Post on 06-Dec-2019
transcript
Banks’ Endogenous Systemic Risk Taking
David Martinez-Miera
Universidad Carlos III
Javier Suarez
CEMFI
Banking and Regulation: The Next Frontier
A RTF-CEPR-JFI Workshop, Basel, 22-23 January 2015
1
Introduction
• The recent crisis has evidenced the need to better understand banks’contribution to systemic risk
• One of the dimensions of this multifaceted phenomenon is the ex-posure to common shocks
• In this paper, we analyze:
— The dynamic trade-offs behind banks’ voluntary exposure toan infrequent & large common shock(attractive to them due to standard risk-shifting incentives)
— The extent to which capital requirements (CRs) contribute toreduce the resulting systemic risk & increase social welfare
— Issues such as the optimal level of CRs, their gradual introduction& cyclical adjustment
2
• Simple dynamic equilibrium model in which bank capital dy-namics is formalized like in other papers in recent literature
(limited wealth of bankers who retain earnings and/or suffer lossesfrom prior investments)
— But the role of bank capital is different
∗Meh-Moran’10: Monitoring incentives a laHolmström-Tirole’97∗ Gertler-Kiyotaki’10: Preventing fund diversion a laHart-Moore’94
— Here, it reduces systemic gambling incentives through twochannels:
∗ Leverage reduction effect (standard)[Van den Heuvel’08 & many micro-banking models]
∗ Last bank standing effect (novel — as for CRs)[akin to Perotti-Suarez’02]
3
Related literature
Papers beyond those already mentioned:
• Ranciere-Tornell-Westermann’08: myopic firms adopt “risky growthstrategies” due to lenders’ expectation of a systemic bailout when acrisis occurs
• Brunnermeier-Sannikov’14, He-Krishnamurthy’14: similar capital dy-namics but no time-varying systemic risk-taking & no discussion onCRs
• Risk taking in banking:— under deposit insurance: Kareken-Wallace’78 & many more
— effect of CRs: Hellmman-Murdock-Stiglitz’00, Repullo’04
— equilibrium/dynamic considerations: Acharya-Yorulmazer’07-08,Farhi-Tirole’12
4
Our modeling of systemic risk taking
1. Firms’ production technology is subject to failure risk & can bemanaged in two modes:
• non-systemic (xi=0): its failure is purely i.i.d.• systemic (xi=1): if a rare shock occurs, all fail at once
2. Firms need bank loans to pay inputs in advance: li=ki+wni
3. Lending to systemic firms is socially inefficient, but...
• Highly levered banks may find it privately profitable• Systemic lending is not ex-ante detectable→ Regulation sets a common capital requirement: ei ≥ γli
4. Bankers competitively allocate their wealth e as capital across banks
5
Key variables
• Capital requirements are satisfied with inside equity
→ Single state variable is bankers’ aggregate wealth e
∗ grows quickly if bank profits are high∗ gets lost if invested systemically and shock realizes
• Two important endogenous variables
v(e) : value of one unit of bankers’ wealth
x(e) : fraction of bankers’ wealth invested in systemic banks
[Banks specialize as systemic or non-systemic]
6
Key insights
1. Systemic risk taking is maximal after several calm periods[bankers’ reaction to the lower shadow value of their wealth]
2. Higher capital requirements...
• reinforce the last bank standing effect [GOOD]
•make bank capital effectively scarcer at all times⇒ less credit⇒ lower economic activity [BAD]
3. The socially optimal capital requirements
• are quite high• should be gradually introduced• should not be lowered after a crisis
7
Key equations*
• Banks fix the terms of their supply of loans to firms taking bankers’required value-weighted return as given
• Bankers allocate their wealth et across banks taking the returnsoffered to them by banks as given
vt = ψ + (1− ψ)βmax{Et(vt+1R0t+1), Et(vt+1R1t+1)}
Rjt+1: gross return on equity under xi = j
vt+1: marginal value of bankers’ wealth at end of t
⇒ Indifference requires Et(vt+1R0t+1) = Et(vt+1R1t+1) (1)
⇒ we look at a representative bank of each class
• Law of motion of total bank capital etet+1 = φ(1 + r)wt + (1− ψ)[(1− xt)R0t+1 + xtR1t+1]et
8
Definition of equilibrium*
• Stationary law of motion for et ∈ [e, e]
• Tuple (v(e), x(e); k(e), w(e), R0(e), R01(e)) describingendogenous variables for each e ∈ [e, e]such that {et} and {vt, xt; kt, wt, R0t+1, R
01t+1} are
compatible with:
1. Individual optimization
2. Market clearing
––––––––––––––––––Indifference condition for xt ∈ (0, 1):
[(1− ε)v(e0t+1) + εv(e1t+1)]R0t+1 = (1− ε)v(e0t+1)R01t+1
⇒ ∃ self-equilibrating mechanism for xt9
Rest of the talk
1. Baseline parameterization
2. Graphical presentation of key results
3. Quantitative results
4. Applications
5. Conclusions
10
Baseline parameterization (1 period = 1 year)
T1. Baseline parameter valuesPatient agents’ discount rate ρ 0.02Impatient agents’ discount factor β 0.96Total factor productivity A 2Physical capital elasticity α 0.3Depreciation rate in successful firms δ 0.05Depreciation rate in failed firms λ 0.35Idiosyncratic default rate of non-systemic firms π0 0.03Idiosyncratic default rate of systemic firms π1 0.018Probability of a systemic shock ε 0.03Bankers’ exit rate ψ 0.20Fraction of wage income earned by bankers φ 0.05
[Parsimonious model: 11 parameters only]
11
•Why these values?
— Low real interest rates such as prior to the recent crisis
—A = 2 is inconsequential (levels in 0 to 100 range)
— α = 0.30 produces labor share ' 70%
— δ and λ match K/Y ' 3-4 & LGD' 45%
— π0, π1, and ε ⇒ sufficient room of risk shifting
[expected default rates 3%—4.7%; systemic shocks every 33y]
— Bank capital dynamics (highly tentative):
ψ: bankers’ expected active life = 5y
φ: capital brought in by active bankers = 5%of agg. labor income
12
Social welfare W as a function of γ ←
2.97
2.975
2.98
2.985
2.99
2.995
3
3.005
6% 8% 10% 12% 14% 16% 18%Capital requirement
Soc
ial w
elfa
re
Figure 1: W (γ) [we compare γ∗=14% with γ=7%]13
v(e) and x(e) under low and optimal γ ←
0
1
2
3
4
5
6
7
8
9
10
0 0.5 1 1.5 2 2.5Aggregate amount of bank capital (e)
Mar
gina
l val
ue o
f ban
k ca
pita
l (v)
optimal capital requirement (14%)
low capital requirement (7%)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.5 1 1.5 2 2.5Aggregate amount of bank capital (e)
Sys
tem
ic ri
sk ta
king
(x)
optimal capital requirement (14%)
low capital requirement (7%)
Figure 2a: v(e) Figure 2b: x(e)
14
Equilibrium dynamics with low and optimal γ ←
Equilibrium dynamics (CR=7%)
0
0.5
1
1.5
2
2.5
3
0 0.5 1 1.5 2 2.5Aggregate bank capital at t
Agg
rega
te b
ank
capi
tal a
t t+1
Dynamics if no shock realizes
Dynamics if shock realizes
45-degree line
Equilibrium dynamics (CR=14%)
0
0.5
1
1.5
2
2.5
3
0 0.5 1 1.5 2 2.5Aggregate bank capital at t
Agg
rega
te b
ank
capi
tal a
t t+1
Dynamics if no shock realizes
Dynamics if shock realizes
45-degree line
Figure 3a (γ =7%) Figure 3b (γ =14%)
15
Equilibrium dynamics with low and optimal γ ←
Ergodic distribution (CR=7%)
00.20.40.60.8
1
0 0.5 1 1.5 2 2.5Aggregate bank capital
Freq
uenc
y
Ergodic distribution (CR=14%)
00.20.40.60.8
1
0 0.5 1 1.5 2 2.5Aggregate bank capital
Freq
uenc
y
Figure 3c (γ =7%) Figure 3d (γ =14%)
16
Quantitative results
• Optimal capital requirements: positive and large (14%)
• Comparison CR=7%→ CR=14% (unconditional means)
— Lower fraction of systemic loans: 71%→ 25%
— Higher loan rates: 4.1%→ 5.6%
— Lower macro aggregates: bank credit (—21%), GDP (—8.5%)
— Higher social welfare: ' +0.9% permanent consumption
• Variation in year-after-shock aggregates:
— CR=7%: loan rate (+11.8pp), bank credit (-66%), GDP (-34%)
— CR=14%: loan rate (+2.6pp), bank credit (-24%), GDP (-10%)
17
Quantitative results (details, 1/3)
T2. Main unconditional means γ = 7% γ = 14% ∆%Welfare (equivalent consumption flow) 2.97 3.00 0.9GDP 4.54 4.15 -8.5Bank credit (l) 19.30 15.28 -20.8Bank equity (e) 1.35 2.14 58.3Loan rate (rL) (in %) 4.1 5.6 1.5ppDeposit insurance costs 0.16 0.04 -76.2Value of one unit of bank capital (v) 1.37 1.90 38.1Fraction of equity in systemic banks (x) 0.71 0.25 -64.9
18
Quantitative results (details, 2/3)
T3. % Change in after-shock period (from PSS) γ=7% γ=14%Aggregate net consumption -17.5 -4.6GDP -33.7 -10.0Bank credit (l) -65.8 -24.4Loan rate (rL) 11.8pp 2.6ppValue of one unit of bank capital (v) 164 25Fraction of equity in systemic banks (x) -50 -24
19
Quantitative results (details, 3/3)
T4. Other macro & financial ratios γ = 7% γ = 14%Labor income/GDP 0.67 0.68Physical capital/GDP 3.58 3.03Bank credit/GDP* 4.25 3.71Deposit insurance costs/GDP (%) 3.5 0.9ROE at non-systemic banks (%) 10.2 17.0ROE at systemic banks if no shock realizes (%) 18.7 21.2
[*: suggests exuberance due to lax regulation]
20
Applications
• Transitional dynamics from moving γ and impact on welfare:
There is value (and limits to the value) ofapplying gradualism in rising γ
[Best: moving from 7% to 13% in 9 years]
• Assessment of countercyclical capital requirements
— They have a bad effect on incentives—Overall, there is no net gain from making them countercyclical— But sticking to flat requirements may not be time-consistent
21
2.973
2.978
2.983
2.988
2.993
2.998
0 5 10 15 20 25 30Years of transition (T)
Soc
ial w
elfa
re
8%
9%
10%
11%12%
13%14%
15%
22
Conclusions
• Dynamic equilibrium model of banks’ endogenous systemic risk-taking
• Allows us to assess the macroprudential role of capital requirementsusing an internally consistent welfare metrics:
They reduce credit and output in calm times but also systemic risktaking⇒ interior socially optimal level
• The identified last bank standing effect implies that systemic risktaking increases as the economy expands...
Yet, systemic risk taking increases if the CRs are cyclically adjusted
23