Bank Capital Buffers in a Dynamic Model 1

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1 Bank Capital Buffers in a Dynamic Model 1 Jochen Mankart 1 Alex Michaelides 2 Spyros Pagratis 3 1 Deutsche Bundesbank 2 Imperial College London 3 Athens University of Economics and Business November The views expressed in this presentation represent the authors personal opinions and do not necessarily reflect those of the Deutsche Bundesbank.

2 Road map How do capital adequacy (risk-weighted) and leverage (unweighted) constraints affect bank behavior? We build a quantitative banking model to replicate cross sectional heterogeneity (small versus large & uninsurable risks) pro-cyclical lending counter-cyclical bank failures. Estimate the model using the Method of Simulated Moments. Use the model to evaluate the effects of capital adequacy requirements leverage requirements. Close the loan market (work in progress) 1 / 25

3 Environment and regulatory requirements Assets Liabilities loans L r L deposits D r D liquid assets S r S wholesale funds F g F equity E Banks choose dividends X t, new loans N t, liquid assets S t, and wholesale borrowing F t to maximize owners utility subject to: (unweighted) leverage constraint (L t + N t) + S t E t X t λ u = (1) (risk-weighted) capital adequacy constraint ω L (L t + N t) + ω S S t E t X t λ w = 16.66, (2) risk weight ω L = 1 on loans and ω S =.2 on liquid assets. Aggregate and idiosyncratic shocks move loan write-offs, deposit growth and returns. 2 / 25

4 Model I: bank s problem, balance sheet, and loan evolution States: deposits D t, loans L t, and equity E t Controls: dividends X t, new loans N t, liquid assets S t, and wholesale borrowing F t Bankers maximize utility subject to (1), (2) and: Balance sheet constraint Evolution of loans L t+ {}}{ L t + N t +S t = D t + F t + E t+ {}}{ E t X t (3) L t+1 = (1 ϑ w t+1 ) L t+ (4) 3 / 25

5 Model II: equity evolution and profits Evolution of equity Profits E t+1 = E t+ + Π t+1 τπ t+1 I Πt+1 > (5) Π t+1 = (r L,t+1 ω t+1 ) L t+ + r S,t+1 S t r D,t+1 D t g N (N t, D t ) g F (F t, D t, E t+ ) cd t (6) where L t loan stock, N t new loans (potentially negative), S t liquid assets, D t deposits, F t wholesale funds, E t equity, X t dividends, ϑ loan repayments, w t+1 loan write offs, Π t+1 profits, τ =.15 corporate tax rate, I Πt+1 > indicator function for positive profits. 4 / 25

6 The bank s problem V C (L t, D t, E t ; w t, r t ) = with default decision subject to max X t,s t,f t,n t { (X t ) 1 γ 1 γ + E t [βv (L t+1, D t+1, E t+1 ; w t+1, r t+1 )]} V (L t, D t, E t ; w t, r t ) = max[v D, V C (L t, D t, E t ; w t, r t )] leverage (1) and capital adequacy (2) constraints, balance sheet constraint (3), loan evolution (4), equity evolution (5), profits (6). 5 / 25

7 Estimated inputs Details Unit root in deposits, deposit growth rates iid. Model normalized for stationarity and estimated separately for small and large banks. Aggregate state: boom and recession. Stochastic processes for idiosyncratic loan write-offs depend on aggregate state. Estimate the model using Method of Simulated Moments. 6 / 25

8 Estimated parameters The 7 estimated parameters are Parameter Large banks Small banks Discount factor β.975 (.4).986 (.11) Concavity γ 1.31 (.4) 1.89 (.6) Operating cost c.11 (.2).1 (.1) Screening cost φ N.63 (.4).9 (.4) Wholesale funding cost φ F.9 (.2).81 (.3) Wholesale funding benefitφ E.7(.4).7(.1) Consumption after exit c D 2e 5 (3e 4 ) 4e 5 (8e 4 ) 7 / 25

9 Moments Moments Big banks Small banks model data model data Mean failure rate (in %) Mean loans/assets Mean deposits/assets Mean equity/assets Mean profit/equity Mean dividends/equity Std. loans/assets Std. deposits/assets Std. equity/assets Std. profit/equity Std dividends/equity / 25

10 The final 82 quarters in the life of a bank Write offs A: Exogenous shocks Deposit growth Equity B: Equity and loan states Loans Booms Recessions New loans C: New loans Liquid assets D: Liquid assets and wholesale funding Wholesale funding Profits 15 x E: Profits and dividends Time x Dividends Leverage F: Regulatory capital ratios 4 2 Lev. constraint,33.3 Cap. constraint, Time Capital adequacy 9 / 25

11 Cross sectional heterogeneity: Leverage Data Model 1 / 25

12 2 counterfactual experiments 1 Taking stock We have a structural model of bank behavior Generates reasonable cross-sectional heterogeneity and time series behavior Use it to conduct counterfactual policy experiments 2 Policy experiments (Unweighted) leverage limit (baseline λ u = 33.3) changed from 25 to 41. Risk-weighted capital adequacy constraint (baseline λ w = 16.6) changed from 13 to 2. Steady state comparison. 11 / 25

13 Experiment I: Capital adequacy constraint (1).8.75 A: Loan to assets Large banks Small banks.4.2 B: % change in agg loan supply C: Equity to assets D: % change in profit to equity ratio.75 2 Large banks Tighter (risk-weighted) capital adequacy 1 constraint leads to:.7 Small banks.651 lower loan supply, since banks substitute into liquid assets E: % change in equity buffers x 1 4 F: Failure rates 12 / 25

14 .8.4 Experiment Large I: banks Capital adequacy constraint (2).75 A: Loan to assets Small banks.2 B: % change in agg loan supply C: Equity to assets E: % change in equity buffers x 1 4 F: Failure rates Tighter 1 (risk-weighted) capital adequacy 1 constraint leads to: 2 an increase in equity, Large banks Small banks 1 Large banks 3 a fall in RoE. Small banks Capital adequacy limit D: % change in profit to equity ratio Capital adequacy limit 13 / 25

15 Introduction Model C: Equity Estimation to assets Results Counterfactuals D: % change Extension in profit to Conclusion equity ratio Back up.75 2 Large banks.7 Small banks 1 Experiment I: Capital adequacy constraint (3) E: % change in equity buffers x 1 4 F: Failure rates 1 Large banks Small banks Capital adequacy limit Capital adequacy limit Tighter (risk-weighted) capital adequacy constraint leads to: 4 lower RoE which reduces incentives to accumulate equity in excess of regulatory minima. 5 increases failure rate. Details 14 / 25

16 Experiment II: Leverage constraint (PE).8.75 Big banks Small banks A: Loan to assets.3.2 B: % change in agg loan supply C: Equity to assets E: % change in equity buffers Leverage limit x 1 4 D: % change in profit to equity ratio F: Failure rates Leverage limit 15 / 25

17 Loan market closing We assume CES demand function with state-dependent intercept L D t = k (b t ) rt ω re-estimate the model with market clearing period by period (Krusell-Smith, R 2 s >.9995, Den Haan s mean errors <.3% and max errors <.1%) Redo policy experiment (so far large banks only) 16 / 25

18 Leverage experiment PE.8.75 Big banks Small banks A: Loan to assets.3.2 B: % change in agg loan supply C: Equity to assets E: % change in equity buffers Leverage limit x 1 4 D: % change in profit to equity ratio F: Failure rates Leverage limit 17 / 25

19 Leverage experiment GE A: Loan to assets B: % change L and rl C: Equity to assets D: % change in profit to equity ratio E: % change in equity buffers 1-3 F: Failure rates Leverage limit Leverage limit 18 / 25

20 Capital adequacy experiment PE.8.75 Big banks Small banks A: Loan to assets.4.2 B: % change in agg loan supply C: Equity to assets E: % change in equity buffers Capital adequacy limit x 1 4 D: % change in profit to equity ratio F: Failure rates Capital adequacy limit 19 / 25

21 Capital adequacy experiment GE A: Loan to assets C: Equity to assets E: % change in equity buffers Capital adequacy limit B: % change L and rl D: % change in profit to equity ratio F: Failure rates Capital adequacy limit / 25

22 Conclusions We estimate a dynamic banking model to examine the interaction of risk-weighted capital adequacy and leverage requirements. Banks hold an equity buffer (equity in excess of the regulatory minimum). Capital requirements interact. Tighter risk-weighted capital requirements: 1 reduce loan supply, 2 lead to endogenous fall in bank profitability and charter value, 3 reduce bank incentives to accumulate higher equity buffers, and 4 increase the incidence of bank failure in PE, but 5 GE in loan market attenuates effects sufficiently so that failure result overturned. 21 / 25

23 Conclusions ctd.... Tighter leverage requirements: 1 increase loan supply, 2 and in PE preserve bank profitability, charter value, incentives to accumulate equity buffers and reduce failure rate, in GE loan returns move against banks so that results are overturned. 22 / 25

24 Related literature 1 theoretical: Allen & Gale (24), Van den Heuvel (27,28), Allen, Carletti & Marquez (211), DeAngelo & Stulz (215),... 2 empirical: Kashyap & Stein (2), Miles, Yang & Marcheggiano (211), Berger & Bouwman (213), Jimenez, Ongena, Peydro & Saurina (214, 217), Adrian & Shin (21,214)... 3 quantitative: Suarez & Repullo (213), De Nicolo & Gamba & Lucchetta (214), Corbae & D Erasmo (215,217),...

25 Model III: Cost functions Cost of accessing wholesale funding markets: Loan adjustment costs: g F (F t, E t, D t ) = r Ft F t + φ F F 2 t D t φ E E 2 t D t (7) g N (N t, D t ) = I nt>φ N N 2 t D t + (1 I nt>)ψφ N N 2 t D t (8) with ψ > 1 capturing costly loan liquidation, and I nt> indicator function for positive new loans. 23 / 25

26 Estimation input Time varying aggregate parameters Parameter (in % exc. AR) Small banks Large banks Loan process: Uncon recession boom Uncon recession boom Loan write-offs: mean Loan write-offs: AR(1) Loan write-offs: std Deposit process: Deposit growth: mean Deposit growth: AR(1) Deposit growth: std Returns: Real deposit rate Loan spread Liquid asset spread Back

27 Leverage for failed and non-failed banks: data vs model Failed banks Non-failed banks 35 3 failed banks non failed banks Time to failure Quarters to failure 14 8 Data Model Back

28 The 2 regulatory constraints Minimum equity E min =1 / (λ u 1) Loan leverage limit L t =λ u E t Loan capital adequacy L t =λ w E t Capital adequacy with S=1+E L> Loans Equity Assumption: D = 1 24 / 25

29 Tightening the 2 regulatory constraints Benchmark Tighter leverage constraint Tighter capital adequacy constraint Loans Equity Assumption: D = 1 25 / 25

30 Experiment I: Equity buffers and capital adequacy limit A: Large banks B: Small banks unweighted risk weighted Capital adequacy limit.2.15 unweighted risk weighted Capital adequacy limit Risk weighted constraint always tighter for large banks. Back

31 Experiment II: Equity buffers and leverage limit A: Large banks B: Small banks unweighted risk weighted Leverage limit.2 unweighted risk weighted Leverage limit Again, risk weighted constraint always tighter for large banks. Back

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