Retirement in the Shadow (Banking)
1
Guillermo Ordoñez
1 University
Facundo Piguillem2
of Pennsylvania
2 EIEF
March 19, 2015
Motivation
I
Does shadow banking serve any “real” function for the economy?
I
Did it generate the lending boom in the 90’s and early 2000?
This paper
I
I
Incorporates:
I
Costly intermediation: traditional and shadow banking
I
Heterogeneous bequest motives:
I
Uncertain life spans: saving for retirement
Main mechanism: in equilibrium households
I
with low bequest motive want insurance (e.g., buy annuities)
I
with high bequest motive want to self insure (e.g., buy equities)
This paper
I
I
I
Incorporates:
I
Costly intermediation: traditional and shadow banking
I
Heterogeneous bequest motives:
I
Uncertain life spans: saving for retirement
Main mechanism: in equilibrium households
I
with low bequest motive want insurance (e.g., buy annuities)
I
with high bequest motive want to self insure (e.g., buy equities)
Why?
I
Care differently about accidental bequests
This paper
I
I
I
Incorporates:
I
Costly intermediation: traditional and shadow banking
I
Heterogeneous bequest motives:
I
Uncertain life spans: saving for retirement
Main mechanism: in equilibrium households
I
with low bequest motive want insurance (e.g., buy annuities)
I
with high bequest motive want to self insure (e.g., buy equities)
Implies: High bequest motive hh’want to borrow from low
I
If intermediation between households is costly
I
⇒ return differential on assets
Large increase in financial intermediation: 1980-2005
Private debt /GNP: Table D.3 Flow of funds.
Excluding Government debt
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
2007
2005
2003
2001
1999
1997
1995
1993
1991
1989
1987
1985
1983
1981
1979
1977
1975
1973
1971
1969
1967
1965
1963
1961
1959
1957
1955
1953
1951
1949
1947
1945
0.4
go
Large increase in retirement funds
Life expectancy increased from 74 to 79 years
Household's assets held in retiretment funds
Table L100 flow of funds Line 20
12
1.2
Pensions assets over GDP
1.1
1.0
0.9
0.8
0.7
0.6
0.5
0.4
1969
1972
1975
1978
1981
1984
1987
1990
1993
1996
1999
2002
2005
2008
2011
No improved efficiency in the financial sector
Value added per unit of loan. Philippon (AER forthcoming)
3.0%
Level based
Quality Adjusted
2.5%
2.0%
1.5%
1.0%
0.5%
2007
2005
2003
2001
1999
1997
1995
1993
1991
1989
1987
1985
1983
1981
1979
1977
1975
1973
1971
1969
1967
1965
1963
1961
1959
1957
1955
1953
1951
1949
1947
0.0%
1945
I
Big drop in Liquidity cost
Use NIPA, Flow of Funds and Philippon data to construct:
"Liquidity cost" of Financial Sector
2.5%
Final-Level based
Final-Quality adjusted
2.0%
1.5%
1.0%
0.5%
2006
2004
2002
2000
1998
1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
1976
1974
1972
1970
1968
1966
1964
1962
1960
1958
1956
1954
1952
1950
1948
0.0%
1946
I
Main Findings
I
I
I
Spread between borrowing and lending fell 1 percentage point
or, the intermediation cost fell by 33%
I
Borrowing and lending increased from 1GDP to 1.7GDP
I
Total assets explode from 4GDP to 10GDP
We account for these facts
I
Almost all the reduction in spread due to Liquidity
I
No increase in efficiency.
I
Increase in life expectancy key to get the right direction of prices
Road Map
1. Accounting for the change in intermediation cost.
2. Model economy
2.1 Individual Decisions
2.2 Intermediation: traditional and shadow banking
2.3 Equilibrium
3. Solution and Parameters
4. Results
5. Conclusions
Accounting for spreads
I
A fundamental equation
Gross output
= Value added + Cost of inputs
Int. received − Bad debt = VA + Int. paid + other services
fre + (1 − f )rL − sb (1 + re ) = φ̂ + (rd + rs )
I
Where:
I
I
I
I
I
I
I
I
re : interest rate charged on a loan.
rL : return on liquid assets.
1 − f : proportion of assets invested in liquid assets.
sb : proportion of assets that are lost.
φ̂: value added per unit of loan.
rd : return to investor (or depositor)
rs : value of other services to investor
Now we define r = rd + rs : opportunity cost for investor.
Accounting for spreads
I
Reorganize equation
fre + (1 − f )rL − sb (1 + re ) = φ̂ + (rd + rs )
re − r
| {z }
Interest spread
I
=
φ̂
|{z}
value added
+ sb (1 + re ) + (1 − f )(re − rL )
{z
}
| {z }
|
risk component
liquidity component
We focus on last the component: (1 − f )(re − rL )
I
If liquid asset have same return as loans re = rL , no liquidity cost.
I
If lenders do not need liquidity, f = 1, no liquidity cost.
I
Cost could depend on level. e.g, if rL = 0 (cash), spread increases
with the level of interest rates.
Accounting for spreads: first look
I
re=interest received/private debt. Table 7.11 Line 28/Table D.3.
I
r =interest paid deposits/deposits. Table 7.11 Line 5/Table L109.
16%
r=Average return on deposits
14%
re = Average return on loans
re-r, Naïve spread
12%
10%
8%
6%
4%
2%
2013
2011
2009
2007
2005
2003
2001
1999
1997
1995
1993
1991
1989
1987
1985
1983
1981
1979
1977
1975
1973
1971
1969
1967
1965
1963
1961
1959
0%
Accounting for spreads: second look
I
Financial sector has changed. Less traditional banking, more non
standard banking. Around 1/3 of “banks” liabilities are deposits.
Deposits over private debt.
Flow of funds: Table L109/Table D.3
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
I
2007
2005
2003
2001
1999
1997
1995
1993
1991
1989
1987
1985
1983
1981
1979
1977
1975
1973
1971
1969
1967
1965
1963
1961
1959
1957
1955
1953
1951
1949
1947
1945
0.0
Plus, financial institutions offer several services besides rd . We
use “Service Furnished without payment” (Table 2.4.5 line 88)
Accounting for spreads: second look
r =(interest paid+Service Furnished without pay.)/private debt.
(Use Table 7.11 Line 4 instead of line 5)
16%
r=Average return on liabilities
14%
re = Average return on loans
re‐r, Less naive spread
12%
10%
8%
6%
4%
2%
2013
2011
2009
2007
2005
2003
2001
1999
1997
1995
1993
1991
1989
1987
1985
1983
1981
1979
1977
1975
1973
1971
1969
1967
1965
1963
1961
0%
1959
I
Accounting for spreads: risk component
I
Table 7.1.6 Line 12 provides “Bad debt expenses” for corporate
business.
I
Not all corporate business are Financial. We follow Mehra et al (2011)
assigning half to Financial.
I
Assigning all of it does not change anything but the level.
3.0%
2.0
Bad deb expenses
B
a 2.5%
d
1.8
Private intermediated quantities
1.6
D
1.4 e
b
t
12
1.2
d
e 2.0%
b
t
v
e
r
G
D
P
o
1.0 v
e
0.8 r
1.5%
1.0%
0.6
0.4
(
0.5%
&
)
0.2
1971
1973
1975
1977
1979
1981
1983
1985
1987
1989
1991
1993
1995
1997
1999
2001
2003
2005
2007
2009
2011
0.0
1945
1947
1949
1951
1953
1955
1957
1959
1961
1963
1965
1967
1969
0.0%
G
D
P
Accounting for spreads: what is left
After taking risk component out we are left with:
r −r
|e {z }
=
Risk adjusted spread
φ̂
|{z}
value added
+ (1 − f )(re − rL )
{z
}
|
liquidity component
5%
risk adjusted spread
j
p
4%
4%
3%
3%
2%
2%
1%
1%
2011
1
2009
9
2007
7
2005
5
2003
3
2001
1
1999
9
1997
7
1995
5
1993
3
1991
1
1989
9
1987
7
1985
5
1983
3
1981
1
1979
9
1977
7
1975
5
1973
3
1971
1
1969
9
1967
7
1965
5
1963
3
1961
1
0%
1959
9
I
Accounting for spreads: what is left
I
Why did the spread fall? Was efficiency, φ̂, or liquidity
(1 − f )(re − rL )?
I
Did the IT revolution reduce the spread or was it liquidity cost?
Accounting for spreads: what is left
I
Why did the spread fall? Was efficiency, φ̂, or liquidity
(1 − f )(re − rL )?
I
Did the IT revolution reduce the spread or was it liquidity cost?
Philippon (2015) shows φ̂ has been constant for more than 100 years.
I He also shows that financial intermediation technology exhibits CRS.
I
Accounting for spreads: what is left
I
Why did the spread fall? Was efficiency, φ̂, or liquidity
(1 − f )(re − rL )?
I
Did the IT revolution reduce the spread or was it liquidity cost?
Philippon (2015) shows φ̂ has been constant for more than 100 years.
I He also shows that financial intermediation technology exhibits CRS.
I
3.0%
Level based
Quality Adjusted
2.5%
2.0%
1.5%
1.0%
0.5%
2007
2005
2003
2001
1999
1997
1995
1993
1991
1989
1987
1985
1983
1981
1979
1977
1975
1973
1971
1969
1967
1965
1963
1961
1959
1957
1955
1953
1951
1949
1947
1945
0.0%
Accounting for spreads: the matter in issue
What is left after subtracting value added?
Liquidity component 2.5%
Final Level based
Final‐Level based
Final‐Quality adjusted
2.0%
1 5%
1.5%
1.0%
0.5%
2006
2004
2002
2000
1998
1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
1976
1974
1972
1970
1968
1966
1964
1962
1960
1958
1956
1954
1952
1950
1948
0.0%
1946
I
Accounting for spreads: some numbers
I
From 1980 to 2007 the spread fell around 1%, all of it due to a
reduction in the liquidity component.
I
In 2007 the liquidity cost was almost 0%!
I
Assume cost in traditional baking, φTB , equal to cost in shadow
banking φSB . Then, φTB = φSB = φ̂
(Philippon claims this is the case.)
I
Shadow banking has no liquidity provisions, fSB = 1, then
(share TB) × (1 − f )(re − rL ) + (share SB) × 0 = Liquidity cost
I
Share TB fell from 2/3 to 1/3 from 1980 to 2007 (Figure with
dep.)
I
ABS used as liquid assets reducing re − rL in TB (numbers?)
Liquid assets in depository institutions
Flow of Funds Table L109. Liquid assets of depository
institutions over total deposits.
0.3
Cash plus deposits in FED
P
r
o
p
o
r
t
i
o
n
Cash+plus deposits in Fed plus Treasuries
p
p
p
0.25
Liquidity: including ABS
0.2
0.15
o
f
0.1
d
e
p
o
s
i
t
s
0.05
0
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
I
Summary
I
Big increase in borrowing and lending.
I
Large drop in financial intermediation spread.
I
All the fall due to “liquidity cost”
I
SB have direct impact: share increased from 1/3 to 2/3
I
and also indirect impact. It generated liquid assets with larger rL
I
Who or what and why provided the additional funds?
After any new borrower there has to be a lender!
I
How important is this change? Isn’t 1% too little?
Summary
I
Big increase in borrowing and lending.
I
Large drop in financial intermediation spread.
I
All the fall due to “liquidity cost”
I
SB have direct impact: share increased from 1/3 to 2/3
I
and also indirect impact. It generated liquid assets with larger rL
I
Who or what and why provided the additional funds?
After any new borrower there has to be a lender!
I
How important is this change? Isn’t 1% too little?
Answer: 1% is huge. Population is aging, need for
retirement insurance.
Answering the question
I
We build on Mehra et al. (2011)
I
OLG with financial intermediaries.
I
We show that the decrease in intermediation cost plus the
increase in life expectancy generates the observed changes in
aggregate quantities and prices.
I
Reduction in spread is welfare improving. Help with provision of
insurance.
I
Disclaimer: we are abstracting from potential instability of
shadow banking. There are enough papers about it.
Model: Technology and Population
I
Overlapping generations with Neoclassical technology
Yt = Ktθ (zt Lt )1−θ
zt+1 = (1 + γ)zt
I
I
θ: share of capital in output
γ: growth rate of labor productivity
Model: Technology and Population
I
Overlapping generations with Neoclassical technology
Yt = Ktθ (zt Lt )1−θ
zt+1 = (1 + γ)zt
I
I
I
θ: share of capital in output
γ: growth rate of labor productivity
Measure 1 of people are born every period
I
I
Each one with a different intensity of bequest motive α ≥ 0
α ∼ f (α)
Agents
I
Agents order consumption according to
U(α, c, b) =
T
X
j=0
β j log cj +
∞
X
β j (1−δ)j−T −1 [(1−δ) log cj +δα log bj ]
j=T +1
I
α ≥ 0: strength of bequest motive
I
0 < δ < 1: probability of death
I
Agents work for
T years, earn wage ωj and then retire
Agents
I
Agents order consumption according to
U(α, c, b) =
T
X
j=0
β j log cj +
∞
X
β j (1−δ)j−T −1 [(1−δ) log cj +δα log bj ]
j=T +1
I
α ≥ 0: strength of bequest motive
I
0 < δ < 1: probability of death
I
Agents work for
I
Bequest bj , equally distribute amongst agents of age
I
At age
T years, earn wage ωj and then retire
j = TI < T receive inheritance b̄
j = TI < T
Investment Decision
I
Assumption: Restricted choice for households
I
Agents choose whether to sign or not annuity contract at age
j =0
Investment Decision
I
Assumption: Restricted choice for households
I
Agents choose whether to sign or not annuity contract at age
j =0
Then agents have two options:
I
Strategy A ⇒ buy annuities
I
I
I
Benefit: Insurance against risk of living long time
Cost: Low return on assets (r )
Strategy B ⇒ go on your own
I
I
Benefit: High return on assets (re )
Cost: No insurance
Investment Decision
I
Assumption: Restricted choice for households
I
Agents choose whether to sign or not annuity contract at age
j =0
An annuity contract between an agent and the intermediary is:
I
While working: payment made by agent to intermediary
I
When retired: payment made by intermediary to agent
I
I
cj if alive
bj when she dies
Investment Decision
I
Assumption: Restricted choice for households
I
Agents choose whether to sign or not annuity contract at age
j =0
Let, interest differential: φ = re − r
Propositions 1 and 2
If φ ≤ φ ≤ φ̄, there exists α∗ > 0 such that,
I
if α < α∗ follow strategy A
I
if α ≥ α∗ follow strategy B
I
From now on assume:

 µa
1 − µa
F (α) =

0
if α = 0
if α = α̂ > 0
otherwise
Agent Problem: Strategy A (annuity)
max
T
X
β t log cj +
j=0
∞
X
β j (1 − δ)j−T −1 [(1 − δ) log cj + δα log bj ]
j=T +1
subject to
T
X
j=0
∞
X
ct
(1 − δ)j−T −1 [(1 − δ)cj + δbj ]
+
≤ v0A
j
(1 + r )
(1 + r )j
j=T +1
v0A =
T
−1
X
j=0
I
r : household lending rate
I
v0A : “wealth” at time 0
I
ωj : wage at age j
b̄
(1 − τ )ωj
+
j
(1 + r )
(1 + r )TI
Solution annuity strategy: consumption (α low)
0.045
Working age
0.040
Retirement age
Type A
0.035
Consumption
0.030
0.025
0.020
0.015
0.010
0.005
0.000
22
26
30
34
38
42
46
50
54
Age
58
62
66
70
74
78
82
Solution annuity strategy: assets accumulation (α low)
20.0
Net Worth/Annual wage
16.0
12.0
Type A
8.0
4.0
0.0
22
26
30
34
38
42
46
50
54
Age
58
62
66
70
74
78
82
Agent Problem: Strategy B (no-annuity)
I
Two problems: before retirement and after that
Agent Problem: Strategy B (no-annuity)
I
Two problems: before retirement and after that
I
After retirement
V (w ) = max{log c + (1 − δ)βV (w 0 ) + δβα log w 0 }
subject to
c+
I
w0
≤w
(1 + re )
re : return on equity and the household borrowing rate
Agent Problem: Strategy B (no-annuity)
I
Solution after retirement
V (w ) = ν̄1 (α) + ν̄2 (α) log w
I
where
ν̄2 (α) =
1 + αβδ
1 − (1 − δ)β
Agent Problem: Strategy B (no-annuity)
I
Solution after retirement
V (w ) = ν̄1 (α) + ν̄2 (α) log w
I
where
ν̄2 (α) =
I
1 + αβδ
1 − (1 − δ)β
The optimal consumption and implicit bequest strategies are:
c = w /ν̄2 (α)
w 0 = (1 + re )(w − c)
I
Bequests are:
bj = wj
j ≥T
Agent Problem: Strategy B (no-annuity)
I
At entry in labor force
max
T
−1
X
β j logcj + β T V (wT )
j=0
subject to
T
−1
X
j=0
v0B
cj
wT
+
≤ v0B
(1 + re )j
(1 + re )T
=
T
−1
X
j=0
(1 − τ )ωj
b̄
+
(1 + re )j
(1 + re )TI
Solution No-annuity strategy: consumption (α high)
0.045
Working age
Retirement age
0.040
Type B
0.035
Consumption
0.030
0.025
0.020
0.015
0.010
0.005
0.000
22
26
30
34
38
42
46
50
54
Age
58
62
66
70
74
78
82
Solution No-annuity strategy: assets accumulation (α high)
20.0
Type B
Net Worth/Annual wage
16.0
12.0
8.0
4.0
0.0
22
26
30
34
38
42
46
50
54
Age
58
62
66
70
74
78
82
Lifetime pattern of consumption
Consumption
0.045
0.040
Type A
0.035
Type B
Working age
Retirement age
0.030
0.025
0.020
0.015
0.010
0.005
0.000
22
26
30
34
38
42
46
50
54
Age
58
62
66
70
74
78
82
Cross sectional distribution of consumption
0.025
Type B
Retirement age
Type A
0.020
consumption
Working age
0.015
0.010
0.005
0.000
22
26
30
34
38
42
46
50
54
age
58
62
66
70
74
78
82
Intermediation: traditional banking
B
A
I
Intermediary pays r for the amount borrowed
I
Lend to other hh’s, with proportional cost of φ, or to the gov’t
at zero cost
Intermediation: traditional banking
B
A
I
Intermediary pays r for the amount borrowed
I
Lend to other hh’s, with proportional cost of φ, or to the gov’t
at zero cost
Assets
Liabilities
Government Debt (D G )
Assets of type A (W A )
Private Debt (D B )
Intermediated services D B (re − r )
Net Worth = 0
Assets = D B (1 + re ) + D G (1 + r )
W A = D B (1 + r ) + D G (1 + r )
Closing the economy
I
Fiscal policy to keep DtG fixed and tax τ on labor income
I
G
− DtG )
τ ωt Lt = rDtG − (Dt+1
D G : government debt
I
Competitive goods market (δk : depreciation rate)
δk + re = FK (Kt , zt Lt )
ωt = FL (Kt , zt Lt )
I
Competitive intermediaries
I
re = φ + r
Aggregates
I
At period t, measure of agents age j of type i = A, B is given by
µi
if j ≤ T
µit,j =
(1 − δ)j−T −1 µi
if j > T
I
Use measures to get aggregates, i = A, B
Ct (α̂, τ, b̄)
=
∞
XX
i
Wti (α̂, τ, b̄)
=
Bt (α̂, τ, b̄)
=
j=1
∞
XX
i
= T
wt,j (αi ; τ, b̄)µit,j
j=1
∞
X
j=T +1
Lt
ct,j (αi ; τ, b̄)µit,j
δbt,j (α̂; τ, b̄)µBt−1,j−1
(stationary) Equilibrium:
An equilibrium is {c i , w i , b i , K , α∗ }, prices re , r and fiscal policy such
that,
1. Households maximize
I
α̂ ≥ α∗
2. Intermediary maximize
3. Government budget constraint holds
4. Market clearing
Market Clearing:
I
A
B
Feasibility
Y = C (α̂, τ, b̄) + X + φ(K −
I
W B (α̂, τ, b̄)
)
1 + re
Assets market
W A (α̂, τ, b̄) W B (α̂, τ, b̄)
+
= DG + K
1+r
1 + re
I
Bequest=inheritance
b̄ = (1 + γ)TI B(α̂, τ, b̄)
Solution Strategy (THIS MUST BE CHANGED)
I
Balanced Growth analysis
I
All variables except interest rates and L grow at a rate γ
Solution Strategy (THIS MUST BE CHANGED)
I
Balanced Growth analysis
I
All variables except interest rates and L grow at a rate γ
I
Given τ , b̄ and α̂ compute individual decisions
I
In balanced Growth: ct,j (α; τ, b̄) =
ct+k,j+k (α;τ,b̄)
(1+γ)k
Solution Strategy (THIS MUST BE CHANGED)
I
Balanced Growth analysis
I
All variables except interest rates and L grow at a rate γ
I
Given τ , b̄ and α̂ compute individual decisions
I
In balanced Growth: ct,j (α; τ, b̄) =
I
Use above to compute aggregates
I
Solve for α̂, τ and b̄ such that feasibility, assets markets and
indifference are satisfied
ct+k,j+k (α;τ,b̄)
(1+γ)k
Calibration
I
Calibrate model economy to 1980.
I
φ = 0.03 (Spread from NIPA discussed before)
Calibration
I
Calibrate model economy to 1980.
I
φ = 0.03 (Spread from NIPA discussed before)
Parameters associated with individuals
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β = 0.99
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δ = 0.08 ⇒ post retirement life expectancy of 12.5 years
Calibration
I
Calibrate model economy to 1980.
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φ = 0.03 (Spread from NIPA discussed before)
Parameters associated with individuals
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β = 0.99
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δ = 0.08 ⇒ post retirement life expectancy of 12.5 years
Agents enter the workforce at 22
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TI = 30 ⇒ inheritance is received at 52
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T = 40 ⇒ retirement at 62
Calibration
Goods production parameters
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θ = 0.3. Share of capital in output
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γ = 0.02. Consistent with observations in labor productivity
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δk = 0.04. Consistent with capital output ratio = 3.
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D G /Y = 0.62. From data (with population growth is smaller)
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µA = 0.76. Measure of annuity guys
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α̂ = 3. These last two determined equilibrium bequest.
Calibration implies
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r = 0.03 and re = 0.06
Summary of Aggregate Results
∗
Economy
Indirect Equity holding∗
Direct Equity holding∗
Model
0.75
0.25
Data
0.72
0.28
National Accounts
Output
Consumption
Intermediated Services
1
0.79
0.03
1
071
0.027
Net Worth
Total
Government Debt/GDP
3.62
0.61
4.59
0.53
Bequest/GDP
Households Debt/GDP
0.045
1.00
0.027
0.99
Equities directly hold/total financial assets. Table B.100e of flow of funds
Discussion
Fig. 1
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With populations growth all the numbers match almost exactly
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There are some implicit government liabilities
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Density of types and α̂ jointly determine bequest
Counterfactual: the 2005 economy
Economy
Interm. Cost
Life expectancy
r
re
Benchmark (1980)
3%
0.08
New δ
3%
0.06
New φ
2%
0.08
2005
2%
0.06
0.030
0.060
0.023
0.053
0.032
0.052
0.026
0.046
National Accounts
Capital stock
Output
Net Worth
Type A (deposits+pensions)
Type B (equity)
Total financial Assets (WA + D G )
Data Fin. Assets (Table L100)
3.00
1.00
3.23
1.03
3.26
1.04
3.47
1.07
1.62
2.00
2.24
2.40
1.72
2.11
2.34
2.27
1.61
2.9
2.36
1.73
3.00
3.30
Government Debt/Y
Bequest/Y
Households Debt/GDP
Data on debt
0.61
0.045
1.00
1.00
0.62
0.045
1.11
0.62
0.035
1.65
0.62
0.036
1.74
1.73
Discussion
I
What do we get from the table?
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Drop in φ gives a large increase in debt, not enough, but wrong
movement in r
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Increase in life expectancy give little additional debt, but right
movement in r
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Both together deliver the right debt and movement in r
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Total household financial assets a bit low. The change is the
right magnitude. Adding land in K will make all numbers right.
I
Population growth rate plus introducing right government debt
would make all numbers be almost perfect.
Type A
Intermed.
back
B
Assets
Liabilities
Pension Assets
0
Net Worth
Pension Assets = D G (1 + r ) + D B (1 + r )
Net Worth = Pension Assets
Type B
Intermed.
back
A
Assets
Liabilities
K (1 + re )
D B (1 + re )
Net Worth
Net Worth = W0B (τ, b̄) = (K − D B )(1 + re )
Quantities intermediated = D B
Lorenz curve for consumption, total net worth and capital
back
100%
90%
Percent of C, K and NW
80%
70%
60%
45° Line
50%
40%
Consumption
30%
Net Worth
20%
Capital
10%
0%
0%
10%
20%
30%
40%
50%
60%
Percent of Population
70%
80%
90%
100%
Balance Sheet of Borrowers
Assets
Corporate Capital
Non Corporate Capital
Real Estate
Liabilities
Corporate Debt
Non Corporate Debt
Mortgages
Net Worth
What could go wrong? Difference of utilities at α = 0
Private Debt over GDP
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