A Quantitative Model of Banking Industry Dynamics. April 11, 2013 (Incomplete)

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1 A Quantitative Model of Banking Industry Dynamics Dean Corbae Pablo D Erasmo Univ. of Wisconsin and NBER Univ. of Maryland April 11, 2013 (Incomplete)

2 Question How much does a commitment to bailout big banks during insolvency contribute to risk taking and how much does this affect smaller banks entry/exit rates as well as the economy-wide fraction of non-performing loans?

3 Question How much does a commitment to bailout big banks during insolvency contribute to risk taking and how much does this affect smaller banks entry/exit rates as well as the economy-wide fraction of non-performing loans? Big banks increase loan exposure to regions with high downside risk.

4 Question How much does a commitment to bailout big banks during insolvency contribute to risk taking and how much does this affect smaller banks entry/exit rates as well as the economy-wide fraction of non-performing loans? Big banks increase loan exposure to regions with high downside risk. Loan supply by smaller banks fall by 15% ( systemic spillover).

5 Question How much does a commitment to bailout big banks during insolvency contribute to risk taking and how much does this affect smaller banks entry/exit rates as well as the economy-wide fraction of non-performing loans? Big banks increase loan exposure to regions with high downside risk. Loan supply by smaller banks fall by 15% ( systemic spillover). Aggregate loan supply rises by 6% resulting in 50 basis point lower interest rates on loans and 2% lower economy-wide borrower default rates.

6 Question How much does a commitment to bailout big banks during insolvency contribute to risk taking and how much does this affect smaller banks entry/exit rates as well as the economy-wide fraction of non-performing loans? Big banks increase loan exposure to regions with high downside risk. Loan supply by smaller banks fall by 15% ( systemic spillover). Aggregate loan supply rises by 6% resulting in 50 basis point lower interest rates on loans and 2% lower economy-wide borrower default rates. Lower markups reduce smaller bank entry by 1/10% and reduce market share of bottom 99% by 7%.

7 Question How much does a commitment to bailout big banks during insolvency contribute to risk taking and how much does this affect smaller banks entry/exit rates as well as the economy-wide fraction of non-performing loans? Big banks increase loan exposure to regions with high downside risk. Loan supply by smaller banks fall by 15% ( systemic spillover). Aggregate loan supply rises by 6% resulting in 50 basis point lower interest rates on loans and 2% lower economy-wide borrower default rates. Lower markups reduce smaller bank entry by 1/10% and reduce market share of bottom 99% by 7%. Lump sum taxes (relative to intermediated output) to pay for bailout rise 10%.

8 Outline 1. Document Banking Industry Facts from Balance sheet panel data as in Kashyap and Stein (2000).

9 Outline 1. Document Banking Industry Facts from Balance sheet panel data as in Kashyap and Stein (2000). 2. A Dynamic Model of the Banking Industry

10 Outline 1. Document Banking Industry Facts from Balance sheet panel data as in Kashyap and Stein (2000). 2. A Dynamic Model of the Banking Industry Underlying Static Cournot Model as in Allen & Gale (2000) embedded in a dynamic model of entry and exit as in Ericson & Pakes (1995) augmented with a competitive fringe as in Gowrisankaran & Holmes (2004).

11 Outline 1. Document Banking Industry Facts from Balance sheet panel data as in Kashyap and Stein (2000). 2. A Dynamic Model of the Banking Industry Underlying Static Cournot Model as in Allen & Gale (2000) embedded in a dynamic model of entry and exit as in Ericson & Pakes (1995) augmented with a competitive fringe as in Gowrisankaran & Holmes (2004). Stackelberg game allows us to examine how policy changes on big banks spill over to the rest of the industry.

12 Outline 1. Document Banking Industry Facts from Balance sheet panel data as in Kashyap and Stein (2000). 2. A Dynamic Model of the Banking Industry Underlying Static Cournot Model as in Allen & Gale (2000) embedded in a dynamic model of entry and exit as in Ericson & Pakes (1995) augmented with a competitive fringe as in Gowrisankaran & Holmes (2004). Stackelberg game allows us to examine how policy changes on big banks spill over to the rest of the industry. Most quantitative macro banking models (eg. Diaz-Gimenez,et.al. (1992)) assume perfect comp. & CRS indeterminate size distn.

13 Outline 1. Document Banking Industry Facts from Balance sheet panel data as in Kashyap and Stein (2000). 2. A Dynamic Model of the Banking Industry Underlying Static Cournot Model as in Allen & Gale (2000) embedded in a dynamic model of entry and exit as in Ericson & Pakes (1995) augmented with a competitive fringe as in Gowrisankaran & Holmes (2004). Stackelberg game allows us to examine how policy changes on big banks spill over to the rest of the industry. Most quantitative macro banking models (eg. Diaz-Gimenez,et.al. (1992)) assume perfect comp. & CRS indeterminate size distn. 3. Estimation (incomplete) using long-run averages of bank industry data.

14 Outline 1. Document Banking Industry Facts from Balance sheet panel data as in Kashyap and Stein (2000). 2. A Dynamic Model of the Banking Industry Underlying Static Cournot Model as in Allen & Gale (2000) embedded in a dynamic model of entry and exit as in Ericson & Pakes (1995) augmented with a competitive fringe as in Gowrisankaran & Holmes (2004). Stackelberg game allows us to examine how policy changes on big banks spill over to the rest of the industry. Most quantitative macro banking models (eg. Diaz-Gimenez,et.al. (1992)) assume perfect comp. & CRS indeterminate size distn. 3. Estimation (incomplete) using long-run averages of bank industry data. 4. Tests: business cycle correlations, cross-sectional moments, banking crises predictions.

15 Outline 1. Document Banking Industry Facts from Balance sheet panel data as in Kashyap and Stein (2000). 2. A Dynamic Model of the Banking Industry Underlying Static Cournot Model as in Allen & Gale (2000) embedded in a dynamic model of entry and exit as in Ericson & Pakes (1995) augmented with a competitive fringe as in Gowrisankaran & Holmes (2004). Stackelberg game allows us to examine how policy changes on big banks spill over to the rest of the industry. Most quantitative macro banking models (eg. Diaz-Gimenez,et.al. (1992)) assume perfect comp. & CRS indeterminate size distn. 3. Estimation (incomplete) using long-run averages of bank industry data. 4. Tests: business cycle correlations, cross-sectional moments, banking crises predictions. 5. Counterfactuals: (i) Bank Competition ( Υ r ), (ii) Branching Restrictions ( Υ n ), (iii) Cost of Loanable Funds r, (iv) Too-Big-To-Fail.

16 Data Summary Entry is procyclical and Exit by Failure is countercyclical. Fig 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). High Concentration: Top 10 (Top 1%) banks have 51% (76%) of loan market share (in 2010). Fig Table Signs of Non Competitive environment: 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 are increasing with bank size. Fixed costs (normalized) are decreasing in size. Table Loan Returns, Margins, Markups, and Delinquency Rates are countercyclical. Table

17 Model Overview Banks intermediate between large numbers of risk averse households who can deposit at a bank with deposit insurance risk neutral borrowers who demand funds to undertake iid risky projects. By lending to a large number of borrowers, a given bank diversifies risk that any particular household cannot accomplish individually. Simple bank balance sheet (assets=private loans, liablities=deposits+equity). Corbae and D Erasmo (2012) adds securities and bank borrowing. Dynamic Stackelberg game in the loan market between big national and regional banks which move first in any period followed by the competitive fringe. A nontrivial size distribution of dominant banks arises out of regional segmentation and entry/exit in response to shocks.

18 Agents 2 Regions j {e, w}. In each period and in each region, a mass B of one period lived ex-ante identical borrowers are born a large mass (H > B) of one period lived ex-ante identical households are born (no deposit market competition) A small number of dominant banks (national (i.e. top 10) and regional (i.e. top 1%)) and a large number of very small banks (a competitive fringe).

19 Stochastic Processes Aggregate Technology Shocks z {z b, z g } follow a Markov Process F (z, z) with z b < z g Regional specific shocks s {e, w} also follow a Markov Process, G(s, s) but negatively correlated across regions Conditional on z and s, borrower failure is iid across individuals and drawn from p(r t, z t+1, s t+1 ).

20 Borrowers (Loan Demand) Risk neutral borrowers in region j 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 j t with prob p j (R j t, z t+1, s t+1 ) 1 λ with prob 1 p j (R j t, z t+1, s t+1 ). (1) Borrowers choose R j t and have limited liability ( risk shifting effect). Borrowers have an outside option (reservation utility) ω t [ω, ω] drawn at start of t from distribution Υ(ω t ).

21 Loan Market Essentials Borrower chooses R j Receive Pay Probability + + Success 1 + z R j 1 + r L,j (µ, z, s) p j (R j, z, s ) Failure 1 λ 1 λ 1 p j (R j, z, s ) West East National Bank success failure success failure Regional and Fringe banks Regional and Fringe banks Depositors

22 Households (Deposit Supply) 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 in a bank in their region they receive r D,j t 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).

23 Banks Three types of banks θ {n, r, f} for national, regional and fringe. Segmentation: National banks are geographically diversified but regional and fringe banks are restricted to a region j {e, w}. Banks face net and fixed operating costs: (c θ, κ θ ) where c f Ξ(c). Entry costs to create national and regional banks are denoted Υ n Υ r 0 and are normalized to zero for fringe banks, but the fringe bank s draw of c f Ξ(c) exceeds the highest cost fringe incumbent in the market at that state. There are deposit capacity constraints d θ with d θ large for θ {n, r}.

24 Bank Profits The end-of-period profits for bank i of type (θ, j) extending loans l i and accepting deposits d i in region j is given by: π (θ,j) i { } p j (R, z, s )(1 + r L,j ) + (1 p j (R, z, s ))(1 λ) l i (θ, j) { (1 + r D )d i (θ, j) + c θ l i (θ, j) + κ θ}. First two terms are returns bank receives from successful and unsuccessful projects while last three terms correspond to its costs.

25 Banks (cont.) There is limited liability on the part of banks. Besides issuing equity to pay for entry costs, banks with negative profits have access to equity finance at cost ξ θ (x) per x units of funds raised to avoid exit if charter value is big enough. We assume that ξ f (x) is arbitrarily large. The industry state is denoted µ t = {µ (n, ) t, µ (r,e) t, µ (r,w) t where each element of µ t is a measure µ (θ,j) t banks of type θ in region j, µ (f,e) t, µ (f,w) t }, corresponding to active

26 Information Only borrowers know the riskiness of the project they choose R, their outside option ω, and their consumption. All other information is observable (e.g. success/failure).

27 Timing At the beginning of period t, 1. Starting from state (µ t, z t, s t ), borrowers draw ω t. 2. Dominant banks θ {n, r} choose how many loans l i,t (θ, j) to extend and how many deposits d i,t (θ, j) to accept. 3. Fringe banks in each region choose loan supply and how many deposits to accept. Borrowers in region j choose whether or not to undertake a project of technology R j t. Depositors in each region decide where to deposit. 4. Return shocks z t+1 and s t+1 are realized, as well as idiosyncratic borrower shocks. 5. Exit under limited liability or possible equity issuance/dividend payouts. 6. Entry occurs sequentially. 7. Households pay taxes τ t+1 to fund deposit insurance and consume.

28 Markov Perfect Equilibrium A pure strategy Markov Perfect Equilibrium (MPE) is a set of value functions and decision rules for borrowers, households, and banks for each region, loan interest rates r L,j, a deposit interest rate r D,j, an industry state µ, and a tax function τ(µ, z, s, z, s ) such that: Given r L,j, v(r L,j, z, s) and R(r L,j, z, s) are consistent with borrower optimization. Borrower problem

29 Markov Perfect Equilibrium A pure strategy Markov Perfect Equilibrium (MPE) is a set of value functions and decision rules for borrowers, households, and banks for each region, loan interest rates r L,j, a deposit interest rate r D,j, an industry state µ, and a tax function τ(µ, z, s, z, s ) such that: Given r L,j, v(r L,j, z, s) and R(r L,j, z, s) are consistent with borrower optimization. Borrower problem At r D,j = r, the household deposit participation constraint (3) is satisfied. depositor problem

30 Markov Perfect Equilibrium A pure strategy Markov Perfect Equilibrium (MPE) is a set of value functions and decision rules for borrowers, households, and banks for each region, loan interest rates r L,j, a deposit interest rate r D,j, an industry state µ, and a tax function τ(µ, z, s, z, s ) such that: Given r L,j, v(r L,j, z, s) and R(r L,j, z, s) are consistent with borrower optimization. Borrower problem At r D,j = r, the household deposit participation constraint (3) is satisfied. depositor problem Given L d,j (r L,j, z, s), the value of the bank, loan decision rules, exit rules and entry decisions are consistent with bank optimization. Bank problem, Investor s problem

31 Markov Perfect Equilibrium A pure strategy Markov Perfect Equilibrium (MPE) is a set of value functions and decision rules for borrowers, households, and banks for each region, loan interest rates r L,j, a deposit interest rate r D,j, an industry state µ, and a tax function τ(µ, z, s, z, s ) such that: Given r L,j, v(r L,j, z, s) and R(r L,j, z, s) are consistent with borrower optimization. Borrower problem At r D,j = r, the household deposit participation constraint (3) is satisfied. depositor problem Given L d,j (r L,j, z, s), the value of the bank, loan decision rules, exit rules and entry decisions are consistent with bank optimization. Bank problem, Investor s problem The law of motion µ = T (µ) is consistent with bank entry and exit decision rules. T operator

32 Markov Perfect Equilibrium A pure strategy Markov Perfect Equilibrium (MPE) is a set of value functions and decision rules for borrowers, households, and banks for each region, loan interest rates r L,j, a deposit interest rate r D,j, an industry state µ, and a tax function τ(µ, z, s, z, s ) such that: Given r L,j, v(r L,j, z, s) and R(r L,j, z, s) are consistent with borrower optimization. Borrower problem At r D,j = r, the household deposit participation constraint (3) is satisfied. depositor problem Given L d,j (r L,j, z, s), the value of the bank, loan decision rules, exit rules and entry decisions are consistent with bank optimization. Bank problem, Investor s problem The law of motion µ = T (µ) is consistent with bank entry and exit decision rules. T operator The interest rate r L,j (µ, z, s) is such that the loan market clears: B ω ω 1 {ω v(r L,j,z,s)}dΥ(ω) = θ l i (θ, j, µ, s, z; σ i )µ (θ,j) (di)

33 Markov Perfect Equilibrium A pure strategy Markov Perfect Equilibrium (MPE) is a set of value functions and decision rules for borrowers, households, and banks for each region, loan interest rates r L,j, a deposit interest rate r D,j, an industry state µ, and a tax function τ(µ, z, s, z, s ) such that: Given r L,j, v(r L,j, z, s) and R(r L,j, z, s) are consistent with borrower optimization. Borrower problem At r D,j = r, the household deposit participation constraint (3) is satisfied. depositor problem Given L d,j (r L,j, z, s), the value of the bank, loan decision rules, exit rules and entry decisions are consistent with bank optimization. Bank problem, Investor s problem The law of motion µ = T (µ) is consistent with bank entry and exit decision rules. T operator The interest rate r L,j (µ, z, s) is such that the loan market clears: B ω ω 1 {ω v(r L,j,z,s)}dΥ(ω) = θ l i (θ, j, µ, s, z; σ i )µ (θ,j) (di) Across all states (µ, z, s, z, s ), taxes cover deposit insurance.

34 Outside Model Parameters Parameter Value Target Mass of borrowers B 1 Normalization Mass of households H 2B Assumption Dep. preferences σ 2 Part. constraint Agg. shock in good state z g 1 Normalization Transition probability F (z g, z g) 0.86 NBER data Transition probability F (z b, z b ) 0.43 NBER data Deposit interest rate (%) r 0.72 Int. expense Discount Factor β 0.99 Int. expense Net. non-int. exp. n bank c n 1.78 Net non-int exp. Top 10 Net. non-int. exp. r bank c r 1.61 Net non-int exp. Top 1% Charge-off rate λ 0.21 Charge off rate

35 Inside Model Parameters Parameter Value Targets Weight agg. shock α Default freq. Success prob. param. b Loan return Volatility borrower s dist. σ ɛ Borrower Return Success prob. param. ψ Loan ret. top 10 to top 1% Regional shock φ Std. dev. net-int. margin Persistence reg. shock G Std. dev. charge-off rate Max. reservation value ω Std. dev. L s /Output Agg. shock in bad state z b Std. dev. Output Dist. net-non int. exp f bank µ c Net non-int exp. bottom 99% Deposit f banks d 0.16 Loan mkt share bottom 99% Fixed cost n bank κ n Fixed cost over loans top 10 Fixed cost r bank κ r Fixed cost over loans top 1% Fixed cost f bank κ f Fixed cost over loans bottom 99% External finance param. ζ0 n Avg. equity issuance/loan top 10 External finance param. ζ0 r 23.0 Avg. equity issuance/loan top 1% External finance param. ζ Max. equity issuance/loan Entry Cost National Υ n Bank entry rate Entry Cost Regional Υ r 24.7 Frac. entry acc. by top 1% Loan mkt share top 1% Note: Upper bound of possible set of entry costs. Functional Forms, Accounting

36 Targeted Moments Moment (%) Definitions Model Data Default freq Loan return Borrower Return Loan ret. top 10 to top 1% Std. dev. net-int. margin Std. dev. charge-off rate Std. dev. L s /Output Std. dev. Output Net non-int exp. bottom 99% Loan mkt share bottom 99% Fixed cost over loans top Fixed cost over loans top 1% Fixed cost over loans bottom 99% Avg. equity issuance to loan ratio top Avg. equity issuance to loan ratio top 1% Max. equity issuance/loan Bank entry rate Entry accounted by top 1% Loan mkt share top 1%

37 Equilibrium Properties National bank does not exit on-the-equilibrium path. Entry off-the-equilibrium path if there is no other national bank.

38 Equilibrium Properties National bank does not exit on-the-equilibrium path. Entry off-the-equilibrium path if there is no other national bank. Regional bank exits when its regional shock turns bad during a recession. Borrowers take on more risk in good times and project failure is more likely in bad states. Borrower Return R j (µ, z, s) The national bank loan decision in good times lowers realized profits of regional banks enough to induce them to exit in bad realizations thereby becoming a regional monopoly next period (consistent with countercyclical markups). strategic int.

39 Equilibrium Properties National bank does not exit on-the-equilibrium path. Entry off-the-equilibrium path if there is no other national bank. Regional bank exits when its regional shock turns bad during a recession. Borrowers take on more risk in good times and project failure is more likely in bad states. Borrower Return R j (µ, z, s) The national bank loan decision in good times lowers realized profits of regional banks enough to induce them to exit in bad realizations thereby becoming a regional monopoly next period (consistent with countercyclical markups). strategic int. Periods of high concentration following recessions raise interest rates and amplify the downturns.

40 Equilibrium Properties National bank does not exit on-the-equilibrium path. Entry off-the-equilibrium path if there is no other national bank. Regional bank exits when its regional shock turns bad during a recession. Borrowers take on more risk in good times and project failure is more likely in bad states. Borrower Return R j (µ, z, s) The national bank loan decision in good times lowers realized profits of regional banks enough to induce them to exit in bad realizations thereby becoming a regional monopoly next period (consistent with countercyclical markups). strategic int. Periods of high concentration following recessions raise interest rates and amplify the downturns. Entry by a regional bank happens if there is no active regional bank in that region and the region has a positive shock during a boom.

41 Test I: Business Cycle Correlations Variable Correlated with GDP Model Data Loan Interest Rate r L Exit Rate Entry Rate Loan Supply Default Frequency Loan Return Charge-off rate Profit Rate New Equity/Loans Price Cost Margin Markup Though none of these moments were targeted, the model does a good job quantitatively with the business cycle correlations. Intuition Equilibrium-Path Behavior Countercyclical markups provides a new amplification mechanism; in a downturn, exit weakens competition higher loan rates, amplifying the downturn.

42 Test II: Moments by Bank Size Top 10 Top 1% Bottom 99% Moment Average Model Data Model Data Model Data Loan returns Variance Return Default Freq Charge-off Rate Loan Interest Rate Net Interest Margin Lerner Markup Note: Moments with are included as calibration targets. The bigger the bank the lower the variance of returns (consistent with diversification) Model consistent with pattern of Margins, Markups and Lerner, but misses on delinquency and chargeoffs for national banks.

43 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).

44 Counterfactuals

45 Effects of Bank Competition Question: How much does competition change risk taking and bank exit? Compute a counterfactual where regional entry costs Υ r rise by 12% (high enough to prevent entry of regional banks). Moment Benchmark Υ r Change (%) Loan Supply Loan Interest Rate (%) Markup Market Share bottom 99% Market Share top 1% Market Share top Borrower Risk Taking R (%) Default Frequency (%) Entry/Exit Rate (%) Int. Output Taxes/Output (%) More concentration reduces loan supply, raises interest rates and bank profitability leading to lower bank exit (as in A-G) but higher default frequency (as in B-D). Volatility and Competition

46 Effects of Branching Restrictions Question: How much do branching restrictions affect risk taking and bank exit? Compute a counterfactual where national bank entry costs Υ n rise 20% (high enough to prevent entry of national banks). Moment Benchmark Υ n Change (%) Loan Supply Loan Interest Rate (%) Markup Market Share bottom 99% Market Share top 1% Market Share top Borrower Risk Taking R (%) Default Frequency (%) Entry/Exit Rate (%) Int. Output Taxes/Output (%) Regional specific monopolies lower loan supply, raise interest rates and bank profitability leading to lower bank exit but higher default frequency.

47 Lowering the Cost of Loanable Funds Question: How much does a lower cost of loanable funds affect risk taking and bank exit? Compute a counterfactual where compare the benchmark model where r is decreased from 0.72% to 0. Moment Benchmark r = 0 Change (%) Loan Supply Loan Interest Rate (%) Markup Market Share bottom 99% Market Share top 1% Market Share top Borrower Risk Taking R (%) Default Frequency (%) Entry/Exit Rate (%) Int. Output Taxes/Output (%) Lower cost leads to more lending, lower interest rates, market shares of fringe banks falls, as well as their entry. Procyclical Interest Rates No exit by regional banks who experience higher default rates.

48 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. Even though intermediaed output is higher, cost of bailouts is even higher.

49 Concluding Remarks We provide 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. A contribution of our model is that the market structure is endogenous and imperfect competition amplifies markups over the business cycle. Future Research Counterfactuals Summary 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. Experiment 2: Branching restrictions induce more regional concentration (s.a.a.) 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. 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.

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51 Directions for Future Research (i) C-D (2012) extends the balance sheet to include net asset holdings (securities minus borrowings). Balance Sheet Higher volatility of liquidity (deposit) shocks to smaller banks imply they have higher capital ratios (a precautionary model of bank net assets consistent with data). Policy experiment: What are the effects of raising capital requirements on banks of different sizes (industry equilibrium version of Van Den Heuvel (2008)). (ii) A simple general equilibrium model This paper assumed a risk neutral deep pockets investor who held a portfolio of bank stocks and made seasoned equity injections. C-D (2013) embeds the IO model into a simple GE framework where risk averse households are infinitely lived and can hold the portfolio (analogous to Hopenhayn and Rogerson (1993)), so the bank discount rate is endogenous and may affect its risk taking behavior. Return

52 Summary Counterfactuals Change (%) Moment Benchmark Υ r Υ n r = 0 Bailout Loan Supply Loan Interest Rate (%) Markup Market Share bottom 99% Market Share top 1% Market Share top Borrower Risk Taking R (%) Default Frequency (%) Entry/Exit Rate (%) Int. Output Taxes/Output (%) Return

53 Competition and Volatility Coefficient of Variation Benchmark Υ r Change (%) Loan Supply/Output Intermediated Output Def. Rate Loan return Markups As the industry becomes more concentrated, the volatility of aggregates increases. Changes in loan supply by the dominant bank have a larger effect when there is less competition. Return

54 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

55 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

56 Loan Returns by Bank Size Table: Loan Return and Volatility by Bank Size Loan Returns Avg.(%) Std. Dev. (%) Corr. with GDP Top 10 Banks 5.24, 1.14, Top 1% Banks Bottom 99% Banks Note: Denotes statistically significant difference with Top 1% value. Denotes statistically significant difference with Bottom 99% value. Higher volatility of small bank returns suggests less diversification Portfolio Composition by Bank Size Liang and Rhoades (1988) present evidence that geographic diversification lowers bank risk. Real estate becoming more important small banks, while Commercial and Industrial is more important for big banks. Return

57 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. Expenses of premises and fixed assets (net of rental income). (excluding salaries and employee benefits and mortgage interest). iii. Goodwill impairment losses, amortization expense and impairment losses for other intangible assets. iv. Other noninterest expense. Return

58 Definition of Competition Measures The Net Interest Margin is defined as: r L it r D it where r L realized real interest return 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 (2) 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

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

60 Depositor Decision Making If rt D = r households are indifferent between depositing at a bank in their region and using the storage technology. Given lump sum taxes τ(µ, z, s, z, s ), depositors choose not to match with an individual borrower if U E z,s z,su(1 + r τ(µ, z, s, z, s )) > z,s [ max E z,s z,s p j ( R, z, s )u(1 + r τ(µ, z, s, z, s )) r<r L,j z,s ] +(1 p j ( R, z, s ))u (1 λ τ(µ, z, s, z, s )) U E. (3) Return i.e. if households are sufficiently risk averse.

61 Borrower Decision Making If a borrower in region j chooses to participate, then given limited liability his problem is to solve: v(r L,j, z, s) = max E z,s z,sp j (R j, z, s ) ( z R j r L,j). (4) R j FOC w.r.t. R j : E z,s z,s ( ) (+) {}}{ { {}}{ p j (R, z, s )z p j (R, z, s ) [ + z R r L,j] } = 0 (5) R The borrower chooses to demand a loan if + + v( r L,j, z, s ) ω. (6) Aggregate demand for loans is given by L d,j (r L,j, z, s) = B ω ω 1 {ω v(r L,j,z,s)}dΥ(ω). (7) Figure Return

62 Incumbent Bank Decision Making σ i = (l i, x i, e) denotes lending, exit, and entry strategies of all other banks. The end-of-period profits for bank i of type (θ, j) extending loans l i in region j is given by: { π li(θ,j)(θ, j, c θ, µ, z, s, z, s ; σ i ) p j (R, z, s )(1 + r L,j ) + (1 p j (R, z, s ))(1 λ) (1 + r) c θ} l i (θ, j). Differentiating w.r.t. l i (+)or( ) dπ j = [ {}}{ p j r L,j (1 p j )λ r c θ ] + dl i { p j R j dr L,j } + R j r L,j dl (rl,j + λ) l i } {{ } (+) ( ) {}}{ p j drl,j dl l i Return

63 Incumbent National Bank Decisions The value function of national incumbent bank i at the beginning of the period is given by V i (n,, µ, z, s; σ i ) = max βe z,s z,s [W i (n,, µ, z, s, z, s ; σ i )] {l i(n,j)} j=e,w subject to θ l i (θ, j, µ, s, z; σ i )dµ (θ,j) (di) L d,j (r L,j, z, s) = 0, j, where W i (n,, µ, z, s, z, s ; σ i ) = { max Wi x=0 (n,, µ, z, s, z, s ; σ i ), {x {0,1}} W x=1 i (n,, µ, z, s, z, s ; σ i ) } Return

64 Incumbent National Bank Decisions (cont.) Continuation Value: W x=0 i (n,, µ, z, s, z, s ; σ i ) = D i + V i (n,, µ, z, s ; σ i ) { j D i = π l i(n,j)(n, j, c n, µ, z, s, z, s ; σ i ) if π li(n,j)( ) 0 j π l i(n,j)(n, j, c n, µ, z, s, z, s ; σ i )(1 + ξ n ( )) if π li(n,j)( ) < 0 Exit Value (limited liability): (n,, µ, z, s, z, s ; σ i ) = max 0, j W x=1 i π li(n,j)(n, j, c n, µ, z, s, z, s ; σ i ) Return

65 Incumbent Regional Bank Decisions The problem of a regional incumbent bank is similar, except confined to their region j. Bank cash flow is given by { D i = π li(r,j)(r, j, c r, µ, z, s, z, s ; σ i ) if π li(r,j)( ) 0 π li(r,j)(r, j, c r, µ, z, s, z, s ; σ i )(1 + ξ r ) if π li(r,j)( ) < 0. unlike a national bank which can transfer profits across regions, a regional bank is more likely to have negative profits. As for National banks, exit decision depends on the continuation value. Return

66 Fringe Bank Decision Making Fringe banks make their loan supply decision after dominant banks and take r L,j as given. The profit function is linear in l i (f, j) so the quantity constraint l i (f, j) d will in general bind the loan decision. Total loan supply by fringe banks in region j will be + + L s (f, j, µ, z, s; σ i ) = MΞ(c j ( µ, z, s; σ i )) d. where c j (µ, z, s; σ i ) denotes the highest cost such that a fringe bank will choose to offer loans in region j Figures Return

67 Bank Entry Banks enter the market sequentially if the net present value exceeds the entry cost. For example, a potential regional entrant in the west region will choose e i ( r, w, {, µ x,(r,w) + µ e,(r,w), }, z, s ) = 1 if V i (r, w, {, µ x,(r,w) + µ e,(r,w), }, z, s ; σ i ) Υ r > 0. (8) where the mass of banks of type (θ, j) in the industry after exit is given by µ x,(θ,j) = µ (θ,j) x i (θ, j, µ, z, s, z, s ; σ i )µ (θ,j) (di). (9) i Return

68 Investor s Problem Investors choose their portfolio of stocks S i,t+1 at the end of period t after the realization of z t+1, s t+1. Their problem is: max C t 0,S i,t+1 0 E 0 β t C t subject to C t + [P i (µ t, z t, s t, z t+1, s t+1 ) + I {e(µt+1,z t+1,s t+1)=1}υ i ]S it+1 µ t+1 (di) = Y + [D i (µ t, z t, s t, z t+1, s t+1 ) + P i (µ t, z t, s t, z t+1, s t+1 )] S it µ t (di) t=0 The FOC to this problem is given by P i (µ t, z t, s t, z t+1, s t+1 ) = βe zt+2,s t+2 z t+1,s t+1 [D i (µ t+1, z t+1, s t+1, z t+2, s t+2 ) +P i (µ t+1, z t+1, s t+1, z t+2, s t+2 )] Return

69 Investor s Problem (cont.) Using recursive notation and letting the price of a share of bank i be P i (µ, z, s, z, s ) = W i (µ, z, s, z, s ) D i (µ, z, s, z, s ), the FOC can be written: W i (µ, z, s, z, s ) D i (µ, z, s, z, s ) = βe z,s z,s [W i(µ, z, s, z, s )] V i (µ, z, s) = βe z,s z,s [D i (µ, z, s, z, s ) + V i (µ, z, s )] which is the dynamic programming problem of each bank i we are solving. Return

70 Industry Evolution The law of motion µ = T (µ) is consistent with entry and exit decision rules: Return µ = {µ x,(n, ) + µ e,(n, ), µ x,(r,e) + µ e,(r,e), µ x,(r,w) + µ e,(r,w), µ x,(f,e) + µ e,(f,e), µ x,(f,w) + µ e,(f,w) }. where the mass of banks of type (θ, j) in the industry after exit is given by µ x,(θ,j) = µ (θ,j) x i (θ, j, µ, z, s, z, s ; σ i )µ (θ,j) (di). (10) i and µ e,(θ,j) denotes the mass of entrants of type (θ, j).

71 Borrower Project and Inverse Loan Demand Panel (a): Borrower Project R j (r L,j,z,s) R j (r L,z b,s=j) R j (r L,z g,s=j) R j (r L,z b,s j) R j (r L,z g,s j) Loan Interest Rate (r L,j ) 0.2 Panel (b): Inverse Loan Demand r j (L,z,s) r j (L,z b,s=j) r j (L,z g,s=j) 0.15 r j (L,z b,s j) r j (L,z g,s j) Loans (L) First figure shows Boyd and De Nicolo s risk shifting effect that higher interest rates lead borrowers to choose more risky projects. Return Eq. Properties Return Borrower Problem

72 Fringe Bank Decision Making - cont. 1 Fraction Operating Fringe Ξ(c f,j (r L,z g,s=j)) Loan Interest Rate (r L,j ) Fraction Fringe After Exit Ξ(c x,f,j (r L,z,s,z",s")) Ξ(c x,j (r L,z g,s=j,z b,s=j)) Ξ(c x,j (r L,z g,s=j,z g,s=j)) Ξ(c x,j (r L,z g,s=j,z b,s j)) Ξ(c x,j (r L,z g,s=j,z g,s j)) Return Loan Interest Rate (r L,j )

73 Functional Forms Borrower outside option is distributed uniform [0, ω]. Fringe net costs are distributed exponential with parameter µ c. For each borrower in region j, let y j = αz + (1 α)ε br ψ where ε is drawn from N(φ(s ), σ 2 ε) where we assume that if s = j, φ(s ) = φ and φ(s ) = φ otherwise. 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 j (R, z, s + br ψ ) ) = 1 Φ (11) (1 α) where Φ(x) is a normal cumulative distribution function with mean (φ(s )) and variance σ 2 ε. Return

74 Taking the Model to the Data We identify national banks with the top 10 banks, regional banks with the top 1% banks and fringe banks with the bottom 99% of the bank loan distribution. The model has a representative national bank, a representative regional bank in each region, and a mass M of potential fringe banks. It delivers aggregate loan supply l(θ, j, µ, z, s) for each bank type given by l(θ, j, µ, z, s) = l i (θ, j, µ, z, s)µ (θ,j) (di) w(θ, j) l(θ, j, µ, z, s) where w(θ, j) is the relative fraction of banks of type θ in region j and l(θ, j, µ, z, s) is the average loan supply by banks of type θ in region j. The relative mass w(θ, j) is only important when reporting parameters or functions expressed in levels (e.g. fixed costs, entry costs, loan decision rules). We set w(θ, j) using data from the distribution of banks. The number of banks in 2010 was 6544 so w(n, ) = = 0.153%, w(r, j) = (654 10)/ = %, and w(f, j) = 0.99/2 = 44.5%. Return

75 Table: Definition Model Moments Aggregate loan supply L s (µ, z, s) = j Ls,j (µ, z, s) { Aggregate Output j Ls,j (µ, z, s) p j (R (µ, z, s), z, s )(1 + z R) } +(1 p j (R (µ, z, s), z, s ))(1 λ) j θ µe,(θ,j) t Entry Rate Default frequency 1 p j (R (µ, z, s), z, s ) Borrower return p j (R (µ, z, s), z, s )(z R (µ, z, s)) Loan return p j (R (µ, z, s), z, s )r L,j (µ, z, s) Loan Charge-off rate (1 p j (R (µ, z, s), z, s ))λ Profit Rate π li(θ,j)(θ, j, µ, z, s, z, s )/l i (θ, j, µ, z, s) Equity Issuance max{ (π li(θ,j)(θ, j, µ, z, s, z, s ) κ θ ), 0} Net Interest Margin p j (R (µ, z, s), z, s )r L,j (µ, z, s) r d Lerner Index 1 [ r d + c θ,exp] / [ { p j (R (µ, z, s), z, s )r L,j (µ, z, s) + [p Markup reg. j (R (µ, z, s), z, s )r L,j (µ, z, s) + c θ,inc] / [ r d + c θ,exp] } 1 /µ (θ,j) t 1 Return

76 Strategic Interaction Compare decision rules on an equil. path of the benchmark dynamic vs. a static economy at µ = {1, 1, 1, }, z = z g, s = e: Loan Decision Rules l(θ, j, µ, z, s) (µ = {1, 1, 1, }, z = z g, s = e) Model l(n, e, ) l(n, w, ) l(r, e, ) l(r, w, ) Dynamic (benchmark) Static Exit Rule x(θ, j, µ, z, s, z = z b, s = w) Model x(n, ) x(r, e, ) x(r, w, ) Dynamic (benchmark) Static Note: Loan values reported correspond to l(θ, j, µ, z, s) in equation (54). While national bank offers less loans in dynamic vs static case to reduce its exposure to z = z b and s = w (column 1), it also raises loans in the region where there are upside possibilities (column 2), thereby lowering profitability of smaller banks potentially inducing them to exit. Return

77 Equilibrium Properties: Off-the-Equilibrium-Path Entry by a big bank happens if there is no other active big bank. Return

78 Test I: Business Cycle Correlations Along the equilibrium path, interest rates are countercyclical primarily due to states where the big bank is a regional monopolist and there is insufficient entry by fringe banks. Return

79 Deposit and Loan Growth Rates Growth Rate (difference from mean) Deposits Loans Percentage (%) year Return

80 Portfolio Composition (Share of Total Loans) of Small and Large Banks Percentage (%) Panel (i): Loan Portfolio Composition Top 10 C&I Top 10 RE Bottom 99% C&I Bottom 99% RE year 10 Panel (ii): Loan Returns 8 Percentage (%) Top 10 C&I Top 10 RE Bottom 99% C&I Bottom 99% RE year Real estate becoming more important small banks Commercial and Industrial is more important for big banks Return

81 Tradeoff Loan Returns d(pr L ) dz = dp dr dr L dr dr L dz rl + drl dz p where dp dr < 0, dr Return dr L > 0, drl dz < 0

82 Banking Industry Evolution Intermediated Output Number of Banks over Business Cycle Output # Banks Period (t) Panel (ii): Market Shares # Banks nat 10 reg fringe time period (t) In most episodes, entry is procyclical and exit is countercyclical. Large swings correspond to entry or exit by regional banks following a switch in the regional shock. Periods of high (n) concentration following recessions raise interest rates and amplify the downturns. Return

83 Lowering the Cost of Loanable Funds - Cont. Table: Counterfactual: Effects of Lower r Correlation with output Benchmark r = 0 Loan Interest Rate r L Exit Rate Entry Rate Loan Supply Default Frequency Loan Return Charge-off rate Profit Rate New Equity/Loans Price Cost Margin Markup Lower cost changes the cyclical properties of interest rates from countercyclical to procyclical. All entry/ exit is by fringe banks since there is no exit by dominant banks. When a bad regional shock hits, there is less exit in that region and more entry in the region which is doing well. Entry turns countercyclical, as do aggregate loans. Return

84 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 (7). Return

85 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

86 Balance Sheet Data by Bank Size Fraction Total Assets (%) Bottom 99% Top 1% Bottom 99% Top 1% Cash Securities Loans Deposits Fed Funds and Repos Equity Capital Source: Call Reports. While Loans and Deposits are the most important components of the bank balance sheet, precautionary holdings of securities and equity capital are also important buffer stocks. Return

87

88 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

89 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

90 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

91 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

92 Measures of Banking Competition Moment Value (%) Std. Error (%) Corr w/ GDP Net 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) and Bikker and Haaf (2002). Countercyclical markups consistent with more competition in good times (new amplification mechanism). Definitions Figures Return

93 Costs by Bank Size Non-Int Inc. Non-Int Exp. Net Exp. Fixed Cost Top 10 (%) , 1.78, 0.485, Top 1% (%) Bottom 99% (%) Note: Fixed costs normalized by total assets. Marginal Non-Int. Income, Non-Int. Expenses (estimated from trans-log cost function) and Net Expenses are increasing in size. Fixed Costs (normalized by loans) are decreasing in size for large banks. Selection of only low cost banks in the competitive fringe may drive the Net Expense pattern. Definitions Return

94 Exit Rate Decomposed Merger Rate Failure Rate Trouble Bank Rate Det. GDP 10 8 Percentage (%) year Correlation of GDP with (Failure, Troubled, Mergers) =(-0.47, -0.72, 0.58) after 1990 Return

95 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

96 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

97 Definition of Competition Measures The Net Interest Margin is defined as: r L it r D it where r L realized real interest return 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 (12) 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