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ALFRED
P.
WORKING PAPER
SLOAN SCHOOL OF MANAGEMENT
INFLATION, GOVERNMENT DEFICITS AND
PRIVATE SAVING
Arlie
WP 1375-82
G.
Sterling
December
1982
MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE, MASSACHUSETTS 02139
Draft.
Comments appreciated.
INFLATION, GOVERNMENT DEFICITS AND
PRIVATE SAVING
Arlie
WP 1375-82
G.
Sterling
December
1982
^V^ ^
B
n
a
Modi
would like to thank Professors Franco
9]!
nts
participants
rt
the
as
well
as
comments,
and Julio Rotemberg for their
Workshops.
of the MIT Money and Applied Economics
I
^^
IV]. I.
I
.
L.
FEB 2
A
RECEIVED
MIT Sloan School
Working Paper 1375-82
November, 1982
Inflation, Government Deficits and Private Saving
ABSTRACT
This
analyzes
paper
influence
inflation
specific issues:
by
which
in
saving.
private
are
ability of consumers to
measured
way
the extent to which
deficits
government
the
national
government
The
over
an
and
analysis focuses on two
called
taxes
future
for
by
reflected in the decision to save, and the
distinguish
income
their
international
aggregate saving spanning the
period
section
1960
that
Implications for these
accountants.
cross
from
income
real
issues are derived in the context of the life cycle
tested
deficits
to
hypothesis,
observations
of
1979.
The
and
on
results
indicate that while consumers are able to correctly distinguish their
true
from their reported income, they do not appear to recognize the
future taxes associated with government deficits.
show that the upwards shift in the
between
private
The estimates also
savings
ratio
observed
the sixties and the seventies is not completely explained by
the model analyzed here.
Arlie G. Sterling
MIT, E40-370
1 Amherst Street
Cambridge, MA. 02144
(617) 253-8049
0745213
INFLATION, GOVERNMENT DEFICITS AND PRIVATE SAVING
Arlie G. Sterling
I.
INTRODUCTION
In this
I
paper analyze the way
private
influence
inflation
specific issues:
and
analysis focuses on two
future
called
taxes
for
by
reflected in the decision to save, and the
are
distinguish
ability of consumers to
deficits
government
The
saving.
the extent to which
deficits
government
which
in
their
from
income
real
that
measured by national income accountants.
Government deficits influence saving through the
and the time pattern of disposable income received by the
constraint
individual.
cycle
In the life cycle
wealth,
and
saving
on
the
simply
depends
consumption
model
consumption and the flow of income.
deficits
budget
cycle
life
difference
To the
on
life
between the rate of
extent
government
that
transfer income from one period to the next without
changing life cycle wealth they should have no affect on consumption,
influencing only the pattern of saving.
deficits
represent
pure
intertemporal
In the limit
transfers,
government
as
private
saving
should increase dollar for dollar with increased deficits.
While inflation may have many effects on private saving,
I
focus upon
the bias it introduces in the measurement of income and saving in the
national income accounts.
inflation
may
characteristics.
affect
As shown below, this channel through which
saving
measured
Furthermore,
it
is
has
shown
specific
testable
this
effect of
that
-2-
inflation
interacts
influence
saving.
with
the
way
which
in
government
deficits
This is because both current real government debt
and future real taxes required to pay off that debt
are
reduced
by
inflation.
The way in which government deficits and inflation enter in a
simple
life cycle model of the determination of the private savings ratio is
presented
section
in
Estimation strategy and difficulties as
II.
well as the data used in the study
discussed
are
in
section
III.
Empirical results are given in section IV, and conclusions in section
V.
Government Deficits and Inflation in the Life Cycle Model
II.
In this section
I
show how
government
influence the private savings ratio.
which
these
function s*(
variables
),
)
is
inflation
In order to focus on the way
I
may
in
take as given a
which describes how variables other than deficits and
discussed below.
S*
=
s*(
The
precise
In the absence of
deficits, true private saving,
(1)
and
private saving,
influence
inflation influence private saving.
s*(
deficits
)Y*,
S*
,
is given
specification
of
inflation and government
by:
3-
where
The distinction between true and reported
is true income.
Y*
saving and
income
influences
the
has
with
do
to
measurement
those
of
way
the
in
which
variables;
inflation
is
it
defined
precisely below.
1.
Government Deficits
Under the Life Cycle Hypothesis (LCH) people are assumed to
utility subject to a lifetime budget constraint.
occurs
maintain
to
consumption
at
wealth rather than current income.
LCH
that
is
consumption
should
maximize
Saving or dissaving
level reflecting life cycle
a
An important implication
the
of
be independent of transfers which
leave life cycle wealth unchanged.
Government deficits appear to
By issuing debt,
scheme.
consumption
proceeds
of
consumption.
value
repaid.
to
or
of
the
the
such
plans
debts.
Thus,
under
the
LCH,
if
are initially optimal, recipients of the
governments
borrowing
will
not
change
their
Instead, they will increase their saving by the present
additional taxes they expect to face when the debt is
As long as the government deficit does not
from
transfer
intertemporal
the government borrows against the future,
and it must generally repay its
private
one
be
those
alive
discount future taxes at the
at
the
rate
time
of
transfer
wealth
of the deficit, and people
interest
on
the
debt,
present value of the taxes must equal the amount of the deficit.
the
4-
The fact that government deficits generate future taxes
not
may
so
was recognized by Patinkin [1965, pp.
wealth
private
increase
and
288-294]. (1> He assumed that a fraction
of
was
debt
the
fact
in
The present value of the requisite
treated as wealth by its holders.
taxes may be less than the value of the government deficit if
future
future taxes are shifted to future generations.
If,
for example,
the
paid
transfer is received solely by retired people and the taxes are
solely by income taxes on wages, such a shift may be obtained.
Recently, however, Barro [1974] has shown that the current generation
may correctly discount
future
all
solely on their descendants.
taxes,
including
those
levied
His result depends on intergenerational
utility of the appropriate form, an unbroken chain of descendants and
the
absence
constraints
of
Barro's analysis has been
[1976],
While the relevance of
bequests.
challenged
among
by,
others,
Feldstein
Drazen [1978], Buiter [1979], Buiter and Tobin [1979], Tobin
Tobin
and
[1980]
on
Buiter
and
[1980],
remains
it
an
important
proposition.
people
The above discussion
suggests
government
as intertemporal transfers,
deficits
that
induce offsetting private saving.
intertemporal
transfers
is
adding
is appropriate,
of(l)
<5
that
a
coefficient.
a
do
in
fact
treat
the deficits should
Furthermore, the reaction to
pure
independent of the underlying forces of
growth and tastes which determine the
suggests
if
private
savings
rate.
This
term of the form 6*D* to the right hand side
where D*
is
the true
government
deficit,
and
The LCH without Barro's bequest motive suggests
-5-
that
must lie between zero and one.
<S
that
analysis
Barro's
suggests
should be unity regardless of the government's attempts at
5
Rewriting (1) to take the effect
intergenerational tax shifting.
of
deficits into account, true saving should be given by:
S*
(2)
=
(s*(
It should be
emphasized
offsetting
saving
consumption
consumption is not a
schemes.
programs,
substitute
perfect
induce
than
simple
finance
government
and
government
if
consumption,
private
for
not
may
other
deficits
If
transfer
that
deficits
something
are
they
if
rather
government
that
transfer
intertemporal
6D*/**)Y*.
+
)
deficits would not influence savings in the manner discussed above.
3.
Anticipated Inflation and Measured versus True Income
In the presence of
assets
persistently
inflation.
by
a
income
lose
a
households
and
fraction
of
in
nominal
interest
rates
as
holding
in
to
this loss is offset
expected
While the increased nominal interest payments are counted
in
the national income accounts, no entry is made for the
a
reconciliation
Though
just
the
same
manner
loss
the
in national balance sheets,
entry
anticipated component is more appropriately considered
income,
nominal
wealth
real
incorporate
to
anticipated loss in value of nominal assets.
appear
their
To the extent that it is anticipated,
rise
inflation.
as
inflation firms
as
nominal
a
does
the
component of
interest.
In
this
-6-
measured
interpretation,
income
overstated by the amount of the
is
equivalently
anticipated capital losses or,
interest income due solely to anticipated inflation.
also
may
overstated,
be
of
Measured saving
no account is made for the capital
since
holders
losses suffered by the
component
the
by
,
of
nominal
assets.
why
(Reasons
saving may not be overstated are discussed below.)
Several authors have estimated the magnitude of the
capital
losses.
for the United States
Their estimates suggest the bias may be large;
Siegal [1979] estimates the true private saving rate to have been 200
points
basis
lower
than
the
reported rate in the postwar period,
while Jump [1980] estimates the average difference to
ponts for the personal saving rate.
and
Masera
1000 basis
points
countries
suggest
[1980]
the
in
Calculations for Italy by Cotula
that the difference could be as much as
Results
seventies.
including Italy) reported by Blades and Sturm [1982]
(not
how
show
I
OECD
several
for
indicate an average difference of roughly 350 basis points.
section
basis
150
be
mismeasurment
the
effect
this
In
be explicitly
can
incorporated into the analysis of saving rates.
people
assume that
I
subtracting
a
fraction
reported income,
interest
losses are
the
A
Y
income)
T e G,
estimate
,
the
reported saving,
TT
e
income
true
and
saving
is the
full
S
.
amount
of
nominal
Their expected capital
anticipated rate of inflation
and
nominal value of government debt held by the private sector.
is the
by
their expected capital losses from their
(which includes
and
where
of
their
fraction of the loss subtracted from reported
income
G
If
and
-7-
saving,
individuals perceive their true income and saving to
y*
=
Y
-
XifG
S*
=
S
-
At^G
Substituting these expressions for Y* and S* in
S -
(3)
Att«G
=
(s*(
The measured savings rate,
S
(4)
It
=
D* = D -
)
true
than
=
S/Y
deficit
into
-
Aff
e
yields
G).
is then given by;
,
e
A^ G/Y)
"
the
and
(4)
A^ e G/Y.
+
income
to
Defining
terms.
substituting
Att^G,
+
6D*/Y*)(1
+
express the
is useful to
rather
(S*(
s
8D'/Y*)(Y
)
(2)
be:
ratio
true
in
measured
deficit
combining
to
like
be
terms
yields:
(5)
s
It can be seen
=
S*(l -
e
A^ G/Y)
+6D/Y
+
A(l
- 6)tt s G/Y.
from (5) that the private saving ratio
will
rise
or
fall with anticipated inflation to the extent that government debt is
regarded
as net wealth.
If debt holders
completely disregard future
-8-
(6=
taxes
inflation
their real wealth can be maintained
0),
only
by
increasing
increased nominal interest
added
If,
to
saving
payments.
Since
increments
equal
(
=
6
tax
measured
the
1),
will tend to fall with anticipated inflation.
case inflation reduces both the value of the debt and
future
are
the future tax liabilities associated with the
government debt are completely capitalized
rate
of
savings and income the measured savings ratio rises.
both
on the other hand,
savings
face
amount of the
full
the
by
the
in
liabilities;
the
individual's
In
value
the
wealth
net
this
is
of
thus
unaffected, and no increase in to private saving is called for.
4.
Other Effects of Inflation
Equation (5) describes the impact of neutral,
on
the
private
savings
rate.
What
anticipated
happens
inflation
inflation is not
if
neutral, or if it is unanticipated?
Non-neutral inflation has no effect on the savings rate
i)
its
non-neutralities do not affect the function s*(
they are permanent.
more detail below;
income.
As
of
)
is
in
real
inflation
many real effects, some of which may influence
favor capital formation
ii)
discussed
essentially, however, it reflects growth in
growth of income.
as
and
),
pointed out by Fischer and Modigliani [1979],
is likely to have
rate
The nature of the function s*(
long
as
the
Among them are factors which tend to both
(as an alternative to holding money),
inhibit
capital formation (due to the taxation of purely nominal gains;
see
Feldstein [1982], Feldstein and Summers [1978] and Summers [1981] for
-9-
affect
and
analysis)
supply
the
labor
of
taxation of nominal rather than real
progressive
(through
The
income).
impact
net
of
these factors is unclear.
Non-neutral inflation has an added impact when its real
to be temporary.
perceived
If
to be maintained in the future,
diminish
but its real effects are expected
dissave
can be expected to save or
are
given rate of inflation is expected
a
the tax system is indexed),
say,
(as,
effects
spread
to
to
life cycle consumers
the
impact
the
of
temporary nonneutrality over their lifetime.
addition
In
generates
a
the
to
is
of
listed
redistribution
depends
on
differences
analysis.
Thus
between
redistributions
corporations have no effects by assumption.
private
sector
aggregated
appears
between
households
and
between
the
Transfers
(given government
explicity
in
this
expenditures).
formulation,
unanticipated inflation should be accounted for.
remains
in
and the government should be reflected in changes in
the government deficit
deficit
the
in
Since the corporate sector
the gainers and the losers.
owned by the household sector, the two sectors are
this
inflation
unexpected
above,
redistribution of wealth between creditors and debtors.
The impact of this
behavior
effects
this
Since
the
effect
of
sector
The foreign
unaccounted for but, since it is relatively small, transfers
it
and the rest of the economy are unlikely to have
influence on private saving.
a
large
-10-
Deaton [1977] has suggested that,
inflation
unexpected
effects,
the
addition to
in
saving because it is
influence
may
confused by consumers with relative price changes.
to
according
high,
unexpectedly
this
redistribution
inflation
If
is
story, consumers mistakenly
interpret price changes as relative price increases, and reduce their
Deaton concludes that evidence from the
consumption.
this
supports
supporting evidence
in
for
that
while
Viren
inflation
actual
and
institutional
components
unexpected
affect
may
the
difficult to estimate
knowledge
To
due
to
effects
effects
other
of
impact beside that due
effects
to
arise
inflation
of the structure of an economy.
other
the
the
may have opposite effects.
These considerations suggest
knowledge is employed in this study.
the
that
varys both across countries and over
which
structure
time in any single country.
quantify
find other
appears
Moreover, it
complicate matters further, these additional
detailed
[1982]
reasons other than mismeasurement of income, it does not
unambiguously sign their direction.
expected
and
States
several OECD countries.
This discussion suggests
saving
Koskela
hypothesis.
United
-
mismeasurement
disguise the mismeasurement effect.
if
would be
even
with
In fact no such
Yet it is important to
inflation
of
it
try
to
it has a consistent
of
income,
it
may
)
-11-
For this reason a simple linear inflation term is
added
to
to
(5)
yield:
(
where
S
If
consumers,
capital
(
1
A^ e G/Y
-
)
+ 6
D/Y
+ A
(
- 6
1
stock
and
which
non-neutralities
should
4>
unanticipated
)
t^g/V +
<jm
is taken
<f>
,
to
be
a
inflation in fact predominantly reduces income growth,
temporary
has
*
the actual rate of inflation and
is
tt
constant.
or
=
S
6
be
negative.
supply
labor
reduce
with
rise
of
the other hand, the
on
If,
income
the
inflation,
the
or
component induces gives rise to the Deaton effect,
4>
may be positive.
5.
The Real Savings Function s*(
The precise nature of s*(
focus
on
the
)
based
unspecified
has been left
role of government debt and inflation.
been accomplished;
s*(
)
).
in this section
I
describe
on the life cycle hypothesis.
the aggregate savings rate under the LCH
-
a
in
order
to
That goal has
specification
of
Two features account for
the asset to income
ratio
and the rate of growth of income.
Early work on the LCH by Modiglia'ni and Brumberg emphasized the
of
income
growth
in
the
determination
of
role
equilibrium aggregate
saving. <2) Further work by Tobin [1967] and Modigliani
and 1975] explored the relationship in more detail.
[1966,
1970,
The link depends
-12-
the
on
observation
retire and
that individuals generally choose to
that the retirement wealth must
consume their accumulated wealth, and
Growth in income then tends
years."
be accumulated during the working
or
increase the proportion of savers,
to (but need not neccessarily
relative to the
wealth,
with higher desired retirement
those
Only if the consumption of
dissavers. Aggregate savings thus rise.
is high relative to the saving of
the young (those below working age)
association between growth and
those of working age will the positive
absence of
There should be no net saving in the
saving be broken.
wealth
since the aggregate stock of
income growth in any case,
3
in that case
demanded by life cycle savers is constant
)
(
)
and
[1969]
Leff
[1982],
Modigliani [1970], Modigliani and Sterling
the two
investigated the relative contribution of
Ram [1982] have
and productivity growth.
sources of income growth, namely population
issues discussed here, so only
This breakdown is not relevant to the
total income growth will be considered.
security and differences
Feldstein has emphasized the role of social
determining the desired stock of wealth
in
retirement behavior
in
generally true that longer retirement
is
upon retirement.'- It
of saving (for any given rate
should be accompanied by higher rates
requires
This is because longer retirement
of growth of income).
while working, which
greater stock of wealth be accumulated
that a
tends to magnify the impact of growth.
6
5
.
,
-13-
Social security has two effects in Feldstein's analysis;
reduce private saving by replacing private wealth
it
earlier
induces
which
retirement,
While Feldstein and others
saving.
effect
of
tends
accumulation,
to
found
social security is to reduce private saving,
(
>
This discussion suggests that the private savings ratio should
savings
The function should conform to the
rate
implication
s*(
measures
the
income, and the
should
be
=
)
length
s
=
positive,
g*(ot
of
qB
+
(7)
+
+
and
retirement
a 2 R)
benefit
security
retirement,
a's coef f icients.
Substituting from
(8)
g*(a
social
the
is
B
the
that
A specification which fits these requirements is:
social security.
where
a
zero in the absence of income growth, and that the
be
response of saving to income growth should depend on
(7)
be
income growth, length of retirement and social security
of
benefits.
net
the
its impact is
theoretically ambiguous and difficult to verify empirically
function
and
increase private
generally
have
it tends to
while
a
(
>
income
R
ratio,
the rate of growth of real
g
According to the LCH,
should
1
to
lie
between
and a
a
and
-1
0.
into (6) yields the complete equation:
a,B + a 2 R)
U
-
ATTe G/y)
+
5
D/Y +A(1
-
6
)
^G/Y
2
+
-14-
ESTIMATING THE PARAMETERS
III.
1.
The Approach
In the next
section the parameters
saving
-j
,
$
A
,
and other data.
and
,
estimated
are treated as coefficients to be
aggregate
pt
of equation
(8)
observations
of
6
using
Before doing so, however,
it
must
be recognized that coefficients estimated using equations of the form
(8)
are vulnerable to two important criticisms.
The
first
that
is
observations on realizations of the relevant variables do not reflect
expectations of agents who make the saving decision.
the
is that the
parameters themselves are implicit
parameters
the
and
structure
criticism implies that,
model,
their
if
of
a
The second
functions
This
model.
larger
reflecting
agents are aware of the structure
second
of
the
responses to policy changes will induce changes in the
values of the parameters.
Finally, the source of the error term must
be carefully specified.
The second criticism, originating with Lucas [1973]
monetary
policy,
is
relevant
to
the
extent
with
that
coefficients differ from the values implied by theory.
of
anticipated
of
their
the estimated
the
In
budget
constraints.
that
If
agents
are
their predicted values,
the
budget
case
completely
agents are aware of their
budget constraints and the estimated coefficients are different
of
to
capital losses, government deficits, social security
and income growth the analysis assumes
aware
regard
it
is an
from
indication that there are components
constraint that are not adequately modeled.
In
that
-15-
case,
since sources
policies
understood,
the
failure
of
which
attempt
to expoit the coefficients may
of
have unexpected implications.
inflation
to
alone
are
In the case of changes in
capital
the
(not
model
the
losses
estimated coefficient is likely to unstable.
This
saving
may
it
well
not
due
imply) the
because
is
any
large impact of inflation is likely to be due to nominal institutions
which will adjust to continued inflation.
The first criticism, that realizations do not
is
likely to be more of a problem.
hand
side
of
expectations,
All of the variables on the right
cyclic and other temporary fluctuations
exhibit
(8)
reflect
which are presumably not relevant for the life cycle planning
assumed
approach
The
here.
nonoverlapping averages of annual
relevant
in
taken
data
here
to
represent
to the life cycle planning decisions.
terms of information lost in the averages, it
likely
reveal
to
to
is
models
take
the
long,
outcomes
While this is costly
is
more
certainly
the relevant secular trends than using each anual
observation.
2.
The Error Term
There are two sources of error in equation (8).
The variables may be
measured with error and the specification, particularly the real life
cycle component s*(
the
general
explanatory
component
)
errors
variables
may be specified incorrectly.
in
are
variables
measured
associated with s*(
).
problems
with
which
error,
I
ignore
will
arise
except
Errors associated with s*(
if
the
for
the
)
cause
-16-
particular problems because of the nonlinear nature of the model.
The measured LCH savings function,
is
only
s*(
approximaton to the true function s**(
an
the approximation introduces
an-
error term
and the true savings ratio equation (8)
(9)
where
Si
n,
=
+
(s*
-
fii)(l
is the residual
notation
postulated in
)
has
also
*CIh)
+
6DEFi
e 1f
section
1.5,
Suppose that
).
so that s**
=
+
s*
changed
i
,
is given by:
+
c^-n-i
+
\(1
-6
)CL,
+
ry,
,
arising from measurement error in Sj.
been
e
for simplicity:
(The
CL refers to the
capital loss to income ratio and DEF the government deficit to income
ratio.)
Combining the errors into
a
single term
d
,
the sum of
the
residuals associated with (9) is given by:
(10)
=
C,
e,
(1
- ACL,)
From (10) it can be seen that the
correlated
with
postive sign.
capital
the
n,- .
residual
loss
^
variable,
will
be
as long as
This is likely to produce estimates of
negatively biased.*
negatively
A
has a
which
A
are
12)
Two stage least squares is the
situation.
+
However,
considered exogenous
natural
technique
to
use
in
this
not all the other explanatory variables can be
-
both the government deficit and
the
rate
of
3
-17-
are likely to respond to aggregate demand and saving.
inflation
The
length of retirement is also endogenous, but forms a recursive system
with the savings ratio equation and so may be
(as
long
as
residuals
the
retirement
the
of
treated
equations can be taken to be independent).
exogenous
as
and savings ratio
remainng
The
variables,
real income growth and the social security replacement rate are taken
to
Though
exogenous.
be
they
may
reflect
interaction with income and saving, it is likely to
instruments
used
are:
a
unit
vector,
simultaneous
some
small.
be
variables
demographic
reflecting the age compostion of the labor force,
and
The
the
rate
of
change of claims against the government held by the central bank.
A further complication is arises from the likely correlation
error
associated
with
each country over time.
technique
contexts.
technique
in
Three stage
least
squares
is
the
this case, as it exploits the information
available in the correlation across residuals as
well
the endogenous variables by their two-stage projection.
IV.
An
which takes this correlation into account will
yield more efficient estimates.
appropriate
the
This corresponds to
the problem of autocorrelation arising in time-series
estimation
of
replacing
as
(
1
)
THE DATA
Data from an international cross-section of 20 OECD countries is used
to estimate the parameters of the aggregate savings function. (7)
data
The
is collected within a standardized system of national accounts,
which should yield at least broad international comparability.
It is
-18-
generally available for the period 1960
-
Income, saving, and price
are
Private
savings
(CPI)
both
include
data
sum
the
consumption
of
from
household
OECD
the
corporate
and
[1982].
savings,
Disposable income is defined
calculated on an expenditure basis.
be
1979.
expenditures
and private saving.
measured private savings ratio is simply the ratio of private
to disposable income.
than
standard
way
adjusting
of
saving
international
on
indicates
the
that
depreciation.
for
basis is the only
Work by Blades and
Sturm
international rank ordering is at least
preserved by sensible adjustments for
However,
Hayashi's
[1982]
indicate
that
distinction
the
data
expenditure
an
feasible approach with the available data.
[1982]
saving
While this is a measure of gross saving rather
computing
Similarly,
The
appropriate net of depreciation measure, there is no
more
the
to
purchases
estimates
recent
of
durable
for the United States
consumption
between
goods.
flows
and
expenditures may be an important one.
The annual rate of growth of real
income
natural
current
logs
of
the
ratio
of
is
calculated
by
taking
to lagged real disposable
income.
The government deficit data is from the
defined
to
of
OECD
source,
and
is
be the difference between government expenditures on the
current account and its receipts.
saving
same
both
central
This includes the current
account
and state and local governments as well as
public social security programs.
It excludes government expenditures
-19-
on the capital account,
since they are unlikely to represent a future
tax burden.
Government debt data is from the International Monetary
whenever
though
available,
some
for
gathered from national sources.
<9)
countries
[1982]
the debt data was
appropriate
The
Fund
measure
of
the
debt for our purposes is general government debt (net of debt
public
held by the government)
held
domestically.
however,
Often,
only
central government debt was available, and it was often impossible to
calculate
fraction held by the private sector.
the
introduce biases which appear to be
small
and
These omissions
of f setting.
(
10
)
The
actual capital loss is measured by taking the ratio of the product of
the
rate of inflation and the public debt to nominal income;
actual
the expected rate is taken to be the average of the actual loss.
length
of
the work of Modigliani and Sterling.
The
social security benefit data is taken from the ILO's publication
The
Estimates
retirement
Cost
of
the
of
are
Social
social
based
on
Security
aggregate pension benefits.
relative
security
(various
benefits
issues)
and
and
the
is
per
To estimate the benefits
to income per worker,
measure of
a
recipient
the aggregate pension to income ratio
is divided by the ratio of nonworking males above 65 to active males.
This population ratio is chosen to represent as closely
the
as
possible
number of social security recipients relative to those expecting
benefits;
data based on those concepts is unavailable.
[1978] has made
replacement
rate
more
detailed
estimates
for twelve countries.
of
the
Haanes-Olsen
social
security
These estimates suffer from
-20-
Most importantly
several drawbacks.
ratio
measure
they
workers in manufacturing only.
for
an alternative source for comparison.
They do, however, provide
00
The retirement variable is the ratio of the
participation
rates
replacement
the
change
in
labor
those in the 50-54 and 65+ age groups,
between
relative to the participation rate of those in the 50-54
The
participation
rates
are
measure
based
is
,
published
the
by
retirement age in the United States by Reimers [1976];
it
represents
an adjustment to the life expectancy at retirement (which is
constant
across
retire at 65.
assumed
to reflect the fact that not all people
countries)
An increase
ILO.
techniques used in the analysis of
the
on
group.
age
those for both men and women, and are
taken from the Yearbook of Labor Statistics
This
force
in
R
signifies
an
increase
in
the
duration of retirement.
Summary statistics for the data used in this study are
the
tables
below.
Table
1
presented
in
shows the means and standard deviations,
tables 2A, 2B and 2C show various correlations, and in
table
3
the
correlations between the capital loss variable and its components are
examined in detail.
-21-
Table
1.
Means and Standard Deviations of the Data.
Variable*
-22-
Table 2B
.
Correlations Among the Variables in the Second Period.
s
g
DEF
CL
B(I)
1
s
0.35
g
B(I)
-0.34
-0.42
R
-0.39
-0.47
0.50
CL
0.04
-0.11
-0.04
1
1
-0.12
1
0.31
77
0.49
DEF
Table 2C
.
0.40
-0.35
-0.24
0.52
Correlations Among the Variables Between Periods.
Variable
s
Correl.
Table
3
0.81
.
g
0.49
B(
I
0.89
)
R
0.94
CL
0.87
Correlations Among CL and its Components.
77
0.23
DEF
0.91
-23-
The summary tables reveal
familiar
a
story.
income
Real
growth
declined, on the average, by more than 25 percent between the sixties
and
seventies;
the
inflation more than doubled, as did the capital
losses (relative to income) suffered by the private sector.
social security replacement rate (however
fraction
income
of
government
retirement
and
Government deficits on the current account as a
considerably.
rose
measured)
Both the
deficits
fell
noticeably.
reflects
the
The
fact
entry
negative
that,
for
on the average, the
general government sector was a net saver.
The savings ratio increased on the average between the
periods,
two
contrary to popular perception.
The summary table conceals one remarkable observation.
22
percent
Japan,
whose
savings ratio matched its 9.5 percent income growth rate
in the sixties,
experienced a dramatic drop in its rate of growth
income
is
(which
of
expected to be permanent), yet slightly increased
appears,
This
its savings ratio to 24 percent of disposable income.
at least, to be inexplicable according to the theory developed here.
V.
PARAMETER ESTIMATES
Estimates of equation (8) are given
coefficients
set,
are
in the left
reported
for
in
table
4. <14)
Two
each restriction tested.
side of each column, are estimates
for
sets
of
The first
the
second
-24-
period.
second
The
set,
estimates for the second period.
the
right
the
in
side of each column, are
(Estimates for each period
reflect
correlation between the residuals of the two periods in the 3SLS
When the coefficients are constrained to be equal
results.)
the
in
two periods their common value is given in the center of the column.
In addition to
measures
of
the
coefficients
goodness
of
their
and
standard
fit are presented.
The first,
labelled "COR", is the correlation between the
the
reported
R2
squares regressions;
unlikely
to
reported here.
squared
this statistic
appropriate
in
nonlinear
the
The second measure, ln(WSSR),
This is just
ordinary
least
weighted estimation
is the weighted sum
of
used as the basis for the chi-square test derived
Jorgenson [1979].
in
in
using
reported here because the conventional R 2 is
meaningful
be
residuals
in Gallant and
it
measure
two
in the row
values
fitted
coefficients and the dependant variable.
the square root of the
errors,
the
The difference between the value of
restricted
unrestricted
and
estimates
is
distributed chi-square with degrees of freedom equal to the number of
restrictions.
In all cases the social security variable
Haanes-Olsen
different
measures
slopes
but
discussed
above.
specification
because
it
was
The
mixture of the ILO and
two
measures
have
are constrained to have the same intercept, a
specification similar to that employed by
The
is a
not
gave somewhat more
rejected
by
reasonable
those found using the ILO data alone.
Modigliani
the
and
Sterling.
data, and was chosen
parameter
estimates
than
-25-
The residual covariance matrix is estimated using the 2SLS
the same matrix is used in all the restricted estimates.
from (4.1);
In the first column of table 4
over
estimated
the
impressive, averaging a
relative
the
to
equation
(4.1),)
independently,
using
In (4.2) the analogous 3SLS
efficiency
The
(equation
periods
two
two-stage least squares.
reported.
residuals
25
gains
due
percent
the
to
reduction
is
nonlinear
estimates
3SLS
in
(8)
are
technique are
standard
errors
This reflects the relatively high
2SLS estimates.
correlation between the residuals in the two periods, estimated to be
roughly 0.47.
The
unrestricted
coefficient
disappointingly insignificant.
and
.6
estimates
Only
a
themselves,
however,
in the second period,
and
are
x
in the first period are estimated to be more than twice their
standard
errors.
The shift in the coefficient estimates between the
2SLS and the 3SLS estimates is also surprising though,
large standard errors,
not
is
significant.
The
in view of the
changes
in
the
coefficient values also markedly reduces the explanatory power of the
equation
the
in
second period, as measured by COR.
One reason for
this weakness is the large number of parameters estimated.
little
reason
to
believe
that
the
between the sixties and the seventies.
tested
by
two periods.
constraining
There
is
behavioral parameters shifted
In (4.3)
this restriction
is
all the coefficients to be equal across the
-26-
The data do not support the restriction that all the coefficients
(8)
The chi-square value at the the 99 percent
are equal over time.
level with
degrees of freedom is 22, while the test
8
specification
(4.3)
nearly
is
Apparently
25.
statistic
have
there
imposing
all
restrictions
equality
the
yields
for
been
significant shifts in coefficient values between the two periods.
fact,
of
In
negative
a
between the fitted values of the savings ratio generated
correlation
by (4.3) and the actual values in the second period!
This conjecture is supported by
(4.4).
estimates
the
reported
in
column
In this case the social security and retirement variables are
constrained
be
to
equal
in
the
two periods, while the remaining
This
specification
coefficients are free to
vary.
rejected
percent
level,
but
greatest
number
of
equality
estimates
in
(4.4)
the
at
95
specification shows the
accepted
by
the
data.
disappointing, however.
The
accepted
marginally
at
the
99
restrictions
remain somewhat
The social security and retirement variables
remain quite weak, and the constant term
the two periods.
is
shifts
puzzlingly
between
The explanatory power of the equation in the second
period also remains very low.
The capital loss, government deficit and pure inflation
tell a somewhat stronger story.
the
period
first
The coefficient on capital losses in
is almost precisely unity,
zero and insignificant in the second period.
though it remains near
The government deficits
variable shows a similar pattern, but it is large
negative
in
the
first
period,
coefficients
and
significantly
contrary to the predictions of the
-27-
The pure inflation coefficient,
theory.
the
periods
two
and
quite
is
consistent with the reservations
weak
$
changes
,
in
expressed
sign
This
both.
earlier
between
pattern is
concerning
the
stability of this coefficient.
The theoretical and empirical weakness of the pure inflation variable
suggests that it should be constrained to zero,
is reported in
the data.
chi-square
The zero restriction on
(4.5).
statistic
The test
statistic
at
the
degrees of freedom is 11.07.
effect
is
the
a
only
has
95
value
a
percent
This suggests
significant
channel
specification which
is not
<f>
rejected by
while
10.62,
of
confidence
that
through
level with
capital
the
the
5
loss
which inflation
affects private saving.
The impact of these restrictions is most noticeable
loss
coefficients.
and
its
the
capital
The first period coefficient falls by 25 percent
(as does its standard error),
rises,
on
while
the
second
period
coefficient
Both the social security and
standard error falls.
retirement coefficients rise in magnitude, though they fail to become
significant.
The restriction has little
impact
on
government
the
deficit coefficients, which continue to have the wrong sign.
The fact that the capital loss coefficients are much closer
that
an equality constraint may be appropriate.
imposed in (4.6).
suggests
This restriction is
It is rejected at the 95 percent confidence level,
but accepted at the 99 percent level.
The capital
drops to 0.58 with a standard error of 0.20.
loss
coefficient
-28-
Two polar cases are tested in equations (4.7) and
the
capital
capital
barely
but
This restriction is rejected at the 95
restriction,
at the 99 percent level.
accepted
coefficient
loss
constrained
is
(4.8) the
This
zero.
be
to
In
percent
with the zero restriction on the other
combination
in
(4.7)
coefficient is constrained to be unity, the value
loss
predicted by theory.
level,
In
(4.8).
effects of inflation, implies that inflation has no impact on private
saving.
It
is
rejected at the
99
percent
confidence
level.
The
explanatory power of the equation also falls steeply in both periods.
2.
Discussion
The results presented in table
puzzling
4
reveal
consistent,
a
if
somewhat
The major puzzle revealed is the inability of the
pattern.
version of the LCH analyzed here to account for the upwards shift
private
savings
ratios
between the sixties and the seventies.
in
The
shift appears as an unexplained but significant shift in the constant
This analysis is also
term in all the equations reported in table 4.
unable to explain as much of the variation in the saving ratio in the
seventies as in the sixties.
the
world
economy
during
This may reflect greater turbulence
the seventies, suggesting that short run
forces played a greater role in that
retirement
-
period
than
the standard life cycle variables
Furthermore,
in
have weak coefficients.
As
shown
-
the
in
sixties.
social security and
in
(4.8),
however,
this is consistent with earlier findings of strong effects in studies
in which the impact of capital losses was neglected.
is
explicitly
accounted
for,
If
this channel
however, the social security and life
5
29-
cycle variables appear to have only a weak influence.
Capital losses have the expected saving-inducing effect.
however,
complete (it is estimated to be 0.58 when the
is not
effect
constrained to be equal in the two periods), and is much stronger
is
in
The effect,
the 1960-69 period than the 1970-79 period.
This
surprising,
is
the capital losses were a much higher proportion of income in the
as
The weaker effect observed in the
second period.
explained
by
persistent underestimation of inflation.
is underestimated capital losses are
overestimated;
these
phenomena
coefficient on average actual
inflation
is
seventies
underestimated
tend
capital
and
reduce
to
If
may
inflation
income
and
saving
Underestimation
losses.
be
is
the
of
also consistent with the negative ex-post real rates of
interest widely observed in the seventies.
The saving-inducing affect of inflation
consistent
with
induced
capital
losses
is
the estimates of the impact of government deficits.
Private saving does not increase with government deficits, indicating
that people do not anticipate paying taxes on the debt in the future.
In fact, private saving appears
deficits
in
the
first
bonds
must
be
least
paid
a
off
not consistent with the
is
fraction
in
with
correlated
negatively
This
period.
prediction of the LCH that at
government
be
to
future
of
the
taxes.
value
of
While the
importance of anticipated taxes has been empirically verified by only
a
few authors, the lack of support for a role
taxes found here is startling.
with
a
(
1
>
.
of
future
of
future
Though this result is consistent
negative correlation induced by countercyclical policy, that
-30-
spurious correlation should have been
Once
procedure.
again
this
eliminated
in
the
two-stage
effect is significantly weaker in the
seventies.
Finally, the data cannot reject the hypothesis that inflation has
consistent
effect
loss channel.
on
private saving other than through the capital
These other effects are likely to arise largely due to
nominal institutions which
Apparently
no
should
adjust
to
continued
inflation.
there is so much institutional variation across countries
and time that the other effects cannot be discerned in this sample.
These
observations
observation.
The
are
not
estimates
unduly
influenced
obtained
when
by
Japan
the
is excluded are
similar to those shown in table 4, except that the upwards
the
constant
term
is
insignificant,
retirement terms are much stronger.
and
shift
in
the social security and
The negative correlation between
government deficits and private saving in the first
much stronger.
Japanese
period
is
also
-31-
V.
CONCLUSIONS
The results reported in this paper support the following conclusions:
+
Anticipated
compensating
capital
losses
nominal
on
assets
induce
increases in saving, though not by the full amount
predicted by the life cycle hypothesis.
+
Contrary to predictions of the life cycle
deficits
do
saving.
There
theory,
government
not appear to be associated with increased private
is
evidence
that
government
deficits
were
associated with reduced private saving in the sixties.
+
Inflation has no consistent affect
on
private
saving
other
than via the capital losses on nominal outside debt.
+ The
relationship between
saving
is
somewhat
cycle
life
unstable.
justification for the magnitude
savings rate in the seventies.
of
variables
There
the
is
upward
and
no
private
theoretical
shift
in
the
However, the significance of the
shift is largely due to the Japanese observation.
+
Estimates of the effect of social security and retirement
highly
correlated
with
induced capital losses.
security
and
retirement
estimates
If
of
are
the impact of inflation
these losses are
neglected,
social
appear to be stronger determinants of
private saving than if the losses are correctly accounted for.
-32-
FOOTNOTES
1) Christ [1957], in a review of the first edition of Patinkin's
book, attributes the recognition that government deficits
imply
increased future taxes to discussions with Milton Friedman.
2)
19
The Modigliani-Brumberg piece referred to here was written in
but not published until 1979.
,
See Appendix A
results.
3)
for
a
more
detailed
derivation
of
these
Initially in Feldstein [1974].
Feldstein has estimated the
in
international cross-section in
impact of
social security
in
Feldstein's time-series
[1980].
[1977] and most recently
analysis for the United States has been more controversial;
see
Leimer and Lesnoy [1982] and the references cited there, as well
as Feldstein's response [1982].
4)
5) See Modigliani and Sterling [1982] for a demonstration of the
empirical difficulties with cross-section estimates, and Leimer
and Lesnoy for difficulties with the US time series.
6) The specification (7) is slightly different from that used in
Modigliani and Sterling. This is because
income growth was
decomposed into its productivity growth and labor force growth
components in that paper, and the length of
retirement entered
in the growth of the labor force terms.
7)
See Appendix B for the data.
for
Denmark are an exception.
8) The income and saving date
Recent data for Denmark are unavailable from the OECD, and an
examination of the Danish statistical yearbook revealed large
differences from the OECD's exstimates. Since the Danish debt
data are taken from Danish sources, I decided to use the Danish
Statistical Yearbook throughout.
Denmark, the United
9) Data from national sources was used for:
Kingdom, and the United States.
For Denmark and the United
Kingdom their statistical yearbooks are the source;
for the
United States the Federal Reserve Flow of Funds Accounts were
used.
In all cases for which a comparison could
be
made
(Japan,
the United Kingdom and the United States) the IMF estimates were
quite close to that obtained in more detailed examination of
10)
national sources.
comprehensive discussion
11) See Modigliani and Sterling for a
of the various possible measures of social security benefits.
-33-
12) The appearence of CLi in the error term may
also introduce
heteroskedasticity;
this potential
source of inefficiency is
ignored.
13) See Theil [1971, sec.
10.6] or Kmenta [1971,
13-4],
sec.
The equations are also weighted by the square root of their
population in each period to correct for heteroskedasticity
introduced by population size differences.
14) Table 4 appears at the end of the paper.
15) Kochin [1974] and Barro [1978] are the only two studies with
which I am familiar that have claimed to test directly the role
of
government deficits in inducing private saving and found
confirming evidence. However, see Buiter and Tobin [1979] and
Feldstein
respectively for a critical analysis of
[1978]
articles.
"
,
-34-
APPENDIX A
determine the implications of the LCH for
saving
behavior is to sum across individuals to obtain
aggregate
and subtract to obtain
income
and consumption,
aggregate
which
can
then
be
related
to characteristics
aggregate savings,
consumption
function.
of the individual's
A simple way to
Aggregation proceeds particularly simply in a world in which
population and productivity growth (defined to be growth in per
Let y(a,t-a)
denote per
capita income are exponential trends.
and
income of an individual aged a at time t
capita labor
describing the probability of
function,
m(a) the mortality
The number of people of age a at
surviving until year
t
The exponential
time t
n(a,t), is then given by m(a)B(t-a).
and n(a,t~a) may be
imply that y(a,t-a)
growth assumptions
written:
,
.
,
(Ala)
y(a,t-a)
=
(Alb)
n(a,t)
=
y(a)e 9<
t
"
a)
m(a)B(0)e p
(
*
a
>
where g and p are the rates of growth of productivity and
(Note:
represents total real
the labor force respectively.
g
the paper.)
In
assuming
growth
in
the body of
income
productivity and population growth of this type, I take the age
profile of earnings and mortality to be constant over time,
while productivity gains are strictly embodied.
Aggregate income at time t
of all those employed at time
Assuming that
wealth at t
w
and
and retire at age r
interest and
W(t)
rate of
aggregate income is given
t
,
.
,
,
(A2)
Y(t)
=
Y(t)
is the sum of the earnings
of
t ,plus interest on the stock
all individuals begin work at age
(fixed)
real
letting
P
be the
the aggregate stock of wealth at
,
by:
n(a,t)y(t-a)da
+
pW(t)
e <g+P>t m (a)y(a)e- (9+p)a da
where
B(0)
+
pW(t),
is taken to be unity without loss of generality.
W(t)
we proceed as
above by summing
In order to determine
An individual's
across individual's to obtain aggregate wealth.
net
w'(a,t-a)
wealth at age a
is given by the sum of his
interest
or her net saving at each age, discounted
to
reflect
charges and earnings.
Letting c(a,t-a) denote an individual's
consumption of age a at time t
and assuming people are born
and begin consuming at age
and do not survive beyond age
1
w'(a,t-a)
is given by:
,
,
,
,
P
P
:
,
-35-
w'(a,t-a)
(A3
[y(x,t-a) -
=
c (x,
t-a) ]e
px
dx
Under the LCH individual's are assumed to solve the utility
lifetime budget
problem
subject
their
maximization
to
constraint
U(c(x) )m(x)e~
max
(A4)
s.t.
m(x)c(x t-a)e"
f
x
P
x
dx
dx = e 9(t a) m(x)y (x)e"
x
dx
assuming for simplicity that the individual's rate of time
Given the additional
preference equals the interest rate.
each succeeding
assumption that tastes are constant over time,
generation will choose the same stream of consumption, up to a
proportionality factor reflecting per capita income growth at
Thus the wealth of an individual of age a of
the
rate
g
is given by:
cohort t-a
.
(A5)
where
w'(a,t-a)
c*(x,p)
=
e 9(t
-
a
>
(y(x)
-
))eP x dx,
c*(x,
represents the solution to (a4).
Tobin [1967] solved the maximization problem (A4) for a specific
utility function and under different assumptions to yield an
explicit expression for w'(a,t-a)
.
The aggregate stock of wealth is
individuals at time t
given
by
sum
the
over
all
:
W(t)
=
W(t)
=
n(a,t-a)w' (a,t-a)da,
or:
(A3)
+ p,a
+
[y(x)
e (9 p)t m(a)e- (9
-
c*(x?)
]e
?x
dxda.
The double integral in (3) is independant of time, implying that
same rate as
the
the aggregate stock of wealth must grow at
ratio is
income
to
wealth
so that a constant
aggregate income,
maintained.
absence of capital gains, saving is given by the time
Differentiating W(t) with respect to
derivative of wealth.
s
and dividing by income to yield the savings ratio,
t
In the
,
,
yields:
-36-
(A7)
s
=
(g+p)W/Y
Equation (A7) expresses the basic result reported in the text,
that the savings ratio increases with the rate of growth of real
However, the wealth to income ratio is also a function
income.
of the rate of growth of income.
It is
this dependancy which
makes the link between real income growth and saving ambiguous
income.
While the derivative of
at high rates of growth of
W/Y
likely to be small, its sign is ambiguous.
If income
is
growth and consumption while young are sufficiently high,
the
wealth to income ratio may fall as g + p rises.
-37-
REFERENCES
Barro, R. J., (1974) "Are Government Bonds Net Wealth," Journal of
Political Economy vol.
82, no.
6.
,
,(1976)
Political Economy
,
"Reply To Feldstein and Buchanen," Journal of
vol.84, no.
2.
Social Security on Private
(1978) The Impact of
Evidence from the US Time Series Washington, D.C.,
Saving;
American Enterprise Institute.
,
,
Blades, D.
and Sturm, P.
(1982), "The Concept and Measurement
Savings:
The United States and Other Industrialized
Countries," forthcoming in U.S. Government Policies Affecting
Predicted Impact and Lessons From Abroad Boston,
Saving:
Federal Reserve Bank of Boston.
,
of
,
"Government Finance in an Overlapping
Buiter, W.H.
(1979)
Generations Model with Gifts and Bequests," in Social Security
ed.,
Cambridge,
versus Private Saving G.M. Von Furstenberg,
Massachusetts, Ballinger.
,
,
A Brief
and Tobin, J., (1979) "Debt Neutrality:
in Social Security versus
Review of Doctrine and Evidence,"
ed.
Cambridge,
Von
Furstenberg,
Private Saving
G.M.
Massachusetts, Ballinger.
,
,
,
Prices,"
Christ, C.F.
(1957), "Patinkin on Morvey, Interest and
1.
Journal of Political Economy vol. LXV, no.
,
Public
"Private Savings,
Cotula, F., and Masera, R.
(1980),
Deficits and The Inflation Tax," Review of Economic Conditions
of Italy
no.
3.
,
Labor
Yearbook of
(various issues)
International Labor Organization.
ILO,
IMF,
Statistics
,
Geneva,
International Financial
(1982) Machine Readable Tape on
Washington, D.C., International Monetary Fund.
Statistics
,
Deaton, A.
(1977), "Involuntary Saving
Inflation," American Economic Review
Through
Unanticipated
,
Drazen, A., (1978) "Government Debt, Human Capital, and Bequests
vol.
86,
in A Life-Cycle Model," Journal of Political Economy
,
no.
3.
Funds Accounts, Assets and
of
Federal Reserve
(1982) Flow
Liabilities Outstanding, 1957 - 1980 Washington, D.C., Board of
Governors of the Federal Reserve System.
,
,
-38-
Feldstein, M.S.
Security,
Induced Retirement
(1974), "Social
and
Aggregate Capital Accumulation," Journal of Political
Economy vol.82, no.
5.
,
Security:
no.
A
in
Bonds and Social
,(1976) "Perceived Wealth
Comment," Journal of Political Economy vol. 84.
,
2.
Security and Private Savings:
(1977) "Social
International Evidence in An Extended Life-Cycle Model," in The
Economics of Public Services edited by M.
Feldstein and R.
Inman, London, MacMillan.
,
and Summers, L.,
and
the
Long-term
Interest
Washington.
(1978)
Rate,"
"Inflation,
Brookings
Tax Rules
Papers I,
in
The
Impact
of
"Reply,"
Social
(1978)
Security on Private Saving:
Evidence from the US Time Series
Washington, D.C., The American Enterprise Institute.
,
,
"International Differences in
(1980)
Security and Saving," Journal of Public Economics 14.
Social
"Social Security and Private
(1982)
Reply," Journal of Political Economy vol.
90, no.
3.
Saving:
,
Fischer,
and
"Towards
S.,
Modigliani,
F.,
(198?)
Understanding of the Real Effects and Costs of Inflation,"
an
Gallant,
A.R.,
and Jorgenson,
D.W.
"Statistical
(1979)
Inference for a System of Simultaneous, Nonlinear, Implicit
Equations in the Context of Instrumental Variables Estimation,"
Journal of Econometrics 11
,
and
(1980) "Interest Rates, Inflation Expectations,
Spurious Elements in Measured Real Income and Saving, " American
Economic Review vol.
5.
70, no.
Jump, G.V.,
,
Haanes-Olsen, L., (1978) "Earnings Replacement Rate of Old Age
Benefits,
1965 - 1975,
Selected Countries," Social Security
Bulletin vol.
no.
1.
41,
,
Hayashi,
F.,
Hypothesis:
"The
Permanent
Income
(1982)
Estimating and Testing by Instrumental Variables," Journal of
Political Economy vol.
90, no 5.
,
Kochin,
L.A.,
by
Future
Taxes
Anticipated
(1974)
"Are
Consumers?"
Journal of Money, Credit and Banking vol.
6 no.
,
3.
Koskela, E., and Viren, M.
(1982) "Saving and
International Evidence," Economics Letters 9.
,
Inflation,
Some
,
-39-
Leff, N.
"Dependancy Rates and Saving
(1969)
f
Economic Review
Rates,"
American
,
Leimer, D.R., and Lesnoy, S.R.
"Social Security and
(1982),
Private Saving: New Time-Series Evidence," Journal of Political
4.
Economy vol.
90, no.
,
R.E.
"Some
Lucas,
International
(1973)
Evidence
Output-Inflation Tradeoffs," The American Ecoonomic Review
,
LXVII, no.
,
on
vol.
3.
Modigliani, F.M., (1966) "The Life Cycle Hypothesis of Saving,
for
Wealth and the Supply of Capital," Social
the Demand
Research vol.
2.
Reprinted in The Collected Works of
33, no.
Franco Modigliani vol.
2, The Life Cycle Hypothesis of Saving,
A.
Abel ed., Cambridge, MIT Press.
,
,
Saving
"The Life Cycle Hypothesis of
Ratio,"
in
Induction
and Intercountry Differences in The Saving
Growth and Trade, Essays in Honor of Sir Roy Harrod edited by
Wolfe, Oxford, Clarendon
W.A.
Eltis, M.
F.G.
Scott, and J.N.
Works
of
Franco
Collected
in
The
Press.
Reprinted
edited
of
Saving,
Hypothesis
,vol.
The
Life
Cycle
Modigliani
2,
MIT
Press.
by A.
Abel, Cambridge,
,
(1970)
,
(1979) "Utility Analysis and
and Brumberg, R.
An
Attempt at Integration," in
Functions:
Aggregate Consumption
Abel,
ed.,
A.
Modigliani
Franco
Works
of
The Collected
Cambridge, MIT Press.
,
,
,
"Determinants of
A.G.,
(1982)
and Sterling,
Role of Social
the
Reference
to
Private Saving with Special
Proceedings
in
the
forthcoming
Tests,"
Security
Cross Country
on
the
Conference
Association
Economic
of the International
London,
Italy,
Bergamo,
Wealth
and
Saving
Determinants of
^
MacMillan Press.
,
—
OECD,
Tables
(1982) National Accounts Statistics
Paris, OECD.
vol.
II;
Detailed
,
Ram, R.,
(1982)
International
Review, June.
"Dependancy Rates and Aggregate Savings: A New
Study," The American Economic
Cross-Section
Retirement
of
Age
the Average
"Is
Re imers,
R.
(1976)
the American Statistical Association
Chaanging?," Journal of
vol.
355.
71, no.
,
,
Siegel,
J.J.,
Government and
and Statistics,
in
Distortions
"Inflation-Induced
(1979)
Private Saving Statistics," Review of Economics
,
•40-
"Taxation and Corporate Investment:
A
Summers, L.
(1981)
q-Theory Approach," in The Brookings Paper on Economic Activity
,
1
in
Tobin, J., (1967) "Life Cycle Saving and Balanced Growth,"
Ten Economic Studies in the Tradition of Irving Fisher Fellner
contributing authors, New York, John Wiley and Sons.
al.
et.
,
Asset Accumulation and Economic Activity
(1980)
Chicago,
The University of Chicago
lectures),
(Yrjo Jahnsson
Press.
,
,
and Buiter, W.
(1980) Fiscal and Monetary Policies,
Capital Formation and Economic Activity," in The Government and
ed.
Cambridge
Von Furstenberg"]
Formation
G.M.
Capital
Massachusetts, Ballinger.
,
,
,
,
41
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