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Michael Dotsey
Currently there is a great deal of controversy surrounding the federal budget deficit. Claims have been
made that the deficit is a burden on future generations and that it crowds out private investment and
reduces the capital stock. For example, in testimony
before the Senate Budget Committee, Rudolph Penner, director of the Congressional Budget Office testified “Certainly one consequence of persistent deficits
about which there seems little disagreement is their
adverse effect on future generations . . . . Slower
growth of the private capital stock would result in
lower productivity than would occur with smaller
deficits and the income of future generations would
be lower.” This crowding-out of investment is
alleged to occur because budget deficits supposedly
raise real rates of interest. The same theme is also
present in the Congressional testimony of Federal
Reserve Board Chairman Paul Volcker as well as in
other public statements. “In essence, the demands of
the Federal Government limit the rate of growth of
other credit-absorbing sectors of the economy. The
rationing device is interest rates held higher than
would otherwise be the case.“1 The basic evils of
budget deficits and the benefits of cutting the deficit
are echoed in numerous market newsletters and by
many private economists. For instance, Martin Feldstein in testimony before the Senate Finance Committee states “The short term effect of enacting a
deficit reduction program of that magnitude would
be a substantial decline in medium term and long
term real interest rates . . . .”
There is a minority view that budget deficits do
not have much consequence for aggregate economic
activity. A major proponent of this line of argument
* I would like to thank Marvin Goodfriend, Thomas
Humphrey, and Roy Webb for their valuable comments
and suggestions.

Remarks given at the Broyhill Executive Lecture
Series, March 22, 1984.

is the University of Rochester’s Professor Robert J.
Barro, who has resurrected the notion of Ricardian
equivalence or neutrality of budget deficits. I n a
recent Wall Street Journal article, Barro states
“There is no evidence that shifts in deficits lead to
higher rates, especially to higher real rates that would
deter investment . . . . Basically, this crowding-out
view of deficits is a myth, which is reinforced mainly
by repetition.”
These opposing viewpoints are irreconcilable and
yet each finds its adherents among respected economists. This article attempts to place these viewpoints
in the context of the economic models from which
they are derived. This procedure focuses attention on
the assumptions that underlie the various conclusions
concerning the effects of budget deficits and helps
appraise the realism or degree of confidence that
should be placed in these various views.
In addition, the article will investigate a fairly
recent area of research concerning optimal deficits.
This literature concludes that the optimal level of
government debt and budget deficits is not generally
zero. The implication is that given an exogenous
time path for government spending, a policy of balancing the government budget in each and every
period is costly in terms of social welfare. Further
the less stringent requirement of the Balance Budget
Amendment that passed the Senate on October 1,
1982 does not generally represent a policy that is
consistent with the literature on optimal deficits. 2

The optimal deficits literature does not consider the
potential relationship between taxing and government
Some proponents of the Balanced Budget
Amendment (see Friedman and Friedman [13]), feel that
there exists a link between the level of government
spending and the constraint of paying for spending as you
go. However, I am unaware of any systematic discussion
concerning this issue.
More importantly, there are
specific portions of the Balanced Budget Amendment that
deal with the level of government spending directly by
attempting to remove certain features of the current
budgetary process that are likely to produce a nonoptimal
level of government spending. These direct limitations
on spending could be enacted independently of the requirement that the expected budget deficit be zero.



The organization of the article follows a historical
approach to the theory of budget deficits. The departure point is the standard Keynesian model which
is discussed in Section II. Section III analyzes some
shortcomings of this model and the conclusions
drawn from it. Section IV moves on to the notion of
Ricardian equivalence, while Section V discusses
criticisms concerning this theory. Section VI examines the notion of optimal budget deficits, while Section VII contains a brief summary and conclusions.

The initial analysis of the effects of budget deficits
will be carried out within the framework of a standard Keynesian model. Starting the analysis in this
manner will provide the theoretical background
necessary for evaluating much of the current discussion involving deficits. It will also serve as a useful
point of departure for examining the more recent
rediscovery of Ricardian equivalence.
The Goods Market

The analysis begins with the closed economy accounting identity of equation (1) that aggregate
output (Y) is equal to the sum of aggregate consumption (C), aggregate investment (I), and government spending (G).

In order to give this identity economic content, the
behavior of consumption, investment, and government spending must be examined. Typically, in these
models consumption is hypothesized to depend positively on disposable income Y d , which is merely
income net of taxes (T). That is, Y d = Y - T and
consumption is given by an equation such as (2).

The coefficient c1 is greater than zero and less than
one implying that only a portion of an extra dollar of
disposable income will be spent. It will be shown
that the nature of the consumption function is crucial
in determining the effects of a budget deficit.
For simplicity, let investment be written as a negative function of the real rate of interest. At higher
real interest rates fewer projects are profitable, since
the opportunity cost of funding a project is higher.
Therefore, at higher real rates of interest there will
be less investment. This is depicted by equation (3)

where r is the real rate of interest.
Finally, let government spending be exogenously
given at the level G1. The analysis concentrates on
the consequences of changes in financing a given
level of government expenditure and not on the
effects of government expenditure itself. Holding
government spending fixed at a predetermined level
will allow the analysis to focus on the financing decision without introducing the complicating effects of
government spending. Also, taxes are initially assumed to be lump sum in nature at the level T 1 .
That is, the level of taxes an individual pays is independent of his income. Within the context of the
model currently under consideration, this assumption
is of little consequence. However, as the analysis
proceeds to examine the nature of budget deficits in
more detail the distinction between lump sum taxes
and proportional taxes will be important.
The income levels and interest rates consistent
with clearing of the goods market can be derived
from equations (l), (2), and (3). This is expressed
as equation (4), and shows the negative relationship
between income levels and interest rates that are
needed to clear the goods market.

To understand this negative relationship, perform the
following thought experiment. Suppose that at an
income level of Y 0 and a real interest rate r 0 t h a t
income equaled consumption plus investment plus
government spending. Now suppose that income increased to Y1. Since consumption only increases by a
fraction of the rise in income, it is easy to see that the
goods market is no longer cleared. Output, Y 1, is
now greater than the sum of C + I + G. If the
real rate of interest were to fall (to, say, rl), so that
investment rose, the goods market would once again
clear. Therefore, the locus of points depicting market
clearing in the goods market, commonly referred to
as the IS curve, is downward sloping as indicated in
Figure 1.
The Money Market

As shown, the IS curve defines an infinite number
of real interest rates and income pairs that are consistent with equilibrium in the goods market. In
order to find the unique level of the real interest rate
and income that will arise in our model economy, the
money market must be analyzed. Equilibrium in the
money market is given by values of income and


nominal interest rates that equate the demand for
money with the supply of money. For simplicity, the
analysis assumes that inflation is zero and therefore
that nominal and real interest are equivalent. This
locus of points, commonly called the LM curve, is
upward sloping and is drawn in Figure 1. An intuitive explanation relies on the observation that the
demand for money is positively related to income and
negatively related to interest rates. Suppose that
money demand were equal to money supply at r l and
Y 1. An increase in income to, say, Y2 would increase
the demand for money making it greater than a given
money supply. Therefore, to return to equilibrium
the interest rate would have to rise (to, say, r 2 )
lowering the demand for money so that it once again
equals money supply.

Figure 1


Equilibrium and the Effects of
Budget Deficits

Equilibrium for the economy as a whole occurs
when demand equals supply in both the money
market and goods market simultaneously. 3 This is
depicted in Figure 1, and occurs at the point E 1 with
an interest rate of r l and an income level of Y 1 .
That is, the point El is consistent with government
spending of G1 and taxes of T1. Now let the government decide to increase the deficit by lowering T1,
while holding government spending fixed. This has
no initial effect on the money market since taxes do
not directly affect the demand or supply of money.
Therefore, the LM curve does not shift. However, a
decrease in taxes increases disposable income for any
given level of income and therefore raises desired
consumption. This means that aggregate demand is
now greater than income at Y1 and that a higher rate
of interest, which lowers investment must now be
associated with Y in order to return to equilibrium.
The result is that the IS curve will shift upward and
to the right (to IS’). The economy wide equilibrium
is now given by E2 with both income and interest
rates higher than at E l. In the Keynesian system
budget deficits are seen to be expansionary raising
the level of both output and interest rates.
The increased budget deficit also changes the composition of output. Since the interest rate has risen,
investment will have fallen. This interest reduced decline in investment is commonly called the crowdingout effect of a budget deficit. Also, since govern3

For this statement to be totally accurate it must be
assumed that the aggregate supply curve is horizontal
and that output is demand determined. This assumption
is unimportant for the basic issues discussed in this paper.

ment spending has not changed, consumption must
have risen substantially in order for output to rise
on net. Therefore, an increase in government deficits
causes the proportion of output comprised by consumption to rise while the ratio of investment to
output falls. With lower investment, the future
capital stock and productivity of the economy will
fall. The opinions of many of the economists quoted
in the introduction therefore seem to be based on the
Keynesian model of the economy.

A major problem with the Keynesian analysis presented in Section II is the myopic nature of individual behavior embodied in the consumption function
(2). Specifically, individuals are assumed to consume a constant proportion of current disposable
income regardless of the future time path of income
or taxes. An individual with $20,000 of disposable
income in each period of his life would consume
exactly the same amount as an individual whose disposable income alternated between $20,000 and $0
over his lifetime, with his current disposable income



being $20,000. The permanent income hypothesis
serves as an alternative way of modelling consumption. According to this theory consumption depends
on the present value of lifetime disposable income or
wealth. 4 Making this one modification essentially
negates the entire effects of a budget deficit that was
presented in Section II.
To show this, assume that the world is two periods
long (a period being of indeterminate length) and
that current consumption depends on the present
value of lifetime disposable income, W, where

and where the subscripts 1 and 2 denote time periods
one and two. Equation (2) is then modified to read

Since the model has taken on dynamic considerations that were not present in Section II, government behavior must be analyzed in more detail. Specifically, a constraint requiring the government to
balance its budget on average is imposed. That is,
the present value of government spending must equal
the present value of tax receipts, but the government
budget need not balance in any particular period.

This constraint is reasonable since no one would
lend to the government without the promise of being
paid back. Suppose that the government ran a deficit
of D1 in period one (i.e., G 1 - T1 = D1 ) . I f t h e
government doesn’t raise enough revenue in period
two to cover its spending plus the repayment of its
debt and interest on the debt, no one would lend to
the government in period one. Basically, in order to
borrow the government must promise to repay or no
one will lend to it in the first place. Extending the
model to include more than two periods does not
change the underlying justification for imposing a
government budget constraint.6

Using (5) and (6) it is straightforward to show
that an increase in the current budget deficit will
have no effect on the economy. Government spending
is given and invariant and hence so is the present
value of taxes. Therefore, wealth will not be changed
by a change in the timing of taxes so long as the
present value of taxes remains unchanged. Therefore, consumption will not be changed and the initial
level of output and interest rates will be consistent
with equilibrium. In essence, the decrease in taxes
in period 1 will be used by consumers to purchase the
additional bonds sold by the government to finance
its unchanged level of spending G 1. These bonds
will then be sold to pay for the increase in taxes that
must occur in period 2. As a result, consumption is
unchanged and the effect of the government deficit is
nil. 7 The basic thrust of this analysis underlies the
Ricardian equivalence proposition, which is discussed in more detail in the next section.

The model presented in Section III still has a
number of unrealistic features. However, it should
be noted that the results of Section II rest on a
consumption function that has very little analytical
appeal. First and foremost is the assumption that
individuals and the government have the same life
span or time horizon. One could alternatively view
the government as having an infinite time horizon,
with individuals being finite lived. In that case the
government need not raise taxes in period 2 to offset
the decline in taxes in period 1, but could wait to
some point in the distant future before bringing its
budget into balance. The absence of offsetting taxes
would imply a rise in current individual wealth and
an increase in current consumption. Consequently,
the results of Section II would obtain.
Barro’s [2] contribution has led to the reemergence of the notion of Ricardian equivalence, or that
pure government financing decisions do not matter
even in the case of finite lived individuals. He


This analysis neglects the potential effects of liquidity
constraints which will be dealt with in more detail in
Section IV.

The parameter a will depend on the individual’s rate of
time preference and perhaps other attributes of his utility
function. For the case where the rate of time preference
is equal to (l/l + r), a = ½.


This line of argument does not exactly hold when the
number of periods is infinite. However, if the economy
grows at rate n < r, then the present value of the future
taxes that must be levied to finance the interest on the


debt net of debt finance is exactly equal to the original
debt issuance (see Barro [3]). McCallum [15] shows
that in an economy with a fixed factor (such as land) that
inefficient capital accumulation does not occur and that
n < r. This inequality holds (without land) if both agents
and the government are infinitely lived. Barro [3, p.
345] conjectures that it holds in an overlapping generations model in which bequests are operational.

This analysis would carry over to proportional income
taxes, since in the current setting the supply of labor is


employs the reasonable assumption that members of a
family care about each others welfare. This assumption ties one generation to another and makes the
problem equivalent to analyzing individuals as if they
were infinitely lived. Since individuals effectively
have the same time horizon as the government, any
restructuring of debt and taxes does not alter individual wealth. Therefore, there are no changes in
behavior due to an increase in government debt.
The nature of Ricardian equivalence can be illustrated by the following simple overlapping generations model. In this model, an individual is assumed
to live for two periods. Further, he is assumed to
care about his own consumption and the attainable
utility or welfare of his heir.8 For simplicity, the
analysis considers an economy with a constant population, that is, one in which there is one child per
parent. An individual maximizes his lifetime utility
subject to a lifetime budget constraint. His earnings
include wages when young and generally a bequest
from his parent that he receives in the second period
of his life. Formally, an individual of generation i
budget constraint of

and a second period budget constraint of

where Ui is the utility of generation i, ci is consumption of generation i, Ti are taxes levied, and Ai a r e
assets of generation i. The superscripts y and o refer
to the periods when the individual is young and old.

assets accumulated by agent i when old that will
serve as a bequest to his heir who is a member of
generation i+l. Wage earnings are denoted by w,
while the real rate of interest is given by r.
In this framework, the consumption and asset demands of the old and young can be written as functions of their net-of-tax bequests, wages, and interest
rates. This is most easily seen by combining the
budget constraints of an agent when young and old
(7(a) and 7(b)) into a total lifetime budget constraint given by

This implies that the maximum utility level of an
individual is indirectly determined by his wages, his
bequest from his parent, and the interest rate.
Suppose that the government engages in deficit
financing by lowering the taxes paid by generation i
and raising the taxes of generation i+1 by enough
to pay off the deficit plus accumulated interest on the
additional debt. Within the framework of the previous section, since the ith generation is paying less
taxes over its lifetime, members would feel wealthier
and increase their consumption in period i. The
deficit would be expansionary. However, that need
not be the case when generation i is concerned about
the welfare of generation i+1 as they are currently
assumed to be. If generation i is sufficiently concerned to leave positive bequests to generation i+1,9
then there will be no wealth effect of the government
deficit in period i.
To see this update and reexamine (8), and recall
that the attainable utility of a member of generation
i+1, U*i+1 , depends on his bequest net of taxes. The
government deficit in period i is financed by an increase in generation i+1’s taxes. Essentially, this
financing is equivalent to the government taking away
money from generation i+1 and giving it to generation i. However, since generation i had decided to
give their descendants a bequest, this option was
already available to them in terms of lowering their
bequests. That generation i did not do this means
that they did not find the lower bequests optimal in
terms of maximizing their own level of utility. Hence,
in order to undo what the government has done,
members of generation i will increase their bequests
by the amount of the deficit. Essentially, the government deficit forced individuals in generation i away
from an optimal allocation of resouces between generations by taking away income from generation i+1
and giving it to generation i. Generation i can easily
offset the actions of the government by increasing its
bequests leaving the net bequest to its heirs unchanged. In doing so the entire profile of market
equilibria is unchanged and the government deficit
is neutral. The same results occur if the analysis is
extended to having taxes being paid by generations
further in the future.


The initial analysis abstracts from the possibility of
transfers from the younger generation to the older


For necessary conditions on the utility function see
Drazen [11].



The Existence of Bequests

The first and perhaps most obvious criticism of
Ricardian equivalence is the assumption of a bequest
motive. As shown in Section IV, a necessary condition for the neutrality of government deficits is the
existence of operational intergenerational transfers.
If bequests between generations are not often observed, then the argument presented above is merely
a theoretical exercise with little policy content. However, it is more difficult to dismiss the bequest motive
than is often realized. For example, bequests can
be of a very general form, such as money spent on a
child’s education, and need not only represent money
left in a will. In fact, any intergenerational transfer
of resources will do. Casual empiricism seems to
indicate that there does indeed exist some form of
intergenerational transfers in most families. If so,
deficits will have an expansionary effect only to the
extent that some members of the older generation do
not want to leave a bequest, and one would probably
expect this effect to be small.
Also, operational intergenerational transfers need
not only flow from the old to the young to derive the
neutrality results of Section IV. Transfers of gifts
from the young to the old would lead to the same
sort of conclusions. Therefore, in a situation where
wages were growing at a relatively fast rate (in
excess, say, of the real rate of interest), making bequests from old to young less likely, the existence of
gifts from young to old would serve to preserve
Ricardian equivalence.
The Difference between Investment in
Education and Bequests

As mentioned, intergenerational transfers are a
necessary condition for deriving the Ricardian
equivalence proposition. Also, no distinction is made
between investment in an heir’s education or human
capital and a monetary bequest. However, Drazen
[11] points out that there may be important differences between these two types of bequests. Specifically, under the condition of unidirectional bequests from old to young that are primarily in the
form of investments in human capital, he finds that
government deficits may imply a change in net
wealth, and therefore have real effects.
His argument is based on the potential difference
between the return to human capital, re, and the real
rate of interest, r. Suppose it is reasonably assumed

that the return on human capital is positively related
to the amount invested in education, but that each
additional dollar of investment yields a slightly lower
return than the previous dollar invested. That is,
there are diminishing marginal returns to investment.
Under these assumptions, and since people do indeed invest in education, the first dollar so invested
yields a return greater than the real rate of interest.
Indeed, one may suppose that the return on education
is greater than the return on capital up to some
critical value of educational investment, denoted by
In this setting the optimal method of bequests would
be for parents to first make investments in their
child’s education up to an amount
and if further
bequests are desired to leave them in the form of a
monetary transfer. In the case where the optimal
level of bequests was less than
the return on human
capital would be greater than the real rate of interest.
In this setting, government debt issuance can have a
real effect. This real rate of government debt results
from a failure of private markets to equalize rates of
return among various investments. Alternatively,
the outcome in which e < represents a situation of
underinvestment in human capital.
It is this existence of a private market failure that
creates the possibility for government debt to have
real effects. This can be seen by reexamining the
analysis of Section IV for the case where e <
Suppose the government decreases the taxes of the
parents (generation i) when they are young and
finances some government spending through the
creation of debt. It then raises the taxes of the
young (generation i+1) to pay off the debt as well
as the interest on the debt. In Section IV, it was
shown that a dollar for dollar change in bequests
entirely offsets the government financing decision.
However, since the return on human capital is
greater than the real rate of interest, parents do not
have to invest all of the tax cut in their child’s education to leave their child’s attainable utility level
unaffected. The parent only has to invest a portion
of the tax cut in his child’s education, and could spend
the rest. A more likely occurrence would be for the
parent to invest enough in the child’s education to
make the child slightly better off and to spend the
rest making the parent slightly better off. As long as
human capital possesses a greater return than the
real rate of interest both generations can be made
better off by an increase in government debt, even
though the increase in debt will raise the real rate of
interest. In this case it is inappropriate to refer to
debt as a burden on future generations.


Again it should be stressed that Drazen’s results
occur because of a market failure. This market
failure arises for three basic reasons. One is the
reasonable assumption that there is no market in
human capital. That is, one can not generally enter
into a contract with his son saying that I will invest
so much in your education and force the son to repay
the loan at an interest rate equivalent to the return
on human capital. Another is that the son can not
invest in his own human capital. This seems less
reasonable, since educational loans (at the post-highschool level) are readily available, and it would not
be optimal to forego investing in one’s own education so long as the rate of return was greater than
the real rate. Allowing for own investment would
tend to equalize the real rate of interest and the
return on human capital, making changes in government financing neutral.
The third reason is the omission of a gift motive
from son to father. If one also allows the son to
care about his father, then it seems that in the presence of operational transfers in both directions the
situation in which r e > r would not represent an
equilibrium. For instance, suppose that intergenerational transfers are operative in both directions and
that re > r. The father will be investing in his son’s
human capital because the return to the son is greater
than the cost to the father. Further, the son gives
gifts to his father because the return on his education
may make him better off in real terms than his father.
Now with r e > r, the father could invest an additional dollar in his son’s education making his son’s
attainable utility higher while decreasing his own
utility. However, we have assumed that the son cares
about the father and that he gives gifts. That is, with
bidirectional transfers operational, a gift of a dollar
from the father (at the margin) will be returned by
the son leaving the proposed equilibrium unchanged.
But, because the return on the investment made in
his education is sufficient to both fully reimburse his
father and still leave enough to make himself better
off the situation with re > r is not optimal. That is,
it pays for the father to invest in the son up to the
point where r e = r.
Alternatively, suppose that the only form of bequest is investment in education (i.e., the case where
e <
and that the bequests motive is operational
in both directions. Suppose the government takes a
dollar from the father (when young) and gives it
with interest to the son. Since the son was already
giving a gift to his father, he could have consumed
more if he desired. That he did not implies that he

will give the dollar plus interest back to his father.
The father, therefore, knows that an additional bequest to the son will be returned with interest. However, since e <
a dollar invested in education will
yield the son more than the real rate of return. This
means that the son will return at least a dollar plus
interest to the father, while still having more for
himself. Both will be better off, and the situation
with r e < r is inefficient. That is the combined
budget sets of both the son and the father will be
maximized when investment in education is made up
to the point where re = r. Having transfers operate
in both directions essentially opens up a market in
human capital between the father and son, driving
the return on human capital down to r. In this situation there are no longer any real effects of government debt.


The situation in which some consumers are liquidity constrained also opens up an avenue that
allows government debt to have real consequences.
It is sometimes assumed that individuals can not
always borrow to the extent that they desire, since
capital markets may not lend money based on future
risky income streams. 10 Or, perhaps, individuals
knowing themselves better than a lending officer
discount their risky income at a lower rate. In any
event, if individuals are constrained to some extent
from borrowing against risky future income streams,
budget deficits will have real effects. The size of the
effects will depend on the proportion of income
earned by those who are constrained.
The effect originates because some portion of the
society would like to consume more of their wealth
but are constrained from doing so. A cut in taxes
today coupled with an appropriate increase in taxes
tomorrow is equivalent to making a loan to constrained individuals at the rate r. Since these individuals were constrained they will increase their consumption by at least some portion of the tax cut.
This will cause the real rate of interest to rise. However, the effect on social welfare of the government
debt is unclear. If the government is providing an
intermediation service that was not available due to
some private market failure then social welfare could
be enhanced. However, the loan to constrained individuals is made at the government’s borrowing rate,
which may not be the appropriate rate. This implies
that some subsidization is occurring between con10

For more detail see Zeldes [21], [22].


strained and unconstrained individuals making the
net effect on social welfare ambiguous.
Further, the apparent credit rationing may not be
due to any private market failure, but could result
as a consequence of optimal lending arrangements in
private markets. 11 In that case the intermediation
process provided by the government may be nonoptimal.
Related to this issue is the question regarding the
relative efficiency of the government in providing
intermediation services. If the government is more
efficient than the private sector, then social welfare
would be increased and the economic effects associated with a positive wealth effect of government debt
would occur. 12 The postulated relative efficiency of
the government may be important in developing
countries with unsophisticated financial sectors but is
unlikely to be relevant for the U. S. economy. Also,
in the case where the government does have a relative
advantage in performing financial intermediation it
is inappropriate to speak of the burden of public debt
since social welfare is enhanced.
Uncertainty over Income Streams

To this point, the analysis of the paper has dealt
with lump sum taxes rather than taxes that are
related to income. Doing so has been of little consequence, since income is exogenously given and an
individual’s income stream has been certain. (To see
that this is true the reader need only replace T by
tY in the preceding discussion, where t is the proportional tax rate.) However, in an analysis that
considers uncertain future income streams and risk
averse individuals, a distinction exists between lump
sum taxes and proportional income taxes, even if
income is taken to be exogenous.
The reason for this is straightforward. 13 R i s k
averse agents do not like risk. Therefore, the usual
effect of a reduction in risk is to make agents feel
wealthier implying that they will consume more.
Consider an agent who lives two periods earning a
known and therefore certain amount of income, Y 1,
in period 1 and an uncertain amount of income, Y 2,
in period 2. The variance of an individual’s after-tax
income in period 1 is zero, since he knows Y1 with
certainty, while the variance of his period 2 after-tax

A discussion of credit rationing in perfectly competitive
markets is given in Stiglitz and Weiss [18].

For a more thorough discussion see Barro [2] and
Chan [9].


See Chan [9] and Barsky, Mankiw, and Zeldes [7].


income is (1-t) 2 times the variance of Y 2 . Reducing this after-tax variability will make individuals
better off and generally increase period 1 consumption.
The government can accomplish this by lowering
the first period tax rate and increasing period 2’s tax
rate by enough to cover the resulting increase in the
deficit. Increasing t will lower the (1-t)2 c o m ponent of the variance of after-tax income. Thus,
individuals will be better off and will wish to consume more. This will cause the real rate of interest
to rise.
In essence, individuals are better off because the
government is operating an income insurance scheme.
This improvement in welfare can be seen by more
closely examining the taxes levied on a particular
agent in period 2, T2 = tY2, which can be rewritten

is the known average income level for individuals in period 2. If our agent has a lower than
average income level he receives an insurance payment, while if his income is relatively high he pays
what amounts to an insurance premium. By changing t, the government can affect the degree of aftertax income risk. Also, if
were uncertain, meaning
that aggregate income was uncertain, then an increase in t would lower aggregate uncertainty about
after-tax income, resulting in a welfare gain.
The provision of this insurance policy by the government improves welfare. If the market were able
to fully insure individuals against income risk there
would be no room for government financing decisions
to affect the economy. As in the previous discussion,
it is the presence of a market failure that allows
government financing decisions to be nonneutral.
Therefore, the existence of an economic effect caused
by government debt in the presence of uncertain
income presumes that the government has a relative
advantage in providing insurance.
Uncertainty over the Incidence of
Future Taxes

If future tax rates are uncertain, perhaps because
aggregate income is uncertain-therefore implying
that the government is unsure about the income tax
rate needed to raise necessary revenue-the wealth
effects of government debt could be negative. This
is because the variance of future after-tax income
may now be higher.


To isolate the effect of future income tax uncertainty, consider the case where taxes are lump sum
and the it h individual pays taxes equal to T+ke i
where e i is a random number and kei represents the
uncertain portion of tax payments faced by individual i. The sum of all random taxes is equal to zero.
This means that some individuals pay more than
average while some pay less. Now suppose that an
increase in future taxes is associated with an increase
in the uncertainty regarding the incidence of future
taxes (i.e., an increase in k). That is, the more
revenue the government needs to raise the greater is
the uncertainty concerning who will have to pay. In
this case, the increased uncertainty caused by an
increase in debt makes agents worse off, and they
therefore reduce consumption demand in period 1,
resulting in a fall in interest rates. Combining both
income and tax rate uncertainty into the analysis will
make the net effect of government debt ambiguous.
Summary of Ricardian Equivalence

In Sections IV and V, an analysis of Ricardian
equivalence has been presented along with a number
of the major criticisms that have been raised against
this theory. The major criticisms involve the absence
of a bequest motive, and the existence of various
market failures. On net these criticisms do not
seem to be capable of generating any large wealth
effects of government debt. The proportion of
society that does not exhibit any intergenerational
altruism does not seem to be very large. Also,
in a country like the United States with sophisticated
financial markets, the importance of liquidity constraints resulting from private market failures may
not be very great. Further, it is hard to believe that
the government is more efficient at providing intermediation services. Finally, the combined effects of
income uncertainty and tax incidence uncertainty are
ambiguous. Therefore, when income is exogenous,
the Ricardian theory of government debt appears to
hold up fairly well and one would expect the wealth
effects of government debt to at best be fairly small.
However, the exogeneity of income is a questionable assumption. Under this assumption the amount
that individuals work is independent of their tax rate.
This means that no consideration is given to substitution between labor and leisure, and that when no
wealth effects result from purely government financing decisions there are no social losses imposed by

the tax system. The implication is that for a given
path of government spending one amount of debt is
as good as another. If so, then the intensity of the
current debate over the size of the deficit is hard to
However, it could also be that the
assumption of income exogeneity is inappropriate and
that relaxing this assumption will provide some useful insights into the importance of deficits. This step
is taken in the next section. The importance of the
Ricardian equivalence theory is that it has forced
one to take this step, since it suggests that wealth
effects are not a major factor in understanding the
effects of government debt.

In this section the assumption regarding the exogeneity of income is dropped. Individuals can use
their time to either work or take leisure. The decision on how to spend their time will generally depend
on their after-tax wage rate. Therefore, tax rates
will affect the amount of labor supplied and will
create distortions in the economy. The job of the
government will be to choose tax rates that minimize
the amount of distortions subject to a future path of
government spending and an inherited amount of
debt. Choosing a path of tax rates for a given path of
government spending amounts to choosing a path for
government debt. This path is chosen to maximize
social welfare and usually involves both positive and
negative deficits. Hence a balanced budget is not
generally optimal.
It is important to note that the literature on optimal government deficits assumes that government
spending is exogenous. This is a fairly extreme
assumption, since government spending should more
appropriately be viewed as a choice variable. However, treating government spending as a choice variable with respect to some specific objective function
is unlikely to change the qualitative results presented
below. This is due to the reasonable belief that the
ratio of government spending to income will vary
optimally over time. For example, a state of war
would cause this ratio to temporarily rise. Also,
(with the exception of wartime spending) individuals
would probably prefer a relatively smooth path of
government spending for the same reasons that they



prefer a smooth consumption stream. This permanent income analogy between consumption of publicly
and privately produced goods implies that the ratio
of government spending to income should move countercyclically. 14 Although a complete analysis that
jointly determines the optimal levels of government
spending and tax rates would be valuable, the article
follows the treatment of the current literature by
assuming that government spending is exogenous.
In analyzing the optimal level of government debt,
the economy examined will be fairly simple. Individuals are assumed to live for two periods as does
the government. 15 Also, the production process involves only labor thereby omitting a discussion of
capital. 16 The relevant points concerning debt optimality can be made without considering capital.

steady state case of ß= 1/(1+r) individuals spend
equal amounts on consumption and leisure in each
p e r i o d i m p l y i n g t h a t c1 = c2 = l 1 = l 2 = ½ .
These values are consistent with economy-wide
market clearing in each period since c 1 = 1 - l 1 =
½ and c2 = 1 - l 2 = ½. That is, aggregate demand equals supply. (Since c and l are consumption
and leisure choices of the representative individual,
it is permissible to equate individual and aggregate
values without affecting the results of the analysis.)

The solution to the individual’s choice problem can
be depicted graphically by defining I = c + l. T h e
budget line has a slope of (1+r) and for the case
where ß = 1/(1+r), the individual will choose
I 1 = I2 = 1.0. This is depicted by the solid line in
Figure 2.

The Model without Taxes

The Model with Government
Spending and Taxation

The representative consumer maximizes his utility
by choosing consumption, c, and leisure, l, in each
period of his life subject to a lifetime budget constraint. Specifically, he maximizes

The analysis now turns to the problem when there
is a government that spends and raises revenue
through distortionary taxes. Taxes are levied against
labor income and government spending is not valued

Figure 2

For simplicity, a time separable quadratic utility
function is used and it is assumed that one unit of
labor yields one unit of output. This means that the
real wage rate is normalized to one. Using a time
separable quadratic utility function allows for easy
numerical calculations that illustrate the nature of
optimal taxation and budget deficits. In this case
the marginal utility of consumption and leisure are
1-c and 1-Z. This can be seen by taking the derivative of U with respect to c and l. For the long-run

Additional complications would arise from considering
the investment type qualities of government spending and
the role of government spending as an input in the production process. There is also the question concerning
the extent that agency type problems make the optimization of social welfare an unrealistic characterization of
government objectives.

The analysis abstracts from the complicated issue of
the time inconsistency of optimal tax policies. However,
many of the essential features corresponding to an optimal level of debt are still illustrated without introducing
the time consistency problem.

For a discussion of taxes on capital in a similar setting
see Aschauer and Greenwood [1].



by consumers or producers.17 The introduction of a
government alters the individual’s budget constraint
as well as the market clearing conditions. The individual’s budget constraint is now

The individual now maximizes his utility (9) subject
to the constraint that the present value of consumption is equal to the present value of after-tax income.
In this case one would not longer expect consumption and leisure to be equal since the relative price of
leisure has fallen. Prior to the introduction of a
government that raises revenue by taxing wages the
foregone income resulting from additional leisure was
one, while now it is
With leisure being
cheaper, people will work less and produce less. This
is the distorting nature of taxes.
The economy-wide market clearing conditions are
also altered to take into account the presence of the
government. In each period the amount of goods
produced must equal consumption plus government
spending. Specifically,

where g is government spending.
The government is also required to satisfy a budget
constraint given by

which indicates that the present value of government
spending equals the present value of government
revenue. This condition requires the government to
pay off any debt acquired in period 1 by raising
revenue in period 2. Without this requirement it
would be unreasonable for anyone to hold government debt and there would be no government debt
issue to consider.
Given the model economy described by equations
(9) (10’) (11) and (12), the government chooses tax
to maximize the utility of its citizens,
given an exogenous time path of government spending. To gain some insight into the nature of optimal
deficits two simple cases are analyzed below.

For the more complicated case where government
spending is productive and valued by consumers see
Aschauer and Greenwood [1].

Case 1. Optimal deficit with equal government
spending, g 1 = g2.
The first case examines the situation when government spending is constant over time. Intuitively,
one would expect the government to equalize the
level of distortions in each period and that
This implies that the government budget will be
balanced in each period.
In particular let g 1 = g2 = .10. In this case the
government chooses tax rates
Individuals therefore choose c 1 = c2 = .3870, and
sumes a little over twenty percent of output. And, as
conjectured, the government balances its budget in
each period.
It is interesting to compare this case to the example
of no government initially discussed in this section.
Consumption and output have fallen, while leisure
has risen.
Because government spending is not
valued by individuals, utility has also declined. In

dotted lines in Figure 2.
as the solution to an optimization problem by the
tral. That is, given that the government has chosen
the level of public debt optimally, small movements
in tax rates and the deficit will have no real consequences. If changes in tax rates are large, or if the
political outcome is one that doesn’t produce optimal
taxation, then government financing decisions will
have real consequences.
Case 2. The optimal deficit when government
spending is unequal, g1 = g 2.
This example investigates the optimal budget
deficit when government spending is unequal across
periods. For example, suppose that g 1 > g2 . This
could occur if the government were financing a war
or a temporary buildup in defense expenditures in
period 1. Similarly, one might view period 1 as
representing a cyclical downturn in which government transfer payments increase, while period 2
represents a cyclical upturn in which government
transfer payments fall.
Intuitively one would no longer expect the government to balance its budget in both periods. Rather,
the government would try to balance the distorting
aspects of taxes over both periods, running a deficit
in period 1 and a surplus in period 2.



The Balanced Budget Amendment

This section discusses the relationship between the
Balanced Budget Amendment (BBA) passed by the
Senate on October 1, 1982 and the literature on optimal budget deficits. Of particular’ relevance is the
material contained in section 1 of the amendment
(see Friedman and Friedman [13; p. 56]), which
requires that actual government spending be less than
or equal to planned government spending which in
turn must be less than or equal to planned receipts.
A formal interpretation of this section is that g t
Compare this to the nonoptimal behavior of balancing the budget period by period. In this case the first
period tax rate is .67, consumption is .l, and leisure
is .7. In the second period tax rates are zero, and
consumption and leisure are .5. The equilibrium real
rate is 1.40. Under an optimal budget deficit consumption and leisure are more effectively smoothed
over time. This smoothing reflects the desire of
individuals to have the burden of taxes appropriated
over each period. Forcing the budget to balance in
each period reduces the welfare of individuals.
Current Political Concerns

The material in this section has shown that under
distorting taxes, individuals care about deficits in
the sense that deficits help to allocate the burden of
uneven levels of government spending optimally over
time. The theory, therefore, implies that today’s
optimal deficit depends on the perceived future time
path of government spending as well as the inherited
existing debt structure of the current government.
The question of whether or not to reduce the current
deficit through increased taxes hinges upon beliefs
of future government spending patterns relative to
GNP. The Reagan administration’s reluctance to
increase taxes may rest largely on the expectation
that government will consume lower fractions of
output in the future. The reluctance to increase taxes
and the inclination to reduce current taxes can be
viewed as an optimal reaction to this expectation.
Proponents of tax increases must therefore feel
that government spending will exhibit secular growth
relative to GNP and that some of this future burden
should be optimally allocated to the current period.
The theoretical analysis presented in this section
indicates that much of the argument concerning the
size of the deficit is directly related to beliefs over
the expected size of the government.

T t is tax revenue, and Et- 1 is the conditional expectation of the variable in question.
As shown in Case 2, it is not generally optimal
for the government to balance its budget in each
and every period. The wording of the Balanced
Budget Amendment does not require the government
budget to balance ex post, since tax revenues are
generally uncertain and may deviate from their
planned or expected value. However, the language
of section 1 requires that the budget balance on
Even though the BBA does not require strict
budget balance in each period it still may force tax
policy to deviate from the optimal policies previously
outlined. This can be shown by means of a simple
example. Consider an economy that wasn’t growing
(growth could easily be incorporated into the analysis) and where government spending was fixed at
in every period. Assume that taxes are income taxes
and that income fluctuates in a predictable way
around some average level
An optimal policy
under these circumstances would be to set taxes so
that there was an anticipated surplus during relatively prosperous times and a deficit when income
was depressed. On average the governments budget
would balance. The BBA does not allow for this
type of behavior which would characterize optimal
tax policy over a business cycle. That is, the BBA
only allows for deviations from budget balance when
income movements are unanticipated, but does not
allow for planned changes in the level of debt that
would optimally accompany anticipated cyclical
changes in economic activity. This lack of response
to anticipated cyclical activity represents a welfare
cost with regard to this amendment.
A similar example exhibiting the welfare costs of
the proposed BBA, could be depicted for the case of
temporary anticipated movements in government expenditure, such as short-term increases in defense
spending. This is because the BBA does not gener-


ally allow for planned government budget deficits and
surpluses that are necessary if taxes are to be optimally smoothed. However, the amendment does contain an important element which allows for departure
from expected budget balance if three-fifths of the
Congress approves it. Therefore, it is conceivable
that optimal budget deficits and surpluses could be
produced under the amendment if economic conditions clearly warrant a departure from expected
budget balance.18 However, there is no guarantee
that the provision of section 1 of this amendment
will produce an optimal time path for taxes.
An Estimate of the Optimal Budget Deficit

In a recent Wall Street Journal article, Professor
Robert Barro estimates $165 billion as the optimal
budget deficit for 1984. The actual deficit was
approximately $170 billion and very close to the
optimum. Also, the size of the deficit which is in the
range of 4-5 percent of GNP, is claimed to be in line
with historical experience.
Barro’s method of estimation is linked with the
second example presented in this section. During
recessions, or periods where government spending
may be temporarily high relative to output, budget
deficits rise. This is part of the tax smoothing role
of deficits. According to Barro, the effect of the last
recession, 1980-83, has contributed approximately
$60 billion to the 1984 deficit. This estimate is a
result of the fact that output is still below its full
employment level and therefore the business cycle is
still contributing to a positive deficit.
Another major consideration is the extent to which
interest on the debt should be financed by taxes. A
financing of the expected inflation component of
interest payments on the debt by the issue of new
debt would leave the debt to GNP ratio unchanged,
and place no further real burden on society. Barro
estimated that $70-$75 billion of an optimal amount
of debt arises from this component.
Another part of interest payments that should be
financed through debt rather than taxes are those
that are due to higher than average real interest rates.
The reason for using debt to smooth these payments
is analogous for using debt to smooth taxes over the
business cycle. When real rates are higher than

The provisions of the amendment may also be waived
in any fiscal year in which there exists a declaration of
war. Since wars are one of the primary examples of
temporary government spending that should not be
totally financed over their duration, the amendment does
take declared wars explicitly into consideration.

normal the debt will grow and when real rates are
lower than normal the debt will fall. On average
there would be no long-run change in government
debt and therefore no reason to shift tax rates to
finance this portion of interest payments. Since real
rates appear to be abnormally high, Barro estimates
that this factor has contributed roughly $30 billion
to the 1984 deficit. Adding up the three factors produces an optimal deficit of $160-$165 billion for 1984.
The prediction for future optimal deficits is much
the same as the prediction for 1984. Basically, the
optimal level of the deficit will change if there is rapid
future economic growth relative to changes in government spending, or if inflation and real interest
rates fall. Current forecasts of these variables over
the near future do not point to any major changes in
the optimal level of the budget deficit. Therefore it
is only to the extent that proposed deficits differ from
the optimum that the deficit should be a matter of
It should be mentioned that Barro’s estimates depend on assumptions regarding the normal level of
the real interest rate, the extent to which the business
cycle downturn of 1980-83 has contributed to the
deficit, and forecasts of expected inflation. Differing
views concerning these factors will produce different
estimates of the optimal deficit. However, Barro’s
analysis is useful in providing a framework for examining the current deficit with respect to some desirable standard.
This article has examined the effects that government budget deficits have on the economy given a
variety of assumptions regarding the actual workings
of the economy. Although the survey presented is
far from exhaustive, it does attempt to highlight the
major issues associated with the economic consequences of budget deficits. In that regard, the article
first focused on the expansionary effects as well as
the economic burdens of government deficits that are
derived in a simple Keynesian framework. Criticisms
of that framework were then discussed in light of the
Ricardian equivalence proposition. Features of that
proposition were explored, with the conclusion that
wealth effects are probably not an important channel
for analyzing the effects of government deficits.
The article then focuses on the notion of optimal
deficits in an economy with taxes on labor income.
Because distortions are introduced into the economy
through the tax system, the government has an in-



centive to minimize these distortions given a projected path of government spending and an inherited
structure of public debt. It does so by smoothing
taxes over time. This process leads to movements in
debt that are associated with temporary changes in
government spending relative to output. Wars and
business cycle phenomena are therefore primary
factors in causing the optimal level of debt to vary
over time.

The paper concludes with a brief analysis of the
political controversy surrounding the current budget
deficit in relation to the ideas concerning the optimal
debt. Perhaps much of the controversy is related to
differing desires or forecasts over movements in the
size of government. A rough estimate of $165 billion
as the optimal level of government debt is given as a
yard stick on which to evaluate proposed budget

1. Aschauer, David, and Jeremy Greenwood. “Macroeconomic Effects of Fiscal Policy.” CarnegieRochester Conference Series on Public Policy, vol.
23, ed. by K. Brunner and A. H. Meltzer. Amsterdam: North Holland, 1985, forthcoming.
2. Barro. Robert J. “Are Government Bonds Net
Wealth?” Journal of Political Economy 82 (November/December 1974) : 1095-117.

“Reply to Feldstein and Buchanan.”
Journal of Political Economy 84 (April 1976) :



“Public Debt and Taxes.” In Federal
Tax Reform: Myths and Realities, ed. by Michael
J. Boskin. San Francisco: Institute for Contemporary Studies, 1978.


“On the Determination of Public
Debt.” Journal of Political Economy 87 (October
1979) : 940-71.


“A Deficit Nearly on Target.” Wall
Street Journal, January 29, 1985, p. 32.


13. Friedman, Milton, and Rose Friedman. Tyranny
of the Status Quo. New York: Harcourt, Brace,
Jovanovich, 1984.
14. Lucas, Robert E., Jr., and Nancy L. Stokey. “Optimal Fiscal and Monetary Policy in an Economy
without Capital.” Journal of Monetary Economics
12 (July 1983) : 55-93.
15. McCallum, Bennett T. “The Optimal Inflation
Rate in an Overlapping Generations Economy with
Land.” Carnegie-Mellon University, June 1985.
16. Penner, Rudolph G. Prepared Statement to Senate
Budget Committee. Hearings before the Committee
on the Budget, U. S. Senate, 99th Cong., 1st sess.,
February 6, 1985.
Washington : Government
Printing Office, 1985.
17. Persson, Torsten, and Lars E. O. Svensson. “TimeConsistent Fiscal Policy and Government CashFlow.” Journal of Monetary Economics 14 (November 1984) : 365-74.
18. Stiglitz, Joseph E., and Andrew Weiss. “Credit
Rationing in Markets with Imperfect Information.”

8. Bryant, John. “Government Irrelevance Results :
A Simple Exposition.” American Economic Review
83 (September 1983) : 758-61.
9. Chan, Louis Kuo Chi. “Uncertainty and the Neutrality of Government Financing Policy.” Journal
of Monetary Economics 11 (May 1983) : 351-72.
10. Dornbusch, Rudiger, and Stanley Fischer. MacroEconomics. New York: McGraw-Hill Book Company, 1978.
11. Drazen, Allan. “Government Debt, Human Capital,
and Bequests in a Life-Cycle Model.” Journal of
Political Economy 86 (June 1978) : 505-16.
“Consequences of Lowering
12. Feldstein, Martin.
Future Budget Deficits,” in Economic Impact of
Spending Reductions. Hearing before the Committee on Finance. U. S. Senate. 98th Cong., 2d
sess., January 2, 1985. Washington: Government
Printing Office, 1985.


19. Tobin James. Asset Accumulation and Economic
Activity. Chicago : University of Chicago Press,
20. Volcker, Paul A. “Opportunities and Dangers.”
Broyhill Executive Lecture Series. Babcock Graduate School of Management, Wake Forest University, March 23, 1984.
21. Zeldes, Stephen. “Optimal Consumption with Stochastic Income : Derivations from Certainty
Equivalence.” Massachusetts Institute of Technology, 1983. (Processed.)

“Consumption and Liquidity Constraints: An Empirical Investigation.” Wharton
School of the University of Pennsylvania, November 1984. (Processed.)


Thomas M. Humphrey

Although critics may dismiss it as a mere empirical
correlation masquerading as a tradeoff, the Phillips
curve relationship between inflation and unemployment has nevertheless been a key component of
macroeconomic models for the past 25 years. In
1960 Paul Samuelson and Robert Solow [16, p. 192]
named the relationship after A. W. Phillips, the New
Zealand economist who in 1958 gave it its best known
(but hardly its first) modern formulation (see Figure 1). Since then it has evolved through at least
five successive versions as analysts sought to expand
its explanatory power, its theoretical content, its
policy relevancy, and its ability to fit the facts.
Phillips’ [15, p. 290] initial wage-change version
w=f (U) related the rate of wage inflation w via the
function f( ) to the excess demand for labor as

measured by U, the deviation of unemployment from
its equilibrium or labor-market clearing rate. Transformed through the assumed markup of prices over
wages into the price-change equation p=f (U), where
p is the rate of price inflation, it was widely interpreted as a stable enduring tradeoff or menu of
inflation-unemployment combinations from which the
authorities could choose. In its shift-adjusted form
p=f (U)+Z, it incorporated a vector of variables Z,
including past price changes, trade union effects,
unemployment dispersion, demographic factors and
the like, to account for observed shifts in the inflationunemployment tradeoff or menu of policy choices.
In its e x p e c t a t i o n s - a u g m e n t e d form p-p e= f ( U ) ,
where pe is the expected rate of inflation, it asserted
(1) that the tradeoff is between unemployment and
unexpected inflation, (2) that the tradeoff vanishes
when expectations are realized, and (3) that unemployment returns to its natural equilibrium rate at
this point. Provided expectations adjust to actual
inflation with a lag, it also implied the accelerationist
notion that unemployment can be pegged permanently
below its natural rate only if inflation is continually
accelerated so as to always stay a step ahead of expectations. That is, while denying a permanent tradeoff between unemployment and the rate of inflation,
it implied that there may be a permanent tradeoff
between unemployment and the rate of acceleration of
The preceding versions reflect a non-marketclearing view of the world, expressing as they do the
disequilibrium response of wages and prices to a
mismatching of demand and supply in the labor
market. By contrast, the alternative New Classical
or market clearing version U=g(p-p e ) assumes
that the labor market is always in equilibrium and
that deviations of unemployment from its natural
rate stem solely from inflation misperceptions and
vanish when those misperceptions end. When com-



bined with the assumption of rational expectations
(according to which actual inflation differs from
expected inflation only by a random forecast error)
this version says that tradeoffs are solely the result
of unpredictable random shocks and cannot be exploited by systematic (predictable) policies.
The foregoing interpretations are well known. Not
so well known, however, is the origin and early history of the inflation-unemployment relationship. For
the most part, textbooks typically trace the idea to
Phillips’ famous 1958 Economica article without saying anything about what went before. They correctly
describe the five versions of the Phillips curve outlined above. But they fail to note that at least three
of those versions (including the version presented by
Phillips himself) had already been spelled out long
before Phillips. The result is to neglect at least ten
predecessors whose names deserve to be associated
with the Phillips curve. In an effort to redress this
oversight and to set the record straight, the paragraphs below document what Phillips’ predecessors
had to say about the inflation-unemployment relationship.
John Law (1671-1729)

It is probably unrealistic to expect to find a
Phillips curve in the writings of John Law, the
famous eighteenth century banker and finance minister whose schemes to promote economic development
via the creation of a paper currency secured by land
ended with the collapse of the Mississippi Bubble in
1720. To be sure, he believed that money stimulates
real activity. But he also believed that it does so at
constant or even decreasing prices owing to the
availability of idle resources and scale economies in
production. As a result, there is either no Phillips
curve inflation-unemployment relation in his analysis
or it works in the wrong direction-falling unemployment being associated with falling, not rising,
David Hume (1711-1776)

The prototypal Phillips curve analysis is to be
found in the writings of the eighteenth century Scottish philosopher-economist David Hume. As early
as 1752, he presented the essentials of a Phillips curve
relationship of the form U=g(dP/dt), where U is
the deviation of unemployment from its natural

(equilibrium) rate and dP/dt is the change in the
price level with respect to time. This relationship
derived straight from his assumption that unemployment disturbances stem from price perception errors
(the difference between actual and perceived prices)
and that such errors persist only when prices are
changing. Expressed symbolically, he assumed that
U = h ( P - PE ) a n d
P - PE = k d P / d t
where P and PE denote actual and perceived prices
and k is a coefficient relating price perception errors
to price level changes. Substitution of the latter
equation into the former yields Hume’s version of the
Phillips curve U=g(dP/dt) mentioned above. That
version embodied his hypothesis that one must continually raise prices to peg unemployment at arbitrarily low levels since only by doing so can one
produce the price perception errors that sustain the
tradeoff. In short, Hume’s explanation stresses the
employment effects of unperceived monetary-induced
price changes. He [8, pp. 37-40] says:
though the high price of commodities be a necessary consequence of the encrease of gold and silver,
yet it follows not immediately upon that encrease;
but some time is required before the money circulates through the whole state and makes its effect
be felt on all ranks of people. At first, no alteration is perceived; by degrees the price rises, first
of one commodity, then of another; till the whole at
last reaches a just proportion with the new quantity of specie . . . . In my opinion, it is only in
this interval or intermediate situation, between the
acquisition of money and rise of prices, that the
encreasing quantity of gold and silver is favourable
to industry . . . . From the whole of this reasoning
we may conclude, that it is of no manner of consequence, with regard to the domestic happiness of a
state, whether money be in a greater or less quantity. The good policy of the magistrate consists
only in keeping it, if possible, still encreasing;
because, by that means, he keeps alive a spirit of
industry in the nation . . . . There is always an
interval before matters be adjusted to their new
situation; and this interval is as pernicious to industry, when gold and silver are diminishing, as it
is advantageous when these metals are encreasing.

Three points stand out in Hume’s analysis [10].
First, the tradeoff is between unemployment and unperceived changes in money and prices; it vanishes
once perceptions fully adjust to reality.
price perceptions, though slow to adjust, eventually
catch up to one-time changes in the level of money
and prices. It follows that such changes can at best
generate temporary but not permanent tradeoffs.


Third, the only way the tradeoff can be sustained is
to generate a continual succession of changes in
money and prices. Hume here makes the distinctly
non-rational-expectations argument that such changes
will, because of the lag in the adjustment of price
perceptions, keep prices forever marching a step
ahead of perceptions, perpetually frustrating the
latter’s attempts to catch up. In this way, he claims,
the gap between actual and perceived prices will be
maintained thus permanently lowering unemployment. Hume notes that this process works symmetrically for price deflation-such deflation, if prolonged, producing an enduring rise in unemployment.
It follows at once that a permanent tradeoff U=
g(dP/dt) exists between unemployment and the rate
of change of money and prices. One must therefore
agree with Charles R. Nelson’s [14, p. 2] recent
judgment that
Hume was clearly of the opinion that the level of
activity would be raised permanently by a steady
increase in the quantity of money, prices, and
wages. Hume was therefore a believer in a stable,
long-run Phillips curve.

in his [19, p. 256] remark that “it is the progressive
augmentation of bank paper, and not the magnitude
of its existing amount, which gives the relief.” In
other words, money and prices stimulate activity only
when they are continually increasing. For, says
Thornton [19, p. 238], “While paper is encreasing,
and articles continue rising, mercantile speculations
appear more than ordinarily profitable.” But “as
soon . . . as the circulating medium ceases to encrease, the extra profit is at an end,” and the stimulus
vanishes. Thus a one-time rise in the money stock
and level of prices cannot sustain the tradeoff. Instead, a continuous increase or “progressive augmentation” is required. The tradeoff is between output
and the rate of change of prices.
As for the tradeoff’s source, Thornton attributed it
chiefly to a tendency for money wages to consistently
lag behind prices. He explicitly stated (1) that
inflation stimulates activity, (2) that it does so by
reducing real wages and raising real profits, (3) that
this output-enhancing redistribution occurs because
money wages lag behind prices, and (4) that this
wage lag persists as long as inflation is sustained.
Like Hume, he did not explain why the lag would

Henry Thornton ( 1760-1815)

Like Hume, Henry Thornton also described a
Phillips curve of the form U=g(dP/dt), where the
variables are as defined above [10]. In his classic
An Enquiry into the Nature and Effects of the Paper
Credit of Great Britain (1802) he [19, p. 237] says
that a monetary expansion stimulates employment
by raising prices:

persist nor why wages would not eventually catch up
with prices once inflationary expectations had fully
adjusted to actual inflation. His analysis is largely
silent about inflation anticipations; he did not incorporate them into his Phillips curve.

. . . additional industry will be one effect of an

Finally, he disagreed with Hume over the desirability of exploiting the Phillips curve for policy
Hume clearly believed that the policy
authorities in the closed world economy should exploit the curve, using monetary gold inflation to
stimulate employment. Hume [8, pp. 39-40] says as
much in his advice to the policymaker.

This same tradeoff, he [19, p. 238] notes, also holds
in reverse as monetary and price deflation bring
painful rises in unemployment.

The good policy of the magistrate consists only in
keeping [money], if possible still encreasing; because, by that means, he keeps alive a spirit of
industry in the nation, and encreases the stock of
labor, in which consists all real power and riches.

extraordinary emission of paper, a rise in the cost
[i.e., price] of articles will be another. Probably
no small part of that industry which is excited by
new paper is produced through the enhancement of
the cost of commodities.

If we assume the augmented paper to be brought
back to its ordinary quantity, we must suppose
industry to languish for a time through the ill
success [of] mercantile transactions.
In his discussion of the Phillips curve, Thornton

was careful to distinguish between alternative levels
of money and prices and continuous changes of those
variables. Only the latter, he said, can affect real
activity and sustain the tradeoff. This is epitomized

In contrast, Thornton opposed the exploitation of
the Phillips curve for policy purposes. Such exploitation involved inflation, which he saw as an
unmitigated evil. All inflationary policy, he [19,
p. 239] said, is “attended with a proportionate hardship and injustice.” True, output and employment
would rise. But such gains, he thought, would be
far too small to be worth the costs (uncertainty, in-



justice, social discontent) of higher inflation. In
short, the Phillips curve at the economy’s normal
level of operations was very steeply sloped, allowing
little increase in output per unit rise in inflation.
Thus while “paper possesses the faculty of enlarging
the quantity of commodities by giving life to some
new industry,” the unfavorable tradeoff ensures that
“the increase of industry will by no means keep pace
with the augmentation of paper.” Moreover, because
the economy normally operates close to its absolute
full capacity ceiling, stimulative policy will quickly
reach the point where
it is obvious that the antecedently idle persons to
whom we may suppose the [monetary inflation] to
give employ, are limited in number; and that,
therefore, if the encreased issue is indefinite, it
will set to work labourers, of whom a part will be
drawn from other, and, perhaps, no less useful
On these grounds he [19, p. 236] concluded that
there exist narrow “bounds to the benefit which is
to be derived from an augmentation of paper; and,
also, that a liberal, or, at most, a large increase of it,
will have all the advantageous effects of the most
extravagant emission.”
The Attwood-Mill Debate

The Phillips curve concept continued to flourish in
the hands of more than one British classical writer
after Henry Thornton. That this is so is evident
from a glance at the celebrated interchange between
Thomas Attwood (1783-1856) and John Stuart Mill
(1806-1873) in the 1820s. Attwood, an inflationist
proponent of inconvertible paper currency regimes
and full employment at any cost, believed in a stable
long-run tradeoff relationship of the form U=g(P)
where U and P denote unemployment and the price
level, both taken relative to their normal (base
period) values. Attwood used this relation, in which
the inflation variable enters as a price level rather
than its Hume-Thornton rate of change, to argue
(1) that high unemployment stems from low prices,
(2) that low unemployment emanates from high
prices, and (3) that the government can and should
achieve a zero target rate of unemployment with
inflationary monetary expansion. For him nothing
short of absolute full employment would suffice. Said
he [3, p. 467], “so long as any number of industrious
honest workmen in the Kingdom are out of employ20

ment, supposing such deficiency of employment not
to be local but general, I should think it the duty,
and certainly the interest, of Government, to continue
the depreciation of the currency until full employment is obtained and general prosperity.” “Restore
the depreciated state of the currency,” he [2, p. 66]
declared, and “you restore everything that constitutes
the commercial prosperity of the nation.”
Opposing him was John Stuart Mill who reasoned
in terms of the relationship U=g(P-P E ) where U
is the discrepancy between unemployment and its
natural steady-state level, P is the price level, and P E
is its expected or perceived level. Using this relationship, Mill argued (1) that tradeoffs are temporary,
(2) that they stem from unexpected price changes
and vanish once perceptions adjust to reality, and
(3) that, contrary to Attwood, one cannot peg real
activity at arbitrarily low levels simply by pegging a
nominal price (or inflation) variable since the two
variables are independent of each other in steadystate equilibrium [9].
To be sure, Mill admitted that a temporary inflationary stimulus is possible. It is true, he [13, p. 79]
said, that an unexpected inflation, if misperceived as a
rise in relative prices, “may create a false opinion of
an increase of demand; which false opinion leads, as
the reality would do, to an increase of production.”
But it is also true that the real expansion is “followed
. . . by a fatal revulsion as soon as the delusion
ceases.” In other words, once producers correctly
perceive price increases as nominal rather than real,
economic activity reverts to its steady-state level,
but only after undergoing a temporary recession to
correct for the excesses of the inflationary boom.
In Mill’s view, the steady-state Phillips curve is a
vertical line at the economy’s natural rate of unemployment. To assert otherwise (as Attwood did), he
thought, was to argue that people can be fooled perpetually into believing that nominal gains are real
and that commodities can be created from paper
money expansion. But according to Mill, one cannot
fool all the people all the time. Money illusion, he
contended, is not permanent. Attempts to peg real
activity are therefore bound to be futile. Inflation
cannot permanently stimulate activity. Mill’s reply
to Attwood dispels the notion that expectationsaugmented Phillips curves and the natural rate hypothesis are of recent origin.


Irving Fisher ( 1867-l 947)

As noted above, Hume and Thornton helped lay
the theoretical foundations of the particular Phillips
curve relationship U=g(dP/dt).
It was Irving
Fisher, however, who provided the first statistical
evidence of that relationship [7]. In his 1926
International Labour Review article, “A Statistical
Relationship Between Unemployment and Price
Changes,” he investigated the correlation between
unemployment U and lagged price changes (dP/dt)L,
where the subscript L denotes a linear distributed lag
(Fisher himself being the inventor of the lag distribution concept) on the price-change variable. Using
monthly U. S. data for the period 1915-1925, he
obtained correlation coefficients as high as 90 percent
between the two variables. Likewise, his time series
chart displayed a similar strong correspondence between lagged price changes and employment (see
Figure 2). From this evidence he concluded that
there was indeed a strong relationship between them.
He [7, p. 502] also concluded that the relationship
was causal as well as empirical, that causality runs
undirectionally from price changes to unemployment,
and that there are good theoretical reasons for this
being so. His theory of price-to-unemployment

causality relies on fixed contracts, the inertia of
custom, and other inhibiting factors that prevent
costs from adjusting as fast as prices when prices
change. Owing to the lag of costs behind prices,
changes in the latter affect profits and thereby the
level of real activity and employment. Via this linkage, causality, he argued, runs from inflation to unemployment as confirmed by his finding that the
former variable leads the latter.
Jan Tinbergen

Although he presented no formal econometric
equations, Fisher was the first to offer empirical
corroboration of the Phillips curve’s market clearing
version U=g(dP/dt) according to which causality
runs from inflation to unemployment. By contrast,
Jan Tinbergen [4] in 1936 was the first to estimate
the alternative shift-augmented wage-change version
w=f(U)+Z in which causality runs from unemployment or some equivalent measure of demand
pressure in the labor market to the wage inflation
rate and a vector of shift variables enters to affect
the wage-unemployment tradeoff. More precisely,
h i s e q u a t i o n w a s o f t h e f o r m d W = F ( E , d P - 1)
where dW is the change in money wages, E is
employment relative to its normal (i.e., trend) level,
and the lagged price-change variable dP-1 represents
catch-up or cost-of-living wage adjustment factors
thought capable of shifting the curve. Thus in his
“An Economic Policy for 1936” he presents the
expression dW = 0.16 E + 0.27 dP -1 in which the
numerical coefficients are estimated from the Netherlands data for the period 1923-1933.
About this equation three things must be said. It
was the first econometric Phillips curve equation ever
to appear in print. It also was the first to explain
the tradeoff in terms of the law of supply and demand
according to which the price of any good or service
(including labor) varies in proportion to the excess
demand for it. In other words, for the first time the
Phillips curve was interpreted as a wage-reaction
function relating the disequilibrium response of
wages to demand pressure in the labor market, this
pressure being measured by employment relative to
Finally, as mentioned above, Tinbergen’s
equation was the first to include a price change shift
variable to account for observed movements in the
wage-employment relationship. In these respects, it



foreshadowed 1960s-vintage wage equations that likewise represented the Phillips curve as a demandpressure wage-response function subject to shifts
owing to changes in the cost of living.
Tinbergen returned to the Phillips curve issue
once again in his Business Cycles in the United
Kingdom 1870-1914, published in 1951 fully seven
years before Phillips’ contribution. There, using W
to denote wages and E to denote employment, he [21,
p. 50] writes the Phillips curve equation as

and gives it the excess-demand wage-reaction interpretation. “The theory expressed” in the equation,
he says, “may be given the well-known formulation
that a high unemployment figure ‘exerts a pressure
on’ the wage rate and that, on the other hand, a
small unemployment figure causes wages to go up.”
He also notes that the equation’s empirical fit might
be improved if the demand-pressure variable were
entered nonlinearly and that this could be accomplished by replacing the employment variable E with
the inverse of the unemployment rate U -1. Finally,
he suggested adding variables representing cost-ofliving changes and the degree of unionization of
the labor force to the equation to improve its statistical fit. On all of these innovations he pioneered
the practice of fitting econometric Phillips curve
Klein and Goldberger

Lawrence Klein and Arthur Goldberger also estimated econometric inflation-unemployment equations
before Phillips. In their famous 1955 study A n
Econometric Model of the United States, 1929-1952,
they [11, p. 19] presented a wage-change Phillips
curve equation of the form dW=F(U,dP -1 ). More
precisely, their equation was

where U is total unemployment, t is a time trend in
years (t=1 in 1929), and the other variables are as
defined above.
Like Tinbergen, Klein and Goldberger expressed
the wage inflation variable in first difference rather
than percentage rate of change form. Besides including a time trend variable, they also entered the unemployment variable linearly rather than nonlinearly

into their equation. Except for these minor differences, their equation is virtually the same as the later
formulations of Phillips and R. G. Lipsey, who
clarified and extended Phillips’ work. And like those
latter writers, Klein and Goldberger interpreted their
equation as a wage-reaction function in which money
wages change in response to excess labor demand in
an effort to clear the market. According to them
[11, p. 18]
the main reasoning behind this equation is that of
the law of supply and demand. Money wage rates
move in response to excess supply or excess demand
in the labor market. High unemployment represents high excess supply, and low unemployment
below customary frictional levels represents excess
Here is the essence of the Phillips-Lipsey interpretation, an interpretation that also runs in terms of
the law of supply and demand.
A. J. Brown and Paul Sultan

As documented above, the theoretical, empirical,
and econometric foundations of the Phillips curve
had been thoroughly established by the mid-1950s
several years in advance of Phillips’ own contribution.
It remained, however, for someone to present a
Phillips-type relationship on a statistical scatter diagram and then to draw the familiar downwardsloping convex tradeoff curve that bears his name.
Credit for being the first to accomplish these tasks
goes not to Phillips himself but rather to two other
economists, A. J. Brown and Paul Sultan.
The former, in his 1955 volume The Great Inflation 1939-1951, presented scatter diagrams similar to
Phillips’ (see Figure 3) that plotted annual wage
inflation rates against unemployment rates for the
United Kingdom for the periods 1880-1914 and 19201951, and for the United States for the period 19211948. From these charts Brown [5, pp. 91-101]
concluded (1) that the two variables are inversely
related, and (2) that the relationship between them
is nonlinear since wages change at faster rates at
low than at high rates of unemployment. He also
used his charts to estimate the critical noninflationary
level of unemployment below which wage inflation
exceeds productivity growth so that prices rise. He
did not, however, fit a curve to his data. Thus,
although he presented a Phillips-type graph, he failed
to draw the eye-catching curve made famous by


Phillips. For this reason, one must reject A. P.
Thirlwall’s [18] contention that the curve should
bear Brown’s name rather than Phillips’.
Priority for drawing the Phillips curve goes to
Paul Sultan, whose contribution predates Phillips’
by one year. Thus, in his 1957 textbook Labor Economics, Sultan presents the curve in a diagram (see
Figure 4) described by him [17, p. 555] as follows :
the vertical scale measures the annual changes in

the price level expressed as a percentage, while the
horizontal scale measures the percentage of the
work force unemployed. The line relating unemployment to inflation . . . is strictly hypothetical,
but it suggests that the tighter the employment
situation the greater the hazard of inflation . . . .
Assuming that a fairly precise functional relationship exists between inflation and the level of employment, it is possible to determine the “safe”
degree of full employment. In our hypothetical
case, we are assuming that when unemployment is
less than 2 percent of the work force, we face the
dangers of inflation. And when unemployment is
larger than 6 percent, we face the problem of
serious deflation.

Here is the first diagrammatic representation of the
price-change Phillips curve as a stable tradeoff relationship p=f(U) between inflation and unemploy-

ment. On the basis of this diagram, three writers [1]
recently have suggested that the Phillips curve could
with equal justification be called the Sultan schedule.


Given the evidence presented in the preceding
paragraphs, the label “Phillips curve tradeoff” must
be judged both misleading and incomplete. For, as
documented above, Phillips was far from the first to
postulate an inflation-unemployment tradeoff or to
draw the curve bearing his name. Even the econometric wage-price equations employed in modern
Phillips curve analysis together with their excess
demand and alternative market clearing interpretations long predate Phillips. In short, Phillips and
his successors inherited (albeit unknowingly) these
concepts; they did not invent them. In this sense at
least, their work may be said to constitute the continuation rather than the origin of Phillips curve
Still, it was Phillips’ formulation and not those of
his predecessors that captured the attention of the
economics profession. One must ask why this was so.
Certainly it cannot be explained by the novelty of his



curve or its empirical derivation; these were hardly
innovations at the time he presented them. Nor can
it be attributed to any originality in his explanation
of his curve. His theory was simply the law of supply
and demand according to which the price of any
commodity or service (including labor) changes at a
rate proportional to the excess demand for it. This
explanation of course had been advanced by Tinbergen years before Phillips. Rather his phenomenal
success probably stemmed from three factors. First
was his striking finding of the apparent near 100-year
empirical stability of his curve, a stability not suspected before. Second was the persuasive early expositions of his work provided by such influential
economists as Lipsey [12], and Samuelson and Solow
[16]. Especially important was the Samuelson-Solow

interpretation of Phillips’ curve as a menu of policy
choices, a menu from which the authorities could
select the best (or least undesirable) inflationunemployment combination and then use their policy
instruments to attain it. By providing a ready-made
justification for discretionary intervention and activist fine tuning, this interpretation helped make the
Phillips curve immensely popular among Keynesian
policy advisors. Third was Phillips’ presentation of
his curve at just the right time to satisfy the Keynesians’ search for an explanation of how changes in
nominal income divide into price and quantity components. Whatever the reason, his name alone was
attached to the tradeoff concept even though at least
ten predecessors over a period of roughly 250 years
also shared in its formulation.

1. Amid-Hozour, E.; D. T. Dick; and R. L. Lucier.
“Sultan Schedule and Phillips Curve; an Historical Note.” Economica 38 (August 1971) : 319-20.
2. Attwood, Thomas. The Remedy; or, Thoughts on
the Present Distresses. Second edition, with additions. London : 1816.

Evidence Before the Select Committee
on the Bank of England Charter, 1831-2, p. 467.

“The Phillips Curve : Another
4. Bacon, Robert.
Forerunner.” Economica 40 (August 1973) : 31415.
The Great Inflation, 1939-1951.
5. Brown, A. J.
London : Oxford University Press, 1955.
6. Donner, Arthur and James F. McCollum. “The
Phillips Curve : An Historical Note.” Economica
39 (August 1972) : 323-24.
7. Fisher, Irving. “A Statistical Relation between
Unemployment and Price Changes.” International
Labour Review 13 (June 1926) : 785-92. Reprinted
as "I Discovered the Phillips Curve.” Journal of
Political Economy 81 (March/April 1973) : 4968. Hume, David. “Of Money” (1752). Reprinted in
his Writings on Economics. Edited by Eugene
Rotwein. Madison : University of Wisconsin Press,
9. Humphrey, Thomas M. “Two Views of Monetary
Policy : The Attwood-Mill Debate Revisited.” Economic Review, Federal Reserve Bank of Richmond
63 (September/October 1977) : 14-22.

“Of Hume, Thornton, the Quantity
Theory, and the Phillips Curve.” Economic Review,
Federal Reserve Bank of Richmond 68 (November/
December 1982) : 13-18.

11. Klein, Lawrence R. and Arthur S. Goldberger. An
Econometric Model of the United States 1929-1952.
Amsterdam : North-Holland Publishing Company,


12. Lipsey, R. G. “The Relation between Unemployment and the Rate of Change of Money Wage Rates
in the United Kingdom, 1862-1957: A Further
Analysis.” Economica 27 (February 1960) : l-32.
13. Mill, John Stuart. “The Currency Juggle.” Tait’s
Edinburg Magazine (1833). Reprinted in Vol. I
of his Dissertations and Discussions. Boston: 1865.
14. Nelson,, Charles R. “Adjustment Lags Versus Information Lags: A Test of Alternative Explanations of the Phillips Curve Phenomenon.” Journal
of Money, Credit and Banking 13 (February
1981) : l-11.
15. Phillips, A. W. “The Relation between Unemployment and the Rate of Change of Money Wage
Rates in the United Kingdom, 1861-1957.” Economica 25 (November 1958) : 283-99.
16. Samuelson, Paul A., and Robert M. Solow. “Analytical Aspects of Anti-inflation Policy.” American
Economic Review 50 (May 1960) : 177-94.
17. Sultan, Paul. Labor Economics. New York: Henry
Holt and Company, Inc., 1957.
18. Thirlwall, A. P. “The Phillips Curve: An Historical Note.” Economica 39 (August 1972) : 325.
19. Thornton, Henry. An Enquiry into the Nature and
Effects of the Paper Credit of Great Britain
(1802). Edited with an introduction by F. A. von
Hayek. New York: Rinehart and Company, Inc.,
20. Tinbergen, Jan. “An Economic Policy for 1936.”
Reprinted in his Selected Papers. Edited by L. H.
Klaassen, L. M. Koyck, and H. J. Witteveen. Amsterdam : North-Holland Publishing Company,

. Business Cycles in the United Kingdom., 1870-1914. Amsterdam: North-Holland Publishing Company, 1951.


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