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July/August 1989

Vol. 71, No.4




3 W h a t Is an “ A c c e p ta b le ” Rate o f
In fla tio n ? — A R e v ie w o f th e Issues
16 D oes D o lla r D e p re c ia tio n Cause
In flation ?
29 H a ve F ed era l S p en d in g and
T a x a tio n C o n trib u te d to the;
D iv e r g e n c e o f State P e r Capita
In co m es in th e 1980s?
43 D oes In fla tio n U n c e rta in ty A ffe c t
O u tpu t G ro w th ? F u rth er
E vid en ce
55 Tests o f C o vered Interest Rate Parity

THE
FEDERAL
A RESERVE
ABWKot
A r s T .m n s

1

Federal R eserve Bank of St. Louis
R e v ie w

July/August 1989

In This Issue . . .




Recent increases in various measures o f inflation have generated
much commentary about the “acceptability” of the current inflation rate
and prospects for future inflation. In the first article of this Review,
"What is an 'Acceptable’ Rate o f Inflation?—A Review of the Issues,"
Michelle R. Garfinkel provides a primer on three issues that must be ad­
dressed in any analysis of what constitutes an acceptable rate of infla­
tion. In discussing the first two issues, which concern the possible costs
and benefits of inflation, she questions the validity of the idea that any
positive inflation could be desirable as a long-run phenomenon. In
discussing the third issue, which revolves around the costs o f reducing
inflation, however, Garfinkel points out that an inflation in excess of the
long-run, desirable rate need not be unacceptable.
*

*

*

The increase in the inflation rate from about 1 percent in 1986 to
over 4 percent more recently has touched o ff a debate about its possible
causes. One culprit often discussed is the decline in the foreign ex­
change value of the dollar since 1985. In the second article in this
Review , "Does Dollar Depreciation Cause Inflation?” R. W. Hafer ex­
plores this connection.
The author notes that there are many facets to the dollar-inflation
linkage. For example, does a change in the exchange rate lead or merely
reflect events in the United States relative to other countries? Also,
should one calculate the exchange rate bilaterally or multi-laterally. The
procedure chosen, as Hafer shows, affects the analysis greatly.
Hafer also demonstrates that declines in the foreign exchange value of
the dollar are not inflationary nor do they promote an upward spiral in
future wages and prices. As the author shows, these relative price
changes are, by definition, not inflation. In fact, the evidence suggests
that, once the effects of domestic money growth are accounted for,
changes in the exchange rate provide no additional explanation of
inflation.
*

*

*

Following nearly 50 years o f convergence, state per capita incomes
have risen faster in high-income than in low-income states since 1978,
resulting in a substantial divergence of state per capita incomes.
Historically, regional disparities in economic growth have been linked to
the federal government’s fiscal policies.
In the third article of this issue, "Has Federal Spending and Taxation
Contributed to the Divergence o f State Per Capita Incomes in the
1980s?” Cletus C. Coughlin and Thomas B. Mandelbaum analyze the
flow of funds between the states and the federal government and con­
clude that changes in these flows have not been a major cause of the in-

JULY/AUGUST 1989

2

creasing inequality of state per capita incomes. More specifically, while
federal transfer payments and taxes reduced the level of inequality,
changes in their distribution did not contribute to the rising inequality.
The evidence suggests, however, that changes in one major federal
spending program—defense spending—may have been a minor factor
contributing to the increasing inequality in this decade.
* * *
Economists have long been interested in inflation’s effects on real
economic variables. In addition to effects arising from the impact of
unexpected inflation, many hold that uncertainty about future inflation
rates affects real variables. In the fourth article in this issue, “Does In­
flation Uncertainty Affect Output Growth? Further Evidence,” Den­
nis W. Jansen studies the hypothesized negative relationship between
inflation uncertainty and output growth. Using a bivariate ARCH-M
(Autoregressive Conditional Heteroskedasticity in Mean) model, the oneperiod-ahead conditional forecast error of inflation is taken as a
measure of inflation uncertainty. Estimates o f this model indicate that
over the last several decades there is little evidence that inflation uncer­
tainty influenced output growth.
* * *
In the final article in this Review, “Tests of Covered Interest Rate Pari­
ty,” Daniel L. Thornton investigates whether "covered interest parity”
holds on average. Covered interest parity implies a certain linear rela­
tionship between domestic and foreign interest rates (for assets of a
given maturity and risk) and spot and forward exchange rates, and is
assumed to hold in many open-economy macroeconomic models. The
author points out that, while previous tests have relied on the markets’
reactions to specific news (usually money announcements), there is a
more general test that can be applied to all observed exchange rate
data, not simply data around the times when specific news is released.
Thornton applies this test, as well as the usual test of market reactions
to money announcements, to daily data for the United States, Canada,
Switzerland, Germany, France, the United Kingdom and Japan for the
period from October 5, 1979 through September 14, 1988. His results
are consistent with the hypothesis that covered interest parity holds on
average over this period.


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3

Michelle Ft. Garfinkel
Michelle R. Garfinkel is an economist at the Federal Reserve
Bank of St. Louis. Thomas A. Pollmann provided research
assistance.

What Is an “Acceptable" Rate
of Inflation?— A Review of the
Issues
"Our strategy continues to be centered on moving toward, and ultimately
reaching, stable prices, that is, price levels sufficiently stable so that expec­
tations of change do not become major factors in key economic decisions.”
Alan Greenspan, T estim on y to H ouse C om m ittee on
Banking, Finance, a n d Urban A ffairs, January 24, 1989

R

ECENT fears of increased future infla­
tionary pressures, heightened by high rates of
capacity utilization, have generated a large body
of commentary concerning what level of infla­
tion would be desirable or at least acceptable.1
While there appears to be a general consensus
that a rise in the rate of inflation is not desir­
able, whether or not many would agree with
Mr. Greenspan’s statement above is not clear.
Indeed, his statement makes a stronger sugges­
tion that even the current rate of inflation is
not acceptable.2
This article points out three central issues for
determining what constitutes an "acceptable”
rate of inflation. The first issue concerns the
costs of inflation. The second issue is whether,
despite these costs, inflation’s benefits are suffi­

1See, for example, Clark (1989) and Stein (1989).
2Mr. Greenspan expressed this view more clearly in his
testimony to Congress in February 1989:
. . let me
stress that the current rate of inflation, let alone an in­
crease, is not acceptable, and our policies are designed to




ciently large to justify some positive rate of in­
flation. The final issue concerns the costs of
reducing inflation. Even if there were convinc­
ing reasons for ultimately eliminating inflation,
some analysts would argue that a positive infla­
tion could be acceptable in the short-run; the
optimal time path along which a long-run goal
of zero inflation is achieved depends on the
temporary costs o f adjustment to reach that
goal eventually.

W H AT ARE THE COSTS OF
INFLATION?
Examining the effects of inflation sheds light
on why price stabilization is a primary objective
of monetary policy. This section focuses on

reduce inflation in coming years.” [Greenspan (1989),
p. 274.] Elsewhere, he has been quoted as suggesting
that the ultimate objective of the Fed is to eradicate infla­
tion [Murray (1989)].

JULY/AUGUST 1989

4

Table 1
Some Effects of Inflation
Anticipated Inflation

Unanticipated Inflation

1. Inflation tax on money balances: transfers
resources from money holders to government
and reduces money demand.

1. Reduction in real value of gross return from holding
nominal debt: transfers resources from net
monetary creditors to net monetary debtors.

2. Inflation-induced increase in marginal income
taxes: transfers resources from taxpayers
to the government and reduces labor supply.

2. Reduction in real wages if wages are fixed in
nominal terms: transfers resources from labor
to employers.

3. Taxation of nominal interest income: transfers
resources from savers to the government and
reduced savings.

Inflation Uncertainty
1. Increase in reluctance to enter into nominal wage
contracts and increase in cost of nominal wage
contract negotiations: increases indexation of
nominal contracts and reduces real economic
growth.

4. Interaction with tax incentives: reduces
cost of borrowing and increases debt
finance.
5. Costs of price adjustments: produces excessive
relative price variability and a misallocation
of resources.

2. Increase in risk premia of longer maturity nominal
bonds: causes a movement from longer to shorter
term maturities and increases the real cost
of capital.
3. Increase in incentive to hedge against unanticipated
inflation: transaction costs incurred in attempts
to hedge against risk associated with inflation
uncertainty and distortions in asset accumulation.
4. Confusion about source of price movements:
causes excessive relative price variability
and a misallocation of resources.

some of the relevant effects given existing in­
stitutional arrangements in the United States.3
These effects, as summarized in table 1, are
organized by their source: the effects arising
from anticipated (or expected) inflation and
those arising from unanticipated inflation (or
the difference between actual inflation and ex­
pected inflation) and the associated uncertainty
about future inflation.

The Effects o f Anticipated
Inflation
Much of modern macroeconomic research has
been devoted to examining how expectations af­

3For a more exhaustive list and detailed analysis of the ef­
fects of inflation, see Fischer and Modigliani (1978). Also,
Kessel and Alchian (1962) provide a useful discussion of
inflation’s consequences. For a survey of the earlier
literature concerning the theory of inflation, see Laidler
and Parkin (1975).
4This assumption is made purely for expositional ease.
When uncertainty is introduced in the discussion, the ef­


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fect economic decisions. In contrast to the idea
that only "surprises” or unanticipated events
can have real effects, economic theory suggests
that even fully anticipated inflation can distort
economic decisions. These “distortions” are said
to be the costs of anticipated inflation. A useful
way to focus solely on the effects o f anticipated
inflation is to assume that the future sequence
of changes in the general price level is known
in advance.4
Anticipated inflation influences the allocation
of resources in the economy primarily through
two types of tax effects. First, inflation effective­
ly imposes a tax on money balances equal to the

fects of anticipated inflation mentioned in this section are
simply added to those effects arising from the unantici­
pated component of inflation and those effects arising from
uncertainty. It should be noted that the assumption of cer­
tainty does not preclude a variable inflation rate.

5

reduction o f purchasing power of money hold­
ings. For example, an individual holding $100
throughout 1988, when the inflation rate was
around 4 percent, lost about $4 in purchasing
power.5
Since inflation imposes a tax on money bal­
ances, it reduces individuals’ demand for
money.6 Because individuals will attempt to
economize on money holdings during periods of
inflation by making extra trips to the bank or
automatic teller machine, inflation is said to
generate “shoe-leather costs." But the costs of
the inflation tax are not merely the physical
resources and time expended to avoid the infla­
tion tax, as that term suggests. The total cost or
the "gross burden" of the inflation tax more im­
portantly includes the increase in the price paid
to maintain real money balances and the value
of lost services otherwise provided by money.
Inflation, however, generates revenue to the
government that indirectly accrues to individ­
uals. The "excess burden” is the difference be­
tween the total costs and the government’s rev­
enues. Under some plausible assumptions, a
in fla tio n as measured by the consumer price index for all
urban consumers was 4.4 percent during 1988, while other
measures indicate that inflation was between 3.0 percent
and 4.5 percent. The current dollar loss of purchasing
power of $100 is calculated by the following equation:

P,4,

’ w^ere * is
3'

9eneral

price level in time t. Since the rate of inflation, nt, equals
P
- P
—— ----- , the loss in purchasing power in current dollar
terms equals 100 n, As noted below, the tax on money
balances generates revenue to the government.
6Another way to see why inflation reduces the demand for
money is by noting that inflation increases the opportunity
cost of holding those balances. The opportunity cost is the
revenue forgone by holding money rather than securities
yielding a nominal interest rate, R. (The assumption that
money does not yield interest is not important here. As
argued by Tatom (1979), among others, even checkable
deposits that pay interest are subject to the inflation tax.)
Suppose, for example, that there is no expected future in­
flation. Then the nominal rate paid on a security is its real
yield, r. An individual holding $100 in cash balances for
transaction services forgoes the real interest payment,
$1 OOr, that would have been obtained if he instead bought
a $100 bond. In this case, the opportunity cost of holding
money balances is r per dollar. Now suppose that inflation,
n, in the next period is expected to be positive. The
nominal yield on the bond R, will increase roughly by the
amount of expected inflation to compensate lenders for the
expected loss in purchasing power of the initial loan; the
nominal yield will equal the real rate plus an expected in­
flation premium. (Strictly speaking, R = (1 +r)(1 +n)-1.
Simply adding the real rate of interest and the rate of infla­
tion will be a reasonable approximation provided that the
product of the real rate of interest and the rate of inflation,




rough estimate of this excess burden from a
"small” inflation tax of 5 percent is about $13.4
billion or about 0.3 percent of gross national
product (GNP) per year.7
The excess burden o f the inflation tax on
money balances is only part o f the total welfare
cost associated with inflation. The second type of
tax effect arises as anticipated inflation interacts
with the structure of the existing income tax
system, exacerbating the distortions contained
therein. Since the progressive income tax
system is not completely indexed against in­
creases in the price level, inflation will subject
individuals’ incomes to higher average and mar­
ginal tax rates. Even if wages fully adjust to in­
flation so that the real (before-tax) wage rate is
approximately constant, an individual's real,
after-tax income will decline.8
Although one would expect that, through the
so-called "bracket-creep” effect, anticipated infla­
tion would influence and distort individual’s
labor supply decisions, empirical evidence on
the effects of marginal taxes suggests that an­
ticipated inflation has little effect on aggregate
rit, is of a small order of magnitude.) The higher nominal
rate forgone by holding money implies that the opportunity
cost of holding money has increased.
TThis estimate is intended to give only a rough order of
magnitude of the excess burden of inflation. The estimate
assumes that the current stock of money (M1) is about
$780 billion and that the interest elasticity of the demand
for money is -.15. This latter assumption means that when
the opportunity cost of holding money increases 1 percent,
the quantity of money demanded falls .15 percent. Thus,
assuming the real rate of interest is 3 percent, the demand
for money would increase by 25 percent to $975 billion if
inflation were zero. It should be noted that the estimate of
the welfare cost ignores the fact that total “ tax” borne by
the individual money holder does not go entirely to the
government. Since the banking system receives part of the
revenue from the inflation tax through money creation, the
estimate above understates the excess burden. See Tatom
(1976, 1979) and Fischer (1981b) for more detailed discus­
sions of estimating the excess burden of the inflation tax
on money balances.
°ln a preliminary study, Baye and Black (1988) table II, p.
480, estimate that the “ bracket-creep-induced inflation tax
rate,” defined as the difference between the rate of
change in gross income necessary to keep utility constant
and the associated rate of change in consumption expen­
ditures, ranges from 0.2 percent to 2.4 percent between
1972 and 1981. Furthermore, they find that changes in the
tax code during this period, intended to mitigate the
bracket-creep effect, were largely offset by simultaneous
increases in Social Security taxes (pp. 481-82).

JULY/AUGUST 1989

6

labor supply.9 Furthermore, to the extent that
the current income tax system has become par­
tially indexed by recent tax reform, the effects
of inflation in terms of the bracket creep effect
have been partially mitigated.1
0
Nonetheless, recent tax reform has not fully
insulated individuals from the tax effects of an­
ticipated inflation. Anticipated inflation produces
an overstatement of interest income subject to
taxation. The nominal interest rate required by
lenders includes two components. The first
component, r, is a payment to the lender for
not consuming today and, hence, constitutes in­
come. The second component, n, is a premium
to compensate the lender for the anticipated
lost purchasing power of the principal due to
inflation. Because the latter component serves to
preserve the value of the principal, it is not in­
come in an economic sense. Yet, like income, it
is taxed.
To see how an increase in anticipated infla­
tion increases an individual’s tax liability for a
given before-tax real return, consider the
following example. Suppose, first, that no infla­
tion is expected and the marginal income tax
rate is 25 percent. A one-year loan that yields a
3 percent (real) return to an individual before
taxes generates an after-tax real return of 2.25
percent. If, instead, the anticipated rate of infla­
tion were 2 percent, with the real interest rate
on the one-year loan remaining at 3 percent,
and the nominal yield rising to 5 percent (the
real rate of interest plus the rate of inflation
that would be required when abstracting from
tax considerations), then the after-tax real rate
of return to the lender would fall to 1.75 per­
cent. A rise in the anticipated inflation rate to 5
percent would erode the expected (and actual)
return dramatically to 1 percent.
Lenders will demand a nominal return higher
than the original real interest rate plus the rate

9See, for example, Hausman (1981), who finds that the taxinduced effects on wages do not significantly reduce ag­
gregate labor supply. Inflation’s effect on the marginal tax
rate could similarly have an insignificant effect on labor
supply.
10Tatom (1985) discusses the impact of the partial indexa­
tion of the income tax system on real tax liabilities. As
discussed by Tatom, the currently used method of indexa­
tion does not fully mitigate the bracket creep effect
because the indexation of tax brackets is calculated using
past increases in the general price level. Furthermore,
some deductions, credits and adjustments that can be
made for tax purposes have maximum dollar limits or
nominal ceilings that are not indexed. Even assuming a
constant real income before taxes, an expected rise in the


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of inflation to be compensated for the increased
future tax liability arising from an increase in
anticipated inflation. In the example above, for
the lender to supply the same dollar amount of
loans as when expected inflation was zero, the
same after-tax real return of 2.25 percent
would be required; this, in turn, would require
a rise in the nominal return from 3 percent to
9.67 percent when expected inflation rises to 5
percent. Hence, the nominal rate of interest
must rise by more than the rate of inflation to
induce the lender to forgo the same amount of
current consumption. If, however, nominal in­
terest rates did not rise enough to keep the
after-tax real rate the same when inflation rises,
savings would be reduced. It has been estimated
that the distortionary effect of a 10 percent rate
of inflation on savings over a 20-year period
produces a total welfare loss (total cost net of
additional revenues to the government in pre­
sent value terms) of about 7 percent of current
savings or, assuming that savings is 10 percent
of GNP, about 0.7 percent of current GNP.1
1
Tax incentives combined with anticipated in­
flation distort financial decisions. Because
nominal interest payments on debt are taxdeductible and dividends are effectively taxed
twice, anticipated inflation will induce corpora­
tions to finance an expansion of their operations
by creating debt rather than issuing additional
stock. If nominal interest rates do not adjust to
anticipated inflation enough to maintain a fixed,
after-tax real rate of return, then an increase in
anticipated inflation can induce individuals to
finance a greater proportion of their consump­
tion and asset purchases with debt.1 This bias
2
for debt finance, which increases with antici­
pated inflation, could be costly if, by increasing
future debt obligation as a fraction of expected
future cash flows, it increases the chances of
future default.

price level implies that a larger portion of real income will
be subject to taxes. Without increasing the marginal tax
rate, anticipated inflation increases the average tax
liability.
11Fischer (1981b), p. 23. As he notes, however, the estimate
is rough and could be as large as 2 percent to 3 percent
of GNP under slightly different, although still plausible,
assumptions.
12Even if nominal rates fully adjusted to increases in an­
ticipated inflation so as to not affect the after-tax real
return, an increase in anticipated inflation decreases the
cost of debt finance to firms provided that the corporate
marginal tax rate exceeds the individual marginal tax rate.

7

The impact of anticipated inflation on eco­
nomic behavior is not restricted solely to in­
flation-induced tax effects. Specifically, by
changing prices, some firms incur lump-sum or
“menu” costs. Even if these costs are small, realworld price adjustments occur at discrete times
rather than continuously. Assuming that price
changes are not sychronized, anticipated infla­
tion (and deflation) can generate relative price
changes in the short run. Since these inflationinduced relative price changes do not reflect
real, fundamental changes in the economy, they
can create a misallocation of resources, resul­
ting in a welfare loss in addition to the explicit
costs of changing prices.1
3

The Effects o f Unanticipated Infla­
tion and Uncertainty
Unanticipated inflation also can result in a
misallocation o f resources. Its impact on in­
dividuals’ behavior, however, is less obvious. In
particular, although unanticipated inflation pri­
marily redistributes wealth among people, it is
the uncertainty associated with these possible
future redistributions that distorts economic
behavior. Before discussing these distortionary
effects, this section focuses on the distributional
effects of unanticipated inflation.
To examine the distributional effects, while in­
itially abstracting from the effects of uncertain­
ty p e r se, suppose there is a one-time shock to
the level of inflation. The shock is temporary in
the sense that, after one period, the rate o f in­
flation will return to the previously expected
time path.1 This unanticipated inflation influ­
4
ences the distribution of wealth through con­
tracts that fix future nominal cash flows, espe­
cially debt contracts.
13Mankiw (1985) demonstrates that, in the presence of even
small price adjustment costs, optimizing behavior by pricesetting firms can produce sticky prices that are inefficient
from a social welfare perspective in a deflationary period.
He shows, however, that sticky prices in an inflationary
period could be more efficient than fully flexible prices.
Since price-setting firms produce at lower-than-sociallyoptimal levels, sticky prices in an inflationary period
reduce the wedge between actual and socially optimal out­
put levels.
14lf the level of inflation were permanently increased above
its previously expected and actual level, but the possibility
of a future shock were arbitrarily close to zero, the discus­
sion to follow is virtually unchanged. It should be noted,
however, that the discussion implicitly assumes that, when
contracts are signed, individuals do not perceive the
possibility of shock in the future. Hence, the discussion is
about a counterfactual and can be misleading. Specifically,
if individuals suspected that such a shock might occur




When debt contracts are fixed in nominal
terms, the main effect of unanticipated inflation
is to redistribute real wealth to net monetary
debtors at the expense of net monetary credi­
tors.1 Not suspecting the possibility of a diver­
5
gence between actual and expected inflation, a
lender would demand a rate of return that com­
pensates him only for not consuming today and
for the lost purchasing power of the initial bor­
rowings due to anticipated inflation. When ac­
tual inflation exceeds anticipated inflation, the
lender unexpectedly suffers a loss on his loan;
the purchasing power of the return on the loan
falls below that expected at the time the loan
was made.
For example, suppose an individual, who ex­
pects zero inflation over the next period, re­
quires a 5 percent nominal (and real) return
next period in exchange for lending $100 today.
Regardless of next period’s inflation, the lender
will receive $105 in the next period. If there is
a 5 percent (unanticipated) inflation, then the
purchasing power o f the $105 payment to the
lender is identical to that o f the $100 lent. In
this case, the real net return is zero.
Just as unanticipated inflation erodes the real
purchasing power of the return from the loan,
it reduces the real liability of the debtor. Along
the same lines, if nominal wages specified in
labor contracts are fixed for an interval of time,
unanticipated inflation reduces an individual’s
real wage while increasing an employer’s in­
come net of the wage bill in real terms.
Although the redistribution of wealth due to
unanticipated inflation is important to the in­
dividual before and after the fact, it is not easy
to say anything meaningful about the welfare
implications of the realized or ex p o st redistrib(with a positive probability), they would adjust their
behavior, so that the terms of the contract reflect the
possibility of a future shock. The implicit assumption is
made for expositional purposes, and the possible ad­
justments in behavior are discussed in turn.
15A net monetary creditor’s (debtor’s) holdings of fixed
nominally denominated assets are greater (less) than his
holdings of nominally denominated liabilities. See, for ex­
ample, Kessel and Alchian (1962). Alchian and Kessel
(1959) present evidence that the market value of equity of
firms classified as net monetary creditors tends to fall dur­
ing inflationary periods. The converse holds for net
monetary debtors.

JULY/AUGUST 1989

8

utions.1 The losses due to unanticipated infla­
6
tion are matched by others’ gains, so that there
is no net change in wealth associated with the
redistribution. In an expected or ex an te sense,
however, the possible (and arbitrary) redistribu­
tions have aggregate welfare implications, be­
cause they distort behavior, especially that of in­
dividuals who dislike risk.
Uncertainty associated with inflation manifests
itself quantitatively and qualitatively in both
nominal and real contracts. In the presence of
fixed nominal wage contracts, uncertainty asso­
ciated with future inflation can depress the
supply and demand for labor. As greater infla­
tion uncertainty increases the difficulties and
costs of forecasting future inflation, wage nego­
tiations become more complex and costly. Con­
sequently, without nominal wage indexation
when future inflation becomes more uncertain,
individuals and firms are less willing to lock
themselves into fixed nominal contracts.
But the effects o f inflation uncertainty will be
partially alleviated as labor markets adjust.
Greater uncertainty about future increases in
the general price level gives risk-averse individ­
uals and firms an incentive to increase the
degree of indexation in wage contracts and to
reduce the duration o f the contract. The in­
creased degree of indexation and the shortening
of the length of the nominal contracts increases
the responsiveness of nominal wages to unan­
ticipated inflation.1 Nevertheless, a recent em­
7
pirical study, which accounts for the greater
wage indexation induced by greater inflation
uncertainty, indicates that an increase in infla­
tion uncertainty similar to that which occurred

16Such a value judgment would depend on the specified
social welfare function—in particular, the relative weights
assigned to each individual’s utility. Nonetheless, the
decline in wealth experienced by some in a period of
positive unanticipated inflation does not necessarily pro­
vide sufficient justification, in terms of a Pareto efficient
criterion, for a “ forced” transfer of resources to restore
the initial distribution of wealth.
17When the economy is subject to real as well as to nominal
disturbances, however, complete wage indexation is not
desirable. See Gray (1976) for example. Also, see Holland
(1984b) for a more detailed discussion of the effects of in­
flation uncertainty on labor markets.
18Holland (1988), p. 478-80. This is a cumulative effect over
a number of years (e.g. 2 to 6 years). In general, however,
there is mixed evidence about the effects of inflation
uncertainty on output growth. For example, Jansen (1989)
finds that the conditional variance of inflation as a
measure of inflation uncertainty has no significant impact
on real output growth.


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roughly between the 1960s and the 1970s
would reduce growth in real GNP in the long
term by approximately 2 percent.1
8
Inflation uncertainty also affects the demand
and supply o f nominally denominated debt of
different maturities. Risk-averse lenders might
be less willing to purchase a long-term nominal
bond over short-term nominal bonds. As fore­
casting future inflation becomes more difficult
with longer time horizons, the opportunity cost
of holding a longer-term nominal bond is more
uncertain. In addition, a given permanent unex­
pected movement in the rate of inflation will
have a greater impact on the market value of
the longer-term bond and, consequently, a
greater impact on the realized rate of return
from selling that bond. To compensate lenders
for taking on additional risk, the required
nominal yield on a bond with a longer maturity
will embody a greater risk premium.
The uncertainty associated with future infla­
tion creates an element o f uncertainty about
real, future rates o f return on all investments
whose returns are not fixed in real terms. The
more uncertain are the future rates of inflation,
holding all else constant, the greater the risk
premia for all bonds o f any given maturity.1 As
9
the required nominal yields on instruments of
all maturities increase with greater inflation
uncertainty, the cost of capital financed by
nominal debt increases. Not all investments,
however, are fixed in nominal terms. The riskaverse individual can hedge, at least partially,
against unanticipated inflation by investing in
projects or holding financial instruments whose
actual and expected real returns are relatively

19Taylor (1981), among others, finds a positive relation bet­
ween the average rate of inflation and the variability of in­
flation across nations and through time. This stylized fact,
however, does not imply any causal link between the two.
Moreover, greater variability does not imply greater uncer­
tainty. Nevertheless, preliminary evidence indicates that in­
flation variability is positively related to uncertainty, as
measured by the variance of the forecast errors from
survey data or from an econometric model for predicting
future inflation, or as measured by the dispersion of infla­
tionary expectations within a survey. But Jansen (1989)
recently found no statistical relation between inflation and
the conditional variance of inflation. See Taylor (1981) and
Holland (1984a), who review the existing evidence on the
relations between average inflation, the variability of infla­
tion and uncertainty.

9

independent of future rates of inflation, such as
human capital, homes and corporate stocks.2
0
Even a complete hedge against unanticipated in­
flation would not eliminate the welfare costs of
uncertainty, however. Substantial transaction costs
can be incurred by those who attempt to eliminate
the risk associated with future inflation from their
portfolios. In any case, as individuals and firms at­
tempt to hedge against unanticipated movements
in the general price level, inflation uncertainty can
distort asset accumulation and the aggregate
allocation of resources.2
1
Another distorting feature of the uncertainty
associated with price movements arises when in­
formation about the source of price movements is
not available without costs. If information were
costless to obtain, the appropriate response to a
given increase in prices is clear. For example, an
unanticipated temporary increase in observed
prices correctly attributed to monetary policy (a
nominal factor), rather than to an increase in de­
mand for some goods relative to others (a real fac­
tor), would not alter the decisions of producers in
the absence of nominal rigidities. If it is costly,
however, to distinguish between general price
movements produced by nominal factors from
those created by real factors, price movements
will be "noisy." Confusion about the source of a
given price movement and the appropriate
response will produce excessive relative price
20While homes appear to be good hedges against expected
and unexpected inflation, the evidence for human capital
is inconclusive, at least for the long run. Moreover, a
puzzling negative relation between stock returns and ex­
pected as well as unexpected inflation has been widely
documented, but not resolved. See, for example, Fama
and Schwert (1977).
21See Jaffee and Kleiman (1977) for a more detailed discus­
sion of the effects of inflation uncertainty on the allocation
of resources.
22To be sure, relative price variability need not be a cost. To
the extent that relative price movements signal real distur­
bances to the economy, those movements contain impor­
tant information facilitating an efficient allocation of
resources. Fischer (1981a) provides a summary of com­
peting approaches to explaining the relation between the
average inflation rate and relative price variability. Taylor
(1981) and Fischer (1981b) do not find evidence indicating
a causal relation between inflation and variability of
relative prices. Rather, Taylor (1981) and Fischer (1981a)
find evidence consistent with the notion that the positive
relations between average inflation, the variability of infla­
tion and relative price variability in the 1970s have been
driven by supply shocks (for example, energy and food
shocks). Taylor (1981) also finds that accommodative
monetary policies aiming to stabilize output and employ­
ment in light of real disturbances to the economy con­
tributed in a large part to the increased variability of infla­
tion in the 1970s. Furthermore, Fischer (1981a) concludes
that policy shocks that could have created confusion about




variability, resulting in a misallocation of
resources.2
2

W H Y NOT A ZERO RATE OF
INFLATION?
While any positive inflation has a large num­
ber of distortionary effects, a zero inflation rate
might not necessarily be desirable—even in the
long run. First, the various measures of infla­
tion (for example, the consumer price index and
the GNP implicit price deflator) do not control
perfectly for quality improvement of products
over time. To the extent that the lower and
higher quality versions of goods are treated as
comparable, the difference in their prices will
be measured as inflation; the resulting measure
will tend to overstate the actual inflation rate.
Given this positive bias in inflation measures, it
has been suggested that a 2 percent inflation
rate measured by the usual price indexes would
be associated with roughly stable prices.2 More­
3
over, some would contend that inflation also
has some important benefits like providing a
cheaper source of government revenue or
creating higher output and employment, so that
the long-run desirable rate of inflation is not
zero, but positive.

Optimal Taxation
Some have argued that inflation is required
for optimal taxation.2 The inflation tax provides
4
the source of price movements do not appear to be
associated with lower aggregate economic activity.
23Friedman (1969), p. 47. According to Friedman (1969),
however, a negative inflation rate (about 2 percent defla­
tion) correctly measured would be optimal. In this case, a
zero inflation rate, as measured by the various price in­
dices would be a desirable target. (See Alchian and Klein
(1973) for a critical assessment of the appropriateness of
the price indexes for policy.)
24See, for example, Phelps (1973). The government’s
revenue from the production of money is the nominal rate
of interest times the stock of the monetary base (total
reserves plus currency). Using the fact that the ratio of the
monetary base to the money stock (M1) is about 40 per­
cent and assuming that the real interest rate is about 3
percent, the revenue with a 5 percent inflation tax on a
stock of M1 of $780 billion is about $25 billion per year in
current dollar terms. The inflation tax alone generates
$15.6 billion per year. It is important to note that unan­
ticipated inflation implicitly generates additional revenue to
the government (a net monetary debtor) through its effect
on the real value of public debt. By reducing the purchas­
ing power of interest payments on outstanding debt, unan­
ticipated inflation lowers the real liability of the government
and the amount of revenue to be raised through income
taxes.

JULY/AUGUST 1989

10

the government an alternative source of reve­
nue to other explicit and distorting taxes—for
example, income taxes.2 The theory of optimal
5
taxation suggests that, to finance a given level
o f public expenditures, the government should
trade o ff the costs of distortions arising from in­
flation against those arising from other taxes.2
6
From this perspective, the optimal inflation tax
rate equates the marginal cost per dollar of
revenue from the inflation tax and from other
distorting taxes.
Recent empirical evidence on the marginal
costs of the inflation tax and other taxes, how­
ever, casts doubt on the relevance of the opti­
mal taxation theory to justify a positive rate of
inflation. These studies suggest that the margin­
al cost per dollar revenue of the inflation tax at
any positive rate o f inflation exceeds that for
alternative taxes set at plausible rates.2 In other
7
words, inflation does not necessarily provide a
cheaper source of government revenue. Fur­
thermore, the interaction between inflation and
the distortions produced by the tax system sug­
gests that the marginal cost of income taxes
could be positively related to the rate o f infla­
tion; thus, lowering the inflation tax not only
would reduce the welfare losses associated with
the inflation tax, but make income taxation a
cheaper source of government revenue.2
8

The Inflation and Unemployment
T ra d e-off
T h e o ld e r a r g u m e n t u sed to ju s tify p o s itiv e in ­
fla tio n h in g e s o n th e so-ca lled P h illip s c u r v e

25lf there were non-distorting taxes, then the excess burden
of the inflation tax discussed above would render inflation
an “ inefficient” tax. But, in the absence of non-distorting
taxes as a source of revenue to the government, the op­
timal rate of inflation could be positive. Browning (1987),
table 1, p. 16, estimates that in 1984 the total welfare cost
associated with the distortionary effects of the labor tax
ranged from $55.9 billion to $212.6 billion under various
assumptions. As a percentage of tax revenues from labor,
the welfare loss ranged from 7.5 percent to 28.5 percent,
well below the inflation-induced welfare loss as a percen­
tage of revenues from the inflation tax (about 86 percent).
26ln recent studies, Mankiw (1987) and Poterba and
Rotemberg (1988) test the implications of the hypothesis
that the government optimally trades off the distortions
from explicit income taxes and inflation. While Mankiw
finds preliminary evidence supporting the hypothesis for
the United States, Poterba and Rotemberg, who look at
different nations, do not find conclusive evidence. That the
hypothesis is not fully supported by the data might be a
result of the maintained assumption that the distortionary
effects of the explicit tax system are independent of the
distortionary effects of the inflation tax. Given the discus­
sion above, this assumption seems inappropriate.


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trade-off between inflation and unemployment.
Figure 1, which depicts the apparent trade-off
that emerged in the 1960s, could be interpreted
as suggesting that, by tolerating a higher level
o f inflation, society could benefit from lower
levels o f unemployment.
One possible story behind such an interpreta­
tion is that an expansionary monetary policy
that increases the general price level can in­
crease output if nominal wages are relatively
fixed. With fixed nominal wages, a rise in infla­
tion can induce firms to increase output. This
incentive arises because the firm’s marginal
profit—that is, the change in real revenues net
of the change in the real wage bill realized by
expanding output—increases with unanticipated
inflation. If nominal wages were not fixed, they
would adjust quickly to the increase in prices to
maintain a given real wage rate; output and un­
employment would be essentially independent
of inflation. But, according to the trade-off view,
the existence of nominal wage contracts means
that, by generating inflation, the government
can decrease the rate of unemployment and
thereby enhance social welfare.
The possibility of exploiting the trade-off be­
tween inflation and unemployment with mone­
tary policy, however, depends on the way in
which inflationary expectations are formed and
incorporated into nominal wages. If inflation is
correctly anticipated and incorporated into
wage contracts, then real output will be in­
dependent o f inflation in the long run. Even if
the government were to generate inflation un-

27For example, Tatom (1976), p. 20, shows that marginal
cost per dollar revenue of the inflation tax, assuming that
the elasticity of demand for money is -.1 5 , is 44 percent.
This estimate is not conditional on the inflation rate, but it
is highly sensitive to the assumed elasticity of demand for
money. For example, an elasticity of - .25 would imply a
marginal cost of 83.33 percent. Browning (1987), table 2,
p. 21, shows that the marginal welfare cost from taxes on
labor earnings ranges from 9.9 percent to 33.2 percent
under the assumption that labor supply is not highly re­
sponsive to the marginal income tax rate (see footnote 9).
28lt should be noted, however, that since the marginal cost
of taxes on labor earnings is positively related to the
marginal tax rate, the theory of optimal taxation in light of
the evidence on marginal welfare costs does not
necessarily imply a zero rate of inflation. Nevertheless, if
the marginal cost of the inflation tax were positively related
to inflation, the optimal rate of inflation would more likely
be zero.

1
1

Figure 1
The Inflation-Unemployment
T rade-off
1960-1969

Inflation

Inflation

1969
•

1968
—

—

1966
•
1967

19.6 5
1962
•
1960
1964 #

#1963

—

19*61
I
3

I
I
4
5
Unemployment

expectedly, the increase in output and decrease
in unemployment would only be transitory.
Subsequent wage changes would restore the
original level of the real wage. As a conse­
quence, the original profit rate would be re­
stored, with output and unemployment return­
ing to their original equilibrium or " natural”
levels; the trade-off between unemployment and
inflation would not exist in the long run.2
9
Indeed, figure 2, which plots the combinations
of unemployment and inflation in the 1970s and
the 1980s, does not support the existence o f a
long-run trade-off. While a short-run trade-off
might exist, whether or not it is operative for
the purpose of enhancing social welfare is un­

29See Fischer (1977), for example. The notion that real output and employment are independent of the inflation rate




I
6

7

clear. Attempts to ‘‘fool" individuals systematic­
ally, by continuously creating surprise inflation
so as to exploit the short-run trade-off, would
not improve the welfare of all individuals
because, although some individuals experience
unexpected wealth gains, others suffer wealth
losses. In addition, attempts to repeatedly fool
individuals would increase the costs associated
with inflation due to increased inflation
uncertainty.
Moreover, as individuals and firms adjust to
the higher inflation uncertainty, the trade-off
becomes less favorable, because greater infla­
tion uncertainty increases incentives for indexa­
tion. With greater wage indexation, a given

in the long run (a vertical Phillips curve) is known as the
“ Natural Rate Hypothesis.”

JULY/AUGUST 1989

12

Figure 2
The Inflation-Unemployment
“ Trade-off”
Inflation
10.0

1970-1988

Inflation
10.0

7.5

-

5.0

2.5
6

7

Unem ploym ent

amount of surprise inflation will have a smaller
transitory effect on output and employment as
nominal wages become more responsive to ac­
tual inflation. Accordingly, the trade-off be­
comes steeper. If attempts to exploit the trade­
o ff also increases average inflation, the trade-off
shifts outward, so that a given rate of inflation
will be associated with a higher rate of
unemployment.

W H AT ARE THE COSTS OF
REDUCING INFLATION?
The suggested benefits of inflation seem hard­
ly compelling to justify any positive, sustained
inflation. The long-run desirability of achieving
stable prices, however, does not necessarily
mean that the current rate of inflation is unac­

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Federal Reserve Bank of RESERVE BANK OF ST. LOUIS

ceptable. Specifically, the latter discussion sug­
gests that policies to reduce inflation and ulti­
mately achieve the long-run desirable inflation
rate can be costly. That is, any short-run trade­
o ff between inflation and unemployment implies
that anti-inflationary policies will produce tem­
porary increases in unemployment.

A re The Costs T oo High?
Table 2 shows the inflation rate, as measured
by the GNP implicit price deflator, and the
civilian unemployment rate; it indicates that the
large reduction in inflation from 1979 to 1988
was accompanied by significantly large rates of
unemployment. These observed high rates of
unemployment, however, can overstate the
costs of the anti-inflationary policy. Regardless
of the current inflation rate or its prospective

13

Table 2
Unemployment and Inflation, 1979-88

inflicts on the econom y is often exaggerated; and
those costs w hich are not mythical can be mini­
m ized o r even elim inated b y indexing. Hardheaded devotion to the principle o f efficien cy thus
argues fo r w o rry in g less about inflation and run­
ning a high-pressure econom y in w hich jobs are
plentiful.31

Year

Civilian
unemployment

Inflatio

1979
1980
1981
1982
1983
1984
1985
1986
1987
1988

5.8%
7.1
7.6
9.7
9.6
7.5
7.2
7.0
6.2
5.5

8.9%
9.0
9.7
6.4
3.9
3.7
3.0
2.7
3.3
3.4

SOURCE: Economic Report of the President (1989) and
Economic Indicators (January 1989).
’ Percentage change from the previous year in the GNP price
deflator.

By definition, excess unemployment is ineffi­
cient, because it implies that resources, other­
wise available to increase consumption oppor­
tunities, have been wasted. But excess un­
employment is only a transitional cost as the
economy adjusts to the long-run desirable infla­
tion rate. When the inflation goal is finally
achieved and sustained, the excess unemploy­
ment will disappear. In contrast, the welfare
costs associated with inflation are incurred
indefinitely—that is, each year in which the
economy’s institutional features (for example,
the explicit tax system) make the distortionary
effects o f inflation discussed above relevant.3
2

The Optimal Time Path o f
Reducing Inflation
path, temporary unemployment is an efficient
response to fundamental changes in the
economy, as individuals search for new jobs.
Consequently, the "natural” rate o f unemploy­
ment (the rate of unemployment consistent with
a steady inflation) can be positive. It has been
estimated that, assuming the natural rate of
unemployment is 6 percent, the decline in infla­
tion from 9 percent in 1980 to 3.2 percent in
the middle of 1987 was associated with about
2.4 percentage points of “excess” unemployment
per percentage-point reduction in inflation.3
0
Similarly constructed estimates have been us­
ed to suggest that reducing inflation is unaccep­
table on efficiency grounds:
The damage that high unem ploym ent does to
econom ic efficien cy is enorm ous and inadequately
appreciated. By contrast, the harm that inflation
30Friedman (1988), p. 66. Each percentage point of
unemployment above the natural rate (or that in a “ fully
employed” economy, with a steady inflation rate) con­
stitutes a percentage point of “ excess” unemployment. Of
course, because the natural rate of unemployment is not
observed and is subject to change during the evolution of
the economy subject to permanent and transitory real
shocks, one could argue that Friedman's estimate
understates (or overstates, for that matter) the welfare loss
associated with the reduction of inflation in the 1980s.

Among the important questions that policy­
makers must face is the timing of anti-inflation­
ary policy actions to reach the long-run desir­
able inflation rate. Given the initial inflation
rate, the speed with which the desirable infla­
tion rate is reached partly determines the cost
of that policy.
One recent study shows that there are large
differences in the costs o f policies that vary
with respect to their timing3 . On the basis of
3
various models, this study calculates the costs of
several policies to bring inflation from 7.5 per­
cent to zero. The costs of the policies are esti­
mated in terms of output losses using a relation­
ship known as Okun’s law that translates each
percentage point of excess unemployment into a
3.2 percent reduction in real output. For exam­
ple, employing a Phillips curve model, this study
duces an inflation above (or below) the optimal rate does
not easily follow from an efficiency criterion. As pointed
out by Meyer and Rasche (1980, p. 14), among others,
however, if the benefits from eliminating inflation (or iden­
tically, the costs of sustaining inflation) increase at the
same rate of real potential output, then any antiinflationary policy would be justified, irrespective of the
policy’s costs, provided that the costs are finite and that
the initial gain from such a policy is positive.
33Meyer and Rasche (1980).

3 Blinder (1987), p. 65.
1
320 f course, not all anti-inflationary policies can be justified.
Rather, without a careful evaluation of the costs and
benefits of reducing inflation, a monetary policy that pro-




JULY/AUGUST 1989

14

found that a gradual policy to eliminate infla­
tion over a 23-year period could generate a dis­
counted cumulative output loss of $1 trillion (in
1972 terms), whereas a policy that reached the
inflation goal in 11 years could result in a dis­
counted cumulative output loss of $1.5 trillion.3
4
The relation between the time path and the
costs o f the policy depends on the dynamic rela­
tion between unemployment and inflation. In
addition to the degree to which the economy is
indexed, this dynamic relation depends on the
credibility of the anti-inflationary policy and ex­
pectations about future inflation. If, as assumed
in the Phillips curve model, expectations depend
on past inflation, a given inflation-reducing
policy will be more costly; with nominal rigid­
ities in the economy and a sluggish adjustment
of expectations, the short-term trade-off be­
tween inflation and unemployment can be large.
To achieve a specific reduction in inflation over
a given time span can require higher levels of
unemployment and greater output losses. If in­
flationary expectations are forward-looking and
the policy is credible, however, the link bet­
ween inflation and unemployment is weaker; in
this case, unemployment is less responsive to
movements in inflation. Accordingly, credible
anti-inflationary policies will be less costly in
terms of output losses than incredible ones.3
5
The time path of the anti-inflationary policy is
also important because it determines the speed
with which the gains from such a policy are
realized fully. For example, a gradual policy that
eliminates inflation over 50 years might not
generate significant output losses, but the pre­
sent discounted value of the benefits from that
policy could be infinitesimally small.

CONCLUSION
Analyses of the acceptability of any particular
positive inflation should start by asking what is
the optimal rate of inflation. In reviewing the
various effects and costs of inflation, this article
questions the validity o f the notion that any

34lbid., pp.7-8.
35Taylor (1983) shows that even if overlapping wage con­
tracts temporarily fix nominal wages, a policy that gradual­
ly reduces inflation can be relatively costless provided that
expectations about future inflation are rationally formed
and everyone believes that the policy will actually be im­
plemented. See Cukierman (1986) and references cited
therein for analyses of the institutional and economic fac-


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positive inflation could be desirable as a longrun phenomenon. The surprisingly large num­
ber of distortionary effects resulting from infla­
tion weakens the possible justifications for sus­
tained positive inflation.
The long-run desirability of zero inflation
need not imply, however, that a positive rate of
inflation is never acceptable for any period. The
transitional costs of reducing inflation over a
short period could be considerably large relative
to the benefits o f quickly eradicating inflation.
But the costs of fighting the current inflation do
not preclude the desirability o f an anti-inflationary policy, either. Indeed, the steady reduction
in monetary aggregate growth since 1987 (mea­
sured by M l, M2 or the adjusted monetary
base) suggests that the trade-off has been faced,
at least implicitly. In any case, the acceptability
of an inflation in excess o f the long-run desir­
able rate depends on the appropriately
measured net benefits of alternative paths to
achieve the ultimate inflation goal.

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15

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JULY/AUGUST 1989

16

R . W. H a fe r
R. V Hafer is a research officer at the Federal Reserve Bank
J.
of St. Louis. Kevin L. Kiiesen provided research assistance.

Does Dollar Depreciation
Cause Inflation?

1 — R IN G the past few years, the rate o f in^U
flation has risen from 1.1 percent in 1986,
measured by the consumer price index, to 4.4
percent in 1988. Though this rate of price in­
crease pales in comparison to the double-digit
inflation of the mid-1970s and early 1980s, it is
high enough to cause concern among economic
analysts, financial market participants and
policymakers. Among the various explanations
for the recent acceleration in inflation is the
decline in the foreign exchange value of the
dollar since 1985.1 According to this view, the
decline in the value of the dollar raises the
dollar price of imported goods and, therefore,
the prices paid by U.S. citizens as well. The con­
sequence is inflation. Or is it?
The purpose of this article is to provide a
framework in which to evaluate the claim that
a decline in the dollar’s foreign exchange value
raises the rate of inflation in the United States.

TFor example, John Paulus, chief economist for Morgan
Stanley & Company, recently is quoted as saying that “ the
weak dollar is finally showing up as an inflation factor.”
(Uchitelle, 1989a) Lawrence (1989) attributes to two wellknown economists the idea that without reducing the
federal budget deficit and, therefore, the trade deficit, “ a
cheaper dollar would only bring higher U.S. inflation.”
Also, Boyd (1989) argues that “ [w]hat the Fed thinks about
the dollar feeds into its fight against inflation. . . .”
The behavior of the dollar also affects monetary policy
discussions. For example, as stated in the Record of the


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THE RELATIONSHIP BETWEEN
THE EXCHANGE RATE AND
INFLATION
What is the foreign exchange rate? Simply
put, the price o f a unit of one currency in
terms of another. W hy would one want to pur­
chase another currency? There are several
reasons. One is the need of foreign currency to
purchase foreign goods. Another is the need of
foreign currency to trade in other countries’
financial assets. Purchases of financial assets,
like stocks or bonds, in another country can
only be completed if one exchanges dollars for
the foreign currency.
The dollar’s foreign exchange value, common­
ly measured against a weighted average of
foreign currencies, has varied considerably
since 1973. To illustrate this, figure 1 plots the

Federal Open Market Committee’s December 15-16, 1987,
meeting, “ [t]he members recognized that the performance
of the dollar in foreign exchange markets might have a
key bearing on policy implementation in this period. No
member wanted to tie monetary policy exclusively to the
dollar, but some strongly emphasized that further substan­
tial depreciation in the dollar could have highly adverse
repercussions on domestic financial markets and the
economy.” (Federal Reserve Bulletin, 1988). For a related
discussion, see Furlong (1989).

17

Figure 1
Trade-Weighted Exchange Rate and Inflation Rates
Percent
25

Index (March 1973 = 100)
150

Annual Data

-1 0

1973

74

85

86

87

80
1988

Federal Reserve's trade-weighted exchange rate
index (March 1973 = 100), which calculates the
change in the value of the dollar against the
currencies of 10 industrial countries.2 As one
can see, during the past 25 years the index has
ranged from 87.4 in 1980 to a high of 143 in
1985. The 1980s have been characterized by
two large swings: an appreciation of about 64
percent between 1980 and 1985, and a depreci­
ation of about 35 percent since 1985. It is this
recent downswing in the exchange rate that has
sounded an inflationary alarm among some
analysts.

tion: the Consumer Price Index (CPI), the Pro­
ducer Price Index (PPI) and the GNP deflator.
These three differ in that they measure price
changes at different levels of aggregation (the
GNP deflator being the broadest measure) and
for different baskets of goods and services.
While some differences in measured rates of in­
flation during certain periods are noticeable,
they typically follow the same general pattern.
The simple correlations between the different
inflation measures, as table 1 reports, range
from 0.64 for the PPI-GNP deflator to 0.81 for
the CPI-PPI over the full period.3

One reason that the recent dollar decline has
aroused inflation fears stems from the casual
observation that the exchange rate and domestic
inflation tend to move in opposite directions. To
illustrate this negative correlation, figure 1 in­
cludes three commonly used measures of infla­

More important to the current discussion is
the fact that these inflation measures typically
fall when the exchange rate is rising and rise
when the exchange rate is falling. As table 1
reports, the correlation between the exchange
rate and CPI inflation is -0.55; between the ex-

2The 10 countries are Belgium, Canada, France, Germany,
Italy, Japan, the Netherlands, Sweden, Switzerland and
the United States.




3The correlations are based on quarterly data.

JULY/AUGUST 1989

18

Table 1
Correlation Coefficients Between
Inflation Measures and the Exchange
Rate
Pairing
CPI-DEF
CPI-PPI
PPI-DEF

1973-88

Pairing

1973-88

0.81
0.73
0.64

TWEX-CPI
TWEX-PPI
TWEX-DEF

-0 .5 5
-0 .5 0
-0 .5 8

NOTE: CPI denotes Consumer Price Index; PPI the Pro­
ducer Price Index; DEF the GNP deflator; and
TWEX is the Federal Reserve’s trade-weighted ex­
change rate index. The correlation coefficients are
all different from zero at the 5 percent significance
level.

change rate and PPI inflation, it is -0.50; be­
tween the exchange rate and inflation using the
GNP deflator, it is -0.58. These negative and
statistically significant correlations demonstrate
that reductions in the exchange value of the
dollar—the depreciation of the dollar—are
associated with increases in domestic inflation.

W H Y SHOULD DEPRECIATION
RAISE THE INFLATION RATE?
When the dollar depreciates relative to other
currencies, the dollar prices of foreign goods in­
crease relative to domestically produced goods,
other things equal, making imports more expen­
sive. Since imports make up part of the basket
of goods purchased by consumers, measures of
inflation based on that basket also will rise.

Measuring the Direct Effect
It often is argued that foreign exporters, fac­
ing higher dollar prices for their goods sold in

4This approach has been used often. See, among others,
Solomon (1985) or Blinder (1979). It may be argued that
the personal consumption expenditure (PCE) deflator is
the appropriate measure to use in this calculation. We use
the CPI because it is more widely recognized and discuss­
ed. Moreover, since the correlation between the CPI and
PCE measures of inflation is over 0.90 for the 1973-88
period, there is no loss of generality by using one measure
or the other. The data used extend through the third
quarter of 1988 because of availability.


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the United States, will simply pass on some or
all of the depreciation-induced price increase to
their U.S. customers. This is referred to as the
"pass through” effect. To get a rough idea of
how much a change in the exchange rate can
directly impact inflation, the percentage of total
consumer expenditures accounted for by im­
ports can be used to derive a crude measure of
the direct effect of a change in the dollar's
value on the domestic inflation rate.4 This effect
is measured as the product of the percentage
change in the exchange rate and the ratio of ex­
penditures on imported consumer goods to total
personal consumption expenditures. The impact
on inflation can then be found by subtracting
this direct effect from the reported rate of
inflation.
To better understand this calculation, consider
1986, when the dollar depreciated 21.7 percent
against a basket o f other currencies. Since im­
ported consumer goods were 6.3 percent of
total expenditures that year, the product of the
two, -1.4 percent, is a rough measure of the
direct effect of the dollar's depreciation on infla­
tion. Using this approach, if the dollar had not
depreciated by almost 22 percent, inflation
(measured using the CPI) would have been
closer to zero percent than the reported value
of 1.9 percent. In other words, the falling value
of the dollar accounted for much o f the ob­
served inflation.
To illustrate how much of a direct impact
movements in the dollar may have had on
domestic inflation over time, figure 2 plots the
effect on domestic inflation from a change in
the exchange rate. As the figure shows, during
periods when the exchange rate is rising, such
as 1980-85, inflation is lower than it would have
been in the absence of the dollar’s appreciation.
During the recent fall in the value of the dollar,
the effect has turned positive, pushing inflation
higher than it otherwise would have been.5

5One aspect of figure 2 that deserves mention is the fact
that, after the exchange rate has fallen to a new level, the
direct effect on domestic inflation diminishes. In other
words, once the foreign exchange value of the dollar has
stopped falling, the direct effect on domestic inflation
tends toward zero. This shows that exchange rate changes
do not impart a permanent effect on the inflation rate, but
cause only temporary changes.

19

Figure 2
Direct Exchange Rate Effect on Domestic Inflation

1973

74

75

76

77

78

79

80

Foreign Exporters as “PriceTakers”
There is another channel through which a fall
in the dollar can affect the prices of U.S. im­
ports and, hence, the domestic inflation rate.
Consider a foreign manufacturer who exports
to the United States. If we assume that the
manufacturer is a price-taker in the U.S. mar­
ket—that is, the individual producer does not in­
fluence the market price of the good—the deci­
sion on how much to produce and export to the
United States will be determined by the given
price and the cost of production.6 As the upper
panel of figure 3 shows, this representative
manufacturer has the usual upward-sloping
marginal cost curve. Since he is a price-taker in

6For a recent analysis of this, see Knetter (1989). His
evidence, based on industry analysis, suggests that exporters to the United States perceive U.S. prices as given.
Based on his study, Knetter notes that “ [t]he variation in




81

82

83

84

85

86

87

1988

the U.S. market, the price in terms of the
manufacturer’s home currency is set at P0.
Given the position of the marginal cost curve,
the quantity produced is given by the intersec­
tion of price and marginal cost, or at Q0.
Now assume that the foreign exchange value
of the dollar falls. This means that, other things
equal, the U.S. price received by the manufac­
turer in term s o f his ow n cu rren cy falls to P,. If
the manufacturer’s costs of production have not
changed, this fall in price means that the quan­
tity produced for the U.S. market falls to Q1
;
where marginal cost is equal to the new price.
The dollar’s depreciation thus has reduced the
supply of goods sent by this representative
foreign manufacturer to the United States.

the results across industries suggests that the link between currency values and domestic price levels is
tenuous at best.” (p. 209)

JULY/AUGUST 1989

20

Figure 3
Price and Quantity Effects of a Decline
in Dollar

Qi

The effect of this reduction in imported goods
is shown in the lower panel of figure 3. Here
the supply and demand curves for the U.S.
market in which the foreign manufacturer sells
is shown. The market supply curve drawn is

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Qq

q

the sum of domestic and foreign producers’ in­
dividual supply curves. Other things the same, a
reduction in the amount exported to the U.S.
market results in a leftward shift in the supply
curve. The effect on U.S. prices? Given the de­

21

mand for the good, the price paid by U.S.
residents increases from P0 to P,. In other
words, a depreciation o f the dollar increases the
prices paid by U.S. residents for this good. Such
an increase will result in a higher price level
and, hence, at least a temporary increase in the
rate of inflation.

Estimating the Total Effect
One problem with the preceding approach is
that it relies solely on the direct effects of the
dollar’s depreciation. An increase in the price of
some imported goods, such as those used in the
manufacturing process, also may lead to in­
direct increases in the prices of domestically
produced goods. Consequently, measuring only
the direct effect may underestimate the total ef­
fect of a depreciation in the dollar on the
domestic inflation. W e will return to this sub­
ject later in the paper.

W H Y DOESN’T DOLLAR
DEPRECIATION CAUSE
INFLATION?
The discussion thus far suggests that there is
a direct relationship between a depreciation in
the dollar and higher domestic inflation. Thus,
if the prices of imports rise because of a fall in
the value of the dollar, it is just arithmetic to
show that U.S. inflation must increase. Unfor­
tunately, while the simplicity of such a view is
seductive, it is not correct. The reasons why are
discussed in the remainder of this article.

What Causes the Exchange Rate to
Change?
An observed exchange rate is determined by
the demand for and the supply of a currency in
international exchange. Movements in the ex­
change rate reflect relative economic conditions
between countries that, in turn, influence the
demand and supply o f the currencies. More­
over, because exchange rates are forwardlooking, their adjustments reflect changes in ex-

pectations about future economic conditions.
Consequently, it may be incorrect to impart a
causal role to exchange rate movements in ex­
plaining domestic economic activity when the
exchange rate merely reflects the underlying
economic conditions, actual and expected, in dif­
ferent countries.
Over long periods o f time, one key factor that
influences the level of the exchange rate be­
tween two countries is their relative price
levels. When one price level changes, the ex­
change rate will adjust accordingly to equate
prices.7 This notion, referred to as purchasing
power parity, means that similar bundles of
goods have a common price across international
boundaries. If prices increase in only one coun­
try, the exchange rate between that country’s
currency and all other currencies will fall,
ceteris p aribu s. Since in the absence of exchange
rate changes the same basket o f goods can be
purchased elsewhere for a lower price, the de­
mand for the country’s goods and for its cur­
rency declines.8 In unfettered foreign exchange
markets, changes in the exchange rate may
simply reflect changes in the countries’ price
levels.9
Exchange rate movements also may reflect dif­
ferences in countries' economic activity. Because
increased demand for imported goods is often
associated with an increased level of economic
activity, those countries experiencing faster
growth may also find that their currency is
depreciating in foreign exchange markets. Recall
that one use o f foreign currency is to purchase
foreign goods and services. If the United States
is growing faster than other countries, and its
demand for imports is likewise increasing, then
the demand by U.S. residents for foreign cur­
rency also is increasing. Consequently, there is
relatively more demand for other currencies
and their value appreciates relative to the
dollar. Thus, movements in the exchange rate
also may reflect differences in the relative
economic conditions of two countries.

7The exchange rate can be defined as the ratio of dollar
prices to prices measured in some foreign currency unit. If
the foreign price rises and the U.S. price remains cons­
tant, the exchange rate will fall.

States changes, demand will shift to U.S. pencil manufac­
turers. This lowers the demand for Japanese pencils and,
other things the same, causes the yen-dollar exchange
rate to depreciate.

8To illustrate, suppose that pencils with identical
characteristics sell for 75 cents in the United States and
93 yen each in Japan. This implies that the exchange rate
is about 124 yen per dollar. If the price of pencils in Japan
should rise to 150 yen, the dollar-equivalent price of pen­
cils in Japan is now $1.21. Unless the price in the United

9To abstract from price level changes, real exchange rates
often are used. The real exchange rate is defined as the
nominal exchange rate times the ratio of the two price
levels, or er = e"(P/P'). Note that for this measure, if the
nominal exchange rate (e") and the foreign price level (P')
double, the real exchange rate will remain unchanged.




JULY/AUGUST 1989

22

Movements in the exchange rate also reflect
differences in interest rates across countries, a
channel of influence thought to be most impor­
tant in explaining exchange rate movements
over short time spans. For example, suppose
that from an initial point of equality, interest
rates on identical financial instruments, say
bonds, in the United Kingdom rise 5 percent
while those in the United States are unchanged.
Other things the same, investors prefer the U.K.
bond’s rate of return to the U.S. bond. Pounds,
therefore, will be in increased demand in order
to purchase the U.K. bond, and the result is a
depreciation o f the dollar relative to the pound.
This discussion points out that movements of
the exchange rate can reflect changes in either
key economic factors between two countries or
people’s expectations. In a very direct way,
these factors are related to changes in money
growth and the process by which such changes
are transmitted to the economy. For example,
consider the effects of an increase in the
growth o f the money supply. If we assume that
prices react somewhat slowly at first to this
change, the brunt of the faster money growth
will be evidenced in faster economic growth
and in lower nominal interest rates. As noted
earlier, faster economic growth in the United
States relative to other countries leads to a fall
in the value of the dollar. The decline in in­
terest rates here relative to abroad also reduces
the relative demand for dollar-denominated
financial assets and, hence, the dollar’s value
falls.
But, as economic theory predicts and much
emprical research shows, an increase in the
growth rate o f the money supply ultimately
leads to an increase in the inflation rate. This
movement to a higher rate of inflation reflects
the increase in money growth, but also will oc­
cur at the same time that the dollar’s value is
falling in foreign exchange markets. In other
words, the decline in the value of the dollar and
the increase in inflation are both manifestations
of the same thing, namely, the increase in the
growth rate of the money stock. Hence, it is in­
correct to assign exchange rate changes an in­
dependent role in determining permanent
changes in inflation once the effects of changes
in money growth have been taken into account.

10We use 1973 since it marks the beginning of the flexible
exchange rate period. Also, March is the base period (i.e.,
= 100) for all exchange rates listed.


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H on Is the Exchange Rate
Measured?
There are numerous exchange rate measures.
As mentioned earlier, the one most often used
in discussions of this issue is the Federal
Reserve Board’s trade-weighted exchange rate
(TWEX). In calculating the change in the dollar’s
value against other industrial countries, the
weight given each country in the index is the
1972-76 average world trade o f that country
divided by the average world trade of all coun­
tries combined. In this way, relatively large
movements in the exchange rate between the
United States and any one country are weighted
by the size of the other country. Exchange rates
also can be measured bilaterally, that is, the ex­
change rate between two countries only.
The fact that the exchange rate can be
measured in different ways gives rise to dif­
ferent perspectives on exchange rate behavior.
For example, consider figure 4, where the
trade-weighted exchange rate and the bilateral
exchange rates between the United States and
three countries—Canada, Germany and Japan—
are plotted for the period 1973 through 1988.1
0
The TWEX declines from 1976 until 1980, when
it begins to rise sharply. The appreciation o f the
dollar between 1980 and 1985 using this broad
measure is 64 percent. Since 1985, however, the
value of the dollar using the TWEX has declined
about 35 percent.
How have bilateral exchange rates behaved
relative to this overall exchange rate measure?
The U.S.-Canadian exchange rate started ap­
preciating in 1976, four years before the
general upward movement in TWEX. Moreover,
it has declined only since 1986. In percentage
terms, the U.S. dollar was about 17 percent
higher in 1985 than it was in 1980 against the
Canadian dollar and has declined about 10 per­
cent since then. These figures are much dif­
ferent from the measurement using the overall
index.
The behavior of the U.S.-Germany and U.S.Japan exchange rates also differs from the
overall measure. During the first half of the
1980s, the dollar appreciated 62 percent against
the German mark, but only 5 percent against
the Japanese yen. Since 1985, the dollar has

23

Figure 4
Trade-Weighted and Bilateral Exchange Rates
Index (March 1973 = 100)
150,

Index (March 1973 = 100)
150

Annual Data

TWEX

Canada

1973

74

75

76

77

78

79

80

depreciated 40 percent against the mark and 46
percent against the yen. Thus, movements in
the foreign exchange value of the dollar clearly
differ among countries.1
1
Since it is the changes in bilateral exchange
rates that influence the prices o f exports in
those countries, how are changes in the bilat­
eral exchange rates related to domestic U.S. in­
flation? Table 2 reports the correlations be­
tween the exchange rates used in figure 4 and
the three measures of inflation. The results
show that the correlations between U.S. infla­
tion and the U.S.-Canadian exchange rate are
similar to those found using the TWEX; for the
U.S.-Germany exchange rate, they are much
smaller. The Japanese result, however, is
somewhat puzzling: it shows a positive relation­

"T h is is the premise upon which broader exchange rate indexes are often constructed. For a discussion and comparison of alternative measures, see, among others,




81

82

83

84

85

86

87

1988

ship, suggesting that a depreciation in the dollar
relative to the yen is associated with a decline
in inflation. The message from this comparison
is that focusing on the TWEX-inflation connec­
tion may obscure bilateral relationships that in­
fluence import prices paid by U.S. residents.

Is It Really Inflation?
Suppose that the value of the dollar declines
and the dollar price o f imported goods subse­
quently increases. W ill this lead to inflation? To
answer this question, it is necessary to define
carefully what is meant by the term "inflation.”
A pragmatic definition o f inflation is a persistent
increase in the general level of prices o f goods
and services. There are two key aspects to this
definition. First, virtually all prices, not simply

Belongia (1986), Cox (1986), Rosenweig (1986) and Ott
(1987).

24

Table 2
Correlation Coefficients Between Inflation Measures and
Exchange Rates: 1973-88____________________________
Exchange rate
Inflation measure
CPI
PPI
DEF

TWEX

Canada

Germany

Japan

-0 .5 5
-0 .5 0
-0 .5 8

- 0 .4 6
-0 .5 6
-0 .6 2

- 0 .2 4
-0 .1 2
-0 .1 4

0.30
0.25
0.38

one or two, have increased. Second, inflation
defines price increases that persist over an ex­
tended period o f time; it is not simply a onceand-for-all increase in the price level. A persis­
tent increase in the price level occurs only
when aggregate demand continues to grow
faster than aggregate supply. Given considerable
evidence showing that the main determinant of
aggregate demand growth over time is the
growth o f the money supply, it is widely agreed
that inflation is a monetary phenomenon.1
2
This definition o f inflation is intended to be
restrictive for a very good reason. If “inflation”
is used to describe situations in which the price
of only one good or a small set of goods in­
creases, for example, import prices, the result
will be a confusion between general inflation
and relative price changes.
To see this, consider the fact that observed
rates of inflation are measured as changes in an
index of various prices. The price indexes used
to measure inflation, such as the CPI or PPI, are
a weighted average of prices covering a wide
variety of goods and services. From one month
to the next, some prices in the index inevitably
will be rising while others will be falling.
Because these price movements are weighted
differently in the index, inflation measured as
the percentage change in the index may reflect
12The quantity theory equation written in logarithmic growth
rate form is
M + V = P + Q ,
where M is the money stock, V is velocity, P is the price
level and Q is the level of output. The dots above each let­
ter denotes rate of change. According to this theory,
because velocity and output are determined independently
of money growth in the long run, there is a one-for-one
relationship between changes in the growth rate of money


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nothing more than relative changes in certain
individual prices that are weighted more heavily
than others. This clearly is a different kind of
"inflation” than the definition used above.
Recent discussions of the inflationary effect of
the dollar’s declining value are subject to this in­
valid line of reasoning. They confuse the tran­
sitory nature o f a relative price shift with infla­
tion and do not explain a persistent increase in
the general level of prices.

Is “Pass-Through” Simply “CostPush?”
Another way o f interpreting the notion o f the
pass-through is in terms of so-called cost-push
explanations of inflation.1 According to this
3
view, which focuses on the input costs o f pro­
ducing a product, if one of the input prices
rises, then the price of the good must also.
Hence, if depreciation of the dollar raises im­
ported goods prices (in dollars), then prices on
items produced with those goods also must rise.
Since goods and services are more expensive,
labor will demand higher wages which, being
another cost of production, feeds into even
higher prices. In this way, a fall in the value of
the dollar, some argue, could start a process of
and changes in the rate of inflation. For recent evidence
on this relationship using a sample of 62 countries, see
Dwyer and Hafer (1988).
13For a discussion of cost-push theories of inflation, see Bat­
ten (1981).

25

cost-push inflation, with wages and prices
spiraling upward.1
4
The notion of cost-push inflation stemming
from a depreciating dollar has little economic
foundation. Suppose that a rise in import prices
increases the measured rate of inflation and
leads consumers to re-evaluate their current
money holdings. With an increase in the
measured price level, individuals will desire to
increase their nominal money holdings to main­
tain current purchasing patterns. If the money
supply is not increased, the increased demand
for money will not be accommodated. As a con­
sequence, the demand for goods and services,
both domestic and imported, will fall, reducing
the upward price pressures and returning the
rate of inflation to that determined by the
relative growth of money supply and demand.1
5
Thus, the view that an increase in one price
(imports) causes inflation again confuses a
relative price change with a persistent increase
in the general price level.
The extent to which this higher dollar cost is
passed through to imported goods that compete
directly with domestically produced goods
depends on economic circumstances.1 For ex­
6
ample, recently it has been noted that the fall­
ing value of the dollar since 1985 has not led to
the price increases for imported goods many
thought would occur.1 One reason often cited
7
is that foreign competitors relinquished profit
margins for market share built up during the
1980-85 appreciation of the dollar. In other
words, importers held dollar prices of their
goods to levels competitive with U.S.-produced
goods to hold their share of the U.S. market.

14The notion of a wage-price spiral often is found in popular
discussions. For example, Uchitelle (1989a), p. 1, states
that “ [inflationary spirals, however, cannot last long . . .
unless they are fed by widespread wage increases that
keep forcing up prices.” Passell (1989) also has suggested
that, on the basis of the nearly 12 percent PPI inflation
rate in January 1989, “ economists are shaken by the first
signs of self-perpetuating cost push inflation.” (italics
added)
15For evidence that exchange rate movements have little ef­
fect on domestic prices once money supply and demand
factors are accounted for, see Darby (1981).
16See, among others, Pigott and Reinhart (1985) for a
discussion of this issue.
17For example, see Hooper and Mann (1987).
18This estimate was attributed to Catherine Mann, an
economist at the World Bank, in Uchitelle (1989b).

An interesting aspect of this argument is that
it has been used to explain both the relatively
small impact of the dollar's appreciation on
domestic inflation during the 1980-85 period, as
well as the relatively small impact on domestic
inflation of the dollar's fall since then. This sug­
gests that the pass-through is not a reliable in­
dicator of domestic price pressures stemming
from exchange rate movements. Indeed, it
recently has been estimated that less than onehalf of one percentage point of the 4.4 percent
rise in the CPI during 1988 is attributable to the
pass-through from a falling dollar.1
8

What A bou t Substitution Effects?
The cost-push view of the depreciating dollar's
effect on domestic inflation also assumes that
consumers do not reduce their purchases of the
more expensive imported goods. Economic
theory (and common sense) predicts, however,
that they will buy more of the less-expensive,
domestically produced items.1 To examine
9
whether there is a substitution effect at work,
the percentage o f total personal consumption
expenditures spent on consumer imports was
calculated.2 This ratio is useful, because it
0
allows us to determine whether consumers alter
their consumption patterns of imports vs.
domestic goods in the face of a change in the
exchange rate.
In figure 5, we plot the ratio of consumer im­
ports to total personal consumption expen­
ditures along with the TWEX since 1973.2 As
1
one would expect, periods of an appreciating

changes in an exchange rate index like the TWEX, the
substitution may be between domestically produced goods
as well as between competing imported goods.
20For the purposes of this calculation, we follow Blinder
(1979) and consider the following to be consumer imports:
food, feed and beverages; passenger cars; other con­
sumer merchandise; travel; passenger fares; and private
payment for other services. Note that this measure pro­
bably overstates consumer spending. For example,
passenger fares do not differentiate between pleasure
travel and business travel—one the expense of con­
sumers, the other of businesses. Also, the component,
passenger cars, does not differentiate between business
and private use. The source is Survey of Current Business,
various issues. Values for 1988 are preliminary estimates.
2 Nominal values of the measures are used since we use
1
the nominal TWEX measure.

19Since the evidence presented earlier shows that bilateral
exchange rate movements may be quite different from




JULY/AUGUST 1989

26

Figure 5
Trade-Weighted Exchange Rate and Consumer Imports
as a Percent of Total Expenditures
Percent
7 .0 1
------

Index (March 1973 = 100)
150

Annual Data

TWEX

1973

74

75

76

77

78

79

80

dollar are associated with an increase in the
ratio o f consumer imports to total expenditures.
Since a rising dollar may mean lower imported
prices, consumers would be expected to pur­
chase larger amounts of imports relative to
domestic goods and services. Note that the ad­
justment of consumer expenditures does not oc­
cur simultaneously with exchange rate changes.
From figure 5, it appears that the adjustment in
consumer expenditures is delayed about two
years after the exchange rate changes course.2
2
The figure also shows that the recently falling
dollar is associated with a decline in the ratio of
imported consumer goods to total expenditures.
Since the relative price of imported goods has
been rising since 1985, along with the fall in the
dollar, the response by consumers—shifting
away from imported goods to domestic goods—
is precisely what economic theory predicts.

Z2This reflects the so-called J-curve phenomenon. See
Meade (1988) for a discussion.



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81

82

83

84

85

86

87

1988

Moreover, the percentage of consumer imports
to total personal consumption expenditures ac­
tually is quite small. On average, consumer im­
ports have accounted for only about 5 percent
of total personal consumption expenditures
since 1973, reaching a maximum value of about
6.6 percent in 1987. This evidence suggests that
the role of dollar depreciation in initiating an in­
flationary spiral is dubious.

EMPIRICAL EVIDENCE
To measure the complete effect of a change
in the exchange rate on domestic prices, one
strategy is to view the domestic price level as a
function of wages, demand pressures and im­
port prices.2 In such models, changes in the ex­
3
change rate affect domestic prices through their
effect on import prices. Hooper and Lowery

23Such price equations are oftentimes referred to as costmarkup models.

27

(1979) report that the various models they ex­
amined indicate that a 10 percent depreciation
in the dollar, other things constant, produces a
long-run increase in consumer prices on the
order of 0.8 percent to 1.5 percent.
Another approach used by Whitt, Koch and
Rosenweig (1986) is to regress the domestic
price level on its own lagged values along with
contemporaneous and lagged values of the ex­
change rate.2 Based on this approach, the
4
authors find that a 10 percent depreciation of
the dollar produces a 1.6 percent increase in
the price level after one year and a 4.6 percent
increase after four years.
Other studies have attempted to capture the
effects of a depreciation by developing struc­
tural models of the economy and gauge the ef­
fects of a dollar depreciation as it works
through various channels, such as labor costs,
input prices and economic activity. Hooper and
Lowery (1979) also compare such models and
find that a 10 percent dollar depreciation on
average produces a 0.8 percent to 2.7 percent
increase in consumer prices. Sachs (1985)
estimates several versions of such a model, fin­
ding that a 10 percent depreciation leads to a
0.42 percent to 1.27 percent increase in the
price level in the first year, and by the third
year, a 1.67 percent to 2.56 percent increase.
Compared with the direct effect approach used
earlier, the results from these other procedures
indicate that the inflationary effects of a dollar
depreciation may persist for several years once
the indirect effects are accounted for.
Some researchers have questioned the em­
pirical effects of a dollar depreciation found in
the preceding studies. For example, W oo (1984)
argues that much of the inflation effect at­
tributed to exchange rate movements really
reflects oil price increases. These price shocks,
which produce sizable but transitory increases
in the inflation rate, follow periods of dollar
depreciation. In contrast to the other findings,
Woo estimates that, once oil price shocks are
accounted for, a 10 percent depreciation in the
24They also estimate an equation that regresses the ex­
change rate on its own lag values and those of the price
level. These results indicate that the price level does not
help explain movements in the exchange rate.
25The following criticisms also are found in Bilson (1979).
26For example, expansionary monetary policy in one country
may lead to an immediate response in foreign exchange
markets as these agents’ expectations for future inflation
differentials have been altered. The effect on actual infla­
tion differentials, however, may not change for some time.




dollar produces a mere 0.02 percent increase in
the price level in the first year, with no longerterm effects. Classman (1985) also argues that
exchange-rate effects on changes in the price
level are overstated because of the high correla­
tion between exchange rate movements and oil
price shocks. Like Woo, he finds that changes
in the foreign exchange value of the dollar have
no appreciable effect on U.S. inflation after oil
price effects are considered.
There also are several general criticisms about
relating changes in domestic prices to exchange
rate movements.2 The exchange rate often is
5
regarded as an exogenous variable. As noted
earlier, however, movements in the exchange
rate reflect relative economic conditions be­
tween different economies. Moreover, since
economic theory suggests that exchange rates
are forward-looking, reflecting market expecta­
tions, a finding that exchange rate movements
appear to statistically "cause” inflation is merely
an indication that they respond faster to
changes in the relative economic conditions
than do observed price levels.2
6
Another criticism is that the dynamic ad­
justments that may occur when the relative
prices of imports rise are sometimes ignored.2
7
Other things the same, unless the domestic
monetary authority accommodates the relative
price increase by expanding the money supply,
desired expenditures on both imported and
domestic goods must fall, offsetting any long­
term effect of a dollar depreciation on domestic
inflation.
Finally, so-called cost-markup models, while
relevant in explaining the transitory movements
in inflation, are not useful for explaining the
underlying determinants of persistent changes
in the price level. In a study of the effects of
exchange rate changes on domestic inflation, it
has been demonstrated that, once the influence
of domestic money growth is accounted for,
changes in the effective exchange rate provide
no additional explanatory power.2
8
27This point also is raised by Darby (1981).
28See Batten and Hafer (1986). This result holds for the
GNP deflator. They also report that, when the PPI is used,
there is a statistically significant effect. This result is not
surprising, however, given the large tradeable-goods com­
ponent in the PPI index relative to the GNP deflator.

JULY/AUGUST 1989

28

CONCLUSION
Does a falling foreign exchange value of the
dollar mean higher U.S. inflation? Some com­
mentators would argue in the affirmative. The
analysis in this paper, however, indicates that
this view is o ff the mark. Inflation is a persis­
tent increase in the general level of prices. This
definition provides a consistent framework in
which to distinguish inflationary trends from
transitory relative price shocks. While a
depreciating dollar may cause an increase in the
dollar price of some imported goods and ser­
vices, these relative price increases are not in­
flationary nor do they promote an upward
spiral of wages and prices in the future.

REFERENCES
Batten, Dallas S. "Inflation: The Cost-Push Myth,” this
Review (June/July 1981), pp. 20-26.
Batten, Dallas S., and R. W. Hafer. “ The Impact of Interna­
tional Factors on U.S. Inflation: An Empirical Test of the
Currency Substitution Hypothesis,” Southern Economic
Journal (October 1986), pp. 400-12.

Furlong, Frederick T. “ International Dimensions of U.S.
Economic Policy in the 1980s,” Federal Reserve Bank of
San Francisco Economic Review (Spring 1989), pp. 3-16.
Glassman, James E. “ The Influence of Exchange Rate
Movements on Inflation in the United States,” Working
Paper No. 46, Federal Reserve Board of Governors (April
1985).
Hooper, Peter, and Barbara R. Lowery. “ Impact of the Dollar
Depreciation on the U.S. Price Level: An Analytical Survey
of Empirical Estimates,” Staff Study 103, Board of Gover­
nors of the Federal Reserve System (April 1979).
Hooper, Peter, and Catherine L. Mann. “ The U.S. External
Deficit: Its Causes and Persistence,” Federal Reserve
Board of Governors, International Finance Discussion
Paper No. 316 (November 1987).
Knetter, Michael M. “ Price Discrimination by U.S. and Ger­
man Exporters,” American Economic Review (March 1989),
pp. 198-210.
Lawrence, Richard. “A Balanced Budget Might Halve the
U.S. Trade Deficit,” New York Journal of Commerce,
February 10, 1989.
Meade, Ellen E. “ Exchange Rates, Adjustment, and the
J-Curve,” Federal Reserve Bulletin (October 1988), pp.
633-44.
Ott, Mack. “ The Dollar’s Effective Exchange Rate: Assessing
the Impact of Alternative Weighting Schemes,” this Review
(February 1987), pp. 5-14.

Belongia, Michael T. “ Estimating Exchange Rate Effects on
Exports: A Cautionary Note,” this Review (January 1986),
pp. 5-16.

Passell, Peter. “ Inflation is Looking Like It’s Going to Cost,”
New York Times, March 5, 1989.

Bilson, John F. O. “ The ‘Vicious Circle' Hypothesis” IMF
Staff Papers (March 1979), pp. 1-37.

Pigott, Charles, and Vincent Reinhart. “ The Strong Dollar
and U.S. Inflation,” Federal Reserve Bank of New York
Quarterly Review (Autumn 1985), pp. 23-29.

Blinder, Alan S. Economic Policy and the Great Stagflation
(Academic Press, 1979).
_______ . “ The Consumer Price Index and the Measurement
of Recent Inflation,” Brookings Papers on Economic Activity
(2: 1980), pp. 539-65.
Boyd, John. “ Economic Beat,” New York Journal of Com­
merce, February 24, 1989.
Cox, W. Michael. “A New Alternative Trade-Weighted Dollar
Exchange Rate Index,” Federal Reserve Bank of Dallas
Economic Review (September 1986), pp. 20-28.
Darby, Michael R. “ The International Economy as a Source
of and Restraint on U.S. Inflation,” in William A. Gale, ed.,
Inflation: Causes, Consequents, and Control (Oelgeschlager,
Gunn & Hain, Publishers, Inc., 1981), pp. 115-31.
Dwyer, Gerald P., Jr., and R. W. Hafer. “ Is Money Irrele­
vant?” this Review (May/June 1988), pp. 3-17.

Rosenweig, Jeffrey A. “A New Dollar Index: Capturing a
More Global Perspective,” Federal Reserve Bank of Atlanta
Economic Review (June/July 1986), pp. 12-22.
Sachs, Jeffrey D. “ The Dollar and the Policy Mix: 1985,”
Brookings Papers on Economic Activity (1: 1985), pp. 117-85.
Solomon, Robert. “ Effects of the Strong Dollar,” in The U.S.
Dollar—Recent Developments, Outlook, and Policy Options
(Federal Reserve Bank of Kansas City, 1985), pp. 65-88.
Uchitelle, Louis. “ Dollar Weakness a Crucial Factor in Infla­
tion’s Rise,” New York Times, March 1, 1989a.
_______ . “A Shaky Lid on an Inflation Threat,” New
York Times, March 12, 1989b.

Federal Reserve Bulletin, “ Record of FOMC Minutes” (April
1988), p. 239.

Whitt, Joseph A., Jr., Paul D. Koch, and Jeffrey A.
Rosenweig. “ The Dollar and Prices: An Empirical
Analysis,” Federal Reserve Bank of Atlanta Economic
Review (October 1986), pp. 4-18.

Fischer, Stanley. “ Relative Shocks, Relative Price Variability,
and Inflation,” Brookings Papers on Economic Activity (2:
1981), pp. 381-431.

Woo, Wing T. “ Exchange Rates and the Prices of Nonfood,
Nonfuel Products,” Brookings Papers on Economic Activity
(2: 1984), pp. 511-30.


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29

Cletus C. Coughlin
and Thomas B. Mandelhaum
Cletus C. Coughlin is a senior economist and Thomas B.
Mandelbaum is an economist at the Federal Reserve Bank of
St. Louis. Thomas A. Pollmann provided research assistance.

Have Federal Spending and
Taxation Contributed to the
Divergence of State Per Capita
Incomes in the 1980s?

ROM THE EARLY 1930s through the late
1970s, per capita incomes rose faster in lowincome than high-income states, resulting in a
substantial reduction in the inequality of state
per capita income. This trend, however, has
been reversed in the last decade (figure l).1 Per
capita income inequality has risen gradually
since 1978 and, by 1987, had returned to the
levels prevailing in the mid-1960s.2
Historically, the federal government’s fiscal
policies have been linked to regional disparities
'T he measure of income inequality used in this article is
the coefficient of variation of annual state per capita in­
come across the 48 contiguous states. For each year, the
measure indicates the degree of dispersion of state per
capita incomes about the mean state per capita income.
Because we consider the state to be the appropriate unit
of observation, each state is weighted equally in com­
puting the inequality measure. However, Coughlin and
Mandelbaum (1988), p.28, found this unweighted coeffi­
cient of variation to be closely correlated with a populationweighted coefficient of variation, and also closely cor­
related with another commonly used measure of inequality,
the standard deviation of the ratio of regional to national
per capita income.
2Ray and Rittenoure (1987) and the U.S. Department of
Commerce (1988) document the rise of per capita income




in economic growth. During the 1970s, for ex­
ample, it was alleged that federal spending had
been biased in favor of the Sun Belt at the ex­
pense of the Frost Belt, resulting in more rapid
Sun Belt growth and slower Frost Belt growth.3
Given the levels of income in these two regions,
this growth differential reduced income ine­
quality across states. Two recent studies argue,
however, that the distribution of grants-in-aid
and procurement has shifted toward the New
England and mid-Atlantic regions.4 Such redistri
inequality between U.S. Census regions since 1979, while
Coughlin and Mandelbaum (1988) show interstate income
inequality has increased since 1978. Ray and Rittenoure
(1987) concluded that changes in energy prices,
agricultural prices and world trade patterns contributed to
the increasing regional income inequality, while Coughlin
and Mandelbaum (1988) concluded that changes in energy
prices have contributed to the rise in inequality but that
the farm crisis did not.
3See, for example, “ The Second War Between the States
(1977)” and “ Federal Spending: The Northeast’s Loss is
the Sunbelt’s Gain (1976).”
“ See Weinstein and Wigley (1987) and Gross and Weins­
tein (1988).

JULY/AUGUST 1989

30

Figure 1
Inequality of State Per Capita Income
Percent
45

Percent
45

Coefficient of Variation

40

35

30

25

20

15

10

1925

30

35

40

45

50

55

bution could potentially increase income in­
equality by stimulating growth in relatively
high-income states at the expense of growth in
low-income states.5
Whether the rising inequality of state per
capita income is really due to changes in federal
spending and taxation is an unsettled issue,
chiefly because there has been no thorough
analysis of the effects of changes in the
distribution of federal spending and taxation on
state income inequality. In this study, we
demonstrate that while the distribution of
transfer payments and the federal tax burden
alters the degree of inequality, no major
changes in this relationship have occurred in
the 1980s. Next, we describe and analyze the
flow of funds between the states and the
federal government. Changes in the size and

5Fierce competition among states for federally funded pro­
jects, such as the superconducting supercollider, suggests
the importance of federal expenditures to state economies.
Competing states spent millions of dollars preparing site
studies and public relations campaigns to attract the $4.4


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60

65

70

85

1990

distribution of these flows do not appear to
have been a cause of the increasing inequality.

HAVE FEDERAL PERSONAL
TAXES AND TRANSFERS
AFFECTED INEQUALITY?
The income measure used in calculating the
inequality measure (that is, the coefficient of
variation) in figure 1 is total personal income.
Total personal income is the sum of: 1) net ear­
nings which are total earnings less personal
contributions to social insurance, by place of
residence; 2) dividends, interest and rent and 3)
transfer payments, which are primarily Social
Security and Medicare payments. The relative
shares of these categories in terms of total per-

billion facility. Texas, which was awarded the supercollider
in November 1988, offered $1 billion in bonds and services
to persuade the U.S. Department of Energy that it should
be chosen. See “ U.S. Picks Small Town” (1988).

31

sonal income for 1969, 1978 and 1987 are listed
in table 1. The share o f net earnings declined
from 77.4 percent in 1969 to 68.7 percent in
1987. Meanwhile, the shares of both dividends,
interest, and rent and transfer payments
increased.
Table 1 also shows two factors, personal con­
tributions for social insurance and federal per­
sonal taxes, that are used below to adjust total
personal income. Personal contributions for
social insurance are subtracted from total earn­
ings in computing total personal income. As a
percentage of total personal income, these con­
tributions rose from 3.4 percent in 1969 to 4.5
percent in 1987. Federal personal taxes, which
include individual income, estate and gift taxes,
declined from 12.3 percent of total personal in­
come in 1969 to 10.8 percent in 1978, then ex­
hibited little change in the 1980s. They
represented 10.7 percent of total personal in­
come in 1987.
To examine how personal taxes and transfers
relate to the interstate inequality o f per capita
income, we compare the inequality (that is, the
coefficient of variation) of total personal income
with the inequality of income, assuming no
federal taxes and no transfer payments exist.
The latter measure of income, which we call
private income, is derived by subtracting
transfer payments from total personal income
and adding personal contributions for social in­
surance. Thus, private income is the sum of
total earnings and dividends, interest and rent.

Table 1
Income Components and Taxes as a
Percent of U.S. Total Personal Income
1969

1978

1987

Components of total personal
income
Net earnings1

77.4% 73.4% 68.7%

Dividends, interest and rent

13.3

13.0

16.7

9.3

13.6

14.6

3.4

3.8

4.5

12.3

10.8

10.7

Transfer payments
Personal contributions for
social insurance
Federal personal taxes

'W age and salary disbursements, other labor income
and proprietors’ income minus personal contributions
for social insurance.

terstate per capita income inequality is negligi­
ble. Since most contributions for social insur­
ance are proportional to earnings up to some
maximum, this finding is not surprising.

Figure 2 reveals two noteworthy facts about
the inequality of private income. First, its trend,
generally decreasing through the late 1970s and
increasing thereafter, is similar to the trend in
the inequality of total personal income. Second,
its level is consistently higher than the inequali­
ty of total personal income. This suggests that
the combined effect of transfer payments and
personal contributions for social insurance is to
reduce income inequality.

Another factor that has potentially important
implications for inequality is federal personal
taxes. As figure 2 shows, the coefficient of
variation of per capita state income after sub­
tracting federal personal taxes increased at a
rate similar to the other inequality measures
since the late 1970s. The direct impact of
federal taxation can be seen by the consistently
lower level of income inequality after federal
taxes are subtracted. The lack of a major
change in the gap between the inequality
measures before and after taxes suggests that
changes in the distribution of federal personal
taxes in the 1980s have not altered interstate in­
come inequality substantially.

Figure 2 also reveals that nearly all o f the dif­
ference between the inequality o f private in­
come and that of total personal income can be
accounted for by transfer payments. The addi­
tion of transfer payments to private income pro­
duces an inequality measure virtually identical
to the inequality of total personal income. Con­
sequently, the effect of contributions for social
insurance programs (that is, Social Security,
Medicare and unemployment insurance) on in­

In summary, while the interstate distributions
of the federal personal taxes and transfer
payments have consistently reduced income ine­
quality, they have had little effect on the
change in inequality. Contributions for social in­
surance have had no substantial influence on
either the level or the change in interstate in­
come inequality. Thus, the evidence suggests
that the increase in income inequality over the
last 10 years is not due to changes in the




JULY/AUGUST 1989

32

Figure 2
Interstate Inequality of Per Capita Income
Measures
Percent

Coefficient of Variation

211
---------

Percent
21

Private income

Private income
plus transfers
Total
personal income
Total personal income
after federal taxes
11
1960
63
66
69
72
75
78
81
84
1987
NOTE: The figure shows the coefficient of variation for four income measures. Total personal
income is transfer payments, dividends, interest, rent and total earnings minus
social insurance contributions. Private income is total personal income plus social
insurance contributions minus transfer payments. Private income plus transfers is
total personal income plus social insurance contributions. Total personal income
after federal taxes is total personal income minus federal personal taxes.

distribution of transfer payments, social in­
surance contributions or federal personal taxes.6

FEDERAL FLOW OF FUNDS
The preceding analysis focuses on components
of income that, in an accounting sense, can be
either added or subtracted to produce different
income measures. While this analysis is infor­
mative, federal fiscal policy entails numerous
tax and spending programs that preclude a
straightforward accounting analysis and that
may have major income effects at the state
6While the method used in this section suggests the direct
impact that the distribution of transfer payments, social in­
surance contributions and federal personal taxes have on
income inequality, it has limitations. If transfer payment
programs or federal taxes actually were eliminated, shifts
in production, consumption and investment eventually


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level. These include federal corporate income
taxes, excise taxes, federal grants to state and
local governments and procurement contracts.
This section considers the effects of the broader
flows of funds between the federal government
and the various economic actors in states in­
cluding state governments, local governments,
individual residents and corporations.
The flow of federal funds to and from a state
is usually calculated as a ratio of a state's share
of total federal expenditures to its share o f total
payments made to the federal government.7 If
the ratio is greater than unity, the state receives
would take place that might lead to changes in interstate
income inequality unlike those indicated in figure 2.
7
Advisory Commission on Intergovernmental Relations
(1980), Erdevig (1986), and Rymarowicz (1988), for exam­
ple, use this ratio in examining the flow of federal funds to
states.

33

a greater share of the national total than it pays
to the federal government, a condition thought
to stimulate the state’s economy and raise per
capita income. Conversely, a ratio less than one
suggests a drain of state funds that potentially
dampens the state’s economic activity. See the
shaded insert for a more complete explanation
of how the federal funds ratio was calculated,
what expenditures and tax payments are in­
cluded and how the data were estimated.

The Conventional Wisdom:
Econom ic Effects o f Federal Funds
A larger federal funds inflow can stimulate
regional economic growth by augmenting a
region’s productive capacity and by stimulating
technological advances. Federal spending, such
as defense procurement expenditures, may con­
tribute directly to the stock of physical capital.
Federal spending for educational programs may
contribute to the growth o f human capital. The
case for federal spending stimulating technologi­
cal advances is frequently illustrated by examin­
ing defense spending. In California and New
England, generally acknowledged as leading in­
novation centers, defense spending is frequently
said to have induced significant amounts of
commercial innovation.8 The importance of fed­
eral expenditures in adding to the capital stock
and promoting technological advances across
states has not been studied widely, however, so
the final distribution of effects from federal
funds flows, especially on state per capita in­
come, remains uncertain.9
Even though a change in a state’s federal
funds flow has potential effects on its produc­
tive capacity, any discussion of the impact of
the federal funds flow usually focuses on the
8Barff and Knight (1988) argue that increasing federal
military spending starting in the late 1970s precipitated
New England’s economic upturn. Browne (1988) found
that, while defense spending apparently spurred commer­
cial high-tech development in Massachusetts and Califor­
nia, the experience of these states is unique. More
generally, she found that defense spending in a state has
had little effect on commercial innovation and hightechnology development.
9Research on the impact of defense procurement on
regional per capita income has yielded mixed results.
Rees, et al. (1988) p.17, conclude that slower growth rates
of defense procurement in the Sun Belt states compared
with other regions during the 1980s was a causal factor in
that region’s slower per capita income growth. The validity
of this conclusion is questionable, however, because no
controls were made for other influences on regional per
capita income growth. Bolton (1966), p. 14, found a
positive, though weak, relationship between defense spen­
ding and state income growth between 1952 and 1962 but




demand side of a state’s economy. If tax
payments to the federal government were
lower, a state's residents and businesses would
retain more income that could be spent locally
on consumption and investment goods or could
be used to finance state and local government
services. Similarly, the argument is made that
higher federal expenditures in the state would
directly boost state income and employment.1
0
For these reasons, a higher federal flow of
funds ratio for a state is thought to be more
stimulative than a lower one, other things
equal.1 In addition, this measure and its com­
1
ponents (federal expenditures, federal tax pay­
ments) are the only available indicators of the
comprehensive influence of the federal govern­
ment on state economies and continues to be
used by policymakers and researchers in
evaluating how federal spending and taxes af­
fect various states and regions.1
2
The following analysis of the association be­
tween federal fiscal policies and the increasing
divergence of state per capita incomes proceeds
in two steps. First, simple correlations of state
per capita income with the federal funds ratio
are discussed. Second, using a categorization of
states according to how their growth rates and
levels of per capita income affected the degree
of inequality in the 1980s, we examine how
federal fiscal policies have changed between
1981 and 1987 for states within these
categories.

Federal Funds Ratio
Table 2 reports simple correlations of state
per capita income with a state's federal funds
ratio for the 12 periods for which data are
no relationship between defense spending and state per
capita income growth in the same period.
10The openness of a state’s economy tends to reduce these
effects. Although lower federal taxes or higher federal ex­
penditures leaves more income in the hands of state
residents, a portion of these funds are spent for goods and
services from outside the state. For example, defense pro­
curement contracts are credited to the state in which the
bulk of production is located, but some of this production
is subcontracted to other parts of the nation.
"A d visory Commission on Intergovernmental Relations
(1980), pp. 82-83, reported a positive relationship between
a state’s flow-of-funds balance and its per capita income
growth between 1950 and 1975.
12See, for example, Advisory Commission on Intergovern­
mental Relations (1980), Erdevig (1986), Rymarowicz
(1988), Weinstein and Wigley (1987) and NortheastMidwest Institute (1988).

JULY/AUGUST 1989

34

W h a t D o

F e d e ra l F lo w

o f F u n d s

The federal funds ratio (FF) compares the
federal expenditures received by those in a
state in a given fiscal year with their federal
tax payments. Ratios o f each state’s share of
national expenditures to its share o f tax
payments are used rather than each state’s
levels. For a given fiscal year, the federal
funds ratio is calculated as follows:
FFS = [(FES
/FE„) / (TPS
/TP„)] x 100,
where the subscripts s and n denote an in­
dividual state (48 contiguous states) and the
continental U.S. total, respectively. FE refers
to federal expenditures made in states and
TP refers to tax payments to the federal
government. If a state has a FF greater than
(less than) 100, it receives a greater (smaller)
proportion of the nation's expenditures than
it pays in federal taxes.
Percentage shares, rather than levels, are
used in computing the ratio to minimize
distortions caused by changes in data
coverage in different years. Expenditures
data for years before 1969, for example, in­
clude payments on the national debt to states
by the federal government whereas these
payments are excluded in more recent data.1
By using shares of national totals, each state’s
expenditures and payments are more com­
parable than if levels were compared. Also,
considering ratios of shares ensures that the
national ratio equals 100, eliminating confu­
sion due to the gap between expenditures
and tax payments. The analysis excludes the
District of Columbia, Hawaii and Alaska
because o f their unique relationship to the
federal government.

Tax Payments
Tax payments include personal income
taxes, corporation income taxes, excise taxes
and social insurance taxes and contributions.
'Federal expenditure and tax payment data for the years
prior to 1981 were from Advisory Commission on In­
tergovernmental Relations (1980). Later data were from
U.S. Department of Commerce (1988), Tax Foundation,
Inc. (1988) and for defense contract data, from U.S.
Department of Defense (various years).
2Long and Settle (1982) found that the estimates from
the Tax Foundation were “ reasonably accurate in-


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M e a s u re ?

Social insurance taxes and contributions in­
clude Social Security, railroad retirement,
federal and unemployment insurance taxes.
The table shows the relative size of each of
the major components in fiscal year 1987. In­
dividual income taxes and social insurance
contributions account for more than fourfifths of the total. Individual income and cor­
poration income taxes have declined slightly
in relative size during the 1980s, while social
insurance contributions have increased 5
percentage points since 1980 to 35.5 percent
in 1987.
To allocate tax liability by state, estimates
from the Tax Foundation, Inc. (1988) were
used.2 Individual income taxes were
distributed among the states according to a
state's actual tax liability for the most recent
prior tax year available, adjusted by changes
in personal income by place of residence.
Corporation income taxes were based on the
distribution of personal income (50 percent)
and property income (50 percent). Excise
taxes were based on consumption and
population data. Most of the social insurance
taxes were distributed by the distribution of
personal income and personal contributions
for social insurance and unemployment in­
surance taxes.

Federal Expenditures
As shown in the table, federal expenditures
distributed by state included 81.6 percent of
the approximately $1 trillion in federal
government outlays for fiscal year 1987. Of
the federal expenditures that the U.S. Depart­
ment of Commerce (1988) was unable to
distribute among states, the largest category
was net interest payments on the national
debt. Of the procurement contracts not
distributed by state, most were defense con­
tracts of less than $25,000.
dicators of the true distribution of financing burdens”
(p. 459) and that, of the several methods tested, the
Tax Foundation methodology minimized overall estima­
tion error (p. 453). See Tax Foundation, Inc. (1988) for
more detail concerning the methodology.

35

Federal Taxes and Outlays, Fiscal Year 1987

Level (billions)

Percent Composition

Tax Payments (Receipts)
Individual income taxes
Corporation income taxes
Excise taxes
Other
Social insurance taxes
and contributions

$ 854.1
392.6
83.9
32.5
41.9

100.0%
46.0
9.8
3.8
4.9

Total Federal Outlays
Net interest
Distributed to territories
Procurement contracts not
distributed
Other outlays not distributed
by state
Expenditures distributed by
state
Direct payments
Procurement contracts
Defense department
Other
Salaries and wages
Grants to state and local
governments
Other programs

$1,003.8
138.6
7.3

303.3

Direct payments to individuals was the
largest category of federal expenditures
distributed by state. Most direct payments
were for Social Security or Medicare. Threefourths of procurement contracts, the nextlargest category, were awarded by the
Department of Defense. The Defense Depart­
ment was also responsible for approximately
half of all federal salaries and wages
distributed among the states in 1987. The
largest programs among grants to state and
local governments in 1987 were Medicaid
($27.2 billion), the Highway Trust Fund ($11.2
billion) and Aid for Dependent Children
($10.5 billion). Almost half of the "other pro­
available. A positive association, indicating that
higher (lower) income states had larger (smaller)
federal funds ratios, would be consistent with a
federal tax and expenditure system that is con­
tributing to divergent state incomes. The results
indicate, however, a statistically significant
negative association for all periods, suggesting



35.5
100.0%
13.8
0.7

19.5

1.9

19.6

2.0

818.8
380.1
176.2
132.5
43.7
125.9

81.6
37.9
17.6
13.2
4.4
12.5

104.0
32.6

10.4
3.2

grams” category consisted of farm subsidy
payments.
The Commerce Department was able to
allocate federal expenditures among the
states through reports from federal govern­
ment executive departments and agencies.
Procurement contracts are distributed accor­
ding to the primary place of performance
rather than the place of the prime contrac­
tor, but no adjustment is made for work per­
formed in other states by subcontractors.
Direct payments w ere allocated to the state
in which the recipient resided, while salaries
and wages reflect the state o f employment.
that federal funds flow from higher to lower
per capita income states.
It is possible, however, that federal fiscal
policy could have contributed to the rising ine­
quality if the degree of redistribution dimin­
ished in the 1980s. The evidence does not sup-

JULY/AUGUST 1989

36

Table 2
Correlation Coefficients: State Per
Capita Income with Various Fiscal

Year
1952
1959
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987

Federal
funds
ratio

Expenditures2

-0 .6 4 *
- 0 .4 9 * 1

0.49*
0.45*1

- 0 .6 2 * 1

0.151

- 0 .6 0 * 1

0.29*1

- 0 .5 8 * 1

0.171

-0 .4 6 *
-0 .4 5 *
-0 .4 5 *
-0 .4 6 *
-0 .4 8 *
-0 .5 8 *
-0 .5 7 *

0.32*
0.34*
0.37*
0.33*
0.34*
0.28
0.26

Defense
contracts3

0.47*
0.46*
0.47*
0.49*
0.47*
0.47*
0.43*
0.42*
0.36*
0.38*
0.35*
0.33*
0.29*
0.30*
0.30*
0.34*
0.38*
0.42*
0.46*
0.49*
0.53*
0.57*
0.59*
0.60*

11959, 1965, 1969 and 1974 refer to three-year periods
ending in years listed.
Expenditures are per capita by state.
3Data are per capita by state and moving averages for the
three years ending in year listed.
'Significantly different than zero at 0.05 significance
level.

port such a conclusion. Rather than declining
during the 1980s, the correlation coefficients in
1986 and 1987 are higher (in absolute value)
than for the early 1980s and are roughly equal
to earlier periods when the level of interstate
per capita income inequality was declining.

13The footnotes in table 3 present the criteria for categoriz­
ing the states. See Coughlin and Mandelbaum (1988) for a
more extensive explanation of the classification.
^Excluding New Mexico, in which extremely high levels of
Energy Department contracts distort the data, the average
federal funds ratio for downwardly divergent states rises
from 102.6 percent of the U.S. average in 1981 to 119.7
percent in 1987. New Mexico received the highest per


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For a closer examination of the distribution of
federal funds in those states most responsible
for the increasing per capita income inequality
in the 1980s, we use a classification o f states
developed in an earlier article. The classifica­
tion, presented in table 3, groups states accor­
ding to their per capita income change between
1978 and 1987 and whether these changes tend­
ed to raise or lower per capita income inequali­
ty.1 Ten states with above-average per capita
3
income in 1978 experienced substantially faster
growth between 1978 and 1987 than the aver­
age. W e call these states “upwardly divergent.”
Ten states with below-average per capita in­
come that experienced substantially slower
growth than the average are called "downward­
ly divergent.”
W e have also identified 10 states whose in­
come changes tended to reduce inequality. Four
were states whose per capita incomes were be­
low the average across states in 1978, but
which have grown much faster than this
average since then. These states are called “up­
wardly convergent.” Six “downwardly con­
vergent” states had per capita incomes above
the average across states in 1978, but grew
much slower than the average and thus con­
tributed to reduced inequality. Finally, 18 states
had relative per capita incomes that changed
less than 5 percentage points between 1978 and
1987 and, therefore, had little effect on the re­
cent changes in inequality.
W e use these classifications to explore how
the federal funds ratio has changed between
1981 and 1987 and whether the change is con­
sistent with rising income inequality. The dis­
cussion will focus on federal funds flows in
those 20 states in the two "divergent” groups
because they were primarily responsible for the
increase in inequality in the 1980s.
Table 3 reveals that the average federal funds
ratio fell between 1981 and 1987 in upwardly
divergent states (from 107.2 percent of the na­
tional average to 96.5 percent) and rose in
downwardly divergent states (from 111 percent
to 127.1 percent).1 Neither of these changes is
4

capita level of non-Defense Department procurement con­
tracts of any state primarily because of the presence of
the U.S. Department of Energy’s Los Alamos and Sandia
Research Laboratories. Since a portion of the funds go to
subcontractors in other states besides New Mexico, the
expenditure data probably overstate the amount spent in
New Mexico.

37

Table 3
Federal Tax Payments and Expenditures by State
Federal funds
ratio

Per capita
payments1

Per capita
expenditures1

Per capita
defense
contracts1’2

Upwardly Divergent3
1981
Connecticut
Massachusetts
New Jersey
New Hampshire
New York
Virginia
Maryland
Rhode Island
Delaware
Florida
Group Average

1987

1981

1987

1981

1987

1981

1987

105
112
74
99
94
146
122
111
91
118
107.2

83
103
63
75
83
154
127
101
74
102
96.5

134
116
88
96
100
141
136
109
101
104
112.5

124
127
88
84
99
155
149
102
83
101
111.2

128
103
119
97
106
97
111
98
111
88
105.8

148
123
139
111
118
101
118
101
112
99
117.0

389
196
69
101
97
180
134
72
94
70
140.2

301
258
81
95
99
199
185
80
64
85
144.7

130
134
103
146
162
120
106
89
194
87
127.1

82
90
97
91
92
85
91
75
150
90
94.3

93
104
77
99
130
82
90
78
143
83
97.9

78
89
85
74
90
79
92
101
80
96
86.4

71
78
75
68
81
68
85
87
74
95
78.2

9
16
89
60
36
13
46
75
71
118
53.3

9
19
63
97
51
8
35
86
66
108
54.2

103
126
92
93
103.5

88
98
88
76
87.5

90
101
79
76
86.5

78
74
79
76
76.8

88
80
85
81
83.5

52
118
76
35
70.3

105
121
44
30
75.0

100
97
94
105
71
114
96.8

128
104
79
69
80
119
96.5

92
100
81
88
74
113
91.3

111
108
100
99
113
109
106.7

91
103
86
84
104
100
94.7

31
24
17
30
54
155
51.8

31
31
16
36
46
121
46.8

Downwardly Divergent4
Idaho
Montana
Louisiana
Utah
North Dakota
West Virginia
Oklahoma
Indiana
New Mexico
Texas
Group Average

106
101
115
124
103
108
99
74
187
93
111.0

Upwardly Convergent5
Georgia
Maine
Vermont
North Carolina
Group Average

112
132
111
99
113.5

Downwardly Convergent6
Wyoming
Nevada
Oregon
Iowa
Michigan
Washington
Group Average




115
96
79
70
71
109
90.0

(continued on next page)

JULY/AUGUST 1989

38

Table 3 (cont’d)
Federal Tax Payments and Expenditures by State_________
Federal funds
ratio

Per capita
expenditures1

Per capita
payments1

Per capita
defense
contracts*’2

No Substantial Change7
Illinois
Ohio
South Dakota
Kentucky
Mississippi
Nebraska
Arkansas
Wisconsin
Kansas
Pennsylvania
Alabama
Colorado
Missouri
Arizona
California
South Carolina
Tennessee
Minnesota
Group Average

67
79
116
102
161
83
122
79
89
93
129
101
128
118
104
124
118
83
105.3

71
89
154
114
164
112
131
81
106
96
137
109
130
124
97
124
116
92
113.7

79
82
92
81
103
81
86
77
94
93
96
101
123
101
115
88
95
83
92.8

78
85
110
81
97
98
89
74
103
93
100
109
121
108
106
89
92
91
95.8

119
103
79
80
64
98
70
98
106
100
74
100
96
85
111
71
80
100
90.8

110
95
71
71
59
87
68
91
97
97
73
100
93
88
110
72
80
99
86.7

25
50
14
22
110
19
18
28
99
54
50
63
221
93
177
34
33
77
65.9

26
80
21
23
95
24
59
37
130
61
67
113
225
142
180
27
35
100
80.3

'Figures are indexed relative to a continental U.S. average of 100.
2Three-year moving average. Data for 1981 refers to three years through 1981, while 1987
figures are averages for 1985-87.
3States with above-average per capita income in 1978 and with a 5 or more percentage-point
increase in per capita income as a percent of the state average. For Rhode Island, a state
with below-average per capita income in 1978 and above-average per capita income in 1987,
the rise in relative income resulted in the state’s income absolutely further from the average in
1987 than in 1978.
“ States with below-average per capita income in 1978 and with a 5 or more percentage-point
drop between 1978 and 1987 in state per capita income as a percent of the state average.
For Indiana and Texas, states with above-average income in 1978 and below-average income
in 1987, the drops resulted in the states' being absolutely further from average per capita in­
come in 1987 than in 1978.
5States with below-average per capita income in 1978 and with a 5 or more percentage-point
increase between 1978 and 1987 in state per capita income as a percent of the state average.
6States with above-average per capita income in 1978 and with a 5 or more percentage-point
decline between 1978 and 1987 in state per capita income as a percent of the state average.
For Wyoming, Oregon and Iowa, states with above-average per capita income in 1978 and
below-average per capita income in 1987, the drop resulted in per capita income closer to the
state average in 1987 than in 1978.
7States whose absolute percentage-point change in per capita income as a percent of the
states was less than 5 percent between 1978 and 1987.


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39

Figure 3
Per Capita Income and Federal Funds Ratios
in Divergent States
Index
—,130

Index
130

Per capita income:
upwardly divergent states

Federal funds ratio:
downwardly divergent states
Federal funds ratio:
upwardly divergent states
Per capita income:
downwardly divergent states
1981
82
83
84
85
86
1987
NOTE: Per capita income is indexed, 100 = 48 - state average. For the federal funds ratio,
100 indicates that the share of federal expenditures received equals the share of
federal taxes paid.

^
consistent with the hypothesis that changes in
the distribution of federal expenditures and
taxes have contributed to rising inequality. To
be consistent with rising inequality, the federal
funds ratios of upwardly divergent states would
have risen, while that of downwardly divergent
states would have fallen. In the upwardly
divergent states, a rising federal funds ratio
would have contributed to the relatively faster
growth of these high-income states, resulting in
greater inequality in per capita income. In the
downwardly divergent states, a falling federal
funds ratio would contribute to these states’
relatively slow growth.
Figure 3 clearly shows the differing trends of
the average federal funds ratio and per capita
income in the two divergent groups of states.
For the upwardly divergent states, the decline
o f the average federal funds ratio contrasts
with the steady increases in per capita incomes.
In downwardly divergent states, the federal



I

funds ratio rose sharply since 1983, while per
capita income fell relative to the state average.
Figure 3 also shows that the federal funds
ratio is consistently higher in the downwardly
divergent than in the upwardly divergent states.
This is consistent with the negative correlations
between state per capita income and the federal
funds ratios indicating that states with lower
per capita income tended to benefit more from
the overall federal spending and taxation pat­
terns than high per capita income states.
These findings suggest that neither the levels
of, nor changes in, the overall flow o f federal
funds contributed to the divergence of state per
capita incomes through their effects on the di­
vergent states. In conjunction with the more
general finding of consistently negative correla­
tions between the federal funds ratio and state
per capita income, this evidence suggests that, if
it had any impact on per capita income growth,

.1111 V/A im il<S T 1QAQ

40

changes in the distribution of the federal funds
flow reduced, rather than increased, per capita
income inequality in the 1980s.

Federal Expenditures in States
Much o f the concern about federal policies
that influence state economies involves the
distribution of federal expenditures rather than
the pattern of federal funds flows or the bur­
den of federal taxes. The interstate distribution
of federal spending, particularly defense spen­
ding, is seen as more discretionary than the fed­
eral tax burden. Although changes in the overall
flows of federal funds among states do not ap­
pear to have contributed to the increasing ine­
quality in the 1980s, it is still possible that fed­
eral expenditures were disproportionately spent
in high-income states and contributed to in­
creasing per capita income inequality.
Simple correlations between state per capita
income and per capita federal expenditures re­
ceived in a state are reported in table 2. The
consistently positive correlations indicate that
states with higher per capita incomes tended to
receive higher per capita federal expenditures.
During the 1980s, however, the evidence sug­
gests that this relationship, if it has changed at
all, has weakened. In fact, for 1986 and 1987,
the positive association is not statistically signifi­
cant at the 0.05 significance level.
Doubts about federal spending contributing to
divergence are heightened when the states are
categorized by their contributions to rising ine­
quality. Table 3 shows that, on average, the
share of federal expenditures received by up­
wardly divergent states declined slightly from
112.5 percent of the national average in 1981 to
111.2 percent in 1987. The direction of this
change does not suggest that changes in spen­
15ln both years, the extremely high expenditures in New
Mexico raised the average of downwardly divergent states.
Nonetheless, excluding New Mexico does not alter the fact
that the share of per capita expenditures in these states
rose between 1981 and 1987. If New Mexico is excluded,
per capita expenditures in downwardly divergent states
averaged 88.1 percent and 92.9 percent of the national
figures in 1981 and 1987.
16Correlation coefficients indicate a close relationship bet­
ween per capita income and per capita federal tax
payments. The correlation coefficients across the 48 states
were high, positive and statistically significant for each of
the 12 periods since 1952 for which data were available.
In addition, the results suggest that the relationship has
not changed substantially during the 1980s, as correlations
ranged from 0.94 in 1981 to 0.98 in 1987.
17No significant correlations (0.05 significance level) were
found between annual state per capita incomes and the


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ding patterns contributed to increases in ine­
quality. Per capita expenditures fell slightly,
while per capita income was growing rapidly. In
downwardly divergent states, the direction in
the change of shares is also inconsistent with
rising inequality: average per capita expen­
ditures rose from 94.3 percent of the national
average in 1981 to 97.9 percent in 1987.1
5
While per capita expenditures w ere above the
national average in upwardly divergent states in
both 1981 and 1987, these expenditures were
offset by relatively high tax payments. Thus, if
one is willing to disregard the consistently high
federal tax outflows made by these high-income
states, it follows that high levels o f federal spen­
ding in upwardly divergent states contributed to
interstate income inequality in a particular year.
The comparatively low per capita federal expen­
ditures received by the downwardly divergent
states also were offset bv low outflows of
federal tax payments.1
6

D efense Procurem ent Contracts
While the evidence that federal expenditures
as a whole contributed to rising inequality is
negligible, there is another possibility. Assuming
that different expenditures have different ef­
fects on growth, changes in the distribution of
certain categories of expenditures may have
contributed to rising inequality. Among the ma­
jor categories of federal spending, only defense
contracts are significantly linked to the level of
state per capita incomes.1 The potential impact
7
of federal procurement contracts on interstate
income inequality has been magnified by their
rapid growth. Procurement has been a rapidly
growing component of those federal expen­
ditures distributed among states, expanding at a
6.9 percent annual rate between 1981 and 1987,
other components of federal spending (per capita grants,
per capita salaries and wages and per capita direct
payments) for any period since 1972. The lack of
systematic relationships between state per capita incomes
and federal grants-in-aid suggests that the positive rela­
tionship between a region’s federal grants-in-aid and its
per capita income discussed by Gross and Weinstein
(1988) and Weinstein and Wigley (1987) does not exist at
the state level. Our finding, however, is consistent with the
results of a study by the U.S. Department of the Treasury
(1985), pp. 197-202, which found no statistically significant
relationship between state per capita income and per
capita grants-in-aid for 1983.

41

compared with 6.3 percent for total federal ex­
penditures. The rapid defense build-up during
the Reagan administration was largely responsi­
ble for the increase in procurement.
Evidence suggests that the distribution of
defense contracts may have increased interstate
inequality since 1978. Simple correlations for
each period between 1964 and 1987 of state per
capita income with state per capita defense con­
tracts are reported in table 2.1 The positive
8
association for each period suggests that highincome states receive above-average amounts of
defense contracts, which is consistent with
defense spending contributing to divergence.
The association has tended to strengthen since
the mid-1970s, a fact that suggests the 1980s
are a continuation of a longer trend.
As table 3 shows, the average of per capita
defense contracts in upwardly divergent states
was well above the national average during
both periods and increased from 140.2 percent
in 1981 to 144.7 percent in 1987. This increase,
however, is relatively less rapid than the income
growth of these states. The upwardly divergent
states are far from homogeneous, as about half
of the states received below-average levels dur­
ing both periods.
On the other hand, table 3 shows that nine of
the 10 downwardly divergent states received
below-average defense procurement contracts in
the three-year periods ending 1981 and 1987.
Per capita defense contracts in downwardly di­
vergent states averaged slightly more than half
of the national average. More importantly, the
share of these states changed little between
1981 and 1987, a fact suggesting no change in
the effect o f defense spending on inequality.
For the convergent states, the changes in the
distribution of federal defense contracts appear
to have reduced income inequality. For example,
between 1981 and 1987, the share o f the na­
tion’s per capita defense contracts received by
upwardly convergent states rose from 70.3 per­
cent of the U.S. average to 75 percent, while
the share of downwardly convergent states
declined from 51.8 percent to 46.8 percent.
Thus, at least in the upwardly divergent
states, defense spending may have contributed
to increasing inequality. In view of the evidence
from the other state categories, however, the
18Defense contract data are expressed in terms of three-year
moving averages because of the volatility of the data and




case for changes in defense spending con­
tributing to increasing inequality is weak.

SUMMARY
Overall, federal fiscal policy does not appear
to have been a cause of the increasing inequali­
ty of state per capita incomes in the 1980s. The
distribution of transfer payments and the
burden o f federal personal taxes w ere shown to
lower the interstate inequality of income con­
sistently since 1958, while the burden of social
insurance contributions apparently had little
effect.
The absence of a consistent time series before
1981 on the distribution of federal expenditures
and taxes among states, as well as other data
limitations, preclude firm identification of causal
factors, but the flows of federal funds generally
were not distributed in a way that benefited
rapidly growing high-income states. On the con­
trary, upwardly divergent states received lower
net inflows of federal funds than downwardly
divergent states, and their net inflows declined
during the 1980s. While upwardly divergent
states tended to receive slightly higher levels of
per capita expenditures than downwardly
divergent states (largely because of the distribu­
tion of procurement contracts), their tax pay­
ments were substantially higher as well.
The pattern of change in per capita federal
expenditures between 1981 and 1987 was op­
posite to those one would expect if federal ex­
penditures contributed to the increase in in­
terstate per capita income inequality since 1978.
The evidence, however, is consistent with the
argument that one major federal spending
program—defense spending—could have been a
minor factor in the rising inequality of state per
capita income this decade.

REFERENCES
Advisory Commission on Intergovernmental Relations.
Regional Growth: Historic Perspective (June 1980).
Barff, Richard A., and Prentice L. Knight III. “ The Role of
Federal Military Spending in the Timing of the New
England Employment Turnaround,” Papers of the Regional
Science Association (1988), p. 151.
Bolton, Roger E. Defense Purchases and Regional Growth
(The Brookings Institution, 1966).
because the contracts sometimes reflect multi-year obliga­
tions of up to three years in duration.

II II V / A I

IC T

1Q O Q

42

Browne, Lynn E. “ Defense Spending and High Technology
Development: National and State Issues,” New England
Economic Review (September/October 1988), pp. 3-22.

Rees, John, Bernard L. Weinstein, and Harold T. Gross.
Regional Patterns of Military Procurement and Their Im­
plications (The Sunbelt Institute, 1988).

Coughlin, Cletus C., and Thomas B. Mandelbaum. “ Why
Have State Per Capita Incomes Diverged Recent­
ly?” this Review (September/October 1988), pp. 24-36.

Rymarowicz, Lillian. “ Federal Tax Payments by State
Residents and Federal Expenditures in Individual States,
Fiscal Year 1987,” Congressional Research Service, Library
of Congress (June 1, 1988).

Erdevig, Eleanor H. “ Federal Funds Flow No Bargain for
Midwest,” Federal Reserve Bank of Chicago Economic
Perspectives (January/February 1986), pp. 3-10.

Tax Foundation, Inc. “ Memorandum on the Allocation of the
Federal Tax Burden by State” (March 1988).

“ Federal Spending: The Northeast’s Loss is the Sunbelt’s
Gain,” National Journal (Government Research Corporation,
June 1976).
Gross, Harold T., and Bernard L. Weinstein. “ Frost Belt vs.
Sun Belt in Aid Grants: Not a Fair Fight,” Wall Street Jour­
nal, August 23, 1988.
Long, Stephen H., and Russell F. Settle. “ Tax Incidence
Assumptions and Fiscal Burdens by State.” National Tax
Journal (December 1982), pp. 449-64.

“ The Second War Between the States.” Business Week
(May 17, 1977).
U.S. Department of Commerce, Bureau of the Census.
Federal Expenditures by State for Fiscal Year 1987 (GPO,
March 1988).
U.S. Department of Defense. Prime Contract Awards by
State (GPO, various years).
U.S. Department of the Treasury, Office of State and Local
Finance. Federal-State-Local Fiscal Relations: Report to the
President and the Congress. (GPO, September 1985).

Northeast-Midwest Institute. The Budget and the Region,
Fiscal 1989. (February 1988).

“ U.S. Picks Small Town Near Dallas as Site of $4.4 Billion
Supercollider.” Wall Street Journal, November 11, 1988.

Ray, Cadwell L., and R. Lynn Rittenoure. “ Recent Regional
Growth Patterns: More Inequality,” Economic Development
Quarterly (August 1987'), pp. 240-48.

Weinstein, Bernard L., and Richard W. Wigley. Regional
Biases in Federal Funding (The Sunbelt Institute, July
1987).


http://fraser.stlouisfed.org/
Federal Reserve F D F RofLSt. E S E R V E B A N K O F S T LO U IS
F Bank A R Louis

43

D en n is W. Jansen
Dennis W Jansen, an associate professor of economics at
.
Texas A&M University, is a visiting scholar at the Federal
Reserve Bank of St. Louis. Scott Leitz provided research
assistance.

Does Inflation Uncertainty
Affect Output Growth?
Further Evidence

CONOMISTS have long been interested in
the effects of inflation on real economic vari­
ables. In the past two decades, this line of re­
search has expanded greatly, spurred on by the
relatively high inflation rates in the developed
economies beginning in the 1970s and the coin­
cident slowing in the rate of output growth.
One traditional and widely accepted notion is
that anticipated inflation has little or no effect
on real variables, except for those effects aris­
ing from institutional features such as incom­
pletely indexed tax codes and zero interest
payments on currency and reserves.1 It is also
widely accepted that unanticipated inflation af­
fects real variables, at least in the short run.
Many analysts also hold that uncertainty
about future inflation rates affects real vari­
ables. Indeed, Marshall (1886) expressed concern
about the negative effects of an uncertain fu­
ture value of the English pound on output over
100 years ago. More recent arguments in this
spirit are contained in Okun (1971) and Fried­
man (1977), who argue that uncertainty about
future inflation is detrimental to real economic
activity.

Furthermore, they suggest that uncertainty
about future inflation is linked to the mean rate
of inflation by the policy environment. Fried­
man, in particular, argues that nations might
temporarily pursue a set o f goals for real vari­
ables (for example, output, unemployment) that
leads to a high inflation rate. The high inflation
rate induces strong political pressure to reduce
it, leading to stop-go policies and attendant
uncertainty about future inflation. Thus, high
inflation coexists with increased inflation uncer­
tainty, as individuals become less certain about
the political choice over future inflation paths.
Friedman postulates a negative effect of a
highly volatile inflation rate on economic effi­
ciency for two reasons. First, increased volatility
in inflation makes long-term contracts more
costly because the future value of dollar pay­
ments is more uncertain. Second, increased vol­
atility in inflation reduces the ability of
markets to convey information to market par­
ticipants about relative price movements. By
reducing economic efficiency, greater inflation
uncertainty should at least temporarily increase

’ Surveys reporting on this general consensus are Taylor
(1981), Cukierman (1983) and Fischer (1981).




JULY/AUGUST 1989

44

the rate of unemployment and reduce economic
growth.2
Though these theoretical concerns about the
effect of inflation uncertainty seem reasonable
and persist in economic discussions, existing
studies provide only mixed support for them.
This paper studies the relationships between the
mean and variance o f the inflation rate and out­
put growth for the United States in another at­
tempt to identify the hypothesized negative rela­
tionship of inflation uncertainty on output
growth. To put this study into perspective, the
following section briefly reviews the findings of
several previous studies, with particular atten­
tion to the relationship between the measure of
inflation uncertainty employed in each study
and evidence about the link between inflation
uncertainty and real economic variables.

A REVIEW OF THE RECENT
LITERATURE
Empirical studies of the effect of inflation
uncertainty tend to follow one of three broad
approaches. The first is that used by Okun
(1971), who gathers data for 17 developed coun­
tries over 17 years and calculates the mean and
variance of the inflation rate for each country.
By plotting the mean inflation rate vs. the stan­
dard deviation o f the inflation rate for these
countries, he finds that these two variables are
positively related. Logue and Sweeney (1981)
use Okun's methodology and find that both the
mean and variance of inflation are positively
related to the variance of output growth.3
This approach has been criticized largely on
two grounds. First, the sample variance of the
inflation rate for a country over 15 or 20 years
is unlikely to be the best measure of uncertain­
ty about future inflation rates, because the sam­
ple variance of inflation confounds predictable
and unpredictable changes in the inflation rate.
For example, if the inflation rate moves in a
perfectly predictable way, inflation uncertainty
is zero, but the computed sample variance of in­
flation would be positive. A second criticism is
2Recent theoretical work demonstrates that, under plausible
conditions, increases in inflation uncertainty lead to reduc­
tions in output. Surveys of the theoretical rationales
underlying relationships between inflation uncertainty and
real variables are contained in Taylor (1981) and Cukierman (1983). These surveys also discuss some of the ex­
tant empirical literature on this topic.
3Logue and Sweeney acknowledge in their text that an
alternative to their approach is to use a time series ap-



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that this approach requires a certain homogene­
ity across countries to make valid inferences
about the variation of inflation and output
growth across those countries. Gale (1981) gives
reasons to doubt that this homogeneity exists,
including noncomparability of indexes and dif­
ferent levels o f development across countries.
Indeed, Katsimbris (1985) strongly rejects the
hypothesis o f homogeneity across countries.
A second approach allows the mean and vari­
ance of inflation to change within a country
through time. Katsimbris (1985) does this for 18
OECD countries. He constructs proxies for the
time-varying mean and variance of inflation and
output growth as eight-quarter, non-overlap­
ping, moving averages. He finds few countries
for which the mean and variance of inflation
are related in a statistically significant way and
even few er for which the variance of inflation
and the mean or variance o f output growth are
related. In particular, he finds no significant
relationship between inflation uncertainty and
output growth in the United States. Thornton
(1988), in a recent study employing this method­
ology, obtains the same results.
Katsimbris' study of individual countries is but
one example of a number of studies that use
this second approach. Their main feature is the
construction of proxies for inflation uncertainty.
In addition to Katsimbris’ eight-quarter, non­
overlapping, moving averages, others estimate
time series models for the inflation rate and the
real variables and use the residuals to construct
overlapping moving-average measures to proxy
for the time-varying variance of inflation.
All of these studies lack a parametric model
for the time-varying variance of inflation. For
instance, Katsimbris’ moving averages for the
mean inflation rate does not necessarily capture
the predictable elements of the inflation pro­
cess. Therefore, his measure o f the variance
confounds the uncertainty of future inflation
with predictable changes in inflation. In con­
trast, studies using proxies for inflation uncer­
tainty constructed from the residuals of a model
proach that relates inflation and its variability to the
variability of production. They write, “ Unfortunately, a neat
measure of the next period’s uncertainty that might be
suitable for use in such a time series test is not available”
(p. 499). It is a contention of this paper that the ARCH-M
model provides the requisite time series test.

45

for the inflation process can claim rightly that
they are attempting to measure only unpredic­
table movements in inflation; but these studies
are prey to an internal inconsistency. In par­
ticular, such an approach estimates a model of
inflation under the maintained hypothesis of
homoskedasticity and then estimates a proxy for
the time-varying (heteroskedastic) conditional
variance from the residuals.
A third approach to measuring inflation un­
certainty uses survey data from individual infla­
tion forecasts. A good example is Mullineaux
(1980), who uses the standard deviation of in­
dividual inflation forecasts about the mean
value to measure inflation uncertainty. He finds
that the sum of current and lagged values of
this measure of inflation uncertainty is signifi­
cantly and positively related to the unemploy­
ment rate and significantly and negatively re­
lated to the level of industrial production. A
more recent study by Hafer (1986) confirms
these results with an alternative survey o f infla­
tion expectations.
A crucial problem with this approach, how­
ever, is that the inflation uncertainty measure
actually measures the dispersion of point esti­
mates of the inflation rate across individuals,
which does not necessarily capture the degree
of uncertainty about future inflation rates.
Within a specific theoretical framework, Cukierman (1983) has shown that these two measures
are related. It is clear, however, that the in­
dividual point estimates reported in the surveys
do not indicate the certainty with which in­
dividuals make their forecasts, so that measur­
ing inflation uncertainty by the dispersion of
these estimates of the inflation rate across fore­
casters can be misleading.4 Consider, for exam­
ple, what would happen if all individuals
surveyed reported the same forecast. Even if
none of the individuals were very certain of the
forecast, that is, if inflation uncertainty were

4One well-known survey, the ASA-NBER survey of profes­
sional forecasters, makes an attempt to gather data on
confidence bands corresponding to forecasts. These data
are relatively crude, however, and are seldom used by
authors investigating the neutrality of inflation uncertainty.
See, e.g., Hafer (1986).
5This is not to say that the information in the dispersion of
inflation forecasts across individuals is not useful. Such in­
formation is not captured by the assumption implicit in this
paper that agents forecast the inflation rate based on com­
mon information. Moreover, other approaches have been
employed to look at related aspects of the relation be­
tween inflation uncertainty and real variables. Blejer and




considerable, the constructed measure would be
equal to zero.5

ESTIMATION RESULTS
This study investigates the effects of inflation
uncertainty by looking at a time series of data
for the United States, following the second ap­
proach discussed above. Unlike most previous
studies, however, this investigation uses a statis­
tical technique, the ARCH model, that parame­
terizes the mean and variance relationships
under investigation. This permits straightfor­
ward estimation and hypothesis testing in an in­
ternally consistent framework. The measure of
inflation uncertainty employed here is the timevarying conditional variance of the inflation
equation. A more detailed description of the
class of ARCH models is provided in the shaded
insert on pages 46 and 47.
W e model the inflation, real output growth
system over the I/1959-II/1988 period using
seasonally adjusted quarterly data on real GNP
and the GNP deflator. The regression model for
the conditional means of inflation and output
growth is a vector autoregression.
Preliminary diagnostic tests were conducted to
check for unit roots and time trends in the vari­
ables. These are reported in table 1. Neither in­
flation nor output growth exhibited a time
trend. For output growth, the null hypothesis of
a unit root was rejected. Tests for a unit root in
the inflation process are inconclusive: the
Dickey-Fuller test rejected the unit root hypoth­
esis, but the augmented Dickey-Fuller test failed
to do so. It is well known that tests for a unit
root have low power when the alternative is a
root close to but less than one. Moreover, the
augmented Dickey-Fuller test is more powerful
when the time series in question is not white
noise after differencing, a situation that appears
to hold for the GNP deflator.6 Additional infor-

Leiderman (1980) look at relative price variability,
measured as the dispersion of price changes in a set of
industries about the average price change of the industry.
They test to see if real output and unemployment are
adversely affected by increases in relative price variability.
Notice that inflation uncertainty is not directly an issue in
Blejer and Leiderman’s work since they examine only the
variability of relative prices. They report that relative price
variability had significant adverse effects on real variables
for the United States.
6lt is also known, however, that the augmented DickeyFuller test has lower power than the unaugmented test
when the series is white noise after differencing.

JULY/AUGUST 1989

46

T h e

A R C H

C la s s

o f M o d e ls

In a series of papers, Robert Engle and his
collaborators have developed a class of
models that allow for explicit parameteriza­
tion o f the variance process for time series
models. These models are known by the
acronym ARCH, for autoregressive condi­
tional heteroskedasticity, and by variants on
that acronym such as GARCH (generalized
ARCH) and ARCH-M (ARCH in mean).1 In
these models, the variance of a regression is
allowed to change over time and, in par­
ticular, to vary with past realizations of
variables, including the regression
disturbances.
The motivation behind the development of
the ARCH class of models derives from
several empirical features of economic data.
First, the restrictive assumption of
homoskedasticity often is rejected by the
data. The ARCH model permits a general
form o f heteroskedasticity that nests the
homoskedastic model as a special case. In
particular, the variance is allowed to depend
on realizations o f past variables including
past disturbances. Second, consistent with
observed data, the ARCH model allows for
the clustering of forecast errors that is often
observed in econometric models. Thus, the
ARCH model permits the occurrence of a
large forecasting error today to increase the
probability o f observing a large forecasting
error tomorrow. Third, the ARCH model ex­
plicitly allows for the leptokurticity that
economic data exhibits. Leptokurticity is the
phenomenon that a distribution has "fat
tails.”2 Finally, the more general ARCH-M
models are especially useful for conducting
hypothesis tests relating means and variances.
The basic structure of the ARCH model is
fairly simple. The univariate ARCH model can
be represented as follows:

(3) h, - a0 +

a i > 0 for all j.

Equation 1 represents a standard univariate
equation with y t as the dependent variable, xt
as the vector of predetermined variables
which can include lags of the dependent
variable, b as the vector of parameters to be
estimated and £, as the stochastic disturbance
term. Equation 2 describes the properties of
e, conditional on in form ation kn ow n at tim e
t-1, represented as I,.,. The disturbance £, is
conditionally normal, with mean zero and
variance ht. Note the explicit dependence of h
on time, as specified in equation 3, so that ht
is dependent on q lags of the squared realiza­
tions of £t. (The homoskedastic model is a
special case of the ARCH model when the
parameters
= 0 for j > 0.)
Equation 3 allows the variance h, to be a
function of past realizations of the distur­
bances, whereby the analysis can capture ex­
plicitly the possibility of phenomenon such as
the clustering in time o f large forecast errors.
Such a phenomenon would be implied by fin­
ding that large past values of £, lead to a
higher variance, h„ and hence to a greater
likelihood of a further large value of £, in the
future.
It is important to note that the uncondi­
tional distribution of £t is not normal. For in­
stance, the unconditional distribution of £,
can be leptokurtic. The conditional distribu­
tion of £, and hence y, is assumed to be nor­
mal, however, and thus the joint density is
merely the product of the conditional den­
sities. The log likelihood function (aside from
a constant term) is given by:
(4) L t (b,a) = 1,1, 1„ where
(5) l,(b,a) = (-1/2) [ log(ht) + £t ] .
V

(1) y, = xlb + £t
(2) £t|lt_, ~ N(0,h,)
’ These include, in addition to the ARCH model, the
GARCH or Generalized ARCH model and the ARCH-M
or GARCH-M for ARCH in Mean models. Relevant cita­
tions are to Engle (1983), Bollerslev (1986) and Engle,
Lilien and Robins (1987).


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Federal Reserve Bank of St. Louis

Estimation of the ARCH model proceeds by
choosing parameters b, a, that give the max2For instance, the t-distribution (with finite degrees of
freedom) is leptokurtic, as the tails of the distribution
contain more mass than the tails of a standard normal
distribution.

47

imum value for Lt(b,a), given the sample of T
observations. In other words, we search for
parameters b and a that maximize the proba­
bility of having observed the sample. Estima­
tion is carried out by a numerical optimiza­
tion procedure. In the case o f the ARCH
model, estimation is simplified somewhat by
the fact that the two sets of parameters a, b
are asymptotically independent, thereby
allowing for maximization of Lx(b,a) with
respect to each set of parameters separately.
The parameters a are restricted to be
positive. As mandated by theoretical con­
siderations, these restrictions preclude large
realizations of £t from driving the variance
negative. For stability, we also require that
the sum of the a ’s is less than one. This is a
necessary condition for restraining the un­
conditional variance to be finite.
In actual applications, it is desirable to be
able to test for ARCH before specifying and
estimating a model with ARCH. This is espe­
cially true because estimation of a model
with ARCH involves nonlinear methods. Engle
(1982) provides a straightforward test, the
ARCH test, based on the Lagrange multiplier
principle. As such, it requires only estimates
of the homoskedastic model. The null hypoth­
esis is homoskedasticity. The test is con­
ducted by squaring the residuals from the
homoskedastic model and regressing the
squared residuals on various lags of the
squared residuals. The test statistic is the
sample size times the R2 from this auxiliary
regression, distributed as chi-square with
degrees o f freedom equal to the number of
lags of the squared residuals included in the
auxiliary regression. Large values for the test
statistic lead to rejection of the null hypothe­

3This model has been used by Engle, Lilien and Robins
(1987) to estimate a model of the term structure in
which the risk premium is modeled as time-varying and
in which the risk premium affects the holding-period




sis of homoskedasticity and motivate estima­
tion of an ARCH specification.
An important generalization of the ARCH
model that we will employ in this paper is
the ARCH-M model, that allows for the vari­
ance term ht to enter the regression equation
for y t. The ARCH-M model is given by
(1’) y t = x;b + h;5 + £,
d
(2’) ejl,., ~ N(0,ht)
(3’) ht = a 0 + 1,1, a,£t.,,
2

a j > 0 for all j.

In equation (1’), d, a parameter to be esti­
mated, measures the effect of the conditional
variance on y t. The term h, 5 entering
equation 1 permits the conditional variance
o f the disturbance £, to affect the conditional
mean of y t. The form of the likelihood func­
tion for this model is the same as that given
in equations 4 and 5 above, though clearly
the parameter estimates will differ between
the two models.
The ARCH-M model, by explicitly incor­
porating variance measures in the equation
describing yt, facilitates estimation and statis­
tical inferences about the effects of variances
on means.3 For our purposes, the ARCH
model allows the explicit parameterization
and estimation of time-varying inflation
uncertainty, defined as the conditional var­
iance of the disturbance to an equation for
the inflation rate. Further, with the ARCH-M
generalization, we can estimate and test
hypotheses about the effect o f the timevarying inflation uncertainty on the condi­
tional means of macroeconomic variables
such as the inflation rate itself and the rate
of growth of output.

yield. The ARCH specification provides a way of
estimating the time-varying risk premium, and the
ARCH-M specification adds the ability to estimate the
effect of the risk premium on the expected yield.

.1 1 V /A llftllS T 1QRQ
11

48

Table 1
Trend and Unit Root Tests
Sample: 1/1960-11/1988
A. Unit root tests. Null hypothesis: Variable has a unit root.

Variable

Dickey-Fuller test
t-ratio

Augmented Dickey-Fuller test
t-ratio

log(p)
log(q)
log(m)
log(v)

2.87
-1 .2 9
5.99
-2 .7 5 *

0.13
-1 .0 6
3.43
-2 .1 0

Alog(p)
Alog(q)
Alog(m )
A log(v)

-4 .1 6 * * *
-8 .0 9 * * *
-6 .4 1 * * *
- 7 .5 2 ***

-2 .1 8
-5 .1 1 * * *
- 4 .2 3 * * *
-4 .3 9 ***

Approximate critical values for rejecting null hypothesis:
Significance
10%
5%
1%

Critical value
-2 .5 8 *
- 2 .8 9 **
-3 .1 7 * * *

B. Tests for time trends. Null hypothesis: Variable has a unit
root and no trend.

Variable
log(p)

log(q)
log(m)
log(v)

Dickey-Fuller
^-statistic
4.26
2.98
7.43
1.41

Approximate critical values for rejecting null hypothesis:
Significance
10%
5%
1%



FEDERAL RESERVE BANK OF ST. LOUIS

Critical value
5.47
6.49
8.73

49

mation on the hypothesis of a unit root in the
inflation rate can be garnered from the em­
pirical distributions o f the Dickey-Fuller test
statistic when the series has non-zero drift.
These distributions have been tabulated by
Schmidt (1988). For the inflation rate, the drift
component would lead to a modification o f the
critical values tabulated by Dickey-Fuller, so that
the 5 percent critical value is -2.11 and we re­
ject the hypothesis of a unit root in the inflation
series.7
The lag structure o f the model was specified
with the aid of the FPE (or Final Prediction Er­
ror) procedure.8 Estimates of the model chosen
under the assumption o f homoskedasticity are
provided in table 2. Diagnostic tests reported in
table 3 indicate no statistically significant serial
correlation and no significant evidence for a
structural break in 1973, the approximate mid­
point of the sample.9 The ARCH test, also re­
ported in table 3, rejects the null hypothesis of
homoskedasticity for the inflation equation.
There is little evidence for rejecting either a
constant conditional variance of the disturbance
to the output equation, or a constant covariance
o f disturbances to the output and inflation
equations.
Given that the results o f our specification
tests indicated ARCH, at least for the inflation
equation, we proceed to specify and estimate
such a model. Since our concern is the effect of
the variance of inflation on output growth, we
allow the variance of inflation to enter the
equations for inflation and output growth. As a
further check of the specification, we also allow
the variance of output growth to enter the in­
flation and output growth equations. That is,
w e specify an ARCH-M model. W e can then
directly estimate and test the hypotheses of
interest.
7Further evidence may be obtained by looking at related
series. Money and velocity are related to the inflation
series and output growth in a known way. We present
evidence in table 1 that M1 money growth and velocity
growth (defined as the first difference of the log of nominal
GNP minus the log of M1) do not contain a unit root.
Since the growth rate of velocity is, by definition, output
growth plus inflation minus money growth, the growth rate
of velocity should exhibit the properties of the component
series. As Engle and Granger (1987) write, “ Because of
the relative sizes of the variances, it is always true that the
sum of an l(0) and an 1(1) will be 1(1)” (p. 253). Thus,
velocity growth as a linear combination of inflation, money
growth and output growth should be 1(1), or integrated of
order 1, if any of the component series are 1(1). Since the
evidence indicates that the growth of velocity does not
contain a unit root, i.e., is l(0), this is indirect evidence
that inflation is also l(0). The only exception would be if




Table 2
VAR Model of Output Growth and
Inflation
Sample: 1/1960-11/1988
DQ, = .00909 + .164 DQt_, + .144 DQ, 2 - .310 DP,.,
(4.15)**

(1.74)

(1.57)

(2.40)**

DP, = .00173 + .413 DP,., + .219 DP,.; + .232 DP,.,
(2.05)**

(4.46)**

(2.21)**

(2.50)**

where the variance-covariance matrix of the disturbances is
estimated to be
Var(eq)
= 1.86 1 0 5
Cov(ep,eq) = -7 .9 2 10 7
Var(ep)
= 8.73 10 5
and the log likelihood value is 830.1.
** indicates significance at the 5 percent level

The bivariate ARCH-M model for inflation (dp)
and real output growth (dq) that we estimate is
given as:1
0
(1) dp, = / ,0 + p u dp,_, + Pi2dp,_2 + / 1 dpt.3
3
J3
+ P,4UP,l + Pl5Hq,. + £P
,.
(2) dq, = p 20 + / 2 dqtM + / 2 dq,_2 + p 2)dp,.,
?1
J2
/ ^ 2 4 ^ P ,t

+

^ 2 5 ^ ,1

+

£ q ,t

where
(3) HP/, =

+ a n [ Z I. t ( S < t.i /10]

+ a l2 [ I i=t(5-i)^,,-i /10]
the variables money, output and inflation were
cointegrated. Tests of cointegration failed to detect such a
relationship. Thus, we find that the inflation series is highly
persistent, but not nonstationary.
8This approach was first suggested by Akaike (1969). Hsiao
(1981) presents a strategy for applying the technique in a
multivariate setting.
9This year also approximately divides the sample into the
fixed or managed exchange-rate period before 1973 and
the relatively flexible exchange-rate period after 1973, as
well as dividing the sample into the pre-1973 period of no
oil price shocks and the post-1973 period marked by a
number of oil price shocks, both positive and negative.
10A dummy variable for the price-control period, taking the
value of 1 when the controls were in place during
111/1971 -1/1973, was found to be statistically insignificant.

.1111 Y /A llfilJ S T 1QRQ

50

Table 3
Diagnostic Tests on VAR
Sample: 1/1960-11/1988
A. Test for serial correlation
Output growth equation

Inflation equation

Order of
serial
correlation

Test
statistic

Marginal
significance

Test
statistic

Marginal
significance

1
2
3
4

0.15
0.15
2.22
2.33

.70
.93
.53
.68

1.29
1.61
2.18
2.18

.26
.45
.54
.70

B. Test for ARCH
Single equation tests

Output growth variance

Inflation variance

Covariance, output
growth and inflation

Order of
ARCH

Test
statistic

Marginal
significance

Test
statistic

Marginal
significance

Test
statistic

Marginal
significance

1
2
3
4
6
8

0.05
0.07
1.45
2.07
2.21
9.59

.82
.96
.69
.72
.90
.30

0.31
0.33
12.96
13.24
15.84
17.05

.58
.85
.00
.01
.02
.03

0.02
2.01
2.05
2.05
3.22
4.11

.88
.37
.56
.73
.78
.85

C. Test for structural change
Subsamples: l/1960-IV/1973, 1/1974-11/1988
Likelihood ratio test statistic: 4.1 ~ x2 (8)

(4) Hq„ = a2 + a 2l [
0

/10]

+ « 2 [ I i=t(5-i)£p,t-i /10]
2
and
I Hp Hp |
„
q
h, = I
I Hp H j
q
This specification of the variance process,
with the conditional variance modeled as a
declining lag structure in the squared residuals,
has been employed extensively in applications of
the ARCH model, but it is restrictive. For exam­
ple, this specification allows just one free para­
meter to be estimated on the four lagged
squared residuals and imposes a linearly declin­

http://fraser.stlouisfed.org/
Federal Reserve Bank ofI St. F S F R V F R A N K O F S T I D IJIR
FFnFRA
R Louis

Marginal significance .85

ing lag structure. Therefore, other specifications
of HPt and Hq)t were tried. One alternative spec­
/
ification had separate coefficients on each of the
four lags of £P and £P)t. This alternative did in­
;t
crease the estimated log likelihood, but only the
coefficients on £Pi,_3 and £q;t_3 were statistically
significant. Further, a likelihood ratio test bet­
ween the model with only £Pit_3 and £q;t_3 affec­
ting the variance of inflation and output
growth, respectively, and a model with all four
lags of £P and £* in the respective variance
;t
equations, indicated no support for the addi­
tional lags. Also, lagged HP and Hq;t were added
it
to the variance specifications (yielding the
generalization of the ARCH model called GARCH)
and again the estimated log likelihood function
did not increase significantly.

51

Table 4
ARCH-M Model of Output Growth and Inflation
Sample: 1/1960-11/1988______________________
DQ, = -.0 1 0 9 + .172 DQ,., + .149 DQ,.; - .410 DP,., + 2.53 Var(eq) ’ - .46 Var(ep) ’
(.54)
(2.33)
(2.33)
(3.55)
(.93)
(.13)
DP, = -.0 0 2 7 + .384 DP, , + .205 DP,.2 + .245 DP,., + .188 Var(eq) 5 + .696 V ar(ep)5
(.38)
(5.17)
(2.79)
(3.63)
(.20)
(.48)
where the variance-covariance matrix of the disturbances is estimated to be:

Var(eq,) = 6.99

4
4
10"! + .131 X [(5 - i)eq2 /10] + .203 S [(5 - ijep2 /10]
,_,
,,,
(1.85) i = 1
(.72) i = 1

CoV(ep, eq.) = 3.39

Var(ep,) = 1.40

10~7

4
4
10'! + .244 1 [(5-i) ep!,_, /10] + .0000 I [(5 -i)e q 2 /10]
,_,
(2.67) i = 1
(.00) i = 1

and the log likelihood is 835.9.
Likelihood ratio test against homoskedastic VAR: 11.6 ~ X2(8) (Marginal significance .17)

Estimates of the model in equations 1-4 are
reported in table 4.” The coefficients on the
conditional variance terms entering the output
growth and inflation equations are insignificant
at the 5 percent level. In addition, the lags of
the output growth residuals have an insignifi­
cant coefficient in the inflation variance equa­
tion. Moreover, the lags of the inflation resid­
uals have an insignificant coefficient in the out­
put variance equation. Finally, a likelihood ratio
test of the model reported in table 4 against the
homoskedastic model reported in table 2 in­
dicates that the null hypothesis, that the
homoskedastic model is a valid restriction to the
ARCH-M model, cannot be rejected at any
reasonable significance levels. These results in­
dicate that inflation uncertainty, measured as
the conditional variance of inflation from an
ARCH specification, does not have a significant
effect on output growth.

" T o estimate the ARCH-M model, indeed all the ARCH
estimates reported in this paper, the ARCH parameters
a n , a n, a2i and oJ were restricted to be non-negative. The
2
shaded insert discusses the rationale for this restriction.

To determine the sensitivity o f the results to
the model specification, we modified the model
to include only the third lag o f the squared in­
flation residual in the inflation variance equa­
tion and only the third lag o f the squared out­
put growth residual in the output variance
equation. This specification was chosen from a
preliminary model including separate coeffi­
cients on each of the four lags of the squared
residuals in each variance equation. Estimates
are reported in table 5. The estimated log like­
lihood function of this specification is nearly
equivalent numerically (and certainly not statisti
cally distinguishable) from the more general
model. A likelihood ratio test against the homo­
skedastic VAR model leads to rejection at the 5
percent significance level of the null hypothesis
that the homoskedastic VAR restrictions are cor­
rect relative to the ARCH-M alternative.1
2

drawn in this paper, is that considerable pretesting was
done in specifying both the VAR and ARCH models. This
greatly complicates the inference problem. A good in­
troduction to this issue is provided in Judge, et al (1988).

12One caveat to the interpretation of the likelihood ratio tests
reported here, indeed to most of the statistical inference




.1111 Y / A IIR IIR T 1QRQ

52

Table 5
ARCH-M Model of Output Growth and Inflation
Sample: 1/1960-11/1988_________________________________________
DQ, = - .0186 + .136 DQ,., + .125 DQ,.; - .3 8 4 DP, ,
(0.89) (2.00)
(2.01)
' (4.29)
+ 2.98 [Var(eq, )] ! + .474 [V ar(ep,)] 1
(1.22)
(0.46)
DP, = .0047 + .345 DP,., + .248 DP, 2 + .296 DP, ,
(0.89)
(5.73)
(4.01)
(4.61)
-

.582 [Var(eq, )] 5 + .493 [Var(ep, )] ’
(0.98)
(1.23)

where the variance-covariance matrix of the disturbances is estimated to be
Var(eq,) = 7.45 10 '5 + .100 eq,J_,
(2.82)
Cov(eq,,ep,) = 1.16 10'*
Var(ep,) = 1.26 10‘ 5 + .301 ep,J ,
(6.31)
and the log likelihood value is 840.9.
Likelihood ratio test against homoskedastic VAR: 21.6 ~ X2(6) (Marginal significance .001)
Likelihood ratio test against ARCH VAR: 4.0 ~ X2(4) (Marginal significance .21)

The estimated parameter values and the asym­
ptotically valid t-statistics reported in table 5
provide further information about the
hypotheses of interest. Table 5 shows that the
variance o f inflation had a positive but statisti­
cally insignificant effect on the rate of growth
of output and a positive but statistically in­
significant effect on the rate of inflation. These
results provide no support for the hypotheses
under investigation. W e also find that the
variance of output has an insignificant positive
effect on the rate of growth of output and an
insignificant negative effect on the rate of
inflation.
Table 5 also reports estimates of the variance
process. The third lag of squared realizations of
the stochastic error in the inflation equation has
a statistically significant effect on the condition­
al variance of the inflation error. In contrast,
the lagged squared realization of the stochastic
error in the output growth equation has a
statistically insignificant effect on the condi­
tional variance of output growth.
Table 5 provides no support for the hypoth­
eses that inflation uncertainty, measured as the

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F P n F R A RFSFR

conditional variance o f inflation forecast errors,
has a negative effect on output growth. Indeed,
o f the six coefficients estimated for the ARCH-M
model that were not estimated for the
homoskedastic VAR model, five w ere statistically
insignificant, including all of those measuring
the effect of the conditional variance o f inflation
on the inflation rate and the rate o f output
growth. This observation leads to the suspicion
that it is only the ARCH process itself that is im­
portant in the rejection of the VAR restrictions
by the likelihood ratio test, a suspicion confirm­
ed by estimation of an ARCH variant o f the
model in table 6. The ARCH model includes the
conditional variance specification as in table 5,
but does not allow the conditional variance to
affect the conditional mean of the inflation pro­
cess or the rate of output growth. Estimates of
this model are reported in table 6.
In table 6 we see that the likelihood value is
almost as high as that reported in table 5. A
likelihood ratio test does not reject the null
hypothesis that the ARCH model is a valid
restriction to the ARCH-M model. Moreover, a
likelihood ratio test of the null hypothesis of the

53

Table 6
ARCH Model for Output Growth and Inflation____________
DQ, = .00947 + .157 DQ„, + .129 DQ,_2 -.3 5 3 DP, ,
(6.55)
(2.42)
(2.09)
(3.97)
DP, = .00147 + .352 DP,., + .262 DP,_2 + .268 DP,_,
(2.67)
(5.84)
(4.26)
’ (4.24)
where the variance-covariance matrix of the disturbances is estimated to be
Var(eq,) = 7.43 10'5 + .125 eq,2.,
(2.32)
Cov(eq, ept) = 1.10 10'6
Var(epJ = 1.30 10'! + .285 ep,2 3
(5.76)
and the log likelihood value is 838.9.
Likelihood ratio test against homoskedastic VAR: 17.6 ~ X2(2) (Marginal significance .0001)

homoskedastic VAR model against the ARCH
alternative leads to a strong rejection of the
null. It seems that the inflation-output growth
process has ARCH disturbances, but that the
changing conditional variance does not feed
back to the inflation rate or the rate of output
growth.

(1988), all report either difficulty in detecting
ARCH in the inflation equation or estimates of
the ARCH conditional variance that are very flat
over this period. This study identifies an ARCH
inflation process, but the process may not have
been sufficiently variable to generate precise
measures of the effect of the conditional vari­
ance of inflation on output growth.

FURTHER PROBLEMS AND
PROSPECTS

Because this study is limited to investigating
the first two moments of the bivariate inflation
rate-output growth rate process, it abstracts
from some potentially important issues, one of
which is the importance of relative energy pri­
ces after the 1973 oil price shock. Of perhaps
more importance is the neglect of a measure of
the mean and variance of the policy stance of
the monetary authority. Uncertainty about the
future inflation rate can arise from several
sources, including uncertainty about future gov­
ernment policy or future values of exogenous
variables impinging on the inflation rate. A
measure of government policy, perhaps by some
monetary aggregate, might be useful to supple­
ment results from the bivariate system reported
here.

The evidence presented here lends no support
to the hypothesis that uncertainty about the fu­
ture inflation rate leads to a reduction in the
rate of output growth. Further, this evidence, in
accord with that provided by both Katsimbris
and Thornton using an alternative methodology,
casts doubt on the existence and relevance of
the hypothesized positive relation between the
rate of inflation and the uncertainty about fu­
ture inflation.
One possible explanation for this lack of sup­
port is that the inflation rate was largely predic­
table over our sample. Indeed, it is difficult to
detect much of an ARCH effect in the inflation
data over this span, especially when the infla­
tion forecasting equation is supplemented with
other exogenous variables, most notably relative
energy prices. Several recent studies, including
Engle (1983), Holland (1984), Cosimano and
Jansen (1988), and Rich, Kanago and Raymond



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tion,” Annals of the Institute of Statistical Mathematics
(January 1969), pp. 243-47.

JULY/AUGUST 1989

54

Blejer, Mario I., and Leonardo Leiderman. “ On the Real Ef­
fects of Inflation and Relative-Price Variability: Some Em­
pirical Evidence,” Review of Economics and Statistics
(November 1980), pp. 539-44.
Bollerslev, Tim. “ Generalized Autoregressive Conditional
Heteroskedasticity,” Journal of Econometrics (April 1986),
pp. 307-27.
Cosimano, Thomas F., and Dennis W. Jansen. “ Estimates of
the Variance of U.S. Inflation Based upon the ARCH
Model: Comment,” Journal of Money, Credit, and Banking
(August 1988, Part 1), pp. 409-21.
Coulson, N. Edward, and Russell P Robins. “Aggregate
.
Economic Activity and the Variance of Inflation: Another
Look,” Economic Letters (January 1985), pp. 71-75.
Cukierman, Alex. “ Relative Price Variability and Inflation: A
Survey and Further Results,” Carnegie-Rochester Series on
Public Policy (Autumn 1983), pp. 103-58.
Cukierman, Alex, and Paul Wachtel. “ Differential Inflationary
Expectations and the Variability of the Rate of Inflation:
Theory and Evidence,” American Economic Review
(September 1979), pp. 595-609.
Dickey, David A., and Wayne A. Fuller. “ Likelihood Ratio
Statistics for Autoregressive Time Series with a Unit Root,”
Econometrica (July 1981), pp. 1057-72.
_______ . “ Distribution of the Estimators for Autoregressive
Time Series with a Unit Root,” Journal of the American
Statistical Association (June 1979), pp. 427-31.

Gale, William A. “ Temporal Variability of United States Con­
sumer Price Index,” Journal of Money, Credit, and Banking
(August 1981), pp 273-97.
Godfrey, L. G. “ Testing Against General Autoregressive and
Moving Average Error Models when the Regressors In­
clude Lagged Dependent Variables,” Econometrica
(November 1978), pp. 1293-1301.
Hafer, R. W. “ Inflation Uncertainty and a Test of the Fried­
man Hypothesis,” Journal of Macroeconomics (Summer
1986), pp. 365-72.
Holland, A. Steven. “ Does Higher Inflation Lead to More
Uncertain Inflation?” this Review (February 1984), pp.
15-26.
Hsiao, Cheng. “Autoregressive Modelling and Money-lncome
Causality Detection,” Journal of Monetary Economics
(January 1981), pp 85-106.
Judge, George G., R. Carter Hill, William E. Griffiths, Helmut
Lutkepohl, and Tsoung-Chao Lee. Introduction to the Theory
and Practice of Econometrics (John Wiley and Sons, 1988).
Katsimbris, George M. “ The Relationship between the Infla­
tion Rate, Its Variability, and Output Growth Variability:
Disaggregated International Evidence,” Journal of Money,
Credit, and Banking (May 1985), pp. 179-88.
Logue, Dennis E., and Richard J. Sweeney. “ Inflation and
Real Growth: Some Empirical Results,” Journal of Money,
Credit, and Banking (November 1981), pp. 497-501.

Engle, Robert F. “ Estimates of the Variance of U.S. Inflation
Based upon the ARCH Model,” Journal of Money, Credit,
and Banking (August 1983), pp. 286-301.

Marshall, Alfred. “Answers to Questions on the Subject of
Currency and Prices Circulated by the Royal Commission
on the Depression of Trade and Industry,” Official Papers of
Alfred Marshall (London: McMillan, 1926).

_______ . “Autoregressive Conditional Heteroskedasticity
with Estimates of the Variance of United Kingdom Infla­
tion,” Econometrica (July 1982), pp. 987-1008.

Mullineaux, Donald J. “ Unemployment, Industrial Production,
and Inflation Uncertainty in the United States,” Review of
Economics and Statistics (May 1980), pp. 163-69.

Engle, Robert F., and C. W. J. Granger. “ Co-Integration and
Error Correction: Representation, Estimation, and Testing,”
Econometrica (March 1987), pp. 251-76.

Okun, Arthur M. “ The Mirage of Steady Inflation,”
Brookings Papers on Economic Activity (2: 1971), pp.
485-98.

Engle, Robert F., David M. Lilien, and Russell P. Robins.
“ Estimating Time Varying Risk Premia in the Term Struc­
ture: The ARCH-M Model,” Econometrica (March 1987), pp.
391-407.

Pagan, A. R., A. D. Hall, and P. K. Trivedi. “Assessing the
Variability of Inflation,” Review of Economic Studies (Oc­
tober 1983), pp. 585-96.

Evans, Paul. “ Price-Level Instability and Output in the U.S.,”
Economic Inquiry (April 1983), pp. 172-87.
Fischer, Stanley. “ Towards an Understanding of the Costs of
Inflation: 1 ,’’Carnegie-Rochester Conference Series on
1
Public Policy (Autumn 1981), pp. 5-42.
Friedman, Milton. “ Nobel Lecture: Inflation and Unemploy­
ment,” Journal of Political Economy (June 1977), pp. 451-72.
Froyen, Richard T., and Roger N. Waud. “An Examination of
Aggregate Price Uncertainty in Four Countries and Some
Implications for Real Output,” International Economic
Review (June 1987), pp. 353-72.


http://fraser.stlouisfed.org/
FEDERAL RESERVE BANK OF ST. LOUIS
Federal Reserve Bank of St. Louis

R ich, R o b e rt W ., B ry c e K anago, a n d J e n n ie R a ym o n e . “ N ew

Evidence on the Variance of U.S. Inflation Based Upon the
ARCH Model,” Vanderbilt University Working Paper No.
88-W06, October 1988.
Schmidt, Peter. “ Dickey-Fuller Tests with Drift,” unpublished
manuscript, Michigan State University, June 1988.
Taylor, John B. “ On the Relation between the Variability of
Inflation and the Average Inflation Rate,” CarnegieRochester Series on Public Policy (Autumn 1981), pp. 57-85.
Thornton, John. “ Inflation and Output Growth: Some Time
Series Evidence, A Note,” American Economist (Fall 1988),
pp 55-58.

55

Daniel L. Thornton
Daniel L. Thornton is an assistant vice president at the Federal
Reserve Bank of St. Louis. David Kelly provided research
assistance.

Tests of Covered Interest Rate
Parity

R
ECENTLY there has been considerable in­
terest in and investigations of whether the cov­
ered interest parity (CIP) holds. At the microeco­
nomic level, CIP is important because is it a
direct consequence of covered interest arbi­
trage. Its failure to hold would suggest 1) that
markets are inefficient in the sense that traders
do not take advantage of known profit oppor­
tunities, 2) that legal restrictions and regula­
tions, such as capital controls, exist or 3) that
costs have been unaccounted for, such as in­
dividual borrowing constraints or differences in
political risks across countries.1
At the aggregate level, CIP is important be­
cause it implies that interest rates and spot and
forward exchange rates are related in a par­
1ln a sense, there are no tests of covered interest ar­
bitrage. It is axiomatic! If tests revealed that CIP was
violated so that known riskless profit opportunities were
being ignored for long periods of time, such results would
undoubtedly be explained in various ways, such as alleg­
ing that relevant costs were ignored.
2lf CIP does not hold, it does not necessarily mean that
there is no other exact linear relationship among these
variables or their subsets. It only means that the nature of
the relationship would be uncertain.
The policy implications of CIP may be especially important
for small open economies where the U.S. interest rate can
effectively be taken as exogenous. If CIP holds, attempts
by such countries' policymakers to move their domestic in­




ticular way. Indeed, this relationship is fre­
quently imposed in open-economy macroeco­
nomic models. Finding that the relationship
among these variables implied by CIP does not
hold would leave their relationship uncertain.2
Generally, there have been two types of em­
pirical investigations of CIP. The first are de­
signed to determine whether markets are effi­
cient in the sense that all known profit oppor­
tunities are arbitraged.3 These tests investigate
whether the actual forward premium deviates
from that implied by CIP by more than the
transaction costs using the most efficient ar­
bitrage. The issues are whether the forward
premia ever exceed estimates of the transaction
costs and, if they do, whether they persist. The
terest rates will immediately get translated into their ex­
change rates and vice versa. This is particularly true if the
forward rate is an efficient predictor of the future spot rate.
Even if this is not the case [for example, see Chrystal and
Thornton (1988)], both forward and spot rates would likely
be affected since they tend to move together. Further­
more, if CIP holds, such economies may be influenced
more by external events, such as changes in U.S.
monetary policy, than if CIP does not hold. See Dufey and
Giddy (1978) and Kubarych (1983) for a discussion of
some of the policy implications.
3For example, see Deardorff (1979), Callier (1981),
Bahmani-Oskooee and Das (1985) and Clinton (1988).

JULY/AUGUST 1989

56

evidence is that frequent violations of CIP oc­
cur, but do not persist.4
The second tests are designed to examine
whether CIP holds on average.5 Specifically,
they test whether domestic and foreign interest
rates and spot and forward exchange rates res­
pond in a way consistent with CIP to economic
news that affects each market individually.
This article provides a generic representation
of the latter tests and shows that, under ap­
propriate conditions, similar tests can be per­
formed that do not require testing the markets'
response to particular sets of information. In so
doing, this article extends empirical investiga­
tions to a larger set of countries and over a
longer time period.6

DOES CIP HOLD ON AVERAGE?
CIP is a direct consequence of covered in­
terest arbitrage.7 In the absence of transaction
costs, the CIP condition requires that
(1) ln (l+ i,)- ln (l + i,*)-lnF,+ lnS, = 0,
where i* and i are the foreign and U.S. interest
rates, respectively, and F, and St are the for­
ward and spot foreign exchange rates (dollars
per unit of foreign currency), respectively.8 The
maturity of the U.S. and foreign assets and the
forward contract are identical. Moreover,
foreign and U.S. securities are assumed to be
identical except for the currency in which
future payments are denominated.

The Markets’ Reactions to
Econom ic New s
Equation 1 asserts that a particular linear
combination of these variables is zero in the
4Much of this literature shows that the difference between
the actual forward premium and that implied by CIP often
falls outside of the neutral band given by transaction
costs, e.g., see Bahmani-Oskooee and Das (1985) and
Clinton (1988). For example, Clinton finds “ that while the
longest sequence of profitable trading opportunities is five
observations [days], the most common run does not ex­
tend beyond a single observation. Thus, in general, profit
opportunities appear to be both small and short-lived, even
though they are not rare.” See Clinton (1988), p. 367. He
suggests, however, that it is unlikely that the quality of the
data will ever be sufficient to provide a rigorous test of
market efficiency, i.e., that there are no unexploited profit
opportunities.
5To date, this work has relied exclusively on investigating
markets’ responses to money announcements. See Roley
(1987), Husted and Kitchen (1985) and Tandon and Urich
(1987).
6Roley (1987) considers Japan and only the Gensaki rate,
while Husted and Kitchen (1985) use data for Canada and


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absence of transaction costs. Other linear com­
binations of the variables need not equal zero.
Tests of CIP that rely on the markets' reactions
to economic news or events make use of the
fact that the particular linear combination of
asset prices implied by CIP is zero. To see this,
assume that U.S. and foreign interest rates and
the spot and forward exchange rates can be
represented by the following equations:
(2) Aln(l + it) = a, + bjn,,
(3) Aln(l + i *) = a2 + b2
nt,
(4) AlnF, = a3 + b 3 and
n„
(5) AlnS, = a4 + b4
n„
where nt denotes the new information that
becomes available in the interval over which the
t,h observation is made. Each asset may respond
differently to the same news.
Investigations of CIP rely on testing the
markets’ responses to specific information by
identifying a particular component of nt and by
making an assumption about the stochastic pro­
perties of the rest. One approach is to estimate
the equations
(6) Aln(l + it) = a, + d,I, + e ]t,
(7) Alnd + i,*) = a2 + d2 + e2
I,
„
(8) AlnF, = a3 + d3 + e3 and
I,
t,
(9) AlnS, = a4 + d4 + e4
I,
„
where I, denotes specific information that
becomes available during the period in which
the tth observation is made, and eit = (bje,)
denotes an individual market’s response to all
other information made available during the inGermany. Roley’s data covers the period from October 6,
1977, through May 30, 1985, while Husted and Kitchen’s
data covers the period from February 8, 1980, through
August 27, 1982.
7Deardorff (1979) shows that covered interest arbitrage re­
quires that the forward rate deviate from that implied by
CIP by no more than |t + t* + t, + t,|, where t, t*, t s and t,
are the transaction costs (proportional to the size of the
transaction) in the United States and foreign securities
markets and the spot and forward foreign exchange
markets, respectively. He also shows that the “ neutral
band” is narrower than this if “ one-way” arbitrage is con­
sidered. This band has been further narrowed by Callier
(1981), Bahmani-Oskooee and Das (1985) and Clinton
(1988).
8AlnF, and AlnS, are weighted by an annualizing factor
equal to 12 divided by the number of months in the for­
ward contract.

57

terval, e,.9 Estimating this equation system in­
volves the additional assumption that E(et) = 0.
Equations 6-9 are estimated and the restrictions
d.1 - d, - d, + d. = a, - a, - a, + a. = 0
2
3
4
1
2
3
4
are tested. If CIP holds, the intercept and slope
coefficients of equations 6-9 will satisfy the par­
ticular homogenous linear restriction implied by
CIP.
An asymptotically equivalent test can be per­
formed by estimating the equation
(10) Aln(l + it) - Aln(l + i,*) - AlnF, + AlnS, = a +
dl, + f„
and testing the hypothesis that a = d = 0. In
this form, the error term, f, = e lt - e2 - e3 +
t
,
e4 vanishes under the null hypothesis that the
t,
markets respond to the new information in a
way consistent with CIP, that is, b , - b 2
- b 3+ b4= 0. A more satisfactory interpretation
of f„ therefore, comes from recalling that equa­
tion 1 holds identically only in the absence of
transaction costs, so that f, represents the
change in the log of these costs.1
0
Another interpretation of f, stems from the
fact that the observations used to examine CIP
generally are not taken at the same time. To il­
lustrate the effect of this, assume that observa­
tions on U.S. and foreign interest rates are
taken at 3 a.m. EST, while the observations on
the spot and forward exchange rates are taken
at 11 a.m. EST. The change in interest rates is
measured from 3 a.m. before the release of the

9This specification assumes that there is no idiosyncratic in­
formation that affects one market but not the others. It is
difficult to see how such idiosyncratic information could
exist in the reduced-form equations 6-9, or how such an
assumption could hold under the null hypothesis. For a
model that looks at the implications of non-synchronous
trading using the assumption of idiosyncratic information,
see Lo and MacKinlay (1989).
10lf transaction costs vary symmetrically around a non-zero
mean, the change in the log of transactions costs will not
vary symmetrically around zero. This stems directly from
the concavity of the log function. This means that if the
distribution of transactions cost is symmetric, the distribu­
tion of the log of the change in the transaction costs will
be asymmetric.
11Since the markets may eventually respond to all informa­
tion, the non-synchronous data implies that changes in
asset prices taken at different periods of time will be
serially correlated. In terms of equations 6-9, this means
that the error terms will be cross-sectionally autocor­
related. In terms of equation 10, this implies that f, will be
serially correlated. Indeed, when equation 10 was
estimated using all of the daily data, this was the case.
The results reported in this paper are for estimates of
equation 10 only on days when the specific information
was available. Not surprisingly, in nearly all cases, these
error terms were serially independent.




specific information to 3 a.m. after the informa­
tion is released. The change in the exchange
rates is defined similarly. Under these assump­
tions, changes in the interest and exchange
rates reflect information that is common to
both, as well as the information unique to each.
For example, changes in the interest rates will
reflect the markets’ reaction to information be­
tween 3 a.m. and 11 a.m., but this information
will not necessarily be reflected in the change
in the exchange rates. Likewise, changes in the
exchange rates reflect the markets' reaction to
information from 3 a.m. to 11 a.m. the next day,
but this information will not be reflected in the
changes in the interest rates. Consequently, the
error term of equation 10 comes potentially
from differences in the information in the asset
prices due to non-synchronous data, as well as
from changes in the log of transaction costs.1 It
1
could not come from the common information
because, as we have already noted, this compo­
nent of the error term vanishes under the null
hypothesis.1
2

Tests o f the Linear Restrictions
Im plied b y CIP
A comparison of equations 6-9 and equation
10 reveals another interesting aspect of these
tests. The hypothesis that a = 0 is a test that
the linear combination implied by CIP, but not
accounted for by I„ is zero. If CIP holds, this
will be true at all times, not simply when the

12For simplicity, let Ai, = Aln(1 + i*) - Aln(1 + i*) and AR, =
AlnF, - AlnS,, so that CIP implies that Ai, - AR, = 0,
under the simplifying assumption of zero transaction costs.
Now let Ai, = < + o ^ l, + d0 +
*o
e,
and AR, =
+ /Jilt
+ d , + d
,£
,co,. Here, £ denotes the information not con­
,
tained in I, that is reflected in both interest rates and ex­
change rates. rj, denotes the information reflected in Ai,
that is not reflected in AR, and to, denotes the information
reflected in AR, that cannot be reflected in Ai,. Since there
is little justification to do otherwise, it is assumed that Ai,
responds the same to £( and rj{; likewise, the response of
AR, is the same for £, and to,. Note that if the response of
these markets to information is consistent with CIP, i.e.,
(°, - P „) = (“ . - P,) = (< „ - <*,) = 0, Ai, - AR, differs
5
from zero by do rj, - d,co,, the response to the nonsynchronous information. [Estimation requires a normaliza­
tion; however, this does not affect the conclusion],
Roley (1987), p. 65, asserts that, “ when testing whether
the responses of these variables to a specific piece of new
information are inconsistent with covered interest parity,
the exact alignment of the data is not necessary.” The
above illustration demonstrates that this is not necessarily
the case. The error term of equation 10 and, hence, the
precision with which the parameters can be estimated is
clearly dependent on the degree to which the data are
synchronous.

.1111 V / A I I R I I S T 1QRQ

58

markets react to specific information. Tests of
CIP using the markets’ response to specific in­
formation generally are performed using data
only for days when the information is released;
however, evidence on CIP can be obtained dir­
ectly from the changes in these four asset
prices even if information that the markets res­
pond to is not identified or is not available.
Rejecting the hypothesis that this linear com­
bination of changes in asset prices is zero is
strong evidence against CIP. A failure to reject
the null hypothesis is not strong evidence in
favor o f it, however, because the same could be
true for other linear combinations of these asset
prices. If asset prices follow a random walk
without drift, the same could be true for any
linear combination of the change in these asset
prices, not simply for the linear combination im­
plied by CIP. Consequently, stronger evidence
consistent with CIP would be obtained if the
null hypothesis is not rejected for the linear
combination implied by CIP, but is rejected for
other linear combinations.

EMPIRICAL EVIDENCE
Tests of CIP using the markets’ response to
specific information have relied exclusively on
their response to money announcements. In this
section, the broader test outlined above is ap­
plied to daily data for the period from October
5, 1979, to September 14, 1988. Tests of CIP us­
ing the markets’ response to information in the
form o f money announcements also are under­
taken. The reported tests using money an­
nouncements are only for days on which there
was an announcement.
The data used in this study are one-, three-,
six- and twelve-month Eurocurrency rates for
the United States (U.S.), United Kingdom (U.K.),
Canada (CA), Germany (GR), Switzerland (SW),
France (FR) and Japan (JA), the corresponding
forward exchange rates and the spot exchange
13The interest rates are from the BIS data tape at the Board
of Governors of the Federal Reserve System. These are
bid rates taken from several markets. The Money Market
Service survey data through 1986 were provided by Graig
Hakkio.
14For example, this is true of Tandon and Urich (1987),
Husted and Kitchen (1985) and Belongia and Sheehan
(1987). Deaves, Melino and Pesando (1987), however,
show that the significance of expected money on U.S. in­
terest rates is due to a few outliers, while Belongia, Hafer
and Sheehan (1986) have shown that the response of U.S.
interest rates to anticipated money is very sensitive to the
sample period. In any event, the presence or absence of



FEDERAL RESERVE BANK OF ST. LOUIS

rates. Anticipated changes in M l are the median
forecasts from the Money Market Services sur­
vey, and the forecast error is the difference be­
tween the forecasted change and the change in
first-announced M l. The interest rates are
reported as o f 3 a.m. EST and the exchange
rates are reported as o f 11 a.m. EST. The in­
terest rates are bid rates from the Bank of In­
ternational Settlements.1 The exchange rates
3
are the average o f bid and ask rates from the
London foreign exchange market.
The test of CIP using money announcements
involves estimating the equation
(11) A ln (l+ it) - Aln(l + i*) - AlnFt+ AlnS, = a +
d,UMt + d2
ME, + et.
Both anticipated money, ME, and unanticipated
money, UM, are included because, as a number
o f researchers found, these asset prices re­
sponded in a statistically significant way to both
anticipated and unanticipated changes in the
money stock.1 The finding that the individual
4
markets respond significantly to ME is, itself,
frequently taken as evidence that the markets
are informationally inefficient.1 For the purpose
5
of testing for CIP, however, the only relevant
issues are whether the markets respond to ME
and whether the responses net out in a way
consistent with CIP.
It has been common to estimate equations like
6-9 or equation 11 over different subsamples to
see if the markets’ response to money announce­
ments changes in response to changes in the
Federal Reserve’s operating procedure.1 Since
6
the interest here is only in testing for CIP,
however, there is no need to split this sample
for this purpose: the difference in magnitude of
the market’s response is unimportant.
It is important to split the sample for another
reason, however: the null hypothesis that d 1 =
d2 = 0 will not be rejected either if the markets
do not respond to money announcements or if
ME from equation 10 is likely to have little bearing on the
test because ME and UM are nearly orthogonal. Further­
more, while the evidence on the importance of ME may be
weak, the cost in terms of lost efficiency for including it is
small.
15While this type of test is generally valid, there are some
important limitations. For a discussion of these, see
Pesaran (1987), especially chapter 8.
16ln October 1982, the Fed switched from a nonborrowedreserves to a borrowed-reserves operating procedure. See
Thornton (1988a) for a discussion of the borrowed-reserves
operating procedure.

59

Table 1
General Tests for CIP; October 5, 1979, through September 14, 1988
Country

One Month
T,

t2

Three Month
t3

T,

t2

Six Month
t3

T,

T2

Twelve Month
t3

T,

T2

t3

CA

- .0 0

-.2 7

- .3 9

.02

-.4 5

- .4 6

.01

- .4 5

-.5 2

.01

- .2 0

-.4 1

SW

.02

- .1 2

-.0 1

.01

- .3 4

- .0 3

.02

- .3 2

-.0 6

.00

- .3 2

-.0 9

GR

.05

- .2 6

- .1 8

.03

- .4 2

-.2 1

.04

- .4 6

-.2 4

.05

-.4 6

- .2 8

FR

.01

- .1 0

-1 .2 3

.00

- .2 3

-1 .2 6

-.0 0

- .2 9

-1 .3 0

.00

- .2 8

-1 .3 1

UK

-.0 1

-.2 1

- .7 7

- .0 2

- .3 7

- .7 9

.00

- .3 8

-.8 2

- .0 0

- .3 2

- .8 4

-.2 1

1.57

.00

- .2 7

1.56

.01

- .4 0

1.55

.00

-.0 1

.10

JA

.03

T i: Ain (1 +i,) - Ain (1 + i*) - AlnF, + AlnS, = 0
T2: Ain (1 + i.) + Ain (1 + i* ) + AlnF, - AlnS, = 0
T3: Ain (1 +i,) + Ain (1 + i* ) + AlnF, + AlnS, = 0

their response is consistent with CIP on
average.
It is well-documented that the markets,
especially U.S. interest rates, responded in a
statistically significant way to unanticipated
changes in the money stock through the early
part of 1984. Their response after early 1984 is
more problematic, however. Consequently, the
period was divided into two subperiods: Oc­
tober 5, 1979, to J a n u a ry 29, 1984, a n d J an u ary
30, 1984, to September 14, 1988. 1 Equations in
7
the form of 6-9 were estimated for both per­
iods, and both anticipated and unanticipated
changes in the money stock had a statistically
significant effect only during the first subperi­
od.1 Consequently, estimates of equation 11 are
8
presented only for the period ending in 1984.
Results for the more general test are presented
for the entire period.
17For example, Dwyer and Hafer (1989) found that essential­
ly there was no statistically significant response of U.S. in­
terest rates to money announcements after July 1984.
More importantly, estimates of equations of the form of 6-9
found no statistically significant response to either an­
ticipated or unanticipated changes in the money stock dur­
ing the second subperiod.
18Estimates of equations like 6-9 for the first subperiod in­
dicate that the markets frequently responded significantly
to anticipated changes in the money stock. This was the




THE RESULTS
Table 1 reports t-statistics for tests of various
linear combinations o f changes in U.S. and
foreign interest rates and spot and forward ex­
change rates, including the linear combination
implied by CIP. The t-statistic for the linear
combination implied by CIP is denoted T,; tstatistics for two other linear combinations of
the changes in these asset prices are denoted T 2
and T,. The alternative linear combinations are
interesting because T 2 is the t-statistic for a test
of a linear combination of changes in these
asset prices that is correlated with that implied
by CIP, while T 3 is the t-statistic for a test of a
linear combination that is orthogonal to that im­
plied by CIP.1 Consequently, if the null
9
hypothesis that CIP holds cannot be rejected, it
would not be surprising to find that T 3> T 2> T r
case for U.S. and Canadian interest rates at all maturities,
except the 12-month maturity for Canada, and is generally
true for both the forward and spot exchange rates. It is not
true for other foreign interest rates, with the exception of
the one-month Euroyen rate.
19Let R , R and R denote the three restrictions on the vec­
tor of changes in’ asset prices that correspond with T,, T;
and T Jf respectively, e.g., R, = (1, - 1 , - 1 , 1 ) . Then the
correlation between R, and R; is - .50, while R, and R3
are uncorrelated.

JULY/AUGUST 1989

60

In every instance, the t-statistics for the test
of CIP are extremely small, suggesting that CIP
holds on average over the sample period. While
supportive of CIP, the fact that the null hypoth­
esis cannot be rejected is not compelling evi­
dence because the same could be true of other
linear combinations of these variables. Tests of
other linear combinations produce t-statistics
that are considerably larger than those for that
implied by CIP, although in no case was the null
hypothesis rejected. In the majority o f cases,
however, T 3> T 2.

Tests o f the R esponse to Specific
Inform ation
Estimates of equation 11 along with the t-statistics for tests o f linear combinations o f the
changes in these variables for the period from
October 5, 1979, through January 29, 1984, are
presented in table 2.2 Two F-statistics are
0
reported. F, is a test that all of the coefficients
are zero. F2 is a test that the two slope coeffi­
cients are zero.
There were four instances in which the coef­
ficient on unanticipated changes in money was
statistically significant at the 5 percent level and
three instances in which the null hypothesis
that both slope coefficients are zero is rejected.
In no instance was the coefficient of anticipated
money alone significant at the 5 percent level.
The occasional statistically significant response
to unanticipated changes in the money supply is
odd given the general lack of such responses.
Even more surprising, one of these occurs at a
maturity of six months while the other three
occur at a maturity of 12 months, despite the
fact there was no statistically significant re­
sponse at shorter maturities.2 This fact along
1
with the extremely low adjusted R-squares leaves
open the possibility that the statistically signifi­
cant responses are due to the influence of a
relatively few observations.2
2

20France devalued its currency three times during this
period, causing excessively large movements in the
Eurofranc rate. These observations were deleted from
tests involving money announcements for France. They
were October 5, 1981, June 14, 1982, and March 21,1983.
2 Most of the empirical evidence suggests that the response
1
of U.S. interest rates to money announcements is the
strongest at the short-term maturities. For example, see
Dwyer and Hafer (1989) and Hafer and Sheehan (1989).
22Thornton (1988b, 1989) has shown that some of the
reported statistically significant responses of U.S. interest
rates, exchange rates and stock prices to unanticipated


http://fraser.stlouisfed.org/
Federal Reserve FEDERAL RESERVE BANK OF ST. LOUIS
Bank of St. Louis

Scatter plots of the dependent variable and
unanticipated changes in the money stock for
the four instances in which the coefficient on
UM was statistically significant are presented in
figures 1-4. In the case o f the six-month maturi­
ty for Japan shown in figure 1, it appears that
two extreme observations (see arrows) could ac­
count for the significant positive coefficient on
UM. The same two observations appear as ex­
treme observations for the 12-month maturity
for Japan in figure 2. To see if the results for
Japan are sensitive to these observations, they
w ere deleted and the equation was re-estimated.
In both instances the coefficient on UM was no
longer statistically significant at the 5 percent
level.2
3
The remaining scatter plots reveal no similarly
dramatic outliers. They do indicate what the
low adjusted R-squares suggest: a relatively
weak relationship between the dependent vari­
able and unanticipated changes in the money
stock.2 Given the spherical nature of the scatter
4
plots and the extremely low adjusted R-squares,
these results do not represent a serious
challenge to the null hypothesis that CIP holds
on average.
Tests of linear combinations of changes in
these variables reported in table 2 are similar to
those for the entire period reported in table 1.
The major difference is the T 3 statistic is signifi­
cant at the 5 percent level for Germany, France
and the United Kingdom for all maturities.2
5
T h is p r o v id e s s tr o n g e v id e n c e th a t CIP h o ld s on
average during the period. This finding is con­
sistent with that of Clinton (1988) who found
that, even though there were numerous in­
stances when deviations from interest rate pari­
ty were larger than those implied solely by
transactions costs, no profitable arbitrage oppor­
tunities exist on average.
Unlike Rolev (1987) who rejected CIP for
Japan, these results suggest that it holds for the

changes in the money stock are due to relatively few
observations.
23The observations are March 7, 1980, and June 10, 1983.
The t-statistics for the coefficient on UM are 0.97 and 1.69
for the six- and twelve-month maturities, respectively.
24Given the results reported here, there is little reason to
perform formal statistical tests for the stability of the coeffi­
cients. In any event, such tests likely will be of low power
given the low adjusted R-squares for these equations.
25Separate tests indicate that many of these asset prices do
not follow a random walk.

61

Table 2
The Markets’ Reaction to Money Announcements: October 5, 1979 January 27, 1984
Test of Linear
Combinations

Estimates of Equation 7
Maturity/
Country

Constant1

ONE MONTH
CA
-.1 0 3 *
(3.78)

UM<

ME1

SEE1

R2

-.0 2 2
(1.86)

.030
(1.67)

0.394

.016

f2

T,

t2

t3

6.69*

2.87

-.0 3

-.1 9

- .8 2

F,

SW

-.1 0 3 *
(2.34)

.006
(0.29)

.022
(0.73)

0.642

-.0 0 6

1.85

0.33

.04

-.1 4

-1.37

GR

-.0 2 9
(081)

.004
(0.21)

.026
(1.12)

0.478

-.0 0 2

0.62

0.75

.06

-.2 0

2.12*

FR

.457*
(2.11)

-.0 1 9
(019)

-.0 0 7
(0.04)

3.155

-.0 0 9

1.54

0.02

.01

- .0 8

3.09*

UK

.026
(0.62)

.016
(0.88)

.023
(0.83)

0.603

-.0 0 2

0.84

0.80

.03

- .1 6

2.08*

JA

-.1 2 5
(1.86)

.019
(0.65)

.011
(0.24)

0.970

-.0 0 7

1.22

0.25

.05

- .1 9

- .2 3

THREE MONTH
CA
- .022
(1.36)

-.0 1 0
(1.38)

.019
(1.81)

0.230

.012

2.06

2.39

-.0 3

- .3 3

-.9 1

SW

.022
(1.21)

-.0 0 1
(0.10)

.001
(0.05)

0.266

-.0 0 9

0.52

0.01

.01

-.3 2

-1.42

GR

-.0 1 7
(1.13)

-.0 0 1
(0.11)

.007
(073)

0.212

-.0 0 7

0.52

0.27

.01

-.3 1

2.20*

FR

.065
(1.00)

.002
(0.06)

.009
(0.21)

0.943

-.0 0 9

0.41

0.03

.02

-.1 9

3.16*

UK

-.0 0 9
(0.59)

-.0 1 2
(1.74)

.001
(0.11)

0.230

.005

1.25

1.52

- .0 5

- .2 9

2.14*

JA

-.0 3 1
(1.29)

.010
(0.97)

-.0 0 1
(0.05)

0.354

-.0 0 5

0.79

0.47

.01

- .2 0

- .2 5

.001
(0.21)

.007
(0.69)

0.213

-.0 0 7

1.54

0.28

-.0 3

- .3 4

-.9 9

SIX MONTH
- .031 *
CA
(2.14)
SW

-.0 2 6
(1.22)

.006
(0.67)

-.0 0 4
(0.30)

0.305

-.0 0 7

0.68

0.26

.04

- .3 4

-1.48

GR

- .036*
(2.73)

.003
(0.47)

.010
(1.18)

0.192

-.0 0 1

2.62

0.86

.03

-.3 5

2.33*

FR

.056
(1.40)

-.001
(0.07)

-.0 3 2
(1.19)

0.584

-.0 0 3

0.93

0.72

.01

- .2 5

3.26*

UK

-.0 4 0 *
(2.63)

-.0 0 0
(0.07)

.000
(0.02)

0.221

-.0 0 9

2.45

0.00

- .0 6

-.3 1

2.23*




JULY/AUGUST 1989

62

Table 2 (Continued)
The Markets’ Reaction to Money Announcements: October 5, 1979 January 27, 1984
Test of Linear
Combinations

Estimates of Equation 7
Maturity/
Country
JA

ME1

SEE'

R2

Fi

f2

.021*
(2.08)

-.0 2 4
(1.56)

0.337

.019

3.86*

3.12*

.004
(0.59)

.004
(0.45)

0.220

-.0 0 6

2.77*

Constant1

UM1

- .050*
(2.18)

TWELVE MONTH
CA
-.0 4 3 *
(2.87)

T,

T2

t3

.00

- .32

- .2 9

0.30

.01

- .2 8

-.9 1

SW

.014
(0.69)

.006
(0.68)

-.0 0 7
(0.54)

0.288

-.0 0 6

0.39

0.35

.00

- .27

-1 .4 9

GR

-.021
(1.75)

.011*
(2.02)

-.0 0 5
(0.56)

0.174

.010

2.33

2.12

.04

-.3 1

-2.38 *

FR

.003
(0.10)

.026*
(2.36)

-.0 1 9
(1.15)

0.364

.019

2.16

3.22*

.02

- .23

-3.21 *

UK

-.0 3 2 *
(2.03)

.000
(0.05)

-.0 0 3
(0.24)

0.230

.009

1.56

0.03

- .04

- .25

-2 .2 4 *

JA

- .073*
(2.83)

.029*
(2.49)

-.021
(1.20)

0.377

.023

5.08’

3.58*

.01

- .2 7

-.3 1

'Actual coefficient is 10 “ 2 times the reported coefficient.
* Indicates statistical significance at the 5 percent level.
T 1 : Ain (1 + i,) - Ain (1 + i*) - AlnF, + AlnS, = 0
T2: Ain (1 + it) + Ain (1 + it ) + AlnF, - AlnS, = 0
*
T3: Ain (1 -t- it) + Ain (1 + i*) + AlnF, + AlnS, = 0

Euroyen rate. Roley used the Gensaki rate and
attributed his failure to support CIP to capital
controls. Since the Eurocurrency rates used
here are not affected by capital controls, the
results are not inconsistent with Roley's. T o ­
gether, however, they suggest that there should
be relatively weak substitutability between the
Euroyen and Gensaki rates.

26Equation 11 was also estimated using all of the daily data,
not simply for days when there was a money announcement. Not surprisingly, the t-statistics for the intercept



FEDERAL RESERVE BANK OF ST. LOUIS

Conflicting Results f o r the T,
Statistics and the Estimated In ­
tercept Coefficients
The Tj statistics reported in table 2 are much
smaller than the t-statistics for the intercept
terms, some of which were significant at the 5
percent level.2 One explanation for this, which
6

terms were not much different from the t-statistics for the
linear combination of these asset prices implied by CIP
reported in table 2.

63

Figure 1
Scatter Plot For Japan: Six-Month Maturity
A in (1 + i t) -

A in (1 + i f ) -

A in F t

+ A ln S t

(UM)

Figure 2
Scatter Plot For Japan: 12-Month Maturity
A in (1 + i t) -




A in (1 + i f ) -

A in F t

+ A ln S t

(UM)

JULY/AUGUST 1989

64

Figure 3
Scatter Plot For Germany: 12-Month Maturity
Ain (1 + it) - Ain (1 + i f ) - Ain F t

+ AlnSt

.008

.008

.007

.007

.006

.006

.005

.005

.004

.004

.003

.0 0 3
.0 0 2

.002

•

.001

•

••

v

•

.•

•

•
•

.0 0 2

•< *

••
*• ■ • •

.000
.001

••

« •.
.
••
• • •
•••
••

.001
.000

•••
• * ^ \
•••• •
• •

•

*: •
- *•
•
•
• •

*.
•
•V . *

..
••

.
••

-.0 0 1

•

-.0 0 2

.003

-.0 0 3

.004

- .0 0 4

.005

-.0 0 5

- .0 0 6

-.0 0 6

-.007
-5

.007
-4

-3

-2

-1

0

1

2

3

4

5

6

7

(UM)

Figure 4
Scatter Plot For France: 12-Month Maturity
Ain (1 + it) - Ain (1 + i f ) - Ain F t

+ AlnSt

.012

.012

.010

.010

.0 08

.0 08

.006

.0 06

.004

.0 04

.002

.

•

•* .

.« :

* ••• •
.*.2

.002

*

.000

.000

•

.002

, ,

,•
-.0 0 2

.004

.004

.006

-.0 0 6

.0 08

-.0 0 8

-.010

-.010

.012

-.0 1 2

- .0 1 4

-.014

- .0 1 6

-.0 1 6
-. 0 1 8
-4

-3

-2


 BANK OF ST. LOUIS
FEDERAL RESERVE

-1

0

1

2

(UM)

3

4

5

6

7

8

9

65

is consistent with the frequent—though not
persistent—violations o f CIP using transaction
cost data, is that shocks to the market in the
form of money announcements are destabiliz­
ing, causing large deviations from CIP on these
days.2 If this is the case, deviations from CIP
7
should be larger on money-announcement days.
Consequently, not only will the means be larger,
but the variance of the dependent variable
in equation 11 should be larger on moneyannouncement days as well.2
8
Table 3 reports test of the equality of the
variances of the dependent variable of equation
11 against the alternative that the variance is
larger on money-announcement days. These
tests are performed only for the period ending
in 1984 because, as has been noted, the in­
dividual markets do not respond significantly to
unanticipated changes in the money stock
thereafter.
In general, the results are not consistent with
the hypothesis that the variance is larger on
money-announcement days. There are six in­
stances in which the null hypothesis o f the
equality of the variances is rejected in favor of
the alternative at the 5 percent significance
level, but there are seven instances in which
the variance of the dependent variable is signif­
icantly lower on money-announcement days.2
9
Moreover, two of the form er cases are for the
six- and 12-month maturities for Japan. Since
the previous results for these maturities were
strongly influenced by these observations, they
were deleted and the tests repeated. When this
was done, the null hypothesis was no longer re­
jected in favor of the alternative in either
case.3 Consequently, the occasional significant
0
intercept term and the occasional significantly
larger variance on money-announcement days
are not strong evidence against CIP holding on
average.
27Another is that the difference in these results are due to
the distributions of the dependent variable. Though not
reported here, the distributions of the dependent variable
have their probability mass more highly concentrated
about the mean and have thicker tails than normally
distributed random variables. Consequently, sample means
vary considerably, even in what conventionally would be
large samples. The evidence of this is obtained from tests
derived from histograms constructed by dividing the inter­
val from ± 2.33 standard deviations around the mean into
11 equal-length groups centered on the mean. The first
and last group were open-ended, theoretically containing 1
percent of the sample in each. These histograms were
created for all observations and for days when there were
and were not money announcements for the first
subperiod. In nearly all instances, the actual frequency in
the first and last group exceeded—in many cases, greatly
exceeded—the expected frequency. But even in those in-




Table 3
Tests of Equality of Variance______
Maturity
One
Month

Three
Month

Six
Month

Twelve
Month

CA

0.57

0.94

1.09

0.97

SW

0.19

0.70

1.58*

1.79*

GR

0.24

0.32

0.90

1.07

FR

2.76*

1.05

1.17

0.78

UK

0.47

0.52

0.97

1.31*

JA

1.02

0.16

1.80*

2.39*

Country

'indicates statistical significance at the 5 percent level.

CONCLUSIONS AND
IMPLICATIONS
Despite a few occasions in which there was a
statistically significant response to unanticipated
changes in the money stock, the results o f tests
of the markets’ response to economic news are
consistent generally with the hypothesis that
CIP holds on average. In two o f the four in­
stances in which there was a significant re­
sponse to unanticipated changes in the money
stock, the results appeared to be due to the
nature of the data and the sensitivity of leastsquares to extreme observations. Also, the few
instances in which the means of the dependent
variable implied by CIP were significantly dif­
ferent from zero on money-announcement days
do not constitute strong evidence against CIP.
stances where this was not the case, the actual frequency
in the first and last group exceeded the actual frequencies
in the second and third and 11th and 12th groups. The
null hypothesis of normality was rejected in every case at
very low significance levels by formal chi-square
goodness-of-fit tests.
280 n e way to conceptualize this is simply to note that there
is an extra source of variation on money-announcement
days. For an example, see Thornton (1988b).
29This may not be too surprising given the transaction-cost
interpretation of the error term because Bahmani-Oskooee
and Das (1985) report that their estimates of transaction
costs were highly unstable.
30The F-statistics for the six- and 12-month maturities are
0.72 and 1.14, respectively. Indeed, for the six-month
maturity, the variance is significantly smaller on moneyannouncement days.

IIII V/AI 1/11I C T 1QQQ

66

This is so because the hypothesis that the mean
of the dependent variable implied by CIP is zero
was never rejected for larger samples using all
of the daily observations.
There is no evidence that the data are con­
sistently more variable on money-announcement
days. Furthermore, the t-statistics for tests that
linear combinations other than that implied by
CIP were zero were much larger than those for
that implied by CIP and, in several instances,
the null hypothesis was rejected during part of
the sample period. Hence, CIP appears to hold
on average for these data.
There are several policy implications of the
finding that, on average, an exact linear rela­
tionship exists between the U.S. and foreign in­
terest rates and the spot and forward exchange
rates. For example, if the U.S. interest rate is
taken as exogenous, foreign central banks can­
not independently and simultaneously control
both their interest rates and their exchange
rates. This means that small open economies are
susceptible to exogenous changes in U.S. mone­
tary policy. Finally, the results indicate the CIP
assumption used in many theoretical models is
appropriate, so long as it is not required to hold
at every point in time. These results, however,
do not provide evidence for the question of
market efficiency which characterizes many
discussions of CIP and covered interest
arbitrage.

Clinton, Kevin. “ Transactions Costs and Covered Interest
Arbitrage: Theory and Evidence,” Journal of Political
Economy (April 1988), pp. 358-70.
Cornell, Bradford. “ The Money Supply Announcements
Puzzle: Review and Interpretation,” American Economic
Review (September 1983), pp. 644-57.
Deardorff, Alan V. “ One-Way Arbitrage and Its Implications
for the Foreign Exchange Markets,” Journal of Political
Economy (April 1979), pp. 351-64.
Deaves, Richard, Angelo Melino, and James E. Pesando.
“ The Response of Interest Rates to the Federal Reserve’s
Weekly Money Announcements: The Puzzle of Anticipated
Money,” Journal of Monetary Economics (May 1987), pp.
393-404.
Dufey, Gunter, and Ian H. Giddy. The International Money
Market (Prentice-Hall, 1978).
Dwyer, Gerald P., and R. W. Hafer. “ The Response of Inter­
est Rates to Economic Announcements,” this Review
(March/April 1989), pp. 34-46.
Engle, Robert F. “Autoregression Conditional Heteroscedasticity With Estimates of the Variance of United Kingdom In­
flation,” Econometrica (July 1982), pp. 987-1008.
Hafer, R. W., and Richard G. Sheehan. “ The Response of
Interest Rates to Unexpected Weekly Money: Are Policy
Changes Important?” unpublished manuscript, March
1989.
Hardouvelis, Gikas A. “ Market Perceptions of Federal
Reserve Policy and the Weekly Monetary Announcements,”
Journal of Monetary Economics (September 1984), pp.
225-40.
Husted, Steven, and John Kitchen. “ Some Evidence on the
International Transmission of U.S. Money Supply An­
nouncement Effects,” Journal of Money, Credit and Banking
(November 1985), pp. 456-66.
Kubarych, Roger M. Foreign Exchange Market in the United
States, revised ed. (Federal Reserve Bank of New York,
1983).
Lo, Andrew W., and A. Craig MacKinlay. “An Econometric
Analysis of Nonsynchronous Trading,” NBER Working
P ape r No. 2 9 6 0 (M ay 1989).

REFERENCES
Bahmani-Oskooee, Mohsen and Satya P Das. “ Transaction
.
Costs and the Interest Parity Theorem,” Journal of Political
Economy (August 1985), pp. 793-99.
Belongia, Michael T., and Richard G. Sheehan. “ The Infor­
mational Efficiency of Weekly Money Announcements: An
Econometric Critique,” Journal of Business and Economic
Statistics (July 1987), pp. 351-56.
Belongia, Michael T., R. W. Hafer, and Richard G. Sheehan.
“A Note on the Temporal Stability of the Interest Rate—
Weekly Money Relationship,” Federal Reserve Bank of St.
Louis, Working Paper 86-002 (1986).
Callier, Phillips. “ One-Way Arbitrage and Its Implications for
the Foreign Exchange Markets,” Journal of Political
Economy (December 1981), pp. 1177-86.
Chrystal, K. Alec, and Daniel L. Thornton. “ On the Informa­
tional Content of Spot and Forward Exchange Rates,” Jour­
nal of International Money and Finance (September 1988),
pp. 321-30.




Pesaran, M. Hashem. The Limits to Rational Expectations,
(Blackwell, 1987).
Roley, V. Vance. “ U.S. Money Announcements and Covered
Interest Parity: The Case of Japan,” Journal of International
Money and Finance (March 1987), pp. 57-70.
Sheehan, Richard G. “ Weekly Money Announcements: New
Information and Its Effects,” this Review (August/September
1985), pp. 25-34.
Tandon, Kishore, and Thomas Urich. “ International Market
Response to Announcements of U.S. Macroeconomic
Data,” Journal of International Money and Finance (March
1987), pp. 71-83.
Thornton, Daniel L. “ The Borrowed-Reserves Operating Pro­
cedure: Theory and Evidence,” this Review (January/
February 1988a), pp. 30-54.
_______ . “ Why Do Market Interest Rates Respond to
Money Announcements?” Federal Reserve Bank of St.
Louis Working Paper No. 88-002 (1988b).
_______ . “ The Effect of Unanticipated Money on the Money
and Foreign Exchange Markets,” Journal of International
Money and Finance (forthcoming).

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Post Office Box 442
St. Louis, Missouri 63166

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