Capital Requirements,

Risk Choice, and Liquidity Provision

in a Business Cycle Model

Juliane Begenau

Harvard Business School

July 11, 2015

1

Motivation

I How to regulate banks?

I Capital requirement: min equity/ risky assets

I Literature: higher capital requirements

I limit banks' risk-takingI reduce lending and liquidity provision

This paper:

I develops general equilibrium model to quantify trade-o�s

I derives optimal capital requirement

I shows importance of e�ect of capital requirements onendogenous prices

I mechanism is based on household's demand for safe assets

2

Quantitative GE model

I Main features

I banks are essential for a part of productionI households' preference for safe & liquid bank debtI banks receive government subsidy

I Quanti�ed with data from the FDIC and NIPA

I Consistent with business cycle facts

I macroeconomic variablesI banking sector aggregates

3

Findings

Optimal capital requirement

I 14% of risky assets

Increasing the capital requirement to 14%

I reduces the supply of liquid bank debt by 9%

I reduces volatility of income-risky-asset ratio by 6%

I increases loans by 2%

Main proposition:

Higher capital requirements leading to a reduction in thesupply of bank debt can in fact result in more lending

Core assumption:

Investors value safe and liquid assets in the form of bank debtmore the scarcer they are

4

Corporate bond spread and bank debt

Bank Debt-to-GDP0.7 0.75 0.8 0.85 0.9 0.95 1

Spr

ead

-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4 1999

2000

2001

20022003

2004

2005

2006

2007

2008

2009

2010

2011

2012

2013

The �gure plots the spread between the Aaa corporate bond rate and the implied

interest rate on bank debt against the bank debt-to-GDP ratio for 1999-2013.

5

Related literature

I Banks' role for productionI Diamond 1984; Sharpe 1990; Boyd & Prescott 1986; Holmström &

Tirole 1997; Winton 2000; Van Den Heuvel 2002; Bolton & Freixas 2006I James 1978; Hoshi, Kashyap & Scharfstein 1991; Gertler & Gilchrist

1992; Dell'Ariccia, Detragiache & Rajan 2008; Iacoviello & Minetti 2008

I Households' demand for liquid bank debtI Diamond & Dybvig 1983; Gorton & Winton 1995; Diamond & Rajan

2000; Kashyap, Rajan & Stein 2002; Van Den Heuvel 2008; Williamson

2012; Dang, Gorton, Holmström & Ordonez 2013; DeAngelo & Stulz

2013; Allen, Carletti & Marquez 2014I Bansal & Coleman 1996; Krishnamurthy & Vissing-Jørgensen 2013;

Greenwood, Hanson & Stein 2014

I Risk-shifting incentivesI Kareken & Wallace 1978; Keeley & Furlong 1990; Gennotte & Pyle

1991; Schneider & Tornell 2004; Farhi & Tirole 2011; Admati et al 2013;

Allen, Carletti, Goldstein & Leonello 2014I Kelly, Lustig & Nieuwerburgh 2012; Gandhi & Lustig 2012; Marques,

Correa & Sapriza 2013; Duchin & Sosyura 2014

I Quanti�cation of capital requirementsI Corbae & D'Erasmo 2011, 2012; Christiano & Ikeda 2013; Clerc et al

2014; Nguyen 2014; Martinez-Miera & Suarez 20146

Outline

I Mechanism

I Model

I Trade-o� Description

I Taking the model to the dataI Welfare

7

Two-sector business cycle model

I Technology f : non-bank dependent

yft = Zft

(kft−1

)α (N ft

)1−αI Technology h : banking sector funded activities as part ofthe overall output (collateralized lending)

yht = Zht

(kht−1

)vI Banks run h production directly

I Choose investment and risk

8

Banks' risk-return trade-o�I Captures menu of investment choices

I Zht productivity level in yht = Zh

t

(kht−1

)vlogZh

t+1

(σht)

= ρh logZht

(σht−1

)+(φ1 − φ2σ

ht

)σht +σht ε

ht+1

Productivity maximizing σh

Risk choice of banks

E[lo

g(Z

h )]

σh

I σht determines mean and exposure to aggregate shock

9

Balance sheet and pro�ts

I Balance sheet at the beginning of t

kht−1 + bt−1 = et−1 + st−1

I Pro�ts

πt = yht − δhkht−1︸ ︷︷ ︸income from kh

+ rBt bt−1︸ ︷︷ ︸interest inc.

− rtst−1︸ ︷︷ ︸interest exp.

I Capital requirementet ≥ ξkht

10

Subsidy to banks

I Capture e�ects of guarantees on banks' liabilities

I Assume: government cannot commit to not bailout banksI Guarantees subsidize leverage and risk-taking

I Unlimited liability and explicit subsidy

TRt = ω3kht−1︸︷︷︸

size

exp

−ω1et−1 + πtkht−1︸ ︷︷ ︸

capitalization

+ ω2 σht︸︷︷︸risk-taking

ω1, ω2, ω3 > 0

I Implies complementarity between leverage and risk-taking

11

Banks' problem

I Maximize present value of dividend payout dtsubject to

dt = πt + TRt −∆et −κ

2

(dt − d̄

)2 − adjkh

I Dividend smoothing motive captured with dividendadjustment costs

12

HouseholdsI Utility of households

U (ct, st) = log ct + θ(st/ct)

1−η

1− ηwhere η > 1.

I Net worth of households

nt = (dt + pt) Θt−1 + (1 + rt) st−1

+(rft + 1− δf

)kft−1

− Taxes

I Maximize discounted expected utility subject to thebudget constraint

ct + st + kft + ptΘt = nt + wftNft

13

Recursive competitive equilibrium

I State vars: capital stocks, productivity levels, households'net worth, equity after pro�ts

I Exog. shocks to logZh & logZk

I Given prices, households, �rms, and banks optimize

I Policies satisfy market clearing forbonds, bank debt, capital stocks, labor, bank shares, andconsumption.

I Gov budget constraint holds: TR +BrB = Taxes

14

Outline

I Mechanism

I Model

I Trade-o� Description

I Taking the model to the data

I Welfare

15

Decisions relevant for trade-o�

I Risk choice

I Leverage choice

I Lending choice

16

Risk choice

I Subsidy: source of excessive risk-taking

Productivity maximizing σh

Risk choice of banks E

[log(

Zh )]

σh

I Higher ξ : reduce σh and increase E[log(Zh)]

17

Leverage choice

I Households' FOC wrt liquid bank debt:

re − r1 + re

= Us (c, s) /Uc (c, s) > 0

⇒ re = 1β− 1 > r

I Discount on bank debt → binding capital requirement:e = ξkh

I debt is preferredI gov. subsidy adds to this

I What happens to r when s falls?

I re − r larger the scarcer sI reduction in s leads to reduction in r

18

Lending choice

1 + vyh

kh− δh + g

(TR

kh

)︸ ︷︷ ︸

Bene�t of kh

= ξ (1 + re) + (1− ξ) (1 + r)︸ ︷︷ ︸Funding costs of kh

I Higher capital requirements→ With rates �xed: banks want to reduce scale→ Reduction in debt reduces r through GE→ Overall funding costs fall if ξ not too large

I Fall in funding costs→ banks want to increase kh

I Strength depends on key parameters: η and v

19

Welfare e�ects of capital requirements

Increase in the capital requirement

I reduces risk-taking

I reduces liquidity through a reduction in bank debt

I increases assets through lower funding costs

Optimal capital requirement

I trades-o� reduction in liquidity against reduction inrisk-taking and an increase in consumption

20

Outline

I Mechanism

I Model

I Trade-o� Description

I Taking the model to the data

I Welfare

21

Mapping from model to data

Model NIPA and FDIC balance sheet & inc stat.yh: bank output income− sec int. incomekh: bank capital loans + trading assetsyf : �rm output NIPA total GDP − bank outputkf : �rm capital NIPA K − khc: consumption NIPA consumptions: bank debt bank liabilitiesπ: pro�ts net income + non interest expenser: rate on bank debt interest expenses / bank liabilitiesσh: risk choice std of BC component log (yh/kh)e: equity tier 1 equity

Period: 1999q1:2013q4

22

Quanti�cation of Parameters

1. natural data counterpart

I e.g. persistences of productivity shocks

2. using steady state conditions of the model and targetingmoments one for one

I e.g. time preference rate of households

3. jointly

I e.g. parameters governing adjustment costs, liquiditypreference, and size of banking sector

23

Key parameters

Par. Governs Target Moment Valueη hh dislike for changes

vol(bank liab/cons)

3.15in bank debt/ consum.

strength of ↓ r to ↑ ξv conversion of risky

inc/risky assets

0.30assets into bank output

strength of ↑ kh to ↑ ξ

24

Business cycle correlations

GDPData Model

Investment 0.97 0.98Consumption 0.94 0.87Bank income 0.66 0.64Bank risky assets 0.37 0.32Bank liabilities 0.31 0.32Interest rate on bank liabilities 0.68 0.64Bank income-risky assets 0.61 0.62Bank pro�t 0.34 0.64Bank investment 0.46 0.55

25

Outline

I Mechanism

I Model

I Trade-o� Description

I Taking the model to the data

I Welfare

26

Welfare

I Compute the optimal capital requirement

I use local approximation methodsI simulate economy under benchmark tier-1-equity/risky

asset and under new requirementsI compute value function of households

I Welfare as a function of capital requirements

27

Optimal ξ = 14%

0.05 0.1 0.15 0.2 0.25

−0.25

−0.2

−0.15

−0.1

−0.05

0

ξ

Wel

fare

in %

con

sum

ptio

n eq

uiva

lent

uni

ts

28

Reduction in funding costs

1 + vyh

kh− δh +

TR

kh

(1 + ω1 (1− v)

yh

kh

)︸ ︷︷ ︸

Bene�t of kh

= ξ (1 + re) + (1− ξ) (1 + r)︸ ︷︷ ︸Funding costs of kh

I Benchmark: kh costs 2.57% with r = 1.5% and re = 10%

I Increase requirement to 14%→ With �xed prices, cost would increase by 10%→ Reduction in debt reduces r to 0.88%→ Overall funding costs fall by 16% to 2.15%

I Fall in funding costs → banks increase kh by 2%

29

Raising capital requirement during crisis or boom?

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

ξ

Wel

fare

in %

con

sum

ptio

n eq

uiva

lent

uni

ts

Start in RecessionStart in Boom

30

Conclusion

I Mechanism:Higher capital requirement can lead to more lending whenbank debt is valued for being safe and liquid

I Optimal capital requirement about ξ = 14%

I Caveat: potential for safe asset substitution from shadowbanks may mitigate channel

31

Thank you

32

Subsidy to banks

I Capture e�ects of guarantees on banks' liabilities

I Assume: government cannot commit to not bailout banksI Guarantees subsidize leverage and risk-taking

I Unlimited liability and explicit subsidy

TRt = ω3kht−1︸︷︷︸

size

exp

−ω1et−1 + πtkht−1︸ ︷︷ ︸

capitalization

+ ω2 σht︸︷︷︸risk-taking

ω1, ω2, ω3 > 0

I Implies complementarity between leverage and risk-taking

Back

33

Key parameters (ctd)

Par. Governs Target Moment Valueφ2 risk-return trade-o�

vol(inc/risky-assets)

0.89

strength of↓ σh& ↑ kh to ↑ ξ

Var(log(yht /k

ht

)| log πt−1

)ω2 risk-taking due to 2.92subsidy

strength of↓ σh to ↑ ξ

34