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A QUANTITATIVE THEORY OF UNSECUREDCONSUMER CREDIT WITH RISK OF DEFAULT
(in pills)
SATYAJIT CHATTERJEE, DEAN CORBAE,MAKOTO NAKAJIMA and (uncle) JOSE’-VICTOR RIOS-RULL
Presenter: Alessandro Peri
University of Carlos III, Madrid
Reading Group, Feb 19, 2013
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Introduction
A Quantitative Theory of Unsecured Consumer Credit with Riskof Default
Facts
1 Large Amount of:
1 Unsecured Consumer Credit2 Unsecured Loans Default
2 Consumers can default on their loan (Chapter 7)
3 Post-bankruptcy: difficult get access to credit (10 years)
4 Bankrupt consumers are in poor financial shape
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Introduction
A Quantitative Theory of Unsecured Consumer Credit with Risk ofDefault
Contribution: Macro Model ←→ Household Bankruptcy
How:
1 Precautionary Saving Model + Heterogenous AgentImrohoroglu (1989), Huggett (1993), Aiyagari (1994)
2 + Default Option
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Introduction
A Quantitative Theory of Unsecured Consumer Credit with Risk ofDefault
Contribution: Macro Model ←→ Household Bankruptcy
Theoretical Results:
1 Existence of a General Equilibrium
2 Default Interval (in terms of earning thresholds)
3 Legal micro foundation of Endogenous Borrowing Constraint
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Introduction
A Quantitative Theory of Unsecured Consumer Credit with Risk ofDefault
1 Account for: Earning, Wealth, Indebtedness Facts
How: Shocks = Reasons why people file for Bankruptcy
1 Earning S.: job-loss
1 Preference S. : marital disruption
1 Liability S.: Med. Expenses → To have Def. in Eq.!!!!
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Introduction
A Quantitative Theory of Unsecured Consumer Credit with Risk ofDefault
1 Account for: Earning, Wealth, Indebtedness Facts
How: Shocks = Reasons why people file for Bankruptcy
1 Earning S.: job-loss
1 Preference S. : marital disruption
1 Liability S.: Med. Expenses → To have Def. in Eq.!!!!
2 Policy Analysis
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The Model
Model Features
Heterogeneous - Stochastic General Equilibrium Model (H-SGE)
Idiosyncratic shock, No Aggregate shock
Default option / Endogenous Borrowing Constraint
Markets:
1 Loan (Competitive, price schedules)
2 Medical Services (Competitive)
3 Output
4 Labour (Supplied Inelastically)
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The Model
Uncertainty
1 Household Characteristics: s = (ξ, η, ζ), Γ(s,ds′)
ξ: Socioeconomic Status (persistent)
ξ1: Super Richξ2: White Collarξ3: Blue Collar
η: Marital Disruption (quasi i.i.d)
ζ: Liability Shock (i.i.d)
2 Labour Efficiency: e, Φ(e|s) = Φ(e|ξ)
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The Model
Decision Problems
State: (l, h, s, e; q, w)
Budget correspondence:
B(l, h, s, d)(e; q, w) = {(c, l′) ∈ R+ × L ∩ (Legal Restrictions)}
B(l, 0, s, 0) = c+ ql′,sl′ ≤ e · w + (l − ζ(s))
B(l, 0, s, 1) = c ≤ e · w, l′ = 0B(l, 1, s, 0) = c+ ql′,sl
′ ≤ e · w(1− γ) + (l − ζ(s)), l′ ∈ R+
B(l, 1, s, 1) = c ≤ e · w(1− γ), l′ = 0
Lifetime Utility: vl,h,s(e; q, w) → v(e; q, w) ∈ RL
Maximum Expected lifetime utility: (Tv)(l, h, s, e, q, w) ∈ RL
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The Model
Good Credit Record (h = 0)
Case 1. (l − ζ(s) < 0) ∩ (B(l, 0, s, 0) 6= ∅)
Case 2. (l − ζ(s) < 0) ∩ (B(l, 0, s, 0) = ∅)
Case 3. (l − ζ(s) ≥ 0) ∩ (B(l, 0, s, 0) 6= ∅)
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The Model
Good Credit Record (h = 0)
Case 1. (l − ζ(s) < 0) ∩ (B(l, 0, s, 0) 6= ∅)
(Tv)(l, 0, s, e, q, w) =
maxd
{max
B(l,0,s,0)U(c, η(s)) + βρ
∫vl′,0,s′(e
′; q, w)Φ(e′|s′)Γ(s, ds′)de′,
U(e · w, η(s)) + βρ
∫v0,1,s′(e
′; q, w)Φ(e′|s′)Γ(s, ds′)de′}
Case 2. (l − ζ(s) < 0) ∩ (B(l, 0, s, 0) = ∅)
Case 3. (l − ζ(s) ≥ 0) ∩ (B(l, 0, s, 0) 6= ∅)
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The Model
Good Credit Record (h = 0)
Case 1. (l − ζ(s) < 0) ∩ (B(l, 0, s, 0) 6= ∅)
(Tv)(l, 0, s, e, q, w) =
maxd
{max
B(l,0,s,0)U(c, η(s)) + βρ
∫vl′,0,s′(e
′; q, w)Φ(e′|s′)Γ(s, ds′)de′,
U(e · w, η(s)) + βρ
∫v0,1,s′(e
′; q, w)Φ(e′|s′)Γ(s, ds′)de′}
Case 2. (l − ζ(s) < 0) ∩ (B(l, 0, s, 0) = ∅)
(Tv)(l, 0, s, e, q, w) = U(e · w, η(s)) + βρ
∫v0,1,s′(e
′; q, w)Φ(e′|s′)Γ(s,ds′)de′
Case 3. (l − ζ(s) ≥ 0) ∩ (B(l, 0, s, 0) 6= ∅)
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The Model
Good Credit Record (h = 0)
Case 1. (l − ζ(s) < 0) ∩ (B(l, 0, s, 0) 6= ∅)
(Tv)(l, 0, s, e, q, w) =
maxd
{max
B(l,0,s,0)U(c, η(s)) + βρ
∫vl′,0,s′(e
′; q, w)Φ(e′|s′)Γ(s, ds′)de′,
U(e · w, η(s)) + βρ
∫v0,1,s′(e
′; q, w)Φ(e′|s′)Γ(s, ds′)de′}
Case 2. (l − ζ(s) < 0) ∩ (B(l, 0, s, 0) = ∅)
Case 3. (l − ζ(s) ≥ 0) ∩ (B(l, 0, s, 0) 6= ∅)
(Tv)(l, 0, s, e, q, w) = maxB(l,0,s,0)
U(c, η(s))+βρ
∫vl′,0,s′(e
′; q, w)Φ(e′|s′)Γ(s, ds′)de′
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The Model
Bad Credit Record (h = 1)
Case 1. (l − ζ(s) ≥ 0)Case 2. (l − ζ(s) < 0)
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The Model
Bad Credit Record (h = 1)
Case 1. (l − ζ(s) ≥ 0)
(Tv)(l, 1, s, e, q, w) =
maxB(l,1,s,0)
U(c, η(s))
+ βρ[λ
∫vl′,1,s′(e
′; q, w)Φ(e′|s′)Γ(s,ds′)de′
+ (1− λ)
∫vl′,0,s′(e
′; q, w)Φ(e′|s′)Γ(s,ds′)de′]
Case 2. (l − ζ(s) < 0)
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The Model
Bad Credit Record (h = 1)
Case 1. (l − ζ(s) ≥ 0)
(Tv)(l, 1, s, e, q, w) =
maxB(l,1,s,0)
U(c, η(s))
+ βρ[λ
∫vl′,1,s′(e
′; q, w)Φ(e′|s′)Γ(s,ds′)de′
+ (1− λ)
∫vl′,0,s′(e
′; q, w)Φ(e′|s′)Γ(s,ds′)de′]
Case 2. (l − ζ(s) < 0)
(Tv)(l, 1, s, e, q, w) = U(e · w(1− γ), η(s))+βρ
∫v0,1,s′(e
′; q, w)Φ(e′|s′)Γ(s, ds′)de′
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The Model
Default Set
l0 > l1 → D̄∗l0,h,s(q, w) ⊆ D̄∗
l1,h,s(q, w)
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The Model
Firms, Fin. Interm., Hospital sector
Firms. maxKt,Nt F (Kt, Nt)− wNt − rKt
Financial Intermediaries.
Hospital Sector.
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The Model
Firms, Fin. Interm., Hospital sector
Firms. maxKt,Nt F (Kt, Nt)− wNt − rKt
Financial Intermediaries.
max∞∑t=0
(1 + i)−tπt
s.t. πt = (1− δ + r)Kt −Kt+1 +∑
(lt,st−1)∈L×Sρ(1− plt,st−1
)alt,st−1(−lt)
−∑
(lt+1,st)∈L×Sqlt+1,stalt+1,st (−lt+1)
Hospital Sector.
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The Model
Firms, Fin. Interm., Hospital sector
Firms. maxKt,Nt F (Kt, Nt)− wNt − rKt
Financial Intermediaries.
i ≥ r + δ
qlt+1,st =
≤ ρ
1+iif lt+1 ≥ 0
≥ ρ1+i
(1− plt+1,st ) if lt+1 < 0
Hospital Sector.
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The Model
Firms, Fin. Interm., Hospital sector
Firms. maxKt,Nt F (Kt, Nt)− wNt − rKt
Financial Intermediaries.
i ≥ r + δ
qlt+1,st =
≤ ρ
1+iif lt+1 ≥ 0
≥ ρ1+i
(1− plt+1,st ) if lt+1 < 0
Hospital Sector.∫ [(1− d∗l,h,s(e; q, w))ζ(s) + d∗l,h,s(e; q, w)max{l, 0} − ζ(s)/m
]dµt
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Quantitative Analysis
Facts
Figure: Reasons for Filing for bankruptcy
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Quantitative Analysis
Calibration
Figure: Baseline Model
Figure: Extended Model
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Quantitative Analysis
Wealth Distribution (Model)
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Quantitative Analysis
(Exp) Default Probabilities
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Quantitative Analysis
Earnings and Bankruptcies
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Quantitative Analysis
Loan Prices
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Quantitative Analysis
Accounting for Debt and Default
Blue Collar:
1 Borrow Frequently2 Small Amount3 Default the most (vs Bad sequence of shocks)
White Collar:
1 Borrow (vs Bad sequence of shocks)2 Big Amount3 Default (when changing status)
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Quantitative Analysis
Model Comparison
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Quantitative Analysis
Model Comparison
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Quantitative Analysis
Model Comparison
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References
References
Aiyagari, S. (1994). Uninsured Idiosyncratic Risk and Aggregate Saving. The Quarterly Journalof Economics 109(3), 659–684.
Huggett, M. (1993, September). The risk-free rate in heterogeneous-agent incomplete-insuranceeconomies. Journal of economic Dynamics and Control 17(5-6), 953–969.
Imrohoroglu, A. (1989). Cost of Business Cycles with Indivisibilities and Liquidity Constraints.The Journal of Political Economy 97(6), 1364–1383.
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References
Forza Milan!!
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