Bank Capital, Agency Costs, and Monetary Policy Césaire Meh Kevin Moran Department of Monetary and Financial Analysis Bank of Canada
Motivation A large literature quantitatively studies the role of financial factors in business cycle dynamics (eg., Bernanke et al., 1999; Carlstrom & Fuerst, 1997, 1998) key feature: asymmetric information between banks and firms Net worth of firms alleviates the effects of asymmetric information becomes an important element in the propagation of shocks 1
Question What about banks themselves? Are they subject to financial market imperfections? If so, do these matter? 2
Evidence Banks face financial frictions in raising funds (eg., Calorimis & Wilson 1998; Kashyap & Stein 2; Schneider 21) Bank capital (bank net worth) has a significant and positive effect on bank lending and economic activity (eg., Bernanke & Lown, 1991; Peek & Rosengren, 1997, 2) In US states with low levels of bank capital, output growth is more sensitive to monetary policy (eg., Van den Heuvel, 22) 3
This paper A framework with a double moral hazard problem: entrepreneurs and bankers bankers and households This framework is embedded into a standard monetary business cycle model The model is used to study the links between bank capital, monetary policy, and economic activity 4
Findings The presence of bank capital lowers the amplification of monetary policy shocks increases the persistence of monetary policy shocks The bank capital-asset ratio is market-generated and is countercyclical as in the data 5
Literature Carlstrom & Fuerst (1997, 1998, 21); Bernanke et al. (1999) No bank capital Holmstrom & Tirole (1997) and Chen (21) No monetary policy Van den Heuvel (22) Partial-equilibrium Regulatory capital requirements Not a monetary model 6
Rest of the Talk Basic Model: economic environment Financial contract and intuition for mechanism Results: Basic and Extended Model Concluding remarks and future work 7
Economic Environment Three types of agents: households, bankers and entrepreneurs Final Good: standard CRS technology Capital Good: produced by entrepreneurs f(i t ) = { Rit, success,, failure 8
Households CIA constraint for consumption Deposit savings with banks (no direct lending to entrepreneurs) Costs of adjusting deposits (limited participation) 9
Monetary Policy log(r d t /r d ) = ρ y log(y t /y) + ρ π log(π t /π) + ɛ mp t 1
Bankers and Entrepreneurs Bankers and entrepreneurs face a probability of exit; exiting agents are replaced by new ones Bank capital and entrepreneurial net worth a t = n t = [ rt k + q t (1 δ) ] kt b rt k + q t (1 δ) ] kt e Next period capital holdings of successful surviving agents kt+1 b = Rti b t kt+1 e = Rti e t 11
Two Sources of Moral Hazard Loans (i t -n t ) Deposits d t Entrepreneurs Banks Households 1. Moral Hazard Entrepreneurs may privately choose low return projects to enjoy private benefits 2. Moral Hazard Banks have an incentive not to monitor in order to save costs Entrepreneurial Net Worth Bank Capital 12
Three types of projects available to the entrepreneur: Project Good Low Priv. Ben. High Priv. Ben. Private benefits bi t Bi t Prob. of success α g α b α b Good project is socially desirable Bank monitoring eliminates the high-private benefit project at cost µi t The projects financed by an individual bank are perfectly correlated 13
Bank Capital Bank capital increases the incentives to monitor reduces the moral hazard problem between depositors and banks increases the ability of the bank to attract deposits increases bank lending increases aggregate investment and output 14
Financial Contract Consider one-period contracts that lead entrepreneurs to choose the good project One optimal contract will have the following structure: the entrepreneur invests all his net worth if success, R is distributed among the entrepreneur, the banker and the households: R = R e t + R b t + R h t if failure, neither party is paid anything 15
Financial Contract, cont. Choose project size and payment shares Maximize expected payoff to entrepreneurs Incentive constraints of bankers and entrepreneurs Participation constraints of bankers and households Resource constraint: a t + d t + n t = (1 + µ) i t 16
Upshot of the contract Shares: R e t = b α ; Rb t = µ q t α ; Rh t = R b α µ q t α Participation constraint of depositors: q t α g R h t i t = r d t d t, d t = [(1 + µ)i t a t n t ] 17
Upshot of the contract, cont. Solve for i t : i t = (1/G t ) }{{} aggregate leverage a t + n t }{{} internal funds G t 1 + µ q tα g r d t [ R b α µ ] q t α When r d t, leverage 18
Aggregation Linearity simplifies aggregation Aggregate investment: I t = A t + N t G t Aggregate bank capital and entrepreneurial net worth: A t = [ r k t + q t (1 δ) ] K b t (I t 1 ) N t = [ r k t + q t (1 δ) ] K e t (I t 1 ) 19
Final good production takes place Households, banks and entrepreneurs agree to finance projects -Returns are realized (public) -Returns are shared between the 3 agents Surviving agents buy capital for future periods; exiting agents sell their capital and consume t t+1 time Aggregate shocks are realized Households make consumption and deposit decisions (1) Banks choose whether or not to monitor (2) Entrepreneurs choose which project to undertake Some bankers and entrepreneurs receive the signal to exit the economy Newborn banks and entrepreneurs enter the economy 2
Market Clearing Conditions labor markets: H t = η h h t Final goods market: Y t = C h t + C e t + C b t + (1 + µ)i t Capital goods market: K t+1 = (1 δ) K t + α g RI t 21
Deposits markets: q t α g R h t I t r d t = M t M c t + X t P t Equilibrium rate of return on bank capital: r a t = αg µ (1 + N t /A t ) G t α 22
Results Basic model - monetary policy shock The extended model - wealth shock - monetary policy shock - cyclical properties of bank capital-asset ratio
Parameter Calibration Household Preferences χ γ φ β 2.75 1.5 5..99 Final Good Production δ θ k θ h θ e θ b ρ z.2.36.6399 5 1 5 5 1 5.95 Capital Good Production with Asymetric Infomation µ α g α b R b Baseline.25.97.67.5.9 More Severe Friction.5.97.67.5.6 Less Severe Friction.1.97.67.5.6 Resulting Steady-State Characteristics CA I/N BOC ROE Baseline 15% 2. 5% 15% More Severe Friction 31% 1.91 11% 15% Less Severe Friction 6% 2.6 2% 15%
.2 Contractionary Monetary Policy Shock: Basic Model Aggregate Output Aggregate Investment Price of Capital.25 Percent deviation from s.s..2.4.6.1.2.3.4.5.6.2.15.1.5.8 1 2 Entrepreneurial Net Worth.1.7 1 2.1 Bank Capital 1 2 1.2 Capital Asset Ratio Percent deviation from s.s..1.2.3.4.5.1.2.3.4.5 1.8.6.4.2.6 1 2 Entrepreneurial Leverage (I/N).1.6 1 2 12 Bank Deposit Rate.2 1 2 5 Inflation Percent deviation from s.s..1.2.3.4.5 Annualized rate, in percentage 11.5 11 1.5 1 9.5 9 Annualized rate, in percentage 4.8 4.6 4.4 4.2.6 1 2 8.5 1 2 4 1 2
Extended Model Risk-aversion: U = log(c t ) + χlog(1 h t V t ) Households insure themselves against idiosyncratic risk collapses to representative agent model Final good producers require external financing for wage bill introduce another type of financial intermediary to provide this lending Wage income and purchases of physical capital now part of the household s CIA constraint
Negative Wealth Shock on Banking Sector: Extended Model Aggregate Output Aggregate Investment Price of Capital.2 Percent deviation from s.s..5.1.15.5 1 Percent deviation from s.s..15.1.5.2 5 1 15 Entrepreneurial Net Worth 5 1 15 Bank Capital 2 5 1 15 Capital Asset Ratio Percent deviation from s.s..5 Percent deviation from s.s. 2 4 6 8 2 4 6 1 5 1 15 Entrepreneurial Leverage (I/N) 1 5 1 15 9.2 Bank Deposit Rate 8 5 1 15 5.15 Inflation Percent deviation from s.s..5 1 Annualized rate, in percentage 9.15 9.1 9.5 9 Annualized rate, in percentage 5.1 5.5 5 4.95 5 1 15 8.95 5 1 15 4.9 5 1 15
Contractionary Monetary Policy Shock: Extended Model Aggregate Output Aggregate Investment Price of Capital.1 Percent deviation from s.s..5.1.15.1.2.3.4.5.6.5.5.2 5 1 15.7 5 1 15.1 5 1 15 Entrepreneurial Net Worth Bank Capital.8 Capital Asset Ratio Percent deviation from s.s..1.2.3.4.5.6.1.2.3.4.5.6.6.4.2.7 5 1 15 Entrepreneurial Leverage (I/N).1.7 5 1 15 1.5 Bank Deposit Rate.2 5 1 15 6 Inflation Percent deviation from s.s..1.2.3 Annualized rate, in percentage 1 9.5 9 Annualized rate, in percentage 5.5 5 4.5 4 3.5.4 5 1 15 8.5 5 1 15 3 5 1 15
Steady State With and Without Bank Capital Variables With Bank Capital Without Bank Capital % Change Investment.215.232 7.9% Output 1.98 1.128 2.8% Entrepreneurial Leverage (I/N) 2. 2.1 5% Aggregate Leverage (I/(N + A)) 1.74 2.1 21% With Bank Capital : Baseline Calibration of the Double Moral Hazard Model. Without Bank Capital : Calibration with moral hazard only between entrepreneurs and bankers (µ.)
Contractionary Monetary Policy Shock: The Importance of Bank Capital Percent deviation from s.s..1.2.3.4.5.6.7.1 Aggregate Investment With Bank Capital Without Bank Capital 5 1 15 Price of Capital.5.1.15 Output With Bank Capital Without Bank Capital.2 5 1 15.8 Capital Asset Ratio Percent deviation from s.s..5.5 With Bank Capital Without Bank Capital.6.4.2 With Bank Capital Without Bank Capital Percent deviation from s.s..1 5 1 15.1.1.2.3.4.5 Bank Capital With Bank Capital Without Bank Capital.6 5 1 15.2 5 1 15.1.2.3.4.5.6.7 Entrepreneurial Net Worth With Bank Capital Without Bank Capital 5 1 15
Contractionary Monetary Policy Shock: Sensitivity Analysis Aggregate Investment Output Percent deviation from s.s..2.4.5.6.15 Baseline Baseline More Severe Agency Costs More Severe Agency Costs Less Severe Agency Costs.8 Less Severe Agency Costs.2 5 1 15 5 1 15.1 Price of Capital.1.8 Capital Asset Ratio Percent deviation from s.s..5.5 Baseline More Severe Agency Costs Less Severe Agency Costs.6.4.2 Baseline More Severe Agency Costs Less Severe Agency Costs Percent deviation from s.s..1 5 1 15.2.2.4.6 Bank Capital Baseline More Severe Agency Costs Less Severe Agency Costs.8 5 1 15.2 5 1 15.2.4 Entrepreneurial Net Worth.6 Baseline More Severe Agency Costs Less Severe Agency Costs.8 5 1 15
Variable Cyclical Properties of the Capital-Asset Ratio: Model and Data Panel A: Model Economy Cross-Correlation of the Capital-Asset Ratio with: σ(x) σ(gdp ) X t 4 X t 2 X t 1 X t X t+1 X t+2 X t+4 Capital-Asset Ratio.53.85.94.98 1..98.94.85 Fixed Non Res. Investment 2.6.7.21.32.44.52.57.6 GDP 1..12.25.35.45.47.48.47 Bank Lending 2.7.1.25.37.51.56.59.59 Panel B: US Economy Capital-Asset Ratio.38.47.79.91 1..91.79.47 Fixed Non Res. Investment 4.41.44.48.44.38.28.2.2 GDP 1..47.4.27.16..8.12 Bank Lending (C & I) 4.67.42.67.75.8.76.69.4 Note: For the US economy, 199:1-23:1. Capital-Asset Ratio: tier1 + tier2 capital over risk weighted assets (source BIS); Fixed Non Res. Investment: Fixed Investment, Non Residential, in billions of chained 1996 Dollars (source BEA); GDP: Gross Domestic Product, in billions of chained 1996 Dollars (source BEA); Bank Lending: Commercial and Industrial Loans Excluding Loans Sold (source BIS). GDP, Investment, and Bank Lending are expressed as real, per capita quantities. All series are detrended using the HP filter.
Conclusion We present a quantitative monetary business cycle model in which bank capital helps mitigate an agency problem between banks and depositors Bank capital affects the transmission mechanism of monetary policy: lowers the amplification of monetary policy shocks increases the persistence of monetary policy shocks The bank capital-asset ratio is market-generated and is countercyclical as in the data
Future Research Heterogeneity in bank size and capital-asset ratio Interaction between market and regulatory discipline on banks Externality of a bank s action Optimal monetary policy when bank capital is present? Should monetary policy respond to bank capital movements?