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 exposure to common shocks In this paper, we analyze: The dynamic trade-offs behindbanks voluntary exposure to an infrequent & large common shock (attractive to them due to standard risk-shifting incentives) The extent to which capital requirements (CRs) contribute to reduce 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 dynamics is formalized like in other papers in recent literature (limited wealth of bankers who retain earnings and/or suffer losses from prior investments) But the role of bank capital is different Meh-Moran 10: Monitoring incentives alaholmström-tirole 97 Gertler-Kiyotaki 10: Preventing fund diversion alahart-moore 94 Here, it reduces systemic gambling incentives through two channels: 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 growth strategies due to lenders expectation of a systemic bailout when a crisis occurs Brunnermeier-Sannikov 14, He-Krishnamurthy 14: similar capital dynamics but no time-varying systemic risk-taking & no discussion on CRs 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 be managedintwomodes: non-systemic (x i =0): its failure is purely i.i.d. systemic (x i =1): if a rare shock occurs, all fail at once 2. Firms need bank loans to pay inputs in advance: l i =k i +wn i 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: e i γl i 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 [Banksspecializeassystemicornon-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 make bank capital effectively scarcer at all times less credit lower economic activity [GOOD] [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 e t across banks taking the returns offered to them by banks as given v t = ψ +(1 ψ)β max{e t (v t+1 R 0t+1 ),E t (v t+1 R 1t+1 )} R jt+1 : gross return on equity under x i = j v t+1 : marginal value of bankers wealth at end of t Indifference requires E t (v t+1 R 0t+1 )=E t (v t+1 R 1t+1 ) (1) we look at a representative bank of each class Law of motion of total bank capital e t e t+1 = φ(1 + r)w t +(1 ψ)[(1 x t )R 0t+1 + x t R 1t+1 ]e t 8
Definition of equilibrium* Stationary law of motion for e t [e, e] Tuple (v(e),x(e); k(e),w(e), R 0 (e),r1 0 (e)) describing endogenous variables for each e [e, e] such that {e t } and {v t,x t ; k t,w t,r 0t+1,R 0 1t+1 } are compatible with: 1. Individual optimization 2. Market clearing Indifference condition for x t (0, 1): [(1 ε)v(e 0 t+1 )+εv(e1 t+1 )]R 0t+1 =(1 ε)v(e 0 t+1 )R0 1t+1 self-equilibrating mechanism for x t 9
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 values Patient agents discount rate ρ 0.02 Impatient agents discount factor β 0.96 Total factor productivity A 2 Physical capital elasticity α 0.3 Depreciation rate in successful firms δ 0.05 Depreciation rate in failed firms λ 0.35 Idiosyncratic default rate of non-systemic firms π 0 0.03 Idiosyncratic default rate of systemic firms π 1 0.018 Probability of a systemic shock ε 0.03 Bankers exit rate ψ 0.20 Fraction 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 =2is inconsequential (levels in 0 to 100 range) α =0.30 produces labor share ' 70% δ and λ match K/Y ' 3-4 & LGD' 45% π 0,π 1, 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 3.005 3 2.995 Social welfare 2.99 2.985 2.98 2.975 2.97 6% 8% 10% 12% 14% 16% 18% Capital requirement Figure 1: W (γ) [we compare γ =14% with γ=7%] 13
v(e) and x(e) under low and optimal γ 10 1 9 0.9 8 0.8 Marginal value of bank capital (v) 7 6 5 4 3 2 optimal capital requirement (14%) low capital requirement (7%) Systemic risk taking (x) 0.7 0.6 0.5 0.4 0.3 0.2 optimal capital requirement (14%) low capital requirement (7%) 1 0.1 0 0 0.5 1 1.5 2 2.5 Aggregate amount of bank capital (e) Figure 2a: v(e) 0 0 0.5 1 1.5 2 2.5 Aggregate amount of bank capital (e) Figure 2b: x(e) 14
Equilibrium dynamics with low and optimal γ 3 Equilibrium dynamics (CR=7%) 3 Equilibrium dynamics (CR=14%) Aggregate bank capital at t+1 2.5 2 1.5 1 Dynamics if no shock realizes Dynamics if shock realizes 45-degree line Aggregate bank capital at t+1 2.5 2 1.5 1 Dynamics if no shock realizes Dynamics if shock realizes 45-degree line 0.5 0.5 0 0 0.5 1 1.5 2 2.5 Aggregate bank capital at t 0 0 0.5 1 1.5 2 2.5 Aggregate bank capital at t Figure 3a (γ =7%) Figure 3b (γ =14%) 15
Equilibrium dynamics with low and optimal γ Frequency 1 0.8 0.6 0.4 0.2 0 Ergodic distribution (CR=7%) 0 0.5 1 1.5 2 2.5 Aggregate bank capital Frequency 1 0.8 0.6 0.4 0.2 0 Ergodic distribution (CR=14%) 0 0.5 1 1.5 2 2.5 Aggregate bank capital 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 0.9 GDP 4.54 4.15-8.5 Bank credit (l) 19.30 15.28-20.8 Bank equity (e) 1.35 2.14 58.3 Loan rate (r L ) (in %) 4.1 5.6 1.5pp Deposit insurance costs 0.16 0.04-76.2 Value of one unit of bank capital (v) 1.37 1.90 38.1 Fraction 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 -17.5-4.6 GDP -33.7-10.0 Bank credit (l) -65.8-24.4 Loan rate (r L ) 11.8pp 2.6pp Value of one unit of bank capital (v) 164 25 Fraction 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 0.68 Physical capital/gdp 3.58 3.03 Bank credit/gdp* 4.25 3.71 Deposit insurance costs/gdp (%) 3.5 0.9 ROE at non-systemic banks (%) 10.2 17.0 ROE 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) of applying 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
2.998 13% 14% 2.993 11% 12% Social welfare 2.988 2.983 15% 9% 10% 8% 2.978 2.973 0 5 10 15 20 25 30 Years of transition (T) 22
Conclusions Dynamic equilibrium model of banks endogenous systemic risktaking Allows us to assess the macroprudential role of capital requirements using an internally consistent welfare metrics: They reduce credit and output in calm times but also systemic risk taking interior socially optimal level The identified last bank standing effect implies that systemic risk taking increases as the economy expands... Yet, systemic risk taking increases if the CRs are cyclically adjusted 23