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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 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 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 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 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
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