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SUMMER 1982
Opinions expressed in the Economic Review do not necessarily reflect the views of the management of
the Federal Reserve Bank of San Francisco, or of the Board of Governors of the Federal Reserve
System.
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2
Time and Economics
I.
II.
Introduction and Summary
4
On Federal Deficits and their Economic Impact
6
Rose McElhattan
... We have found that deficits have significant real output effects when we measure changes
in their components, high employment expenditures and receipts, relative to their past
average rates of change.
I ll.
Consumption and the Term Structure of Interest Rates and
Inflation: An International Comparison
18
Joseph Bisignano
... The aim of this paper was to determine whether real consumption was influenced by the
term structure of interest rates in a model which captured the influence of permanent
income and the impact of price level movements. The answer was found generally to be in
the affirmative.
Editorial Committee:
Charles Pigott, Brian Motley, Roger Craine
3
In economics, timing is often all-important. The
articles in this Review demonstrate that economic
decisions made today, and their outcomes, can depend crucially upon what happens, and can be expected to happen, in the future.
In the first article, Rose McElhattan discusses the
duration of the impacts of fiscal· budget deficits on
prices, inflation, and real output. She distinguishes
between the long-run and the short-run effects of
deficits caused by spending and tax policies.
McElhattan notes that, by conventional reasoning, federal deficits are likely to have short-run
stimulative effects on aggregate demand but that, in
the long-run, deficits occurring without an accommodating change in the money supply can have one
of three impacts: (I) they may crowd out an equal
amount of private sector spending and leave the
nation's productive capacity unchanged; (2) they
may crowd out a greater amount of private spending
because the government expenditures replacing private investment are less productive; (3) they may
increase the nation's productive capacity if they
have positive supply-side effects. McElhattan explains the concept of crowding out as the result of
"additional demand related to the deficit which
places upward pressures on market prices and interest rates which then reduce some private sector
interest-sensitive spending."
To test the impact of federal spending and tax
policies upon real GNP and inflation, McElhattan
used reduced form equations in which changes in
real GNP and inflation are functions mainly of
changes in money growth and changes in real federal high employment expenditures and tax revenues. The sample period used to estimate the equations range from the second quarter of 1966 to the
fourth quarter of 1979.
McElhattan found significant real output effects
when deficits were measured by their components
-high employment expenditures and tax receipts
-relative to the components' past average rates of
change. She suggests that these measures may serve
"as crude estimates of unanticipated changes in the
deficit." Anticipated changes, she notes, can be
immediately incorporated by the public into higher
market prices and interest rates and have but little
effect on real output.
The results of McElhattan's study point to the
existence of temporary output and inflation effects
and lasting price level changes. An increase in tax
revenues or real expenditures steadily raises the
level and the rate of growth of real GNP. After I to 3
years, the effects die out leaving no traces after
another 2 to 3 years. McElhattan cites the lack of a
long-run output effect as evidence of complete
crowding out.
A sustained tax cut, or an increase in real government spending, also temporarily raises the inflation
rate. The rate change peaks in 2 to 3 years and
disappears at the end of 5 years. Price levels, however, remain at a higher level. A I percent tax cut
leaves the price level 1.2 percentage points higher
than its initial level, while a I percent increase in
real expenditures leaves the price level .4 percentage points higher.
In summary, McElhattan writes: "The real GNP
response to changes in federal deficits appears to be
transitory, and in the long-run, changes in the deficit appear to crowd out about an equal amount of
some private sector spending ... Changes in deficits
also appear to change the rate of inflation in the
short-run and the price level in the longer run ... "
The second article, by Joseph Bisignano, extends
the simplest consumption model in which an individual decides between present and future consumption on the basis of the "price" at which a
dollar of consumption today can be transformed
into a dollar of consumption in some future period.
The price is the real interest rate relevant to the two
periods but the exact effect on present consumption
is ambiguous because of opposing income and substitution effects. Bisignano's article extends this
4
simple model beyond two periods by using the
entire term structure of real interest rates-because
consumption depends "on the entire structure of
interest rates over the horizon of potential future
consumption.' ,
Bisignano's analysis uses the framework of the
Life Cycle-Permanent Income model in which
"individuals make consumption decisions about
what individual goods to purchase in a temporal
framework" subject to wealth or permanent income
constraints. He points out that while economists
have recognized that consumption decisions depend
on the term structure of real interest rates, they have
seldom used the term structure in their studies. His
analysis therefore attempts to isolate the effects on
consumption of permanent income, term structures
of interest rates and inflation, and price levels in
four countries: the United States, the United
Kingdom, Canada, and the West German Federal
Republic.
Changes in price levels, Bisignano notes, can
create a "money illusion" of short-run changes in
relative prices. Inflation affects consumption in
three ways: by changing real taxes if the tax system
is not indexed to inflation, by changing real liabilities and therefore real net wealth, and, when future
inflation is uncertain, by reducing current consumption in risk averse individuals.
The results of his analysis show that, in general,
in the context of a permanent income consumption
model, the term structure of real interest rates plays
a significant role in consumption behavior. He
found that a rising term structure of real interest
rates decreases current consumption in the cases of
the United States, the United Kingdom, and Canada
and increases current consumption in the case of
Germany. Holding real interest rates constant, he
found that a rise in inflation "appears to increase
real consumption in the U. S. and Canada and to
reduce consumption in the U.K. and W. Germany."
These findings, Bisignano notes, have implications for the national economy. According to
Bisignano, recovery from the recession of 1982 will
likely be led by improvements in the consumption
sector, with the response of that sector to future
expectations embodied in the term structure of real
rates determining the strength and duration of the
recovery. Based on his findings, he concludes that
the quantitative effect of the major decline in real
interest rates from June to August 1982 should outweigh the effect of the decrease in inflation and
"should provide a major boost to consumption and
to the general economic recovery."
5
Rose McElhattan*
There is considerable concern these days about
the prospect of high and perhaps rising federal deficits and their effects on intlation, private investment
and other aspects of our economic lives. In this
paper, we will review some considerations regarding the economic impact of deficits and provide
some empirical results derived from reduced form
equations for real GNP and inflation which we have
estimated.
The best known reduced fonn estimates of fiscal
policy effects are those from the St. Louis equation.
In that equation, the impact of fiscal actions upon
nominal GNP, when unaccompanied by changes in
the money supply, essentially disappear within four
to five quarters. A recent update by the Federal
Reserve Bank of St. Louis reaffirms these results
and also finds that fiscal variables exert no statistically significant effect in any quarter. I Thus, fiscal
policy has no significant short or long-run effect
upon nominal GNP according to these results.
Our question is whether the seeming ineffective-
ness offiscal policy will hold up in an analysis of the
impact of fiscal policy upon the components of
nominal GNP, that is, real GNP and inflation considered separately. Eve!} should nominal GNP be
unaffected by changes in deficits, there may be
considerable movements in real output and inflation. Changes in these measures concern policy
makers and form the focus of theoretical discussion.
The results of our analysis suggest that deficits do
have significant effects upon real output and inflation. Deficits, when measured relative to their past
average values, appear temporarily to stimulate real
output, although they have no permanent real impact. This finding suggests that federal deficits ultimately crowd out some private spending. Increases
in deficits also seem to raise inflation in the short
run, and the price level in the long run, as convention theory suggests. In our analysis, we measure
deficits by their high employment estimates, and
consider separately the leverage of expenditures
and revenues.
I. Theoretical Considerations
Economists are divided as to whether fiscal
actions matter in the determination of aggregate
output. Some argue along convention lines that
federal deficits, which are the result of changes in
spending or tax policies, or some combination of
these, will lead to changes in aggregate demand at
least in the near future. Many believe, however, that
deficits will have little or no impact upon aggregate
output in the long-run. Still others contend that
deficits which are matched with increases in the
national debt do not increase the nation's net wealth
and therefore will not lead to any sizable changes in
aggregate output in the short or longer run.
*Senior Economist, Federal Reserve Bank of
San Francisco. Eileen Dixon provided research
assistance.
6
II. Conventional View
The model from which the conventional argument stems is the aggregate demand-aggregate supply paradigm discussed in standard economic textbooks and the foundation of several forecasting
models of the U.S. economy.2 Along the supply
schedule, greater quantities of output are supplied
only at higher prices. This is because the greater
quantities of labor and other resources needed to
increase output places upward pressure on unit production costs.
The aggregate supply schedule is derived from
the assumption of constant money wages and other
factor prices and a fixed stock of business plant and
equipment. According to conventional models,
money wages will increase with tighter labor market conditions and with expectations of future increases in inflation. Any increase in money wages
will shift the entire supply schedule upward and to
the left so that higher prices are associated with the
original supplies of output. Alternatively, an increase in the capital stock will shift the supply curve
in the opposite direction, indicating lower prices for
the original quantities.
The aggregate demand schedule indicates that
total demand for goods and services will be greater
at lower price levels. This occurs because lower
prices tend to ease monetary conditions and hence
to lower interest rates which in tum stimulate interest-sensitive spending. Similarly, higher prices tend
to tighten monetary conditions, raise interest rates
and depress aggregate demand.
The demand schedule is derived from the assumption of constant monetary and fiscal policy. A
change in either wili shift the entire schedule. To
clarify terms, a constant monetary policy means the
maintenance of a given level (or rates of change) in
the supply of money as measured in this paper by
MI (currency and checkable deposts). A constant
fiscal policy means no change in federal government expenditure programs or the federal tax
structure.
An increase in federal spending or a reduction in
taxes, or any combination of these that increases the
federal deficit shifts the entire demand schedule
upward and to the right. This means that greater
quantities of output will be demanded at the original
prices. A decrease in the deficit is associated with a
downward shift in demand and consequently with
smaller quantities of output demanded at the original prices. The same can be said for changes in
monetary policy: an increase (decrease) in the
money supply is associated with more (less) output
demanded at the original prices.
III. Deficit Impact
Second, the increased demand for output increases
the need for greater quantities of money balances to
cover the increased volume of transactions. With a
constant monetary policy, this increased demand
for money balances will tend to tighten monetary
conditions and raise (real) interest rates. These
higher interest costs, in tum, will limit interestsensitive spending and the expansionary impact of
the original deficit. Real GNP, then, will tend to
increase after an increase in the federal deficit, but
the stimulative effect will be partly mitigated by
crowding out of some private spending through
higher prices and interest rates.
This behavior is illustrated in part in Figure 1.
The increase in the deficit raises aggregate demand
from DI to D2. At the original equilibrium level of
prices, PI, more output (Yl) will be demanded.
Given the aggregate demand and supply schedules, we may now analyze the effect of an increase
in the federal deficit, assuming no accommodating
change in the money supply, i.e., holding monetary
policy constant. This assumption is equivalent to
financing the increase in the deficit through the sale
of bonds.
The increased deficit (due to increased expenditures, reduced taxes or some combination) shifts the
entire demand schedule upward and to the right.
Although demand rises, two important effects limit
the stimulative power of the deficit. First, the increased demand tends to drive prices up, since
greater quantities of output will be supplied only at
higher prices according to the supply schedule.
Consequently, part of the expansionary effect of
fiscal spending will be dissipated in higher prices.
7
and demand. An equal increase in both would leave
the price level the same as the original equilibrium
level while greater (smaller) increases in supply
relative to demand would lead to lower (higher)
prices than initially.
However, positive supply-side effects are not a
certain outcome. For instance, according to the
theory of labor supply, while a lower tax rate may
encourage some people to enter the work force (an
income effect), others may be encouraged by the
higher take-home pay to spend less time at work and
more at leisure (substitution effect). As a second
case, we consider that the fiscal programs underlying the deficit may have no net effect on aggregate
supply in the long-run.
In this second case, complete crowding out of
some private ,spending by federal deficits occurs.
The increased level of output, (Y2) in the previous
chart, leads to increased demands for labor, tighter
labor market conditions, higher money wages and
higher prices. Furthermore, the higher prices tend
to increase expectations of future prices. These increased wage and price expectations produce an
upward shift in the supply schedule and a further
increase in final product prices. Higher prices, in
tum, reduce real money balances, tightening money
market conditions, and leading to further increases
in interest rates. As a result, real GNP is reduced
further as additional private sector spending is
crowded out of markets by the combined effects of
continuing price and interest rate increases.
Economic adjustments in prices, interest rates,
wages and price expectations will continue until the
initial increase in the deficit displaces an equal
amount of some private sector spending. Ultimately, real output equals the level that would have
existed without the change in fiscal policy because,
as long as output is greater than it otherwise would
have been, employment will be higher and so will
money wages and prices. These higher prices,
given an unchanged monetary policy, will lead to
higher real interest rates which reduce interestsensitive spending. Only when aggregate output
equals the level it would have been had the deficit
not occurred will we observe no further adjustments
in employment, wages and prices.
Although complete crowding out occurs in real
GNP, it will not occur in nominal GNP. Some permanent effect will be left on the level of nominal
Figure 1
Transitory Effect of a Deficit Increase
... more output but at higher prices
Prices
P,
P,
Y,
Y,
Output
But, with an upward sloping supply curve, a new
short-run equilibrium occurs at E2. As a result, the
increase in the deficit leads to higher prices (P2) and
more output (Y2) than before the change in the
deficit. However, output rises less than would have
occurred if no change in prices had taken place
(Yl).
This new equilibrium is likely to be short-lived
because the changed prices (P2) and output (Y2)
will set off a chain of reactions in factor costs and
investment that lead to further shifts in aggregate
demand and supply and which will culminate in any
one of three final cases.
In the first case, deficits have positive supply-side
effects increasing the economy's productive capacity. Public expenditures, for instance, may finance
projects such as road construction, rural electrification, research and development which, on balance,
may be more productive than equal sums spent by
the private sector. Alternatively, deficits may result
from a reduction in income taxes which may increase incentives to enter the work force and, on
balance, increase the supply of labor and again, the
nation's productive resources. In these situations,
the supply curve is shifted downward and to the
right. Ultimately, more output will be produced,
and the change in the price level will be determined
by the size of the relative shifts in long-run supply
8
deficits will raise the price level, but have an ambiguous impact on nominal GNP.
From these alternatives-positive supply side
effects, crowding out and super-crowding out, we
observe that the ultimate effect of a deficit will
depend materially upon the particular types of
spending and/or tax policies associated with the
deficit. Deficits due to corporate tax reductions, for
instance, are likely to have a more stimulative impact on aggregate supply than an equal-size deficit
that results from aid to state and local govemments
who then incur surpluses in their own budgets. In
partial recognition of this, we separate the effects of
spending and tax policies in our estimations.
GNP because the crowding out process is achieved
largely through a rise in prices and interest rates
which increases velocity and money income. 3
In the final case, deficits may ultimately lead to
a decline in aggregate supply and an increase in
prices-the case of super-crowing out. This occurs
when the reduction in private sector spending which
the deficit crowds out of markets is replaced with
government spending that is less productive. The
increased interest costs associated with the initial
stimulative impact of deficits may .reduce private
spending on productive capital and lead to a decline
in the nation's productive resources. In this case,
IV. Some Further Considerations
In formulations of the conventional model, individuals are assumed to change their expectations of
future prices on the basis of past price behavior.
Peo'ple, however, may be wiser and use all relevant
information to form their expectations, not just the
past behavior of inflation. Their rational expectations open further possibilities with regard to fiscal
policy effectiveness in the short run.
For example, anticipated deficits may quickly
crowd out private spending, and have little if any
impact upon real GNP in the short run. This occurs
because individuals, applying their knowledge of
the conventional model, anticipate the initial stimulative effects of an increased deficit. These anticipations are quickly incorporated in market prices and
interest rates. The existence of rational expectations
suggests that we consider the different leverages of
anticipated and unanticipated fiscal deficits. 4
Another case in which federal deficits may have
little real stimulative impact in the short run is one in
which the public does not regard the increase in the
national debt associated with the deficit as an increase in its net wealth. According to this view
people will anticipate the compensating future taxes
implied by their holdings of government debt. The
important implication of this view is that federal
deficits which are bond-financed will have the saIne
impact upon aggregate demand as a balanced budget.
Consider a tax cut and the corresponding deficit
which is financed by selling bonds to the public.
Each dollar of tax reduction is matched with an
extra dollar of federal debt that will be repaid and
serviced with future taxes with the same present
value. Since there is no change in the present value
of net tax liabilities, there will be no change in
household permanent income, net wealth or spending. The same type of reasoning applies to federal
deficits which are the result of increased government spending which is bond-financed.
To the extent that bonds are not net wealth, fiscal
policy will have little if any significant impact upon
either real or nominal GNP in the short run. 5
V. Summary
According to conventional reasoning, federal
deficits are likely to have short-run stimulative effects on aggregate demand, although the size of
these effects is an empirical issue. Ultimately, in the
long run, deficits may (a) crowd out an equal
amount of private sector spending, (b) crowd out a
greater amount of private spending because deficits
lower the nation's capital stock, or (c) increase the
nation's productive capacity as in the case of federal
investment in the economy's infrastructure.
Fiscal actions may have little, if any, leverage in
the near or more distant future when individuals
equate federal deficits with future tax liabilities,
or anticipate future price and interest rate changes
caused by deficits and change market prices quickly
to conform to their expectations.
9
VI. Estimation Model and Data
(dHR). In equation (lB) changes in the rate of
growth of real GNP occur when monetary or fiscal
policies deviate from their anticipated courses. The
dHEBAR and dHRBAR represent changes in real
high employment expenditures and receipts relative
to their respective anticipated rates of change.
Equation (2) states that changes in money growth
determine changes in inflation, reflecting earlier
considerations that both anticipated and unanticipated monetary changes will have an impact upon
inflation. This equation also allows changes in the
growth of real high employment expenditures
(dHE) and receipts (dHR) to determine changes in
the inflation rate. It incorporates the assumption
that both anticipated and unanticipated fiscal policies may affect the rate of inflation.
The monetary variable is M I, currency in the
hands of the public plus checkable deposits. To
approximate unanticipated monetary changes, we
estimated dMBAR as the current rate of change in
Ml less its average rate over the past two years,
measured in logs.
The high employment budget estimates are provided by the U. S. Commerce Department. 7 The
measures we use here are adjusted to exclude the
automatic effects of inflation on revenues and expenditures. There are several reasons why revenues
and expenditures respond automatically to price
changes. For example, federal interest payments
depend on interest rates which tend to change with
What has been the impact of federal spending and
tax policies upon real GNP and inflation? To answer
this question, we tum to reduced form equations in
which changes in real GNP and inflation are determined mainly by changes in money growth and
changes in real federal high employment expenditures and tax revenues.
These reduced form equations may be derived
from a model which was detailed in a previous
paper. 6 Underlying this model is an aggregate
demand-supply framework similar to that discussed
earlier, with the additional assumption that anticipations of future monetary and fiscal policies are determined by the past history of these policies. The
real economy is assumed to be stable in the sense of
growing at a steady pace; it will depart from this
pace temporarily when either monetary and/or
fiscal policies deviate from their anticipated patterns. The economy is also assumed to have the
classic long-run neutrality property associated with
money growth. This means that a permanent change
in the rate of growth of money ultimately results in
an equal change in the rate of inflation, but in no
change in the rate of growth or level of real GNP.
Also, in the long-run, the leve of prices will change
with the stock of money so that the public's holdings
of real money balances are at desired levels, given
interest rates and the level of income.
The reduced-form equations (lB) and (2) below
follow directly from this model. Equation (lA) is a
more general depiction of how fiscal policy might
affect real growth for it makes no distinction between anticipated and unanticipated fiscal values.
dRGNP = F(c, dMBAR, dHE, dHR)
(lA)
dRGNP = F(c, dMBAR, dHEBAR, dHRBAR)(lB)
dP = F(c, dM, dHE, dHR)
(2)
Equation (IA) states that the rate of change in real
GNP (dRGNP) deviates from a constant rate, c,
when money growth differs from its anticipated
rate, (dMBAR). In addition, the rate of growth in
real GNP will change with changes in real high
employment federal expenditures (dHE) and
changes in real high employment federal receipts
10
changes in the rate of inflation. If not corrected for
such inflation-induced components, the high employment measures would provide biased estimates
of the economic effects of fiscal policy. To approxi-
mate changes in unanticipated real high employment expenditures (dHEBAR) and receipts
(dHRBAR), we measured the current rate of change
in each variable less its average rate of change over
the past two years, measured in logs.
VII. Empirical Results
The estimation of equation lA, in which changes
in real GNP are determined by changes in money
from its past average (dMBAR) and by changes in
real high employment expenditures (dHE) and tax
revenues (dHR), indicated that neither of the fiscal
variables contributed significantly to the determination of real GNP. The results are summarized n
Table I.
This should be interpreted with some caution,
however, since there is reason to believe that the
monetary and fiscal policy measures were closely
related during the sample period. For instance, we
estimated changes in real GNP with the monetary
measures alone. These were statistically significant, and adding fiscal policy measures did not
matter in the determination of real GNP. Conversely, when estimating changes in real GNP with
the fiscal measures alone, they were also significant
and adding monetary measures did not matter. Each
policy variable did about as well as the other in
II
forecasting changes with real GNP both in and
outside the sample. These results, along with the
estimation in Table I, suggest that one type of policy
served as a fairly good proxy for the other.
The close relationship among the variables
implied by these results presents an estimation
problem in that their covariance prevents us from
obtaining a very precise estimate of any independent effects. In the case of monetary measures, this
was not as important and the results were still statistically significant. But the case of fiscal policy is, at
best, inconclusive.
We may approach this estimation problem by
respecifying the fiscal policy measures. Fiscal variables may have significant real output effects when
fiscal policy deviate~ from anticipated patterns, as
suggested earlier. This appears to be the case in the
results shown in Table 2. Both fiscal measures are
statistically significant (revenues at the 5 percent
level and expenditures at the 10 percent level) and,
together with money, account for 39 percent of the
variation in real GNP growth rates. According to
these results, fiscal policy has an independent and
temporary influence upon real GNP.
12
To illustrate this, Chart 1A shows the response of
the real GNP growth rate to a I percentage point
reduction in tax revenues in the initial quarter only.
This is equivalent to a permanent cut beginning in
1980 in constant dollar tax revenues of approximately $3.2 billion. This tax cut steadily increases
the rate of growth of real GNP from the initial
quarter to a maximum response of .3 percentage
points (annual rates) by the end of the first year.
Thereafter, the effect steadily dies out, following a
cyclical pattern, and ceases to have any impact
within 5 to 6 years.
The tax multipliers derived from these estimates
are illustrated in Chart 2A. The level of real GNP
steadily increases for about two and a half years. By
that time, each billion dollars of the tax cut has
increased the level of real GNP by $2.4 billion.
Thereafter the impact upon the level of GNP dies
out. Within 5 to 6 years, the additional deficit resulting from the tax cut has completely crowded out
some types of private expenditures not favored by
the tax reduction.
Chart 1
Response of Annual Rates of Growth
in Real GNP and Prices to a
One Percentage Point Reduction in Real
Tax Revenues in the Initial Period Only
Percent
Chart 2
(A)
Response of the Level of Real GNP
and Prices to a One Percent;:ige
Point Reduction in Real Tax
Revenues in the Initial Period Only
.40
.30
(A)
.20
Billions of
Constant Dollars
.10
2.5
0.0 I----~r-------~
2.0
-.10
1.5
-.20
1.0
-.30&...1..;
o
~
5
10
15
........J
20
Real GNP
.. Tax Multipliers
0.5
25
Periods following
Initial Change
0.0 &...I..;
o
~......
"""-
5
10
15
20
25
Periods following
Initial Change
Percent
(8)
.40
(8)
Percent
.30
1.4
.20
1.0
.10
0.5
0.0
o
......"
5
10
O.OIllll;"
....
15
20
o
25
Periods following
Initial Change
........J
...o..l.
5
10
15
20
25
Periods following
Initial Change
13
out an equivalent amount of some private spending
within 5 to 6 years.
Table. 3 provides the inflation equation estimates.
Both. fiscal. measures are statistically significant in
these estimates. Chart 1B illustrates the impact
upon the rate of inflation ofa sustained decrease in
real tax revenues of $3.2 billion. The inflation rate
steadily increases and reaches its maximum of .34
percentage points (annual rate) about 2 years after
the initial tax cut. Thereafter, the inflationary
response dies out, with no further impact after
Charts 3A and 4A illustrate the effects on real
GNP of a sustained $3.2 billion increase in federal
high employment real expenditures. (Again, this is
the equivalent of a 1 percentage point increase in
these expenditures in the initial quarter only.) The
real output response is somewhat less inthis case
than. in the case of tax cuts.. The real expenditure
multiplier reaches a maximum value of $1. 7 billion
about 3 years after the initial change, relative to a
maximum of $2.4 billion in the former case. The
increase in federal expenditures eventually crowds
Chart 3
Chart 4
Response of Annual Rates of Growth
in Real GNP and Prices to a One
Percentage Point Increase in Real
Expenditures in the Initial Period Only
Percent
Response ofthe Level in Real GNP
and Prices to a One Percentage
Point Increase in Real Federal
Expenditures in the Initial Period Only
(A)
Billions of
Constant Dollars
.20
(A)
2.0
.10
1.5
0.0 r------~-----,
1.0
-.10
0.5
-.20
O.OIl..l-............................_ _......._ ..............i:IIiIooI
5
10
15
o
20
25
5
10
15
20
Periods following
Initial Change
25
Periods following
Initial Change
Percent
Percent
(8)
.30
.30
.20
Price Level
~
.20
.10
.10
0.0
0.01----':1-------
-.10
-.10
-.20
-.30
(8)
.40
-.20 ....._
o
0
_...&.lo_....._ ................
......
5
10
15
20
25
Periods following
Initial Change
10
Periods following
Initial Change
14
Chart 5
approximately 5 years. However, the sustained tax
cut does have a permanent effect upon the price
level, as shown in Chart 2B. The tax cut increases
the price level by 1.2 percentage points from its
initial level.
Together, Charts 2A and 2B illustrate the croWding out features of the initial federal deficit. The tax
cut first increases aggregate output and prices.
These price increases, in tum, act as a major vehicle
by which other types of spending not favored by the
tax cut are crowded out of markets. Eventually, the
initial deficit crowds out an equal ameunt of some
private sector spending and has no long-run effect
on the level of real GNP. It does, however, have a
permanent effect on the price level, and consequently, on nominal GNP. The results for nominal
GNP are shown in Chart 5.
The inflationary impact of a $3.2 billion increase
in real expenditures is shown in Chart 3B. At first,
the inflationary response is negative, but it steadily
increases to a maximum of .2 percentage points
within approximately 3 years of the initial spending
increase. Eventually, the inflation rate response
dies out, leaving the price level .4 percentage points
higher, as shown in Chart 4B. Together, Charts 4A
and 4B illustrate that the increased deficit crowds
out some private spending, but will permanently
raise the price level.
Response of Nominal GNP
to a One Percentage Point Reduction in
Real Tax Revenues in the Initial Period Only
Percent
(A)
Annual! Rates of Change
.40
.30
.20
.10
0.0 I------~r__---_
-.10
-.20
o
....
5
10
15
20
25
Periods following
Initial Change
Percent
(B)
1.5
1.0
0.5
0.0
0
5
10
15
20
25
Periods following
Initial Change
15
VIII. Summary andiConclusions
Economists are divided regarding . whether
changes in the federal deficit willproduceany.significant effects upon the total level of real GNP and
prices. According to conventional reasoning,. the
impact of deficits in the long-run dependsuponthe
particular expenditure and tax. programs which
make up the deficit. Certain govemmenttaxand
expenditure. policies may induce positive supply
side effects through incentives which incr~ase the
supply of labor, for example. Other polici s ay
l11
transfer the nation's resources away from productive private spending towards less efficient
government expenditures and reduce the nation's
productive capacity. This would be a case ofsl.lpercrowding out. Another case is that of complete
crowding out, when deficits replace private sector
spending.
In any case, an increase in federal deficits initially is likely to stimulate aggregate demand. Thereafter, if some degree of crowding out takes place, it
occurs as the additional demand related to the deficit places upward pressures on market prices and
interest rates which, then, reduce some private sector interest-sensitive spending.
We must make a further distinction, between
anticipated and unanticipated deficits. An anticipated deficit may quickly crowd out private spending as the public incorporates the stimulatory effects
into higher market prices and interest rates. Anticipated deficit changes, then, may have little effect on
real output even though they raise prices. Unanticipated deficits, on the other hand, may have dynamic
effects on real output and inflation as explained in
the conventional model.
\Vehave found that deficits have significant real
output effects when wcITleasure changes in its components, high employment expenditures and receipt~, r~lative totheir past averag~ratesofshange.
Thes~measures.111ayserve .as ciUde estimates of
unanticipated changes ~in. the deficit. The real GNP
response, then, to changes in federal deficits
appears. to be. transitory, \ and in the long-run,
changes in the deficit appear to crowd out about an
equal amount ofs?me private sector spending.
Changes in deficits also appear to change the rate
of inflation in the shortrunand the. price levelin the
lon~er run,according to our estimates.These results are consistent with the conventional view that
federal crowding out of private sector spending
achieved in part through higher prices.
A few final statements are probably in order. It
should be clear that the deficits we are addressing in
both theoretical discussions and empirical w?rk are
those best measured at high employment because
these are adjusted for automatic changes in the
deficit due to changes in business conditions. Consequently, the high employment measures, more
accurately than their corresponding actual deficit
measures, depict fiscal policy initiatives which can
alter market conditions.
Lastly, we regard our results as tentative, at best a
depiction of experience during the sample period
from 1966.2-1979.4. The exact timing and size of
fiscal economic effects remains uncertain subject to
a fairly wide range of estimation error, probably in
part because historical movements in fiscal measures have been closely related to monetary growth.
This correlation may reflect responses ofthe respective policy makers to unfolding economics developments of the past.
r
16
FOOTNOTES
1. SeeHafer, R.W, "The Role of Fiscal Policy in the St.
Louis Equation," FRB of St. Louis Review, vol. 64, no. 1,
Jan. 1982.
5. For a discussion olthe theoretical and empirical results,
see Barro, Robert J., "Are Government Bonds Net
Wealth?" Journal of Political Economy, Dec. 1974; Arak,
Marcelie, Are Tax Cuts Stimulatory?, The Review of Economics and Statistics, Feb. 1982, and Feldstein, Martin,
GovElrnment Deficits and Aggregate Demand, Journal of
Monetary Economics (9),1982.
2. As examples of the standard model, see Rudiger Dornbusch and Stanley Fischer, Macro-Economics, McGraw
Hill Book CompanY,1978.
3. For further discussion of how fiscal actions completely
crowd out real spending but have a permanent effect on the
level of nominal spending see Franco Modigliani and Albert
Ando, Impact of Fiscal Actions on Aggegate Income and
the Monetarist Controvery: Theory and Evidence, Monetarism, editor Jerome Stein.
6. McElhattan, Rose, The Response of Rea! Output and
Inflation to Monetary Policy, FRB San Francisco Economic
Review, Summer 1981.
7. Frank de Leeuw and Thomas M. Holioway, "The HighEmployment Budget: Revised Estimate and Automatic Inflation of Effects, Survey of Current Business, UnitEld States
Department of Commerce, Bureau of Economic Analysis,
April 1982, volume 62, NO.4.
For empirical results from a large econometric model see,
Probyn, Christopher, Properties of the 1981C Edition of the
DRI Macro Model, Data Resources U.S. Review, September 1981,especially pages 1.34-1.39.
8. For details of this method see Appendix A in McElhattan,
Rose, op.cit.
4. Hall presents a model assuming rational expectations
and price stickiness. Hall, Robert E., The Macroeconomic
Impact of Changes in Income Taxes in the Short and Medium Runs, Journal of Political Economy, vol. 86, no. 2, April
1978.
17
Joseph Bisignano*
and West German Federal Republic.
The plan of this paper is, first, to discuss the life
cycle-permanent income model of consumption and
the role of interest rates, irl particular the spectrum
of interest rates over all maturities, in influencing
real consumption behavior. Second, several related
theoretical issues are discussed, such as the concept
of "money illusion" and the alternative ways a
change in interest rates may influence consumption.
Third, the form of the consumption equation to be
empirically estimated is considered, followed by an
analysis of related data measurement problems.
Fourth, we discuss the estimated consumption
equations for the U.S., U.K., Canada and Germany
and, fifth, we conclude with the implications of the
empirical findings, given the recent behavior of
interest rates and inflation in the U. S. (Chart I).
This paper seeks to provide an answer to the
question of how interest rates affect the level of real
consumption. The framework used to solve this
problem is one in which consumers make consumption plans using information about the entire term
structure of interest rates. In theory, real consumption decisions are determined by relative prices and
real interest rates, the latter defined as the nominal
rate less the anticipated rate of inflation. Both determinants will be tested in the following analysis, the
former, by testing whether the level of prices influences consumption, and the latter, by attempting to
separate the effects on consumption of the term
structure of nominal interest rates from the effects
on consumption of the term structure of inflation.
The same empirical analysis is undertaken for four
countries: United States, United Kingdom, Canada
I. The life Cycle-Permanent Income Model
The life cycle-permanent income model of consumption characterizes the consumption behavior
of individuals as maximizing the utility or satisfaction derived from consumption over their entire
lifetimes. The "constraint" on this implicit maximization we all perform in planning current consumption is not simply current income but current
and all expected future income. So-called "lifecycle" models emphasize that aggregate wealth,
defined as current wealth plus discounted expected
income from labor and non-labor sources, is the
variable which determines the "scale" of current
consumption. Since an estimate of aggregate wealth
involves an estimate of discounted future income,
the models implicitly require some consideration of
current and future interest rates. Thus, the term
structure of interest rates is important for its influence on both the determination of the consumption
allocation decision and the calculation of the
wealth/income constraint.
As total wealth may be considered the "stock"
constraint on the total lifetime consumption decision, the "flow constraint," that is, period-byperiod, may be considered to be "permanent income. " The concept of permanent income rests on
the argument that consumers "smooth" the estimates of their income and base their consumption
decisions on the non-transitory components of income. The basic idea to keep in mind, nonetheless,
is the stock/flow distinction between wealth and
permanent income. Both are constructed concepts
to determine the lifetime and period-by-period constraints on the consumption decision.
*Yice President and Associate Director of Research, Federal Reserve Bank of San Francisco.
Margaret Saunders provided research assistance.
My thanks to Professors Roger Craine, Milton
Friedman, Kevin Hoover, Thomas Mayer, Jurg
Niehans and John Seater for comments on earlier
drafts of this paper.
18
In short, the consumer is pictured as maximizing
his utility of consumption over his lifetime. The
constraint on this exercise is his total wealth. Permanent income is then some fraction of total wealth
which the consumer uses as the constraint on period-by-period consumption. Empirically one can
use, with equal justification, either total wealth or
permanent income in the consumption equation.
For practical reasons one often finds in estimated
consumption equations some estimate of permanent
income, for example, some weighted average of
recent income levels, rather than wealth because of
the difficulty in estimating the latter with readily
available data. In theory, at least, either permanent
income or wealth can be used in consumption functions since they are part and parcel of the same
theoretical paradigm.
II. A Simple Model of Consumer Choice
consumption decisions depend. Rather, there is a
spectrum of interest rates depending on the maturities of financial assets. I (We abstract here from
default risk and its effect on interest rates and assume default-free securities.) The interest rate for
each maturity corresponds to the price at which
today's consumption can be' 'traded" for consumption at some specific date in the future. Decisions to
consume today or to postpone consumption thus
depend on the entire structure of interest rates over
the horizon of potential future consumption.
To achieve an optimal allocation of consumption
expenditures in each time period, a consumer must
consider relative prices by equating the desired rate
of substitution between consumption today and
consumption in each future period to the ratio of the
Individuals make consumption decisions about
what individual goods to purchase in a temporal
framework, now and in the future. Consumption
decisions at anyone point in time are determined by
the prevailing relative prices. The intertemporal
decision to consumer a good today or at some time
in the future must necessarily involve interest rates,
as well as the current and expected future prices of
goods. The reason is simple enough: interest rates
are th~ unit of exchange, the' 'prices," determining
the rate at which a dollar of consumption today can
be transformed into a dollar of consumption in some
future period.
One problem offormulating and empirically testing a model of consumption decisions over time is
that there is no unique interest rate upon which
Chart 1
Percent
Three-Month Treasury Bill Rate and Inflation
3-Month Treasury Bill Rate ..
14
12
Consumer Inflation:,
10
8
6
4
1964
1966
1968
1970
1972
1974
1976
1978
1980
1982
'Consumer inflation is measured by the twelve-month percent change in the implicit price
deflator for personal consumption expenditures.
19
prices. In the simple two-period case this is given by
equation (I). The marginal rate of substitution is the
slope of the indifference curve at a given point.
When the rate of consumption substitution is made
equal to the ratio of discounted prices the consumer
achieves the highest level of satisfaction for a given
level of expenditure. In the case where the decision
is between consumption today, period I, and consumption in some future period beyond period 2,
say, perioqk, the relevant relative price is given by
the product of one-period interest rates, as seen in
the expression given in Chart 2. This describes the
role of the entire sequence of future interest rates in
determining today's consumption decision vis-a-vis
consumption in all future periods.
Since consumption deci~ions involve more than
the choice of consumption today versus consumption in the immediately adjacent period, equation
(1) must be generalized to display the decision rule
which permits an optimal allocation of consumption
between the current period (say, period t) and any
and all future periods over the consumers' consumption horizon. This equilibrium relationship
can be expressed as simply
discounted prices for each period. Consider the
simplest two-period case. Here the consumer
achieves an optimal allocation of his expenditures
between the two periods by allocating his consumption according to the rule:
MRS u
PI
P 2/(1+l r 2)
1+ h = 1+ IZJ
1+, 7T 2
-
(I)
where MRS 1.2 is the marginal rate of substitution
between consumption in period I and consumption
in period 2; Pi the price level in period i, Ir2 the
short-term nominal interest rate between periods I
and 2, and 17T2 the rate of change in prices between
periods I and 2. The marginal rate of substitution,
MRS 1.2' is the ratio of the incremental satisfaction
derived from consuming an additional unit of consumption in period 2 to that derived from consuming the good in period I.
Equation (I) reveals that the consumption allocation decision between periods I and 2 depends on
the "real interest rate," IZ2. Hence both nominal
interest rates and the rate of inflation must be considered in the consumption decision. As equation
(1) reveals, I plus the nominal interest rate divided
by 1 plus the rate of change in prices is defined as I
plus the real interest rate.
Equation (1) may be described graphically, as
seen in Chart 2. Alternative combinations of consumption between any two periods leading to the
same level of consumer utility describe the' 'indifference curve," U O , along which the consumer is
equally satisfied. Where optimal consumption takes
place along this curve is determined by relative
MRS U +N = P'+N/[(l +l,+) (I +'+l r'+2)··· (I +'+N+lr'+N)]
_ [(l+lrt') (l+'tl r ,+?)···(1+'+N_l r'+N)]
(1 +,7T N)
==(I+,Z'+N)
(2)
Equation (2) states that the optimal allocation of
consumption between period t and period t + N is
given by the ratio of the discounted prices between
the two period, where, for example, '+lr'+2 is simply the one-period interest rate between period t + I
and t + 2. Rewritten we see this to be equal to the
"real interest rate" prevailing over the period t
to t+N.
Equation (2) provides a link between optimal
consumption allocation and the term structure of
interest rates. Consumers do not know with certainty what short-term interest rate will prevail at some
future time. However, because individuals arbitrage between yields available on short-term and
long-term financial assets, there must necessarily
be an equilibrium relationship between currently
known long-term yields and current and expected
short-term interest rates. If there are no market
Chart 2
Representation of Consumer Equilibrium
HN-1
r(1+,r
I
s
H
)
t
c,
20
the future in order to maintain an optimal allocation.
It has long been recognized that in theory, intertemporal consumption-saving decisions involve the
entire maturity structure of interest rates. Empirically, however, investigators have, for the most part,
swept the issue under the rug, often opting for the
use of a particular interest rate for a given maturity,
or attempting to model interest rate expectations by
some ad hoc weighting of selected interest rates.
These are but two of the reasons that the empirical
I iterature on interest rate effects on consumption
finds little agreement on the direction of the effect,
let alone any agreement on the magnitude of such
effects.
As seen in equation (2) above, real (pricedeflated) consumption decisions are dependent on
real interest rate. Thus, in principle, it is the term
structure of real, and not nominal, interest rates
whose influence on consumption we wish to determine. To uncover such a structure, however, presents several theoretical and empirical difficulties,
since it requires the approximation of not only an
anticipated rate of inflation over a given time period, but the approximation of the term structure of
inflation for all maturities on the available financial
assets. In principle, such an undertaking is required
if we are to identify the effect on real consumption
of changes in the term structure of real interest rates.
As will be seen shortly, the procedure we chose will
allow us to measure indirectly the effect of changes
in the term structure of real interest rates on real
(price deflated) consumption.
impediments to traders of financial assets of different maturities, and investors have similar risk preferences, the long-term interest rate will be approximately equal to the geometric average of the yield
on current and expected future one-period securities, given by equation (3).
(l +,rN) =
[(I +trt+l) (11+lrt+2)"· -(I
+t+k_lrt+N)]ilN
(3)
A bar over a variable in equation (3) denotes a
currently known value. Equation (3) is often referred to as the Hicksian "expectational model" of the
term structure of interest rates because it defines an
equilibium relationship between a known long-term
interest rate and current and expected future shortterm (one-period) interest rates. The r's in equation
(3) without bars over them are implied "forward"
(or expected) one-period interest rates. Equation (3)
can be used to obtain any forward one-period rate by
simply taking the ratio on known adjacent longterm bonds, as follows:
1+
r.
= (l +,r,+j+l)j+1
'+1 '+1+1
(l-L, ,r'+jY
"
.
(4)
Equations (2), (3), and (4) show the natural interrelationship between intertemporal consumption
theory and term structure theory. A change in any
long-term rate, or any expected future short-term
rate, with given current and expected future prices,
will change the right-hand side of equation (2).
Hence the left-hand side must change, implying the
consumer must marginally adjust his consumption
between current consumption and consumption in
III. Other Theoretical Issues Regarding Consumption
It has been traditional in empirical studies to
assume that the demand for real consumption is
unaffected by the level of all prices. This proposition, called the "absence of money illusion," is
held to apply in both the short-run and the long-run.
In theory, this proposition is quite logical: a scaling
of all nominal quantities, prices, income and
wealth, should leave real demands unchanged. In
recent years, however, changes in price levels have
been argued to have short-run impacts on perceptions of changes in relative prices, and thereby to
give rise to a real demand or supply response. Little
empirical work has been attempted to isolate these
so-called money illusion effects on consumption. 2
Our empirical estimation, however, will attempt to
capture both the effects of the term structure of
interest rates and the effects of the price level, or
money illusion, on aggregate real consumption.
Above, we noted that inflation played a role in
the consumption decision by determining the real
interest rate. (See equation 2.) But aside from this
role, is there any independent role inflation can play
in determining real consumption? Such a role is
possible in that, because they lack information on
all prices, consumers may interpret a rise in a particular good's price with a change in its relative price.
This confusion may lead to systematic changes in
their consumption patterns. Thus, inflation has re21
consumption. The higher interest rate means that
"forward prices," or, equivalently, discounted expected future prices, have fallen, creating the incentive to postpone current consumption in favor of
purchasing goods in the future at lower effective
prices. It is an empirical matter whether this latter
negative substitution effect will dominate the posi-
cently been given an additional separate role in
consumption studies, that of confusing consumers'
perceptions of relative prices.
Inflation can also have an independent role in
consumption via three other avenues: real taxes,
wealth and uncertainty. First, income taxes are not
indexed in many countries, so inflation often results
in a rise in rea! tax rates. This rise reduces the rea!
returns on financial assets and may possibly induce
increased expenditures on goods where the tax is
either absent or sheltered, such as real estate. The
deductibility of interest payments from taxable income is hence a greater haven from taxes when the
real tax rate is raised by inflation. Second, while
inflation reduces the real value of financial assets, it
also decreases the real value of financial liabilities.
It is thus possible for changes in consumption to
result from changes in the real net wealth position of
households. Such effects would not likely be captured with available income or wealth data series.
Third, uncertain knowledge of future inflation
makes future real income uncertain, and, it has been
argued, reduces current consumption in some
cases. That is" with an equal probability that future
real income will be greater or less by the same
amount, risk-averse individuals will choose to reduce current consumption. 3
Is it possible, a priori, to establish what the sign
of the effect of a rise in rea! interest rates will be on
consumption? The answer in general is no. 4 The
reason is well known and common to all empirical
demand equations. A rise in an interest rate has two
opposing effects on consumption: a positive income
effect and a negative substitution effect. With a
higher interest rate, individuals can increase current
consumption without decreasing future consumption because a higher interest rate will generate
greater future cash flow; this is the positive income
effect. In contrast, a rise in the interest rate also
induces a negative substitution effect on current
tive income effect.
The ambiguity of the effect of interest rates on
consumption is readily apparent in the empirical
literature on consumption as well. To mention two
recent studies. Michael Boskin and Warren Weber
have estimated aggregate consumption functions
with interest rates as explanatory variables and have
obtained opposite results, Boskin finding that a rise
in interest rates decreases consumption, and Weber
finding that consumption is increased with a rise in
interest rates. 5
Weber's results are interesting because they hint
at the importance of future interest rates. Weber
finds that a rise in the weighted average of current
and past nominal interest rates increases consumer
expenditures on nondurables and services. He argues that the increase in the weighted average of
current and past nominal interest rates suggests that
nominal interest rates will be lower in the future.
Hence the expected decline in interest rates would
tend to increase the present value of future income.
This rise in the present value of future income,
Weber argues, causes consumers to increase current
consumption. Weber's study suggests that understanding how changes in current interest rates may
affect current consumption requires that one posit a
relationship between currently observed interest
rates and expectedfuture interest rates. Such a relationship can resemble the expectational theory of
the tenn structure, as was seen above. We now tum
to the specification of our estimable consumption
function.
IV. Consumption Function Specification
The arguments above have concentrated on why
the tenn structure of real interest rates should iNfluence consumption decisions. This section will
briefly outline the functional specification of the
consumption equation.
The basic life-cycle consumption argument is
that consumption depends on total wealth. This
relationship may be specified as simply:
(5)
where c is real consumption, W real wealth, and k a
parameter. Equation (5) represents current consumption as dependent on the stock of current real
wealth. Assume that the consumer's planning hori-
22
zon is infinite so that his stock of real wealth generates a flow of income each period proportional to his
stock of wealth. This permanent income flow from
wealth can be written as
yf
iW(
inflation rate over the past m years. Equation (8)
also includes the effects of changes in the price
levels on disaggregate price indices. The reason for
the inclusion of the disaggregate price indices is
primarily statistical. Statistically, we can capture
the presence or absence of money illusion with one
aggregate price level variable only if all subaggregate indices move proportionately. Since this requirement is unlikely to be satisfied by the observed
components of the aggregate index, we disaggregate the price level variable.
Recall that by definition the nominal interest rate,
r, includes both a real interest rate and an anticipated
inflation component. Equation (8) includes as independent variables both the level of nominal interest
rates and the rate of inflation. This implies that in a
regression equation the effect ofthe real interest rate
on consumption is captured by the coefficient on the
nominal interest rate while the independent effect of
inflation on real consumption is captured by the sum
of the coefficients on the nominal rate and the inflation variables. Since the nominal interest rate includes an anticipated inflation component its effect
must be added to the separately measured observed
inflation variable.
Three measurement problems remain before subjecting equation (8) to statistical estimation. The
first is to devise some approximation for the time
series data on permanent income. The other two
measurement problems are related. Statistically, it
is difficult to obtain reliable estimates of the effects
of interest rates and inflation on consumption if
more than a couple of these variables, for different
maturities, are included in the equation. Hence, we
devised proxy variables for the term structure of
nominal interest rates and inflation.
(6)
where yP is permanent income and i a real interest
rate. Solving for W in (6) and substituting into (5)
yields
ct
=
k yPt == K(i) y\
(7)
The proportionality factor K is now written as a
function of the real interest rate. If we define the real
interest rate i as the nominal interest rate, r, less the
rate of inflation, and argue, as above, that real
consumption depends on the tenn structure of real
interest rates, the function K( ) would have to include more than one real interest rate. In addition, if
individuals' real consumption decisions are altered
by movements in the price level and the rate of
inflation, these variables should also be incorporated in the K function. These considerations lead to
the general specification of our real consumption
equation.
C{ == K(r 1t ,f 2t"
..
,rmt,1Tit,1T2t""
,7T rn t'
(8)
Equation (8) captures the effects of the term
structure of real interest rates but includes both
nominal interest rates and inflation variables. The
first subscript on the interest rate and inflation variables represents the maturity of the financial assets.
Thus, r!TIt is the nominal interest rate at time t on an
asset with m years to maturity and 1T !TIt the observed
V. Measurement Problems
In theory, what we wish to explain is consumption, not expenditures on consumer goods. The
latter would include expenditures on durable goods,
only a part of which can economically be considered current consumption. We therefore define consumption as expenditure on consumer nondurable
goods and services plus a portion (the current service flow or depreciation) of the stock of consumer
durables. This definition of current consumption
was implemented where data provided a means of
approximating the service flow of consumer dur-
able goods, namely, in the U.S. and the U.K. (see
Appendix). For Canada, our consumption variable
is simply expenditure on consumer nondurable
goods and services. In the case of Germany, disaggregated consumption data were not available and
hence what we will seek to explain will be total
consumer expenditures.
As described above, the hypothesis that consumption is dependent on permanent, and not currently
observed income, derives basically from the argument that consumption is, in principle, dependent
23
on wealth, where wealth is defined as discounted
future income from both labor and non-labor
sources. Wealth is thus a stock and permanent income, the flow; permanent income being some proportion of total wealth. Real consumption is thus
dependenrohtheflow ofcurrent permanent income}
Permanent income is assumed to adjust by some
amount each> period· in proportion to the flo\v of
current income. Hence, the estimate of permanent
income is updated by the flow of observed income.
To estimate permanent income according to this
assumption, we use> the following well-known approximation. 7
y;
=
Ay,
(I-A) (l+o)Y~i
Equation (9) is nonlinear in the adjustment
parameter A. Hence alternative consumption functions are estimated for different meaSures of permanent income, iterating on values of A. between 0 and
I. That value of A. is selected with minimizes the
standard error of the estimated consumption equation. 0 is obtained by first regressing the log of
income on a quadratic in time.
Economic theory provides little guidance as to
which interest rates are appropriate to. include. in
consumer demand equations. Intertemporal consumer choice implies that the entire term structure
of interest rates is relevant, yet, since many interest
rates, particularly those along the short-end of the
maturity structure, move together, using mOre than
a couple of interestrates in demand equations often
leads to statistical problems of multicollinearity.
Multicollinearity, in tum, results in the inability to
distinguish statistically among the effects of different interest rates on aggregate demand.
Instead of including several interest rates in an
aggregate demand equation, we adopt a parameterization suggested by Heller and Khan and used with
some success in their study of money demand. 8 The
procedure, for each time period, is to regress the
vector of short-to-long-term interest rates, the term
structure, against a quadratic in the maturities of the
(9)
In equation (9), y represents observed real per capita personal disposable income, yP permanent income, 0 the estimated growth rate (trend) of real per
capita income and A the permanent income adjustment coefficient, revealing what proportion of current observed personal disposable income is used to
update the estimate of permanent income. The notion behind equation (9) is that future income is
uncertain and variable, so the consumer obtains a
"smoothed" estimate of his permanent income by
updating it by some portion of recently observed
income.
Chart 3
Representation of the Term Structure
of Observed and Expected Inflation
Rate of Inflation
Observed Inflation
t-N
t-j
Expected Inflation
HI
t-I
24
Hj
HN
Period
ture. The intercept term does not by itself determine
the average level of interest rates because a change
in the other two terms can change the average level
even with the intercept term held constant. (The
same applies to the B coefficients for the term
structure of inflation.) Note that the slope of the
term structure is a function of its maturity. The signs
and
will determine whether the term structure is positively or negatively sloped.
'rheestimatedcoefficients •AO'.r\I,ir\2 andB. o '
BI , B 2will all be entered as explanatpryvariables to
explain.the. behaviorofreal·consumption.lfreal
interest rates were important in determining consUlIlption, the A coefficients would have to. be of
opposite signs from the B coefficients.Thereason
is .as follows: Assume that arise in real interest rates
decreases current consumption. This implies that
with inflation held constant (the B coefficients), a
rise in the nominal structure of interest rates (the A
coefficients) would cause real consumptiontofall.
Thus the estimated consumption function coefficients on the A variables should be negative. That
is, a rise in the nominal term structure ofinterest
rates, holding the term structure of inflation constant, increases the term structure of real interest
rates, reducing consumption.
Alternatively, assume that the term structure of
nominal interest rates remains fixed and the term
structure of inflation rises. Real rates thusfall and,
by assllmption, should increase real consumption.
This implies that the consumption functioncoefficients on the B variables should be positive. Moreover,the effect of the inflation rate on real consumption is .given by the sum of the respective
coefficients on the Ai and B i variables. Since nominal .interest rates inclllde the anticipated rate of
inflation, this effect, captured in the coefficient on
theA variables, must be added to the impact of
inflation captured by the coefficients of the B
variables.
Because the forward-looking. term structure. of
inflation is being proxied in the estimationofequation (ll) by the. observed past term structure of
inflation, •the •ass~mption is that a reasonableestimate of future inflation, for allmaturities,<isthe
observed inflation rate. The term. structure ofpast
inflation .is thus assllmedtobe symmetrical to the
tennstructure of future inflation expectations. (See
Chart3. ) Given this empirical assumption, the esti-
corresponding financial assets. The estimated coefficients are then saved and used as explanatory
variables in the estimation of the consumption function. Formally, assuming that there are financial
assets of N different maturities and T observations
on the market yields, we estimated the following
regression for each sample period:
(10)
1, •... ,
t=
"',T
where r mt is the market interest rate ·at timeton the
asset with a maturity of myears. We thusapproximate the maturity structure of rates with a quadratic
in the maturities (v t is the stochastic error for the
term structure vector, (r" ... ,rN)p for which coefficients are to be estimated). The estimation of (10)
will yield three term structure coefficients for each
time period, t = I, ... ,T. These coefficients are
saved and used as explanatory variables in our consumption function. 9
Since real interest rates determine real consumption decisions, we require either an estimate of the
term structure of real rates or a direct estimate of the
term structure of inflation. Given the effects of the
latter on consumption, the former can be derived.
We, therefore, follow a procedure similar to the
above for estimating inflation. In this case, we
estimate coefficients of the term structure of inflation over the immediate past and assume that this is
the best directly available. estimate of the future
term structure of inflation. This assumption is represented graphically in Chart 3. The following
equation is estimated for each sample period.
2
(rrrr mt = Bat + B!tm + B 2tm + u t
(II)
m = I, ... ,N; t = I, ... , T
where 1T mt is the annual rate of inflation which has
occurred over the immedediate past m years, and
where the maturities of the measured past inflation
rates correspond to the maturities of the financial
assets. The coefficientsB o , HI and B2thuscapture
the prevailing (past) tenn structure of inflation.
Equations(1Q)and (II) may be viewed as an
exponential approximation to the term structure of
interest rates· and inflation respectively. Thecoefficient Ao is the. shift or intercept parameter for the
interest rate term structure, A 1+ 2A 2m the slope of
the term structure at maturity m and 2A 2 its curva25
year interest rate term structure, requires that the
term structure of inflation estimation use ten years
of past inflation observations. Thus the availability
of price data constrains the period for the estimation
of the consumption function.
The above consid~rations lead us to the specifica-
mation of equation (II) required to obtain the three
B coefficients, for each period over which the consumption function is to be estimated, limits the
sample period for consumption function estimation.
The reason is obvious enough: to estimate a consumption function which uses, for example, a ten-
26
tion of our consumption function with tenn structure effects, specified in logarithmic fonn:
tYJ c t
=
4> + AtYJY; + YJ/YJP lt + ... +YJNt'l')P N
t
+ lYoA Ot + lYlA it + O!zA Zt + .BoB at
+ .B I B it + .BzB Zt + e t
(12)
Recall in equation (12) that AOt ' Alt' and A Zt are the
parameters derived from the regression of the log of
the vector of interest rates on a quadratic in the
maturity structure. Similarly, Bot' B It and B Zt are
the parameters derived from the regression of the
log of inflation on a quadratic in the maturity of
inflation. The A's and B's in equation (12) are
treated as explanatory variables representing the
tenn structure of nominal interest rates and inflation, respectively.
To summarize, we argue that if real interest rates,
more specifically the tenn structure of real interest
rates, affect real consumption, then the coefficients
on theinterest rate and inflation proxy variables in
(12) ought to be of opposite sign. If a rise in the term
structure of nominal interest rates, represented by
the Ai s (representing a rise in real interest rates with
inflation held constant) decreases current consumption, a rise in the tenn structure of inflation, which
implies a decline in real interest rates, should increase current consumption. We now tum to estimation of equation (12) for the U.S., Canada, the U.K.
and Germany.
VI. The Empirical Consumption Function
addition of rent, food, consumer industrial products
and services price components.
The next thing to note in the empirical estimates
is that the coefficients of the tenn structure of nominal interest rates and of inflation are of opposite
sign, as suggested above, for three of the fourcountries considered, the exception being the U.K. A
Empirical estimates of equation (12) appear in
Table I. Note that the price level explanatory variables are the disaggregate components of consumer
price indices. For the U.S. and the U.K., these
components are the price indices for durables, nondurables and services; for Canada, these three plus a
series for semi-durables; and for W. Gennany, the
Chart 4
U.S. Real Consumption Equation
Dollars Per Capita
4800
4600
4400
Without Term Structure Effects
...
4200
4000
3800
3600
3400
_-a.._.. . ._. . . . . . _. . . .
3200 ...........,j"-.......
1970
_ . . L . _ . . . L - _.............IL.........
1974
1976
27
1978
1980 1981
rise in the term structure of nominal interest rates,
holding the term structure of inflation constant, is
seen to decrease real consumption for the U.S.,
Canada and the U.K. The t-statistics reported below
the coefficients in Table I suggest that the shape
of the term structure, and not simply the general
level of interest rates, helps determine current real
consumption.
As suggested earlier, the coefficients on the Ao'
AI and A 2 variables can be interpreted as representing the impact of the term structure of real interest
rates on consumption. All three coefficients on
these variables are negative for the consumption
equations estimated for the U. S., Canada and the
U. K. These results suggest that a rise in the term
structure of real interest rates will decrease real
consumption. The estimated coefficients are significant at the 5-percent significance level for a twotail test except for the Ao coefficients for Canada
and the U. K. This last result suggests that it may be
the shape of the term structure, as well as of the
general level of interest rates, which is affecting real
consumption. In the case of Germany the coeffi~
cients on the interest rate variables are all positive,
but none are significant. We conclude from this that
neither the level nor the shape of the term structure
has any impact on real consumption in Germany.
The estimated equations capture expected inflation in two ways. First, the Bo' B I and B2 variables
act as proxies for inflation. Second, since the nominal interest rate is assumed to contain an expected
inflation premium, the expected inflation rate is
also captured in the coefficients of the A variables.
Hence, summing the respective coefficients on the
A and B variables yields the total impact of expected inflation on real consumption. Carrying out
this exercise, we find that a rise in expected inflation increases real consumption in the U.S. and
Canada and reduces real consumption in the U.K.
and W. Germany. The coefficients on the directly
estimated expected inflation proxy variables for the
W. German equation are all negative and very significant at conventional significance levels.
The assumption that real consumption can be
represented with a permanent income hypothesis is
supported by the estimated equations. The permanent income variable coefficients are all significant.
The elasticities of real consumption with respect to
permanent income are very similar for Canada and
the U.S.
Except for the German case, the appearance of
widespread "money illusion," displayed by significant coefficients in the price level variables, is not
confirmed by the equations for the U. S., Canada
and the U.K. While nne or more individual price
level coefficients are found to be significant, we do
not establish the degree of money illusion in consumption which other investigators have uncovered. 1O Only in the case of Germany is significant
money illusion evident, and here it may be due to a
data. measurement problem, since the dependent
variable includes expenditures on durable goods
which cannot accurately be called consumption.
The general impression one obtains from viewing
the results in Table I is that, within the context of a
permanent income consumption model, the term
structure of real interest rates plays a significant
role. This result has not previously been noted in
other empirical consumption functions studies but it
is implicit in much of the theoretical literature on
intertemporal consumption. Furthermore, in three
of the four countries considered, a rise in the term
structure of nominal interest rates, holding constant
the term structure of inflation, was found to decrease real consumption. In the U.S. and Canada,
inflation appears to increase real consumption, but
it appears to decrease real consumption in the U.K.
and W. Germany.
As we have stated above, it is not possible to
determine a priori whether a rise in real interest rates
will increase or decrease current consumption. The
sign of the effect depends on whether the negative
substitution effect is greater or less than the positive
income effect. Our empirical results appear to indicate that for the U.S., Canada and the U.K. the
substitution effect dominates the income effectReal interest rates have a negative impact on real
consumption.
The quantitative impact of the term structure of
interest rates and inflation can be summarized for
the U.S. by viewing Chart 4. Here, the estimated
equation in Table I is fitted over the estimation
period with and without the effects of the interest
rate and inflation term structure variables, along
with the actual values of real per capita consumption. As can readily be seen, real per capita consumption is considerably overstated when the term
structure effects are dropped from the equation. I!
28
VII. Conclusion
cients on permanent income or price levels, that is,
the term structure coefficients changed much less
when alternative functional specifications or sample periods were chosen for ~stimation.
Consider now the policy significance of the empirical results. From June to August 1982, interest
rates in the U.S. declined dramatically. The threemonth Treasury bill rate fell from an average .12.47
percent in June to 7.92 percent in September. From
the results .of this analysis, this rapid declille in
interest rates in the U.S. can be expected to contribute to growth in real consumption spending in the
U. S. Since we found that inflation generally had a
positive impact on real consumption in the U.S., we
can expect the declining inflation rate .to weaken
real consumption. Quantitatively, however, the
major decline in real interest rates, particularly at
the short-end of the maturity spectrum, should provide a major boost to consumption and to the general economic recovery.
The aim of this paper \Vas to determine whether
real consumption was influenced by the term structure of interest rates in a model which captured the
influence. ofpeflllanentincome and the impact of
price level movements. The answerwasfotindgenerally to be in the affirmative for the four countries
considered. A rising term structure of real interest
rates was found to decreasecllrr~nt consumption in
the case of the U.S., U.K., and Canada, and to
increase current consumption in the case of Germany. By holding constant the effect of inflation
over varying maturities, it was found that the impact
of the term structure comes from the impact of
changes in real interest rates. Holding constant the
term structllre of real interest rates, a rise in inflation
appears to increase real consumption in the U. S.
and Canada and to reduce consumption in the U.K.
and Germany. Although not reported here, it was
also found that the coefficients on the term structure
variables were often more robust than the coeffi-
Data Appendix
This appendix briefly describes the source of the
data and the construction of variables used in the
test. The constructed variables include the real per
capita permanent personal disposable income for
the U.S., U.K., Canada and Germany, the Ao' AI
and A 2 and Bo' B I and B1 variables used to approximate the term structure of interest rates and infla-
tion, respectively, for each country, the generation
of the service flow from durable goods forthe U.S.,
and the quarterly interpolation from annual data on
capital consumption at current replacement cost for
the U. K. personal sector. Population series for the
U.K. and Gef!l1anyareobtained by interpolating
annual to quarterly observations.
I. Data Sources
(A) Germany
Statistical Office's National Income and Expenditures, 1981 Edition (the Blue Book), an
annual series, and interpolated to quarterly figures.
Series for personal disposable income, consumer
expenditures and prices are taken from the Central
Statistical Office's. Monthly. Digest of Statistics, various issues. An annual population series
was obtained from the GSO'sNationallncome
and Expenditure, 1981 Edition, interpolated to
get quarterly series. Interest rates used to construct
the term structure variables inclUded. the threemonth interbank rate, the gross redemption yield on
local authority one-year bonds, and the gross redemption yield on 5-, 10-, and 20-year gilts. These
interest rate data were kindly provided by Mr. Paul
Temperton, Economics Division, Bank of England.
Disposable income, private consumption and the
cost of living index for all households are taken
from Statistical Supplement, Series 4, to the
Monthly Reports of the Deutsche Bundesbank. Annual population, series •were obtained
from the annualO.E.C.D. country reports for Germany. Disaggregate prices for Germany were obtained from the Data Resources, Inc., databank.
Interest rates are Eurocurrency deposit rates for 1-,
3-, 6... and 12-rnonth, and 2-, 3-, 4-. and 5-year
maturities, taken from the Data Resources, Inc.,
databank.
(B) United Kil19c1om
Capital consumption at current replacement cost
for the personal sector is taken from the Central
29
(D) Canada
Data for personal disposable income, personal
expenditures on consumer and services goods (services and nondurables), and price indices for personal expenditures on consumer goods and services
were .• obtained from the. National Income and
Expenditure Accounts, Volume 2 (the quarterly
estimates 1947-1974), and quarterly issues of the
same publication. The population series came from
the. Canadian Statistical Review, various
issues. Canadian term structure of interest rate data
on Canadian Government securities: 3- and 6month Treasury bills, bonds of 1-3,3-5,5-10 and
IO-years-and-over maturities were kindly provided
by the Bank of Canada.
(C) United States
Personal disposable income, consumer expenditure series for durable and nondurable goods and
services, the personal consumption expenditure
price deflator, and its components, are taken from
the National Income and Product Accounts.
Interest rate data used to approximate the term
structure included the 3- and 6- month Treasurj bill
yields and the yields on constant maturity 1-,3-,5-,
10- and 20-year Treasury bonds, available from the
Federal Reserve Bulletin. The benchmark stock of
consumer durables used to derive the service flow
from durable goods held by the household sector
was obtained from the Flow of Funds Accounts.
II. Construction of the Service Flow from Durable Goods for the U.S.
DDt = .02761(ED t) + .21784(SDt-!)
SD t = .25(ED t - DDt) + SDt-!
where
.
EDt = expenditure on durable goods in period t
SD t = the stock of durables in period t
DDt = the service flow from durables in period t
This methodology is that used in the Board of Goven:wrs staff's quarterly econometric model. Personal consumption is then defined as expenditures
on nondurables and services plus the derived DD
variable.
To accurately reflect total quarterly consumption
of durable goods, it is necessary to separate the
service flow derived from these goods in each period from total expenditures on durable goods in each
period. To do so requires a benchmark estimate of
the stock of durable goods held by households. This
stock was taken as the end of the year 1953 value
from the Flow of Funds Accounts of October 1981.
For the period 1954.1 to 1981.II we then solved the
following two equations:
III. Construction Quarterly Data from Annual Observations
Where interpolation is used to derive quarterly
series from annual observations, the method of
cubic splines interpolation was employed.
FOOTNOTES
Bank of England Quarterly Bulletin, (March 1976). The
role of. the misperception of the price level on aggregate
demand is considered in a theoretical model by R. J. Barro,
"Rational Expectations and the Role of Monetary Policy,"
JOurnal of Monetary Economics, (1976).
1. There are several ways of formulating the simple intertemporal consumption problem. Two of the clearest presentations can be seen in J. M. Henderson and R. E.
Quandt, Microeconomic Theory, 2nd edition, pp. 293309, and E. F. Fama and M. H. Miller, The Theory of
Finance, Holt, Rinehart and Winston. The role of discounted prices in intertemporal consumption analysis is emphasized in Henderson and Quandt and in A. Deaton and J.
Muelbauer, Economics and Consumer Behavior, Cambridge University Press, (1980).
3. See especially Deaton (1977), cited above, with respect
to the role of inflation in causing confusion over true relative
price changes. With respect to the effect of uncertain real
income on consumption, see J. Dreze and F. Modigliani,
"Consumption Decisions Under Uncertainty," Journal of
Economic Theory, (December 1972).
2. An early attempt to estimate money illusion effects on
real consumption is W H. Branson and A. K. Klevorick,
"Money Illusion and the Aggregate Consumption Function," American Economic Review, (December 1969).
See also A. Deaton, "InVOluntary Saving Through Unanticipated Inflation," American Economic Review, (December
1977), and J. C. Townsend, "The Personal Saving Ratio,"
4. An illustration of the theoretical ambiguity in determining
alternative interest rate effects on consumption can be
seen in J. I. Bernstein and D. Fisher, "Consumption, the
Term Structure of Interest Rates and the Demand for
Money," Working Paper #1976-8, Concordia University.
See also Henderson and Quandt, cited above.
30
5. See M. J. Boskin, "Taxation, Saving and the Rate of
Interest," Journal of Political Economy, (April 1978, Part
2), andW E. Weber, "Interest Rates, Inflation and Consumer Expenditures," American Economic Review,
(December 1975).
6-month and 1-, 2-, 3-, 4-, and 5-year Eurocurrency deposit
rates from 1973.IVto 1981.111. Data for the U.K., supplied by
the Bank of England, included the three-month interbank
rate, the gross redemption yield on local authority one-year
bonds, and the gross redemption yields on 5-, 10-, and
20-year gilts. While the U.K. data are not all yields on
government securities, they were suggested to be representative market yields for the given maturities. For Canada
yield data were for 3- and 6-month Treasury bills and government bond yields for 1-3-year, 3-5-year, 5-1 O-year and
10-year-and-over maturities, provided by the Bank of
Canada.
6. See Milton Friedman, A Theory of the Consumption
Function, Princeton University Press, (1956). A recent test
of the permanent income hypothesis which utilizes the concept of rational expectations is given in M. A. Flavin, "The
Adjustment of Consumption to Changing Expectations
About Future Income," Journai of Poiitical Economy,
(1981).
10. The arguments for introducing the disaggregated
components of the general index of consumer prices instead of the aggregate index were offered by A. Cukierman,
"Money Illusion and the Aggregate Consumption Function:
Comment," American Economic Review, (March 1972).
Cukierman argues that the "plim" of the money illusion
coefficient is dependent on the individual components of
the aggregate price index. J. van Daal argues that the
appearance of money illusion in macro consumption functions may likely be due to aggregation bias. See J. van
Daal, "Money Illusion and Aggregation Bias," De Economist, (1980).
7. See M. R. Darby, "The Permanent Income Theory of
Consumption-A Restatement," Quarterly Journal of
Economics, (May 1974), and J. J. Seater, "On the Estimation of Permanent Income," Journal of Money, Credit and
Banking, (February 1982).
8. H. R. Heller and M. S. Khan, "The Demand for Money
and the Term Structure of Interest Rate," Journal of Political Economy, (February 1979).
9. Quarterly term structure of interest rate data were used
to estimate equation (10) for each quarterly sample period
over which the consumption function was to be estimated.
Data for the U.S. included yields on the three-month and
six-month Treasury bills and the constant maturity 1-, 3-, 5-,
10-, and 20-year government bonds. In the case of Germany the term structure data were yields on 1-, 3-, and
11. Both fitted series plotted in Chart 3 utilized the second
order autocorrelated error structure estimated for the U.S.
in Table I.
31
@FedFRASER