asset price (than it should be) and expected price decline tightens healthy firms’ credit constraint (negative externality), which lowers the firms’ investments.

• Healthy banks’ profit lowers as well, as they lose lending opportunities.

• If financial accelerator effect is strong, higher asset price could boost firms’ investment.

• Policy responses would be non-monotonic

4. Discussions


Appendix: revival of zombies?

• During the “resolving NPL” stage from 2002 to 06, 10 tn Yen loans were downgraded and 10tn Yen were upgraded

• Banks choose the fraction of zombie borrowers θ (collectively) cumulative chg FY2002 - FY06 JPY TLNNPLs based on the FRL (Financial Reconstruction Law) -31.3 (of which) Special attention Loans (3m arrears or renegotiated loans) -12.6 　 Increase factors Newly generated loans due to weakened business activities 12.3 　　 Upgrade from riskier categories 2.6 Improvement of business condition of borrowers 1.4 Establishment of restructuring plans 1.2 　 Decrease factors Return to normal claims -12.1 Improvement of business condition of borrowers -9.7 Establishment of restructuring plans -2.7 　 Downgrade to riskier categories -10.3 repayments etc -5.2 (of which) Doubtful and bankrupt/de facto bankrupt -18.7 Increase factors Newly generated loans due to weakened business activities 15.0 Downgrade from safer categories 10.3 Decrease factor Removal from B/S -44.1

5. Appendix


Competitive equilibrium (at t > 0)

• When η is larger: No equilibrium (crisis)

ktf kt

b K

qt

(1 – h)Et[qt+1]

2. Benchmark model

HIDDEN CHARTS



•Low Productivity (Hughes and Saleheen, 2012)• Unusual fall in the level of productivity after the crisis (except for US)

1. Introduction



•Property Price Puzzle• Residential property price experienced 250% increase from 2000 till

2007, the price dropped by only 20% after the crisis

19 19 19 19 19 19 19 19 20 20 20 20 20 20 20 20 200

50

100

150

200

250

300

350

400

UK House Price US House Price

(1991Q1 = 100, nominal price)

+137%(‘00 – ’07)

-10%(‘07 – ’12)

+62%(‘00 – ’07)

-19%(‘07 – ’12)

1. Introduction



•Slow develerage (especially in less performing sectors)

1. Introduction

Dec-97 Dec-00 Dec-03 Dec-06 Dec-090

20

40

60

80

100

120

NFCs - Non-property related NFC - CRENFC-Property related (non CRE)

Sep-12

(Mar-08 = 100)

80 85 90 95 00 05 100

20

40

60

80

100

120

140

160

PNFC - non-CRECREConstruction

1991 = 100

Market peak

Banking crisis NPL resolved

Japan UK



•Slow develerage (especially in less performing sectors)

1. Introduction

2000-01 2002-03 2004-05 2006-07 2008-09 2010-11 2013-01-20%

-15%

-10%

-5%

0%

5%

10%

15%

20%

25%

Commercial and industrialResid real estateComm. real estateReal estate

-20

-10

0

10

20

30

40

Corporates

Households

(YOY %)

Spain US


Forbearance: impact on price and investment

• bad borrowers stay at their land without producing any • … and squeeze total available production capital• Asset price should be pushed up in any equilibrium


k1f k1

b K

q1

θγk0f

q1 s.t. W1=W


Static Equilibrium (when η is high)

• When η is larger: Multiple equilibria• Demand curve becomes Z-shape• Focus only on the stable equilibrium

ktf kt

b K

qt

(1 – h)Et[qt+1]

2. Benchmark model


Is forbearance good or bad?

• Forbearance is rational for ‘stricken’ banks

• Forbearance lowers investment (and output)• Some production capital is wasted• Productive firms reduce investment• Healthy banks (and the stricken banks) reduce profit

• Forbearance increases investment (and output)• If the economy is highly leveraged, the positive ‘wealth effect’

outweighs everything else


forbearance and broken credit cycles

Documents

broken credit cyclemotivations

credit cycleespecially

forbearance empiricalpeek

penalisedbut forbearance

postcrisisbroken credit

benchmark model t

firms atomless

crisis property price