The Macroeconomics of Consumer Finance Cedric Ehouarne
Credit Card Balance-to-income ratios in 2007-09 8
Change in balance-to-income ratio
6
4
2
0
-2
-4
-6
-8 -10
-8
-6
-4 -2 Balance-to-income ratio
0
2
4
1 / 18
Credit Card Tightening vs Deleveraging in 2007-09 8
Change in balance-to-income ratio
6
4
2
0
-2
-4
-6
-8 -8
-6
-4
-2 0 Change in limit-to-income ratio
2
4
6
2 / 18
Contribution of my Job Market Paper Develop and estimate an incomplete-market, heterogeneous-agent, general equilibrium model for understanding the cyclical nature and macroeconomic effects of consumer financial decisions.
3 / 18
Contribution of my Job Market Paper Develop and estimate an incomplete-market, heterogeneous-agent, general equilibrium model for understanding the cyclical nature and macroeconomic effects of consumer financial decisions. Households de-lever during recessions as optimal response to credit tightening to stay away from default boundary. → deleveraging is distressed.
3 / 18
Contribution of my Job Market Paper Develop and estimate an incomplete-market, heterogeneous-agent, general equilibrium model for understanding the cyclical nature and macroeconomic effects of consumer financial decisions. Households de-lever during recessions as optimal response to credit tightening to stay away from default boundary. → deleveraging is distressed. Distressed deleveraging exacerbates systemic risk because of spillovers between levered and non-levered consumers.
3 / 18
Contribution of my Job Market Paper Develop and estimate an incomplete-market, heterogeneous-agent, general equilibrium model for understanding the cyclical nature and macroeconomic effects of consumer financial decisions. Households de-lever during recessions as optimal response to credit tightening to stay away from default boundary. → deleveraging is distressed. Distressed deleveraging exacerbates systemic risk because of spillovers between levered and non-levered consumers. Paradox: Deleveraging leads to more financial instability!
3 / 18
The Model A rich interplay between credit risk & labor risk
Overview of the Model I
Household i’s income is subject to transitory shocks (εit , zit ): Yit = (1 − τ )εit zit + (1 − τ )(1 − εit )%zit | {z } {z } | if employed
I
otherwise
Government collects taxes τ , insures unemployment at rate %, and spends all tax surplus as public consumption Gt .
4 / 18
Overview of the Model I
Household i’s income is subject to transitory shocks (εit , zit ): Yit = (1 − τ )εit zit + (1 − τ )(1 − εit )%zit | {z } {z } | if employed
otherwise
I
Government collects taxes τ , insures unemployment at rate %, and spends all tax surplus as public consumption Gt .
I
Credit accounts with balance Bit ∈ R and price qit ≤ 1.
I
Option to default: Bit = 0, | {z }
debt is discharged
B = 0, | it+1{z }
no saving/borrowing
Yit = Y | {z }
income is garnished
4 / 18
Overview of the Model I
Household i’s income is subject to transitory shocks (εit , zit ): Yit = (1 − τ )εit zit + (1 − τ )(1 − εit )%zit | {z } {z } | if employed
otherwise
I
Government collects taxes τ , insures unemployment at rate %, and spends all tax surplus as public consumption Gt .
I
Credit accounts with balance Bit ∈ R and price qit ≤ 1.
I
Option to default: Bit = 0, | {z }
debt is discharged I
B = 0, | it+1{z }
no saving/borrowing
Yit = Y | {z }
income is garnished
Intermediaries are risk neutral, discount time at rate δ ∈ (0, 1) when receive deposits, and φt ∈ (0, δ) when make a loan. 4 / 18
Details on Financial Decision Making I
Each period, households observe all the realized shocks and then decide whether to default on their debt (if any): n o Vit = max Vitpay , Vitdef .
5 / 18
Details on Financial Decision Making I
Each period, households observe all the realized shocks and then decide whether to default on their debt (if any): n o Vit = max Vitpay , Vitdef .
I
The value of paying off captures the option to roll-over debt: Vitpay
= max Bit+1 ≤B
Citθ
+ β Et
h
1−γ Vit+1
i
θ 1−γ
θ1 ,
where: Yit + qit Bit+1 ≥ Bit + Cit .
5 / 18
Details on Financial Decision Making I
Each period, households observe all the realized shocks and then decide whether to default on their debt (if any): n o Vit = max Vitpay , Vitdef .
I
The value of paying off captures the option to roll-over debt: Vitpay
= max Bit+1 ≤B
Citθ
+ β Et
h
1−γ Vit+1
i
θ 1−γ
θ1 ,
where: Yit + qit Bit+1 ≥ Bit + Cit . I
The value of defaulting is simply one-period autarky: Vitdef =
Y θ + β Et
h
1−γ Vit+1
i
θ 1−γ
θ1 ,
Bit+1 = 0.
5 / 18
Optimal Pricing of Credit Card Accounts I
Under perfect competition and risk neutrality, the price of deposit only reflects impatience of intermediary: qf B | {zit+1}
deposit received at t
−
δBit+1 | {z }
PV of repayment t + 1
=
0 |{z}
no expected profit
⇒ The risk-free interest rate is 1 + r f = 1/q f = 1/δ
6 / 18
Optimal Pricing of Credit Card Accounts I
Under perfect competition and risk neutrality, the price of deposit only reflects impatience of intermediary: qf B | {zit+1}
deposit received at t
−
δBit+1 | {z }
PV of repayment t + 1
=
0 |{z}
no expected profit
⇒ The risk-free interest rate is 1 + r f = 1/q f = 1/δ I
The price of debt equates marginal cost of loan origination and marginal benefit of expected recovery: garnishment z }| { qit Bit+1 = φt E 1 def (Yit+1 − Y ) +1 def Bit+1 pay pay Vit+1 ≥Vit+1 Vit+1
6 / 18
Budget Constraints and Aggregation Household budget: C = Y + qB 0 − (1 − d)B − d · (Y − Y ). Intermediaries balanced budget: Z Π = −qB 0 + (1 − d)B + d · (Y − Y ) dµ = 0 Intermediaries + Households ⇒ C = Y.
7 / 18
Budget Constraints and Aggregation Household budget: C = Y + qB 0 − (1 − d)B − d · (Y − Y ). Intermediaries balanced budget: Z Π = −qB 0 + (1 − d)B + d · (Y − Y ) dµ = 0 Intermediaries + Households ⇒ C = Y. R Government balanced budget: G = τ εz − %(1 − τ )(1 − ε)z dµ Definition of disposable income: Y = εz − τ εz + %(1 − τ )(1 − ε)z. Production: Z Z Z Z GDP = εz dµ = ε dµ z dµ = ε dµ·1 = π·1+(1−π)·0 = π Government + disposable income + production ⇒ GDP = Y + G. 7 / 18
General Equilibrium Definition & Computational Strategy
Curse of dimensionality & Bounded rationality I
Individual state space is composed of net worth Nit = Yit − Bit , aggregate shock φt , and net worth distribution µt .
8 / 18
Curse of dimensionality & Bounded rationality I
Individual state space is composed of net worth Nit = Yit − Bit , aggregate shock φt , and net worth distribution µt .
I
An equilibrium is a value function V (N, φ, µ), policies B 0 (N, φ, µ), C (N, φ, µ), a time-varying employment rate π(φ, µ) and a law of motion µ0 = Γ(µ, φ, φ0 ) such that (i) households solve their optimization problem, (ii) the aggregate resource constraint holds, and (iii) the law of motion Γ is consistent with the households’ policies.
8 / 18
Curse of dimensionality & Bounded rationality I
Individual state space is composed of net worth Nit = Yit − Bit , aggregate shock φt , and net worth distribution µt .
I
An equilibrium is a value function V (N, φ, µ), policies B 0 (N, φ, µ), C (N, φ, µ), a time-varying employment rate π(φ, µ) and a law of motion µ0 = Γ(µ, φ, φ0 ) such that (i) households solve their optimization problem, (ii) the aggregate resource constraint holds, and (iii) the law of motion Γ is consistent with the households’ policies.
I
Problem: π depends on the entire net worth distribution µ! In steady state, only need to guess and verify one π ∗ . With aggregate uncertainty, consider bounded-rationality: ⇒ forecast π 0 only based on current π, rather than guessing Γ. 8 / 18
Steady State. Finding the equilibrium employment rate
Public and private consumption minus GDP (% diff.)
0.04 0.03 0.02 0.01 0 -0.01 -0.02 -0.03 -0.04 -0.05 89
90
91
92
93 94 95 Employment rate (in %)
96
Equilibrium employment π ∗ solves GDP(π ∗ ) =
97
R
98
99
C (π ∗ , µ∗ )dµ + G (π ∗ ) 9 / 18
Aggregate Uncertainty. Finding the forecasting rules 98 If an expansion occurs next quarter Otherwise, if next quarter is a recession
Next quarter's employment rate (in %)
97 96 95
Shortage of goods 94 93 92 91
Excess of goods
90 89 88 89
90
91
92 93 94 95 Today's employment rate (in %)
96
97
98
10 / 18
Data. Are the bounded-rationale forecasts reasonable? 98 If an expansion occurs next quarter Otherwise, if next quarter is a recession
Next-quarter's employment rate (in %)
97 96 95 94 93 92 91 90 89 89
90
91
92 93 94 95 Today's employment rate (in %)
96
97
98
11 / 18
Simulated Method of Moments SCF Data, 1995-2013
SMM: Actual vs Simulated Moments Data
Model
Credit card interest spread Bankruptcy rate (non-business, Chapter 7) Credit card charge-off rate Unemployment rate Total balances as % of aggregate annual income
11.26 0.42 5.28 6.01 0.29
11.20 0.50 2.65 5.35 0.26
Cross section of balance-to-income ratios – mean – standard deviation – skewness – kurtosis
8.48 11.12 2.25 8.60
8.12 8.87 2.38 9.67
Cross section of credit card interest rates – mean – standard deviation – skewness – kurtosis Correlation between balances & interest rates
11.79 6.03 0.10 2.35 0.00
11.79 6.69 0.29 2.31 −0.15 12 / 18
SMM: Estimated Parameters
Discount on borrowing UI replacement rate Income tax rate Coefficient of relative risk aversion Volatility of idiosyncratic productivity shock Discount on lending
Symbol
Value
δ % τ
0.9985 40% 25%
γ σz E[φ]
2.7970 0.3127 0.9942
Household types
Subjective discount factor EIS Mass of households
Symbol
Normal
Low β
Low ψ
β ψ
0.9934 − 0.9502
0.8387 1.5494 0.0351
− 0.6116 0.0147
13 / 18
Stacked densities
SMM: Identification of Preferences Groups
-1
0 1 2 3 Household net worth distribution (income minus debt)
4
5
Frequency
Stacked frequencies
-2
Normal Low Low
0 10 20 30 40 Credit balances as % of annual income
50
0
10 20 Annual credit card interest rates, %
30
14 / 18
Main Results Micro → Cross-Section → Macro
Result 1. Distressed deleveraging distorts consumption
Consumption
2 1.5 1 0.5 0 -2
-1
0 1 Net worth
2
15 / 18
2
1
1.5
0.8
Bond schedule
Consumption
Result 1. Distressed deleveraging distorts consumption
1 0.5 0
0.6 0.4 0.2
-2
-1
0 1 Net worth
2
0
1
2
3
Loan size
15 / 18
2
1
1.5
0.8
Bond schedule
Consumption
Result 1. Distressed deleveraging distorts consumption
1 0.5 0
0.4 0.2
-2 Next-period credit balance
0.6
-1
1.5
0 1 Net worth
2
0 1 Net worth
2
0
1
2
3
Loan size
1 0.5 0 -0.5 -2
-1
15 / 18
2
1
1.5
0.8
Bond schedule
Consumption
Result 1. Distressed deleveraging distorts consumption
1 0.5 0
0.4 0.2
-2
-1
1.5
0 1 Net worth
2
0
1
1 0.5 0 -0.5
2
3
Loan size
50 Annual interest rate, %
Next-period credit balance
0.6
40 30 20 10 0
-2
-1
0 1 Net worth
2
-2
-1
0 1 Net worth
2
15 / 18
Result 1. Distressed deleveraging distorts consumption 1 Expansion Recession
1.5
Bond schedule
Consumption
2
1 0.5 0
0.6 0.4 0.2
-2
-1
1.5
0 1 Net worth
2
0
1
1 0.5 0 -0.5
2
3
Loan size
50 Annual interest rate, %
Next-period credit balance
0.8
40 30 20 10 0
-2
-1
0 1 Net worth
2
-2
-1
0 1 Net worth
2
15 / 18
Result 2. Contagion from distressed consumers to others Employment
% deviation from steady date
0
−0.1
−0.2
−0.3
−0.4
−0.5
0
10
20
30
40
Quarters
16 / 18
Result 2. Contagion from distressed consumers to others Consumption
Employment
% deviation from steady date
0
0
−0.1 −0.5 −0.2
−0.3 −1
Q5 Q4 Q3 Q2 Q1
−0.4
−0.5
0
10
20
Quarters
30
40
−1.5
0
10
20
30
40
Quarters
16 / 18
Result 2. Contagion from distressed consumers to others Consumption
Employment
% deviation from steady date
0
Interest rate
0
12 Q2 Q1
10 −0.1 8 −0.5
6
−0.2
4 −0.3
2
−1
Q5 Q4 Q3 Q2 Q1
−0.4
−0.5
0
10
20
Quarters
30
40
−1.5
0
10
20
Quarters
30
0 −2 40
−4
0
10
20
30
40
Quarters
16 / 18
Result 2. Contagion from distressed consumers to others Employment
Consumption
% deviation from steady date
0
12 Q2 Q1
10 −0.1 8 −0.5
6
−0.2
4 −0.3
2
−1
Q5 Q4 Q3 Q2 Q1
−0.4
−0.5
0
10
20
30
40
−1.5
0
10
Income
20
30
0 −2 40
−4
0
10
Balance
0
% deviation from steady date
Interest rate
0
30
40
30
40
2
−1 −0.2
20
Net worth
0
1.5
−2 1 −3
−0.4
0.5
−4 −5
−0.6
0
−6
−0.5
−7
−0.8
−1
−8 −1
0
10
20
Quarters
30
40
−9
0
10
20
Quarters
30
40
−1.5
0
10
20
Quarters
16 / 18
Result 3: Risk spillovers have large macro impact
Volatility ÷ mean
First-order auto-correlation
Correlation with unemployment
Data
Model
Data
Model
Data
Model
Credit card spread
0.15
0.11
0.96
0.91
0.78
0.95
Revolving credit
1.09
1.01
0.35
0.24
−0.31
−0.13
Leverage
1.32
0.96
0.05
0.10
−0.21
−0.13
Bankruptcy rate
0.34
0.13
0.71
0.31
−0.04
0.34
Charge-off rate
0.35
0.14
0.93
0.33
0.51
0.47
Unemployment
0.27
0.28
0.98
0.99
...
...
17 / 18
Main Results of the Paper
18 / 18
Main Results of the Paper What drives the household deleveraging process? I
Deleveraging is distressed and triggered by credit tightening.
I
Highly levered households cut back on consumption, which increases unemployment through demand channel.
I
More income risk affects credit tightening of all the other households who in turn de-lever ⇒ risk spillovers.
18 / 18
Main Results of the Paper What drives the household deleveraging process? I
Deleveraging is distressed and triggered by credit tightening.
I
Highly levered households cut back on consumption, which increases unemployment through demand channel.
I
More income risk affects credit tightening of all the other households who in turn de-lever ⇒ risk spillovers.
What are the aggregate consequences? I
In typical general equilibrium model, savers consume more when interest rates fall during a recession, thus compensates for lower consumption from levered households: wash-out.
I
But here, interest rate channel is shut down because of intermediation. Due to higher risk, savers save more for precautionary reasons, consume less! ⇒ amplification
I
Deleveraging exacerbates financial instability ⇒ paradox! 18 / 18
Cross-sectional mean
Cross-sectional standard deviation
10
14
9 12 8 10 7 Balance-to-income ratio 6 1995
2000
2005
2010
2015
8 1995
Cross-sectional skewness
2000
2005
2010
2015
Cross-sectional kurtosis
2.6
12
2.4 10 2.2 8 2 1.8 1995
2000
2005
2010
2015
6 1995
2000
2005
2010
2015
Cross-sectional mean
Cross-sectional standard deviation
10
24
9
22
8 7 6 1995
14
25
12
20
10
15
20
Balance-to-income ratio Limit-to-income ratio 2000
2005
2010
18 16 2015
8 1995
Cross-sectional skewness 1.25
2.4
1.2
2.2
1.15
1.8 1995
2005
2010
10 2015
Cross-sectional kurtosis
2.6
2
2000
12
3.8
10
3.6
8
3.4
1.1
2000
2005
2010
1.05 2015
6 1995
2000
2005
2010
3.2 2015
