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