slide 1

Welfare Implications of the Transition to High Household Debt

Jeffrey R. Campbelland

Zvi Hercowitz

Presentation at the Conference

Household Finances and Housing Wealth

Banco de España

April 2007

slide 2

Introduction

Who benefits in the economy from relaxing a borrowing constraint? Borrowers or Savers?

Microeconomic level

Macroeconomic level

Relaxation of borrowing constraints in the US: Aggressive deregulation of the mortgage market in early 1980s

Background:

Homes and vehicles collateralize most household debt: 90% in 2001 (1962: 85%). Typical debt contract: equity requirements

Deregulation in 1982: Greater access to sub-prime mortgages and refinancing. Lowering “equity requirements”

slide 3

Housing equity 1982: 71% of GDP

Household Debt/GDP: 43% in 1983 56% in 1990

Model: borrower-saver model in Campbell and Hercowitz (2006)

10th wealth decile. 72.8% of financial assets in 2001 "saver"

1st-9th wealth deciles. 73.4% of household debt in 2001 "borrower"

M

slide 4

Rest of the Talk

The model

Quantitative results: Computed transition dynamics

Interpretation of the data through the eyes of the model

Welfare effects

Conclusions

slide 5

The Borrower-Saver Model Main Features

Borrowing is collateralized – equity requirement

The two household differ in time preference and in labor supply. Only the borrower supplies labor

In equilibrium: saver holds all the assets, borrower owes all the debt. Borrower’s only asset: equity on durable goods

The capital stock is constant

slide 6

Preferences

0 ,10

,ˆ1lnˆln1ˆlnˆ0

t

tttt NCS

ttt

t

CS~

ln1~

ln~

0

~ˆ

slide 7

Technology

10 ,1 tt NKY

tttXCY

tttSSX 1

1

slide 8

Trade

Markets are competitive: Households sell capital services and labor to the firms – make loans to each other

Factor prices: Ht , Wt

Only security traded: Collateralized debt with a period-by-period adjustable rate

Notation:ttt RBB ,

~,ˆ

11

slide 9

Equity Requirement

Equity requirement parameters:

0 < < 1: initial equity share

δ ≤ < 1: equity accumulation

Required equity share for a good j periods old:

11

11

j

je

slide 10

The equity constraint on a household is:

jjt

j

jttt

eXBRS

11)1(

011

This constraint can be rewritten as:

11 tt VB

jt

tt

t

tt X

RV

R

RV

111 1

1

slide 11

Optimization and Equilibrium

Equity constraint: binds for at most one type of household at a time

Conjecture: It binds for the borrower from t* ≥ 0. This is verified in the solution

slide 12

Utility Maximization by Savers

Budget constraint and first-order conditions:

tttttttt SSCBRKHB ~

1~~~~~

11

t

t

t R

1~1

1~

~

1~

11

11

t

t

t

t

S

C

slide 13

Utility Maximization by Borrowers

Constraints:

ttt

tt

t

tt X

RV

R

RV

111 1

1

ttttttttt

SSCBRNWB ,ˆ1ˆˆˆˆˆ11

tttt VB 11

slide 14

First-order conditions:

11

1

11 )1(111ˆ

ˆ

1ˆ)1(1

1t

t

t

t

t

t

tt RS

C

R

t

tt

t

ttt R

R 11

1 1ˆ

t

tt

N

CW ˆ1

ˆ

1

tt

tt R

1ˆ1

slide 15

Production and Equilibrium

1

1

tt

tt

N

KH

N

KW

111

11

~ˆ

)ˆ~(1ˆ~ˆ~

~ˆ

ttt

ttttttt

tt

BBB

SSSSCCY

KK

NN

slide 16

The Deterministic Steady State

~/1R

0

1ˆ1

~ˆ

1

slide 17

Quantitative Results

The experiment

• Initial pre-reform steady state calibrated to the equity requirements observed through 1982:IV

• Lower equity requirements: and π values calibrated to the period from 1995:I onwards

• Computation of the transition path to the new steady state

slide 18

Calibration – Main Features

015.1/1~

01.1/1ˆ

Data:

Cars: Average loan-to-value ratios and terms from the data

Homes: SCF, and actual change in debt/asset ratio

High requirement regime: = 0.16, = 0.0315

Low requirement regime: = 0.11, = 0.0186

:

111 :

R

loan to value ratio

repayment rate

slide 19

Computation procedure

Equilibrium path beginning at the old steady state

Modified version of Fair and Taylor's (1983) procedure

Borrower's equity constraint does not bind until t *

≥ 0

t * = 30

slide 20

Simulation Results – The Interest rate and the Debt

slide 21

Simulation Results – Individual Decisions

slide 22

Simulation Results – Wealth Distribution

slide 23

Interpretation of the Evidence

Evolution of wealth distribution from the SCF. Every 3 years: 1983-2001

Comovement of household debt and interest rates

slide 24

Shares of the Wealthiest 10% Households (1) Wealth

slide 25

Shares of the Wealthiest 10% Households(2) Housing and Vehicles

slide 26

Household Debt and the Real Interest RateDebt/Assets Ratios and Real 3-year T Bill Rate

fed

slide 27

Welfare Analysis

Equivalent permanent change in both consumption goods

Across steady states:– Saver: 12 % – Borrower: -4.4 %

Including the transition:– Saver: 2.02 %– Borrower: 0.26 %

Wage rate, capital income and interest rate constant:– Saver: 0 %– Borrower: 1.35 %

Wage rate and capital income constant:– Saver: 1.36 %– Borrower: 0.45 %

slide 28

Concluding Comments

The transition is characterized by a prolonged increase in household debt accompanied by high interest rates.

Since 1983: Positive comovement of household debt and interest rates.

The main result: Savers gain from the financial reform more than borrowers---in spite of the fact that the relaxation of equity requirements applies directly to the latter.

slide 29

Extension of the Model: Irreversible Investment

0ˆ,0~ tt XX

The constraint binds only for the saver, and only initially.

t** = 17, t* = 33

slide 30

Irreversible Investment – The Debt and the Interest Rate

slide 31

Irreversible Investment – Individual Decisions

slide 32

Irreversible Investment – Wealth Distribution

slide 33

Mortgage Terms from the Survey of Consumer Finances

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slide 34

Federal Funds and 3-Year Treasury Bill Rate

0

4

8

12

16

20

1980 1985 1990 1995 2000 2005

federal funds rate 3-year treasury bill rate

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