Look again at the government's budget constraint developed in the previous
topics.
G 
= T + ΔB + ΔH
The government reduces T and increases ΔB by
the same amount. The public receives a reduction in its taxes but ends up
buying an equivalent amount of bonds issued by the government.
It would seem that the public gains from this policy since it now receives
bonds for the money, and hence goods, it gives to the government and these
bonds bear interest. In order to pay the interest on these bonds, however,
the government has to levy appropriate additional future taxes.
Let us suppose that the government cuts taxes by $100 per person and sells
everyone $100 worth of government bonds bearing interest at 8 percent. In
every future year the government must raise $8 additional taxes per person to
pay these same people their $8 interest. The public receives a $100 reduction
of this year's taxes in return for an $8 increase in taxes in all future years.
Letting i be the nominal interest rate, the present value of future
taxes is
PV
= $8 / i = $8 / 0.08 = $100
which is identical to the tax cut. We assume here that the
bonds are perpetuities or consols---if they were not, the result
would be the same except that the above equation would take a more
complicated form.
Consider, for example, a case where the government cuts
taxes this year and finances its revenue short-fall with an issue
of government debt maturing in one year. This means that taxes
must be raised next year to pay interest on and retire the debt.
A per-person tax cut of $100 this year will be financed by $100
worth of bonds which will cost $108 to redeem (at 8 percent
interest) next year. This means that each person gets a $100 tax
break this year buy pays $108 additional taxes next year. The
present value of these tax changes is
PV
= − 100 + 108 / (1 + i )
= − 100 + 108 / (1 + 0.08) = 0
The tax cut is really nothing more than a tax postponement on
which interest must be paid at market rates. If people are
forward looking they will realize that they can't get something
for nothing---the present value of the future taxes equals the
amount of the current tax cut.
The public is no better off than it would have been by
paying the $100 taxes in the first place. By buying bonds it
gives the government $100 for the privilege of paying itself $8
interest each year. By paying taxes it gives the government $100
outright. The transfer to the government is the same in both
cases. Wealth does not increase, so there appears to be no
reason why consumption should increase.
This idea that the community's wealth and consumption will
be the same whether the government finances its expenditure by
levying taxes or borrowing from the public is called Ricardian
Equivalence after the famous 19th Century British economist David
Ricardo (1772 - 1823).
Another way of visualizing the Ricardian Equivalence idea is to recall that
when the government makes an amount of expenditure G it must
take G-dollars worth of resources away from the private sector to create the
government goods it will give free to private individuals. This amount of
resources will be the same whether the government borrows them from the
private sector or obtains them through taxation. Private sector output will
be reduced by the same amount in the two cases. And since the government
acts as agent of the public, the public must transfer to it the necessary
resources without any ultimate compensation other than the free goods the
government is going to produce and distribute using those resources.
In the case of bond as opposed to tax finance the government is perpetrating
what seems to be a slight-of-hand. Rather than simply taking the funds
directly, the government is giving paper assets in return on which the public
gets to pay itself interest every year. This interest is simply a switch of
funds from one of the public's pockets to another with no net gain. Why
might the government want to do this? We will see why in the next topic.
Before proceeding it should be noted that the Ricardian Equivalence Principle
does not apply unequivocally to situations where the government finances a tax
cut by printing money. To be sure, the same resources are taken from the
private sector but, when the price level is fixed and there is
less-than-full-employment, private wealth will increase because real money
holdings rise. In the full-employment case the equivalence principle holds
unequivocally because the government is simply substituting a tax
on money holdings for a tax on something else.
Its time for a test. Be sure to think up your own answers to the
questions before looking at the ones provided.
We now analyze the effects of a tax cut when the short-fall of revenue
from expenditure is financed by selling bonds to the public. The
government borrows funds from the private sector to finance the expenditure
that was previously being paid for by the tax revenue that is now forgone.