Features to Include • Banks may be worth saving even if bankrupt: 1. New loans are partially independent of old loans. 2. Capacity to attract deposits is valuable. 3. May get better over time on average. 5
Features to Include • Banks may be worth saving even if bankrupt: 1. New loans are partially independent of old loans. 2. Capacity to attract deposits is valuable. 3. May get better over time on average. 4. Large bankruptcy costs. 5
Features to Include • Banks may be worth saving even if bankrupt: 1. New loans are partially independent of old loans. 2. Capacity to attract deposits is valuable. 3. May get better over time on average. 4. Large bankruptcy costs. • Banks may take time to develop. They grow slowly in size due to exogenous loan productivity process and need for internal accummulation of funds. 5
Features to Include • Banks may be worth saving even if bankrupt: 1. New loans are partially independent of old loans. 2. Capacity to attract deposits is valuable. 3. May get better over time on average. 4. Large bankruptcy costs. • Banks may take time to develop. They grow slowly in size due to exogenous loan productivity process and need for internal accummulation of funds. • Useful also for Shadow Banking 5
Model • A bank is ξ = [ ξ d , ξ ℓ ] , exogenous, idyosincratic, Markovian with transition Γ z ,ξ . Its access to deposits; its costs of making new loans. z is aggregate and shapes the transition of ξ. 6
Model • A bank is ξ = [ ξ d , ξ ℓ ] , exogenous, idyosincratic, Markovian with transition Γ z ,ξ . Its access to deposits; its costs of making new loans. z is aggregate and shapes the transition of ξ. • A bank has liquid assets a that can (and are likely to) be negative and long term loans ℓ (decay at rate λ ). 6
Model • A bank is ξ = [ ξ d , ξ ℓ ] , exogenous, idyosincratic, Markovian with transition Γ z ,ξ . Its access to deposits; its costs of making new loans. z is aggregate and shapes the transition of ξ. • A bank has liquid assets a that can (and are likely to) be negative and long term loans ℓ (decay at rate λ ). • Banks make new loans n , distribute dividends c and issue risky bonds b ′ at price q ( z , ξ, ℓ, n , b ′ ) . 6
Model • A bank is ξ = [ ξ d , ξ ℓ ] , exogenous, idyosincratic, Markovian with transition Γ z ,ξ . Its access to deposits; its costs of making new loans. z is aggregate and shapes the transition of ξ. • A bank has liquid assets a that can (and are likely to) be negative and long term loans ℓ (decay at rate λ ). • Banks make new loans n , distribute dividends c and issue risky bonds b ′ at price q ( z , ξ, ℓ, n , b ′ ) . • The bank is subject to shrinkage shocks to its portfolio of loans δ , π δ/ z , that may bankrupt it. Costly liquidation ensues. 6
Model • A bank is ξ = [ ξ d , ξ ℓ ] , exogenous, idyosincratic, Markovian with transition Γ z ,ξ . Its access to deposits; its costs of making new loans. z is aggregate and shapes the transition of ξ. • A bank has liquid assets a that can (and are likely to) be negative and long term loans ℓ (decay at rate λ ). • Banks make new loans n , distribute dividends c and issue risky bonds b ′ at price q ( z , ξ, ℓ, n , b ′ ) . • The bank is subject to shrinkage shocks to its portfolio of loans δ , π δ/ z , that may bankrupt it. Costly liquidation ensues. • New banks enter small ξ at cost c e 6
Model: What are Aggregate Shocks • Determines the distribution of δ and may determine the transition of ξ . 7
Model: What are Aggregate Shocks • Determines the distribution of δ and may determine the transition of ξ . • Determines the countercyclical capital requirement θ ( z ) . 7
Model: What are Aggregate Shocks • Determines the distribution of δ and may determine the transition of ξ . • Determines the countercyclical capital requirement θ ( z ) . • Note that in this version there is no interaction between banks. The distribution is not a state variable of the banks’ problem. 7
Model: What are Aggregate Shocks • Determines the distribution of δ and may determine the transition of ξ . • Determines the countercyclical capital requirement θ ( z ) . • Note that in this version there is no interaction between banks. The distribution is not a state variable of the banks’ problem. • The state of the economy is a measure x of banks that evolves over time itself via banks decisions and shocks (an extension of Hopenhayn’s classic) 7
Model: Bank’s Problem V ( z , ξ, a , ℓ ) = max { 0 , W ( z , a , ℓ, ξ ) } 8
Model: Bank’s Problem V ( z , ξ, a , ℓ ) = max { 0 , W ( z , a , ℓ, ξ ) } � Γ z ξ, z ′ ξ ′ π δ ′ | z ′ V [ z ′ , ξ ′ , a ′ ( δ ′ ) , ℓ ′ ( δ ′ )] W ( z , ξ, a , ℓ ) = max u ( c ) + β s.t. n ≥ 0 , c ≥ , b ′ , z ′ ,ξ ′ ,δ ′ 8
Model: Bank’s Problem V ( z , ξ, a , ℓ ) = max { 0 , W ( z , a , ℓ, ξ ) } � Γ z ξ, z ′ ξ ′ π δ ′ | z ′ V [ z ′ , ξ ′ , a ′ ( δ ′ ) , ℓ ′ ( δ ′ )] W ( z , ξ, a , ℓ ) = max u ( c ) + β s.t. n ≥ 0 , c ≥ , b ′ , z ′ ,ξ ′ ,δ ′ ℓ ′ = ( 1 − λ ) ( 1 − δ ′ ) ℓ + n ( TL ) 8
Model: Bank’s Problem V ( z , ξ, a , ℓ ) = max { 0 , W ( z , a , ℓ, ξ ) } � Γ z ξ, z ′ ξ ′ π δ ′ | z ′ V [ z ′ , ξ ′ , a ′ ( δ ′ ) , ℓ ′ ( δ ′ )] W ( z , ξ, a , ℓ ) = max u ( c ) + β s.t. n ≥ 0 , c ≥ , b ′ , z ′ ,ξ ′ ,δ ′ a ′ = ( λ + r )( 1 − δ ′ ) ℓ + r n − ξ d − b ′ ( TA ) 8
Model: Bank’s Problem V ( z , ξ, a , ℓ ) = max { 0 , W ( z , a , ℓ, ξ ) } � Γ z ξ, z ′ ξ ′ π δ ′ | z ′ V [ z ′ , ξ ′ , a ′ ( δ ′ ) , ℓ ′ ( δ ′ )] W ( z , ξ, a , ℓ ) = max u ( c ) + β s.t. n ≥ 0 , c ≥ , b ′ , z ′ ,ξ ′ ,δ ′ c + c f + n + ξ n ( n ) ≤ a + q ( z , ξ, n , ℓ, b ′ ) b ′ + ξ d ( BC ) 8
Model: Bank’s Problem V ( z , ξ, a , ℓ ) = max { 0 , W ( z , a , ℓ, ξ ) } � Γ z ξ, z ′ ξ ′ π δ ′ | z ′ V [ z ′ , ξ ′ , a ′ ( δ ′ ) , ℓ ′ ( δ ′ )] W ( z , ξ, a , ℓ ) = max u ( c ) + β s.t. n ≥ 0 , c ≥ , b ′ , z ′ ,ξ ′ ,δ ′ n + ℓ − ξ d − q ( z , ξ, ℓ, n , b ′ ) b ′ ( KR ) ω r ( n + ℓ ) + ω s 1 b ′ < 0 b ′ q ( z , ξ, ℓ, n , b ′ ) ≥ θ ( z ) or 8
Model: Bank’s Problem V ( z , ξ, a , ℓ ) = max { 0 , W ( z , a , ℓ, ξ ) } � Γ z ξ, z ′ ξ ′ π δ ′ | z ′ V [ z ′ , ξ ′ , a ′ ( δ ′ ) , ℓ ′ ( δ ′ )] W ( z , ξ, a , ℓ ) = max u ( c ) + β s.t. n ≥ 0 , c ≥ , b ′ , z ′ ,ξ ′ ,δ ′ ( KR ) c = n = 0 and capital ratio > .02 8
Model: Bank’s Problem V ( z , ξ, a , ℓ ) = max { 0 , W ( z , a , ℓ, ξ ) } � Γ z ξ, z ′ ξ ′ π δ ′ | z ′ V [ z ′ , ξ ′ , a ′ ( δ ′ ) , ℓ ′ ( δ ′ )] W ( z , ξ, a , ℓ ) = max u ( c ) + β s.t. n ≥ 0 , c ≥ , b ′ , z ′ ,ξ ′ ,δ ′ Note that the bank can lend b ′ < 0, it has operating costs c f (nonlinear 8
Model: Bank’s Problem V ( z , ξ, a , ℓ ) = max { 0 , W ( z , a , ℓ, ξ ) } � Γ z ξ, z ′ ξ ′ π δ ′ | z ′ V [ z ′ , ξ ′ , a ′ ( δ ′ ) , ℓ ′ ( δ ′ )] W ( z , ξ, a , ℓ ) = max u ( c ) + β s.t. n ≥ 0 , c ≥ , b ′ , z ′ ,ξ ′ ,δ ′ ℓ ′ = ( 1 − λ ) ( 1 − δ ′ ) ℓ + n ( TL ) a ′ = ( λ + r )( 1 − δ ′ ) ℓ + r n − ξ d − b ′ ( TA ) c + c f + n + ξ n ( n ) ≤ a + q ( z , ξ, n , ℓ, b ′ ) b ′ + ξ d ( BC ) n + ℓ − ξ d − q ( z , ξ, ℓ, n , b ′ ) b ′ ( KR ) ω r ( n + ℓ ) + ω s 1 b ′ < 0 b ′ q ( z , ξ, ℓ, n , b ′ ) ≥ θ ( z ) or ( KR ) c = n = 0 and capital ratio > .02 Note that the bank can lend b ′ < 0, it has operating costs c f (nonlinear 8
Model: Solution of Banks Problem given q ( ξ ′ , ℓ, n , b ′ ) • The solution to this problem is a set of functions 9
Model: Solution of Banks Problem given q ( ξ ′ , ℓ, n , b ′ ) • The solution to this problem is a set of functions • b ′ ( z , ξ, a , ℓ ) bonds borrowing (or safe lending) 9
Model: Solution of Banks Problem given q ( ξ ′ , ℓ, n , b ′ ) • The solution to this problem is a set of functions • b ′ ( z , ξ, a , ℓ ) bonds borrowing (or safe lending) • n ( z , ξ, a , ℓ ) new loans 9
Model: Solution of Banks Problem given q ( ξ ′ , ℓ, n , b ′ ) • The solution to this problem is a set of functions • b ′ ( z , ξ, a , ℓ ) bonds borrowing (or safe lending) • n ( z , ξ, a , ℓ ) new loans • c ( z , ξ, a , ℓ ) dividends 9
Model: Solution of Banks Problem given q ( ξ ′ , ℓ, n , b ′ ) • The solution to this problem is a set of functions • b ′ ( z , ξ, a , ℓ ) bonds borrowing (or safe lending) • n ( z , ξ, a , ℓ ) new loans • c ( z , ξ, a , ℓ ) dividends • The solution yields a probability of a bank failing 9
Model: Solution of Banks Problem given q ( ξ ′ , ℓ, n , b ′ ) • The solution to this problem is a set of functions • b ′ ( z , ξ, a , ℓ ) bonds borrowing (or safe lending) • n ( z , ξ, a , ℓ ) new loans • c ( z , ξ, a , ℓ ) dividends • The solution yields a probability of a bank failing • δ ∗ ( z , ξ, ℓ, n , b ′ ) 9
Model: Equilibrium The only relevant equilibrium condition is 1. Zero profit in the bonds markets: q ( z , ξ, ℓ, n , b ′ ) = 1 − δ ∗ ( z , ξ, ℓ, n , b ′ ) 1 + r 10
Model: Aggregate State, { z , x } • The choices of the bank { n ( z , ξ, a , ℓ ) , b ′ ( z , ξ, a , ℓ ) , c ( z , ξ, a , ℓ ) } and the exogenous shocks { z ′ , ξ ′ , δ ′ } generate a transition for the state of each bank and in turn of the distribution of banks.. 11
Model: Aggregate State, { z , x } • The choices of the bank { n ( z , ξ, a , ℓ ) , b ′ ( z , ξ, a , ℓ ) , c ( z , ξ, a , ℓ ) } and the exogenous shocks { z ′ , ξ ′ , δ ′ } generate a transition for the state of each bank and in turn of the distribution of banks.. 11
Model: Aggregate State, { z , x } • The choices of the bank { n ( z , ξ, a , ℓ ) , b ′ ( z , ξ, a , ℓ ) , c ( z , ξ, a , ℓ ) } and the exogenous shocks { z ′ , ξ ′ , δ ′ } generate a transition for the state of each bank and in turn of the distribution of banks.. Definition A, equilibrium is a function x ′ = G ( z , x ) , a price of bonds q , and decisions for { n , b ′ , c } such that banks maximize profits, lenders get the market return, and the measure is updated consistently with decisions and shocks. 11
Putting the Model to use • We pose an economy that (after many periods in good times) resembles a current distribution of banks. 12
Putting the Model to use • We pose an economy that (after many periods in good times) resembles a current distribution of banks. • Then explore what happens upon the economy entering a recession, under various scenarios: 12
Putting the Model to use • We pose an economy that (after many periods in good times) resembles a current distribution of banks. • Then explore what happens upon the economy entering a recession, under various scenarios: 1. No Countercyclical Capital Requirement and adjusted ω r to reflect that the loans are riskier. 12
Putting the Model to use • We pose an economy that (after many periods in good times) resembles a current distribution of banks. • Then explore what happens upon the economy entering a recession, under various scenarios: 1. No Countercyclical Capital Requirement and adjusted ω r to reflect that the loans are riskier. • More loans are destroyed 12
Putting the Model to use • We pose an economy that (after many periods in good times) resembles a current distribution of banks. • Then explore what happens upon the economy entering a recession, under various scenarios: 1. No Countercyclical Capital Requirement and adjusted ω r to reflect that the loans are riskier. • More loans are destroyed • Outlook of loans is worse 12
Putting the Model to use • We pose an economy that (after many periods in good times) resembles a current distribution of banks. • Then explore what happens upon the economy entering a recession, under various scenarios: 1. No Countercyclical Capital Requirement and adjusted ω r to reflect that the loans are riskier. • More loans are destroyed • Outlook of loans is worse 2. No Countercyclical Capital Requirement but no adjustment in ω r w. 12
Putting the Model to use • We pose an economy that (after many periods in good times) resembles a current distribution of banks. • Then explore what happens upon the economy entering a recession, under various scenarios: 1. No Countercyclical Capital Requirement and adjusted ω r to reflect that the loans are riskier. • More loans are destroyed • Outlook of loans is worse 2. No Countercyclical Capital Requirement but no adjustment in ω r w. 3. Countercyclical Capital Requirement to 1. 12
Putting the Model to use • We pose an economy that (after many periods in good times) resembles a current distribution of banks. • Then explore what happens upon the economy entering a recession, under various scenarios: 1. No Countercyclical Capital Requirement and adjusted ω r to reflect that the loans are riskier. • More loans are destroyed • Outlook of loans is worse 2. No Countercyclical Capital Requirement but no adjustment in ω r w. 3. Countercyclical Capital Requirement to 1. 4. Countercyclical Capital Requirement to 2. 12
Plan • Describe Targets 13
Plan • Describe Targets • Describe properties of the stationary allocation in good times. 13
Plan • Describe Targets • Describe properties of the stationary allocation in good times. • Describe the transition when the economy switches to a recession. 13
Long Good Times Targets Capital Requirement: θ = . 105 • We have the following industry properties (Canadian) Data Model Bank failure rate 0.22% 0.26% Capital ratio 14.4% 14.4% Wholesale Funding 27.0% 21.8% 14
Long Good Times Targets Capital Requirement: θ = . 105 • We have the following industry properties (Canadian) Data Model Bank failure rate 0.22% 0.26% Capital ratio 14.4% 14.4% Wholesale Funding 27.0% 21.8% 14
Long Good Times Targets Capital Requirement: θ = . 105 • We have the following industry properties (Canadian) Data Model Bank failure rate 0.22% 0.26% Capital ratio 14.4% 14.4% Wholesale Funding 27.0% 21.8% Normalized T-Account of Banking Industry Canadian Data New Loans 1.07 Deposits 3.31 Existing Loans 4.87 Wholesale Funding 1.63 Own Capital 1.00 Model New Loans 1.26 Deposits 4.40 Existing Loans 5.69 Wholesale Funding 1.51 Own Capital 1.00 14
Model Parameters Parameter Value Description ξ 0 Loan issuance cost: χ ( n , ξ n ) = ξ 0 0.075 n n + 0 . 5 ξ n ξ 1 Loan issuance cost: χ ( n , ξ n ) = ξ 0 0.15 n n + 0 . 5 ξ n ξ d 5 Deposits 0.95 Subjective discount factor β λ 0.2 Maturity rate of long-term loans 0.1 Bank lending rate r r f 0.005 Risk-free rate u ( c ) = c σ σ 0.9 1 Risk weight on risky loans ω r ω s 0 Risk weight on safe assets Pr( z ′ = G | z = G ) Γ z = G , z ′ = G 0.99 Pr( z ′ = B | z = B ) Γ z = B , z ′ = B 0.80 E ( δ | z = G ) 0.025 Σ δ δ · π ( δ | z = G ) 15 V ( δ, Z = G ) 0.0015 α ( Z = G ) = 0 . 3847, β ( Z = G ) = 15 . 0011
Distribution of Banks 0.2 measure of banks 0.15 0.1 0.05 0 8 -3 7 -4 6 -5 5 loans -6 cash in hand 16
Banks Dividends 5 4.5 4 3.5 3 dividend 2.5 2 1.5 1 0.5 0 14 12 0 10 8 -5 6 4 -10 2 loans 17 cash in hand 0 -15
Banks New Loans Issue 5 4.5 4 3.5 3 new loans 2.5 2 1.5 1 0.5 0 14 12 0 10 8 -5 6 4 -10 2 loans cash in hand 0 -15 18
Banks Wholesale Funding (Deposits plus Bonds) 20 15 wholesale borrowing 10 5 0 -5 14 12 0 10 8 -5 6 4 -10 2 loans cash in hand 0 -15 19
Banks Value Function 18 16 14 12 10 value 8 6 4 2 0 14 12 0 10 8 -5 6 4 -10 2 loans cash in hand 0 -15 20
A Nasty Crisis with and without CCyB • Imagine the shock △ E ( δ ) = 0 . 015 (from .025 to .04) hits all banks, which happens with a very small probability, 0.01. The crisis continues for two periods and ends to go back to the good aggregate state thereafter. • Some banks are in better financial shape than others. • We explore the recovery of the Banking sector under the four scenarios. • What happens upon 21
A Nasty Crisis with and without CCyB Bank distribution - one period after the shock 0.2 0.2 measure of banks 0.15 0.15 0.1 0.1 0.05 0.05 0 0 8 8 7 -3 7 -4 -4 6 6 -5 -5 5 5 loans loans -6 cash in hand -6 cash in hand 22
A Nasty Crisis with and without CCyB Comparison of bank distributions before and after the shock 0.25 0.2 0.15 0.1 0.05 0 8 -3 7 -4 6 -5 5 loans 23 -6 cash in hand
Ulterior Path of the Economies after the shock • Recall that it is a recession for two periods and then we have a recovery. • We compare Countercyclical Capital Requirement with a constant weight to risk assests (left )and with a variable weight (right) • We look at impulse responses 24
New Lending Small difference between non-contingent policy and CCyB during the downturn. CCyB (if low capital requirement extends for a longer period) provides some help during the recovery. New Loans 5 percentage change from the common initial state 0 -5 -10 -15 -20 -25 Always 10.5% -30 CCyB 8% during recovery -35 0 2 4 6 8 10 12 14 16 18 20 25
Stock of Loans Loan Balance 2 percentage change from the common initial state 0 -2 -4 -6 -8 -10 -12 Always 10.5% CCyB -14 8% during recovery -16 0 2 4 6 8 10 12 14 16 18 20 26
Dividends Dividend 30 Percentage Change from the common initial state Always 10.5% 20 CCyB 8% during recovery 10 0 -10 -20 -30 -40 -50 -60 0 2 4 6 8 10 12 14 16 18 20 27
Wholesale Funding Wholesale Funding (QB) 10 Percentage Change from the common initial state 0 -10 -20 -30 -40 -50 -60 Always 10.5% CCyB -70 8% during recovery -80 0 2 4 6 8 10 12 14 16 18 20 28
Capital Ratio Average Capital Ratio 25 Always 10.5% CCyB 8% during recovery 20 15 Percentage 10 5 0 0 2 4 6 8 10 12 14 16 18 20 29
Bank Failure Rates Bank Default Probabiliity 1.8 Always 10.5% 1.6 CCyB 8% during recovery 1.4 1.2 percentage 1 0.8 0.6 0.4 0.2 0 0 2 4 6 8 10 12 14 16 18 20 30
Bank Equity Equity 25 Percentage Change from the common initial state Always 10.5% CCyB 20 8% during recovery 15 10 5 0 -5 -10 0 2 4 6 8 10 12 14 16 18 20 31
Fraction of Capital Requirement Violation Measure of Banks Subject to PCA 3.5 Always 10.5% CCyB 3 8% during recovery 2.5 percentage 2 1.5 1 0.5 0 0 2 4 6 8 10 12 14 16 18 20 32
Directions of Current Work • To replicate the Industry structure properly 33
Directions of Current Work • To replicate the Industry structure properly • Size of Banks in terms of Numbers and Dollars (large and small banks) 33
Directions of Current Work • To replicate the Industry structure properly • Size of Banks in terms of Numbers and Dollars (large and small banks) • Cross-Sectional (and temporal) Dispersion of 33
Directions of Current Work • To replicate the Industry structure properly • Size of Banks in terms of Numbers and Dollars (large and small banks) • Cross-Sectional (and temporal) Dispersion of • New Loan issues 33
Directions of Current Work • To replicate the Industry structure properly • Size of Banks in terms of Numbers and Dollars (large and small banks) • Cross-Sectional (and temporal) Dispersion of • New Loan issues • Dividends 33
Directions of Current Work • To replicate the Industry structure properly • Size of Banks in terms of Numbers and Dollars (large and small banks) • Cross-Sectional (and temporal) Dispersion of • New Loan issues • Dividends • Outiside financing (bonds) 33
Shortcomings and Extensions • Competitive Theory of Lending (Corbae and D’Erasmo (2016)) 34
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