Introduction
Chapter 22
Taxes on Savings
Does the existing structure of income taxation in the
United States reduce the amount of savings done by
individuals?
This is an important policy question because making
more capital available to business can be a key
determinant of economic growth.
What is the appropriate role of capital income
taxation – the taxes levied on the returns from
savings?
Jonathan Gruber
Public Finance and Public Policy
Aaron S. Yelowitz - Copyright 2005 © Worth Publishers
TAXATION AND SAVINGS – THEORY
AND EVIDENCE
Traditional theory
Introduction
The traditional theory of savings is to smooth
consumption across periods.
This lesson proceeds as follows:
Basic theoretical model with two-period
consumption
Empirical evidence
Precautionary savings models
Self-control models
Retirement accounts
Taxation and savings – Theory and evidence
Traditional theory
This is an implication of diminishing marginal utility
of income.
Intertemporal choice is the choice individuals
make about how to allocate their consumption over
time.
As with hours of work in the labor supply model,
savings is not valued directly, but is rather a means to
an end. It can be thought of as a “bad” – where the
complementary “good” is “future consumption.”
Figure 1
C2
We define savings as the excess of current income
over current consumption.
It earns a real rate of return, r, that buys
consumption in future periods.
Figure 1 illustrates the basic model.
Y(1+r)
Y(1+r(1-τ))
C2
slo
pe
Initially savings is S, and
consumption is C1.
=(1+
r)
slop
e=
-(1 +
r(1-
τ))
A
Taxing savings rotates the
budget constraint, and creates
income and substitution effects.
S(1+r)
BC2
C1
BC1
Y
C1
S
1
Taxation and savings – Theory and evidence
Traditional theory
Taxation and savings – Theory and evidence
Traditional theory
The slope of the intertemporal budget constraint is
–(1+r), meaning that the opportunity cost of firstperiod consumption is the interest income not
earned on savings for second period consumption.
Savings (as with hours of work in the labor supply
model), is measured going toward the origin on the
x-axis.
The initial blue line represents the budget constraint,
given income Y in period 1, BC1.
The intertemporal budget constraint is the
measure of the rate at which individuals can trade off
consumption in one period for consumption in
another period.
Jack has preferences over consumption goods today
and consumption in the future.
It is the difference between income and
consumption.
He initially chooses bundle A.
Taxation and savings – Theory and evidence
Traditional theory
If the government taxes all income, including
interest income, then the rate of return falls from r
to (1-t)r, because the government collects tr.
The slope therefore changes from –(1+r) to –(1+((1t)r), shifting the intertemporal budget constraint to
red budget constraint, BC2.
Figure 2 shows possible responses to the taxation
of savings.
The model assumes the person can freely borrow, if
his preferences dictate.
Figure 2
C2
C2
Substitution effect
is larger
Income effect
is larger
Savings can fall.
Or rise.
C2
C2
C 2*
C 2*
BC2
BC1
BC2
C1
C 1 C 1*
S
BC1
C 1* C 1
S
C1
Taxation and savings – Theory and evidence
Traditional theory
Taxation and savings – Theory and evidence
Traditional theory
The lower after-tax rate of return will cause an
increase in first period consumption through the
substitution effect.
But the fall in the after-tax return makes Jack feel
poorer, which reduces his consumption in the first
period (and increases savings).
One way to think about the income effect from a
fall in the after-tax rate of return is to think about a
“target level” of consumption in retirement.
As the interest rate falls, Jack has to save more to
meet this target level.
The first panel shows that when the substitution
effect dominates, savings falls.
The second panel shows that when the income effect
dominates, savings increases.
2
Taxation and savings – Theory and evidence
How does the after-tax interest rate affect savings?
Taxation and savings – Theory and evidence
Inflation and the taxation of savings
In the late 1970s, the U.S. experienced double-digit
inflation rates. At that time, neither the income tax
brackets nor the treatment of capital income was
indexed for inflation.
Unlike the empirical literature on labor supply, the
empirical work on after-tax interest rates and
savings has not reached a clear consensus.
The elasticity of savings with respect to interest rates
varies from 0 to 0.67.
This led to “bracket creep” whereby individuals
would see an increase in their tax rate despite no real
increase in their real income.
It is more difficult to compute the appropriate
interest rate.
In addition, it is more difficult to find appropriate
treatment and control groups.
Taxation and savings – Theory and evidence
Inflation and the taxation of savings
The nominal interest rate (i) is the interest rate earned by a
given investment.
The real interest rate (r) is the nominal interest rate minus
the inflation rate.
This measures an individual’s actual improvement in
purchasing power due to savings.
These are related by r=i+π, where π is the inflation rate.
The tax system taxes nominal returns, not real returns.
Table 1 illustrates the impact of capital taxation in an
inflationary environment.
Taxation and savings – Theory and evidence
Inflation and the taxation of savings
In the first panel, there is no inflation.
With no taxes, the number of skittles that can be bought is
110.
With a 50% tax rate, only 105 bags can be bought.
In the second panel, imagine that inflation equals the
nominal rate of return. Thus, the real rate of return is 0%.
With inflation but no taxes, 100 bags can be bought.
With inflation and taxes, even though real purchasing power is
unchanged, the taxation of nominal returns means only 95.5 bags
can be bought.
In the third panel, if the nominal rate adjusts for inflation (to
21%), then in the absence of taxation inflation will not erode
the purchasing power of savings.
Although the treatment of income tax brackets
changed in 1981 by becoming indexed to inflation,
the rules about capital income taxation have
remained the same.
Table 1
Capital taxation in an inflationary environment
Case
Inflation
Tax rate
on
interest
Savings
Nominal
rate
Interest
earnings
After-tax
resources
Price
of
skittles
Bags
of
skittles
0%
0%
100
10%
$10
$110
$1.00
110
0%
50%
100
10%
$10
$105
$1.00
105
Inflation
10%
0%
100
10%
$10
$110
$1.10
100
10%
50%
100
10%
$10
$105
$1.10
95.5
Constant real rate
10%
0%
100
21%
$21
$121
$1.10
110
10%
50%
100
21%
$21
$110.5
$1.10
100.5
No inflation
The nominal rate
will likely adjust for
inflation, however.
With taxes on
nominal returns,
the real return is
negative!
With 10% inflation
and a 10% return,
the real return is
zero.
Taxation and savings – Theory and evidence
Inflation and the taxation of savings
The problem in the second and third panels, with
taxation, is that taxes are levied on nominal, not real
earnings. Individuals, when making savings
decisions, care about the real interest rates.
Because taxes are levied on nominal returns, the
impacts of inflation on the tax code remain
important.
Higher inflation lowers the after-tax real return to
savings.
3
ALTERNATIVE MODELS OF SAVINGS
Precautionary saving models
The precautionary saving model is a model of
savings that accounts for the fact that individual
savings serve at least partly to smooth consumption
over future uncertainties.
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Social insurance and
personal savings
The intuition for precautionary savings are barriers
to borrowing during an emergency. Liquidity
constraints are barriers that limit the ability of
individuals to borrow.
There are a number of studies in support of the
precautionary model. They show that greater
uncertainty leads to higher savings, and that social
insurance programs that lower income uncertainty
lead to lower savings.
Chou, et al. (2003) find that the introduction of
National Health Insurance in Taiwan led to a
decrease in savings among affected workers.
Gruber and Yelowitz (1999) find that Medicaid
expansions in the U.S. lowered the need for
precautionary savings.
Alternative models of savings
Self-control models
Alternative models of savings
Self-control models
An alternative formulation of the savings decision
comes from behavioral economics models.
Investment devices such as “Christmas club” bank
accounts or tax-preferred retirement accounts are
consistent with self-control problems.
Self-control problems also may explain why
individuals have substantial savings in illiquid forms
(housing, retirement accounts), while at the same
time carrying credit card balances at high interest
rates.
One of the most commonly given reasons for saving
is for “emergencies.”
This is a form of self-insurance.
Individuals have a long-run preference to ensure
enough savings for smooth consumption throughout
their lives, but their impatient short-run preferences
may cause them to consume all their income and not
save for future periods.
These self control problems require commitment
devices.
Alternative models of savings
Self-control models
A final piece of evidence for self-control problems is from
an innovative experiment run by Thaler and Benartzi (2004),
called “Save More Tomorrow.”
Employees committed a portion of future pay increases to
their retirement savings. By arranging the decision this way,
the decision seemed less difficult.
Although this should not have any attractiveness to a
rational saver, 78% of the employees offered the plan
decided to join it, and 80% of those employees stuck with it
through four pay raises.
The bottom line is that “Save More Tomorrow” raised
savings for employees.
TAX INCENTIVES FOR
RETIREMENT SAVINGS
Because of concern about workers under-saving for
retirement, the U.S. government has introduced a
series of tax subsidies for retirement savings.
There are four major incentives:
Tax subsidy to employer-provided pensions
401(k) accounts
Individual Retirement Accounts
Keogh Accounts
4
Tax incentives for retirement savings
Available tax subsidies for retirement savings
A pension plan is an employer-sponsored plan through which employer
and employees save on a (generally) tax-free basis for the employees’
retirement.
A defined benefit pension plan is one in which worker accrue
pension rights during their tenure at the firm, and when they retire
the firm pays them a benefit that is a function of the workers’ tenure
at the firm and their earnings.
A defined contribution pension plan is one in which employers set
aside a certain proportion of a worker’s earnings in an investment
account, and the worker receives this savings and any accumulated
investment earnings when he or she retires.
The percentage of earnings varies, but 5% is not uncommon.
The contributions that employers make to pension plans are not taxed
until the money is withdrawn at retirement.
Tax incentives for retirement savings
Available tax subsidies for retirement savings
An Individual Retirement Account (IRA) is a
tax-favored retirement savings vehicle primarily for
low-income and middle-income taxpayers, who
make pretax contributions and are then taxed on
future withdrawals.
The contribution limit is currently $3,000 per
person.
Tax incentives for retirement savings
Why do tax subsidies raise the return to savings?
All of the tax subsidies have the following
characteristics:
Individuals avoid paying income tax on their
contributions.
Earnings accumulate at the before-tax rate of return.
Withdrawals are taxed as ordinary income, not the
lower capital gains tax rate.
Tax incentives for retirement savings
Available tax subsidies for retirement savings
A 401(k) account is a tax-preferred retirement
savings vehicle offered by employers, to which
employers will often match employees’
contributions.
The analog in the non-profit sector is 403(b).
Many firms offer an employer “match” on
contributions made to such a plan to encourage
participation.
The contribution limit for 2005 is $14,000, schedule
to rise to $15,000 in 2006, and indexed for inflation
thereafter.
Tax incentives for retirement savings
Available tax subsidies for retirement savings
A Keogh account is a retirement savings account
specifically for the self-employed, under which up to
$40,000 per year can be saved on a tax-free basis.
They function much the same as 401(k) accounts,
except they are not run through an employer.
Tax incentives for retirement savings
Why do tax subsidies raise the return to savings?
Since taxes are paid at retirement, how are these accounts
“tax subsidized?”
The key ingredient is that you get to earn the interest on the
money that would have otherwise been paid in taxes. This is
composed of three important parts:
The initial deductibility of the contributions
Having earnings accumulate at the before-tax rate of return
Having the potential to withdraw the money when a person is
in a lower tax bracket.
These tax subsidies can dramatically increase the rate of
return to retirement savings.
5
Tax incentives for retirement savings
Why do tax subsidies raise the return to savings?
Table 2 illustrates the difference between a regular,
taxed investment and a deductible IRA.
We assume in this table that the earnings
accumulations are taxed as ordinary income, not as
capital gains.
Tax incentives for retirement savings
Theoretical effects of tax-subsidized retirement savings
These tax subsidies to retirement savings rotate the
intertemporal budget constraint in an opposite way
to the taxation.
This is illustrated in Figure 3.
3
Table 2
The tax advantage of IRA savings
Account
type
Earnings
Tax on
earnings
Regular
$100
(☺=25%
)
$25
IRA
$100
0
Initial
deposit
Interest
earned
(r=10%)
Taxes paid
upon
withdrawal
Total amount
withdrawn
$75
$7.50
$1.88
=0.25x($7.50)
$80.62
=$75+$7.50-$1.88
$100
$10
$27.50
=0.25x($110)
$82.50
=$100+$10-$27.50
This “tax subsidy” leads
to greater overall wealth.
With an IRA (or 401k), the
investment accrues at the
before-tax rate of return.
Figure 3
C2
Y(1+r(1-τρ))
Y(1+r(1-τ))
IRAs increase the
after-tax rate of
return, and rotate
the budget
constraint.
slo
pe
=-
slop
e=
(1+
r(1
- τρ
-(1 +
r(1-
))
B
C
τ))
C2
A
S(1+r(1-τ))
BC2
The effect of IRAs on savings
is ambiguous, however.
Tax incentives for retirement savings
Theoretical effects of tax-subsidized retirement savings
Initially the after-tax rate of return is r(1-τ).
With the tax-subsidy, however, the delay in tax payments
reduces the tax burden by , so the effective tax rate on
retirement savings is only τρ.
Thus, the rate of return rises to r(1- τρ).
The substitution effect leads to more savings, while the
income effect leads to less savings. Thus, the change in total
savings is ambiguous.
Moving from point A to B results in an increase in savings
(where the substitution effect dominates), while moving
from A to C results in a decrease in savings (where the
income effect dominates).
C1
BC3 = BC1
Y
C1
S
Tax incentives for retirement savings
Theoretical effects of tax-subsidized retirement savings
One key institutional feature of 401(k) accounts,
IRAs, and so forth is that the annual contributions
are capped.
This creates a non-linearity in the budget constraint,
where the tax-advantaged rate of return from saving
below the cap is higher than taxed rate of return
above the cap.
Figure 4 illustrates this situation.
6
Tax incentives for retirement savings
Theoretical effects of tax-subsidized retirement savings
Figure 4
C2
D
With a cap, savings
is subsidized, but
only up to a point.
slope = -(1+r(1-τ))
Y(1+r(1-τ))
A
E
slope = -(1+r(1-τρ))
The slope on segment BE is -(1+r(1- τρ)), while the
slope on segment DE is -(1+r(1- τ)).
This kinked budget constraint has potentially
different effects on different “types” of savers.
Consider an initially low saver in Figure 5a.
5a
B
Y
C1
$3,000
Figure 5a
Tax incentives for retirement savings
Theoretical effects of tax-subsidized retirement savings
Low saver
C2
On the marginal $1 of savings, this individual now
gets a higher rate of return.
Thus, he faces both the income and substitution
effects discussed before, so savings could increase
(to point B) or decrease (to point C).
On the other hand, consider an initially high saver in
Figure 5b.
5b
Y(1+r(1-τ))
B
C
?
A
Thus, the net
effect is
ambiguous for
low savers.
Figure 5b
For a low saver, the
income and
substitution effects go
in opposite directions.
C1g
Y
C1
1,000
Tax incentives for retirement savings
Theoretical effects of tax-subsidized retirement savings
High saver
C2
B
Y(1+r(1-τ))
A
For high-savers, IRAs
represent an income
effect only and therefore
lower savings.
Y
C 1W C 2W
C1
On the marginal $1 of savings, this individual receives the
same rate of return as before.
He faces only an income effect, but not a substitution effect,
so savings decreases (to point B).
The income effect for high savers such as the person in
panel (b) arises as they “reshuffle” their existing assets into
an IRA; they take $3,000 of savings they were already putting
aside and label it as tax-preferred IRA savings.
It is possible that IRAs actually lower overall private savings
through this income effect.
$4,000
$5,000
7
i on
cat
pli
p
A
The Roth IRA
A Roth IRA is a variation on normal IRAs to which
taxpayers make after-tax contributions but may then
make tax-free withdrawals later in life.
Unlike traditional IRAs, individuals are never
required to make withdrawals from Roth IRAs, so
the earnings on assets can build up indefinitely.
Why was the Roth IRA created? Budget politics
clearly came into play: traditional IRAs entail
immediate loss in tax revenue, while Roth IRAs
entail loss of future tax revenue.
Tax incentives for retirement savings
Implications of alternative models
Second, the hallmark of self-control models is the
search for commitment devices to provide selfcontrol.
401(k) accounts, taken directly out of the paycheck,
provide such a commitment device, because the
money cannot be easily accessed until retirement.
Beyond the demand for these accounts due to tax
incentives will be demand that arises because of
commitment.
Tax incentives for retirement savings
Private versus national savings
This example illustrates the notion of marginal impacts
versus inframarginal impacts.
The marginal impact is the 30¢ of new private
saving.
The inframarginal impact is the 70¢ of existing
saving that was going to happen even in the absence
of a tax subsidy.
Tax incentives for retirement savings
Implications of alternative models
The retirement tax incentives may have stronger positive
effects on savings than implied by the traditional theory and
intertemporal budget constraint analysis.
Consider, first, the precautionary savings motive. Imagine a
person who had more than $3,000 in savings, but was using
it for precaution against job loss. The illiquid IRA would not
be viewed as a good substitute, so contributions to the IRA
are not simply “reshuffling.” Thus, there may be more
savings due to retirement incentives than is suggested by
traditional models.
Tax incentives for retirement savings
Private versus national savings
The discussion so far has focused on private savings,
but what matters for investment and growth is
national savings.
Retirement tax incentives have an offsetting effect
on national savings because they are financed by a
tax break.
For example, imagine that 401(k)s raised private
savings by 30¢ per $1 of contribution. If the tax rate
were 43%, then 30¢ of tax revenue (43%x 70¢ of
existing savings) is forgone, and there is no new
national savings.
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The impact of tax incentives
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Em vide for savings on savings behavior
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Empirical work examining the impact of IRAs and 401(k)s
has proven difficult.
Those who contribute to IRAs also save more in every form
than non-savers who don’t contribute to IRAs. Thus, noncontributors do not form a good control group.
The same kinds of comparisons have been made for workers
in firms that offer a 401(k) to workers in firms that do not
offer a 401(k). The workers in these different firms appear
to be different in observable ways, and therefore are likely to
be different in unobservable ways as well.
8
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Engelhardt (1996) studies the Canadian Registered Home
Ownership Savings Plan. Unlike the programs in the U.S.,
this created quasi-experimental variation because:
It was available to renters but not owners.
It was in effect from 1974 to 1985, but not afterwards.
The benefit varied by marginal tax rate, which varied widely
across Canadian provinces.
The results indicated that each $1 contributed to the
program resulted in up to 93¢ in new private savings, and up
to 57¢ of new national savings.
9