Bank Capital Requirements: A Quantitative Analysis

Bank Capital Requirements: A Quantitative Analysis Thiên T. Nguyễn

Introduction Motivation Motivation Key regulatory reform: Bank capital requirements 1

Introduction Motivation Motivation Key regulatory reform: Bank capital requirements Policymakers: Strong consensus for higher bank capital requirements 1

Introduction Motivation Motivation In 2010, the Basel Committee on Banking Supervision: Raised Tier 1 capital requirement from 4 to 6 percent Tier 1 common stock + retained earnings In July 2013, the Fed adopted the same Tier 1 capital requirement for all U.S. banks. 2

Introduction Motivation Motivation The Ben S. Bernanke on regulatory capital framework: [T]his framework requires banking organizations to hold more and higher quality capital, which acts as a financial cushion to absorb losses, while reducing the incentive for... [banks] to take excessive risks. 3

Introduction Motivation Motivation Do new bank-capital requirements pose a risk to growth? The Economist, 8/20/2010 4

Introduction Motivation Motivation Do new bank-capital requirements pose a risk to growth? The Economist, 8/20/2010 Is imposing higher bank capital requirements beneficial? 4

Introduction Question Question What are the welfare implications of bank capital requirements? 5

Introduction Question Question What are the welfare implications of bank capital requirements? I propose a general equilibrium banking model to study this question. 5

Introduction Question Question What are the welfare implications of bank capital requirements? I propose a general equilibrium banking model to study this question. In this paper, bank capital affects growth and risk: Dynamic banking sector Banks risk-shift due to government bailouts. Banking regulation reduces risk-shifting incentive, fostering growth 5

Overview Outline of the model Capital producing firms Banks Final good producers Households 6

Overview Outline of the model Capital producing firms Banks Capital Final good producers Households 7

Overview Outline of the model Capital Capital producing firms Interest Loans Banks Final good producers Households 8

Overview Outline of the model Interest Capital Capital producing firms Loans Interest Dividend Banks Deposit Equity Final good producers Households 9

Overview Outline of the model Interest Capital Capital producing firms Loans Wage Interest Dividend Banks Deposit Equity Final good producers Labor Households 10

Households Households Representative household U 0 = E 0 t=0 t 1 1 1/ψ β t C1 1/ψ Endowed with 1 unit of labor supply inelastically 11

Capital-Producing Firms Capital-producing firms (j = island, f = firm) Large number of islands indexed by j: state or industry Firms are short-lived i t : required investment today for production tomorrow Two types of firms Normal firm capital produced tomorrow = z j,t+1 i t Risky-low-productivity firm capital produced tomorrow = z j,t+1 ɛ jf,t+1 i t log ɛ jft N ( µ 12 ) σ2ɛ, σ ɛ j, f, t 12

Capital-Producing Firms Capital-producing firms Small operating cost = o i t internal fund Funding need from bank i t 13

Capital-Producing Firms Capital-producing firms Small operating cost = o i t internal fund Funding need from bank i t Net income tomorrow = p I t+1z t+1 [χɛ f,t+1 + (1 χ)] i t }{{} R l (χ, z t ) i t }{{} Revenue Debt repayment Zero-profit condition Default option {}}{ E t M t+1 max{0, Net income tomorrow} = Current operating cost 13

Road map Road map Capital producing firms Banks Final good producers Households 14

Bank Banks Each bank chooses one firm to finance 15

Bank Banks Each bank chooses one firm to finance Bank s net cash at the beginning of next period π t+1 (χ t, z t, z t+1, ɛ f,t+1 ) = i t [R l (χ t, z t ) 1 {zt+1 z t+1 } Liquidated asset value {}}{ ] + η p I t+1z t+1 [χ t ɛ f,t+1 + (1 χ t )] 1 {zt+1 < z t+1 } R b t+1b t+1 }{{} Deposit liability Recovery rate η 15

Bank Banks Bank monitoring cost: m per unit of investment d t : net equity payout 16

Bank Banks Bank monitoring cost: m per unit of investment d t : net equity payout Bank s budget constraint π }{{} t Current net cash m i t }{{} Monitoring cost +b t+1 = i }{{} t +d t Lending 16

Bank Banks Bank monitoring cost: m per unit of investment d t : net equity payout Bank s budget constraint π }{{} t Current net cash m i t }{{} Monitoring cost +b t+1 = i }{{} t +d t Lending Net distribution to bank shareholders: d t Φ(d t ) }{{} Equity issuance cost 16

Bank Equity Valuation Bank equity valuation Bank s problem V (z t, π t ) = max{0, π t, max b t+1,χ t,d t d t Φ(d t ) + E t M t+1 V (z t+1, π t+1 )} subject to the budget constraint and loan demand Three cases: (1) Default, (2) Exit but not default, and (3) Operate 17

Deposit Valuation Bank deposit valuation Bank default: bailed out with probability λ Bailouts are financed with lump sum taxes If not bailed out, recovery rate θ 18

Deposit Valuation Bank deposit valuation Bank default: bailed out with probability λ Bailouts are financed with lump sum taxes If not bailed out, recovery rate θ Required return for depositors, Rt+1 b (z t, π t ), satisfies the condition Bank not default Bank default bail out {}}{{}}{ Rt+1b b t+1 1 {Vt+1 >0} + λr b t+1b t+1 1 {Vt+1 =0} b t+1 = E t M t+1 + (1 λ)θ Revenue t+1 1 {Vt+1 =0} }{{} Bank default not bail out 18

Policy Functions Bank s policy functions: Risk-shifting (on one industry/z j ) Exit decision 1.5 1 1 0.8 Equity payout asset ratio 0.6 0.4 0.2 0 0.5 0 0.5 1 Deposit asset ratio 0.5 0 0.5 1 0.5 0 0.5 1 Net cash 1 0.8 0.6 0.4 0.2 0 0.5 0 0.5 1 Net cash 19

Policy Functions Bank s policy functions: No risk-shifting (different z j ) Exit decision 1.5 1 1 0.8 Equity payout asset ratio 0.6 0.4 0.2 0 0.5 0 0.5 1 Deposit asset ratio 0.5 0 0.5 1 0.5 0 0.5 1 Net cash 1 0.8 0.6 0.4 0.2 0 0.5 0 0.5 1 Net cash 20

Distribution of Banks Distribution of banks Banks are heterogeneous only in terms of their idiosyncratic shocks and net cash: B }{{} t Γ(z t, π t ) }{{} Mass cdf 21

Distribution of Banks Distribution of banks Banks are heterogeneous only in terms of their idiosyncratic shocks and net cash: B }{{} t Γ(z t, π t ) }{{} Mass cdf Bank entry cost: e i t e i t E z V t (z t, π t = 0) If bailed out, banks can continue to operate with π t = 0 21

Equilibrium Capital Production Equilibrium capital production Capital produced next period I s t+1 = i t z t+1 [χ t ɛ f,t+1 + (1 χ t )] (Adjustments due to bankruptcies) dp (ɛ t+1 z t+1, π t+1 )B t+1 dγ t+1 22

Road map Road map Capital producing firms Banks Final good producers Households 23

Final Good Producer Final good producer A measure one of final good producers indexed by u [0, 1] Technology y ut = A t k α ut(k t l ut ) 1 α 24

Final Good Producer Final good producer A measure one of final good producers indexed by u [0, 1] Technology y ut = A t k α ut(k t l ut ) 1 α Investment demand i d ut Investment adjustment cost ( ) a i d 2 ut k u,t 1 2 k u,t 1 24

Final Good Producer Equilibrium Growth Aggregate output Y t = A t K t Growth Y t+1 Y t = A t+1 A t K t+1 K t 25

Final Good Producer Equilibrium Growth Aggregate output Y t = A t K t Growth Y t+1 Y t = A t+1 A t K t+1 K t Aggregate capital accumulation Capital market clearing K t = (1 δ)k t 1 + I d t 1 0 i d utdu = I d t = I s t 25

Quantitative Assessment Quantitative Assessment Calibrate the model to U.S. regulation: ē =.04 Benchmark Welfare calculations are relative to this benchmark 26

Calibration Calibration Period = quarter No aggregate uncertainty 27

Calibration Calibration Period = quarter No aggregate uncertainty Description Symbol Value Source/Target TFP level A 0.11 Match consumption growth 27

Calibration Calibration Period = quarter No aggregate uncertainty Description Symbol Value Source/Target TFP level A 0.11 Match consumption growth Subjective discount factor β 0.987 Cooley and Prescott (1995) Income share of capital α 0.45 Cooley and Prescott (1995) Capital depreciation rate δ 0.025 Jermann and Quadrini (2012) Intertemporal elasticity of substitution ψ 1.1 Bansal, Kiku, and Yaron (2013) Loan recovery parameter η 0.8 Gomes and Schmid (2010) Investment adjustment cost a 5 Gilchrist and Himmelberg (1995) Monitoring cost m 0.02 Philippon (2012) 27

Calibration Calibration Description Symbol Value Target Firm s operating cost o 0.023 Average return on loans Standard deviation of ɛ σ ɛ 0.363 x-std return on loans Bank entry cost e 0.06 Exit rate Reduction in productivity of risky firm µ 0.02 Average net interest margin Persistence of island specific shock ρ z 0.95 x-std net interest margin Volatility of island specific shock σ z 0.011 Default log z t+1 = ρ z log z t + σ zɛ z,t+1 28

Results Main Statistics Macro moments Data Model (ē =.04) c 0.49 Bank moments c/y 0.76 Data Top 1% Top 5% Top 10% Targeted moments Return on loan mean 4.33 4.63 4.92 x-std 2.95 3.51 3.99 Net interest margin mean 2.89 3.18 3.43 x-std 3.05 3.55 4.03 Failure 0.33 0.29 0.28 Exit rate 1.02 1.17 1.20 Other moments Net charge-off rate mean 2.70 0.93 0.76 x-std 17.94 13.74 11.00 Fraction risk-shifting Leverage ratio 7.74 8.29 8.51 Tier 1 capital ratio 10.25 12.18 12.62 Number of banks 113 564 1129 Source: Call Reports 1984-2010. Top x% column indicates statistics calculated from the top x% banks in term of total assets. mean is the time-series average of cross-sectional, and x-std is the time-series average of cross-sectional standard deviation. 29

Results Main Statistics Macro moments Data Model (ē =.04) c 0.49 0.49 Bank moments c/y 0.76 0.69 Data Top 1% Top 5% Top 10% Targeted moments Return on loan mean 4.33 4.63 4.92 4.01 x-std 2.95 3.51 3.99 5.23 Net interest margin mean 2.89 3.18 3.43 1.95 x-std 3.05 3.55 4.03 6.09 Failure 0.33 0.29 0.28 1.07 Exit rate 1.02 1.17 1.20 4.27 Other moments Net charge-off rate mean 2.70 0.93 0.76 2.86 x-std 17.94 13.74 11.00 10.09 Fraction risk-shifting 4.14 Leverage ratio 7.74 8.29 8.51 11.63 Tier 1 capital ratio 10.25 12.18 12.62 11.63 Number of banks 113 564 1129 Source: Call Reports 1984-2010. Top x% column indicates statistics calculated from the top x% banks in term of total assets. mean is the time-series average of cross-sectional, and x-std is the time-series average of cross-sectional standard deviation. 30

Results Welfare implications Let c t be the consumption-capital ratio C t = c t K t 1 = k t 1 c K 0 }{{} Initial level 31

Results Welfare implications 1.2 Welfare (%) 1 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6 0.8 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 Minimum capital requirements 32

Results Welfare implications 5.5 Exit rate 9 Measure of banks 5 8 4.5 7 4 6 3.5 5 3 4 0.03 Capital produced 0.495 Consumption growth (%) 0.49 0.0299 0.485 0.0298 Minimum capital requirements 0.48 Minimum capital requirements 33

Results Welfare implications 1.5 Welfare (%) 2 Bank failure (%) 1 1.5 0.5 0 1 0.5 0.5 1 0 1.08 Average productivity 0.076 Consumption capital ratio 1.06 0.0755 1.04 0.075 1.02 0.0745 1 0.074 0.98 Minimum capital requirements 0.0735 Minimum capital requirements 34

Results Welfare implications Why welfare decreases after 8 percent? 1. Romer learning-by-doing externality 35

Results Welfare implications Why welfare decreases after 8 percent? 1. Romer learning-by-doing externality 2. Equity issuance cost 35

Results Role of equity issuance cost: φ 1.5 Welfare (%) Capital produced 1 0.03 0.5 0.0299 0 0.5 1 Benchmark φ = 0 Minimum capital requirements 0.0298 0.0297 Minimum capital requirements 36

Results Role of probability of bailout: λ 2 Welfare (%) 1.5 1 0.5 0 0.5 1 1.5 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 Minimum capital requirements Benchmark λ =.95 37

Results Role of productivity loss due to risk-shifting: µ 1.5 Welfare (%) 2.5 Bank failure (%) 1 2 0.5 1.5 0 1 0.5 1 1.08 1.06 1.04 1.02 1 0.98 Benchmark µ =.01 Average productivity 0.5 0 Minimum capital requirements 0.96 Minimum capital requirements 38

Results Role of additional risk exposure due to risk-shifting: σ ɛ 1.5 Welfare (%) 1 0.5 0 0.5 1 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 Minimum capital requirements Benchmark σ ɛ =.37 39

Conclusion Conclusion Dynamic general equilibrium banking model The calibrated version of the model suggests an 8% minimum Tier 1 capital requirement significant welfare improvement: 1.1% of lifetime consumption Punch-line: Optimal level is higher than in both Basel II and Basel III Broader level: The need to re-examine current bank capital regulations 40