Half of the population is composed of A-people and half of
B-people. Each A-person purchases $200 of government debt and
everyone gets a tax cut of $100. Taxes are paid in equal shares
by everyone. At an assumed interest rate of 5 percent, everyone
pays $5 of additional taxes in all future years and the A-people
receive $10 in interest payments per year. As noted earlier,
each A-person is, in effect, loaning $100 to a B-person. This is
shown in the Table below.
The simple Ricardian Equivalence idea rests on the fact that
all public debt must be serviced in perpetuity or paid back, so
the future tax revenues raised to pay the interest on the debt
must be equal in present value to the current tax cut. But this
assumes that people live for ever.
Suppose that a particular B-person, who buys no bonds, knows
he is going to die within a few years. At an interest rate of 5
percent, the present value of future tax increases that he will
pay is much less than his $100 tax cut. If he lived only one
year, for example, he would pay back only $5. His wealth has
increased and he will consume more. The remaining future taxes
to service and amortize the debt will paid by the people living
after he has died.
But surely this won't matter, you might think, because the
next generation will inherit the bonds as well as the tax
liabilities that service them so that the amount paid in taxes
will be exactly matched by the amount received in interest at
every future date, regardless of who is living at the time.
This is true, but since all individuals have finite lifespans,
everyone will still have an incentive to consume more. They have
more resources available for consumption now, and could care
less whether future generations' tax liabilities are matched by
interest earned on bonds. Consumption will be higher than
otherwise, and investment and the future capital stock smaller,
so the next generation will be clearly worse off.
Since the current generation has an incentive to consume
more the IS curve will shift to the right and under fixed
exchange rates the tax cut will be expansionary, Ricardian
equivalence notwithstanding.
But there is a problem with this. As economist Robert
Barro (1944- ) has pointed out, a large fraction of people
deliberately leave inheritances to their children. During
their lifetimes they will make a utility-maximizing decision as
to how much of their incomes to consume and how much to plough
into assets that will eventually be left to their children. When
the government cuts taxes now and raises future taxes by an amount
equal in present value, it shifts wealth to the current generation
from its heirs, disturbing that equilibrium. The current generation
is being induced to consume more, letting the next generation pay the
interest and amortize the debt.
This is inconsistent, however, with the plans of the current generation
to leave an inheritance to its children. Should not the reaction of private
individuals currently living be to restore the integrity of their desired
bequest to their children by simply saving the additional
disposable income resulting from the tax cut to leave to their children
to keep them as well off as before the tax cut? Why would there be any
effect on current consumption?
But since the next generation receives the bonds as well
as the future interest liabilities on them why should the current
generation have to save the tax cut? It is true that the next generation
will receive the bonds, but those bonds will not be received by the heirs
of anyone who does not purchase them. By not buying bonds and by spending
the tax cut, individuals currently living ensure that their heirs will not
inherit bonds equal to their inherited future tax liability.
By buying bonds with the receipts from the tax cut, on the
other hand, each person now alive can guarantee that her heirs
will receive an asset that will yield interest equal to the
future taxes that will have to be paid to service the additional
public debt resulting from the tax cut.
The argument that a tax cut will shift wealth from future
generations to the present generation assumes that the current
generation does not care about its children. The Ricardian
Equivalence approach essentially regards the family tree as the
unit of decision, not the current generation in that family tree.
The individual will eventually die, but the family will continue
forever. The utility of the family will be maximized by an
optimal path of intergenerational consumption which the government cannot
affect by adjusting the intergenerational timing of its taxation.
Obviously, however, not everyone will have heirs that he/she cares
about. In that case any cut in taxes received late in life is an
invitation to spend more and let other people's heirs pay the
interest and amortize the debt in years to come. As a result, a
cut in current taxes will have some intergenerational effect on
current consumption, though not as much as might at first be
supposed. This, of course, assumes that those of the current generation
that care about their heirs do not reduce their current consumption
enough, and pass on enough to future generations, to compensate their
heirs for the fact that a fraction of the population, not having
heirs, will consume the revenue from the current tax cut. The problem
is that it will be difficult for those that have heirs they care about
to figure out how much extra savings will be required to offset the
additional current consumption of those who have no heirs they care
about.
The Ricardian Equivalence argument also assumes that people
know that a tax cut must be financed by higher future taxes.
Surely, a major expansion of the government debt over a period of
years will not go unnoticed, and people will implicitly realize
that future taxes will have to be levied to service it. But a
tax cut of a couple of hundred dollars in any given year may be
hardly noticed. Disposable income will increase and the increase
may be automatically spent. Tax cuts may therefore have some
effect on consumption due to an misinformation-driven illusory wealth
effect even if there is no actual effect on wealth.
The upshot of the discussion here and in the previous topic is that
a tax cut will probably lead to an increase in consumption, though
the magnitude of this increase will probably be smaller than
envisaged in the simplistic Keynesian presentation.
It is time for a test. Be sure and think up your own answers to the
questions before looking at the ones provided.
We commonly hear it said that excess government borrowing is bad
because we are placing a burden on future generations. We are enjoying
additional consumption now, but our children will pay for it later on.
This topic investigates the intergenerational effects of bond vs. tax
finance of government expenditure. As in the previous topic we will
assume that the government cuts taxes by $100 dollars and floats bonds,
all of which are purchased by a segment of the population, called
A-people. The remaining population, B-people, purchase no bonds.
A-People
B-People
Current Year
Tax Cut $100 $100 Bonds Purchased $200 0
All Future Years
Interest Received (at 5%) $10 0 Tax Increase $5 $5