Capital Requirements in a Quantitative Model of Banking Industry Dynamics

Transcription

1 Capital Requirements in a Quantitative Model of Banking Industry Dynamics Dean Corbae Pablo D Erasmo 1 Wisconsin and NBER FRB Philadelphia May 24, 2017 (Preliminary and Incomplete) 1 The views expressed here do not necessarily reflect those of the FRB Philadelphia or The Federal Reserve System. 1 / 112

2 Introduction Bank market structure differs considerably across countries. For example, the 2011 asset market share of the top 3 banks in Japan (Germany) was 44% (78%) versus 35% in the U.S. (World Bank) 2 / 112

3 Introduction Bank market structure differs considerably across countries. For example, the 2011 asset market share of the top 3 banks in Japan (Germany) was 44% (78%) versus 35% in the U.S. (World Bank) This paper is about how policy (e.g. capital requirements) affects bank lending by big and small banks, loan rates, exit, and market structure in the commercial banking industry. 2 / 112

4 Introduction Bank market structure differs considerably across countries. For example, the 2011 asset market share of the top 3 banks in Japan (Germany) was 44% (78%) versus 35% in the U.S. (World Bank) This paper is about how policy (e.g. capital requirements) affects bank lending by big and small banks, loan rates, exit, and market structure in the commercial banking industry. Main Question 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.? 2 / 112

5 Introduction Bank market structure differs considerably across countries. For example, the 2011 asset market share of the top 3 banks in Japan (Germany) was 44% (78%) versus 35% in the U.S. (World Bank) This paper is about how policy (e.g. capital requirements) affects bank lending by big and small banks, loan rates, exit, and market structure in the commercial banking industry. Main Question 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 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. 2 / 112

6 Outline 1. Data: Document U.S. Banking Facts from Balance sheet and Income Statement Panel Data. 3 / 112

7 Outline 1. Data: Document U.S. Banking Facts from Balance sheet and Income Statement Panel Data. 2. Model: 3 / 112

8 Outline 1. Data: Document U.S. Banking Facts from Balance sheet and Income Statement Panel Data. 2. Model: Underlying static Cournot banking model with exogenous bank size distribution is from Allen & Gale (2004), Boyd & De Nicolo (2005)). 3 / 112

9 Outline 1. Data: Document U.S. Banking Facts from Balance sheet and Income Statement Panel Data. 2. Model: Underlying static Cournot banking model with exogenous bank size distribution is from Allen & Gale (2004), Boyd & De Nicolo (2005)). 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). 3 / 112

10 Outline 1. Data: Document U.S. Banking Facts from Balance sheet and Income Statement Panel Data. 2. Model: Underlying static Cournot banking model with exogenous bank size distribution is from Allen & Gale (2004), Boyd & De Nicolo (2005)). 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). Calibrate parameters to match long-run industry averages. 3 / 112

11 Outline 1. Data: Document U.S. Banking Facts from Balance sheet and Income Statement Panel Data. 2. Model: Underlying static Cournot banking model with exogenous bank size distribution is from Allen & Gale (2004), Boyd & De Nicolo (2005)). 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). Calibrate parameters to match long-run industry averages. Test model against other moments: (1) business cycle correlations, and (2) the bank lending channel. 3 / 112

12 Outline 1. Data: Document U.S. Banking Facts from Balance sheet and Income Statement Panel Data. 2. Model: Underlying static Cournot banking model with exogenous bank size distribution is from Allen & Gale (2004), Boyd & De Nicolo (2005)). 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). Calibrate parameters to match long-run industry averages. Test model against other moments: (1) business cycle correlations, and (2) the bank lending channel. 3. Capital Requirement Policy Counterfactuals: 3 / 112

13 Outline 1. Data: Document U.S. Banking Facts from Balance sheet and Income Statement Panel Data. 2. Model: Underlying static Cournot banking model with exogenous bank size distribution is from Allen & Gale (2004), Boyd & De Nicolo (2005)). 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). Calibrate parameters to match long-run industry averages. Test model against other moments: (1) business cycle correlations, and (2) the bank lending channel. 3. Capital Requirement Policy Counterfactuals: Basel III CR rise from 4% to 6% 3 / 112

14 Outline 1. Data: Document U.S. Banking Facts from Balance sheet and Income Statement Panel Data. 2. Model: Underlying static Cournot banking model with exogenous bank size distribution is from Allen & Gale (2004), Boyd & De Nicolo (2005)). 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). Calibrate parameters to match long-run industry averages. Test model against other moments: (1) business cycle correlations, and (2) the bank lending channel. 3. Capital Requirement Policy Counterfactuals: Basel III CR rise from 4% to 6% Countercyclical CR (add 2% in good states) 3 / 112

15 Outline 1. Data: Document U.S. Banking Facts from Balance sheet and Income Statement Panel Data. 2. Model: Underlying static Cournot banking model with exogenous bank size distribution is from Allen & Gale (2004), Boyd & De Nicolo (2005)). 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). Calibrate parameters to match long-run industry averages. Test model against other moments: (1) business cycle correlations, and (2) the bank lending channel. 3. Capital Requirement Policy Counterfactuals: Basel III CR rise from 4% to 6% Countercyclical CR (add 2% in good states) Size dependent CR (add 2.5% to big banks) 3 / 112

16 U.S. Data Summary from C-D (2013) Entry is procyclical and Exit by Failure is countercyclical. Almost all Entry and Exit is by small banks. Table Loans and Deposits are procyclical (correl. with GDP equal to 0.72 and 0.22 respectively). Bigger banks have less volatile funding inflows (implications for buffers). Table High Concentration: Top 10 have 52% of loan share. Fig Table Signs of Noncompetitive Behavior: Large Net Interest Margins, Markups, Lerner Index, Rosse-Panzar H < 100. Table Signs of Geographic Diversification: Loan returns are decreasing in bank size but volatility is increasing. Table Net marginal expenses increase, Fixed operating costs (normalized) decrease, Average costs decrease with bank size (IRS?). Table Loan Returns, Margins, Markups, Delinquency Rates and Charge-offs are countercyclical. Table Fig 4 / 112

17 Balance Sheet Data Key Components by Size Fraction total assets (%) Fringe top 10 Fringe top 10 Assets Liquid assets Securities Loans Liabilities Deposits fed funds/repos equity Bank capital (rw) Note: Data corresponds to commercial banks in the US. Source: Consolidated Report of Condition and Income. Balance Sheet (Long) Definitions While loans and deposits are the most important parts of the bank balance sheet, precautionary holdings of securities and liquid assets are an important buffer stock. 5 / 112

18 Capital Ratios by Bank Size from C-D (2014a) 18 Top 10 Fringe Tier 1 Bank Capital to risk weighted assets ratio Percentage (%) year 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 6 / 112

19 Distribution of Bank Capital Ratios Fraction of Banks (%) Panel (i): Distribution year 2000 Top 10 Fringe Cap. Req. Fraction of Banks (%) Tier 1 Capital Ratio (risk weighted) Panel (ii): Distribution year 2010 Top 10 Fringe Cap. Req Tier 1 Capital Ratio (risk weighted) 7 / 112

20 Undercapitalized bank exit % % % % % % # banks CR in [0% - 4%] (left axis) Frac. Exit at t or t+1 (right axis) 0.00% Number of small U.S. banks below 4% capital requirement rose dramatically during crisis and most exited. 8 / 112

21 Capital Ratios Over the Business Cycle 2.5 Det. Tier 1 Bank Capital Ratios over Business Cycle (risk weighted) Capital Ratios (%) GDP CR Top 10 CR Fringe GDP (right axis) Period (t) Risk-Weighted capital ratio is countercyclical for small and big banks (corr and respectively). Fig Ratio to Total Assets 9 / 112

22 Banks intermediate between Model Essentials 10 / 112

23 Banks intermediate between Model Essentials 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. 10 / 112

24 Banks intermediate between Model Essentials 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. Unit mass of identical risk neutral borrowers who demand funds to undertake i.i.d. risky projects (Loan demand). 10 / 112

25 Banks intermediate between Model Essentials 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. Unit mass of identical risk neutral borrowers who demand funds to undertake i.i.d. risky projects (Loan demand). By lending to a large # of borrowers, a given bank diversifies risk. 10 / 112

26 Banks intermediate between Model Essentials 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. Unit mass of identical risk neutral borrowers who demand funds to undertake i.i.d. risky projects (Loan demand). By lending to a large # of borrowers, a given bank diversifies risk. Loan market clearing determines interest rate r L t (η t, z t) where η t is the cross-sectional distribution of banks and z t are beginning of period t shocks. 10 / 112

27 Banks intermediate between Model Essentials 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. Unit mass of identical risk neutral borrowers who demand funds to undertake i.i.d. risky projects (Loan demand). By lending to a large # of borrowers, a given bank diversifies risk. Loan market clearing determines interest rate r L t (η t, z t) where η t is the cross-sectional distribution of banks and z t 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. 10 / 112

28 Model Essentials - cont. Deviations from Modigliani-Miller for Banks (influence costly exit): Limited liability and deposit insurance (moral hazard) Equity finance and bankruptcy costs Noncontingent loan contracts Market power by a subset of banks 11 / 112

29 Stochastic Processes Aggregate Technology Shocks z t+1 {z b, z g } follow a Markov Process F (z t+1, z t ) with z b < z g (business cycle). Conditional on z t+1, project success shocks which are iid across borrowers are drawn from p(r t, z t+1 ) (non-performing loans). Liquidity shocks (capacity constraint on deposits) which are iid across banks given by δ t {δ,..., δ} R ++ follow a Markov Process G θ (δ t+1, δ t ) (buffer stock). 12 / 112

30 Borrowers - Loan Demand Risk neutral borrowers demand bank loans in order to fund a project/buy a house. Project requires one unit of investment at start of t and returns { 1 + zt+1 R t with prob p(r t, z t+1 ). (1) 1 λ with prob 1 p(r t, z t+1 ) Borrowers choose R t (return-risk tradeoff, i.e. higher return R, lower success probability p). Borrowers have limited liability. Borrowers have an unobservable outside option (reservation utility) ω t [ω, ω] drawn at start of t from distribution Υ(ω t ). 13 / 112

31 Borrower Decision Making If a borrower chooses to demand a loan, then given limited liability his problem is to solve: v(rt L, z t ) = max E zt+1 z t p(r t, z t+1 ) ( z t+1 R t r L ) t. (2) R t The borrower chooses to demand a loan if + v( rt L, z t ) ω t. (3) Aggregate demand for loans is given by L d (r L t, z t ) = N ω ω 1 {ωt v(r L t,zt)} dυ(ω t ). (4) 14 / 112

32 Loan Market Outcomes Borrower chooses R Receive Pay Probability + Success 1 + z t+1r t 1 + r L (η t, z t) p (R t, z t+1) Failure 1 λ 1 λ 1 p (R t, z t+1) 15 / 112

33 For a bank of type θ which makes loans l θ t at rate r L t accepts deposits d θ t at rate r D t, Banks - Cash Flow holds net securities A θ t at rate r a t, 16 / 112

34 For a bank of type θ which makes loans l θ t at rate r L t accepts deposits d θ t at rate r D t, Banks - Cash Flow holds net securities A θ t at rate r a t, Its end-of-period profits are given by Current Profit Trade-offs { πt+1 θ = p(r t, z t+1 )(1 + rt L ) + (1 p(r t, z t+1 ))(1 λ) c θ} l θ t where +r a A θ t (1 + r D )d θ t κ θ. p(r t, z t+1 ) are the fraction of performing loans which depends on borrower choice R t and shocks z t+1, Charge-off rate λ, (c θ, κ θ ) are net proportional and fixed costs. 16 / 112

35 Banks - Capital Ratios and Borrowing Constraints After loan, deposit, and security decisions have been made, we can define bank equity capital ẽ θ t as e θ t A θ t + l θ t }{{} d θ t }{{}. assets liabilities Banks face a Capital Requirement: e θ t ϕ θ (l θ t + w A θ t ) (CR) where w is the risk weighting (i.e. w = 0 imposes a risk-weighted capital ratio). 17 / 112

36 Banks - Capital Ratios and Borrowing Constraints After loan, deposit, and security decisions have been made, we can define bank equity capital ẽ θ t as e θ t A θ t + l θ t }{{} d θ t }{{}. assets liabilities Banks face a Capital Requirement: e θ t ϕ θ (l θ t + w A θ t ) (CR) where w is the risk weighting (i.e. w = 0 imposes a risk-weighted capital ratio). Banks face an end-of-period Borrowing Constraint: a θ t+1 = A t (1 + r B )B t+1 0 (BBC) 17 / 112

37 Banks - Optimization When π θ t+1 < 0 (negative cash flow), bank can issue equity (at unit cost ζ θ ( )) or borrow (B θ t+1 > 0) against net securities (e.g. repos) to avoid exit but beginning-of-next-period s assets fall. 18 / 112

38 Banks - Optimization When π θ t+1 < 0 (negative cash flow), bank can issue equity (at unit cost ζ θ ( )) or borrow (B θ t+1 > 0) against net securities (e.g. repos) to avoid exit but beginning-of-next-period s assets fall. When π θ t+1 > 0, bank can either lend/store cash (B θ t+1 < 0) raising beginning-of-next-period s assets and/or pay out dividends. 18 / 112

39 Banks - Optimization When π θ t+1 < 0 (negative cash flow), bank can issue equity (at unit cost ζ θ ( )) or borrow (B θ t+1 > 0) against net securities (e.g. repos) to avoid exit but beginning-of-next-period s assets fall. When π θ t+1 > 0, bank can either lend/store cash (B θ t+1 < 0) raising beginning-of-next-period s assets and/or pay out dividends. Bank dividends at the end of the period are { Di,t+1 θ πi,t+1 = θ + Bi,t+1 θ if πi,t+1 θ + Bi,t+1 θ 0 πi,t+1 θ + Bi,t+1 θ ζ θ (πi,t+1 θ + Bi,t+1, θ z t+1) if πi,t+1 θ + Bi,t+1 θ < 0 18 / 112

40 Banks - Optimization When π θ t+1 < 0 (negative cash flow), bank can issue equity (at unit cost ζ θ ( )) or borrow (B θ t+1 > 0) against net securities (e.g. repos) to avoid exit but beginning-of-next-period s assets fall. When π θ t+1 > 0, bank can either lend/store cash (B θ t+1 < 0) raising beginning-of-next-period s assets and/or pay out dividends. Bank dividends at the end of the period are { Di,t+1 θ πi,t+1 = θ + Bi,t+1 θ if πi,t+1 θ + Bi,t+1 θ 0 πi,t+1 θ + Bi,t+1 θ ζ θ (πi,t+1 θ + Bi,t+1, θ z t+1) if πi,t+1 θ + Bi,t+1 θ < 0 Bank type θ chooses loans, deposits, net securities, non-negative dividend payouts, exit policy to maximize the future discounted stream of dividends Problem [ ] E β t Dt+1 θ t=0 18 / 112

41 Banks - Entry & Exit At the end of the period, 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. 19 / 112

42 Banks - Entry & Exit At the end of the period, 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. Entry: Banks which choose to enter incur cost Υ θ. Entry 19 / 112

43 Bank Size Distribution and Loan Market Clearing The industry state is given by the cross-sectional distribution of active banks ηt θ (a, δ) of a given type θ (a measure over beginning-of-period deposits δ t and net securities a t ). Distn The cross-sectional distribution is necessary to calculate loan market clearing: [ ] l θ t (a t, δ t, z t )dηt θ (a t, δ t ) = L d (rt L, z t ) (5) θ {b,f} 20 / 112

44 Defn. Markov Perfect Industry EQ Given policy parameters: Capital requirements,ϕ θ, and risk weights, w. Borrowing rates, r B, and securities rates, r a, a pure strategy Markov Perfect Industry Equilibrium (MPIE) is: 1. Given r L, loan demand L d (r L, z) is consistent with borrower optimization. 2. At r D, 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 η is consistent with bank entry and exit decision rules. Dist 5. The interest rate r L (η, z) is such that the loan market clears. 6. Across all states, taxes cover deposit insurance. timing Solution Approach/Computation 21 / 112

45 Long-run Model vs Data Moments Param. chosen to minimize the diff. between data and model moments. Moment (%) Data Model 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 Loans to asset ratio fringe Deposit mkt share fringe Fixed cost over loans Top Fixed cost over loans Fringe Bank entry rate Bank exit rate Freq. Top 10 bank exit 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 Sec. to asset ratio Fringe Avg Loan Markup Loan Market Share Fringe Parameterization, AR1 Defn Moments Param Values 22 / 112

46 Untargeted Business Cycle Correlations Variable Correlated with GDP Data Model Loan Interest rate Exit rate Entry rate Loan Supply Deposit Demand Default Frequency Loan return Charge-off rate Price Cost Margin Capital Ratio Top 10 (rwa) Capital Ratio Fringe (rwa) The model does a good qualitative job with the business cycle correlations. Kashyap-Stein 23 / 112

47 Capital Ratios over the Business Cycle 20 Bank Equity Ratios over Business Cycle 0.37 avg. e f /l f e b /l b GDP (right axis) Equity Ratios (%) GDP Period (t) Capital Ratios are countercyclical because loans are more procyclical than precautionary asset choices. 24 / 112

48 Frac Banks constrained by Min Cap. Req. 10 Frac. e f /l f = ϕ Output (right axis) 0.4 Frac. at Cap. Req Output Period (t) Fraction of capital requirement constrained banks rises during downturns (correlation of constrained banks and output is -0.85). 25 / 112

49 Counterfactuals 26 / 112

50 Higher Capital Requirements Question: How much does a 50% increase of capital requirements (from 4% to 6% as in Basel III) affect outcomes? Higher cap. req. banks substitute away from loans to securities lower profitability. Figure Decision Rules Lower loan supply (-8%) higher interest rates (+50 basis points), more chargeoffs (+12%), lower intermediated output (-9%). Entry/Exit drops (-45%) lower taxes (-60%), more concentrated industry (less small banks (-14%)). Table CR Competition Cyclical CR 27 / 112

51 Conclusion 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. 28 / 112

52 Conclusion 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. We find that a rise in capital requirements from 4% to 6% leads to a significant reduction in bank exit probabilities, but a more concentrated industry. 28 / 112

53 Conclusion 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. We find that a rise in capital requirements from 4% to 6% leads to a significant reduction in bank exit probabilities, but a more concentrated industry. Strategic interaction between big and small banks generates higher volatility than a perfectly competitive model. 28 / 112

54 Conclusion 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. We find that a rise in capital requirements from 4% to 6% leads to a significant reduction in bank exit probabilities, but a more concentrated industry. Strategic interaction between big and small banks generates higher volatility than a perfectly competitive model. Countercyclical interest margins provide a new amplification mechanism; in a downturn, exit weakens competition higher loan rates, amplifying the downturn. Crises 28 / 112

55 Conclusion 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. We find that a rise in capital requirements from 4% to 6% leads to a significant reduction in bank exit probabilities, but a more concentrated industry. Strategic interaction between big and small banks generates higher volatility than a perfectly competitive model. Countercyclical interest margins provide a new amplification mechanism; in a downturn, exit weakens competition higher loan rates, amplifying the downturn. Crises Stackelberg game allows us to examine how policy changes which affect big banks spill over to the rest of the industry. other 28 / 112

56 Related Research C-D (2013) A Quantitative Model of Banking Industry Dynamics A quantitative 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. Counterfactuals: Branching restrictions induce more regional concentration and leads to more nonperforming loans. Too-big-to-fail induces biggest banks to increase loan exposure which substitutes for small bank lending leading to lower profitability and entry. 29 / 112

57 Related Research C-D (2013) A Quantitative Model of Banking Industry Dynamics A quantitative 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. Counterfactuals: Branching restrictions induce more regional concentration and leads to more nonperforming loans. Too-big-to-fail induces biggest banks to increase loan exposure which substitutes for small bank lending leading to lower profitability and entry. C-D (2015) Foreign Competition and Banking Industry Dynamics A General Equilibrium version of our model calibrated to the Mexican Economy to quantitatively assess how restrictions on foreign bank entry affect domestic loan rates and welfare. Foreign entry leads to lower interest rates but higher volatility due to exposure to foreign bank funding shocks. 29 / 112

58 Related Research - cont. C-D-G-I-S (2017) Structural Stress Tests A structural model to conduct stress tests with endogenous hurdle (exit decision) which can be used to assess regulatory changes without Lucas critique concerns of reduced form statistical models (e.g. CLASS model) Adds borrower heterogeneity (commercial vs residential) and maturity transformation to the framework. 30 / 112

59 Appendix 31 / 112

60 Test III: Empirical Studies of Banking Crises, Default and Concentration Model Logit Linear Dependent Variable Crisis t Default Freq. t Concentration t (0.86) (0.001) GDP growth in t (0.09) (0.021) Loan Supply Growth t (1.39) (0.0289) R Note: SE in parenthesis. 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). As in Berger et. al. (2008) we find that concentration is positively related to default frequency (consistent with B-D). Return 32 / 112

61 Open Questions Why is market structure so different across countries? In 2011, this is evident in the asset market share of the top 3 banks in the following countries (1/N with symmetric banks): Germany: 78% Japan: 44% Mexico: 57% Portugal: 89% Spain: 68% UK: 58% US: 35% 33 / 112

62 Open Questions Why is market structure so different across countries? In 2011, this is evident in the asset market share of the top 3 banks in the following countries (1/N with symmetric banks): Germany: 78% Japan: 44% Mexico: 57% Portugal: 89% Spain: 68% UK: 58% US: 35% Does competition matter for crises? 33 / 112

63 Stress Tests - Reduced Form Approach Hirtle, et. al. (2014) CLASS (Capital and Loss Assessment under Stress Scenarios) model: 1. Reduced form regressions: y i,t = β 0 + β 1 y i,t 1 + β 2 macro t + β 3 x i,t + ε i,t (6) where y i,t is an N vector of key income or expense ratios across loan classes (e.g. net interest margin, net charge-offs), x i,t are firm specific characteristics such as shares of different types of loans in bank i s portfolio, etc. NIMAR1 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. 34 / 112

64 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 (l, d, A, δ, ζ, z ) > W x=0 (l, d, A, δ, ζ, z ) a, δ, z, ζ ) (7) where W x=1 and W x=0 are the charter values of the bank under exit and no-exit options. Evolution of the state variables (asset position a and bank size distribution ζ) and exit decision are endogenously determined. RW Capital ratios at which failure arises are higher than in CLASS model. Hurdle Return 35 / 112

65 Entry and Exit Over the Business Cycle 8 Entry Rate Exit Rate Det. GDP 6 4 Percentage (%) year Trend in exit rate prior to early 90 s due to deregulation 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 36 / 112

66 Entry and Exit by Bank Size Fraction of Total x, x accounted by: Entry Exit Exit/Merger Exit/Failure Top 10 Banks Top 1% Banks Top 10% Banks Bottom 99% Banks Total Rate Note: Big banks that exited by merger: 1996 Chase Manhattan acquired by Chemical Banking Corp First American National Bank acquired by AmSouth Bancorp. Definitions Frac. of Loans Return 37 / 112

67 Increase in Loan and Deposit Market Concentration Top 4 Banks Top 10 Banks Panel (i): Loan Market Share Percentage (%) year Top 4 Banks Top 10 Banks Panel (ii): Deposit Market Share Percentage (%) Return year 38 / 112

68 Measures of Concentration in 2010 Measure Deposits Loans Percentage of Total in top 4 Banks (C 4 ) 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) (%) Note: Total Number of Banks 7,092. Top 4 banks are: Bank of America, Citibank, JP Morgan Chase, Wells Fargo. High degree of imperfect competition HHI 15 National measure is a lower bound since it does not consider regional market shares (Bergstresser (2004)). Return 39 / 112

69 Measures of Banking Competition Moment Value (%) Std. Error (%) Corr w/ GDP Interest margin Markup Lerner Index Rosse-Panzar H All the measures provide evidence for imperfect competition (H< 100 implies MR insensitive to changes in MC). Estimates are in line with those found by Berger et.al (2008),Bikker and Haaf (2002), and Koetter, Kolari, and Spierdijk (2012). Countercyclical interest margins imply amplification of shocks to real side of the economy. Definitions Figures Return 40 / 112

70 Costs by Bank Size Table: Period Net Exp. Fixed Cost Moment (%) Non-Int Inc. Non-Int Exp. (c θ ) (κ θ /l θ ) Avg Cost Top Fringe Marginal Non-Int. Income, Non-Int. Expenses (estimated from trans-log cost function) and Net Expenses increase with size. Fixed Costs (normalized by loans) decrease in size. Average Costs decrease in size (consistent with evidence (e.g. Mester) for IRS in banking). Selection of only low cost banks in the competitive fringe may drive the Net Expense pattern. Definitions Return 41 / 112

71 Exit Rate Decomposed 15 Merger Rate Failure Rate Trouble Bank Rate Det. GDP 10 Percentage (%) year Correlation of GDP with (Failure, Troubled, Mergers) =(-0.47, -0.72, 0.58) after 1990 Return 42 / 112

72 Definitions Entry and Exit by Bank Size Let y {Top 4, Top 1%, Top 10%, Bottom 99%} let x {Enter, Exit, Exit by Merger, Exit by Failure} 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. For example, Top y = 1% banks that x =enter in period t over total number of banks that x =enter in period t. Return 43 / 112

73 Entry and Exit by Bank Size Fraction of Loans of Banks in x, x accounted by: Entry Exit Exit/Merger Exit/Failure Top 10 Banks Top 1% Banks Top 10% Banks Bottom 99% Banks Note: Big banks that exited by merger: 1996 Chase Manhattan acquired by Chemical Banking Corp First American National Bank acquired by AmSouth Bancorp. Return 44 / 112

74 Definition of Competition Measures The Interest Margin is defined as: pr L it r D it where r L realized real interest income on loans and r D the real cost of loanable funds The markup for bank is defined as: Markup tj = p l tj mc ltj 1 (8) where p ltj is the price of loans or marginal revenue for bank j in period t and mc ltj is the marginal cost of loans for bank j in period t The Lerner index is defined as follows: Lerner it = 1 mc l it p lit Return 45 / 112

75 Cyclical Properties 6 Panel (i): Net Interest Margin Perc. (%) year Panel (ii): Markup Perc. (%) year Panel (iii): Lerner Index Perc. (%) 50 Return year 46 / 112

76 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). Return 47 / 112

77 Balance Sheet: all variables Fraction Total Assets (%) Small Top 10 Small Top 10 1 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) Def. Short BS Return 48 / 112

78 Balance Sheet Short Definitions Liquid Assets = 1+ 2 (=cash + fed funds sold ) Securities= (=Safe securities + safe trading assets ) Loans = (=risky securities + risky trading assets + loans - trading liabilities ) Other assets= (=fixed assets + int. + other assets- sub. debt - other liabilities) fed funds/repos =15+16 (fed funds/repos + other borrowed money) Normalized Assets= (=Total Assets - Other assets) Capital Ratio (rw) = 21 (= Tier 1 capital (rw)) Balance Sheet (Long) Return 49 / 112

79 Regulation Capital Ratios Tier 1 to Tier 1 to Risk Total Capital to Risk Total Assets w/ Assets w/ Assets Well Capitalized 5% 6% 10% Adequately Capitalized 4% 4% 8% Undercapitalized < 4% < 4% < 8% Signif. Undercapitalized < 3% < 3% < 6% Critically Undercapitalized < 2% < 2% < 2% Source: DSC Risk Management of Examination Policies (FDIC). Capital (12-04). Return 50 / 112

80 Capital Ratios by Bank Size 11 Top 10 Fringe Tier 1 Bank Capital to assets ratio 10 9 Percentage (%) year Capital Ratios (equity capital to assets) are larger for small banks. On average, capital ratios are above what regulation defines as Well Capitalized ( 6%) further suggesting a precautionary motive. Return 51 / 112

81 Capital Ratio Over the Business Cycle 2.25 Det. Tier 1 Bank Capital Ratios over Business Cycle Capital Ratios (%) GDP GDP (right axis) CR Top 10 CR Fringe Period (t) Capital Ratio (over total assets) is countercyclical for small banks (corr ) and big banks (corr ). Return 52 / 112

82 Business Cycle Correlations Variable Correlated with GDP Data Loan Interest Rate r L Exit Rate Entry Rate 0.25 Loan Supply 0.72 Deposits 0.22 Default Frequency Loan Return Charge Off Rate Interest Margin Lerner Index Markup Return 53 / 112

83 Depositors Each hh is endowed with 1 unit of a good and is risk averse with preferences u(c t ). HH s can invest their good in a riskless storage technology yielding exogenous net return r. If they deposit with a bank they receive rt D even if the bank fails due to deposit insurance (funded by lump sum taxes on the population of households). If they match with an individual borrower, they are subject to the random process in (1). Return 54 / 112

84 Borrower Project Choice & Inverse Loan Demand R(r L,z b ) Panel (a): Borrower Project R 0.13 R(r L,z g ) Loan Interest Rate (r L ) Panel (b): Inverse Loan Demand r L (L,z b ) 0.15 r L (L,z g ) Loan Demand (L) Risk shifting effect that higher interest rates lead borrowers to choose more risky projects as in Boyd and De Nicolo. Thus higher loan rates can induce higher default frequencies. Loan demand is pro-cyclical. Borrower Problem Fig. Return Mkt Essentials Return Timing 55 / 112

85 Loan rates and default risk p(r(r L,z b ),z" b ) p(r(r L,z b ),z" g ) Loan Interest Rate (r L ) p(r(r L,z g ),z" b ) p(r(r L,z g ),z" g ) Loan Interest Rate (r L ) Higher loan rates induce higher default risk Return 56 / 112

86 Big Bank Problem The value function of a big incumbent bank at the beginning of the period is then given by V b { (a, δ, z, ζ) = βez zw b (l, d, A, ζ, δ, z ) }, (9) s.t. max l,d [0,δ],A 0 a + d A + l (10) e = l + A d ϕ b l (11) l + L s,f (z, ζ, l) = L d (r L, z) (12) where L s,f (z, ζ, l) = l f i (a, δ, z, ζ, lb )ζ f (da, dδ). Market clearing (12) 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 57 / 112

87 Big Bank Problem - Cont. Return OPT The end of period function is given by W b (l, d, A, η, δ, z { ) = W b,x=0 (l, d, A, η, δ, z ), W b,x=1 (l, d, A, η, δ, z ) } max x {0,1} W b,x=0 (l, d, A, η, δ, z ) = s.t. D b = { max B A (1+r B ) { } D b + Eδ b δ V b (a, δ, z, η ) π b (l, d, a, η, z ) + B if π b ( ) + B 0 π b (l, d, a, η, z ) + B ζ b (π b ( ) + B, z ) if π b ( ) + B < 0 a = A (1 + r B )B 0 η = H(z, η, z ) W b,x=1 (l, d, A, η, δ, z ) = max { ξ [ {p(r, z )(1 + r L ) + (1 p(r, z ))(1 λ) c b }l ] + (1 + r a )A d(1 + r D ) κ b, 0 }. 58 / 112

88 Bank Entry Each period, there is a large number of potential type θ entrants. The value of entry (net of costs) is given by { V θ,e (z, η, z ) max (a + Υ θ ) ζ θ (a + Υ θ ) (13) a } +E δ V θ (a, δ, z, H(z, η, z )) Entry occurs as long as V θ,e (z, η, z ) 0. The argmax of (13) defines the initial equity distribution of banks which enter. Free entry implies that V θ,e (z, ζ, z ) E θ = 0 (14) where E f denotes the mass of fringe entrants and E b the number of big bank entrants. Return EE 59 / 112

89 Evolution of Cross-sectional Bank Size Distribution Given any sequence (z, z ), the distribution of fringe banks evolves according to η(a D) = Q((a, δ), z, z, A D)η(da, δ) (15) δ Q((a, δ), z, z, A D) = (1 x f (a, δ, z, η, z ))I {a f (a,δ,z,η) A)}G f (δ, δ) δ D +E f I {a f,e (z,η) A)} G f,e (δ). (16) δ D (16) makes clear how the law of motion for the distribution of banks is affected by entry and exit decisions. Return BSD 60 / 112

90 Taxes to cover deposit insurance Across all states (η, z, z ), taxes must cover deposit insurance in the event of bank failure. Let post liquidation net transfers be given by [ ] θ = (1 + r D )d θ ξ {p(1 + r L ) + (1 p)(1 λ) c θ }l θ + ã θ (1 + r a ) where ξ 1 is the post liquidation value of the bank s assets and cash flow. Then aggregate taxes are τ(z, η, z ) Ξ = x f max{0, f }dη f (a, δ) + x b max{0, b } Return Timing 61 / 112

91 Incumbent Bank Decision Making Differentiating end-of period profits with respect to l θ we obtain dπ θ dl θ = [ pr L (1 p)λ r a c θ ] + l θ[ p + p R ] dr L }{{}}{{} R r L (rl + λ) }{{}}{{} dl θ (+) or ( ) (+) ( ) ( ) drl dl f Return = 0 for competitive fringe. 62 / 112

92 Fringe Bank Problem The value function of a fringe incumbent bank at the beginning of the period is then given by V f { (a, δ, z, η) = βez zw f (l, d, A, δ, η, z ) }, s.t. max l 0,d [0,δ],A 0 a + d A + l (17) l(1 ϕ f ) + A(1 wϕ f ) d 0 (18) l b (η) + L f (ζ, l b (η)) = L d (r L, z) (19) Fringe banks use the decision rule of the dominant bank in the market clearing condition (19). Return 63 / 112

93 Solution Approach Return Def. Eq. Solve the model using a variant of Krusell and Smith (1998) and Farias, Saure, and Weintraub (2012). Main difficulty arises in approximating the distribution of fringe banks and computing the reaction function from the fringe sector to clear the loan market: l b (a, δ, z, η) + l f (a, δ, z, a b, δ b, η, l b )dη(a, δ) = L d (r L, z) A D } {{ } =L s,f (z,a b,δ b,η,l b ) Approximate the cross-sectional distn of fringe banks using a finite set of moments: the cross-sectional avg of assets plus deposits (denoted A) since that determines feasible loan and asset choices at the beginning of the period and the mass of incumbent fringe banks (denoted M) where A = (a + δ)dη(a, δ), M = dη(a, δ) A D A D 64 / 112

94 Solution Approach (cont.) Return Def. Eq. The evolution of these moments is approximated using a log-linear function that has {a b, δ b, z, A, M, z } as states. The mass of entrants E f and incumbents M are linked since η (a, δ ) = T (η(a, δ)) + E f I a =a f,egf,e (δ) where T ( ) is the transition operator. For each combination of state variables {a b, δ b, z, A, M} we iterate on l b ( ) and and the reaction function L s,f ( ) until we find a fixed point (i.e. the equilibrium in the Stackelberg game). l b (a b, δ b, z, A, M) + L s,f (a b, δ b, z, A, M, l b ( )) = L d (r L, z) D 65 / 112

95 Computational Algorithm 1. Guess aggregate functions. Make an initial guess of L f (a b, δ b, z, A, M) and the law of motion for A and M. L f = H L (a b, δ b, z, A, M). log(a ) = H A (a b, δ b, z, A, M, z ). log(m ) = H M (a b, δ b, z, A, M, z ). 2. Solve the dominant bank problem. 3. Solve the problem of fringe banks. 4. Solve the entry problem of the fringe bank and big bank to obtain the number of entrants as a function of the state space. 5. Simulate to obtain a sequence {a b t, A t, M t } T t=1 and update aggregate functions. If convergence achieved stop. If not, return to (2). Return Parametrization Return Def. Eq. 66 / 112

96 Parameterization For the stochastic deposit matching process, we use data from our panel of U.S. commercial banks: Assume dominant bank support is large enough so that the constraint never binds. For fringe banks, use Arellano and Bond to estimate the AR(1) log(δ it ) = (1 ρ d )k 0 +ρ d log(δ it 1 )+k 1 t+k 2 t 2 +k 3,t +a i +u it (20) where t denotes a time trend, k 3,t are year fixed effects, and u it is iid and distributed N(0, σ 2 u). Discretize using Tauchen (1986) method with 5 states. Discrete Process Computation: Variant of Ifrach/Weintraub (2012), Krusell/Smith (1998) Details Return 67 / 112

97 Parameterization Parameter Value Target Dep. preferences σ 2 Part. constraint Agg. shock in good state z g 1 Normalization Deposit interest rate (%) r = r d 0.86 Int. expense Net. non-int. exp. n bank c b 1.55 Net non-int exp. Top 1% Net. non-int. exp. r bank c f 1.87 Net non-int exp. bottom 99% Charge-off rate λ 0.21 Charge off rate Autocorrel. Deposits ρ d 0.83 Deposit Process Bottom 99% Std. Dev. Error σ u 0.20 Deposit Process Bottom 99% Securities Return (%) r a 0.92 Avg. Return Securities Cost overnight funds r B 0.00 Fed Funds Rate Capital Req. Top 10 (ϕ b, w) (4.0, 0) Capital Regulation Capital Req. Fringe (ϕ f, w) (4.0, 0) Capital Regulation Return Mom 68 / 112

98 Parameters Chosen within Model Parameter Value Targets Agg. shock in crisis state z c 0.95 Freq. Top 10 bank exit Agg. shock in bad state z b Std. dev. Output Weight agg. shock α Std. dev. net-int. margin Success prob. param. b Borrower Return Volatility borrower s dist. σ ɛ Std. deviation default frequency Success prob. param. ψ Net Interest Margin Mean Entrep. project Dist. µ e Default freq. Max. reservation value ω Elasticity Loan Demand Discount Factor β 0.96 Loans to asset ratio Top 10 Salvage value ξ 0.71 Loans to asset ratio fringe Mean Deposits µ d Deposit mkt share fringe Fixed cost b bank κ b Fixed cost over loans top 10 Fixed cost f banks κ f Fixed cost over loans fringe Entry Cost f banks Υ f Bank entry rate Entry Cost b bank Υ b Bank exit rate Equity Issuance Cost ζ Equity Issuance over Assets Top 10 Equity Issuance Cost ζ Equity Issuance over Assets Fringe Equity over (r-w) assets top 10 Equity over (r-w) weighted assets fringe Note: Functional Forms Return Mom 69 / 112

99 Markov Process Matched Deposits The finite state Markov representation G f (δ, δ) obtained using the method proposed by Tauchen (1986) and the estimated values of µ d, ρ d and σ u is: G f (δ, δ) = , The corresponding grid is δ {0.019, 0.028, 0.040, 0.057, }. The distribution G e,f (δ) is derived as the stationary distribution associated with G f (δ, δ). Return 70 / 112

100 Functional Forms Borrower outside option is distributed uniform [0, ω]. For each borrower, let y = αz + (1 α)ε br ψ where ε is drawn from N(µ ε, σ 2 ε). Define success to be the event that y > 0, so in states with higher z or higher ε e success is more likely. Then ( αz p(r, z + br ψ ) )1 Φ (21) (1 α) where Φ(x) is a normal cumulative distribution function with mean (µ ε ) and variance σ 2 ε. Return 71 / 112

101 Definition Model Moments Aggregate loan supply L s (z, η) { = l b + L f (z, η, l b ) } Aggregate Output L s (z, η) p(z, η, z )(1 + z R) + (1 p(z, η, z ))(1 λ) Entry Rate E f / η(a, δ) Default frequency 1 p(r, z ) Borrower return p(r, z )(z R ) Loan return p(r, z )r L (z, η) + (1 p(r, z ))λ Loan Charge-off rate (1 p(r, z ))λ Interest Margin p(r, z )r L (z, ( η) r d ) Loan Market Share Bottom 99% L f (η, l b (η))/ l b (η) + L f (η, l b (η)) a,δ Deposit Market Share Bottom 99% (a,δ,z,η)dζ(a,δ) a,δ df (a,δ,z,η)dη(a,δ)+d b (a,δ,z,η) Capital Ratio Bottom 99% a,δ [ẽf (a, δ, z, η)/l f (a, δ, z, η)]dη(a, δ)/ dη(a, δ) a,δ Capital Ratio Top 1% ẽ b (a, δ, z, η)/l b (a, δ, z, η) a,δ Securities to Asset Ratio Bottom 99% (a,δ,z,η)/(l f (a,δ,z,η)+ã f (a,δ,z,η))]dζ(a,δ) a,δ dζ(ã,δ) Securities to Asset Ratio Top 1% ã b (a, δ, z, η)/(l b (a, δ, z, η) + ã b (a, δ, z, η)) π li (θ)( ) Profit Rate l i (θ) [ Lerner Index 1 r d + c θ,exp] / [p(r (η, z), z, s )r L (η, z) + c θ,inc] [ Markup p j (R (η, z), z, s )r L (η, z) + c θ,inc] [ / r d + c θ,exp] 1 Return 72 / 112

102 Fringe Bank Exit Rule across δ s Panel (i): Exit decision rule fringe δ L and δ H banks at z b x f (δ L,z b,z b ) x f (δ L,z b,z g ) x f (δ H,z b,z b ) x f (δ H,z b,z g ) a x 10 3 Panel (ii): Exit decision rule fringe δ L and δ H banks at z g x f (δ L,z g,z b ) x f (δ L,z g,z g ) x f (δ H,z g,z b ) x f (δ H,z g,z g ) a x 10 3 Fringe banks with low assets are more likely to exit, particularly if they are small δ L. Return 73 / 112

103 Big and Median Buffer and Cash Flow Policy Panel (i): Net Cash Flow (CF) and a big at zb CF b (z b,z b ) CF b (z b,z g ) a b (z b,z b ) a b (z b,z g ) a Panel (ii): Net Cash Flow (CF) and a fringe(δm) bank at zb CF f (z b,z b ) CF f (z b,z g ) a f (z b,z b ) a f (z b,z g ) a Banks issue equity (CF = π + B < 0) to continue when assets are low They pay dividends (CF 0) when unconstrained optimum level of assets can be achieved without external finance Banks accumulate more assets in good times (marginal value is higher) return 74 / 112

104 Fringe Banks a f (different δ s) Panel (i): a decision rule fringe δl and δh banks at zb a f (δ L,z b,z b ) a f (δ L,z b,z g ) a f (δ H,z b,z b ) a f (δ H,z b,z g ) 45 o a Panel (ii): a decision fringe δl and δh banks at zg a f (δ L,z g,z b ) a f (δ L,z g,z g ) a f (δ H,z g,z b ) a f (δ H,z g,z g ) 45 o a The smallest fringe bank is more cautious than the largest fringe bank. Return 75 / 112

105 Big and Median Fringe Capital Ratios ẽ θ /l θ Equity Ratios (ẽ θ /l θ ) big and fringe(δm) banks ẽ b /l b (zb) ẽ b /l b (zg) ẽ f /l f (zb) ẽ f /l f (zg) cap. req a Recall that ẽ θ /l θ = (l θ + ã θ d θ )/l 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 Return Definition 76 / 112

106 Monetary Policy and Bank Lending Benchmark Lower r B (%) Capital Ratio Top Capital Ratio Fringe Entry/Exit Rate (%) Loans to Asset Ratio Top Loans to Asset Ratio Fringe Measure Banks Fringe Loan mkt sh. Fringe (%) Loan Supply L s to Int. Output ratio (%) Loan Interest Rate (%) Borrower Project (%) Default Frequency (%) Avg. Markup Int. Output Taxes/Output (%) Return Reducing the cost of funds increases the value of the bank resulting in a large influx of fringe banks Reduction in borrowing cost relaxes ex-post constraint: higher big bank loan supply, lower interest rates and lower default rates. 77 / 112

107 Higher Capital Requirements and Equity Ratios Comparison Equity Ratios (e θ /l θ ) big and fringe(δ H ) banks when z b 0.4 e b /l b (bench.) 0.3 e b /l b (high c.r.) e f /l f (bench.) e f /l f (high c.r.) securities (ã) Comparison Equity Ratios (e θ /l θ ) big and fringe(δ H ) banks when z g e b /l b bench. e b /l b high c.r. e f /l f bench. e f /l f high c.r securities (ã) 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 78 / 112

108 Capital Requirement Counterfactual Question: How much does a 50% increase of capital requirements affect outcomes? Return Table No Cap. Requirements Benchmark Higher Cap. Req. Change Moment (%) (ϕ = 4%) (ϕ = 6%) (%) Capital Ratio Top Capital Ratio Fringe Entry/Exit Rate (%) Sec. to Asset Ratio Top Sec. to Asset Ratio Fringe Measure Banks Fringe Loan mkt sh. Fringe (%) Loan Supply L s to Int. Output ratio (%) Loan Interest Rate (%) Borrower Project (%) Default Frequency (%) Avg. Markup Int. Output Taxes/Output (%) / 112

109 Capital Requirements and Competition Question: How much does imperfect competition affect capital requirement counterfactual predictions? Return Benchmark Model Perfect Competition Moment (%) ϕ = 4% ϕ = 6% (%) ϕ = 4% ϕ = 6% (%) Capital Ratio (%) Entry/Exit Rate (%) Measure Banks Loan Supply Loan Int. Rate (%) Borr. Proj. (%) Def. Freq. (%) Avg. Markup Int. Output L s to output (%) Taxes/output (%) Policy effects are muted in the perfectly competitive environment. 80 / 112

110 Imperfect Competition and Volatility Benchmark Perfect Competition Coefficient of Variation (%) Model ( Υ b ) Change (%) Loan Interest Rate Borrower Return Default Frequency Int. Output Loan Supply Capital Ratio Fringe Measure Banks Markup Loan Supply Fringe Return 81 / 112

111 Imperfect Competition and Business Cycle Correlations Benchmark Perfect Comp. data Loan Interest Rate r L Exit Rate Entry Rate Loan Supply Deposits Default Frequency Loan Interest Return Charge Off Rate Markup Capital Ratio Top 1% Capital Ratio Bottom 99% Return 82 / 112

112 The role of Capital Requirements Question: What if there are no capital requirements? Return Benchmark Model Perfect Competition Moment ϕ = 4% No CR (%) ϕ = 4% No CR (%) Cap. ratio top Cap. ratio bottom Fringe Entry/Exit Rate (%) Loan mkt sh. Fringe (%) Measure Banks Loan Supply Loan Int. Rate (%) Borrower Proj. (%) Default Freq. (%) Avg. Markup Int. Output L s to output ratio (%) Taxes/GDP (%) 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. 83 / 112

113 Countercyclical Capital Requirements Question: What if capital requirements are higher in good times? Benchmark Countercyclical CR (ϕ = 0.04) (ϕ(z b ) = 0.06, ϕ(zg ) = 0.08) (%) Capital Ratio Top Capital Ratio Bottom Fringe Entry/Exit Rate (%) Measure Banks Fringe Loan mkt sh. Fringe (%) Securities to Asset Ratio Top Securities to Asset Ratio Fringe Loan Supply L s to Int. Output ratio (%) Loan Interest Rate (%) Borrower Project (%) Default Frequency (%) Avg. Markup Int. Output Taxes/Output (%) Return 84 / 112

114 The Role of Imperfect Competition Question: How much does imperfect competition affect capital requirement counterfactual predictions? Our model nests perfect competition ( Υ b No big bank entry) 85 / 112

115 The Role of Imperfect Competition Question: How much does imperfect competition affect capital requirement counterfactual predictions? Our model nests perfect competition ( Υ b No big bank entry) Without big banks higher mass M of fringe banks and higher loan supply interest rates drop 50 basis points. Table Lower profitability leads to lower entry (drops 50%) but higher total exits (M x) higher taxes/output. 85 / 112

116 The Role of Imperfect Competition Question: How much does imperfect competition affect capital requirement counterfactual predictions? Our model nests perfect competition ( Υ b No big bank entry) Without big banks higher mass M of fringe banks and higher loan supply interest rates drop 50 basis points. Table Lower profitability leads to lower entry (drops 50%) but higher total exits (M x) higher taxes/output. Volatility of almost all variables decrease average capital ratio is 12% lower (reduced precautionary holdings). Table Return CR 85 / 112

117 The Role of Imperfect Competition Question: How much does imperfect competition affect capital requirement counterfactual predictions? Our model nests perfect competition ( Υ b No big bank entry) Without big banks higher mass M of fringe banks and higher loan supply interest rates drop 50 basis points. Table Lower profitability leads to lower entry (drops 50%) but higher total exits (M x) higher taxes/output. Volatility of almost all variables decrease average capital ratio is 12% lower (reduced precautionary holdings). Table 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 85 / 112

118 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 Benchmark Nat. Bank Bailout Change (%) Loan Supply Loan Interest Rate (%) Markup Market Share bottom 99% Market Share Top 10 / Top 1% / / Prob. Exit Top 10 / Top 1% 0 / 1.67 n.a. / Borrower Risk Taking R (%) Default Frequency (%) Entry/Exit Rate (%) Int. Output Taxes/Output (%) National bank increases loan exposure to region with high downside risk while loan supply by other banks falls (spillover effect). Net effect is higher aggregate loans, lower interest rates and default frequencies. more Lower profitability reduces smaller bank entry. 86 / 112

119 National Bank Problem under Too Big to Fail If realized profits for a national bank are negative, then the government covers the losses so that the bank stays in operation. The problem of a national bank becomes V i (n,, µ, z, s; σ i ) = max {li(n,j)} j=e,w E z,s z,s[ j=e,w { } ] max 0, π li(n,j)(n, j, c n, µ, z, s, z, s ; σ i ) + βv i (n,, µ, z, s ; σ i ) subject to θ l i (θ, j, µ, s, z; σ i )µ (θ,j) (di) L d,j (r L,j, z, s) = 0, where L d,j (r L,j, z, s) is given in (4). Return 87 / 112

120 Too-Big-to-Fail (cont.) Table: Benchmark vs Too Big to Fail Loan Decision Rules l(θ, j, µ, z, e) (µ = {1, 1, 1, }, z = z b, s = e) Model l(n, e, ) l(n, w, ) l(r, e, ) l(r, w, ) Dynamic (benchmark) National Bank Bailouts 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 88 / 112

121 Allowing Foreign Bank Competition Moment Data Υ f = Benchmark 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 Less concentrated industry with lower interest rate margins, higher exit rates with banks more exposed to risk and more volatile Lower interest rates lower default frequency and charge off rates Higher output, loan supply but higher taxes as well 89 / 112

122 Foreign Bank Competition: Real Effects Foreign bank competition induces higher output and larger output and credit contractions/expansion due to changes in domestic conditions Volatility of output and loan supply increases (+12.91% and 10.11%) 90 / 112