Welfare Implications of the Transition to High Household Debt
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Transcript of Welfare Implications of the Transition to High Household Debt
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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
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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”
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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
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Rest of the Talk
The model
Quantitative results: Computed transition dynamics
Interpretation of the data through the eyes of the model
Welfare effects
Conclusions
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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
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Preferences
0 ,10
,ˆ1lnˆln1ˆlnˆ0
t
tttt NCS
ttt
t
CS~
ln1~
ln~
0
~ˆ
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Technology
10 ,1 tt NKY
tttXCY
tttSSX 1
1
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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
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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
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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
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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
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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
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Utility Maximization by Borrowers
Constraints:
ttt
tt
t
tt X
RV
R
RV
111 1
1
ttttttttt
SSCBRNWB ,ˆ1ˆˆˆˆˆ11
tttt VB 11
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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
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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
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The Deterministic Steady State
~/1R
0
1ˆ1
~ˆ
1
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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
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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
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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
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Simulation Results – The Interest rate and the Debt
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Simulation Results – Individual Decisions
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Simulation Results – Wealth Distribution
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Interpretation of the Evidence
Evolution of wealth distribution from the SCF. Every 3 years: 1983-2001
Comovement of household debt and interest rates
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Shares of the Wealthiest 10% Households (1) Wealth
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Shares of the Wealthiest 10% Households(2) Housing and Vehicles
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Household Debt and the Real Interest RateDebt/Assets Ratios and Real 3-year T Bill Rate
fed
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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 %
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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.
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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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Irreversible Investment – The Debt and the Interest Rate
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Irreversible Investment – Individual Decisions
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Irreversible Investment – Wealth Distribution
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Mortgage Terms from the Survey of Consumer Finances
back
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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
back