A QUANTITATIVE THEORY OF UNSECURED CONSUMER CREDIT …mkredler/ReadGr/PeriOnChatterjeeEtAl07.pdf ·...

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

1 / 21QT of unsecured consumer credit with Risk of Default

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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


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


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


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


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


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


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


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


+ (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


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


+ (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




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




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




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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Calibration

Figure: Baseline Model

Figure: Extended Model


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Wealth Distribution (Model)


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(Exp) Default Probabilities


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Earnings and Bankruptcies


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Loan Prices


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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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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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A QUANTITATIVE THEORY OF UNSECURED CONSUMER CREDIT …mkredler/ReadGr/PeriOnChatterjeeEtAl07.pdf ·...

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