Banking and Shadow Banking Ji Huang Princeton University
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Banking and Shadow Banking Ji Huang Princeton University
Banking and Shadow Banking Ji Huang Princeton University May 2014 1 / 15 Introduction Relationship between financial instability and regualtion I A model without incorporating shadow banking predicts financial instability financial regulation 2 / 15 Introduction Relationship between financial instability and regualtion I This paper, which incorporates shadow banking, predicts financial instability financial regulation 2 / 15 Introduction Relationship between financial instability and regualtion I This paper, which incorporates shadow banking, predicts financial instability financial regulation conventional wisdom 2 / 15 Introduction Relationship between financial instability and regualtion I This paper, which incorporates shadow banking, predicts financial instability financial regulation conventional wisdom regulatory paradox 2 / 15 Contribution This paper I reconciles two seemly contradictory ideas and 3 / 15 Contribution This paper I reconciles two seemly contradictory ideas and I provides a guideline to consider financial instability in the presence of shadow banking. 3 / 15 Contribution This paper I reconciles two seemly contradictory ideas and I provides a guideline to consider financial instability in the presence of shadow banking. I models shadow banking as off-balance sheet financing. 3 / 15 Flow of Funds I: Investment asset bankers log utility discount factor ρ households risk neutral discount factor r 4 / 15 Flow of Funds I: Investment asset bankers log utility discount factor ρ households risk neutral discount factor r shadow banking with credit limit regular banking without credit limit regulatory authority 4 / 15 Flow of Funds I: Investment asset bankers log utility discount factor ρ households risk neutral discount factor r shadow banking with credit limit regular banking without credit limit regulatory authority no equity financing 4 / 15 Flow of Funds II: Return asset R bankers log utility discount factor ρ R<R households risk neutral discount factor r 5 / 15 Flow of Funds II: Return asset R<R R bankers log utility discount factor ρ r r households risk neutral discount factor r shadow banking with credit limit regular banking without credit limit r r regulatory authority 5 / 15 Flow of Funds II: Return asset R<R R bankers log utility discount factor ρ r r+τ households risk neutral discount factor r shadow banking with credit limit regular banking without credit limit r r τ τ regulatory authority 5 / 15 Endogenous Risk and Financial Instability liability 1 asset equity 6 / 15 Endogenous Risk and Financial Instability exogenous liability 1 asset 1−κ equity asset liability equity κ 6 / 15 Endogenous Risk and Financial Instability exogenous liability 1 asset 1−κ equity endogenous asset liability equity κ asset (1 − κ )κ q κ liability equity κ + (1 − κ )κ q ≡ κ Q 6 / 15 Balance Sheet of Bankers liability regular asset bank S equity W shadow asset liability S∗ bank ln[W ] ρ +h 7 / 15 Balance Sheet of Bankers liability regular asset bank equity W shadow asset liability S∗ bank ln[W ] ρ liability S asset bad shock (W +S)κ Q S equity W asset liability S∗ S∗ κ Q +h 7 / 15 Balance Sheet of Bankers liability asset (W +S)κ Q S equity W asset liability S∗ S∗ κ Q ln[W ] ρ +h not default S S∗ κ Q (W +S)κ Q ln[W −(W +S+S∗ )κ Q ] ρ +h W S∗ 7 / 15 Balance Sheet of Bankers liability asset S equity W (W +S)κ Q asset liability S∗ S∗ κ Q ln[W ] ρ default +h not default S (W +S)κ Q W S∗ S S∗ κ Q (W +S)κ Q ln[W −(W +S+S∗ )κ Q ] ρ +h W S∗ S∗ κ Q 7 / 15 Balance Sheet of Bankers liability asset S equity W (W +S)κ Q asset liability S∗ S∗ κ Q ln[W ] ρ default +h not default S (W +S)κ Q W lose access to shadow banking ln[W −(W +S)κ Q ] ρ + ĥ S∗ S S∗ κ Q (W +S)κ Q ln[W −(W +S+S∗ )κ Q ] ρ +h W S∗ S∗ κ Q 7 / 15 Enforceability Constraint ln W − W + S̃ κ Q ln W − W + S̃ + S∗ κ Q +h ≥ + ĥ ρ ρ 8 / 15 Enforceability Constraint ln W − W + S̃ κ Q ln W − W + S̃ + S∗ κ Q +h ≥ + ĥ ρ ρ ⇓ ∗ ∗ s ≤ s̄ ≡ (1 − exp [−ρH ]) where s∗ = 1 − (1 + s̃) , κQ S∗ S̃ , s̃ = , H = h − ĥ W W 8 / 15 Enforceability Constraint ln W − W + S̃ κ Q ln W − W + S̃ + S∗ κ Q +h ≥ + ĥ ρ ρ ⇓ ∗ ∗ s ≤ s̄ ≡ (1 − exp [−ρH ]) where s∗ = 1 − (1 + s̃) , κQ S∗ S̃ , s̃ = , H = h − ĥ W W financial instability κ Q & =⇒ s̄∗ % 8 / 15 Enforceability Constraint ln W − W + S̃ κ Q ln W − W + S̃ + S∗ κ Q +h ≥ + ĥ ρ ρ ⇓ ∗ ∗ s ≤ s̄ ≡ (1 − exp [−ρH ]) where s∗ = 1 − (1 + s̃) , κQ S∗ S̃ , s̃ = , H = h − ĥ W W financial instability κ Q & leverage for regular banking s̃ & =⇒ s̄∗ % =⇒ s̄∗ % 8 / 15 Enforceability Constraint ln W − W + S̃ κ Q ln W − W + S̃ + S∗ κ Q +h ≥ + ĥ ρ ρ ⇓ ∗ ∗ s ≤ s̄ ≡ (1 − exp [−ρH ]) where s∗ = 1 − (1 + s̃) , κQ S∗ S̃ , s̃ = , H = h − ĥ W W financial instability κ Q & leverage for regular banking s̃ & opportunity cost of default H % =⇒ s̄∗ % =⇒ s̄∗ % =⇒ s̄∗ % 8 / 15 What is H Probabilistic representation of H Z ∞ su∗ τ ∼ du Ht ≡ ht − ĥt = Et exp [− (ρ + ξ + χ) u] ρ t tax rate τ % =⇒ H % =⇒ s̄∗ % 9 / 15 Regulatory Paradox Markov equilibrium with a single state variable, bankers’ wealth share ω. 10 / 15 Regulatory Paradox Markov equilibrium with a single state variable, bankers’ wealth share ω. Without Shadow Banking 0.06 With Shadow Banking 0.06 loose, = 3.5% modest, = 4% tight, = 4.5% 0.05 0.04 0.05 0.04 qq 0.03 qq0.03 0.02 0.02 0.01 0.01 0 0 0.1 0.2 0.3 0.4 0.5 Bankers' Wealth Share, 0.6 0 0 0.7 Cost of Default 1 2.5 0.8 2 s* 1.5 0.2 0.3 0.4 0.5 Bankers' Wealth Share, 0.6 0.7 loose, = 3.5% modest, = 4% tight, = 4.5% 0.6 0.4 1 loose, = 3.5% modest, = 4% tight, = 4.5% 0.5 0 0 0.1 Leverage for Shadow Banking 3 H loose, = 3.5% modest, = 4% tight, = 4.5% 0.1 0.2 0.3 0.4 0.5 Bankers' Wealth Share, 0.6 0.2 0.7 0 0 0.1 0.2 0.3 0.4 0.5 Bankers' Wealth Share, 0.6 0.7 10 / 15 Where is Conventional Wisdom Result I does conventional wisdom result still hold in my model ? 11 / 15 Where is Conventional Wisdom Result I does conventional wisdom result still hold in my model ? I yes, when s∗ = 0 in equilibrium 11 / 15 Feedback Loop Enforceability constraint s∗ ≤ s̄∗ ≡ (1 − exp [−ρH ]) 1 − (1 + s̃) κQ (1) (1) H s∗ 12 / 15 Feedback Loop Enforceability constraint s∗ ≤ s̄∗ ≡ (1 − exp [−ρH ]) 1 − (1 + s̃) κQ Probabilistic representation of H Z ∞ su∗ τ ∼ Ht ≡ ht − ĥt = Et exp [− (ρ + ξ + χ) u] du ρ t (1) (2) (1) s∗ H (2) 12 / 15 Two Equilibria I Degenerate equilibrium (always exists): I I I where shadow banking does not exist effectively, i.e., st∗ = 0 and Ht = 0; Non-degenerate equilibrium (might exist): st∗ > 0 and Ht > 0. 13 / 15 Equilibrium Uniqueness Define mapping Γ ΓH [ω ] ≡ Et where ∞ Z t s∗ [ωu ]τ du ωt = ω exp [− (ρ + ξ + χ) u] ρ s∗ [ω ] ≤ s̄∗ [ω ], and ∗ s̄ [ω ] = (1 − exp [−ρH [ω ]]) 1 − (1 + s̃[ω ]) . κ Q [ω ] Theorem if τ < (ρ + ξ + χ) κ, then H [ω ] = 0 is the unique fixed point of mapping Γ 14 / 15 Equilibrium Uniqueness Define mapping Γ ΓH [ω ] ≡ Et ∞ Z t s∗ [ωu ]τ du ωt = ω exp [− (ρ + ξ + χ) u] ρ where s∗ [ω ] ≤ s̄∗ [ω ], and ∗ s̄ [ω ] = (1 − exp [−ρH [ω ]]) 1 − (1 + s̃[ω ]) . κ Q [ω ] Theorem if τ < (ρ + ξ + χ) κ, then H [ω ] = 0 is the unique fixed point of mapping Γ τ, ↓ H, ↓ s∗ , ↓ 14 / 15 Equilibrium Uniqueness Define mapping Γ ΓH [ω ] ≡ Et ∞ Z t s∗ [ωu ]τ du ωt = ω exp [− (ρ + ξ + χ) u] ρ where s∗ [ω ] ≤ s̄∗ [ω ], and ∗ s̄ [ω ] = (1 − exp [−ρH [ω ]]) 1 − (1 + s̃[ω ]) . κ Q [ω ] Theorem if τ < (ρ + ξ + χ) κ, then H [ω ] = 0 is the unique fixed point of mapping Γ τ, ↓ H, ↓ s∗ , ↓ ⇒ s∗ = 0, H = 0 14 / 15 Regulatory Financial Instability 0.11 0.105 Q 0.1 0.095 0.025 0.03 0.035 , tax rate 0.04 0.045 0.04 0.045 Leverage for Shadow Banking 0.8 0.6 s* 0.4 0.2 0 0.025 0.03 0.035 , tax rate 15 / 15