Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Capital Requirements in a Quantitative Model of Banking Industry Dynamics Dean Corbae

Pablo D’Erasmo1

Wisconsin and NBER

FRB Philadelphia

October 9, 2015 (Preliminary and Incomplete)

1 The views expressed here do not necessarily reflect those of the FRB Philadelphia or The Federal Reserve System. Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Introduction I

Bank market structure differs considerably across countries. For example, the 2011 asset market share of the top 3 banks in Norway was 95% versus 35% in the U.S. (World Bank)

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Introduction I

Bank market structure differs considerably across countries. For example, the 2011 asset market share of the top 3 banks in Norway was 95% versus 35% in the U.S. (World Bank)

I

This paper is about how policy (e.g. capital requirements) affects bank lending by big and small banks, loan rates, and market structure in the commercial banking industry (positive analysis).

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Introduction I

Bank market structure differs considerably across countries. For example, the 2011 asset market share of the top 3 banks in Norway was 95% versus 35% in the U.S. (World Bank)

I

This paper is about how policy (e.g. capital requirements) affects bank lending by big and small banks, loan rates, and market structure in the commercial banking industry (positive analysis).

Main Question I

How much does a 50% rise in capital requirements (4%→6% as proposed by Basel III) affect failure rates and market shares of large and small banks in the U.S.?

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Introduction I

Bank market structure differs considerably across countries. For example, the 2011 asset market share of the top 3 banks in Norway was 95% versus 35% in the U.S. (World Bank)

I

This paper is about how policy (e.g. capital requirements) affects bank lending by big and small banks, loan rates, and market structure in the commercial banking industry (positive analysis).

Main Question I

How much does a 50% rise in capital requirements (4%→6% as proposed by Basel III) affect failure rates and market shares of large and small banks in the U.S.?

Answer I

A 50% ↑ capital requirements reduces exit rates of small banks by 40% but results in a more concentrated industry. Aggregate loan supply shrinks and interest rates are 50 basis points higher.

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Outline 1. Data: Document U.S. Banking Facts from Balance sheet and Income Statement Panel Data.

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Outline 1. Data: Document U.S. Banking Facts from Balance sheet and Income Statement Panel Data. 2. Model:

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Outline 1. Data: Document U.S. Banking Facts from Balance sheet and Income Statement Panel Data. 2. Model: I

Underlying static Cournot banking model with exogenous bank size distribution is from Allen & Gale (2004), Boyd & De Nicolo (2005)).

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Outline 1. Data: Document U.S. Banking Facts from Balance sheet and Income Statement Panel Data. 2. Model: I

Underlying static Cournot banking model with exogenous bank size distribution is from Allen & Gale (2004), Boyd & De Nicolo (2005)).

I

Endogenize bank size distribution by adding shocks and dynamic entry/exit decisions. Solve for industry equilibrium along the lines of Ericson & Pakes (1995) and Gowrisankaran & Holmes (2004).

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Outline 1. Data: Document U.S. Banking Facts from Balance sheet and Income Statement Panel Data. 2. Model: I

Underlying static Cournot banking model with exogenous bank size distribution is from Allen & Gale (2004), Boyd & De Nicolo (2005)).

I

Endogenize bank size distribution by adding shocks and dynamic entry/exit decisions. Solve for industry equilibrium along the lines of Ericson & Pakes (1995) and Gowrisankaran & Holmes (2004).

I

Calibrate parameters to match long-run industry averages.

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Outline 1. Data: Document U.S. Banking Facts from Balance sheet and Income Statement Panel Data. 2. Model: I

Underlying static Cournot banking model with exogenous bank size distribution is from Allen & Gale (2004), Boyd & De Nicolo (2005)).

I

Endogenize bank size distribution by adding shocks and dynamic entry/exit decisions. Solve for industry equilibrium along the lines of Ericson & Pakes (1995) and Gowrisankaran & Holmes (2004).

I

Calibrate parameters to match long-run industry averages.

I

Test model against other moments: (1) business cycle correlations, and (2) the bank lending channel.

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Outline 1. Data: Document U.S. Banking Facts from Balance sheet and Income Statement Panel Data. 2. Model: I

Underlying static Cournot banking model with exogenous bank size distribution is from Allen & Gale (2004), Boyd & De Nicolo (2005)).

I

Endogenize bank size distribution by adding shocks and dynamic entry/exit decisions. Solve for industry equilibrium along the lines of Ericson & Pakes (1995) and Gowrisankaran & Holmes (2004).

I

Calibrate parameters to match long-run industry averages.

I

Test model against other moments: (1) business cycle correlations, and (2) the bank lending channel.

3. Capital Requirement Policy Counterfactuals:

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Outline 1. Data: Document U.S. Banking Facts from Balance sheet and Income Statement Panel Data. 2. Model: I

Underlying static Cournot banking model with exogenous bank size distribution is from Allen & Gale (2004), Boyd & De Nicolo (2005)).

I

Endogenize bank size distribution by adding shocks and dynamic entry/exit decisions. Solve for industry equilibrium along the lines of Ericson & Pakes (1995) and Gowrisankaran & Holmes (2004).

I

Calibrate parameters to match long-run industry averages.

I

Test model against other moments: (1) business cycle correlations, and (2) the bank lending channel.

3. Capital Requirement Policy Counterfactuals: I

Basel III CR rise from 4% to 6%

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Outline 1. Data: Document U.S. Banking Facts from Balance sheet and Income Statement Panel Data. 2. Model: I

Underlying static Cournot banking model with exogenous bank size distribution is from Allen & Gale (2004), Boyd & De Nicolo (2005)).

I

Endogenize bank size distribution by adding shocks and dynamic entry/exit decisions. Solve for industry equilibrium along the lines of Ericson & Pakes (1995) and Gowrisankaran & Holmes (2004).

I

Calibrate parameters to match long-run industry averages.

I

Test model against other moments: (1) business cycle correlations, and (2) the bank lending channel.

3. Capital Requirement Policy Counterfactuals: I I

Basel III CR rise from 4% to 6% Countercyclical CR

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Outline 1. Data: Document U.S. Banking Facts from Balance sheet and Income Statement Panel Data. 2. Model: I

Underlying static Cournot banking model with exogenous bank size distribution is from Allen & Gale (2004), Boyd & De Nicolo (2005)).

I

Endogenize bank size distribution by adding shocks and dynamic entry/exit decisions. Solve for industry equilibrium along the lines of Ericson & Pakes (1995) and Gowrisankaran & Holmes (2004).

I

Calibrate parameters to match long-run industry averages.

I

Test model against other moments: (1) business cycle correlations, and (2) the bank lending channel.

3. Capital Requirement Policy Counterfactuals: I I I

Basel III CR rise from 4% to 6% Countercyclical CR Size dependent CR

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Data Summary from C-D (2013) I

Entry is procyclical and Exit by Failure is countercyclical.

I

Almost all Entry and Exit is by small banks.

I

Loans and Deposits are procyclical (correl. with GDP equal to 0.72 and 0.22 respectively).

I

High Concentration: Top 1% banks have 76% of loan market share in 2010. Fig Table

I

Large Net Interest Margins, Markups, Lerner Index, Rosse-Panzar H < 100. Table

I

Net marginal expenses are increasing with bank size. Fixed operating costs (normalized) are decreasing in size. Table

I

Loan Returns, Margins, Markups, Delinquency Rates and Charge-offs are countercyclical. Table

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Fig

Table

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Balance Sheet Data Key Components by Size Fraction total assets (%) Assets Liquid assets Securities Loans Liabilities Deposits fed funds/repos equity Bank capital (rw)

2000 Fringe top 10

2010 Fringe top 10

9.88 17.20 72.91

14.19 11.49 74.32

9.77 18.15 72.07

15.95 15.15 68.91

74.55 19.04 6.41 10.19

75.46 18.42 6.11 7.81

79.94 13.84 6.23 13.93

81.34 13.66 5.00 11.35

Note: Data corresponds to commercial banks in the US. Source: Consolidated Definitions Report of Condition and Income. Balance Sheet (Long) I

While loans and deposits are the most important parts of the bank balance sheet, “precautionary holdings” of securities are an important buffer stock.

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Capital Ratios by Bank Size from C-D (2014a) Tier 1 Bank Capital to risk−weighted assets ratio

18 Top 10 Fringe 16

Percentage (%)

14

12

10

8

6

I

I

1996

1998

2000

2002

2004 year

2006

2008

2010

2012

2014

Risk weighted capital ratios ((loans+net assets-deposits)/loans) are larger for small banks. On average, capital ratios are above what regulation defines as “Well Capitalized” (≥ 6%) suggesting a precautionary motive. Fig. non-rw

Regulation Details

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Distribution of Bank Capital Ratios Panel (i): Distribution year 2000 Fraction of Banks (%)

25 Top 10 Fringe Cap. Req.

20 15 10 5 0

0

0.05

0.1 0.15 0.2 Tier 1 Capital Ratio (risk−weighted)

0.25

0.3

Panel (ii): Distribution year 2010 Fraction of Banks (%)

25 Top 10 Fringe Cap. Req.

20 15 10 5 0

0

0.05

0.1 0.15 0.2 Tier 1 Capital Ratio (risk−weighted)

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

0.25

0.3

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Undercapitalized bank exit 90

120.00%

80 100.00% 70 60

80.00%

50 60.00% 40 30

40.00%

20 20.00% 10 0

0.00% 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 # banks CR in [0% - 4%] (left axis)

Frac. Exit at t or t+1 (right axis)

I

Number of small U.S. banks below 4% capital requirement rose dramatically during crisis.

I

High percentage of those geographically undiversified banks exit.

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Capital Ratios Over the Business Cycle 0.03

1.5

0.015

0.5

0

−0.5

GDP

Capital Ratios (%)

Det. Tier 1 Bank Capital Ratios over Business Cycle (risk−weighted) 2.5

−0.015

CR Top 10 CR Fringe GDP (right axis) −1.5 1996

I

1998

2000

2002

2004 2006 Period (t)

2008

2010

2012

−0.03 2014

Risk-Weighted capital ratio is countercyclical for small and big banks (corr. -0.40 and -0.64 respectively).

Fig Ratio to Total Assets

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Model Essentials I

Banks intermediate between

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Model Essentials I

Banks intermediate between I

Unit mass of identical risk averse households who are offered insured bank deposit contracts or outside storage technology (Deposit supply). Insurance funded by lump sum transfers.

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Model Essentials I

Banks intermediate between I

Unit mass of identical risk averse households who are offered insured bank deposit contracts or outside storage technology (Deposit supply). Insurance funded by lump sum transfers.

I

Unit mass of identical risk neutral borrowers who demand funds to undertake i.i.d. risky projects (Loan demand). Borrowers

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Model Essentials I

Banks intermediate between I

Unit mass of identical risk averse households who are offered insured bank deposit contracts or outside storage technology (Deposit supply). Insurance funded by lump sum transfers.

I

Unit mass of identical risk neutral borrowers who demand funds to undertake i.i.d. risky projects (Loan demand). Borrowers

I

By lending to a large # of borrowers, a given bank diversifies risk.

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Model Essentials I

Banks intermediate between I

Unit mass of identical risk averse households who are offered insured bank deposit contracts or outside storage technology (Deposit supply). Insurance funded by lump sum transfers.

I

Unit mass of identical risk neutral borrowers who demand funds to undertake i.i.d. risky projects (Loan demand). Borrowers

I

By lending to a large # of borrowers, a given bank diversifies risk.

I

Loan market clearing determines interest rate rtL (ζt , zt ) where ζt is the cross-sectional distribution of banks and zt are beginning of period t shocks.

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Model Essentials I

Banks intermediate between I

Unit mass of identical risk averse households who are offered insured bank deposit contracts or outside storage technology (Deposit supply). Insurance funded by lump sum transfers.

I

Unit mass of identical risk neutral borrowers who demand funds to undertake i.i.d. risky projects (Loan demand). Borrowers

I

By lending to a large # of borrowers, a given bank diversifies risk.

I

I

Loan market clearing determines interest rate rtL (ζt , zt ) where ζt is the cross-sectional distribution of banks and zt are beginning of period t shocks.

Shocks to loan performance and bank financing along with entry and exit induce an endogenous distribution of banks of different sizes. Shocks

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Model Essentials - cont.

Deviations from Modigliani-Miller for Banks (influence costly exit): I

Limited liability and deposit insurance (moral hazard)

I

Equity finance and bankruptcy costs

I

Noncontingent loan contracts

I

Market power by a subset of banks

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Banks - Cash Flow For a bank of type θ which I

makes loans `θt at rate rtL accepts deposits dθt at rate rtD ,

I

holds net securities Aθt at rate rta ,

I

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Banks - Cash Flow For a bank of type θ which I

makes loans `θt at rate rtL accepts deposits dθt at rate rtD ,

I

holds net securities Aθt at rate rta ,

I

Its end-of-period profits are given by n o θ πt+1 = p(Rt , zt+1 )(1 + rtL ) + (1 − p(Rt , zt+1 ))(1 − λ) − cθ `θt +ra Aθt − (1 + rD )dθt − κθ . where I

p(Rt , zt+1 ) are the fraction of performing loans which depends on borrower choice Rt and shocks zt+1 ,

I

Charge-off rate λ,

I

(cθ , κθ ) are net proportional and fixed costs.

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Banks - Capital Ratios and Borrowing Constraints I

After loan, deposit, and security decisions have been made, we can define bank equity capital e˜θt as eθt ≡ Aθt + `θt − dθt . | {z } |{z} assets

I

liabilities

Banks face a Capital Requirement: eθt ≥ ϕθ (`θt + w · Aθt )

(CR)

where w is the “risk weighting” (i.e. w = 0 imposes a risk-weighted capital ratio).

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Banks - Capital Ratios and Borrowing Constraints I

After loan, deposit, and security decisions have been made, we can define bank equity capital e˜θt as eθt ≡ Aθt + `θt − dθt . | {z } |{z} assets

I

liabilities

Banks face a Capital Requirement: eθt ≥ ϕθ (`θt + w · Aθt )

(CR)

where w is the “risk weighting” (i.e. w = 0 imposes a risk-weighted capital ratio). I

Banks face an end-of-period Borrowing Constraint: aθt+1 = At − (1 + rB )Bt+1 ≥ 0

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

(BBC) Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Banks - Optimization I

θ < 0 (negative cash flow), bank can issue equity (at unit When πt+1 θ > 0) against net securities (e.g. repos) cost ζ θ (·)) or borrow (Bt+1 to avoid exit but beginning-of-next-period’s assets fall.

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Banks - Optimization I

θ < 0 (negative cash flow), bank can issue equity (at unit When πt+1 θ > 0) against net securities (e.g. repos) cost ζ θ (·)) or borrow (Bt+1 to avoid exit but beginning-of-next-period’s assets fall.

I

θ θ < 0) raising > 0, bank can either lend/store cash (Bt+1 When πt+1 beginning-of-next-period’s assets and/or pay out dividends.

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Banks - Optimization I

θ < 0 (negative cash flow), bank can issue equity (at unit When πt+1 θ > 0) against net securities (e.g. repos) cost ζ θ (·)) or borrow (Bt+1 to avoid exit but beginning-of-next-period’s assets fall.

I

θ θ < 0) raising > 0, bank can either lend/store cash (Bt+1 When πt+1 beginning-of-next-period’s assets and/or pay out dividends.

I

Bank dividends at the end of the period are  θ θ πi,t+1 + Bi,t+1 θ Di,t+1 = θ θ θ θ θ

πi,t+1 + Bi,t+1 − ζ (πi,t+1 + Bi,t+1 , zt+1 )

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

θ θ if πi,t+1 + Bi,t+1 ≥0 θ θ if πi,t+1 + Bi,t+1 < 0

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Banks - Optimization I

θ < 0 (negative cash flow), bank can issue equity (at unit When πt+1 θ > 0) against net securities (e.g. repos) cost ζ θ (·)) or borrow (Bt+1 to avoid exit but beginning-of-next-period’s assets fall.

I

θ θ < 0) raising > 0, bank can either lend/store cash (Bt+1 When πt+1 beginning-of-next-period’s assets and/or pay out dividends.

I

Bank dividends at the end of the period are  θ θ πi,t+1 + Bi,t+1 θ Di,t+1 = θ θ θ θ θ

πi,t+1 + Bi,t+1 − ζ (πi,t+1 + Bi,t+1 , zt+1 )

I

θ θ if πi,t+1 + Bi,t+1 ≥0 θ θ if πi,t+1 + Bi,t+1 < 0

Bank type θ chooses loans, deposits, net securities, non-negative dividend payouts, exit policy to maximize the future discounted stream of dividends Problem "∞ # X t θ E β Dt+1 t=0

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Banks - Entry & Exit

At the end of the period, I

Exit: If a bank chooses to exit, its asset net of liabilities are liquidated at salvage value ξ ≤ 1 and lump sum taxes on households cover depositor losses.

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Banks - Entry & Exit

At the end of the period, I

Exit: If a bank chooses to exit, its asset net of liabilities are liquidated at salvage value ξ ≤ 1 and lump sum taxes on households cover depositor losses.

I

Entry: Banks which choose to enter incur cost Υθ .

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Entry

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Bank Size Distribution and Loan Market Clearing I

The industry state is given by the cross-sectional distribution of active banks ζtθ (a, δ) of a given type θ (a measure over beginning-of-period deposits δt and net securities at ). Distn

I

The cross-sectional distribution is necessary to calculate loan market clearing:  X Z θ θ `t (at , δt , zt )dζt (at , δt ) = Ld (rtL , zt ) (1) θ∈{b,f }

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Defn. Markov Perfect Industry EQ Given policy parameters: I

Capital requirements,ϕθ , and risk weights, w.

I

Borrowing rates, rB , and securities rates, ra ,

a pure strategy Markov Perfect Industry Equilibrium (MPIE) is: 1. Given rL , loan demand Ld (rL , z) is consistent with borrower optimization. 2. At rD , households choose to deposit at a bank. 3. Bank loan, deposit, net security holding, borrowing, exit, and dividend payment functions are consistent with bank optimization. Decision Rules 4. The law of motion for cross-sectional distribution of banks ζ is consistent with bank entry and exit decision rules. Dist 5. The interest rate rL (ζ, z) is such that the loan market clears. 6. Across all states, taxes cover deposit insurance. timing Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Long-run Model vs Data Moments Param. chosen to minimize the diff. between data and model moments. Moment (%) Freq. Top 10 bank exit Std. dev. Output Std. dev. net-int. margin Borrower Return Std. deviation default frequency Net Interest Margin Default freq. Elasticity Loan Demand Loans to asset ratio Top 10 Loans to asset ratio fringe Deposit mkt share fringe Fixed cost over loans Top 10 Fixed cost over loans Fringe Bank entry rate Bank exit rate Capital Ratio Top 10 (rwa) Capital Ratio Fringe (rwa) Equity Issuance over Assets Top 10 (%) Equity Issuance over Assets Fringe (%) Sec. to asset ratio Top 10 Sec. to asset ratio Fringe Avg Loan Markup Loan Market Share Fringe AR1 Industry Defn Moments Capital Requirements in a Quantitative Model of Banking Dynamics

Data 3.03 1.46 0.89 12.94 1.49 4.70 2.33 -1.40 55.52 60.63 74.44 1.41 2.08 1.55 0.71 9.09 12.65 0.02 0.17 25.34 30.04 102.73 66.61

Param Values

Model 6.00 2.27 0.50 11.99 3.13 3.94 2.06 -1.01 58.32 85.52 40.58 2.57 2.31 2.03 1.95 4.33 9.69 0.05 0.40 28.70 9.77 95.69 42.56 Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Untargeted Business Cycle Correlations Variable Correlated with GDP Loan Interest rate Exit rate Entry rate Loan Supply Deposit Demand Default Frequency Loan return Charge-off rate Price Cost Margin Markup Capital Ratio Top 10 (rwa) Capital Ratio Fringe (rwa) I

Data -0.18 -0.33 0.21 0.55 0.16 -0.66 -0.27 -0.35 -0.39 -0.34 -0.64 -0.18

Model -0.90 -0.67 0.46 0.98 0.70 -0.32 -0.05 -0.32 -0.59 -0.91 0.14 -0.17

The model does a good qualitative job with the business cycle Kashyap-Stein correlations. Fig. Cap. Ratios

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Frac Banks constrained by Min Cap. Req. 10

0.4

5

0

I

0.35

0

10

20

30

40

50 Period (t)

60

70

80

90

Output

Frac. at Cap. Req.

Frac. ef /`f = ϕ Output (right axis)

0.3 100

Fraction of capital requirement constrained banks rises during downturns (correlation of constrained banks and output is -0.85).

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Counterfactuals

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Higher Capital Requirements Question: How much does a 50% increase of capital requirements (from 4% to 6% as in Basel III) affect outcomes? I

Higher cap. req. → banks substitute away from loans to securities → lower profitability. Figure Decision Rules

I

Lower loan supply (-8%) → higher interest rates (+50 basis points), more chargeoffs (+12%), lower intermediated output (-9%).

I

Entry/Exit drops (-45%) → lower taxes (-60%), more concentrated industry (less small banks (-14%)).

Table CR

Competition

Cyclical CR

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Conclusion I

One of the first papers to pose a structural dynamic model with imperfect competition and an endogenous bank size distribution to assess the quantitative significance of capital requirements.

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Conclusion I

One of the first papers to pose a structural dynamic model with imperfect competition and an endogenous bank size distribution to assess the quantitative significance of capital requirements.

I

We find that a rise in capital requirement from 4% to 6% leads to a significant reduction in bank exit probabilities, but a more concentrated industry.

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Conclusion I

One of the first papers to pose a structural dynamic model with imperfect competition and an endogenous bank size distribution to assess the quantitative significance of capital requirements.

I

We find that a rise in capital requirement from 4% to 6% leads to a significant reduction in bank exit probabilities, but a more concentrated industry.

I

Strategic interaction between big and small banks generates higher volatility than a perfectly competitive model.

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Conclusion I

One of the first papers to pose a structural dynamic model with imperfect competition and an endogenous bank size distribution to assess the quantitative significance of capital requirements.

I

We find that a rise in capital requirement from 4% to 6% leads to a significant reduction in bank exit probabilities, but a more concentrated industry.

I

Strategic interaction between big and small banks generates higher volatility than a perfectly competitive model.

I

Countercyclical markups provides a new amplification mechanism; in a downturn, exit weakens competition → higher loan rates, amplifying the downturn.

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Conclusion I

One of the first papers to pose a structural dynamic model with imperfect competition and an endogenous bank size distribution to assess the quantitative significance of capital requirements.

I

We find that a rise in capital requirement from 4% to 6% leads to a significant reduction in bank exit probabilities, but a more concentrated industry.

I

Strategic interaction between big and small banks generates higher volatility than a perfectly competitive model.

I

Countercyclical markups provides a new amplification mechanism; in a downturn, exit weakens competition → higher loan rates, amplifying the downturn.

I

Stackelberg game allows us to examine how policy changes which affect big banks spill over to the rest of the industry.

other Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Open Questions I

Why is market structure so different across countries? I

In 2011, this is evident in the asset market share of the top 3 banks in the following countries (1/N with symmetric banks): I I I I I I I

Germany: 78% Japan: 44% Mexico: 57% Portugal: 89% Spain: 68% UK: 58% US: 35%

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Open Questions I

Why is market structure so different across countries? I

In 2011, this is evident in the asset market share of the top 3 banks in the following countries (1/N with symmetric banks): I I I I I I I

I

Germany: 78% Japan: 44% Mexico: 57% Portugal: 89% Spain: 68% UK: 58% US: 35%

Does competition matter for crises?

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Crises

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Some Directions for Future Research in Structural Financial IO I

Deposit insurance and deposit market competition (Ali and Victor’s papers contribute here).

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Some Directions for Future Research in Structural Financial IO I

Deposit insurance and deposit market competition (Ali and Victor’s papers contribute here).

I

Regulatory Effects on: I I

Mergers and Increasing Concentration Competition I I

Within commercial banking industry (today’s paper) Bank substitutes (Shadow banking industry)

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Some Directions for Future Research in Structural Financial IO I

Deposit insurance and deposit market competition (Ali and Victor’s papers contribute here).

I

Regulatory Effects on: I I

Mergers and Increasing Concentration Competition I I

I

Within commercial banking industry (today’s paper) Bank substitutes (Shadow banking industry)

Foreign Bank Competition

Global

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Some Directions for Future Research in Structural Financial IO I

Deposit insurance and deposit market competition (Ali and Victor’s papers contribute here).

I

Regulatory Effects on: I I

Mergers and Increasing Concentration Competition I I

Within commercial banking industry (today’s paper) Bank substitutes (Shadow banking industry)

I

Foreign Bank Competition

I

Stress tests I I

Global

Stress

Add Borrower Heterogeneity (Commercial vs Residential markets) Add Maturity Structure Differences

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

—————————————————————————————-

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Test III: Empirical Studies of Banking Crises, Default and Concentration Model Dependent Variable Concentrationt GDP growth in t Loan Supply Growtht R2

Logit Crisist -3.77 (0.86)∗∗∗ 0.81 (0.09)∗∗∗ -3.38 (1.39)∗∗ 0.76

Linear Default Freq.t 0.0294 (0.001)∗∗∗ -1.423 (0.021)∗∗∗ 1.398 (0.0289)∗∗∗ 0.53

Note: SE in parenthesis.

I

As in Beck, et. al. (2003), banking system concentration (market share of top 1%) is negatively related to the probability of a banking crisis ( e.g. 2xhigher exit rate) (consistent with A-G).

I

As in Berger et. al. (2008) we find that concentration is positively related to default frequency (consistent with B-D). Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

C-D 2014b: Global Banking Competition Question: How much do restrictions on foreign bank entry affect domestic loan rates and welfare?

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

C-D 2014b: Global Banking Competition Question: How much do restrictions on foreign bank entry affect Return to Directions domestic loan rates and welfare? Table I After calibrating a GE version to Mexico (where foreign bank loan market share is currently 70%), we run a counterfactual where entry costs for foreign banks are set prohibitively high. We find foreign bank competition yields:

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

C-D 2014b: Global Banking Competition Question: How much do restrictions on foreign bank entry affect Return to Directions domestic loan rates and welfare? Table I After calibrating a GE version to Mexico (where foreign bank loan market share is currently 70%), we run a counterfactual where entry costs for foreign banks are set prohibitively high. We find foreign bank competition yields: I

Higher loan supply (32%) → less concentration and lower interest rate margins (- 200 basis points).

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

C-D 2014b: Global Banking Competition Question: How much do restrictions on foreign bank entry affect Return to Directions domestic loan rates and welfare? Table I After calibrating a GE version to Mexico (where foreign bank loan market share is currently 70%), we run a counterfactual where entry costs for foreign banks are set prohibitively high. We find foreign bank competition yields: I

Higher loan supply (32%) → less concentration and lower interest rate margins (- 200 basis points).

I

Higher exit rates with banks more exposed to foreign shocks inducing more domestic volatility (output and loan supply volatility rises (+12.91% and 10.11%, respectively)).

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

C-D 2014b: Global Banking Competition Question: How much do restrictions on foreign bank entry affect Return to Directions domestic loan rates and welfare? Table I After calibrating a GE version to Mexico (where foreign bank loan market share is currently 70%), we run a counterfactual where entry costs for foreign banks are set prohibitively high. We find foreign bank competition yields: I

Higher loan supply (32%) → less concentration and lower interest rate margins (- 200 basis points).

I

Higher exit rates with banks more exposed to foreign shocks inducing more domestic volatility (output and loan supply volatility rises (+12.91% and 10.11%, respectively)).

I

Lower interest rates → lower default (-2.85%) and charge offs (-3.2%).

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

C-D 2014b: Global Banking Competition Question: How much do restrictions on foreign bank entry affect Return to Directions domestic loan rates and welfare? Table I After calibrating a GE version to Mexico (where foreign bank loan market share is currently 70%), we run a counterfactual where entry costs for foreign banks are set prohibitively high. We find foreign bank competition yields: I

Higher loan supply (32%) → less concentration and lower interest rate margins (- 200 basis points).

I

Higher exit rates with banks more exposed to foreign shocks inducing more domestic volatility (output and loan supply volatility rises (+12.91% and 10.11%, respectively)).

I

Lower interest rates → lower default (-2.85%) and charge offs (-3.2%).

I

Higher output (+30%),higher taxes, and higher household welfare (CE equivalent) (+0.79%).

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Stress Tests - Reduced Form Approach Hirtle, et. al. (2014) CLASS (Capital and Loss Assessment under Stress Scenarios) model: 1. Reduced form regressions: yi,t = β0 + β1 · yi,t−1 + β2 · macrot + β3 · xi,t + εi,t

(2)

where yi,t is an N vector of key income or expense ratios across loan classes (e.g. net interest margin, net charge-offs), xi,t are firm specific characteristics such as shares of different types of loans in bank i0 s portfolio, etc. I

Hirtle, et.al. p. 17: “model projections are sensitive to the first-lagged value of bank data used to “seed” the projections.”

2. To translate the above ratios into dollar values to calculate net income position etc, the CLASS model assumes each bank’s total assets (liabilities) grow at a fixed percentage rate of 1.25% per quarter over the stress test horizon and evaluates their capital buffer in response to shock. Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Stress Tests - Structural Approach After solving for optimal lending, capital buffer, dividend, and exit decision rules as a function of bank specific (e.g. a, δ) and macro (e.g. z, ζ) state variables, we can simply compute P(x = 1|a, δ, z, ζ) = P W x=1 (`, d, A, δ, ζ, z 0 ) > W x=0 (`, d, A, δ, ζ, z 0 )|a, δ, z, ζ (3) where W x=1 and W x=0 are the charter values of the bank under exit and no-exit options. I

Evolution of the state variables (asset position a and bank size distribution ζ) are endogenously determined.

Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo




Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Entry and Exit Over the Business Cycle 8 Entry Rate Exit Rate Det. GDP 6

Percentage (%)

4

2

0

−2

−4

1975

1980

1985

1990

1995 year

2000

2005

2010

I

Trend in exit rate prior to early 90’s due to deregulation

I

Correlation of GDP with (Entry,Exit) =(0.25,0.22); with (Failure, Troubled, Mergers) =(-0.47, -0.72, 0.58) after 1990 (deregulation) Exit Rate Decomposed

Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Entry and Exit by Bank Size

Fraction of Total x, accounted by: Top 10 Banks Top 1% Banks Top 10% Banks Bottom 99% Banks Total Rate

Entry 0.00 0.33 4.91 99.67 1.71

Exit 0.09 1.07 14.26 98.93 3.92

x Exit/Merger 0.16 1.61 16.17 98.39 4.57

Exit/Failure 0.00 1.97 15.76 98.03 1.35

Note: Big banks that exited by merger: 1996 Chase Manhattan acquired by Chemical Banking Corp. 1999 First American National Bank acquired by AmSouth Bancorp.

Definitions

Frac. of Loans

Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Increase in Loan and Deposit Market Concentration Panel (i): Loan Market Share 60

Percentage (%)

50

Top 4 Banks Top 10 Banks

40 30 20 10 0 1975

1980

1985

1990

1995 year

2000

2005

2010

2005

2010

Panel (ii): Deposit Market Share 60

Percentage (%)

50

Top 4 Banks Top 10 Banks

40 30 20 10 0 1975

1980

1985

1990

1995 year

2000

Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Measures of Concentration in 2010 Measure Percentage of Total in top 4 Banks (C4 ) Percentage of Total in top 10 Banks Percentage of Total in top 1% Banks Percentage of Total in top 10% Banks Ratio Mean to Median Ratio Total Top 10% to Top 50% Gini Coefficient HHI : Herfindahl Index (National) (%) HHI : Herfindahl Index (by MSA) (%)

Deposits 38.2 46.1 71.4 87.1 11.1 91.8 .91 5.6 19.6

Loans 38.2 51.7 76.1 89.6 10.2 91.0 .90 4.3 20.7

Note: Total Number of Banks 7,092. Top 4 banks are: Bank of America, Citibank, JP Morgan Chase, Wells Fargo.

I

High degree of imperfect competition HHI ≥ 15

I

National measure is a lower bound since it does not consider regional market shares (Bergstresser (2004)).

Return Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Measures of Banking Competition Moment Interest margin Markup Lerner Index Rosse-Panzar H

Value (%) 4.56 102.73 49.24 51.97

Std. Error (%) 0.30 4.3 1.38 0.87

Corr w/ GDP -0.309 -0.203 -0.259 -

I

All the measures provide evidence for imperfect competition (H< 100 implies MR insensitive to changes in MC).

I

Estimates are in line with those found by Berger et.al (2008),Bikker and Haaf (2002), and Koetter, Kolari, and Spierdijk (2012).

I

Countercyclical markups imply more competition in good times (new amplification mechanism).

Definitions

Figures

Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Costs by Bank Size

Moment (%) Top 1% Bottom 99%

Non-Int Inc. 2.32† 0.89

Non-Int Exp. 3.94† 2.48

Net Exp. (cθ ) 1.62† 1.60

Fixed Cost (κθ /`θ ) 0.72† 0.99

I

Marginal Non-Int. Income, Non-Int. Expenses (estimated from trans-log cost function) and Net Expenses are increasing in size.

I

Fixed Costs (normalized by loans) are decreasing in size.

I

Selection of only low cost banks in the competitive fringe may drive the Net Expense pattern.

Definitions

Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Exit Rate Decomposed 15 Merger Rate Failure Rate Trouble Bank Rate Det. GDP

Percentage (%)

10

5

0

−5 1975

I

1980

1985

1990

1995 year

2000

2005

2010

Correlation of GDP with (Failure, Troubled, Mergers) =(-0.47, -0.72, 0.58) after 1990

Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Definitions Entry and Exit by Bank Size I

Let y ∈ {Top 4, Top 1%, Top 10%, Bottom 99%}

I

let x ∈ {Enter, Exit, Exit by Merger, Exit by Failure}

I

Each value in the table is constructed as the time average of “y banks that x in period t” over “total number of banks that x in period t”.

I

For example, Top y = 1% banks that “x =enter” in period t over total number of banks that “x =enter” in period t.

Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Entry and Exit by Bank Size

Fraction of Loans of Banks in x, accounted by: Top 10 Banks Top 1% Banks Top 10% Banks Bottom 99% Banks

Entry 0.00 21.09 66.38 75.88

Exit 9.23 35.98 73.72 60.99

x Exit/Merger 9.47 28.97 47.04 25.57

Exit/Failure 0.00 15.83 59.54 81.14

Note: Big banks that exited by merger: 1996 Chase Manhattan acquired by Chemical Banking Corp. 1999 First American National Bank acquired by AmSouth Bancorp.

Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Definition of Competition Measures I

The Interest Margin is defined as: L D prit − rit

I

where rL realized real interest income on loans and rD the real cost of loanable funds The markup for bank is defined as: Markuptj =

I

p`tj −1 mc`tj

(4)

where p`tj is the price of loans or marginal revenue for bank j in period t and mc`tj is the marginal cost of loans for bank j in period t The Lerner index is defined as follows: mc`it Lernerit = 1 − p`it

Return Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Cyclical Properties Panel (i): Net Interest Margin

Perc. (%)

6 5 4 3 2

1985

1990

1995

2000 year Panel (ii): Markup

2005

2010

1985

1990

1995

2000 year Panel (iii): Lerner Index

2005

2010

1985

1990

1995

2005

2010

Perc. (%)

200 150 100 50 0

Perc. (%)

100

50

0

2000 year

Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Definitions Net Costs by Bank Size Non Interest Income: i. Income from fiduciary activities. ii. Service charges on deposit accounts. iii. Trading and venture capital revenue. iv. Fees and commissions from securities brokerage, investment banking and insurance activities. v. Net servicing fees and securitization income. vi. Net gains (losses) on sales of loans and leases, other real estate and other assets (excluding securities). vii. Other noninterest income. Non Interest Expense: i. Salaries and employee benefits. ii. Goodwill impairment losses, amortization expense and impairment losses for other intangible assets. iii. Other noninterest expense. Fixed Costs: i. Expenses of premises and fixed assets (net of rental income). (excluding salaries and employee benefits and mortgage interest). Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Balance Sheet: all variables Fraction Total Assets (%) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Def. Short BS

cash fed funds sold securities safe risky trading assets safe risky loans fixed assets and other real estate intangibles other assets deposits insured fed funds/repos other borrowed money trading liabilities subordinated debt other liabilities equity Tier 1 capital (rw) Total capital (rw)

Small 5.52 3.72 20.73 16.01 4.72 0.94 0.07 0.87 62.88 1.33 1.30 3.58 69.69 58.63 7.49 10.31 0.31 0.87 2.30 9.03 10.19 12.71

2000 Top 10 6.23 5.47 12.39 8.18 4.21 11.38 1.29 10.09 55.52 1.15 2.22 5.64 62.22 56.51 7.67 7.52 8.54 2.18 4.16 7.71 7.81 11.33

Small 7.61 1.19 19.10 16.18 2.92 1.31 0.17 1.14 61.45 1.82 2.79 4.73 71.99 68.23 3.41 9.05 0.60 0.72 2.05 12.18 13.93 16.56

2010 Top 10 7.73 5.83 19.86 12.05 7.80 9.75 0.83 8.93 45.75 1.01 3.50 6.57 69.17 67.27 5.13 6.49 3.88 1.55 3.46 10.32 11.35 14.57

Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Balance Sheet Short Definitions I

Liquid Assets = 1+ 2 (=cash + fed funds sold )

I

Securities= 4 + 7 (=Safe securities + safe trading assets )

I

Loans = 5 + 8 + 9 - 17 (=risky securities + risky trading assets + loans - trading liabilities )

I

Other assets= 10+11+12- 18-19 (=fixed assets + int. + other assets- sub. debt - other liabilities)

I

fed funds/repos =15+16 (fed funds/repos + other borrowed money)

I

Normalized Assets= 1+ 2 +4 + 7 +5 + 8 + 9 - 17 (=Total Assets - Other assets)

I

Capital Ratio (rw) = 21 (= Tier 1 capital (rw))

Balance Sheet (Long)

Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Regulation Capital Ratios

Well Capitalized Adequately Capitalized Undercapitalized Signif. Undercapitalized Critically Undercapitalized

Tier 1 to Total Assets ≥ 5% ≥ 4% < 4% < 3% < 2%

Tier 1 to Risk w/ Assets ≥ 6% ≥ 4% < 4% < 3% < 2%

Total Capital to Risk w/ Assets ≥ 10% ≥ 8% < 8% < 6% < 2%

Source: DSC Risk Management of Examination Policies (FDIC). Capital (12-04).

Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Capital Ratios by Bank Size Tier 1 Bank Capital to assets ratio 11 Top 10 Fringe 10

Percentage (%)

9

8

7

6

5

1994

1996

1998

2000

2002

2004 year

2006

2008

2010

2012

2014

I

Capital Ratios (equity capital to assets) are larger for small banks.

I

On average, capital ratios are above what regulation defines as “Well Capitalized” (≥ 6%) further suggesting a precautionary motive. Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Capital Ratio Over the Business Cycle Det. Tier 1 Bank Capital Ratios over Business Cycle 2.25

0.03

1.75

0.015

0.75 0

GDP

Capital Ratios (%)

1.25

0.25

−0.25 −0.015

−0.75 GDP (right axis) CR Top 10 CR Fringe −1.25 1994

I

1996

1998

2000

2002

2004 Period (t)

2006

2008

2010

2012

−0.03 2014

Capital Ratio (over total assets) is countercyclical for small banks (corr. -0.42) and big banks (corr. -0.25).

Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Business Cycle Correlations Variable Correlated with GDP Loan Interest Rate rL Exit Rate Entry Rate Loan Supply Deposits Default Frequency Loan Return Charge Off Rate Interest Margin Lerner Index Markup

Data -0.18 -0.47 0.25 0.72 0.22 -0.61 -0.26 -0.56 -0.31 -0.26 -0.20

Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Depositors I

Each hh is endowed with 1 unit of a good and is risk averse with preferences u(ct ).

I

HH’s can invest their good in a riskless storage technology yielding exogenous net return r.

I

If they deposit with a bank they receive rtD even if the bank fails due to deposit insurance (funded by lump sum taxes on the population of households).

I

If they match with an individual borrower, they are subject to the random process in (22).

Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Borrower Decision Making I

If a borrower chooses to demand a loan, then given limited liability his problem is to solve:
v(rL , z) = max Ez0 |z p(R, z 0 ) z 0 R − rL . (5) R

I

The borrower chooses to demand a loan if − + v( rL , z ) ≥ ω.

I

(6)

Aggregate demand for loans is given by d

L

Z

ω

1{ω≤v(rL ,z)} dΥ(ω).

L (r , z) = N ·

(7)

ω Return

Return Timing

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Borrower Project Choice & Inverse Loan Demand Panel (a): Borrower Project R

0.135

R(rL,zb) L

R(r ,zg)

0.13

0.125

0.12 0

0.02

0.04

0.06

0.08

0.1

0.12

Loan Interest Rate (rL) Panel (b): Inverse Loan Demand 0.2

rL(L,zb) rL(L,zg)

0.15 0.1 0.05 0 0

I I I

0.05

0.1

0.15

0.2 0.25 0.3 Loan Demand (L)

0.35

0.4

0.45

0.5

“Risk shifting” effect that higher interest rates lead borrowers to choose more risky projects as in Boyd and De Nicolo. Borrower Problem Thus higher loan rates can induce higher default frequencies. Fig. Loan demand is pro-cyclical.

Return Mkt Essentials

Return Timing

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Loan rates and default risk 1 0.8 0.6 0.4

p(R(rL,zb),z"b)

0.2

p(R(rL,zb),z"g)

0 0.01

0.02 0.03

0.04 0.05

0.06 0.07

0.08 0.09

0.1

0.11

0.1

0.11

Loan Interest Rate (rL) 1 0.8 0.6 0.4

p(R(rL,zg),z"b)

0.2

p(R(rL,zg),z"g)

0 0.01

0.02 0.03

0.04 0.05

0.06 0.07

0.08 0.09

Loan Interest Rate (rL)

I

Higher loan rates induce higher default risk

Return Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Big Bank Problem The value function of a “big” incumbent bank at the beginning of the period is then given by Current Profit Trade-offs  βEz0 |z W b (`, d, A, η, δ, z 0 ) , (8) V b (a, δ, z, η) = max `,d∈[0,δ],A≥0

s.t. a+d e=`+A−d ` + Ls,f (z, η, `) where Ls,f (z, η, `) = I

R

≥ A+` b

(9)

≥ ϕ `

(10)

= Ld (rL , z)

(11)

`fi (a, δ, z, η, `b )η f (da, dδ).

Market clearing (11) defines a “reaction function” where the dominant bank takes into account how fringe banks’ loan supply reacts to its own loan supply.

Fringe Decision Making

Return OPT

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Big Bank Problem - Cont.

Calibration

Counterfactuals

Conclusion

Return OPT

The end of period function is given by  W b (`, d, A, η, δ, z 0 ) = max W b,x=0 (`, d, A, η, δ, z 0 ), W b,x=1 (`, d, A, η, δ, z 0 ) x∈{0,1}

W b,x=0 (`, d, A, η, δ, z 0 ) =

s.t.



max

B0 ≤

A (1+r B )

π b (`, d, a0 , η, z 0 ) + B 0 if π b (·) + B 0 ≥ 0 π b (`, d, a0 , η, z 0 ) + B 0 − ζ b (π b (·) + B 0 , z 0 ) if π b (·) + B 0 < 0

b

=

a0

=

A − (1 + rB )B 0 ≥ 0

0

=

H(z, η, z 0 )

D

η

n o Db + Eδb0 |δ V b (a0 , δ 0 , z 0 , η 0 )

( W

b,x=1

0

 (`, d, A, η, δ, z ) = max ξ {p(R, z 0 )(1 + rL ) + (1 − p(R, z 0 ))(1 − λ) )  a D b −c }` + (1 + r )A − d(1 + r ) − κ , 0 . b

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Bank Entry I

Each period, there is a large number of potential type θ entrants.

I

The value of entry (net of costs) is given by n V θ,e (z, η, z 0 ) ≡ max − (a0 + Υθ ) − ζ θ (a0 + Υθ ) a0 o +Eδ0 V θ (a0 , δ 0 , z 0 , H(z, η, z 0 ))

(12)

I

Entry occurs as long as V θ,e (z, ζ, z 0 ) ≥ 0.

I

The argmax of (12) defines the initial equity distribution of banks which enter.

I

Free entry implies that V θ,e (z, η, z 0 ) × E θ = 0 f

(13) b

where E denotes the mass of fringe entrants and E the number of big bank entrants. Return EE Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Evolution of Cross-sectional Bank Size Distribution I

Given any sequence (z, z 0 ), the distribution of fringe banks evolves according to 0

η f (A × D) =

Z X

Q((a, δ), z, z 0 , A × D)η f (da, δ)

(14)

δ

Q((a, δ), z, z 0 , A × D) =

X

(1 − xf (a, δ, z, η, z 0 ))I{af (a,δ,z,η)∈A)} Gf (δ 0 , δ)

δ 0 ∈D

+E f I{af,e (z0 ,η)∈A)}

X

Gf,e (δ).

(15)

δ 0 ∈D

I

(15) makes clear how the law of motion for the distribution of banks is affected by entry and exit decisions.

Return BSD

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Taxes to cover deposit insurance I

Across all states (η, z, z 0 ), taxes must cover deposit insurance in the event of bank failure.

I

Let post liquidation net transfers be given by h i 0 ∆θ = (1 + rD )dθ − ξ {p(1 + rL ) + (1 − p)(1 − λ) − cθ }`θ + a ˜θ (1 + ra ) where ξ ≤ 1 is the post liquidation value of the bank’s assets and cash flow.

I

Then aggregate taxes are Z τ (z, η, z 0 ) · Ξ = xf max{0, ∆f }dη f (a, δ) + xb max{0, ∆b }

Return Timing

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Incumbent Bank Decision Making I

Differentiating end-of period profits with respect to `θ we obtain dπ θ = d`θ



h i drL  ∂p ∂R L prL − (1 − p)λ − ra − cθ + `θ p + (r + λ) |{z} |∂R ∂rL{z {z } | d`θ } |{z} (+) or (−)

L I dr f d`

I

(+)

(−)

(−)

= 0 for competitive fringe.

The total supply of loans by fringe banks is Z Ls,f (z, η, `b ) = `f (a, δ, z, ζ, `b )η f (da, dδ).

(16)

Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Fringe Bank Problem The value function of a fringe incumbent bank at the beginning of the period is then given by  βEz0 |z W f (`, d, A, δ, η, z 0 ) , V f (a, δ, z, η) = max `≥0,d∈[0,δ],A≥0

s.t. a+d≥A+` f

f

(17)

`(1 − ϕ ) + A(1 − wϕ ) − d ≥ 0

(18)

`b (η) + Lf (ζ, `b (η)) = Ld (rL , z)

(19)

Fringe banks use the decision rule of the dominant bank in the market clearing condition (19). Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Computing the Model I

Solve the model using a variant of Krusell and Smith (1998) and Farias et. al. (2011).

I

We approximate the distribution of fringe banks using average assets ¯ average deposits δ¯ and the mass of incumbent fringe banks M A, where Z X M= dη f (a, δ) δ

I

Note that the mass of entrants E f and M are linked since X 0 η f (a0 , δ 0 ) = T ∗ (η f (a, δ)) + E f Ia0 =af,e Gf,e (δ) δ

where T ∗ (·) is the transition operator. Return Parametrization

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Computational Algorithm (cont.) 1. Guess aggregate functions. Make an initial guess of ¯ that determines the reaction function and the ¯ z, ab , M, `; δ) `f (A, law of motion for A¯0 and M0 . 2. Solve the dominant bank problem. 3. Solve the problem of fringe banks. 4. Using the solution to the fringe bank problem V f , solve the ¯ ¯ z, ab , M, `; δ). auxiliary problem to obtain `f (A, 5. Solve the entry problem of the fringe bank and big bank to obtain the number of entrants as a function of the state space. 6. Simulate to obtain a sequence {abt , A¯t , Mt }Tt=1 and update aggregate functions. Return Parametrization Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Computational Algorithm (cont.) I

We approximate the fringe part by A¯0 and M0 that evolve according to 0

log(A ) = ha0 + ha1 log(z) + ha2 log(ab ) + ha3 log(A) + ha4 log(M ) + ha5 log(z

m m m b m m log(M0 ) = hm 0 + h1 log(z) + h2 log(a ) + h3 log(A) + h4 log(M) + h5 log(z

I

We approximate the equation defining the “reaction function” Lf (z, ζ, `) by Lf (z, ab , A, M, `) with ¯ M, `) = `f (A, ¯ z, ab , M, `) × M Lf (z, ab , A,

(20)

¯ z, ab , M, `) is the solution to an auxiliary problem where `f (A, Return Parametrization

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Markov Process Matched Deposits I

The finite state Markov representation Gf (δ 0 , δ) obtained using the method proposed by Tauchen (1986) and the estimated values of µd , ρd and σu is:   0.632 0.353 0.014 0.000 0.000 0.111 0.625 0.257 0.006 0.000   f 0  G (δ , δ) =  0.002 0.175 0.645 0.175 0.003 , 0.000 0.007 0.257 0.625 0.111 0.000 0.000 0.014 0.353 0.637

I

The corresponding grid is δ ∈ {0.019, 0.028, 0.040, 0.057, 0.0.081}.

I

The distribution Ge,f (δ) is derived as the stationary distribution associated with Gf (δ 0 , δ).

Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Functional Forms I

Borrower outside option is distributed uniform [0, ω].

I

For each borrower, let y = αz 0 + (1 − α)ε − bRψ where ε is drawn from N (µε , σε2 ).

I

Define success to be the event that y > 0, so in states with higher z or higher εe success is more likely. Then   −αz 0 + bRψ p(R, z 0 )1 − Φ (21) (1 − α) where Φ(x) is a normal cumulative distribution function with mean (µε ) and variance σε2 .

Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Definition Model Moments Aggregate loan supply Aggregate Output Entry Rate Default frequency Borrower return Loan return Loan Charge-off rate Interest Margin Loan Market Share Bottom 99% Deposit Market Share Bottom 99% Capital Ratio Bottom 99% Capital Ratio Top 1% Securities to Asset Ratio Bottom 99% Securities to Asset Ratio Top 1% Profit Rate Lerner Index Markup

Ls (z, η)n= `b + Lf (z, η, `b ) o Ls (z, η) p(z, η, z 0 )(1 + z 0 R) + (1 − p(z, η, z 0 ))(1 − λ) R E f / η(a, δ) 1 − p(R∗ , z 0 ) p(R∗ , z 0 )(z 0 R∗ ) p(R∗ , z 0 )r L (z, η) + (1 − p(R∗ , z 0 ))λ (1 − p(R∗ , z 0 ))λ p(R∗ , z 0 )r L (z,η) − r d  Lf (η, `b (η))/ `b (η) + Lf (η, `b (η)) R f a,δ d (a,δ,z,η)dζ(a,δ) R df (a,δ,z,η)dη(a,δ)+db (a,δ,z,η) a,δ R R [˜ ef (a, δ, z, η)/`f (a, δ, z, η)]dη(a, δ)/ a,δ dη(a, δ) a,δ b b e˜ (a, δ, z, η)/` (a, δ, z, η) R af (a,δ,z,η)/(`f (a,δ,z,η)+˜ af (a,δ,z,η))]dζ(a,δ) a,δ [˜ R a,δ) a,δ dζ(˜ b b b

a ˜ (a, δ, z, η)/(` (a, δ, z, η) + a ˜ (a, δ, z, η)) π` (θ)(·) i `i (θ) h d

i h i 1 − r + cθ,exp / p(R∗ (η, z), z 0 , s0 )r L (η, z) + cθ,inc h i h i pj (R∗ (η, z), z 0 , s0 )r L (η, z) + cθ,inc / r d + cθ,exp − 1

Return Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Fringe Bank Exit Rule across δ 0 s Panel (i): Exit decision rule fringe δL and δH banks at zb 1

xf(δL,zb,z′b)

0.8

xf(δL,zb,z′g)

0.6

xf(δH,zb,z′b)

0.4

xf(δH,zb,z′g)

0.2 0 0

2

4

6

8

10

12

14

16

18

a

20 −3

x 10

Panel (ii): Exit decision rule fringe δL and δH banks at zg 1

xf(δL,zg,z′b)

0.8

xf(δL,zg,z′g)

0.6

xf(δH,zg,z′b)

0.4

xf(δH,zg,z′g)

0.2 0 0

2

4

6

8

10

a

I

12

14

16

18

20 −3

x 10

Fringe banks with low assets are more likely to exit, particularly if they are small δL .

Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Big and Median Buffer and Cash Flow Policy Panel (i): Net Cash Flow (CF ) and a0 big at zb

0.015

0.01

0.005 CFb(zb,z′b) 0

CFb(zb,z′g) ab′(zb,z′b)

−0.005

ab′(zb,z′g) −0.01

0

0.005

0.01

0.015

0.02

0.025

a

Panel (ii): Net Cash Flow (CF ) and a0 fringe(δM ) bank at zb

0.015

0.01

0.005 CFf(zb,z′b) CFf(zb,z′g)

0

af′(zb,z′b)

−0.005

−0.01

af′(zb,z′g) 0

0.005

0.01

0.015

0.02

0.025

a

I Banks issue equity (CF = π + B < 0) to continue when assets are low I They pay dividends (CF ≥ 0) when unconstrained optimum level of assets can

be achieved without external finance I Banks accumulate more assets in good times (marginal value is higher) Capital Requirements in a Quantitative Model of Banking Industry Dynamics

return

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

0

Fringe Banks af (different δ 0 s) Panel (i): a0 decision rule fringe δL and δH banks at zb 0.01 af(δL,zb,z′b)

0.008

af(δL,zb,z′g) af(δH,zb,z′b)

0.006

af(δH,zb,z′g)

0.004

45o

0.002 0

0.002

0.004

0.006

0.008

0.01

a

0.012

0.014

0.016

0.018

0.02

Panel (ii): a0 decision fringe δL and δH banks at zg 0.01 af(δL,zg,z′b)

0.008

af(δL,zg,z′g) af(δH,zg,z′b)

0.006

af(δH,zg,z′g)

0.004

45o

0.002 0

I

0.002

0.004

0.006

0.008

0.01

a

0.012

0.014

0.016

0.018

0.02

The smallest fringe bank is more cautious than the largest fringe bank.

Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Big Bank and Median Fringe B θ Panel (i): Borrowings decision rule big and fringe(δM) banks at zb 0.015 Bb(zb,z′b)

0.01

Bb(zb,z′g)

0.005

Bf(zb,z′b) Bf(zb,z′g)

0 −0.005 −0.01 −0.015

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

a Panel (ii): Borrowings decision rule big and fringe(δM) banks at zg 0.015 Bb(zg,z′b)

0.01

Bb(zg,z′g)

0.005

Bf(zg,z′b) Bf(zg,z′g)

0 −0.005 −0.01 −0.015

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

a

I

The only type bank which borrows short term to cover any deficient cash flows is the big bank at low asset levels when z = zg and z 0 = zb .

Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Fringe Banks B f (different δ 0 s) Panel (i): Borrowings rule fringe δL and δH banks at zb 0.01 Bf(δL,zb,z′b) Bf(δL,zb,z′g)

0.005

Bf(δH,zb,z′b) Bf(δH,zb,z′g)

0

−0.005

−0.01

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

a Panel (ii): Borrowings rule fringe δL and δH banks at zg 0.01 Bf(δL,zg,z′b) Bf(δL,zg,z′g)

0.005

Bf(δH,zg,z′b) Bf(δH,zg,z′g)

0

−0.005

−0.01

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

a

I

the largest fringe stores significantly less as the economy enters a recession.

Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Big and Median Fringe Buffer Choice aθ

Conclusion

0

Panel (i): a0 decision rule big and fringe(δM ) banks at zb 0.01 ab(zb,z′b)

0.008

ab(zb,z′g) af(zb,z′b)

0.006

af(zb,z′g)

0.004

45o

0.002 0

0.002

0.004

0.006

0.008

0.01

a

0.012

0.014

0.016

0.018

0.02

0

Panel (ii): a decision rule big and fringe(δM ) banks at zg 0.01 ab(zg,z′b)

0.008

ab(zg,z′g) af(zg,z′b)

0.006

af(zg,z′g)

0.004

45o

0.002 0

0.002

0.004

0.006

0.008

0.01

a

0.012

0.014

0.016

0.018

0.02

0

I

aθ < aθ implies that banks are dis-saving

I

In general, when starting assets are low and the economy enters a boom, banks accumulate future assets.

Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Big and Median Fringe Loan/Deposit Panel i: Loan decision rules big and fringe(δM) banks

0.16 0.14

lb(zb)

0.12

lb(zg)

0.1

lf(zb)

0.08

lf(zg)

0.06 0.04 0.02

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

a Panel (ii): Deposit decision rules big and fringe(δM) banks 0.16 0.14

db(zb)

0.12

db(zg) df(zb)

0.1

df(zg)

0.08 0.06 0.04 0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

a

I

I I

If the dominant bank has sufficient assets, it extends more loans/accepts more deposits in good than bad times. However at low asset levels, loans are constrained by level of capital Loans are always increasing in asset levels for small banks.

Return Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Big and Median Fringe Capital Ratios e˜θ /`θ Equity Ratios (˜ eθ /`θ ) big and fringe(δM ) banks

0.25

0.2

0.15

0.1

e˜b /`b (zb ) e˜b /`b (zg ) e˜f /`f (zb ) e˜f /`f (zg ) cap. req.

0.05

0

I I

0.002

0.004

0.006

0.008

0.01

a

0.012

0.014

0.016

0.018

0.02

0

Recall that e˜θ /`θ = (`θ + a ˜θ − dθ )/`θ The capital requirement is binding for the big bank at low asset levels but at higher asset levels becomes higher in recessions relative to booms.

Return Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Big Bank and Median Fringe Dividends Panel (i): Dividend decision rule big and fringe(δM) banks at zb 0.02 Db(zb,z′b) Db(zb,z′g)

0.015

Df(zb,z′b) Df(zb,z′g)

0.01

0.005

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

0.018

0.02

a Panel (ii): Dividend decision rule big and fringe(δM) banks at zg 0.02 Db(zg,z′b) Db(zg,z′g)

0.015

Df(zg,z′b) Df(zg,z′g)

0.01

0.005

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

a

I

Strictly positive payouts arise if the bank has sufficiently high assets.

I

There are bigger payouts as the economy enters good times.

Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Fringe Banks Dividends (different δ 0 s) Panel (i): Dividend rule fringe δL and δH banks at zb 0.02 Df(δL,zb,z′b) Df(δL,zb,z′g)

0.015

Df(δH,zb,z′b) Df(δH,zb,z′g)

0.01

0.005

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

0.016

0.018

0.02

a Panel (ii): Dividend rule fringe δL and δH banks at zg 0.02 Df(δL,zg,z′b) Df(δL,zg,z′g)

0.015

Df(δH,zg,z′b) Df(δH,zg,z′g)

0.01

0.005

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

a

I

The biggest fringe banks are more likely to make dividend payouts than the smallest fringe banks.

Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Fringe Capital Ratios e˜f /`f (across δ 0 s) Equity Ratios (˜ eθ /`θ ) fringe δL and δH banks ef/lf(δL,zb) ef/lf(δL,zg) ef/lf(δH,zb)

0.25

ef/lf(δH,zg) cap. req. 0.2

0.15

0.1

0.05

0

I

0.002

0.004

0.006

0.008

0.01

a

0.012

0.014

0.016

0.018

Big fringe banks behave like the dominant bank.

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

0.02

Return

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Capital Ratios over the Business Cycle Bank Equity Ratios over Business Cycle 0.37

20 avg. ef/lf

15

0.36

10

0.35

5

0.34

0

I

0

10

20

30

40

50 Period (t)

60

70

80

90

GDP

Equity Ratios (%)

eb/lb GDP (right axis)

0.33 100

Capital Ratios are countercyclical because loans are more procyclical than “precautionary” asset choices. Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Monetary Policy and Bank Lending Capital Ratio Top 1% Capital Ratio Bottom 99% Entry/Exit Rate (%) Loans to Asset Ratio Top 1% Loans to Asset Ratio Bottom 99% Measure Banks 99% Loan mkt sh. 99% (%) Loan Supply Ls to Int. Output ratio (%) Loan Interest Rate (%) Borrower Project (%) Default Frequency (%) Avg. Markup Int. Output Taxes/Output (%)

Benchmark 4.23 13.10 1.547 96.31 93.47 2.83 53.93 0.229 89.47 6.79 12.724 2.69 111.19 0.26 0.07

Lower rB 5.43 13.39 1.904 73.84 43.47 11.63 45.69 0.344 89.23 3.85 12.652 1.61 35.20 0.39 0.09

∆ (%) 28.43 2.19 23.09 -23.33 -53.49 311.07 -15.28 50.19 -0.26 -43.23 -0.57 -40.02 -68.34 50.58 24.99

Return

I Reducing the cost of funds increases the value of the bank resulting in a large

influx of fringe banks I Reduction in borrowing cost relaxes ex-post constraint: higher big bank loan

supply, lower interest rates and lower default rates. Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Higher Capital Requirements and Equity Ratios Comparison Equity Ratios (eθ/lθ) big and fringe(δH) banks when zb

0.4

eb/lb (bench.) eb/lb (high c.r.)

0.3

ef/lf (bench.) ef/lf (high c.r.) 0.06 0.08

0.2

0.1

0

0.02

0.03

0.04

0.05

0.06

0.07

securities (˜ a) Comparison Equity Ratios (eθ/lθ) big and fringe(δH) banks when zg 0.4 eb/lb bench. eb/lb high c.r.

0.3

ef/lf bench. ef/lf high c.r. 0.06 0.08

0.2

0.1

0

0.02

0.03

0.04

0.05

0.06

0.07

securities (˜ a)

I I

Major impact for big bank: higher concentration and profits allow the big bank to accumulate more securities. Fringe banks with very low level of securities are forced to increase its capital level resulting in a lower continuation value (everything else equal).

Return Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Capital Requirement Counterfactual Question: How much does a 50% increase of capital requirements Table No Cap. Requirements affect outcomes? Return Moment (%) Capital Ratio Top 1% Capital Ratio Bottom 99% Entry/Exit Rate (%) Sec. to Asset Ratio Top 1% Sec. to Asset Ratio Bottom 99% Measure Banks 99% Loan mkt sh. 99% (%) Loan Supply Ls to Int. Output ratio (%) Loan Interest Rate (%) Borrower Project (%) Default Frequency (%) Avg. Markup Int. Output Taxes/Output (%)

Benchmark (ϕ = 4%) 4.23 13.10 1.547 3.68 6.52 2.83 53.93 0.229 89.47 6.79 12.724 2.69 111.19 0.26 0.07

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Higher Cap. Req. (ϕ = 6%) 6.09 15.67 0.843 5.57 7.00 2.41 52.15 0.209 89.54 7.30 12.742 3.01 123.51 0.23 0.03

Change (%) 44.19 19.57 -45.54 51.19 7.36 -14.64 -3.30 -8.71 0.08 7.56 0.14 12.19 11.08 -8.78 -58.97

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Capital Requirements and Competition Question: How much does imperfect competition affect capital requirement counterfactual predictions? Return

Moment (%) Capital Ratio (%) Entry/Exit Rate (%) Measure Banks Loan Supply Loan Int. Rate (%) Borr. Proj. (%) Def. Freq. (%) Avg. Markup Int. Output Ls to output (%) Taxes/output (%)

Benchmark Model ϕ = 4% ϕ = 6% ∆ (%) 13.10 15.667 19.57 1.55 0.84 -45.54 2.83 2.414 -14.64 0.23 0.21 -8.71 6.79 7.30 7.56 12.724 12.742 0.14 2.69 3.01 12.19 111.19 123.51 11.08 0.26 0.23 -8.78 89.47 89.54 0.08 0.07 0.03 -58.97

Perfect Competition ϕ = 4% ϕ = 6% ∆ (%) 9.92 11.77 18.64 0.81 0.69 -14.81 5.36 5.13 -4.13 0.25 0.24 -2.46 6.27 6.43 2.50 12.71 12.71 0.04 2.44 2.51 3.07 113.91 118.58 4.11 0.28 0.27 -2.47 89.42 89.43 0.02 0.126 0.107 -15.20

I Policy effects are muted in the perfectly competitive environment. Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Imperfect Competition and Volatility

Coefficient of Variation (%) Loan Interest Rate Borrower Return Default Frequency Int. Output Loan Supply Capital Ratio Fringe Measure Banks Markup Loan Supply Fringe

Benchmark Model 4.92 6.99 2.08 7.46 7.208 13.83 0.79 4.73 3.13

Perfect Competition (↑ Υb ) 1.78 6.17 2.15 2.09 1.127 12.07 1.90 1.56 1.127

Change (%) -63.78 -11.75 3.36 -72.03 -84.37 -12.70 139.71 -67.02 -64.05

Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Imperfect Competition and Business Cycle Correlations Loan Interest Rate rL Exit Rate Entry Rate Loan Supply Deposits Default Frequency Loan Interest Return Charge Off Rate Price Cost Margin Rate Markup Capital Ratio Top 1% Capital Ratio Bottom 99%

Benchmark -0.96 -0.07 0.01 0.97 0.95 -0.21 -0.47 -0.22 -0.47 -0.96 -0.16 -0.03

Perfect Comp. -0.36 -0.16 -0.19 0.61 0.02 -0.80 0.65 -0.80 0.65 0.29 -0.05

data -0.18 -0.25 0.62 0.58 0.11 -0.08 -0.49 -0.18 -0.47 -0.19 -0.75 -0.12

Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

The role of Capital Requirements Question: What if there are no capital requirements? Moment Cap. ratio top 1% Cap. ratio bottom 99% Entry/Exit Rate (%) Loan mkt sh. 99% (%) Measure Banks Loan Supply Loan Int. Rate (%) Borrower Proj. (%) Default Freq. (%) Avg. Markup Int. Output Ls to output ratio (%) Taxes/GDP (%)

Benchmark Model ϕ = 4% No CR ∆ (%) 4.23 0.19 -87.41 13.10 15.73 20.05 1.55 4.81 210.75 53.93 87.44 62.14 2.83 4.54 60.54 0.23 0.16 -28.44 6.79 8.47 24.83 12.72 12.81 0.67 2.69 4.74 76.39 111.19 177.73 59.84 0.26 0.18 -28.57 89.47 89.63 0.18 0.07 0.11 55.80

Return

Perfect Competition ϕ = 4% No CR ∆ (%) 9.92 6.67 -32.71 0.81 1.04 28.50 100 100 0.0 5.36 5.32 -0.68 0.25 0.24 -3.06 6.27 6.47 3.11 12.71 12.71 0.04 2.44 2.53 3.79 113.91 119.74 5.12 0.28 0.27 -3.08 89.42 89.44 0.02 12.60 17.22 36.72

I No capital requirement relaxes ex-ante constraint: higher entry/exit rate, larger

measure of small banks, big bank acts strategically lowering its loan supply leading to higher interest rates and higher default rates. Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Countercyclical Capital Requirements Question: What if capital requirements are higher in good times? Benchmark

Countercyclical CR

(ϕ = 0.04)

(ϕ(zb ) = 0.06, ϕ(zg ) = 0.08)

4.23 13.10 1.547 2.83 53.93 3.68 6.52 0.229 89.47 6.79 12.724 2.69 111.19 0.26 0.07

25.13 12.66 0.001 1.55 26.47 21.09 25.51 0.206 89.53 7.38 12.748 2.98 114.02 0.23 0.01

Capital Ratio Top 1% Capital Ratio Bottom 99% Entry/Exit Rate (%) Measure Banks 99% Loan mkt sh. 99% (%) Securities to Asset Ratio Top 1% Securities to Asset Ratio Bottom 99% Loan Supply Ls to Int. Output ratio (%) Loan Interest Rate (%) Borrower Project (%) Default Frequency (%) Avg. Markup Int. Output Taxes/Output (%)

∆ (%) 494.65 -3.38 -99.94 -45.33 -50.91 472.48 291.26 -10.08 0.07 8.76 0.19 10.91 2.55 -10.11 -87.57

Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Stochastic Processes

I

Aggregate Technology Shocks zt+1 ∈ {zb , zg } follow a Markov Process F (zt+1 , zt ) with zb < zg (business cycle).

I

Conditional on zt+1 , project success shocks which are iid across borrowers are drawn from p(Rt , zt+1 ) (non-performing loans).

I

“Liquidity shocks” (capacity constraint on deposits) which are iid across banks given by δt ∈ {δ, . . . , δ} ⊆ R++ follow a Markov Process Gθ (δt+1 , δt ) (buffer stock).

Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

—————————————————————————————-

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Borrowers - Loan Demand I

Risk neutral borrowers demand bank loans in order to fund a project/buy a house.

I

Project requires one unit of investment at start of t and returns  1 + zt+1 Rt with prob p(Rt , zt+1 ) . (22) 1−λ with prob 1 − p(Rt , zt+1 )

I

Borrowers choose Rt (return-risk tradeoff, i.e. higher return R, lower success probability p).

I

Borrowers have limited liability.

I

Borrowers have an outside option (reservation utility) ωt ∈ [ω, ω] drawn at start of t from distribution Υ(ωt ).

Loan Market Outcomes

Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Loan Market Outcomes

Borrower chooses R

Receive

Pay

Success

1 + zt+1 Rt

1 + rL (ζt , zt )

Failure

1−λ

1−λ

Borrower’s Problem

Probability − + p (Rt , zt+1 ) 1−p

(Rt ,

zt+1 )

Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Parameterization For the stochastic deposit matching process, we use data from our panel of U.S. commercial banks: I

Assume dominant bank support is large enough so that the constraint never binds.

I

For fringe banks, use Arellano and Bond to estimate the AR(1) log(δit ) = (1−ρd )k0 +ρd log(δit−1 )+k1 t+k2 t2 +k3,t +ai +uit (23) where t denotes a time trend, k3,t are year fixed effects, and uit is iid and distributed N (0, σu2 ).

I

Discretize using Tauchen (1986) method with 5 states.

I

Computation: Variant of Ifrach/Weintraub (2012), Krusell/Smith (1998) Details

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Discrete Process

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Parameterization Parameter Dep. preferences Agg. shock in good state Deposit interest rate (%) Net. non-int. exp. n bank Net. non-int. exp. r bank Charge-off rate Autocorrel. Deposits Std. Dev. Error Securities Return (%) Cost overnight funds Capital Req. Top 10 Capital Req. Fringe

σ zg r¯ = rd cb cf λ ρd σu ra rB (ϕb , w) (ϕf , w)

Value 2 1 0.86 1.55 1.87 0.21 0.83 0.20 0.92 0.00 (4.0, 0) (4.0, 0)

Target Part. constraint Normalization Int. expense Net non-int exp. Top 1% Net non-int exp. bottom 99% Charge off rate Deposit Process Bottom 99% Deposit Process Bottom 99% Avg. Return Securities Fed Funds Rate Capital Regulation Capital Regulation

Return Mom

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Parameters Chosen within Model Parameter Agg. shock in crisis state Agg. shock in bad state Weight agg. shock Success prob. param. Volatility borrower’s dist. Success prob. param. Mean Entrep. project Dist. Max. reservation value Discount Factor Salvage value Mean Deposits Fixed cost b bank Fixed cost f banks Entry Cost f banks Entry Cost b bank Equity Issuance Cost Equity Issuance Cost

Note:

Functional Forms

zc zb α b σ ψ µe ω β ξ µd κb κf Υf Υb ζ0 ζ1

Value 0.95 0.978 0.886 3.870 0.106 0.793 -0.84 0.252 0.96 0.71 0.043 0.001 0.001 0.002 0.007 0.050 30.00

Targets Freq. Top 10 bank exit Std. dev. Output Std. dev. net-int. margin Borrower Return Std. deviation default frequency Net Interest Margin Default freq. Elasticity Loan Demand Loans to asset ratio Top 10 Loans to asset ratio fringe Deposit mkt share fringe Fixed cost over loans top 10 Fixed cost over loans fringe Bank entry rate Bank exit rate Equity Issuance over Assets Top 10 Equity Issuance over Assets Fringe Equity over (r-w) assets top 10 Equity over (r-w) weighted assets fringe

Return Mom

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

The Role of Imperfect Competition Question: How much does imperfect competition affect capital requirement counterfactual predictions? I Our model nests perfect competition (↑ Υb → No big bank entry)

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

The Role of Imperfect Competition Question: How much does imperfect competition affect capital requirement counterfactual predictions? I Our model nests perfect competition (↑ Υb → No big bank entry) I

Without big banks → higher mass M of fringe banks and higher loan supply → interest rates drop 50 basis points. Table

I

Lower profitability leads to lower entry (drops 50%) but higher total exits (M · x) → higher taxes/output.

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

The Role of Imperfect Competition Question: How much does imperfect competition affect capital requirement counterfactual predictions? I Our model nests perfect competition (↑ Υb → No big bank entry) I

Without big banks → higher mass M of fringe banks and higher loan supply → interest rates drop 50 basis points. Table

I

Lower profitability leads to lower entry (drops 50%) but higher total exits (M · x) → higher taxes/output.

I

Volatility of almost all variables decrease → average capital ratio is 12% lower (reduced precautionary holdings). Table

Return CR Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

The Role of Imperfect Competition Question: How much does imperfect competition affect capital requirement counterfactual predictions? I Our model nests perfect competition (↑ Υb → No big bank entry) I

Without big banks → higher mass M of fringe banks and higher loan supply → interest rates drop 50 basis points. Table

I

Lower profitability leads to lower entry (drops 50%) but higher total exits (M · x) → higher taxes/output.

I

Volatility of almost all variables decrease → average capital ratio is 12% lower (reduced precautionary holdings). Table

I

Some correlations are inconsistent with the data; for example, strong countercyclicality of the default frequency (10 times the data) results in procyclical loan interest returns and markups. Table

Return CR Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

C-D 2013: Too-Big-To-Fail Question: How much does too big to fail affect risk taking? Counterfactual where the national bank is guaranteed a subsidy in states with negative profits. National Bailout Bank Problem

Moment Loan Supply Loan Interest Rate (%) Markup Market Share bottom 99% Market Share Top 10 / Top 1% Prob. Exit Top 10 / Top 1% Borrower Risk Taking R (%) Default Frequency (%) Entry/Exit Rate (%) Int. Output Taxes/Output (%)

Benchmark 0.78 5.69 108.44 39.64 20.97 / 39.38 0 / 1.67 14.78 1.22 2.78 0.89 17.84

Nat. Bank Bailout Change (%) 6.13 -8.85 -15.04 -7.06 52.02 / -20.57 n.a. / 65.87 -0.02 -2.13 -0.11 6.15 9.79

National bank increases loan exposure to region with high downside risk while loan supply by other banks falls (spillover effect). Net effect is more higher aggregate loans, lower interest rates and default frequencies. Capital Requirements in a Quantitative Model of Banking Industry Dynamics Dean Corbae and Pablo D’Erasmo I

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

National Bank Problem under Too Big to Fail I

If realized profits for a national bank are negative, then the government covers the losses so that the bank stays in operation.

I

The problem of a national bank becomes

hP Vi (n, ·, µ, z, s; σ−i ) = max{`i (n,j)}j=e,w Ez0 ,s0 |z,s j=e,w n o i max 0, π`i (n,j) (n, j, cn , µ, z, s, z 0 , s0 ; σ−i ) + βVi (n, ·, µ0 , z 0 , s0 ; σ−i ) subject to XZ

`i (θ, j, µ, s, z; σ−i )µ(θ,j) (di) − Ld,j (rL,j , z, s) = 0,

θ

where Ld,j (rL,j , z, s) is given in (7). Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Too-Big-to-Fail (cont.)

Table : Benchmark vs Too Big to Fail

Model Dynamic (benchmark) National Bank Bailouts

¯ j, µ, z, e) Loan Decision Rules `(θ, (µ = {1, 1, 1, ·}, z = zb , s = e) ¯ e, ·) `(n, ¯ w, ·) `(r, ¯ e, ·) `(r, ¯ w, ·) `(n, 7.209 85.837

82.562 82.562

45.450 32.668

31.483 31.483

The possible loss of charter value without too-big-to-fail is enough to induce national banks to lower loan supply in order to reduce exposure to risk. Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Allowing Foreign Bank Competition Moment Loan Market Share Foreign % Loan Interest margin % Dividend / Asset Foreign % Dividend / Asset National % Avg. Equity issuance Foreign % Avg. Equity issuance National % Exit Rate Foreign % Exit Rate Domestic % Entry Rate % Default Frequency % Charge off Rate % Output Loan Supply Taxes / Output

Data 69.49 6.94 4.15 2.07 3.65 2.83 2.29 3.78 2.66 4.01 2.12 -

Υf = ∞ 0.00 9.89 6.56 1.44 0.00 0.00 6.31 1.25 0.33 0.28 0.00

Benchmark 56.63 7.76 3.94 4.11 0.83 0.30 2.72 3.98 5.66 6.13 1.21 0.43 0.37 1.57

Less concentrated industry with lower interest rate margins, higher exit rates with banks more exposed to risk and more volatile I Lower interest rates → lower default frequency and charge off rates I Higher output, loan supply butDynamics higher taxes as well Capital Requirements in a Quantitative Model of Banking Industry Dean Corbae and Pablo D’Erasmo I

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Foreign Bank Competition: Real Effects

I

Foreign bank competition induces higher output and larger output and credit contractions/expansion due to changes in domestic conditions

I

Volatility of output and loan supply increases (+12.91% and 10.11%)

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Welfare Consequences Question: What are the welfare consequences of allowing foreign bank competition?

f (µ = {0, 1}, z, η) αh (µ = {0, 1}, z, η) αh αe (µ = {0, 1}, z, η) αe αe (µ = {0, 1}, z, η) αe

zc ηL ηH 10.72 2.81 0.54 0.52 4.09

3.89

4.63

4.42

Decomposing Effects: Higher Competition vs Foreign Competition

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

zb ηL ηH 30.02 9.90 0.72 0.73 0.799 5.44 5.27 5.527 6.17 6.00 6.326

zg ηL ηH 38.65 7.90 0.93 0.96 6.11

5.87

7.04

6.83

Return

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Decomposing Effects: Higher Competition or Foreign Competition? Question: What are the welfare consequences of allowing foreign bank competition from a domestic banking sector with high competition? zc αh (µ = {0, 1}, z, η) αh (µ = {1, 0}, z, η) αh (µ = {1, 1}, z, η) αh αe (µ = {0, 1}, z, η) αe (µ = {1, 0}, z, η) αe (µ = {1, 1}, z, η) αe αe (µ = {0, 1}, z, η) αe (µ = {1, 0}, z, η) αe (µ = {1, 1}, z, η) αe

ηL 0.11 0.60 0.48

ηH 0.13 0.74 0.48

1.21 0.73 0.85

0.94 0.71 0.82

1.32 1.33 1.32

1.07 1.45 1.30

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

zb ηL ηH 0.14 0.23 0.38 0.66 0.49 0.52 0.577 1.66 0.97 0.84 0.82 0.86 0.80 0.960 1.80 1.20 1.21 1.48 1.35 1.31 1.537

zg ηL 0.11 0.78 0.69

ηH 0.41 0.74 0.64

1.06 0.98 1.11

0.94 0.93 1.04

1.16 1.76 1.80

1.34 1.67 1.68

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Test 2: The Bank Lending Channel Question: Kashyap and Stein (2000) ask “Is the impact of monetary policy on lending behavior stronger for banks with less liquid balance sheets, where liquidity is measured by the ratio of securities to assets? I

They find strong evidence in favor of this bank lending channel.

I

We analyze a reduction in rB (overnight borrowing rate) from 1.2% to 0% on a pseudo-panel of banks from the model.

I

In the first stage, we estimate the following cross-sectional regression for each t: ∆Lit = a0 + βt Bit−1 + ut where ∆Lit =

I

`it −`it−1 , `it−1

and Bit =

a0it (a0it +`it )

is the measure of liquidity

Then use the sequence of βt to estimate the second stage as follows βt = b0 + b1 ∆outputt + φdMt where dMt is a dummy variable that equals 1 if rtB = 0%

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Expansionary Policy and Bank Lending - cont. Question: Kashyap and Stein ask “Is the impact of monetary policy on lending behavior stronger for banks with less liquid balance sheets, where liquidity is measured by the ratio of securities to assets? Sample Monetary Policy: dMt s.e. ∆outputt s.e. N R2 Note:

∗∗∗

Bottom 99% βt -0.929 0.2575∗∗∗ 2.53 0.619∗∗∗ 5000 0.35

Bottom 92% βt -1.177 0.2521∗∗∗ 2.306 0.586∗∗∗ 5000 0.46

significant at 1% level

I

Our results are consistent with those presented in Kashyap and Stein.

I

∂Bit We find that ∂M < 0 and that ∂Bit ∂Mtit∂sizeit > 0 (i.e. the t mechanism at play is stronger for the smallest size banks).

∂



∂Lit



∂L3

Return Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

—————————————————————————–

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Long Run Asset Distn. of Big/Small Banks Avg Distribution of Fringe and Big Banks 20 fringe δL fringe δM

18

fringe δH big bank

16

Fraction of Firms (%)

14

12

10

8

6

4

2

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

a

I

Average asset holdings of the big bank is lower than that of fringe banks.

Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Timing At the beginning of period t, 1. Liquidity shocks are realized δt . 2. Starting from beginning of period state (ζt , zt ), borrowers draw ωt . 3. Dominant bank chooses (`bt , dbt , Abt ). 4. Having observed `bt , fringe banks choose (`ft , dft , Aft ). Borrowers choose whether or not to undertake a project and if so, Rt . 5. Return shocks zt+1 are realized, as well as idiosyncratic project success shocks. θ 6. Banks choose Bt+1 and dividend policy. Exit and entry decisions are made (in that order).

7. Households pay taxes τt+1 to fund deposit insurance and consume. Taxes

Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Parameterization For the stochastic deposit matching process, we use data from our panel of U.S. commercial banks: I

For fringe banks, use Arellano and Bond to estimate the AR(1) log(δit ) = (1−ρd )k0 +ρd log(δit−1 )+k1 t+k2 t2 +k3,t +ai +uit (24) where t denotes a time trend, k3,t are year fixed effects, and uit is iid and distributed N (0, σu2 ).

I

Discretize using Tauchen (1986) method with 5 states.

I

Consistent with observed lower variance of deposits, assume dominant bank δ = δ¯b is constant and large enough so that the constraint never binds.

Discrete Process

Computation: Variant of Ifrach/Weintraub (2012), Krusell/Smith (1998) Details

Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

The Role of Imperfect Competition Question: How much does imperfect competition affect capital requirement counterfactual predictions? I Our model nests perfect competition (↑ Υb → No big bank entry)

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

The Role of Imperfect Competition Question: How much does imperfect competition affect capital requirement counterfactual predictions? I Our model nests perfect competition (↑ Υb → No big bank entry) I

Without big banks → higher mass M of fringe banks and higher loan supply → interest rates drop 50 basis points. Table

I

Lower profitability leads to lower entry (drops 50%) but higher total exits (M · x) → higher taxes/output.

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

The Role of Imperfect Competition Question: How much does imperfect competition affect capital requirement counterfactual predictions? I Our model nests perfect competition (↑ Υb → No big bank entry) I

Without big banks → higher mass M of fringe banks and higher loan supply → interest rates drop 50 basis points. Table

I

Lower profitability leads to lower entry (drops 50%) but higher total exits (M · x) → higher taxes/output.

I

Volatility of almost all variables decrease → average capital ratio is 12% lower (reduced precautionary holdings). Table

Return Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

The Role of Imperfect Competition Question: How much does imperfect competition affect capital requirement counterfactual predictions? I Our model nests perfect competition (↑ Υb → No big bank entry) I

Without big banks → higher mass M of fringe banks and higher loan supply → interest rates drop 50 basis points. Table

I

Lower profitability leads to lower entry (drops 50%) but higher total exits (M · x) → higher taxes/output.

I

Volatility of almost all variables decrease → average capital ratio is 12% lower (reduced precautionary holdings). Table

I

Some correlations are inconsistent with the data; for example, strong countercyclicality of the default frequency (10 times the data) results in procyclical loan interest returns and markups. Table

Return Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Countercyclical Capital Requirements Question: What if capital requirements are higher in good times (i.e. ϕ = 0.04) → (ϕ(zb ) = 0.06, ϕ(zg ) = 0.08))? Table I

Bank exit/entry drops to nearly zero and 60 basis point rise in interest rates.

I

Intermediated output drops 10% but taxes/output drop 90%.

I

Lower fringe bank entry → 50% drop in small bank market share (more concentrated industry).

Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Other Counterfactual Experiments C-D 2013. I A segmented markets model where “big” national geographically diversified banks coexist in equilibrium with “smaller” regional and fringe banks that are restricted to a geographical area.

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Other Counterfactual Experiments C-D 2013. I A segmented markets model where “big” national geographically diversified banks coexist in equilibrium with “smaller” regional and fringe banks that are restricted to a geographical area. I Counterfactuals: I

Experiment 1: More concentration reduces bank exit (banking crises) as in A-G but increases default frequency (fraction of nonperforming loans) as in B-D.

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Other Counterfactual Experiments C-D 2013. I A segmented markets model where “big” national geographically diversified banks coexist in equilibrium with “smaller” regional and fringe banks that are restricted to a geographical area. I Counterfactuals: I

Experiment 1: More concentration reduces bank exit (banking crises) as in A-G but increases default frequency (fraction of nonperforming loans) as in B-D.

I

Experiment 2: Branching restrictions induce more regional concentration (s.a.a.)

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Other Counterfactual Experiments C-D 2013. I A segmented markets model where “big” national geographically diversified banks coexist in equilibrium with “smaller” regional and fringe banks that are restricted to a geographical area. I Counterfactuals: I

Experiment 1: More concentration reduces bank exit (banking crises) as in A-G but increases default frequency (fraction of nonperforming loans) as in B-D.

I

Experiment 2: Branching restrictions induce more regional concentration (s.a.a.)

I

Experiment 3: Lower cost of loanable funds leads dominant banks to raise their loans at the expense of fringe bank market share. Different cyclical properties of interest rates.

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Other Counterfactual Experiments C-D 2013. I A segmented markets model where “big” national geographically diversified banks coexist in equilibrium with “smaller” regional and fringe banks that are restricted to a geographical area. I Counterfactuals: I

Experiment 1: More concentration reduces bank exit (banking crises) as in A-G but increases default frequency (fraction of nonperforming loans) as in B-D.

I

Experiment 2: Branching restrictions induce more regional concentration (s.a.a.)

I

Experiment 3: Lower cost of loanable funds leads dominant banks to raise their loans at the expense of fringe bank market share. Different cyclical properties of interest rates.

I

Experiment 4: While national banks increase loan exposure with too-big-to-fail, their actions spill over to smaller banks who reduce loans. Lower profitability of smaller banks induces lower entry.

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

C-D 2014b: Global Banking Competition Question: How much do restrictions on foreign bank entry affect domestic loan rates and welfare?

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

C-D 2014b: Global Banking Competition Question: How much do restrictions on foreign bank entry affect domestic loan rates and welfare? Table I After calibrating a GE version to Mexico, we conduct a counterfactual where entry costs for foreign banks are set prohibitively high resulting in:

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

C-D 2014b: Global Banking Competition Question: How much do restrictions on foreign bank entry affect domestic loan rates and welfare? Table I After calibrating a GE version to Mexico, we conduct a counterfactual where entry costs for foreign banks are set prohibitively high resulting in: I

Higher loan supply (32%) → less concentration and lower interest rate margins (- 200 basis points).

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

C-D 2014b: Global Banking Competition Question: How much do restrictions on foreign bank entry affect domestic loan rates and welfare? Table I After calibrating a GE version to Mexico, we conduct a counterfactual where entry costs for foreign banks are set prohibitively high resulting in: I

Higher loan supply (32%) → less concentration and lower interest rate margins (- 200 basis points).

I

Higher exit rates with banks more exposed to foreign shocks inducing more domestic volatility (output and loan supply volatility increases (+12.91% and 10.11%, respectively)).

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

C-D 2014b: Global Banking Competition Question: How much do restrictions on foreign bank entry affect domestic loan rates and welfare? Table I After calibrating a GE version to Mexico, we conduct a counterfactual where entry costs for foreign banks are set prohibitively high resulting in: I

Higher loan supply (32%) → less concentration and lower interest rate margins (- 200 basis points).

I

Higher exit rates with banks more exposed to foreign shocks inducing more domestic volatility (output and loan supply volatility increases (+12.91% and 10.11%, respectively)).

I

Lower interest rates → lower default frequency (-2.85%) and charge off rates (-3.2%).

I

Higher output (+30%), but higher taxes as well.

Welfare (CE equivalent) increases by 0.79% for households and 5.53% for entrepreneurs. Capital Requirements in a Quantitative Model of Banking Industry Dynamics Dean Corbae and Pablo D’Erasmo I

Introduction

Data

Model

Equilibrium

Calibration

Counterfactuals

Conclusion

Future Research I

Stress tests

I

Interbank market clearing adds another endogenous price and systemic channel.

I

Deposit insurance and deposit market competition

I

Mergers

I

Maturity Transformation - long maturity loans

I

Heterogeneous borrowers that leads to specialization in banking

Stress

Return

Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Dean Corbae and Pablo D’Erasmo