Welfare Implications of the Transition to
High Household Debt
Jeffrey R. Campbell
and
Zvi Hercowitz
Presentation at the Conference
Household Finances and Housing Wealth
Banco de España
April 2007
slide 0
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 1
 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 2
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 3
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 4
Preferences




ˆ t  ln Sˆ  1    ln Cˆ   ln 1  Nˆ ,


t
t
t
t 0
0    1,   0


~
~
   ln St  1   ln Ct
~t

t 0
~
ˆ

slide 5
Technology
Yt  K Nt  , 0    1

1
Yt  Ct  X t
X t  S t 1  1    S t
slide 6
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-byperiod adjustable rate
Notation:
~
Bˆt 1 , Bt 1 , Rt
slide 7
Equity Requirement
 Equity requirement parameters:
 0 <  < 1: initial equity share
 δ ≤  < 1: equity accumulation
 Required equity share for a good j periods old:
1 
ej  1 
 1   
1   
j
slide 8
The equity constraint on a household is:

(1   ) St 1  Rt Bt 1  1    1    X t  j e j
j
j 0
This constraint can be rewritten as:

Rt 1
1   1   
Vt 1  1   
Vt 
X t j
Rt
Rt
Bt 1  Vt 1
slide 9
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 10
Utility Maximization by Savers
Budget constraint and first-order conditions:
~
~
~
~ ~ ~
Bt 1  H t K  Rt Bt  Ct  St 1  1    St
~  t 1  

1
 1 

 t 
t
~

Ct 1
~  1    
St 1
 
~  t 1
1
Rt
t
slide 11
Utility Maximization by Borrowers
Constraints:
Bˆ t 1  Wt Nˆ t  Rt Bˆ t  Cˆ t  Sˆt 1  1    Sˆt ,
t

Rt 1
1   1   
Vt 1  1   
Vt 
Xt
Rt
Rt
t  t
Bt 1  Vt 1
t t
slide 12
First-order conditions:
   Cˆ t
Wt  

 1    1  Nˆ t

t  1  ˆ t 1 Rt
t

R
 t  t  ˆ t 1  t 1 1    t 1
t
Rt
1  t
1   (1   )
Rt
t 1  
ˆ


t 1  


Cˆ t 1
1   (1   )  
 
 1    1  t 1
ˆ
Rt 1
St 1


slide 13
Production and Equilibrium

K
Wt  1    
 Nt 
 1
K
H t    
 Nt 
N t  Nˆ t
~
K K
~ ˆ ~
~ ˆ
ˆ
Yt  Ct  Ct  St 1  St 1  1   ( St  St )
~
B  Bˆ   B
t 1
t 1
t 1
slide 14
The Deterministic Steady State
~
R  1/ 
ˆ
  1 ~



0
1  ˆ 1   
slide 15
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 16
Calibration – Main Features
~
ˆ  1 / 1.01   1 / 1.015
 : 1
:
1   1   
loan to value ratio
R
repayment rate
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
slide 17
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 18
Simulation Results – The Interest rate and the Debt
slide 19
Simulation Results – Individual Decisions
slide 20
Simulation Results – Wealth Distribution
slide 21
Interpretation of the Evidence
 Evolution of wealth distribution from the SCF. Every 3
years: 1983-2001
 Comovement of household debt and interest rates
slide 22
Shares of the Wealthiest 10% Households
(1) Wealth
slide 23
Shares of the Wealthiest 10% Households
(2) Housing and Vehicles
slide 24
Household Debt and the Real Interest Rate
Debt/Assets Ratios and Real 3-year T Bill Rate
fed
slide 25
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 26
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 27
Extension of the Model: Irreversible Investment
~
X t  0,
Xˆ t  0
The constraint binds only for the saver, and
only initially.
t** = 17, t* = 33
slide 28
Irreversible Investment – The Debt and the Interest Rate
slide 29
Irreversible Investment – Individual Decisions
slide 30
Irreversible Investment – Wealth Distribution
slide 31
Mortgage Terms from the Survey of Consumer Finances
back
slide 32
Federal Funds and 3-Year Treasury Bill Rate
20
16
12
8
4
0
1980
1985
1990
federal funds rate
back
1995
2000
2005
3-year treasury bill rate
slide 33