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

Introduction

A Quantitative Theory of Unsecured Consumer Credit with Riskof Default

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

Introduction

A Quantitative Theory of Unsecured Consumer Credit with Risk ofDefault

Contribution: Macro Model ←→ Household Bankruptcy

1 Precautionary Saving Model + Heterogenous AgentImrohoroglu (1989), Huggett (1993), Aiyagari (1994)

2 + Default Option

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

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.!!!!

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

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)

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)

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

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= ∅)

The Model

Case 1. (l − ζ(s) < 0) ∩ (B(l, 0, s, 0) 6= ∅)

(Tv)(l, 0, s, e, q, w) =

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= ∅)

The Model

Case 1. (l − ζ(s) < 0) ∩ (B(l, 0, s, 0) 6= ∅)

(Tv)(l, 0, s, e, q, w) =

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= ∅)

The Model

Case 1. (l − ζ(s) < 0) ∩ (B(l, 0, s, 0) 6= ∅)

(Tv)(l, 0, s, e, q, w) =

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′

The Model

Bad Credit Record (h = 1)

Case 1. (l − ζ(s) ≥ 0)Case 2. (l − ζ(s) < 0)

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)

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′

The Model

Default Set

l0 > l1 → D̄∗l0,h,s(q, w) ⊆ D̄∗

l1,h,s(q, w)

The Model

Firms, Fin. Interm., Hospital sector

Firms. maxKt,Nt F (Kt, Nt)− wNt − rKt

Financial Intermediaries.

Hospital Sector.

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.

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.

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

Quantitative Analysis

Figure: Reasons for Filing for bankruptcy

Calibration

Figure: Baseline Model

Figure: Extended Model

Wealth Distribution (Model)

(Exp) Default Probabilities

Earnings and Bankruptcies

Loan Prices

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)

Model Comparison

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.

References

Forza Milan!!

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