A QUANTITATIVE THEORY OF UNSECURED CONSUMER CREDIT WITH RISK OF DEFAULT

A QUANTITATIVE THEORY OF UNSECURED CONSUMER 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 / 21

Introduction A Quantitative Theory of Unsecured Consumer Credit with Risk of Default Facts 1 Large Amount of: 1 Unsecured Consumer Credit 2 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 2 / 21

Introduction A Quantitative Theory of Unsecured Consumer Credit with Risk of Default Contribution: Macro Model Household Bankruptcy How: 1 Precautionary Saving Model + Heterogenous Agent Imrohoroglu (1989), Huggett (1993), Aiyagari (1994) 2 + Default Option 2 / 21

Introduction A Quantitative Theory of Unsecured Consumer Credit with Risk of Default 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 2 / 21

Introduction A Quantitative Theory of Unsecured Consumer Credit with Risk of Default 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 / 21

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) 3 / 21

The Model Uncertainty 1 Household Characteristics: s = (ξ, η, ζ), Γ(s, ds ) ξ: Socioeconomic Status (persistent) ξ 1 : Super Rich ξ 2 : White Collar ξ 3 : 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) 4 / 21

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 + q l,sl e w + (l ζ(s)) B(l, 0, s, 1) = c e w, l = 0 B(l, 1, s, 0) = c + q l,sl e w(1 γ) + (l ζ(s)), l R + B(l, 1, s, 1) = c e w(1 γ), l = 0 Lifetime Utility: v l,h,s (e; q, w) v(e; q, w) R L Maximum Expected lifetime utility: (T v)(l, h, s, e, q, w) R L 5 / 21

The Model Good Credit Record (h = 0) Case 1. (l ζ(s) < 0) (B(l, 0, s, 0) ) Case 2. (l ζ(s) < 0) (B(l, 0, s, 0) = ) Case 3. (l ζ(s) 0) (B(l, 0, s, 0) ) 6 / 21

The Model Good Credit Record (h = 0) Case 1. (l ζ(s) < 0) (B(l, 0, s, 0) ) (T v)(l, 0, s, e, q, w) = { max max U(c, η(s)) + βρ v l d,0,s (e ; q, w)φ(e s )Γ(s, ds )de, B(l,0,s,0) U(e w, η(s)) + βρ v 0,1,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 / 21

The Model Bad Credit Record (h = 1) Case 1. (l ζ(s) 0) Case 2. (l ζ(s) < 0) 7 / 21

The Model Bad Credit Record (h = 1) Case 1. (l ζ(s) 0) (T v)(l, 1, s, e, q, w) = max U(c, η(s)) B(l,1,s,0) [ + βρ λ v l,1,s (e ; q, w)φ(e s )Γ(s, ds )de + (1 λ) v l,0,s (e ; q, w)φ(e s )Γ(s, ds )de ] Case 2. (l ζ(s) < 0) 7 / 21

The Model Bad Credit Record (h = 1) Case 1. (l ζ(s) 0) (T v)(l, 1, s, e, q, w) = Case 2. (l ζ(s) < 0) max U(c, η(s)) B(l,1,s,0) [ + βρ λ v l,1,s (e ; q, w)φ(e s )Γ(s, ds )de + (1 λ) v l,0,s (e ; q, w)φ(e s )Γ(s, ds )de ] (T v)(l, 1, s, e, q, w) = U(e w(1 γ), η(s))+βρ v 0,1,s (e ; q, w)φ(e s )Γ(s, ds )de 7 / 21

The Model Default Set l 0 > l 1 D l 0,h,s (q, w) D l 1,h,s(q, w) 8 / 21

The Model Firms, Fin. Interm., Hospital sector Firms. max Kt,N t F (K t, N t) wn t rk t Financial Intermediaries. Hospital Sector. 9 / 21

The Model Firms, Fin. Interm., Hospital sector Firms. max Kt,N t F (K t, N t) wn t rk t Financial Intermediaries. max (1 + i) t π t t=0 s.t. π t = (1 δ + r)k t K t+1 + ρ(1 p lt,s t 1 )a lt,s t 1 ( l t) (l t+1,s t ) L S Hospital Sector. q lt+1,s t a lt+1,s t ( l t+1 ) (l t,s t 1 ) L S 9 / 21

The Model Firms, Fin. Interm., Hospital sector Firms. max Kt,N t F (K t, N t) wn t rk t Financial Intermediaries. Hospital Sector. q lt+1,s t = i r + δ ρ 1+i if l t+1 0 ρ 1+i (1 p l t+1,s t ) if l t+1 < 0 9 / 21

The Model Firms, Fin. Interm., Hospital sector Firms. max Kt,N t F (K t, N t) wn t rk t Financial Intermediaries. q lt+1,s t = i r + δ ρ 1+i if l t+1 0 ρ 1+i (1 p l t+1,s t ) if l t+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 ] dµ t 9 / 21

Quantitative Analysis Facts Figure: Reasons for Filing for bankruptcy 10 / 21

Quantitative Analysis Calibration Figure: Baseline Model Figure: Extended Model 11 / 21

Quantitative Analysis Wealth Distribution (Model) 12 / 21

Quantitative Analysis (Exp) Default Probabilities 13 / 21

Quantitative Analysis Earnings and Bankruptcies 14 / 21

Quantitative Analysis Loan Prices 15 / 21

Quantitative Analysis Accounting for Debt and Default Blue Collar: 1 Borrow Frequently 2 Small Amount 3 Default the most (vs Bad sequence of shocks) White Collar: 1 Borrow (vs Bad sequence of shocks) 2 Big Amount 3 Default (when changing status) 16 / 21

Quantitative Analysis Model Comparison 17 / 21

Quantitative Analysis Model Comparison 18 / 21

Quantitative Analysis Model Comparison 19 / 21

References References Aiyagari, S. (1994). Uninsured Idiosyncratic Risk and Aggregate Saving. The Quarterly Journal of Economics 109 (3), 659 684. Huggett, M. (1993, September). The risk-free rate in heterogeneous-agent incomplete-insurance economies. 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. 20 / 21

References Forza Milan!! 21 / 21