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The Federal Reserve Bank of San Francisco’s Economic Review is published quarterly by the
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nia 94120. Phone (415) 544-2184.
2
Windfall Proffits? Interest !at© s
and Index Numbers
I.
Introduction and Summary
4
II. Crude Oil Price Controls and the Windfall Profit Tax:
Deterrents to Production?
Yvonne Levy
6
. .. As a measure to reduce dependence on foreign-oil imports and improve
the allocation of resources, decontrol is a step in the right direction — but
the windfall profit tax is a step in the wrong direction.
III.
Interest Rate Forecasts and Market Efficiency
29
Adrian W. Throop
. .. By making use of the information contained in market professionals’
forecasts, an investor in Treasury bills could have improved his return.
IV.
Indexes, Inflation, and Public Policy
44
Herbert Runyon
...T h e personal consumption “ deflator” has provided a more equitable
choice recently than the consumer-price index for determining cost-ofliving adjustments.
Editorial committee for this issue:
John Scadding, Brian Motley, and Robert Jacobson
3
Production, investing, and household-buying decisions have all come to be influenced by
the past decade's upsurge in inflation and
increased government participation in market
decisions. This issue of the Economic Review
presents three studies of this type of influence.
One article examines the production losses
attributable to price controls - and more
recently, windfall-profit taxes - on domestic
petroleum producers. Another article evaluates the ability of financial markets, in an inflationary era, to incorporate the best possible
interest-rate forecast into current market
prices. And a third article analyzes the composition of the price indexes which play such a
prominent role, through indexation formulas,
in determining household incomes and
government expenditures.
Yvonne Levy describes the nation's recent
experience with price controls on
domestically-produced crude oil, which held
the average price of domestic crude below the
world market level for almost a decade. Controls thus tended to reduce production substantially below the level that would otherwise
have prevailed, aggravating a decade-long
downtrend in U.S. production. "As a reSUlt,
controls worked against the nation's goal of
energy independence and led to an inefficient
allocation of resources."
Crude-oil price controls were finally eliminated this past January, but producers still are
not realizing the world price - although they
are receiving considerably more than they
would have done with continued controls. The
reason is the windfall-profit tax, which has
been returning to the Federal Government
much of the added revenue that otherwise
would have accrued to producers through
decontrol. "With the tax, future domestic production will be lower than it otherwise would
have been, although higher than with continued controls. Similarly, imports will be
higher than otherwise, and the misallocation
of resources will continue."
Levy provides a number of scenarios of production possibilities with different long-run
supply elasticities and with different rates of
increase of (uncontrolled) crude prices. All of
the scenarios show that the decline in domestic
production expected over the 1979-85 period
with continued controls might have been
reversed without controls. But the windfallprofit tax would substantially reduce the positive impact.
Levy thus concludes, "As a measure to
reduce dependence on foreign-oil imports and
improve the allocation of resources, decontrol
is a step in the right direction. But by the same
token, the windfall-profit tax is a step in the
wrong direction." She adds that policymakers
should consider altering the tax to make it a
true tax on profits, rather than an excise tax on
a portion of the selling price. In that way, it
would not affect production decisions at the
margin.
Adrian Throop points out that volatile financial markets in this inflationary period have
put a premium on accurate forecasts of interest
rates. Thus, he examines the degree to which
the Treasury-bill market efficiently utilizes all
available information so as to incorporate the
best possible interest-rate forecast into current
market prices. This involves an evaluation of
the applicability of the "efficient market"
hypothesis to the Treasury-bill market. Hence
he examines two types of independent
forecasts - an autoregressive forecasting
4
equation based on the past history of the bill
rate, and the forecast of a selected panel of
market professionals.
If the market is not efficient, Throop argues,
a group of investors could improve their
returns by altering the maturity of their investments in light of superior interest-rate
forecasts. "Whether or not investors can profit
by 'speculating' on interest rates, through
holding other than their normally preferred
maturities, depends critically on whether
available interest-rate forecasts are more
accurate than the market's." If the market is
efficient, the information in these forecasts
would already be incorporated into the prices
of securities, and therefore nothing would be
gained. In that case, investors would be better
off by simply "hedging" their positions with
maturities equal to their planned investment
periods, thereby avoiding possible risk.
Throop shows that professional analysts'
predictions of the Treasury- bill rate two quarters ahead are significantly more accurate than
market predictions. "This indicates that the
market does not efficiently utilize all available
information in making bill-rate forecasts." The
analysts' ability to "beat the market" stems
from a better utilization of information about
past movements in the bill rate, and also from
a more efficient utilization of other sorts of
information.
Herbert Runyon then turns to the question
of measuring inflation, which, as he emphasizes, means an increase in the general price
level rather than separate price increases for
individual commodities. Since numerous
goods and services are bought and sold daily in
the markets, an index number represents the
only feasible way of describing the general
movement of prices through time. But this
index number should give an accurate representation of changes in living costs - at least
indirectly through market observations as consumers reveal their individual preferences by
purchasing certain goods and services. For the
household sector, the standard measures
include the Consumer Price Index (Cpn and
the Personal Consumption Expenditure
(PCE) deflator.
The CPI - a "Laspeyres" index - uses
quantities purchased in a certain base year as a
reference point from which to measure
changes in prices of a basic (presumably
unchanging) consumer-expenditure pattern.
The PCE - a "Paasche" index - uses the
current-period expenditure pattern as a
reference base for comparison with expenditures in earlier periods. For structural
reasons, the cpr tends to overstate - and the
PCE to understate - what consumers actually
pay for at the checkout counter. As a practical
matter, the CPI and PCE were quite close in
their measurement of living costs from 1960
through 1977. But in the 1978-80 period, the
CPI rose at a much faster rate - not so much
because of the indexes' different statistical
composition as because of their different treatment of sharply rising homeownership costs.
Among other things, the CPI's weightiDg of
homeownership overstates its importance in
the cost of living.
Runyon argues that the use of the CPl in
recent years has overcompensated many
income recipients - especially beneficiaries of
Federal programs, since the Federal government depends on the CPI as a standard index
in its efforts to offset the impact of inflation on
such individuals. This overcompensation has
several public-policy consequences. "Overcompensation leads to unwarranted increases
in Federal expenditures and in the Treasury
deficit. Beyond that, it introduces inequities
relative to those individuals not receiving
indexed benefits, and thus amounts to an
unintended redistribution of income." Thus,
he concludes, recent experience suggests that
the PCE index is the more equitable choice for
determining cost-of-living adjustments.
5
Yvonne levy'"
Throughout the decade of the 1970's, a
complex system of Federal controls governed
prices for domestically-produced crude oil.
Those controls held the average price of
domestically-produced crude below the world
market level. Consequently, controls tended
to reduce production substantially below the
level that would otherwise have prevailed,
aggravating a decade-long downtrend in U.S.
crude-oil production.
For any given level of refiners' crude-oil
demand, the reduction in domestic production
raised imported-oil requirements by an
equivalent amount. Moreover, that added
import volume involved greater resource costs
than would have been required through
domestic production. As a result, controls
worked against the nation's goal of energy
independence and led to an inefficient allocation of resources.
Despite President Reagan's January 1981
lifting of controls on domestically-produced
crude, producers still are not realizing the
world price. The Windfall Profit Tax - which
went into effect March 1, 1980 and could
extend through 1990 - has been returning to
the Federal government much of the added
revenue that otherwise would have accrued to
producers through decontrol. With the tax,
producers are realizing less than the world
market price,. although of course more than
they would have realized with continued con-
trois. Thus, with the tax, future domestic production will be lower than it otherwise would
have been with decontrol and no tax, although
higher than with continued controls. Similarly,
imports will be higher than otherwise, and the
misallocation of resources will continue.
Section I presents a simple model of the supply of domestically-produced crude oil which
shows how supply responds positively to prices
received by producers. It also shows that, in
the absence of controls, domestic crude oil
would sell at approximately the world price
because domestic producers operate in a world
market. Section II describes the major features
of the crude-oil price-control program contained in the recently terminated Energy
Policy and Conservation Act of 1975. That section shows how that program held the average
domestic price below the world market price,
and thus kept domestic output below the
amount that would have been produced in a
free market. Section III outlines the major provisions of the Crude Oil Windfall Profit Tax of
1980. It shows how the tax leaves the price
realized by producers still below the world
, reducing the positive impact of
decontrol on domestic crude-oil production.
Finally, Section IV presents a range of estimates of the domestic production losses that
resulted from the Energy Policy and Conservation Act, and that potentially could result over
the next decade from the Windfall Profit Tax.
The recently-passed Reagan tax program contains minor changes in the windfall-profit tax,
but these do not materially affect the conclusions of this paper.
'Senior economist, Federal Reserve Bank of San Francisco. Research assistance provided by Alane Sullivan and
Lloyd Dixon.
6
I.
Domestic Oil Production in a Free Market
Long-run Supply Model
Building upon this foundation, we can
further clarify the concept of the long-run supply schedule for representative individual properties, the domestic crude-oil producing
industry and the combined domestic and
import sectors through Charts lA-C. The
charts show, at a particular period in time, the
quantity of crude oil that will be available to
the U .5. market from those various sources at
various selling prices. We assume, throughout
the analysis, that the crude-oil producing
industry is workably competitive, in line with
the bulk of the evidence presented in the
recent academic literature. With regard to
structure, the producing and refining sectors
of the industry are clearly different. Thousands
of U.5. firms are engaged in the exploration
and extraction of crude oil, with no firm dominant - in contrast to the oligopolistic refining
sector of the industry.4
Chart 1A shows the long-run supply
schedule for the representative individual property. This is the long-run marginal cost curve
(MC) - the addition to total cost resulting
from the last unit of output. The marginal cost
of producing additional barrels from a given
reservoir increases because firms must invest
in higher-cost recovery techniques, such as
enhanced oil-recovery methods and deeper
development wells, as more oil is extracted
from a finite reservoir. In a competitive
market, each firm maximizes profit by expanding output to the point where marginal cost
equals price. The schedule is upward sloping;
as the price rises, it pays firms to
the
higher-cost barrels that would have been
uneconomic to produce at a lower price.
Chart lB shows the long-run supply
schedule, 5 0 5 0 , for the entire domestic crudeoil producing industry. That schedule is
derived by summing the amounts produced by
all properties at each price - that is, summing
horizontally the marginal cost-output curves
for all producing properties. Again, the
schedule is upward sloping because, with
Domestic crude-oil production can be
increased over the long-run in a number of
ways, all of which are encouraged by a rise in
selling price. "Long-run" means a planning
period long enough to permit producers to
invest in new productive capacity to achieve
higher production rates. In crude-oil production, new productive capacity can be installed
either at existing (i.e., already-producing) properties or at entirely new sites. I
At existing properties, producers can
increase the rate of extraction by drilling more
development wells. Alternatively, they can
invest in enhanced oil-recovery technologies.
This involves drilling service wells through
which steam, chemicals, or gases may be
injected to increase well pressure, thus raising
the recoverable proportion of the total reservoir.
In addition, producers can expand production through the discovery of new properties
- reservoirs in unproven regions as well as
near already-producing areas. But first, producers must do some exploratory drilling and
identify resources that are recoverable under
current economic and technological conditions.
The addition of development wells at known
reservoirs permits a higher rate of extraction
from a given deposit, but it does not increase
the ultimate, or total cumulative, production
potential. 2. This potential can be expanded
only through an increase in proved reserves,
resulting from investments in enhanced oilrecovery technologies and the discovery of
new economic resources. "Proved reserves"
refer to the portion of the resource base that
has been identified and explored, and from
which crude oil can be recovered profitably at
current prices and with current technology. J
While the occurrence of oil is finite, being
governed by geology, a host of other factors economic, technological, environmental and
political - determine the rate at which oil
resources are discovered, developed and transferred to the category of reserves.
7
Chart 1
United States Crude Oil Supply Without Controls
A. INDIVIDUAL DOMESTIC PROPERTY
Price
(dollars
per barrel)
Pw
MC
1---------1
qw
Quantity (barrels/unit of time)
Price
(dollars
per barrel)
Pw
B. TOTAL DOMESTIC INDUSTRY
t-------------.y
Qw
Quantity
(barrels/unit of time)
C. TOTAL U. S. CRUDE OIL MARKET
Price
(dollars
per barrel)
___
Pw t------------,-~~------
S
Domestic + Imports
Qw QD
Quantity
Domestic Domestic (barrels/unit of time)
production consumption
8
increased production, firms must locate,
develop and extract oil from less accessible and
poorer quality resources. 5
Chart lC shows the long-run supply
schedule for domestic and foreign oil available
to U.S. refiners at various selling prices. At
prices below the world price, P w , the supply
comes entirely from domestic sources. The
price cannot exceed P w , since imports are
available essentially without limit at that price.
Hence, the total supply schedule is represented by the kinked curve, So as. Schedule
DD meanwhile represents U.S. refiners'
crude-oil demand schedule. In the absence of
price controls, domestic crude oil would sell at
approximately the world price, P w - the
landed price for imported oil. 6 This is because
U.S. producers operate in a world market. At
the world price, domestic production cannot
meet the total quantity demanded by U.S.
refiners. The price of imported crude thus
represents the marginal cost of an additional
barrel - and thus determines the marginal
domestic producer price. At the world price the domestic price that would prevail without
controls - domestic producers would be willing to supply Qw barrels. Domestic demand
would be QD, and imports in the amount of
QD-Qwwould be required.
Efficiency in the allocation of resources
requires that the total cost of satisfying any
given quantity demanded be as low as possible. 1 When the alternative to domestic oil is
imported oil purchased at the world price, efficiency requires that production from all
domestic properties be expanded to the point
where the marginal cost of the last unit of output is equal to the price of imported oil.
Beyond that point, resources could be saved by
reducing domestic output and replacing that
output with imported oil. But below that point,
where the cost of the last barrel produced is
less than the price of imported oil, resources
could be saved by reducing imports and
expanding domestic production.
Since the supply schedule So So reflects the
marginal cost of producing domestic oil, the
uncontrolled market solution for domestic and
foreign supply, So as, represents an efficient
allocation of resources. In this allocation, the
marginal cost of production for all domestic
producers is equal to the world price. There is
no opportunity to reduce total cost by shifting
supply between domestic and foreign sources.
II. Domestic Oil Production Under Price Controls
The Federal price-control programs of the
1970's held the average selling price of
domestically-produced crude below the world
market price, and thereby disturbed the efficient free-market solution. But government
attempts to influence domestic prices first
developed in the 1930's - although their purpose was to hold the producer price above
(rather than below) the competitive level.
During the 1930's, oil producing states
instituted "conservation" programs - ostensibly to prevent "wasteful" production practices, but in reality, to keep prices high by
limiting production. 8 Those programs were
effective until the mid-1950's, when increas-
ing quantities of foreign oil became available at
prices well below the average domestic producer price. After trying (unsuccessfully) to
restrict imports voluntarily, the Federal
government in 1959 introduced a program of
mandatory import quotas, using national
security as justification.
The early 1970's witnessed a fundamental
change in the nation's demand for imports.
Despite the quota system, domestic crude-oil
production peaked by 1970, as import competition prevented the domestic price from rising as fast as production costs. By 1973, U.S.
petroleum consumption had outgrown
domestic production, and imported oil had
9
become the required source of marginal supplies. The marginal cost of imported oil, i.e.,
the world price, thus became the determinant
of the domestic producer price.
tives.Since decisions to expand production are
determined on the margin, they permitted production in excess of the base level to receive a
higher ceiling price. In that way, they hoped to
provide sufficient incentive to stimulate production. But they also wanted to prevent
owners of wells brought into production before
the OPEC price run-up from receiving profits
far higher than originally anticipated and so
held the lower-tier price not only below the
world level but the upper-tier price. In this
view, the removal of such unanticipated profits - "windfalls" - would have little impact
on production decisions. (A similar philosophy
apparently underlies the new Windfall Profit
Tax.) Nevertheless, because controls generally
held the price at the margin below the world
price, production was less than it otherwise
would have been.
Charts 2A-C illustrate the price and production effects of the Energy Policy and Conservation Act for representative properties and the
entire domestic industry. 12 Properties in existence before 1975 faced the marginal revenue
(MR) schedule shown in Chart 2A. Output of
q, or less qualified as stripper oil and received
the uncontrolled (world) price, P w. Output
from qs to the base production control level
(BPCL) received the lower-tier price, PL' Output in excess of BPCL received the upper-tier
price, P u. "New" properties - those brought
into production after 1975 - faced the
marginal revenue schedule shown in Chart 2B,
and except for small stripper properties,
received the upper-tier price.
Existing stripper properties were unaffected
by this system of price controls. Those properties received the world price, with or without
controls, and hence production remained the
same at q,. But for other existing properties,
production was lower than it would have been
without controls, since production was not
permitted to receive the world price. The magnitude of the impact depended on whether
costs had risen since the 1975 base year.
Producers not incurring higher costs would
have found it profitable to expand production
past the base-period level, to earn the uppertier price on the new production. Production
Energy Policy and Conservation Act
The Federal government first placed direct
controls on prices of domestic crude oil on
August 15, 1971, when Presiden t Nixon froze
wages and prices throughout the economy. 9 A
multi-tier pricing system evolved in Phase IV
of the controls program, announced in August
1973, and in the Emergency Petroleum
Allocation Act, passed in November 1973 during the Arab oil embargo. These then led to
the Energy Policy and Conservation Act of
1975 (EPCA). That legislation controlled
domestic producer selling prices on a propertyby-property basis, with production above and
below the "base production control level"
(BPCL) -the 1975 average monthly production - subject to different price ceilings.
Under the act, "lower-tier" oil referred to output at or below the BPCL, while "upper-tier"
oil referred to output in excess of this base
level or output from new properties brought
into production after 1975.
The law stipulated a lower price ceiling for
lower-tier oil than for upper-tier oil, and stipulated that ceilings would be set to achieve a
target average price for domestic oil. That price
could rise to reflect inflation, but by no more
than 10 percent annually. 10 Initially, the law
classified oil from "stripper" properties those producing ten barrels or less daily - as
upper-tier oil. But in September 1976, the
energy agency decontrolled stripper oil and thus
permitted it to receive the world market price.
Policy makers designed the control program
to hold the average price of domestically-produced crude below the world market level, and
thereby protect consumers from the full
impact of sharply rising world prices - in
effect, transfering to consumers much of the
added income that would otherwise have
accrued to producers. II At the same time,
policy makers sought, through the multi-tier
system, to accomplish that objective with the
least possible reduction in production incen10
Chart 2
United States Crude Oil Supply
Under Energy Policy and Conservation Act
A. INDIVIDUAL DOMESTIC PROPERTY
B. INDIVIDUAL DOMESTIC PROPERTY
(High-cost Existing)
(New)
Price
Prir.e
(dollars
(dollars
per barrel)
per barrel)
Pw
Pw
MR
Pu
Pu
qs
ql
quqw
BPCL
Quantity (barrels/unit of time)
Price
(dollars
per barrel)
Quantity (barrels/unit of time)
C. TOTAL U. S. CRUDE OIL MARKET
------------r--ilIItf---------
Pw ......
S
Domestic + Imports
Pc 1-"""""""""""''''''''''''''''''''''''''''''''''''''''
So
0c
QW
QD
Quantity
Domestic Domestic (barrels/unit of time)
production consumption
11
still would have been lower than it would have
been without controls, however, since the
upper-tier price was below P w. Producers
incurring higher costs than faced in 1975
would have fared less well. (See the marginal
cost schedule, MC I> in Chart 2A.) For those
properties, producers would not have found it
profitable to expand production beyond the
base-period level. The new production up to
the base level would earn only P b the lowertier price, which would be below the cost of
producing it. The profit earned on upper-tier
oil (shaded area) would not cover the loss
incurred on lower-tier oil (striped area) and
the firm would choose to remain producing at
ql' Producers incurring an extremely sharp rise
in costs since 1975 would have an incentive to
actually lower production to 10 barrels or less
per day, to qualify for the uncontrolled price
afforded strtpper properties.
Producers with new properties would have
found less incentive to produce than in a situation with no controls (Chart 2B). When the
world price was P w , output from new properties was only qu because they were permitted
to receive only the price P u. Had price controls
not existed, output on new properties would
have been qw, because that output would have
received the world price.
At the industry level, this system of controls, like its predecessors, tended to hold the
average domestic producer price below the
world market level, thereby reducing production below the level that would otherwise have
prevailed (Chart 2C). When the world price is
P w , controls hold the average domestic producer price at Pc. As a result, the domestic
industry produces only Qc instead of the quantity Qw produced in the absence of controls.
For a given level of refinery crude oil demand,
the consequent reduction in domestic output
is offset entirely by imports. Thus the control
program tended to increase the nation's dependence on foreign oil.
The control program also led to inefficiency
in the allocation of resources. Between output
levels Qc and Qw, each additional barrel of
crude could be produced domestically at a cost
below the world price, and thus at a smaller
expenditure of resources than for imported oil.
Area dca, which equals the difference between
the world price and the domestic supply
schedule SoSo at each increment between Qc
and Qw, represents resources wasted on
expenditures for imported oil because of controis. 1]
Intertemporal Production Decisions
Thus far, we have considered the effects of
controls only in a static framework. We have
assumed that firms consider only the current
price, without regard to price expectations,
when making production decisions. Also, we
have ignored the potential effects of the current level of output on future production. We
have assumed that firms could obtain optimal
production and profit paths over time by producing at the point where marginal cost equals
price in each planning period.
But there is an important difference between
the marginal-cost (supply) schedule of a typical manufacturing firm and the schedule of a
firm extracting an exhaustible resource such as
petroleum. As petroleum is removed from a
reservoir, the pressure of the reservoir declines, and so too does the total amount of
petroleum available - a tendency known as
the "natural decline function." Because of the
exhaustible nature of the resource, a barrel of
oil produced today will not be available in
some future period. Petroleum producers thus
face an additional cost of production not incurred by manufacturers. That additional cost the user cost - is the opportunity cost or profit
foregone of being unable to sell that unit of
output in the future.
In order for a producer to decide to produce
a barrel of oil in the present, the price of each
additional barrel of oil produced today must be
sufficient to cover this opportunity cost as well
as normal production costs. Moreover, in view
of the effect of current output on future output
- the "natural decline" problem - the firm
cannot simply select the output level in each
period where marginal revenue equals
marginal cost (defined to include user cost).
Instead, the firm must maximize a stream of
profits over time, which involves a discounting
12
troIs on current prices may have created just
such an expectation of higher prices in the
future when controls eventually might be
lifted. The expected price path in moving from
control to decontrol would have been steeper
than had prices never been subject to controls.
As a result, controls may have raised the user
cost of controlled oil, thereby causing producers to restrict current production even
more than they would have done because of
receiving less than the world-market price.
This was especially true of the 1978-80 period,
when market participants widely expected
eventual decontrol. 15
procedure. This present-value analysis, in
effect, states that for production of an additional barrel to take place, the present profit
invested at the market rate of interest must at
least be equal to the profit from selling that
barrel any time in the future. 14
By affecting price expectations, the controls
program may have exerted still another
restraining effect on current production. If the
expected path of future prices rises, the user
cost increases and producers can expand profits by deferring current production to the
future. In this case, the present value of the
future profit would exceed today's profit. Con-
III. Domestic Oil Production Under "Decontrol"
On June 1, 1979, the Energy Department
began to implement a program, mandated by
President Carter, for decontrolling domestic
crude-oil prices by October 1, 1981. Under
that program, production that previously
would have been subject to the lower-tier price
was permitted to move gradually to the uppertier category. Then, beginning on January 1,
1980, production previously classified as
upper-tier oil, plus the lower-tier oil moving
into the upper-tier category, was permitted to
move to a free-market classification at a rate of
4.6 percent per month.
The Energy Department decontrolled oil
discovered after January 1, 1979 on June 1 of
that year, and it lifted controls on "heavy"
crude on August 17,1979. Finally, the Reagan
Administration - in its first major economicpolicy move - lifted all remaining price controls on domestically produced crude on January 28, 1981.
In moving to decontrol domestic prices,
both the Carter and Reagan Administrations
hoped to encourage domestic production and
to slow down the growth of U.S. petroleum
consumption. To the extent that the higher
refiner costs for domestic crude were reflected
in higher refined-product prices, consumption
should be curtailed. 16
Windfall Profit Tax
At the same time, Congress was unwilling to
permit producers to realize all the added
revenue that would accrue through decontrol,
especially since that step could boost producer
revenues by about $1 trillion over the 1980-90
period, according to estimates of the Joint
Committee on Taxation. 17 As a result, Congress enacted the Crude Oil Windfall Profit
Tax of 1980 to divert to the U.S. Treasury
some of the incremental revenues that would
otherwise be received by producers through
decontrol. The tax became effective March 1,
1980.
The tax is perhaps the largest ever imposed
on a single industry. Over the 1980-90 period,
the tax could yield about $236 billion, in addition to a $332-billion increase in corporate
income taxes resulting from decontrol. Thus,
the U.S. Treasury could receive $568 billion of
the projected $l-trillion additional industry
revenue received from decontrol. 18
Although called a tax on profit, the tax really
is a Federal excise tax on a portion of the selling price received from crude oil. The tax paid
per barrel is determined by applying various
tax rates to the "windfall profit" - the
difference between the decontrolled producer
price and the price that would have prevailed
13
under continued controls (less state severance
tax) .
The tax rates and base prices applicable to
various properties vary according to type of
production and size of producer (Table 1). The
Internal Revenue Service established these
new oil categories for tax purposes. Producers
are classified either as "majors" or as "independents" (producers with gross annual sales
of $5 million or less and with refining
capacities of no more than 50,000 barrels a
day). Identical tax rates are applied, except for
the first 1,000 barrels a day of Tier 1 and Tier 2
production by independents. To provide
greater incentive for certain investments, the
lowest tax rates apply to newly discovered and
incremental tertiary oil, the latter being oil
obtai ned t hroug h a qual ified tertiary
(enhanced) recovery method, i.e., production
in excess of the projected decline rate for the
property without the tertiary technique. 19
In computing the tax, producers first
subtract a base price, adjusted for inflation,
from the decontrolied producer price (Appendix A). Next they subtract a state severance
tax - estimated to average about 5.4 percent
of the selling price - to determine the
"windfall profit." Then they apply the
appropriate tax rate to determine the amount
of tax to be paid.
Table 1
Provisions of the Windfall Profit Tax 1
Tax Rate
Integrated
Independent
Producer
Producer 3
(percent)
Base Price
($ per bbl.)
Annual Adjustment
to Base Price
(percent)
Tier 1
Controlled oil discovered before 1979 2
70
50
1281
Inflation 6
Tier 2
Stripper well oil
60
30
15.20
Inflation
National Petroleum reserve oil
60
30
15.20
Inflation
Tier 3
Newly discovered oil
30
30
16.55
Inflation
Heavy oil
30
30
16.55
Inflation
Incremental tertiary oil 4
30
30
16.55
+ 2%
+ 2%
Inflation + 2%
ExemptS
1
The Windfall Profit Tax of 1980 was enacted into law on April 2, 1980. But the tax was retroactive, i.e., applicable to
crude-oil production removed from properties after February 29, 1980.
2
For purposes of the windfall-profit tax, the pricing categories conform to those in effect in May 1979, before the process
of gradual decontrol began.
3
The special reduced-tax rates afforded independent producers for Tiers I and 2 are applicable only to their first 1,000 barrels per day of production. Production in excess of 1,000 bid is taxed at the regular windfall-profit tax rates, i.e., the rates
applicable to integrated producers.
4
Incremental tertrary oil is the amount of production from a property on which a producer uses a qualified tertiary
(enhanced) recovery method in excess of the projected decline rate if a tertiary technique had not been used on that property.
5
Categories of crude exempt from the tax include: qualified governmental-interest oil, qualified charitable-interest oil, certain Indian oil, Alaskan oil (other than from the Sadlerochit reservoir) north of the Alaska-Aleutian mountain range and
over 75 miles from the pipeline, and tertiary oil from properties owned by independent producers.
6
Inflation is measured by the change in the Gross National Product deflator.
14
Chart 3 shows how the windfall-profit tax
will affect U.S. crude oil production as long as
the uncontrolled domestic price remains above
the adjusted base price. 20 So So represents the
long-run supply schedule for the domestic
crude-oil producing industry. Decontrol with
no tax would provide producers with the maximum incentive to increase production, and
would lead to an efficient ailocation of
resources in meeting with the nation's
petroleum requirements. In this situation, producers would realize the uncontrolled price,
P w , and produce at output Qw. With continued controls, producers would realize price,
Pc, and supply Qc. The tax lowers the price
realized by producers below the free-market
price to an intermediate price, PT' Since the
uncontrolled domestic selling price is determined by the world price, producers must
absorb the tax as a reduction in realized price,
and cannot pass it on to consumers. The tax
thus reduces the incentive to increase production provided by decontrol. At price, P T, quantity QT is produced - more than would be produced with continued controls but less than
would be produced with decontrol and no tax.
Production is greater than with continued controls because only part of the so-called
"windfall" is diverted to the U.S. Treasury.
Chart 3
Effects of
Windfall Profit Tax on
Domestic Crude Oil Production
Price
per barrel
Pw t--------~"
Pr
Q
C
Q
r
Q
W
Quantity of Crude Oil
IV. Estimating Production losses
Crude-oil production in the United States
dropped 10 percent over the 1970-79 period,
and would have dropped 24 percent except for
the addition of 1.4 million barrels per day of
Alaskan North Slope production. The decadelong decline in production resulted inevitably
from a decline in the amount of oil added to
reserves annually, through new discoveries
and enhanced oil recovery, during the 1970-79
period compared with the decade of the
1960' s. Unless gross annual addi tions to
reserves exceed the rate of extraction, the total
inventory of proved reserves declines. Producers were forced to lower production so as
not to experience an even greater run-down in
their proved reserve inventory. Even with a
cutback in production, proved reserves - the
industry's working "in the ground" inventory
- declined steadily over the 1970-79 period
from 39.0 to 27.1 billion barrels.
Even with controls, the average wellhead
price for domestically-produced crude rose
three-fold over the 1973-79 period (TapIe 2).
This price upsurge led to a reversal of the
prolonged decline in exploration activity that
had occurred over the preceding decade and a
half. Between 1973 and 1979, the total number
of oil wells drilled nearly doubled, rising at an
average annual rate of 16 percent.
Nonetheless, additions to reserves still
dropped from an average annual rate of 2.7 billion barrels during the 1965-69 period to 2.0
15
servation Act production?
billion barrels during the 1971-74 period, and
then to only 1.3 billion barrels during the
1975-78 period. The rate of reserve additions
only began to pick up, to 2.2 billion barrels,
with a new price upsurge during the period of
gradual decontrol in 1979.
Without price controls, drilling activity
would have increased somewhat faster, raising
annual additions to reserves as weB as production at existing properties through development drilling. How much did the controls more specifically the Energy Policy and Con-
contribute to the decline in
Energy Policy and Conservation Act
To answer that question, we could develop a
petroleum-supply model to project production
under an uncontrolled price assumption.
Then, that outcome could be compared with
actual production to estimate production
losses. Given the fact that the oil-supply process involves several phases - exploration,
reservoir development, and production - the
development of such a model would be a vast
Table 2
Relationship Between Controlled Domestic Crude Oil Prices
and World Price, 1972·80
Average
Domestic Price:
Controlled as Percent
of Uncontrolled
Average Refiner
Acquisition Price Average Domestic Price at Wellhead
Year Imported Crude' Without Controls (est.) With Controls
1972
3.22
3.39"
3.39
100.0
1973
4.08
3.89"
3.89
100.0
1974
12.52
11.66'
6.87
1975
13.93
12.95'
7.67
1976
13.48
12.56'
8.19
5.13
1977
14.53
13.59"
8.57
1978
14.57
13.95"
9.00
1979
21.67
22.93"
33.82
35.54';
1980
Old 011'
New 011"
5.03
10.13
58.9
5.03
12.03
Lower-Tier Upper-Tier Stripper
59.2
11.71
12.16
5.19
11.22
13.59
6.35
12.34
63.1
5.46
12.15
13.95
5.22
12.85
64.5
12.64
5.95
13.20
22.93
10.57
19.40
55.1
21.20
6.49
14.34
3554
14.14
3306
59.6
Naval
Alaska Petroleum
North Slope Reserves
65.2
I
Before entitlement benefit.
2
In 1972 and most of 1973, petroleum prices were subject to the Phase I-IV price provisions of the Economic Stabilization
Act. The average domestic wellhead price during that period did not differ substantially from the refiner acquisition cost
of crude, so it can be assumed that controls had little effect on domestic crude-oil prices. As a reSUlt, prices are assumed
to be the same with or without controls.
;i Estimated by excluding domestic producers' transportation costs from the refiner acquisition price for imported oil, the
adjustment being based on the post-1976 price of stripper oil. This adjustment reflects the fact that the wellhead price for
stripper oil-deconlrolled in September 1976-represents an uncontrolled price for domestic oil exclusive of transportation costs.
4
Under the Emergency Petroleum Allocation Act in effect throughout 1974 and 1975, "old" oil in any given month was
defined as the quantity produced from a given property in the corresponding month of 1972.
" Under the Emergency Petroleum Allocation Act, "new" oil was defined as any production in excess of output in the
same month of 1972.
" The post-1976 (decontrolled) stripper price was used as a proxy for the uncontrolled domestic producer price. Actually, in
1979 and 1980, stripper oil sold at a substantial premium above comparable-quality imported oil, due to tight worldwide
supply conditions and the willingness of refiners to pay a premium for security of supply.
Source: Uncontrolled domestic price at the wellhead estimated by author as described in footnote 3 above. Actual prices as
published by U.S. Department of Energy, Monthly Energy Review.
16
production, as we also have done here. 23 These
studies have yielded a wide range of elasticity
estimates - ranging from .3 to .8 - with the
variation perhaps due in part to the different
time periods involved. 24
Utilizing these published elasticity estimates, we estimated production losses for the
1976-79 price-control period under several
different elasticity assumptions (Table 3). The
elasticity of production from existing properties
was assumed to be .2 in each scenario.
However, the elasticities of production from
new properties ranged from .3 (low), to .5
(medium) to .8 (high assumption).
All these elasticity estimates pertain to the
long-run. They show how production eventually might respond to a given change in price
after time had elapsed for exploration and
development. In our estimates, however, we
have recorded the response as if it shows up
fully within a year. For example, the estimated
production losses for 1976 represent the additional production that would be forthcoming in
the long-run as a result of closing the differentials between controlled and uncontrolled
prices prevailing during that year. Although
recorded for that single year, in reality the production response would take considerably
longer.
The results indicate a substantial lowering of
production by controls in the 1976-79 period,
under all scenarios (Table 3). The likeliest outcome would probably arise from the lowresponse assumption, because elasticity of
supply would surely fall in the wake of a substantial widening of price differentials. Under
this low-response scenario, production with
uncontrolled prices eventually could have
been 10 percent higher in 1976, and 29 percent
higher in 1979, than actual production with
controlled prices. The comparable production
increases under the high-response scenario
would have been 15 percent in 1976 and 73
percent in 1979 - although the underlying
elasticity estimates in that scenario appear to
be unrealistically high. The limited nature of
the resource base, and the further depletion in
recent years, would preclude the likelihood of
very high supply elasticities - .8 for new dis-
undertaking. Instead, we have relied upon
already existing models to obtain long-run
price elasticities of supply upon which to estimate the production losses resulting froJ1.l that
particular control program. Elasticity of supply
is a measure of the responsiveness of the quantity supplied of a given product to an increase
in its price.
In the absence of controls, the average
wellhead prices of lower and upper-tier crude
oil would have risen from their respective controlled levels to the world market level. 21 At
existing properties - those in operation
before 1975 - an increase in prices would
have: (1) raised investment in development
wells, thereby raising the rate of extraction
from proved reserves and (2) encouraged
greater investment in enhanced oil-recovery
methods, thereby increasing additions to
reserves through improved technology. An
increase in the upper-tier price also would
have encouraged more exploratory drilling,
leading to the discovery of more new reserves
at new properties.
This study attempts to estimate how much
extra production would have been forthcoming had prices been allowed to rise to the world
price. It does so by drawing on outside estimates of the elasticity of supply, the percentage change in quantity supplied divided by the
percentage change in price. In estimating production losses as a result of controls, we calculated the percentage difference between the
uncontrolled and controlled prices in any given
year, multiplied that by the supply elasticity to
get the percentage change in output, and then
converted that percentage change to an
arithmetic change by multiplying it by the
existing quantity.
Recent studies by the Department of Energy
suggest a long-run price elasticity of about .2
for categories of production equivalent to
"existing properties."22 Numerous
econometric studies are available for deriving
elasticity estimates for new properties. These
studies relate price to additions to reserves
from new discoveries. The authors then
assume that a given increase in new reserves
leads to an equivalent percentage increase in
17
Table 3
Domestic Crude Oil Production Losses Under the Energy Policy and Conservation Act,
1976-79
(Production in millions of barrels)
Domestic Crude 011 Prices'
(Dollars per barrel)
Prices with Controls
Domestic Crude Oil Production
(Millions of barrels)
Year
lower-Tier
Upper-Tier
Estimated Price
Without Controls"
Total Production
With Controls
1976
5.13
11.71
12.56
2968
1977
5.19
11.22
13.59
3009
1978
5.46
12.15
13.95
3178
1979
5.95
13.20
22.93
3115
Domestic Crude Oil Production
(Millions of barrels)
Estimated Production
Losses Due to Controls"
Low
Response
Year
Existing Properties'
1976
267
1n","J
~..,..,
New Properties'
18
Estimated Total
Production
Without Controls
Additional
Domestic Production
Without Controls as
a Percent of Production with Controls
3253
9.6
1 A 1
p"
J'11"'''7
.... L.I
"IJ.'7"
3495
10.0
1'7'(
£.//
1978
228
89
1979
350
561
4026'
29.2
1976
267
115
3350
12.9
1977
277
330
3616
20.2
1978
228
244
3649
14.8
1979
350
1102
4566
46.6
1976
267
187
3421
15.3
1977
277
544
3830
27.3
1978
228
398
3804
19.7
1979
350
1924
5389
73.0
Medium Response
Year
High Response
Year
, Annual averages; producer prices at the wellhead.
, For an explanation of the derivation of this price series, see Table 2.
Derived by the author on the basis of three separate assumptions regarding price elasticity of supply for new properties.
Each response is assumed to become fully effective within a single year, although in reality, the production response to
closing any given differential between controlled and uncontrolled prices would take more than a year.
:j
1
Elasticity figures for existing properties are .2 in all cases; for new properties .3 for low response, .5 for medium response,
and .8 for high response.
Source: Price and actual production data: U.S. Department of Energy, Monthly Energy Review. Estimated production losses
computed by author using methodology described in text.
18
coveries - included in that scenario. 25
In all scenarios, the potential losses with
controls would have been very large on the
basis of 1979 prices because of the huge
increase estimated for wellhead prices in the
absence of controls. The average refiner
acquisition price for imported crude (before
entitlements) rose by only 41f2 percent over the
entire 1975-78 period, but then jumped 49
percent within 1979 alone (Table 2), as OPEC
members sharply boosted prices in the wake of
the cutoff of Iranian exports and consequent
world-wide tightening of supplies. The average
domestic wellhead price without controls the average refiner acquisition price for
imported crude less transportation costs from
domestic wells to refineries - thus would
have risen about 58 percent in 1979. Indeed,
that wellhead price probably would have risen
even more, because of refiners' willingness to
pay a premium for domestic oil for security of
supply. In this situation, controlled prices of
lower-tier and upper-tier oil would have been
only 17 and 39 percent, respectively, of the
estimated uncontrolled price for domestic oil.
Windfall Profit Tax
The windfall profit tax will dilute the
stimulus to increased production provided by
decontrol. The amount of dilution will depend
principally upon the future behavior of the
uncontrolled domestic-producer selling price
- and thus the after-tax realized price - and
upon the production response to any given
increase in realized price.
Based upon an assumed 2 percent "real"
average annual increase in the uncontrolled
domestic producer selling price over the 198090 period, we have developed different sets of
estimates of the offsetting effect of the
windfall-profit tax on the positive production
response from decontrol for the years 1985
and 1990. 26 This involves the development of
three alternative policy assumptions: (l)
Scenario I, continued price controls; (2)
Scenario II, decontrol with no windfall-profit
tax, and (3) Scenario III, decontrol with a
windfall-profit tax. As before, we have
assumed a lower elasticity of supply for oil
from existing properties - Tiers 1 and 2, as
well as heavy oil and incremental tertiary oil -
Table 4
Estimated Domestic Producer Oil Prices, 1985 and 1990,
Under Three Alternative Policy Assumptions!
Scenario I
I
2
:J
4
Scenario II
Prices with Decontrol but
No Windfall Profit Tax"
Scenario III
Prices with Decontrol and
Windfall Profit Tax'
Tier 1
Tier 3
Tier 2
Year
Prices with Continued Controls'
Tier 1
Tier 2
Tier 3
1985
19.92
23.64
28.23
53.93
29.57
35.10
45.25
1990
26.78
31.77
41.92
79.84
41.84
49.96
67.03
Annual averages in dollars per barrel; producer sales prices.
For 1985 and 1990, prices with controls were estimated by making inflation adjustments to the base prices for each tier (as
defined in the Crude Oil Windfall Profit Tax of 1980, Table O. For 1980, the adjustment factors were based on the GNP
deflator. Thereafter, the inflation rate was assumed to decline gradually, reaching a 6.0-percent annual rate by mid-1986
and remaining at that rate through 1990. For Tier 3, the base price was adjusted upward by an additional 2 percent each
year, as allowed in the law.
The author estimated that domestic oil, without controls, would have sold for $35/barrel in the fourth quarter of 1980.
For 1985 and 1990, the decontrolled price was estimated by adjusting the 1980 price to reflect inflation plus an assumed 2percent annual increase. The anticipated price of heavy oil in 1980 was assumed to be $7.50 less than the average domestic
price, reflecting the traditional price differential.
The author assumed that the windfall profit tax effectively reduces the selling price actually realized by domestic producers. For a description of the derivation of these prices, see Appendix A. The tiers represent the categories of domestic
oil as defined by the Crude Oil Windfall Profit Tax of 1980, as shown in Table 1.
19
than for oil from newly discovered properties.
And again, we have assumed a range of
elasticities for Tier 3 newly-discovered oil,
ranging from .3 (low), to .5 (medium) to .8
(high assumption).
To develop production estimates, we first
estimate producer prices under each of the
three scenarios (Table 4), making the estimates in nominal terms to conform with the
actual computation of the windfall-profit tax.
The tax affects production in any given period
through its impact on the realized relative
price of oil compared with what it would be
without the tax.
Under continued controls (Scenario I), we
calculate prices for Tier 1 and Tier 2 oil for the
years 1985 and 1990 as equal to certain base
prices (defined by the Windfall Profit Tax)
Table 5: Estimated Domestic Crude Oil Production, 1985
Low Response'
Tier 1
I
:J
4
Scenario II
Production with Decontrol but
No Windfall Profit Tax'
Total"
Tier 1
Tier 2
Tier 3
Total"
2,046
500
97
3,113
U)
U)
(.3)
1985
730
536
907
2,748
891
632
1,530
3,628
1990
318
637
1,035
2,464
396
766
1,611
3,248
Medium Response'
1979 (Actual)
2,046
500
97
3,113
U)
U)
(.5)
1985
730
536
907
2,748
891
632
2,094
4,192
1990
318
637
1,035
2,464
396
766
2,112
3,749
High Response'
1979 (Actual)
2,046
500
97
3,113
U)
U)
(.8)
1985
730
536
907
2,748
891
632
2,993
5,091
1990
318
637
1,035
2,464
396
766
2,912
4,549
1979 (Actual)
2
Scenario I
Production with
Continued
Price
Tier 2
Tier 3
In millions of barrels.
Low, medium and high responses refer to the assumed elasticities of supply for various categories of crude. Tier 1 and
Tier 2 oil, as well as heavy oil and incremental tertiary (enhanced) oil in Tier 3, were assumed to be oil from existing properties. Oil from new properties appears in Tier 3. In each response case, oil from existing properties (Tiers 1 and 2 and
heavy oil and incremental tertiary oil in Tier 3) was assumed to have a price elasticity of .2. The elasticity for new properties (Tier 3) varied from .3 in the low case to .5 in the medium case and .8 in the high case.
Assumes domestic oil prices behave as described in Table 4, Scenario I, with a continuation of the controls embodied in
the Energy Policy and Conservation Act. Production estimates for the years 1985 and 1990 under this assumption are
from the Congressional Budget Office study cited below, page 76. These production estimates were used to derive our
Scenarios II and III.
Assumes domestic oil prices behave as described in Table 4, Scenario II. Production was estimated on the basis of the
same supply elasticities utilized in estimating producing losses under the Energy Policy and Conservation Act.
20
ing the inflation-plus-2-percent adjustment to
the uncontrolled stripper price ($35 a barreD
in the fourth quarter of 1980. (We use the
same methodology, although a higher base
price, as the Joint Committee on Taxation
uses in estimating windfall-profit tax
revenue.) 28 Under decontrol and the tax
(Scenario III) we calculate the realized producer price by adding the extra after-tax
adjusted by inflation (measured by the GNP
deflator). The Tier 3 inflation adjustment
equals the inflation rate plus 2 percent
annually, as specified in the law. 27 Thus, in this
scenario, prices for Tier 1 and Tier 2 production remain constant in real terms, while the
price for Tier 3 production rises at a 2-percent
real annual rate. Under decontrol (Scenario
II) , we estimate the free market price by apply-
and 1990, Under Three Alternative Policy Assumptions]
Scenario III
Percent Increase
in Total Production
Due to DecontroF
r,
Production with Decontrol and
Windfall Profit Tax'
Tier 1
Tier 2
Tier 3
Total"
Percent Increase In
Total Production
After Tax'
(.2)
(.2)
(.3)
32.0
790
580
1,314
3,259
18.6
31.8
348
697
1,416
2,936
19.2
(.2)
(.2)
(.5)
52.5
790
580
1,690
3,635
32.3
52.2
348
697
1,752
3,272
32.8
(.2)
(.2)
(.8)
85.3
790
580
2,243
4,188
52.4
84.6
348
697
2,247
3,767
53.7
Assumes domestic oil prices behave as described in Table 4, Scenario Ill.
,; Alaskan oil from proved reserves has been included in the production totals, but not in any tier. The author estimated
this Alaskan production at 575 and 475 million barrels in 1985 and 1990, respectively, compared with 471 million barrels
in 1979.
7
This refers to the amount (percent) by which total production without controls (Scenario ll) would exceed total production with continued controls (Scenario during the years 1985 and 1990, respectively.
n
, This refers to the amount (percent) by which total production without price controls but with the windfall profits tax
(Scenario III) would exceed total production with continued controls (Scenario I) during the years 1985 and 1990, respectively.
Source: Production estimates in Scenario I, Congressional Budget Office, The Windfall Profits Tax: A Comparative Ana(ysis of
Two Bills. 1979. All other estimates by the author.
21
revenue per barrel to the estimated price
under continued controls (Appendix A).
With these assumptions, the nominal free
market price rises from $35/barrel during
1980-IV to about $54/barrel by 1985 and $80/
barrel by 1990 (Table 4). After-tax producer
prices thus range (depending on tier) from 55
to 84 percent of the uncontrolled price by
1985, and from 52 to 84 percent of the
uncontrolled price by 1990.
With these price estimates, and with Congressional Budget Office estimates of production under continued controls, we derive
(Scenario II and III) production estimates by
applying appropriate supply elasticities, just as
we did in estimating the effects of the Energy
Policy and Conservation Act. 29 The use of
nominal prices to estimate production losses is
justified by the use of the same inflation
adjustment for both controlled and
uncontrolled prices, so that inflation has a
neutral effect.
As seen in Table 5, domestic oil production
undoubtedly would have continued to trend
downward over the 1979-90 period under continued price controls. But all three sets of
assumed elasticities suggest that production is
likely to rise substantially between 1979 and
1985 under decontrol. The Congressional
Budget Office's forecast for production under
continued controls shows total production
dropping from 3,113 million barrels in 1979 to
2,748 million barrels by 1985, and then to
2,464 million barrels by 1990. Under the "low
response" set of elasticities, total production
with decontrol and no tax would reach 3,628
million barrels in 1985 and 3,248 million barrels in 1990. With the tax, production could
still reach 3,255 million barrels in 1985 and
2,936 million barrels in 1990. Production
figures in the "high response" case would be
considerably higher, but as already indicated,
the elasticity figures involved appear to be
unrealistically high.
Here again, the production differentials between the scenarios would not necessarily
occur specifically in 1985 and 1990. Rather,
the differentials represent the ultimate production responses to the estimated price differentials existing in those years as a result of the
tax.
Domestic production probably would rise
Table 6: Estimated Domestic
Under Three Alternative Domestic Oil PriCE
Scenario I
Total Production
with Continued
Controls"
2748
Total Production
With Decontrol but
No Windfall
Profit Tax
3790
Percent Increase
in Production
With Decontrol but
No Windfall
Profit Tax
37.9
2748
3962
44.2
+2
2748
4192
52.5
+5
2748
4555
65.8
+10
2748
5209
89.6
Annual Percent
Increase in
the Decontrolled
Domestic Price
in Real Terms
~2
o
l
Annual production in millions of barrels.
2
Medium response assumes an elasticity of.2 for tiers 1 and 2, respectively, and also for heavy oil and incremental tertiary
oil in tier 3. It assumes an elasticity of .5 for newly discovered oil in tier 3.
22
Unfortunately, increased drilling activity has
not been translated into an increase in proved
crude-oil reserves. In 1979, total reserves continued a decline that began in 1968. But gross
additions to reserves amounted to 2.2 billion
barrels, the highest figure since 1971. This
meant a narrowing of the deficit between the
gross volume added to reserves and the
amount extracted. The inventory of proved
reserves dropped by only 0.8 billion barrels the smallest amount since 1968.
In any event, our analysis indicates that the
windfall-profit tax would reduce the production response expected from decontrol. As a
measure to reduce dependence on foreign-oil
imports and improve the allocation of
resources, decontrol is a step in the right direction. But by the same token, the windfall-profit
tax is a step in the wrong direction. Perhaps
policymakers should alter the tax to make it a
true tax on profits rather than an excise tax on
a portion of the selling price. In that way, it
would not affect production decisions at the
margin.
even faster than projected, under all three sets
of elasticity assumptions, if the uncontrolled
price rose at more than 2 percent above the
inflation rate (Table 6). For example, in the
medium-response situation, an increase from
2 percent to 5 percent in the real rate of oilprice rise would mean an increase, from 53
percent to 66 percent, in the production
differential achieved by 1985 because of the
shift from controlled to uncontrolled prices.
With the windfall profit tax in effect, the production differential would be 32 percent with a
2-percent real increase in prices, and 41 percent with a 5-percent real rate of increase.
The higher prices being realized by producers as a result of decontrol apparently are
now exerting a dramatic impact on exploration
and development activity. Drilling activity set
a new record in 1980, surpassing the previous
highs reached in the mid-1950's. During the
year, the industry drilled nearly 65,000 wells of
all types - about 26 percent more than during
1979. For the year, total footage drilled rose 23
percent, while the number of drilling rigs in
operation rose 32 percent. New records appear
in prospect for 1981.
Crude Oil Production, 1985,
Assumptions l and with Medium Response 2
-'S=cc'-'e=nac.'-'rio~II"_I
.
Total Production
With Decontrol and
Windfall
Profit Tax
3379
_
Percent Increase
in Production
With Decontrol and
Windfall
Profit Tax
23.0
Amount of Production
Lost Due to the Tax
as a Percent of Production with Decontrol
and No Windfall
Profit Tax'
10.8
3487
26.9
12.0
3635
32.3
13.3
3871
40.9
15.0
4301
56.5
17.4
, Production under this scenario depends upon the controlled price, and therefore is not influenced by alternative assumptions with regard to the decontrolled price.
4
Actual production losses under each price assumption are as follows: -2%, 411; 0%, 475;
+ 10%,908.
23
+ 2%,
557;
+ 5%,
684;
24
V.
Summary and Conclusions
Federal price-control programs in effect
throughout most of the 1970's held the
average domestic producer price of crude oil
below the world market level. By permitting
refiners to pay less than the world price for
domestic crude, Congress attempted to protect
consumers from bearing the full impact of rising world prices. There is considerable debate
as to whether that objective was achieved.
Moreover, controls affected the supply side of
the u.s. market, both by creating greater dependence on foreign oil and by leading to an
inefficient allocation of resources. In this
respect, the Energy Policy and Conservation
Act - as well as earlier control programs reduced domestic production substantially
below the level that would have prevailed
without controls.
Efficiency in satisfying any given level of
national consumption requires that domestic
producers expand crude-oil production to the
point where the cost of the last barrel equals
the cost of acquiring an additional barrel of
foreign crude. Federal controls violated that
condition, by holding the domestic selling
price below the landed price of foreign oil, and
thereby causing the industry to produce at less
than the optimum production level. For every
barrel not produced, the nation's dependence
on foreign oil rose by an equivalent amount at
a greater cost of resources.
The removal of price controls (January 28,
1981) has forced refiners to pay free-market
prices for domestic crude oil. That means
higher refined-product prices also, to the
extent that refiners pass on those higher costs
to consumers. But decontrol also should raise
domestic production above the level that
would prevail under continued controls. In
fact, decontrol may bring about at least a temporary reversal in the production decline of the
past decade.
But the windfall-profit tax will reduce that
positive impact. For example, with supply
elasticities of .2 and .3 for existing and new
properties, respectively, and with a 2-percent
Appendix A
Windfall Profit Tax (WPT) Calculation, 19851
Tier III
Estimated Decontrolled Price'
Less Adjusted 1979 Base Price'
Windfall Profit Before Severance
Less Severance Tax'
Windfall Profit
Windfall Tax
Heavy
Oil
42.38
-28.23
All Other
TIer III Oil
53.93
-28.23
Tier I
53.93
-19.92
Tier II
53.93
-23.64
34.01
- 1.84
30.29
1.64
14.15
.76
25.70
- 1.39
32.17
- 22.52
28.65
-1719
13.39
- 402
24.31
- 7.29
9.65
11.46
9.37
17.02
19.92
23.64
+ 965
+ 11.46
28.23
+ 9.37
28.23
+17.02
29.57
35.10
37.60
45.25
Amount of Windfall Retained by Producers
Producer Realized Prices with Decontrol after WPT
Adjusted Base Price
Amount of Windfall Retained by Producers
Producer Price with Decontrol after WPT
I
All data in dollars per barrel.
, Price assumed to rise at the inflation rate plus 2 percent annually between 1980 and 1985.
1
Base price adjusted upward over the 1980-85 period according to the method described in the law.
, Tax imposed by the states, assumed 10 average 5.4 percent of the windfall profit before severance.
Source: All computations by aUlhor.
25
real rate of price increase, decontrolled production would be 31 percent higher in 1985,
and 30 percent higher in 1990, than the
amounts that might be produced with continued controls. But the windfall-profit tax
could reduce that production differential to
about 18 percent in 1985 and 1990 respectively. And the more the decontrolled price of
oil rises relative to prices of other goods and
services, the greater will be the production
losses attributable to the tax.
FOOTNOTES
1, The term Ilproperty" is used as defined in the
rather than the price actually paid. That approach
made it possible to increase the price of stripper-well
oil without lowering the price of some other category
of domestic oil. See Montgomery (1977, pp. 9 and 12)
for a discussion of this point as well as the inflation
adjustment.
Energy Policy and Conservation Act to mean a separate and distinct producing reservoir. (U.S. Department of Energy, Monthly Energy Review, January
1981, p. 99). A "reservoir" is a porous and permeable
underground formation containing an individual and
separate natural accumulation of producible oil or of
oil and natural gas. In most situations, reservoirs are
classified as oil or gas reservoirs by a regulatory
agency. See American Petroleum Institute (1976, p.
7).
11. Economists generally agree that controls held
the average domestic producer selling price below
the world market level. Economists also agree that the
so-called entitlement program equalized the average
cost of crude oil to each refi ner regardless of the relative amounts of imported, lower-tier, or upper-tier
imputs used - and that refiners paid a common
average price for all oil that was below the world
market level. See, for example, Cox and Wright (1978,
p. 4) and Montgomery (1977, p. 37). There is
widespread disagreement, however, about whether
crude-oil price controls reduced refined-product
prices below the level that would have prevailed without controls. Montgomery has argued that the entitlement program utilized competitive market forces to
pass through the increased refiners' profits from
price-controlled crude oil, from crude-oil producers to
refined product consumers (1977, pp. 37 -40). Phelps
and Smith (1977) maintain that refined-product
prices were not held down by the controls and entitlements, and profits were transferred from producers to
refiners. They argue that world refined products are
made from world crude. The U.S. imports refined products and therefore, U.S. refined product prices must
reflect world crude prices. This is basically an empirical question, but with much conflicing evidence. See,
for example, Deacon (1978).
2. In this regard, crude-oil production differs from
most manufacturing processes. With the latter, we
assume that increasing capacity, (i.e., rate of attainable production), causes something like a proportionate increase in the amount of product that ultimately
will be forthcoming. Crude-oil investments, however,
must be described with reference to two dimensions:
the rate of output to be achieved, and the total volume
of crude available for ultimate production. For a discussion of this point, see Bradley (1967, p. 16).
3. American Petroieum Institute, American Gas Association, Canadian Petroleum Association (1980, p.
14).
4. See, for example, Duchesneau (1975) and Eppen
(1975)
5. Herfindahl and Kneese (1974, p. 123).
6. This would be the average delivered price for
imported oil at the refinery gate, including transportation costs. In actuality, average domestic producer
prices probably would not exactly equal the average
landed cost of imported oil because of quality
differences. Crude oil is not a homogeneous commodity; viscosity, sulfur content and other characteristics vary and affect its value. Nevertheless, the
price of imported oil would determine domestic prices
in the manner described in the text.
12. The following analysis synthesizes an even more
detailed analysis of the production effects of the
Energy Policy and Conservation Act, made by Kall
(1980, pp. 107-111). For an earlier discussion, see
Roush (1976, pp. 16-20).
13. There are also resources wasted on the demand
side as a a result of controls. The entitlement program
reduced the price of imported oil to a common
average price for domestic and imported oil (P r) which
was below the world market price (P w)' In doing so, it
raised the quantity of imported oil demanded above
the quantity that would have been demanded had
refiners been required to pay the world price for an
incremental barrel of crude. The additional oil
demanded had an incremental value to the economy
of Pro But to realize that value, the nation paid the
world price, Pw' to foreign sellers of crude. The
resources consequently wasted on the demand-side
equalled the difference between the world price and
the average refiner acquisition price for both foreign
and domestic oil, times the additional quantity
7. The requirements for efficiency on the supply and
demand sides of the U.S. crude-oil market, as well as
the inefficiencies created by price controls, are discussed in detail by Arrow and Kalt (1979, pp. 9-27).
Their work draws upon an earlier study by Roush
(1976).
8. For a detailed discussion of these state programs,
see McDonald (1971, pp. 29-55) and Bohi and
Russell (1978, pp. 250-253).
9. For a description of the various Federal crude-oil
price-control programs of the late 1970's, see
MacAvoy (1977) and Montgomery (1977 and 1978).
10. In computing the average target price, the energy
agency assigned stripper-well oil an upper-tier price
26
demanded as a result of the entitlement program. We
should note that the average refiner acquisition price
for domestic and imported oil, Pr , under the entitlement program was between the world price, Pw ' and
the average controlled domestic price, Pc as shown in
Chart 2. That price was not shown on the chart
because it did not affect the domestic production of
crude oil.
22. In its 1979 Annual Report to Congress, the U.S.
Department of Energy forecast production for 1985
and 1990 under several categories that would correspond to existing properties, the most responsive
being production from enhanced oil-recovery techniques. The imputed price elasticity for existing properties derivable from these forecasts is approximately.2.
14. If marginal profit is increasing like compound
interest, an owner of a reservoir will be indifferent at
the margin between extracting and holding at every
instant of time. Hotelling (1931) established the
profit-maximizing condition for a firm managing a depletable resource. For a further discussion of the
point see Solow (1974, pp. 1-6).
23. That assumption was employed in most models
of reserve additions. See Bohi and Russell (1978, p.
237) for a discussion of this point.
24. For example, Fisher (1964) estimated an
eillsticity for new-oil discoveries of .3 using data for
1946-55, but Erickson and Spann (1971) obtained an
estimate of .8 using 1946-59 data. The U.S. Department of Energy, in its 1979 Annual Report to Congress, developed forecasts for 1985 and 1990 which
imply an elasticity for new fields of around .3. For a
survey of these and other models, see Kimmel (1977).
15. Kalt found that, on balance, controls tended "to
encourage later rather than earlier extraction." See
Kalt (1980, p. 132).
16. As indicated in footnote 11, some economists
argued that refined-product prices already reflected
world oil prices. They maintained that decontrolling
domestic crude-oil prices would have no effect on
refined-product prices.
25. Estimates vary widely concerning the total
amount of oil remaining to be discovered in the United
States, both on and offshore. For example, one official
source places the total undiscovered recoverable
resource base at somewhere between 50 and 127
billion barrels; see U.S. Geological Survey (1975,
p. 4). Another recent assessment places the estimate
at between 14 and 32 billion barrels; see Nehring
(1981, p.175).
17. This estimate was based on the assumption that
the uncontrolled domestic-producer price rose at the
inflation rate plus 2 percent - i.e., at a 2 percent real
annual rate - over the 1980-90 period. Reported in
"U.S. Windfall Tax Bonanza Based on $75 Oil Price in
1990" (1980, p. 3)
26. This is the same price assumption employed by
the Joint Committee on Taxation in developing its
1979 estimates of the Federal revenues to be derived
from the windfall-profit tax. The price assumption is
used to analyze the production effects of decontrol,
with and without the windfall-profit tax. Note that
there would be no tax unless the uncontrolled
domestic price remains above the adjusted base
price.
18. See assumption described in footnote 17.
19. The projected decline rate ("base level") is the
average daily amount of oil removed from the property
during the six-month period ended March 31, 1979,
reduced by one percent per month (after 1978) for
each month before the project-beginning date. See
Price Waterhouse and Company (1980, p. 21).
20. There would be no "windfall" upon which to base
the tax unless this condition prevailed.
27. Tier 3 encompases newly discovered oil, heavy
oil and incremental tertiary oil. It receives preferential
treatment in the law through a lower tax rate and an
extra 2-percent annual increase in its base-adjusted
price.
21. Since controls were imposed on the selling price,
average selling prices of. lower- and upper-tier crude
in the absence of controls would have risen to
approximately the landed price for imported oil
(before entitlements). The uncontrolled wellhead
price would have roughly equalled the world price
minus the average transportation costs incurred by
domestic producers in supplying refiners. For
reasons of data availability we used actual and estimated uncontrolled wellhead prices, rather than seIling prices, in calCUlating possible production losses
resulting from the Energy Policy and Conservation
Act.
28. Their estimate, made in early 1979, underestimated the actual increase in uncontrolled prices that
actually occurred by the latter part of that year.
29. For estimates of production under continued
controls, see U.S. Congress, Congressional Budget
Office (1979, p. 76).
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American Petroleum I nstitute. Standard Definitions
for Petroleum Statistics. Technical Report No.1.
Washington, D.C.: American Petroleum Institute,
1976.
Natural Gas in the United States and Canada as
of December 31,1979. Washington, D.C.: American Petroleum Institute, 1980.
Arrow, Kenneth J. and Kalt, Joseph P. Petroleum
Price Regulation: Should We Decontrol?
Washington, D.C.: American Enterprise Institute
for Public Policy Research, 1979.
American Petroleum Institute, American Gas Association, Canadian Petroleum Association.
Reserves of Crude Oil, Natural Gas liquids and
27
Bohi, Douglas R. and Russell, Milton. limiting Oil
Imports. Baltimore: Johns Hopkins University
Press, 1978.
Force. Washington, D.C.: American Enterprise
Institute for Public Policy Research, 1977.
Montgomery, W. David. "A Case Study of Regulatory
Programs of the Federal Energy Administration,"
Study on Federal Regulations. U.S. Senate,
Committee on Government Affairs. Washington,
D.C.: U.S. Government Printing Office, 1978,
pages 733-833.
Bradley, Paul G. The Economics of Crude Petroleum
Production. Amsterdam: North-Holland Publishing Company, 1967.
Cox, James C. and Wright, Arthur W. "The Effects of
Crude Oil Price Controls, Entitlements and Taxes
on Refined Product Prices and Energy Independence," land Economics. February 1978, pages
1-15.
__, The Transition to Uncontrolled Crude Oil
Prices. Prepared for the National Bureau of Economic Research Conference on Public Regulation, Washington, D.C., December 15-17, 1977.
Pasadena: California Institute of Technology,
1977.
Deacon, Robert T. "An Economic Analysis of Gasoline
Price Controls," Natural Resources Journal.
October, 1978, pages 801-814.
Nehring, Richard and Van Driest, E. Reginald. The
Discovery of Significant Oil and Gas Fields in
the United States. Santa Monica: Rand Corporation, 1981.
Duchesneau, Thomas D. Competition in the U.S.
Energy Industry. Cambridge: Ford Foundation,
1975.
Eppen, Gary. Energy: The Policy Issues. Chicago:
University of Chicago Press, 1975.
Phelps, Charles E. and Smith, Rodney T. Petroleum
Regulation: The False Dilemma of Decontrol.
Santa Monica: Rand Corporation, 1977.
Erickson, Edward W. and Spann, Robert M. "Supply
Response in a Regulated Industry: The Case of
Natural Gas," Bell Journal of Economics and
Management Science. Spring, 1971, pages 94121.
Price Waterhouse and Company. Windfall Profix Tax.
New York: Price Waterhouse and Company,
1980.
Roush, Calvin T., Jr. Effects of Federal Price and
Allocations Regulations on the Petroleum
Industry. U.S. Federal Trade Commission Staff
Report, 1976.
Fisher, Franklin M. Supply and Costs in the U.S.
Petroleum Industry. Baltimore: John Hopkins
Press, 1964.
Haiimark, Fred O. Heavy Oil in California. Sacramento: California Division of Oil and Gas, 1980.
(Unpublished memo)
Solow, Robert M. "'The Economics of Resources or
the Resources of Economics," The American
Economic Review, Papers and Proceedings. May
1974, pages 1-14.
Herfindahl, Orris C. and Kneese, Allan V. Economic
Theory of Natural Resources. Columbus:
Charles E. Merrill Publishing Company, 1974.
U.S. Congress, Congressional Budget Office. The
Windfall Profits Tax: A Comparative Analysis of
Two Bills. Washington, D.C.: U.S. Government
Printing Office, November 1979.
Hotelling, Harold. "The Economics of Exhaustible
Resources," Journal of Political Economy. April
1931, pages 133-75.
U.S. Department of Energy, Energy Information Administration. Amwal Report to Congress 1979,
Volume 3. Washington, D.C.: U.S. Government
Printing Office, 1980.
Kalt, Joseph. Federal Regulation of Petroleum
Prices: A Case Study of the Theory of Regulation. Unpublished Ph.D. dissertation, University
of California, Los Angeles, 1980.
U.S. Department of Energy. Monthly Energy Review.
Washington, D.C.: U.S. Government Printing Office.
Kimmel, David. The Price-Responsiveness of
Petroleum Supply: A literature Review.
Washington, D.C.: American Petroleum Institute,
1977.
U.S. Geological Survey. Geological Estimates of
Undiscovered Recoverable Oil and Gas
Resources in the United States. Geological
Survey Circular 725 Washington, D.C.; June
1975.
Lewin and Associates. Enhanced Oil Recovery
Potential in the United States. Study prepared
for the U.S. Congress, Office of Technology
Assessment. Washington, D.C.; Office of Technology Assessment, 1978.
"U.S. Windfall Tax Bonanza Based on $75 Oil Price in
1990," Petroleum Intelligence Weekly. March
10,1980, pages 3-6.
MacAvoy, Paul W., ed. Federal Energy Administration
Regulations. Report of the Presidential Task
28
Adrian W. Throop*
Increasingly volatile financial markets have
put a premium on accurate forecasts of interest
rates. To the extent, however, that market participants base their decisions on available
interest-rate forecasts, the value of these
forecasts to an individual investor is
diminished because security prices would
already tend to reflect that information. At the
extreme, the efficient-market hypothesis
asserts that the market efficiently utilizes all
available information in the pricing of
securities, so that market participants
generally can not profit from more accurate
forecasts than those already incorporated in
security prices.
This article examines the degree to which
the Treasury-bill market efficiently utilizes all
available information so as to incorporate the
best possible interest-rate forecast into current
market prices. In other words, it evaluates the
applicability of the efficient-market hypothesis
to the Treasury-bill market. Two types of independent forecasts are examined: an
autoregressive forecasting equation based on
the past history of the bill rate, and the forecast
of a selected panel of market professionals.
Statistical tests are used to determine whether
all useful information contained in these two
forecasts is efficiently incorporated into Treasury-bill market prices. The market's forecast is
derived from the "forward rate" implied by
the term structure of yields.
If the market is not efficient, a group of
investors could improve their returns by altering the maturity of their investments in light of
superior interest rate forecasts. Near a peak in
the business cycle, for example, if such
forecasts correctly foresee a larger decline in
interest rates than anticipated by the market,
then investors should buy securities with a
maturity longer than their expected investment periods. The yields obtained by investors
would be greater than those obtainable if they
had chosen maturities equal to their investment period, due to larger capital gains than
had been anticipated by the market. Alternatively, if the available forecasts correctly
foresee interest rates falling more slowly than
the market does, the investors utilizing those
forecasts should buy maturities shorter than
their investment periods. This is because
investors would obtain a higher return from
"rolling over" a series of short-term securities
than from buying maturities equal to their
investment periods.
Whether or not investors can profit by
"speculating" on interest rates, through holding other than their normally preferred
maturities, depends critically on whether
available interest-rate forecasts are more
accurate than the market's. If the market is
efficient, the information in these forecasts
would already be incorporated into the prices
of securities, and therefore nothing would be
gained. In that case, investors would be better
off by simply "hedging" their positions with
maturities equal to their planned investment
periods, thereby avoiding possible risk.
This study shows that professional analysts'
prediction of the Treasury-bill rate two quarters ahead are significantly more accurate than
market predictions. This indicates that the
market does not efficiently utilize all available
information in making bill-rate forecasts. By
'Senior Economist. Federal Reserve Bank of San Francisco. Coleman Kendall provided research assistance for
this article.
29
scribed and performed, on the basis of these
three forecasts. Both the analysts' forecast and
the forecast from the autoregressive forecasting equation are found to contain useful information which is not fully incorporated into the
market's forecast
indicating market inefficiency. Section III shows that the analysts'
forecast contains information similar to that in
the autoregressive forecasting equation, plus
other useful information which is also not fully
incorporated into the market's forecast. Investors could have traded on both types of information to improve their returns in the period
examined. Section IV provides a summary and
some further conclusions.
making use of the information contained in the
analysts' forecast, an investor in Treasury bills
could have improved his return. We show that
the analysts' ability to "beat the market"
stems from a better utilization of information
about past movements in the bill rate, and also
from a more efficient utilization of other sorts
of information.
Section I explains the concept of market efficiency and examines the forecasting accuracy
of the market, compared with that of both a
panel of professional analysts and a simple
autoregressive forecasting equation based on
the past history of the bill rate. In Section II,
statistical tests for market inefficiency are de-
I. The Concept of Market Efficiency
Efficient financial markets exist when the
prices, or yields, of securities fully reflect all
available information relevant for their valuation. In the case of riskless fixed-income
securities, such as Treasury bills, the relevant
information consists of expectations about the
future course of interest rates. Investors then
bid the prices of securities to the point where
expected holding-period yields for securities of
different maturities are roughly the same,
given these expectations. For example, given
the current six-month bill rate, the price and
yield of a nine-month bill depends upon the
expected three-month rate for six months
ahead. New information can develop, but
when it does it is rapidly reflected in revised
expectations and in the prices of securities.
Consequently, in an efficient Treasury-bill
market, investors would not have significant
opportunities for making profits on the basis of
information about future interest rates l .
The hypothesis of an efficient market is an
extreme one, and therefore could not be
expected to be literally true. Past tests of the
efficient-market hypothesis have thus
attempted to pinpoint the level of information
at which the hypothesis breaks down. In these
tests, all available information can be separated into three distinct types, or subsets, as
shown in Table 1. The first subset consists of
the past history of rates of return, or prices. A
test of whether the market efficiently utilizes
information in the past history of rates of
return, or prices, is called a test of weak-form
efficiency. The second information subset consists of any other information publicly available at little or no cost - such as government
statistics on other relevant variables. Tests of
whether the market efficiently utilizes this
kind of information in securities pricing are
called semistrong-form tests. The third information subset consists of information that is privileged or available only at significant cost.
Tests of whether the market efficiently utilizes
this kind of information, so that profits cannot
be made from trading on it, are called strongform tests.
Table 1
Types of Market Efficiency
Subset of Information
Test of Whether
Particular Information
Subset Is Efficiently
Utilized by Market
I. Past History of Prices,
or Rates of Return
Weak-Form Test
2. All Other Publicly
Available Information
Semistrong-Form Test
3. Privileged or Costly
Information
30
Strong-Form Test
of professional analysts, and compiled by the
Goldsmith-Nagan Bond and Money Market Letter since Septem ber 1969. 6 The forecast period
is again 1970-1 through 1979-III. This period
begins with the first Goldsmith-Nagan sampling of professional forecasts and continues
through the quarter just prior to the Federal
Reserve's October 1979 shift in operating procedures, which emphasized controlling bank
reserves for achieving its monetary objectives.
We excluded later data on the ground that
both the market and professional forecasters
had to go through a learning experience which
reduced the forecasting accuracy of each by
perhaps differing amounts.
Professional analysts use, either directly or
indirectly, information in the past history of
the bill rate - but they undoubtedly use other
sources of information as well. So the analysts'
forecasts contain information relevant to all
three kinds of efficiency. However, it is not
possible here to distinguish between a semistrong and strong test of efficiency. Some
interest-rate forecasts in the Goldsmith-Nagan
sample are not widely circulated, being privileged or costly to obtain, while other information may be publicly available. Since we cannot
discriminate between these two types of information in the analysts' forecasts, we simply
use the term "strong-form efficiency" to refer
to efficient market use of all types of information besides the past history of the rate.
In order to test the bill market's efficiency,
we need a measure of the market's forecast of
the 3-month bill rate for two quarters ahead.
This can be obtained from the term structure
of Treasury bill rates - specifically, from the
market's two quarter ahead "forward rate."
This is the interest rate on a 3-month Treasury
bill two quarters ahead that would be required
to equalize expected returns on 6- and 9month bills over a 9-month holding period. 7
The forward rate also contains a "liquidity premium," which compensates investors in the
longer-term security for their sacrifice of
liquidity. So an adjustment for that premium
must be made to provide an estimate of the
market's forecast of the bill rate. A n Appendix
develops the concept of the forward rate more
The three subsets of information exhaust
the universe of all available information; thus,
a market is fully efficient only if it passes all
three kinds of tests. According to previous
studies, the Treasury-bill market tends to be
efficient in the weak-form sense of utilizing
information in the past behavior of the bill
rate. However, the evidence has generally
been confined to very near-term market
forecasts of only up to a few months ahead. 2
Also, little evidence is available on the bill
market's efficiency in the strong or semistrong form sense of incorporating other
available information useful for forecasting. 3
In this study, we consider two specific types
of information that the Treasury-bill market
could utilize in formulating a two-quarter
ahead forecast of the 3-month bill rate. The
first is simply an autoregressive forecast based
on the past history of the bill rate. The yield on
Treasury bills may vary somewhat predictably
over time, due to the business cycle and/or
predictable patterns in monetary policy. To
pass the weak-form test, the market's forecast
of the future bill rate needs to take into
account any systematic behavior evidenced by
its past history. 4
For the period 1951-IV through 1969-III, we
estimated a simple autoregressive forecast that
could have been used by the market. In this
period, quarterly movements in the 3-month
bill rate followed a significant autoregressive
pattern, ie., past movements of the rate were
significantly related to future movements. An
equation explaining quarterly changes in the
bill rate contained significant lags at 1, 2, 3,
and 6 quarters, as well as a significant constant
term indicating a positive time trend. We then
obtained autoregressive forecasts for the
period 1970- I through 1979-III by reestimating
this equation on a growing sample of available
observations and computing two quarter ahead
forecasts from the latest coefficient estimates
at each point in time. 5 Whether or not the
market efficiently utilized the information
contained in this autoregressive forecast is a
test of weak-form efficiency.
The second type of information is the
average interest-rate forecast made by a panel
31
precisely, and details the technique used to
estimate the liquidity premium.
For a preliminary view of market efficiency,
we can compare the market's two-quarter
ahead forecast of the 3-month Treasury bill
rate (F;':2) with the professional analysts'
forecast (F~: 2) and the forecast from the
autoregressive equation(F:l~2)' To measure
forecast accuracy, we use the mean squared
error (MSE), the arithmetic average of the
squares of the forecast errors - or better still,
the root mean squared error (RMSE), since it
measures the error in the same units as the
forecasted variable (Table 2) . As a baseline for
comparison, we use the RMSE for a forecast of
no change.
After extraction of the estimated liquidity
premium, the RMSE of the market's forecast,
1.24 percentage points, is only slightly lower
than that for the forecast of no change - but
substantially higher than the RMSEs of the
analysts' and autoregressive forecasts.
Moreover, the approach used to estimate the
market's liquidity premium is more likely to
have understated rather than overstated the
true difference between forecast errors, as
shown in the Appendix. These differences
thus suggest the possibility of market inefficiency. If the estimated difference between the
RMSEs of the autoregressive forecast and the
market's forecast were statistically significant,
then the condition of weak-form efficiency
would not be met. An autoregressive forecast
based on available past information on the
Table 2
Accuracy of Forecasts
Root Mean Squared Error (RMSE)
19701 - 1979111
(percentage points)
Forecast of No Change (it)
1.25
Market's Forecast (F:"t-2)
(Adjusted for Liquidity
Premium as Estimated from
Appendix Table 1, Eq. 3)
1.24
Analysts' Forecast (Fg n
)
1.10
Autoregressive Forecast
(Ff't)
t+2
.94
Treasury- bill yields would have provided a
means for investors to "beat the market". By
altering the maturity of their holdings in light
of a superior forecast they could have
improved their returns.
The RMSE of the analysts' forecast is lower
than the market's, but higher than that of the
autoregressive forecast. Thus, the analysts
may not have made full use of the available
autoregressive information. Still, the analysts'
forecast could contain other information
besides that embodied in the past history of
the rate. If an investor could have profited
from trading on such other information, the
market would also be inefficient in a strongform sense. 8 The next two sections provide
tests of forecast accuracy that distinguish between strong-form and weak-form inefficiency.
II. Evidence of Market Inefficiency
Il1
We first test for weak-form inefficiency by
examining whether the autoregressive forecast
could have been systematically used to reduce
the error in the market's forecast. This could
have been done if the market's forecast error is
at least partially explained by the difference between the autoregressive forecast and the
market's forecast. Symbolically, this relationship is:
i 1+ 2 - F:: 2
=
B I (F;"t2 - F;':2)
+ e'+2'
where i'+2 - F 2 = the market's forecast
error for two quarters
ahead;
F;t~2
=
the autoregressive
forecast for quarter t+ 2
made at time t;
F;': 2 = the market's forecast for
quarter t+ 2 made at time
t;
(1)
e t+ 2 = a random error term.
32
Note that this equation can be rearranged to
give the optimal forecast'of the interest rate as
a weighted average of the two forecasts. That
is, it implies:
i t +2 = BIF:~2
+
(l - B I ) F:: 2+ e t +2
A similar test can be performed with the
forecast of the Goldsmith-Nagan panel of
analysts, F~:2' as the alternative to the
market's forecast. When the difference between the analysts' and the market's forecast is
used to explain the market's forecast error, we
obtain the following estimated equation:
(2)
In the case of weak-form inefficiency, the
autoregressive forecast would receive a significant weight. On the other hand, if there were
no weak-form inefficiency, the weight of the
autoregressive forecast would be insignificantly different from zero, and the weight of
the market's forecast would be close to one.
Thus, the test of weak-form inefficiency is that
the estimated value of B I be significantly
different from zero, so that the autoregressive
forecast could have been used to improve
upon the accuracy of the market's forecast.
F:~2 and F~:2 are apt to be highly correlated
in equation (2), tending to increase the standard errors of the estimated coefficients. So it
is preferable to test for weak-form inefficiency
by estimating equation (1); in addition, this
equation constrains the weights to add up to
unity. We estimated this and other equations
using ordinary least squares, with a correction
for a moving-average pattern of serial correlation in the error term. 9 The estimate of equation (l) is:
S.E. = .893
The estimated value of the B I coefficient, at
1.15, is over six times its estimated standard
error. It is clearly significantly different from
zero and also not significantly different from
one. Thus, only the analysts' forecast should
be used in an optimal forecast combining both,
because the market's forecast provides little or
no additional information.
This test also supports a finding of market
inefficiency. Whether it is of the weak or
strong form, or both, depends upon the type of
information embodied in the analysts'
forecast. If the analysts' forecast were based
only on the historical behavior of the bill rate,
only weak-form inefficiency would be confirmed. But if it contains other information as
well, both weak and strong-form inefficiency
would be indicated.
Two additional tests can be made for the
presence of strong-form inefficiency. The first
explains the forecast error of the autoregressive equation by the difference between the
analysts' forecast and the autoregressive
forecast. The significant coefficient estimated
in this equation, given below, indicates that
the analysts' forecast can be used to explain an
important part of the error in the
autoregressive forecast. Therefore, that
forecast contains other useful information
besides the past history of rates.
(3)
(.163)
2
"R =
.467
S.E. = .900
The value of B b at .664, is more than four
times its estimated standard error, given in the
parentheses, indicating that it is indeed significantly different from zero. Thus, the
autoregressive forecast could have been used
to reduce the market's forecast error, confirming the existence of weak-form inefficiency. In
fact, in an optimal forecast combining the two,
the autoregressive forecast would be given a
larger weight (.664) than the market's forecast
(.336). Also note that the unexplained forecast
error has been reduced to .90 percentage
points (equals the equation's standard error,
S .EJ from 1.24 percentage points (equals
RMSE in Table 2).
i'+2 - F:~2 = .685
(F~:2 - F;1~2)
(5)
(.187)
"R
2
=
.155
S.E.
=
.862
A second test for confirming the existence
of strong-form inefficiency involves generaliz-
33
ing the form of the original test. That is,
error in the market's forecast might be
plained by both the difference between
autoregressive and the market's forecast
the difference between the analysts' and
market's forecast. In symbols,
the
exthe
and
the
i'+2 - F~:2 = B I (F;"1-2 - F~+2)
(6)
-I- Q
I
{pgn
_
U2 \.1·1+2
\
than their standard errors and significantly
different from zero at the 5-percent level,
indicating both weak- and strong-form inefficiency.
To summarize the results so far, we have
found that two different types of information
could have been used to improve upon the
market's forecasts of the 3-month Treasury
bill rate, as embodied in the forward rate. The
significance of an autoregressive equation in
explaining the market's forecast error indicates weak-form inefficiency, and the added
significance of the analysts' forecast confirms
strong-form inefficiency. By incorporating the
information contained in an autoregressive
model and the analysts' forecast, the RMSE
for a two-quarter ahead forecast of the 3month Treasury bill rate could have been
reduced from the market's 1.24 percentage
points to .87 percentage points (equal to S.E.
of equation (8). In fact, when all three
forecasts are combined into an optimal
forecast, as in equation (7), the weight
attached to the market's forecast is not significantly different from zero, at .022 (equals 1 .657 - .321). Thus, the autoregressive
forecast and the analysts' forecast contain all
the useful information embodied in the
market's forecast, plus other useful information as well.
-'- ~
l+2JT C;t+2
or in the alternative form,
i'+2
=
BIF;I~2
+ (l
+ B2F~:2
- BI
-
(7)
B 2) F:: 2 + e'+2
If both B I and B 2 were significantly different
from zero, then both weak and strong-form
inefficiency would be confirmed. We again
choose the first form of the equation for
estimation, in order to reduce the extent of
multicollinearity among the independent
variables. The estimate of the equation in this
form is:
(8)
(.337)
+ .321
(F:~2 - F:: 2)
(.201)
R2=
.498
S.E.
=
.873
Both of the estimated coefficients are larger
III. Information in the Analysts' Forecast
used by the professional analysts was efficiently
incorporated into the market's forecast. In
fact, we shall see that the autoregressive information contained in the analysts' forecast is
substantially the same as that in our
autoregressive equation.
To approach this question, we decomposed
both the professional analysts' forecast and the
market's forecast into the portion related to
current and past bill rates (extrapolative component) and the remainder that is not so
related (autonomous component) .10 The
difference between the two forecasts can then
be decomposed into the difference between
The previous section tested whether information from a simple autoregressive model
that could have been used to predict the Treasury-bill rate was fully incorporated into the
market's forecast, as embodied in the forward
rate. However, some judgment enters into the
construction of even such a simple
au toregressi ve forecast. Specifically, if the
time pattern of rate movements is unstable,
the forecasting power of the estimated
autoregressive equation could depend importantly upon the period of estimation chosen.
Therefore, we should also test whether the
autoregressive information that was actually
34
the extrapolative components of the two
forecasts plus the difference between the
autonomous components. If the difference between the extrapolative components were
statistically significant in explaining the
market's forecast error, this would indicate
that autoregressive information actually incorporated into the analysts' forecasts was useful
in predicting the interest rate, but nevertheless
was not fully incorporated into the market's
forecast - an instance of weak-form inefficiency. Similarly, if the difference between the
two autonomous components were significant
in explaining the market's forecast error, this
would mean that the market did not incorporate other useful information available to the
analysts - an instance of strong-form inefficiency.
The extrapolative components of the two
forecasts were estimated by regressing the
difference between each forecast and the current rate on lagged quarterly differences in the
bill rate. Such components can be divided conceptually into three parts (Figure 1). The first
is simply the current interest rate, or a prediction of no change corresponding to a randomwalk hypothesis. If there were no significant
coefficients in the above regression, the estimated extrapolative component would contain
only the current interest rate. The second
component is a time trend, or drift factor, indicated by a significant constant term in the
above regression. The third component is the
part of the forecast related to past changes in
the interest rate, indicated by any significant
coefficients on past changes in the rate.
The best equation explaining the difference
between the market's two-quarter ahead
forecast of the bill rate and the current rate,
chosen on the basis of a minimum standard
error, contained no constant term and no lagged changes in the bill rate. Thus the
extrapolative component of the market's
forecast, E:: 2, is estimated to be simply a
Figure 1
Elements of a Forecast
Realized interest rate - - - - - -....."'.
Forecast error
Forecasted interest rate ---,-----_. ",'
j
Related to
past changes
!'"
Autonomous
component
of forecast
'"
."
Time-Trend [
Current
interest rate
_
.1$!
Extrapol ative
component
of forecast
Forecast of
no change
1
1+2
Time
Note: For simplicity, this illustration assumes that elements of the forecast other than the current interest rate all
contribute to reducing the forecast error. Of course, this need not be true in general. For example, the time trend,
the part of the extrapolative component related to past changes, and the autonomous component could all be
negative, instead of positive as assumed here. In that case, and given the same realized interest rate, the
forecasted interest rate would be below, rather than above, a forecast of no change; and the forecast error would
be increased, rather than reduced, by these three elements.
35
forecast of no change, equal to the current
interest rate (i t). Symbolically,
shows that the analysts made better use of
information in the bill rate's past history than
did the market. In addition, the significant
coefficient on the difference between the two
autonomous elements indicates that the
analysts made superior use of other information besides past rates. The first finding confirms weak-form inefficiency, and the second
substantiates a strong form of inefficiency.
A final point of interest is whether the
extrapolative component of the analysts'
forecast utilizes available information on past
bill-rate movements as efficiently as possible.
To examine this question, we simply added to
the right-hand side of equation (12) the
difference between the forecast from the
autoregressive equation and the market's
forecast, and then reestimated the equation.
This gives
(9)
In contrast, the extrapolative component of
the analysts' two quarter-ahead forecast, E~:2'
estimated in the same fashion, was found to be
more complex. It contains a constant term,
indicating a positive time trend in the interest
rate of 54 basis points per year, and significant
lags at 1, 3, 4, and 5 quarters on past changes
in the bill rate. Specifically, the extrapolative
component of the analysts' forecast is estimated to be:
E~:2
=
it + .270 - .196(it - it-I)
+ .186 (it-J +
iH
(10)
)
.306(iH - i t - s )
+
.200(i t • s - i H
)
The autonomous components, denoted by
2 and A~:), are simply the difference be-
A:
tUloan
tho
t"ocn.a.r"ttUA fArAf"''lC'f -:lnrl
i t +2- F:: 2 = .650 (A~:2 - A:)
ite' p-vtr<.:lnf\lo:l_
,.,,\.:1. ""'"p ....... ~~
tive element. It follows that the difference between the analysts' forecast and the market's
forecast equals the sum of the differences between the autonomous and extrapolative components; or
F~:2 -
1+2
(A~:2+ E~:2)
- (A: 2 +
+ .766 (E~:2 - E: 2) + .323
(.584)
+ .323 (F:I~2- F~:2)
(.215)
(1 I)
E::
R 2 = .484
2)
E:':2)
To test for both weak and strong-form inefficiency in terms of the autoregressive information actually used by analysts in the
Goldsmith-Nagan survey, we substitute equation (1 I) into equation (4) and reestimate the
latter. The resulting estimated equation is:
i t + 2- F: 2= 1.10 (A~n~2 - A:: 2)
(12)
(.200)
(,377)
R2 =
.464
S.E.
=
S.E. = .885
The estimated standard error of the equation
is reduced somewhat by the addition of the
difference between these two forecasts.
However, neither the coefficient on this variable nor the coefficient on the difference between the extrapolative elements is significantly different from zero at the 5-percent
level. Thus, neither the extrapolative component of the analysts' forecast nor the
autoregressive equation's forecast significantly
reduces the market's forecasting error once
the other is already being utilized. Both contain a positive time trend and extrapolate from
past changes in the bill rate, in contrast to the
prediction of no change in the extrapolative
element of the market's forecast. On the basis
of this evidence, we conclude that the analysts
have utilized the available information on past
movements in the bill rate about as efficiently
as possible in their forecast.
= (A~:2 - A::)
+ (E~:2 -
(13)
(.348)
L YV \,.1\,;1.1 Ll1'-' .l \,.IJP,",,"""-1 V ...... J. VI. ",,-,,"-,U'-'\. Ul.1. ..... l .. oJ ....
.902
The significant coefficient on the difference
between the two extrapolative components
36
These analysts also efficiently incorporated
other publicly available information into the
autonomous component of their forecast. As
Friedman (1980) has shown, the forecasting
errors of the Goldsmith-Nagan panel for shortterm interest rates have not been significantly
related to costlessly available information on
past values of macroeconomic series affecting
the interest-rate outlook. These series include
the unemployment rate, industrial production,
price inflation, the money stock, and the
Federal government's deficit.
IV. Summary and Conclusions
We have investigated whether the Treasurybill market has efficiently utilized all available
information, so as to incorporate the best
possible two-quarter ahead forecast of the 3month interest rate into its pricing of Treasury
bills. A forecast by a panel of professional
analysts was used as a measure of all available
information, and the subset of information
relating to the bill rate's past history was estimated by a simple autoregressive forecasting
equation. We found that the analysts' forecast
contained a similar extrapolative component,
based on past movements in the bill rate.
Either this extrapolative component of the
analysts' forecast or a forecast from the
autoregressive equation could have been used
to reduce the error in the market's forecast significantly; but both contained substantially the
same information. In addition, the analysts'
forecast contained other useful information for
explaining a portion of the market's forecast
error. Altogether, the tests performed indicate
the existence of both weak-form and strongform inefficiency.
Earlier studies of the efficiency of the Treasury-bill market, focusing on shorter term
interest-rate forecasts, have usually indicated
weak-form efficiency. In contrast, our results
for a two-quarter ahead forecast of the bill rate
show the existence of weak-form inefficiency.
This reflects the positive time trend found in
both the extrapolative component of the
analysts' forecast and the autoregressive
forecasting equation, but not in the market's
forecast. The market's forecast of the 3-month
bill rate failed to incorporate the upward drift
in the bill rate attributable to rising inflation in
the forecast period, even though this drift
could have been extrapolated from past data.
In testing for a stronger form of efficiency in
the bill market, earlier studies have generally
used current and past values of relevant
macroeconomic variables to measure other
available information besides the past history
of the bill rate. This study used the nonextrapolative component of the professional
analysts' forecast for this purpose. We found
that this component also contributed significantly to reducing the market's forecast error,
indicating strong-form inefficiency as well.
The difference between the overall forecast
error of the analysts and the market in the
1970's was a modest 14 basis points, as
measured by the root mean square error.
Nevertheless, our results indicate that the
above types of market inefficiency would have
allowed an investor to trade on the information contained in the analysts' forecast. An
investor could have improved his overall
returns with a strategy of shortening maturities
when the analysts' forecast was above the
market's and lengthening them when the
opposite was true.
37
Appendix
Estimation of the Market's Forecast
are generally unbiased, so that the realized
interest rate is approximately equal to the anticipated interest rate plus a random error:
The market's two-quarter ahead forecast of
the 3-month Treasury bill rate is embodied in
the differential between yields on 6- and 9month bills. To see this, first consider that
market arbitrage makes the yield on a 9-month
Treasury bill equal to the expected return on a
3-month Treasury bill that is rolled over twice,
plus premiums for the sacrifice of liquidity. In
algebraic terms, the yield on the 9-month
Treasury bill is:
(4)
The market's forward rate (f) is composed of
an anticipated interest rate and a liquidity premium (p), or:
(5)
Subtracting (4) from (5), we obtain the
liquidity premium as equal to the difference
between the market's forward rate and the
realized interest rate plus the random (expectationaO error:
0)
where
i = yield at a quarterly rate,
p = liquidity premium,
left subscript = maturity of security in
quarters,
right subscript = time at which
investment in security begins in quarters,
superscript "e" = interest rate
expected by the market as of time t.
Similarly, for a 6-month Treasury bill:
0+
2it)2=
0 +
lit)
0 +
li e t + l
+
IPt+l)
(6)
If the liquidity premium were constant, it
could be estimated simply from the average
difference between the forward rate and subsequently realized interest rate. But previous
research indicates that liquidity premiums are
in fact somewhat variable. Three not mutually
exclusive hypotheses have received support in
the literature.
The first hypothesis views short-term
securities as better substitutes for money balances than longer-term securities. If this is so,
the liquidity premium would tend to be
affected by the level of interest rates. When
interest rates are high, the foregone interest
income in holding money is larger; and so the
public desires to exchange part of its money
balances for securities. However, if the public
prefers short to long securities in this
exchange, prices of short-term securities
would be bid up relative to those on longerterm ones. This would increase long-term
interest rates relative to returns on short-term
securities, or in other words increase the
liquidity premium. Thus, if short-term
securities are better substitutes for money than
longer-term ones, liquidity premiums would
vary positively with the level of interest rates. II
(2)
Dividing (0 by (2) and rearranging terms, we
obtain equation (3) for the market's twoquarter ahead "forward rate." This is the
expected return (including a liquidity premium) on a 3-month Treasury bill two quarters ahead that is required to bring about
equality between the expected returns on 6and 9-month bills over a 9-month holding
period.
o+
3i ) 3
To evaluate the accuracy and information
content of the market's two-quarter ahead
forecast, it is necessary to separate the liquidity
premium from the forward rate. The approach
used here assumes that market expectations
38
n,
Two other hypotheses relate to the fact that
liquidity premiums on longer-term securities
compensate investors for exposure to the risk
of capital losses. The greater the probable
variation in interest rates, the larger would be
such risk. If the variation in interest rates is
expected to approximate its recent variance,
liquidity premiums ought to vary positively
with that variance. Moreover, at times when
interest rates are abnormally low (high), there
is a large likelihood of unanticipated increases
(decreases) producing unanticipated capital
losses (gains) for holders of longer-term
securities. Therefore, liquidity premiums
might also be expected to vary inversely with
the height of interest rates relative to recently
experienced levels. 12
These three hypotheses were tested with
available data for the period 1963-IV through
1979-III (Table A.1). Following equation (6),
we regressed the difference between the twoquarter ahead forward rate and the realized
Treasury-bill rate on the current level of the
Treasury-bill rate (j), the difference between
its current level and a weighted average of its
and the
value over the previous 2 years (i standard deviation of the bill rate over the
same period (SD).13 When no explanatory
variables other than a constant term are
included, the constant term is significantly
pQ$itive - indicating a positive average
liquidity premium of 54 basis points.
The level of the bill rate (reflecting the
effect of better substitutability between shortterm securities and money) and the deviation
of the bill rate from its recent trend (proxying
for the probability of unanticipated capital
gains on long-term securities) show significant
effects when entered together. So also does the
moving standard deviation of the bill rate
when entered alone. But when all three variables are entered together, only the standard
deviation retains at least marginal significance.
Also the equation containing only the moving
standard deviation of the bill rate explains
more of the variation in the liquidity premium
than does the equation containing the other
two variables. Mainly on statistical grounds,
we chose this equation ((3) in Table A.1) for
separating out the liquidity premium from the
Table A.1.
Estimation of liquidity Premium in the Two-Quarter Ahead
Three-Month Forward Rate (percentage points)
19631V - 1979111
Constant
(I)
.540
(.134)**
(2)
-1.30
(.565)**
(3)
-1.56
(.565)**
(4)
-1.49
(.578)**
(5)
-1.49
(.582)**
(6)
-1.58
(.560)*-
3.54
(I.03)**
D.W.
1.28*
S.E.
.148
1.67**
1.08
.162
(.0424)**
.175
1.53**
1.07
.195
(.0611)**
.169
1.62**
1.07
-.0746
(.126)
.158
(.0431)**
.166
1.62**
1.07
.545
(.675)
.409
(.273)
.165
1.51 **
1.07
-.443
(.153)**
-.0909
(.120)
-.602
(.645)
R2
.000
SO
i-i
117
Note: Standard errors are in the parentheses .•• indicates a regression coefficient that is significantly different
from zero at the 1- percent level on the basis of a single-tailed test; and' indicates significance at the 5-percent
level. The same symbols on the Durbin-Watson statistic (OW.) indicate the absence of significant serial correlation in the residuals at the 5- and 1-percent levels, respectively.
39
expectational error, because the additional
data allowed more of an ex ante estimation. A
purely ex post fit of the forward rate's forecasting error against the liquidity-premium variables would have generated a larger bias.
Even so, our estimate of the liquidity premium appears to have picked up some of the
true expectational error in the market's
forecast. This was tested for by removing from
both the analysts' forecast and the market's forward rate the portion of the respective
forecast error associated with the moving standard deviation of the bill rate (and a constant
term) during 1971-1 thru 1979-IIl. These
adjusted forecasts were obtained by regressing
each forecast error on the moving standard
deviation of the bill rate, and subtracting the
values predicted by these regression equations
from each respective forecast. The procedure
removes a similar amount of true expectational error from both forecasts, but also an
estimated liquidity premium from the
market's forward rate. The RMSE's of these
adjusted forecasts are 1.01 and 1.18 percentage
points for the analysts' and the forward rate,
respectively. The difference of 17 basis points
exceeds the 14- basis-point difference between
the RMSE's of the analysts' forecast and our
estimate of the market's forecast, suggesting
that our estimate of the latter tends to underestimate the size of its forecasting error.
The procedure used for estimating the
liquidity premium has thus tended to understate the difference in true expectational errors
between the market's forecast and the two
alternative forecasts. A possible bias in the
opposite direction could result from the omission of an important variable for explaining the
liquidity premium. However, we have already
considered all such possibilities. On balance, it
is more likely that our estimate of the market's
liquidity premium has understated, rather than
overstated, the true difference between the
forecast errors of the market and those of alternative forecasts.
forward rate to arrive at an estimate of the
market's anticipated 3-month bill rate.
Because this equation has a minimum standard
error, the resulting estimate of the market's
forecast has a minimum forecast error.
However, equations incorporating the other
variables did about as well; and our results are
not particularly sensitive to this choice.
The procedure used to estimate the liquidity
premium assumes that the market's true
expectational error, v, is uncorrelated with the
variables used to model the liquidity premium.
To the extent that this condition is not met,
the estimated liquidity premium captures a
portion of the market's true expectational
error. This portion of the true expectational
error would then be removed from the estimate of the market's forecast when the estimated liquidity premium is subtracted from
the forward rate. As a simple example of the
problem, if the true expectational error is
positively biased, the procedure would overestimate the liquidity premium and correspondingly underestimate the size of the market's
forecast errors.
We investigated the seriousness of this
problem by regressing the difference between
the forecast of the Goldsmith-Nagan panel and
the realized interest rate on the variables used
in Table A.l to explain the liquidity premium.
The estimated coefficients from these regressions carried the same signs as those in Table
A.l and were frequently statistically significant, indicating that these variables are capable
of proxying for a portion of the analysts'
forecast errors. However, the size of these
coefficients was generally considerably smaller
than those in Table A.I., as would be true if
these variables were also related to the
market's liquidity premium.
To minimize inclusion of expectational
errors, we estimated the liquidity-premium
models on all available data going back to
1963, rather than just on the forecast period of
1971-1 thru 1979-111. This reduced contamination of the estimated liquidity premium with
40
FOOTNOTES
1. Tests of market efficiency were first applied to the
stock market. Surveys of this literature are contained
in Cootner (1964), Fama (1970), and Lorie and
Hamilton (1973, Ch. 4).
market prices. Any systematic pattern in expected
short-period returns would quickly be eliminated as
investors bid prices up or down in attempts to profit
from them. In contrast, the returns on 3-month Treasury bills held to maturity cannot be affected by this
kind of speculation, because the price at the end. of
the 3 months is fixed contractually. Therefore, even a
fully anticipated time pattern in 3-month Treasury bill
yields is not likely to be arbitraged away in an efficient market. However, an efficient market would take
such a pattern into account in its bill-rate forecasts.
2. The weak form of the efficient-market hypothesis
has been tested in several ways in the bill market.
One approach is to determine whether the forward
rate applicable to any particular point in time follows a
random walk. If the market's adjustment to new information is virtually instantaneous, as in an efficient
market, successive changes in the forward rate
applicable to any particular period should be random.
This approach is followed in Shiller (1973) and Roll
(1970).
5. The data sample was extended back to 1951-IV
using Salomon Brothers, An Analytical Record of
Yields and Yield Spreads. The best autoregressive
equation for explaining quarterly changes in the 3month Treasury bill rate during 1951-IV thru 1969-111
was found to be:
A second approach to testing the weak form is to
determine whether the market reacts appropriately to
any autocorrelation in the bill rate. While changes in
the forward rate applicable to any particular time
period should be random, it does not follow that for
weak-form efficiency the spot rate should also follow
a random walk. Indeed, in an efficient market the forward rate should extrapolate any systematic autocorrelation that tends to occur in the spot rate. Evidence
of weak-form efficiency in market forecasts of up to a
few months ahead is contained in Hamburger and
Platt (1975), Fama (1975b), and Fildes and Fitzgerald
(1980).
Li t = .118 + .239 Li t _1 - .241 Li t _2
(.120)
(.055) (1.19)
- .126 Li t _3 - .338 Li t_6
(.124)
(.122)
f'l2=.193
S.E.
=
.449
DW.=1.93
Standard errors are indicated in the parenthesis. A
two-step ahead forecast from this autoregressive
model of quarterly changes was found to be considerably more accurate than a one-step ahead
forecast from past changes over six-month periods.
Hence, the two-step ahead forecast (with coefficients
reestimated at each point in time) was used for Ff~2'
Fama (1975a, 1977) takes a rather different
approach by focusing on the relationship between the
nominal Treasury-bill rate and the subsequently
observed inflation rate. For weak-form efficiency, the
nominal interest rate would summarize all the information about future inflation rates contained in the
time series of past inflation rates, so long as the
expected real return is constant. Fama argues that
the Treasury-bill market is efficient in this sense, and
also that expected real returns on Treasury bills are
approximately constant. Carlson (1977), Joines
(1977), and Nelson and Schwer! (1977) present contrary evidence on the constancy of the expected real
rate, but their evidence with respect to weak-form
efficiency is not conclusive.
6. The author wishes to thank Mr. Peter Nagan of The
Goldsmith-Nagan Bond and Money Market Letter for
permitting use of this data.
7. A large body of literature exists on the term structure of interest rates. Useful surveys are contained in
Dodds and Ford (1974), Malkiel (1966), and Van
Horne (1966).
An alternative measure of the market's forecast can
be obtained from yields on Treasury-bill futures contracts. We did not examine the accuracy of this type
of forecast because a futures market in 3-month
Treasury bills has existed only since January 1976,
reducing the number of observations by more than
half. For a comparison of yields on futures contracts
and implied forward rates, see Lang and Rasche
(1978) and Poole (1978).
3. Hamburger and Platt (1975) conduct a test of the
semistrong form of efficiency by investigating
whether variables other than current and past levels
of interest rates are better than forward rates in predicting future bill rates. They considered such potential predictors as the current and past values of personal income and three alternative monetary aggregates, but found that the root-mean-squared error for
such forecasts was no smaller than from a forecast
using the forward rate, consistent with the semistrong
form of efficiency.
8. Prell (1973) compared the accuracy of forecasts
by the Goldsmith-Nagan panel of analysts with those
of no change and an autoregressive model for 1970
through 1973. In that period, the RM8E of the
Goldsmith-Nagan panel for a two-quarter ahead prediction of the 3-month bill rate was smaller than for
both of these forecasts. However, for long-term bond
yields, the panel's forecasts were no more accurate
than a forecast of no change. Prell (1973) did not
compare the accuracy of the analysts' forecast with
those of the market implied by the forward rate, as
would be necessary for a test of bill-market effi-
4. For the market to be considered efficient, the
Treasury-bill rate does not necessarily have to follow
a random walk, in which the change in the return from
one period to the next is completely random. A random walk would be consistent with weak-form efficiency in stock and bond markets because shortperiod returns on these securities are dominated by
capital gains or losses resulting from changes in
41
quarter. The tw o-quarter ahead 3-m onth forward rate,
and the 3-m onth spot rate, were converted to a bonde q uiva le nt yie ld (as was the fo re c a s t by the
G oldsm ith Nagan panel). The form ula for converting
the T reasu ry-bill rate on a discount basis into its
bond-equivalent yield is:
ciency. For another study of the accuracy of interestrate forecasts by market professionals, see Fraser
(1977).
9. A moving-average pattern follow s from overlap
ping of forecasts, i.e. quarterly observations on twoquarter ahead forecasts. The Chi Square statistic
indicated an absence of significant serial correlation
after this correction.
10. This approach is sim ilar to one used in Diller
(1969).
'_
11. Cagan (1969), Conard (1966, Ch. 7), Friedman
(1 979) and Kessel (1 965) find evidence of a positive
relationship between estim ated liquidity premiums
and the level of interest rates, consistent with the
th e o ry th a t s h o rt-te rm s e c u ritie s are c lo s e r
substitutes for money than long-term securities.
~d m
360
1 - d-H5___
360
365
m
where i is the bill rate on a bond-equivalent yield
basis, d is the bill rate on a discount basis, and m is
the m aturity of the bill in days. From equation (3) in
the Appendix, the tw o-quarter ahead forw ard rate on
a bond-equivalent basis is seen to be:
12. Evidence for this is contained in Fildes and
Fitzgerald (1980), M alkiel (1966, Ch. 7), Nelson
(1972, Ch. 6) and Van Horne (1 966). Studies in dica t
ing a positive relationship between liquidity premiums
and recent variance in the interest rate include Fildes
and Fitzgerald (1980), M cElhattan (1975), M odigliani
and Shiller (1973), and Talley (1979).
'3 ° t
1 ft+ 2 “
1 - 2 dt
In estim ating a liquidity premium for the Aaa corpor
ate bond rate, M cElhattan (1975) found a response to
the recent variation in inflation, in addition to the
recent variance in the nominal interest rate. We
experim ented with this form ulation, but could find no
significant response of the liquidity premium in the
tw o-quarter ahead forward rate to the variance in
inflation, after allowing for the impact of the variance
in the interest rate.
273
360
365
91
182
360
where 2dt and 3dt are the 6- and 9-m onth Treasurybill rates on a discount basis.
Besides the current spot rate, the variables in the
equation explaining the liquidity premium are the
standard deviation of the spot rate about its mean
over the past two years (SD), and the deviation of the
current spot rate from a weighted average of its value
over the same period (i - i). W eights in this average of
past spot rates were declining, with:
1 3. We obtained interest-rate data from daily closing
quotations tabulated by the Federal Reserve Bank of
New York. The original data from this source con
sisted of bid-side interest rates on a discount basis
for 3, 6, and 9-m onth Treasury bills at the end of each
( i - i ) t= i t- S
n=1
n_ it-n
28
REFERENCES
Dodds, J.C. and Ford, J.L. Expectations, Uncertainty
and the Term Structure of Interest Rates. New
York: Barnes and Noble, 1974.
Cagan, Philip. “ A Study of Liquidity Premiums on
Federal and M unicipal Government S ecurities,”
in Jack M. G uttentag and Phillip Cagan (eds.),
Essay s on Interest Rates, Volume. I. New York:
National Bureau of Economic Research, 1969.
Fama, Eugene F. "E fficie n t Capital M arkets: A Review
of Theory and Em pirical W ork,” The Journal of
Finance, May 1 970, pp. 383-41 7.
Carlson, John A. “ Short-Term Interest Rates as Pre
dictors of Inflation: Comment,” American E co
nomic Review, June 1977, pp. 4 6 9-7 5.
____“ Short-Term interest Rates as Predictors of
Inflation,” American Economic Review, June
1975, pp. 26 9-8 2.
Conard, Joseph W. The Behavior of Interest Rates,
National Bureau of Econom ic Research, 1966.
____“ Forward Rates as Predictors of Future Spot
Rates,” Journal of Financial Economics, July
1976, pp. 36 1 -7 7 .
Cootner, Paul H., ed. The Random Character of Stock
Market Prices. Cambridge: M.l.T. Press, 1964.
____“ Interest Rates and Inflation: The Message in
the Entrails,” American Economic Review, June
1977, pp. 48 7 -9 6 .
Diller, Stanley. “ E xpectations in the Term S tructure of
Interest Rates,” in Jacob Mincer, (ed.), Economic
F o re c a sts and E xp e ctatio n s: A n alyse s of
Forecasting Behavior and Performance. New
Fraser, Donad R. “ On the Accuracy and Usefulness of
Interest Rate Forecasts,” Business Economics,
September 1977, pp. 38 -44 .
York: National Bureau of Econom ic Research,
1969, pp. 112-66.
42
Nelson, Charles. The Term Structure of Interest
Rates. New York: Basic Books, Inc., 1972.
Fildes, Robert A. and Fitzgerald, M. Desmond. “ E ffi
ciency and Premiums in the Short-Term Money
M arket,” Journal of Money, Credit and Banking,
November 1980 (Part I), pp. 61 5 -2 9 .
___ and Schwert, G. W illiam. "S hort-Term Interest
Rates as Predictors of Inflation: On Testing the
Hypothesis that the Real Rate of Interest is Con
stant,” American Economic Review, June 1977,
pp. 4 7 8-8 6.
Friedman, Benjamin M. “ Interest Rate Expectations
Versus Forward Rates: Evidence from an Expec
tations Survey,” The Journal of Finance, Sep
tember 1979, pp. 96 5 -7 3 .
____“ Survey Evidence on the Rationality of Interest
Rate E xpectations,” Journal of Monetary E co
nomics, O ctober 1980, pp. 45 3 -6 5 .
Poole, W illiam . “ Using T -B ill F utures to Gauge
Interest Rate Expectations” , Federal Reserve
Bank of San F rancisco, Econom ic Review,
Spring 1 978, pp. 7-1 9.
Hamburger, M ichael J. and Platt, E lliott N. “ The
Expectations Hypothesis and the E fficiency of
the Treasury Bill M arket,” Review of Economics
and Statistics, May 1975, pp. 190-99.
Prell, Michael J. “ How Well Do the Experts Forecast
Interest R ates?” Federal Reserve Bank of K an
sas City, Monthly Review, Septem ber-O ctober
1973, pp. 3-13.
Joines, Douglas. “ Short Term Interest Rates as Pre
dictors of Inflation: Comment,” American E co
nomic Review, June 1977, pp. 467-77.
Roll, Richard. The Behavior of Interest Rates: An
Application of the Efficient Market Model to
U.S. Treasury Bills. New York: Basic Books, Inc.,
1970.
Kessel, Reuben A. The C yclica l Behavior o f The
Term S tru ctu re o f In te re s t Rates. New York:
National Bureau of Economic Research, 1965.
Sargent, Thomas J. “ Rational Expectations and the
Term S tructure of Interest Rates,” Journal of
Money, Credit, and Banking, February 1 972, pp.
74-97.
Lang, Richard W. and Rasche, Robert H. “ A Com
parison of Yields on Futures C ontracts and
Implied Forward Rates,” Federal Reserve Bank
of St. Louis, Review, December 1 978, pp. 21 -30.
Shiller, Robert J. “ Rational Expectations and the Term
S tructure of Interest Rates: A Comment,” Journal
of Money, Credit, and Banking, August 1973, pp.
85 6 -6 0 .
Lorie, James H. and Hamilton, Mary T. The Stock
M arket: Theories and Evidence. C h icag o:
Richard D. Irwin, Inc., 1973.
Talley, Ronald J. “ M arket Interest Rate Expectations
as Reflected in the Term S tructure,” Business
Economics, September 1979, pp. 10-18.
Malkiel, Burton G. The Term S tru c tu re of Interest
Rates: Expectations and Behavior Patterns.
Van Horne, James C. “ Interest Rate Risk and the
Term S tructure of Interest Rates,” Journal of Po
litical Economy, December 1966, pp. 6 2 9 -3 5 .
Princeton: Princeton U niversity Press, 1966.
M cElhattan, Rose. “ The Term S tructure of Interest
R ates and In fla tio n U n c e rta in ty ,” F ederal
Reserve Bank of San Francisco, Economic
Review, December 1975, pp. 27-35.
____Financial Market Rates and Flows. New York:
Prentice-Hall, 1 978.
Modigliani, Franco and Shiller, Robert J. “ Inflation,
Rational Expectations and the Term S tructure of
Interest Rates,” Economica, February 1973, pp.
1 2-42.
43
Herbert Runyon*
In published polls, inflation generally tops
the list of problems troubling the public.
Indeed, television news programs are full of
discussions of the rampancy of inflation. But
most audiences remain unaware of how to
measure inflation - or of what it really is.
Inflation may best be described as a substantial and continued rise in the general price
level. However, the general price level is hard
to define in practice and presents a number of
measurement problems, since it is a single
number that represents the average behavior
of a great many prices during a given period of
time. In a system of freely functioning
markets, there can be a great deal of disparity
in the movement of prices of individual commodities or services. This is to be expected, as
shifting demand-and-supply conditions for
specific items become reflected in their prices.
As demand presses against supply for some
goods, their market prices may rise relative to
other goods. Of itself, this does not constitute
inflation, because other prices may be falling
- witness color television sets or hand-held
calculators. Relative price movements of this
sort are a normal manifestation of functioning
markets for resources and final goods. But
inflation exists only if the prices of most goods
are rising, or if increases in the prices of some
goods consistently outweigh declines in the
prices of other goods.
As inflation has accelerated - with consumer prices doubling over the last decade policymakers have attempted to offset its
impact on living standards by indexing
incomes to the cost of living. Workers, still
active in the labor market, have tried to
minimize their inflation-caused loss of economic welfare by negotiating cost-of-living
*Research Officer, Federal Reserve Bank of San Francisco. Steve Kamin provided research assistance.
44
adjustments (COLAs) into bargaining agreements. Other groups now outside the labor
market - such as the retired or disabled instead have depended upon the political process to ensure income maintenance. These two
methods of adjusting to inflation - the market
process and the political process - are not
necessarily comparable, and consequently
have sometimes produced inequities.
The official measures of the cost of living
playa significant role in public-policy decisions
affecting both wages and income-maintenance
programs. About two-fifths of the Federal
budget consists of expenditures that are tied,
or "indexed," to some such measure. As a
result, inflation significantly affects the
Federal budget. And in the private sector,
COLAs are imbedded in most large union
contracts. Altogether, about 80 million persons are affected by indexed payment of wages
or nonwage benefits. Thus, policymakers must
use an index that accurately reflects change in
the price level of the pattern of consumer
expenditures.
The choice of a measure raises fiscal-policy
questions. If the growth of the official index
exceeds the increase in the actual expenditure
pattern of individuals (designated here as the
cost of living), real government expenditures
will rise and contribute to a Treasury deficit.
Moreover, if the index is upwardly biased,
many wage and benefit recipients will be overcompensated. However, many cost-of-living
adjustments (at least in government transfer
programs) are based on the inflation rate in
some earlier period (generally the preceding
year). Hence, when inflation accelerates, the
amount of actual overcompensation may be
less than might appear; on the other hand,
when inflation decelerates, the overcompensation increases.
I.
Measuring Changes in the Cost of Living
base period. Suppose now that the prices of
both commodities double, as in the move from
P to P". In such a case we can say unequivocally that the cost of living has doubled,
since clearly the cost of obtaining the same
level of satisfaction has exactly doubled.
But suppose the price of commodity 1 more
than doubles while that of commodity 2 less
than doubles, as in the movement of prices
from P to P'. The total cost of the consumption
bundle may have exactly doubled, but this
does not mean a doubling of the cost of living
as we have defined it. In fact, it will probably
have less than doubled. The consumer can
probably obtain his previous level of satisfaction at less than double the cost, by buying less
of commodity 1 (whose price has more than
doubled) and more of commodity 2 (whose
price has less than doubled). However, we
cannot tell precisely how much the cost of living has risen, because we do not know how
much commodity-substitution the household
will undertake in any particular price situation.
Statisticians have developed index numbers
to deal with the problem of measuring changes
in the cost of living. Their calculations utilize
the following quantities:
Po = price ofa given commodity in the consumer's expenditure pattern in time
period to
qo = quantity of the given commodity
purchased by the consumer in to
PI = price of the commodity purchased in t l
q I = quantity of the commodity purchased
in t l .
One approach - the Laspeyres index maintains a fixed composition of the pattern of
goods and services consumed in the base
period. (The index was developed by the I9thcentury French-German economist, Etienne
LaspeyresJ Here, the amount spent on an
individual commodity is represented by the
price multiplied by the amount purchased, or
Po qm for the base year. Hence total expenditures of consumers in the base period to are
simply the sum of these products of price and
quantity, or Po qo. In order to compute a
Before attempting to measure the cost of living, we must first define what we wish to
measure. The term "living" refers to
individuals' consumption patterns - the sum
of commodities and services they consume
within a given period. We assume that consumers plan their expenditure patterns so as to
achieve the maximum amount of pleasure or
well-being within the income fixed for a given
time period. I Hence an increase in the cost of
living may occur when the income needed to
secure a given level of satisfaction increases
from one period to another. In principle, then,
the change in the cost of living between two
periods may be represented as the ratio of two
incomes - with the denominator being the
income in the first or "base" period, and with
the numerator being the smallest income
required in the second period to buy the group
of commodities that affords the base period's
level of satisfaction. 2
However, this concept is not amenable to
direct measurement, since we cannot observe
degrees of individual satisfaction, and hence
cannot know whether an individual is maintaining the same level of satisfaction. 3 This
basic problem may be illustrated by considering a simple situation in which a household
consumes only two commodities with prices PI
and P 2 (Figure 1) .
In this illustration, the point P represents
the level of prices of both commodities in the
Figure 1
P"
P
45
Laspeyres index for a later period, t j, we must
calculate the quantities purchased in the base
period to at the market prices prevailing in the
later period tj, or pj qo. Total consumer expenditures are then represented by PI qo and the
entire index by
=
:l,Pjqo
L
:l,Poqo
while the denominator represents how much
that bundle would have cost in the past period.
How Do Indexes Differ?
Because of their difference in approach, the
two indexes may differ considerably as
measures of the cost of living. The base-period
consumption bundle is fixed for the Laspeyres
index, so that it makes no allowance for
substitution in the consumption pattern.
However, as relative prices of goods change,
consumers may find it advantageous to switch
from higher-priced goods to lower-priced
substitutes. The classic example is the relative
price of beef and chicken. As the price of beef
rises, the consumer can substitute chicken in
his diet and expenditure pattern. But the
Laspeyres index, being a base-period fixedweight index, assumes that consumers will
continue to buy the same quantity of beef
purchased in the base period rather than turn
to chicken. With substitutions disallowed in
the base-year consumption pattern, expenditures for the more expensive beef receive
too great a weight and chicken too small a
weight. Hence the index overstates the true
increase in the cost of living.
The Paasche index, being based upon the
In this formula, the denominator represents
the amount actually spent in the base period,
while the numerator represents how much that
same bundle of commodities would have cost
in the second period.
An alternative approach - the Paasche
index - weights prices at current-period quantities. (This index was developed by
Laspeyres' German contemporary, Hermann
Paasche.) Where the Laspeyres index projects
the consumer-expenditure pattern forward
from the base period til the Paasche index
projects the pattern backward from the current
period t j to the past period to' The formula for
the Paasche index is therefore
=
:l,Pjqj
P
:l,Poqj
In this formula the numerator represents the
amount actually spent in the current period,
Figure 2
Paasche (B)
Laspeyres (A)
Expenditures
Expenditures
E
Prices
Prices
46
current consumption-expenditure pattern,
does allow for substitution - but in a way that
understates the rise in the cost of living
(Figure 2). Consumers may substitute on the
basis of changes in relative prices, and thus
avoid part of the burden of generally rising
prices, but in doing so they lose the satisfaction
of consuming the more expensive good which
they originally desired.
In each panel of Figure 2, the curve EE' is
the consumer's expenditure function, or the
amount of money necessary to maintain the
same level of satisfaction in periods to and t I,
assuming unchanged tastes. The consumer
faces different sets of relative prices in the two
periods, with some prices rising, some falling
and others remaining unchanged. However,
on average, in a period of inflation, the total
expenditure necessary to maintain the same
standard of living (in terms of personal
satisfaction) will rise. The curve EE' traces out
the amount of expenditures needed at
different times to maintain a given standard of
living.
In Panel A (Laspeyres index), the expenditure line EE denotes the total cost of the
base-period consumer-expenditure pattern at
the prices prevailing in period to (as expressed
by the vector PoqJ and at the prices prevailing
in t l (as expressed by the vector PIqoJ
Although no allowance is made for substitution, the consumer will adjust his expenditures
if faced with a different set of relative prices in
period t i . He will substitute lower-priced for
higher-priced goods in order to minimize total
expenditures while maintaining the same level
of satisfaction, thereby moving along expenditure function EE' rather than EE. The quantity PIq' I represents the expenditures required
to maintain the same level of satisfaction in
period t l as in period to'
In panel B (Paasche index), we project the
consumer-expenditure pattern PIqI in t l backwards along EE to period to' where the expenditure vector is PoqI' However, this ignores the
substitutions made in the expenditure package
between to and t j, which would make the actual
expenditure line EE'. The quantity Poq' represents the expenditure which would have been
required in period to to achieve the same level
of satisfaction attained in period t I'
Substitution makes a considerable
difference between the measured and "real"
change in the cost of living. In the case of the
Laspeyres index, the measured change is the
ratio of p Iqo to p oqo' If the consumer makes
substitutions in his consumption pattern on
the basis of changes in relative prices, the true
change in the cost of living will reflect these
substitutions and will be the ratio of PIqi to
Poqo' The Laspeyres index thus overstates the
change in the cost of living. Empirical studies
of the substitution phenomenon suggest that
the effect, while negligible with stable prices,
becomes significant as the inflation rate rises. 4
The expenditure schedule in panel B can be
considered in much the same way. Here again,
the schedule EE' represents substitution in the
expenditure pattern between to and t i . The
Paasche index assumes that at base-period
prices Pm consumers would have made expenditures Poq I' which is not what consumers
would have spent given the change in relative
prices. The pattern of q I consumption is
heavily weighted with goods and services
which were relatively expensive in the earlier
period. Thus, by overstating base-period
expenditures, the Paasche index understates
the rise in the cost of living. 5
Durable Goods and Price Indexes
When dealing with price indexes, we assume
that the goods and services purchased during a
specified time period are consumed in the
course of that period. This is obvious in the
case of nondurable goods and services, such as
a hamburger, an opera performance or a haircut. None of these items can be used more
than once. But problems occur with durable
goods, such as houses, autos, furniture and
appliances. By definition, such items provide
services for at least three years, and some of
them much longer.
We expect a new house to provide shelter
for up to 80 years, and an auto to provide
transportation for (say) ten years. 6 However,
the full cost of a durable good is picked up in
the first period rather than being allocated over
0
47
its useful service life.
The present value of an asset is determined
by the value of the stream of services that it is
expected to yield during its service life, as well
as by the market rate of interest. For this
reason, the inclusion of durable goods in a
cost-of-li ving index distorts the pattern of
actual consumption expenditures over a single
period. By including the actual market price of
such an asset in the index at the time of
purchase, we greatly overstate the price of the
services of this durable good for that period.
Moreover, the value of durable goods
II.
belongs in the consumer's balance sheet as
part of his stock of wealth, rather than in his
consumption-expenditure pattern. To the
extent that ownership of a home or other durable good generates capital gains, it effectively
reduces the cost of the services yielded by that
good. The effectiveness of any price index thus
depends, to a great extent, upon the way that
statisticians handle these two attributes of
durable-goods purchases - the stream-of-services attribute and the investment-good
attribute.
Two Indexes of the Cost of Living
quarterly over a IS-month period. For less
expensive day-to-day purchases, the agency
utilized diaries of actual expenditures kept
over a t\:'1o-\veek period. These t\VO efforts
were supplemented by a point-of-purchase
survey conducted in 1974, and updated on a
regular schedule. 7
BLS includes almost 400 categories of goods
and services in its statistical market basket,
pricing them on a monthly basis. Interviewers
contact a sample of about 18,000 retail establishments, such as supermarkets, cleaning establishments, repair shops and professional offices. Questionnaires provide other data such as utility rates, transportation fares, and
information not requiring personal visits and Federal agencies and private research
organizations add further information.
The PCE deflator is widely used as a cost-ofliving index, although it was not designed for
that purpose. It results from the procedure
used to deflate personal-consumption expenditure values into constant (I972) dollars, in
order to obtain a measure of change in the
physical volume of consumption. With its current-period reference weights, the PCE is a
Paasche index 8 with the form:
The most widely used price index, which has
official sanction in the indexing of labor agreements and retirement benefits, is the Consumer Price Index (Cpn. The Bureau of Labor
Statistics (BLS) has compiled this index ever
since World War I, when it was developed to
help determine wage rates in the shipbuilding
industry. The other major index is the implicit
price deflator for the personal-consumption
expenditure (PCE) sector of the nationalincome accounts. The two indexes differ in
several respects, such as population coverage.
The CPI covers the expenditures of urban consumers, and represents about 80 percent of the
population; the personal-consumption deflator
covers "persons" as defined in the nationalincome accounts, chiefly individuals and nonprofit institutions. The indexes also differ in
terms of items covered; the CPI regularly
covers a selected list of about 400 items, while
the PCE includes all goods and services currently consumed.
The CPI is a straightforward Laspeyres
index with the form
CPI,
=
P Q1972-73
P oQ 1972-73
(3)
BLS chose the base-year weights on the basis
of a 1972-73 survey of expenditures by about
20,000 family units. For most durable-goods
purchases, the agency utilized interview panels
in which consumer units were interviewed
PCE,
=
P,Q,
(4)
P 1972Q,
The two indexes differ in commodity composition, as well as in population coverage and
48
statistical form. About three-quarters of the
components of the CPI and the PCE indexes
are comparable, largely because of the deliberate use of CPI components in generating the
PCE index. Most of the differences occur in
the components of homeownership, autos and
allied services, and hospital charges and health
insurance. The homeownership cost in the
III.
PCE is based upon the imputed rental cost of
owner-occupied homes, whereas the comparable item in the CPI is based on home purchase
prices and new-home mortgage rates. Both
indexes treat durable goods on the basis of current purchase prices, rather than the cost of
the stream of services which they yield. 9
Relative Performance of the CPI and peE
above that of the PCE, a Paasche index. For
the entire 20-year period, however, the
average difference amounted to only 0.6 percentage points (Table 1).
In the first half of the 1960's, when prices
were reasonably stable, the CPI perversely
showed the lower rate of change - but the
difference was hardly significant, especially in
view of the low rate of inflation prevailing at
that time. Again, the two indexes showed
much less correlation than would normally be
expected, in view of the heavy use of CPI
In comparing the historical performance of
the CPI and PCE, we should keep in mind the
conceptual differences of the indexes and the
manner of their construction. Neither captures
the "real" cost of living; rather they form an
upper bound (Laspeyres) and a lower bound
(Paasche) to the cost of living. This can be
seen from an analysis of the past two decades,
which contained one period of relative price
stability and two episodes of high inflation
(Chart 3). For most of this period, the rate of
change in the CPI, a Laspeyres index, was
Chart 1
Consumer Price Movements
Annual
Change (0/0)
14
12
Consumer price index
~
10
8
6
...
4
Personal consumption
expenditure deflator
2
0 1960
1964
1972
1968
49
1976
1980
prices in the generation of the PCE. The much
lower correlation in this period reflects the fact
that both indexes moved within a fairly narrow
range,given the .low level of inflation. Because
the general price level was comparatively stable,. variations in relative. prices thus tended to
cause greater variation about the general price
level.
The 1973-75 and 1978-80 episodes of inflation were different, both
other and in relation to the earlier period of
stability. As expected, the.CPImt>asured mOre
inflation than thePCE in both episodes. But
meanwhile, the inflation of 1973-75 was more
general in scope than the 1978-80 episode. In
1973 -7 5, the U.S . economy felt the impact of
world-wide inflation in the prices of internationally traded commodities, partly food but
especially petroleum. Food and energy prices
also contributed to the 1978-80 run-up in
inflation, but the divergence in the two
indexes in this later period largely reflected a
sharp rise in the price of houses and in homemortgage rates (Chart 4). The divergence thus
could be explained by the fact that the PCE
incorporates only the CPI's relatively slow-rising rental component, rather than the CPI's
fast-rising home-ownership component.
measures (Table 2). The fixed-weight PCEis a
Laspeyres index - like the CPI but with a
1972 expenditure pattern. At the same time,
the fixed-weight PCE weights specific consumer items in the same way that the PCE
does.
Consider the weight, or relative importance,
of three major PCE components on a fixedweight vs. a current-weight basis. In 1972,
housing expenditures accounted for 15.3 percent of total consumer spending, but by 1980,
this had increased to 17.6 percent of the total
in terms of 1972 dollars. At the Same time, the
weight of food in the index dropped from 20.5
percent in 1972 to 19.4 percent in 1980, while
gasoline and oil dropped from 3.4 percent to
2.8 percent. Thus, in terms of 1980 consumption patterns, the fixed weight PCE underrepresented housing and over-represented
food and gas and oil. Of course, the composition of weights can change in a currentweighted index as changes occur in relative
prices, and in consumer tastes and income.
Weighting differences were not significant
in 1977-78, but they began to tell in 1979.
Home prices and mortgage costs began to soar,
leading to a spread of 1.9 percentage points between the CPI and the fixed-weight PCE
(Table 2, line 4). But at the same time, a significant amount of substitution took place in
the consumer-expenditure package because of
sharp changes in relative prices, leading to a
spread of 2.8 percentage points between the
fixed-weight PCE and the current PCE (line
5). An increase of more than 50 percent in
retail gasoline prices resulted in a decline of 11
percent in real purchases of gasoline and
nearly 10 percent in real purchases of fuel oil
Weighting Problem
The differences in the CPI and the PCE are
rooted in their basic conceptual natures,
including differences in weights and the effects
of substitution in the consumer-expenditure
package. To understand these differences, we
can compare the rates of change in CPI, the
PCE, and also the fixed-weight PCE, which
has some of the features of the other two
Table 1
Average Annual Rates of Change in the CPI and PCE Indexes,
and Coefficients of Determination between the Indexes
(change in percent)
19601-19801V
19601-19651V
CPI
5.29
1.35
9.59
11.81
PCE
4.69
1.50
8.34
9.35
.975
.667
19731-19751V
.969
50
19781-19801V
.947
and coal, not to mention an 11-percent cut in
auto spending. As a result of these changes in
current consumption, the composition of
weights changed substantially between the
current-weight and fixed-weight PCE.
In 1980, the situation was reversed, with the
largest difference occurring between the CPI
and the fixed-weight PCE (line 4), reflecting
the different treatment of homeownership.
The homeownership component of the CPI
rose by nearly 17 percent from the end of 1979
to the end of 1980, as compared with a 9-percent increase in the PCE in the same period.
Because of this difference, and the heavier
weighting of homeownership in the CPI, that
single component accounted for roughly half
of the difference in the overall indexes in
1980. The much smaller difference between
the two PCE indexes was due to declines in
real expenditures for food and gas and oil,
which changed the composition of PCE expen
ditures for the year.
Homeownership Problem
BLS’ problem with measurement of homeownership costs stems partly from its treat
ment of home prices. The agency computes
the weight from the purchase prices of homes
bought in the survey year, minus the prices of
homes sold in that year, plus transaction costs
accompanying the purchase or sale. It then
derives the index from price data supplied by
the Federal Housing Administration. But the
FHA sample is a small and unrepresentative
segment of the market. The coverage is not
geographically uniform; also, with its ceiling
cutoff on mortgage loans, higher-priced homes
are effectively eliminated from the sample.
Problems also occur with the computation of
mortgage cost. BLS assumes that the mortgage
Chart 2
Rental, Homeownership and M ortgage Costs
Annual
Change (%)
Year-over-year rate of change
51
borrower pays interest equal to the sum of all
interest payments over the first half of the life
of the mortgage, each year's interest cost being
equal to the first. But this results in overcounting, in comparison with discounting the value
of future house services (as reflected in the
future stream of interest payments) to their
present value. Moreover, many analysts suggest using the actual interest paid on all
mortgages instead of the current new-home
rate, to diminish the impact from sharp fluctuations in mortgage rates.
The CPI's weighting of homeownership
overstates its importance in the cost of living.
Homeownership accounts for nearly onequarter of the total weight of the index. With
that weight, it has five times the importance of
the rental component. In the PCE, homeownership is only about 2 1/2 times as important
as rental housing - a more reasonable figure,
in view of the 2-to-l relationship of owners to
renters in the national housing stock.
In response to these and other criticisms,
BLS is currently publishing five experimental
measures of housing costs. These range from a
rental index to various "shelter" and "asset"
concepts. Conceptually, much can be said for a
rental-equivalence measure, such as is used in
the PCE index, since it directly measures the
price of the services of a home. However, BLS
does not at this time possess a true rentalequivalence sample; that is, one made up of
housing units comparable in type and location
to its sample of owner-occupied units. The
rental index, as presently constituted, is based
upon market observations of rental payments.
The units involved in this sample generally
differ from owner-occupied dwellings in such
terms as age and income of inhabitants, as well
as age, location and size of dwelling. Thus, the
current CPI rental index cannot serve as proxy
for the imputed rent of the different and larger
population of owner-occupied units. The concentration of the rental sample in inner-city
areas - many of them rent-controlled - also
tends to bias the sample downwards, so that
this is one of the slowest rising components of
the entire CPI.
Other considerations must be kept in mind
when choosing an inflation index. The CPI in
its present form substantially overestimates
the rate of inflation - even more than might
be expected from a Laspeyres index. However,
a Laspeyres (Cpn index number seldom
needs to be revised, being based on actual
prices taken from primary sources and on fixed
base-year quantities. On the other hand, the
PCE index depends heavily on estimation procedures and thus is subject to frequent revisions, which can create problems of interpretation for policymakers. However, over the
1960-80 period, revised estimates of PCE rates
of change were only slightly higher than the
initial observations. Both the average rate of
change and its variation were smaller for the
PCE than for the CPI over this period.
Table 2
Average Annual Rates of Change
in the CPI, PCE and Fixed-Weight PCE Indexes
(percent)
1960-80
1977
1978
1979
1980
mCPI
5.29
6.5
7.7
11.3
13.5
(2)PCE
4.69
5.8
7.3
8.5
9.0
(3)PCE (fixed weight)
47]
63
7.6
9.4
9.6
(4)CPI - PCE (fw)
0.58
0.2
0.1
1.9
39
(5)PCE (fw) - PCE
0.02
0.5
0.3
2.8
06
52
IV.
Indexes and Public Policy
The current Congressional debate on the
Federal budget has focussed attention on the
role of indexation in increasing expenditures.
By linking increases in certain spending
categories to changes in the cost of living,
Congress originally sought to assure that
benefit recipients would be able to cope with
increases in the cost of living without further
Congressional action. In other words, recipients of Federal payments would almost automatically preserve their "real" income. Payments to individuals account for more than
half of Federal-budget expenditures, and 90
percent of such programs are indexed. Thus,
nearly two-fifths of Federal budget outlays,
whether paid out as wages or transfer payments, are linked to a price index (Table 3).
In the case of social-security benefits, Congress ironically adopted an escalator approach
as a means of capping the extraordinarily
generous benefits it had adopted in the early
1970s. (Between 1970 and 1974, benefits
increased by about 70 percent - just about
double the increase in the cost of living,) The
current indexation formula essentially provides for a benefit adjustment equal to the
annual percentage increase in the CPI Cfirstquarter to first-quarter). The benefit formula
thus called for a 14.3-percent increase in July
1980 and an 11.2-percent increase in July
1981. If the cost of living had been measured
by the PCE instead, the increase in benefits
would have amounted to 8.2 percent in 1980
and to about 9.4 percent in 1981.
Congress recently has begun to consider
several less costly indexing alternatives. One
of these would delay the first payment of
increased benefits from July to October each
year. This lag would lessen the extent of overstatement of the previous year's inflation rate
if inflation were accelerating, but it would
worsen the overstatement if inflation were
decelerating. Another suggestion would peg
the increase in benefits to the increase in
either the CPI or average wages, whichever is
smaller. Still another suggestion would put an
85-percent "cap" or ceiling on the increase in
the CPI.
According to the General Accounting Office, inflation accounted for approximately half
of the increase in expenditures for indexed
programs over the 1970-77 period. The GAO
study indicated that such spending increases
automatically by $15-25 billion at a 10-percent
inflation rate, and increases by $1.5 billion to
$2.5 billion more for each additional percentage point of measured inflation. If the PCE
index had been used in place of the CPI during
the 1970-77 period, roughly 11l/2 percent
($12.5 billion) of the cumulative spending
increase could have been saved.
A Congressional Budget Office study argued
that CPI-based indexation could account for
three-fourths of a $200-billion increase in
Federal payments to individuals projected for
the 1980-85 period. But again, a shift from the
CPI to the PCE index could mean savings of
$11 billion through 1986 for the social-security
program alone. 11
Table 3
Major Indexed Programs
Directly indexed
Social security
Supplemental security income
Railroad retirement
Veterans' pensions
Civilian retirement and disability
Military retirement
Black lung
Food and nutrition assistance
Subtotal, directly indexed
As percent of total outlays
Outlays, FY 1980
(billions)
$117.1
6.4
4.7
3.6
14.7
11.9
1.8
13.3
$173.5
29.9%
Indirectly indexed
Medicare
Medicaid
Subtotal, indirectly indexed
As percent of total outlays
$ 35.0
14.0
$ 490
8.5%
Total indexed programs
Total outlays
As percent of total outlays
$222.5
38.4%
Source: Office of Management and Budget, American Council of Life
[nsurance
53
Compensation and Equity
Table 4
Annual Change in
the CPI, PCE and
Average Wages*
(percent)
When indexation overcompensates for
inflation, questions of equity arise. Federal
payments to individuals are made only to certain individuals, while taxpayers who pay for
benefits may be falling behind the
increase in living costs. The cost-of-living
adjustments (COLAs) that are written into
many labor contracts are generally capped, so
that workers fail to receive full compensation
for their higher living costs (Table 4). And
those whose income is not indexed at all may
fall even further behind.
Increases in social-security benefits have
been tied to the CPI since 1975. From 1976
through 1978, the yearly increase in wages
exceeded the annual indexed increase in
social-sec uri ty benefi ts. However, the
difference was smaller than indicated, because
social-security benefits are not taxed as wages
are. When annual CPI increases ran ahead of
wage increases, from 1979 through 1981, the
V.
CPI
PCE
Average
Wages
1975/76
6.4
5.7
7.2
1976/77
5.8
5.3
7.7
1977/78
6.6
6.3
7.7
1978/79
9.8
9.1
8.3
1979/80
14.3
8.2
8.4
1980/81
11.2
9.4
9.8
Annual Average 9.0
7.3
8.2
*First quarter to first quarter
taxability factor made the gap even wider.
In contrast, the PCE index - though rising
more slowly than wages - would have placed
wage earners and benefit recipients on a
reasonably equitable basis during this period.
Summary and Conclusions
Many analysts have used the term "inflation" rather loosely in describing the recent
sharp rises in prices of certain individual commodities, such as oil and food. Nonetheless,
the inflationary process primarily involves an
increase in the general price level. Within this
context, the relative prices of individual goods
may rise or fall according to market forces.
Since numerous goods and services are bought
and sold daily in the markets, an index number
represents the only feasible method of describing the general movement of prices through
time.
An index number designed to measure
inflation should give an accurate representation of changes in living costs. The true cost of
living cannot be measured directly, since it is a
matter of personal satisfaction or well-being.
However, it can be measured indirectly by
market observations as consumers reveal their
individual preferences by purchasing certain
goods and services. The Consumer Price Index
has long been used as the common indicator of
the cost of living, and thus as a basis for indexing cost-of-living adjustments.
The CPI, as a Laspeyres index, uses quantities purchased in a certain base year as a
reference point from which to measure
changes in prices of a basic - presumably
unchanging - consumer-expenditure pattern.
The unchanging nature of the base-year consumption pattern ignores substitution of less
expensive for more expensive goods in the
reference expenditure package as relative
prices change in succeeding periods. This
imparts an upward bias to the index, as the
increasingly expensive base-period expenditure pattern (in current prices) overstates
what consumers actually bought and paid for at
the checkout counter.
The Personal Consumption Expenditure
index (or deflator) has come to be used as an
alternative index, although it was not
specifically designed to measure changes in the
54
cost of living. The PCE, as a Paasche index,
uses the current-period expenditure pattern as
a reference base for comparison with expenditures in earlier periods. This approach thus
allows for substitution of goods in the expenditure pattern. However, when that pattern is
projected backward from the current year, the
substitute goods of the current period may not
have been as desirable to consumers in earlier
periods. The consumer's loss of satisfaction,
relative to the current period, thus causes a
PCE (Paasche) index to understate changes in
the "true" cost of living.
As a practical matter, the CPI and the PCE
were quite close in their measurement of living
costs from 1960 through 1966. But from 1978
through 1980, the CPI rose at a much faster
rate. This disparity resulted not so much from
the indexes' different statistical composition as
from their different treatment of sharply rising
homeownership costs. The housing component of the CPI overstated the inflation in
housing costs, because it included the full cost
of a house, which includes its value as an asset,
rather than merely the cost of shelter services.
The treatment of mortgage interest also contributed to this overweighting of the costs of
homeownership.
The Federal government uses the CPI as a
standard index in its efforts to offset the
impact of inflation on benefits paid to
individuals. But since individuals receive
roughly half of all total budget outlays, and
since 90 percent of these payments contain a
cost-of-Iiving adjustment, the indexing formula should measure living costs as closely as
possible. In the past several years, most evidence has suggested that the use of the CPI
overcompensates benefit recipients.
This overcompensation has raised two public-policy questions. First, overcompensation
leads to unwarranted increases in Federal
expenditures and in the Treasury deficit.
Beyond that, it introduces inequities relative to
those individuals not receiving indexed
benefits, and thus amounts to an unintended
redistribution of income. Indexed transfer payments are not taxable, and this widens the gap
between benefit increases and wage increases.
A comparison of index movements since the
Federal government's widespread adoption of
indexing suggests that the PCE index is a more
equitable choice for determining cost-of-living
adjustments.
FOOTNOTES
1. Allen. RD.G., Index Numbers in Theory and Practice. Aldine: Chicago, 1975.
70 period. However, an examination of their results
indicates a steady increase in the percentage error
from 1964 (when the CPI rose by 1.2 percent) to
1970 (when it rose by 6.1 percent). For a class of 20
expenditure categories, the percentage error
increased from 0.005 to 0.326, or at a compound
annual rate of 100.6 percent - more than three times
the annual rate of increase in the CPI in this period.
Steven D. Braitwait, ("The Substitution Bias of the
Laspeyres Price Index", The American Economic
Review, March 1980, vol. 70, no. 1, p. 71), using
1958-70 data, found that the substitution bias
increased significantly the longer that weights were
held constant, rising from 0.36 for the 1958-63 period
to 1.5 for the 1958-73 period. As Braitwait points out,
relative prices change more in a high-inflation period
than in a low-inflation period. His index of relative
price dispersion increased from .11 in 1956-63 to 3.5
in 1958-73. And it is this dispersion of relative prices
that affords greater opportunity for commodity
substitution. Alan S. Blinder ("The Consumer Price
Index and the Measurement of Recent Inflation",
2. Klein, Lawrence and Rubin, Alan, "A Constant
Utility Index of the Cost of Living ", The Review of
Economic Studies, 1949, p. 84.
3. Houthakker, Hendrik, "Compensated Changes in
Quantities and Qualities Consumed", The Review of
Economic Studies, Vol. XIX, no. 50, 1952-53, pp. 156159.
4. Consumer substitution with a Laspeyres index can
make a difference between the measured cost of living and the "true" or perceived change in the cost of
living as measured by an index. A number of studies
have indicated that the amount of error involved
increases rapidly with the rate of inflation. Nicholas N.
Noe and George von Furstenburg, ("The Upward Bias
in the Consumer Price Index due to Substitution",
Journal of Political Economy, November/December
1972, Vol. 80, p. 1283) found the percentage error in
the CPI due to substitution to be "trivial" in the 1963-
55
Brookings Papers on [;conomicActivity, 1geO:2,p.
545J,.found.thatdifferences in·weiQhting accounted
foraboUlone-.half of the difference betweenthe CPI
andPCEin.t979. Indeed,thepost- 1978 period,an
almostcontinuous perioqofhighinflation, "ha~b~en
one .of • tho~erare .timesinwh.ich. sUbstantial
differences. between the Laspeyres and Paasche
indexe.sareexpected to arise."
5. Blinder, Alan $., "The Consumer Price Index and
the Measurement of Recenllnflation", Brookings
Papers on Economic Activity, NO.2,igeO, p. 542.
6.• "Fixeq Nonresidential and Residential Gapital in
the UnitedStates, 1925-1975", U.s. Depwtment of
Commerce, Washington, June 1976, pp. T-6, T-7.
not
berlavi,or to
period. Katz, Arnold J. and
Value of Services Provided by the
Durables, 1947-1977; An uooortumtv
Measure", Survey of Current Business,
22
n.
7. U.S. Department of Labor, Bureau of Labor
Statistics, Consumer Expenditure Survey: Interview
SurveY,1972-73,Bulietin 1997, u.S. Government
Printing Office, 1978 and Consumer Expenditure
Survey: Diary Survey, July 1972-June 1974, Government Printing Office, 1977.
10. "An Analysis of the Effects of IndexinQ for Inflation on Federal Expenditures," General Accounting
Office, August 15, 1979, p. 40.
8. The PCE is not a perfect Paasche index in the
theoretical sense, because it cannot follow every
price for the commodities and services that it covers.
The Bureau of Economic Affairs combines the 107
personal-consumption categories, expressed in
nominal dollars, into 70 categories which are
11. "Reducing the Federal Budget: Strategies and
Examples", Congressional Budget Office, February
1981, p.145.
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