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FEDERAL RESERVE BANK
OF ST. LOUIS
JUNE 1977

Treasury Bill Futures Market and
Market Expectations of Interest Rates
Energy Resources and Potential G N P ....
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Vol. 5 9 , No. 6

,0

The Treasury Bill Futures Market and
Market Expectations of Interest Rates*
ALBERT E. BURGER, RICHARD W. LANG, and ROBERT H. RASCHE

CON OM ISTS and other analysts seek to measure
expectations of future interest rates because such ex­
pectations have important effects on economic behav­
ior. Changes in expectations can lead to changes in
economic activity, both at the level of the individual
firm or consumer, and at the level of the national
economy. For example, interest rate expectations
enter into investment decisions of firms, portfolio de­
cisions of financial intermediaries and other investors,
and borrowing decisions of state and local govern­
ments. If these groups alter their expectations of the
future level of interest rates, changes in investment,
portfolio, and borrowing decisions will occur which
affect not only each group individually, but which
also affect the level of economic activity in the econ­
omy as a whole. Consequently, policymakers and
researchers have been interested in measuring market
expectations of interest rates — first, to understand
the behavior of economic units in individual markets,
and second, to monitor changes in expectations which
result from policy actions, in order to judge the im­
pact which the policy may have on the economy.

actions would be made much easier if market expec­
tations of future interest rates were readily observable.
A considerable amount of economic research has
been devoted to formulating measures of market ex­
pectations of interest rates, since data on expectations
are not directly observable unless survey methods are
used. Efforts at measurement have taken the form of
everything from “informed judgement” to elaborate
econometric models. Another means of obtaining an
estimate of the level of short-term interest rates ex­
pected to prevail at some future date has become
available since early 1976. This method employs the
yield quotations of the futures market in U.S. Treas­
ury bills. These quotations, which are available on a
daily basis, embody market expectations of future
short-term interest rates. This paper focuses on the
information about market expectations which can
be obtained from yields on Treasury bill futures
contracts.

THE ROLE OF THE
TREASURY RILL FUTURES MARKET

For example, consider the discussion surrounding
the recently aborted Federal income tax rebate. The
argument for such a policy was that it would stimu­
late consumer spending, and thus stimulate aggre­
gate output and employment. However, there was
considerable concern that the policy would cause an
upward revision of short-term interest rate expecta­
tions if there were general agreement that the Treas­
ury would have to increase its borrowing substantially
during the second half of 1977 to finance the in­
creased deficit. Under such circumstances, much, if
not all, of the alleged stimulus that would be pro­
vided by the tax rebate could be offset by the negative
impact of higher interest rate expectations on firms’
decisions to invest in real capital. Such a negative
effect arises because the higher the expected level of
future interest rates, the less profitable the income
stream associated with each particular investment
project. T he examination of such effects of policy

T he futures market in three-month U.S. Treasury
bills was opened on the International Monetary Mar­
ket of the Chicago Mercantile Exchange in January
1976, soon after the opening of a mortgage futures
market on the Chicago Board of Trade in October
1975.1 Both of these futures markets in financial in­
struments operate in essentially the same way as the
traditional commodity futures markets. Futures trad­
ing in financial instruments allows the separation of
the risk of unexpected interest rate movements from
other types of risk. Futures contracts can be used to
hedge against interest rate movements in order to
protect actual or expected cash positions of market
participants. Profits are thereby protected in much
the same way as hedging in commodity futures mar­
kets protects against price fluctuations of a particular
commodity. Speculation is facilitated by the existence
of futures markets, which allow the assumption of

“The authors gratefully acknowledge the assistance of Ms.
Jeanne Rickey and the Statistical Department of the Chicago
Mercantile Exchange for providing data used in this paper.

'F o r details on the Treasury bill futures market, see the ac­
companying section: “Characteristics of the Treasury Bill
Futures Market.”

2
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FEDERAL RESERVE BANK OF ST. LOUIS

1977

Characteristics of the Treasury Bill Futures Market
The Treasury bill futures market began active trad­
ing on January 6, 1976, in contracts of three-month
(thirteen-week) U.S. Treasury bills for delivery in
March, June, September, and December. Originally,
there were only four contracts traded, the latest being
for delivery only one year in the future. But in July
1976 the number of contracts was increased to six, the
latest being for delivery eighteen months in the future.
The size of each contract is $1 million, in terms of
the face value at maturity. Thus, a sale of eight futures
contracts of March 1978 Treasury bills is a sale of
$8 million of thirteen-week Treasury bills to be deliv­
ered in March 1978 at an agreed upon price. Simi­
larly, a purchase of eight futures contracts of March
1978 Treasury bills is a purchase of $8 million of
thirteen-week Treasury bills to be delivered in March
1978 at an agreed upon price. If held to delivery, a
futures contract is settled on the business day follow­
ing the last day of trading in the delivery month.1
Futures trading terminates on the second business day
following the Treasury auction of three-month bills in
the third week of the delivery month. For example,
March 1978 Treasury bill futures contracts are deliv­
ered in the third week of March, with the delivered
1Details on the Treasury bill futures market are contained
in Chicago Mercantile Exchange, Opportunities in Interest
Rates: Treasury Bill Futures (Chicago, 1976), and Inter­
national Monetary Market Division, International Mone­
tary Market Year Book 1975-76 (Chicago, 1976). Con­
tract information was also provided by the Statistical
Department of the Chicago Mercantile Exchange.

interest-rate risk by individuals willing to bear such
risk in return for the possibility of making a profit.2

Futures Markets, Information, and Market
Expectations
Trading in futures markets provides information
to the cash market about the commodity being
traded.3 Prices of futures contracts for delivery of a
2For a discussion of the futures markets and the roles of hedg­
ing and speculation, see Thomas A. Hieronymus, Economics
of Futures Trading: For Commercial and Personal Profit, 2nd
ed. (New York: Commodity Research Bureau, Inc., i9 7 7 ).
Uses of the Treasury bill futures market in terms of hedg­
ing and speculation are basically the same as those of the
mortgage futures market. In addition, a discussion of the
costs and benefits of the Treasury bill futures market would
be essentially the same as a discussion of the costs and bene­
fits of the mortgage futures market. For such analyses of the
mortgage futures market, see Neil A. Stevens, “A Mortgage
Futures Market: Its Development, Uses, Benefits, and Costs,”
this Review (April 1976), pp. 12-19.
3For a discussion of the effect of futures trading on information
in spot markets, see Charles C. Cox, “Futures Trading and
Market Information,” Journal of Political Economy ( Decem­
ber 1976), pp. 1215-37.



Treasury bills maturing at the end of three months
(the third week of June 1978).
Although the size of a single contract is $1 million,
a person interested in buying or selling a contract can
trade in this futures market on margin. The minimum
initial margin is $1,500 per contract, and the commis­
sion for executing an order is $60 per contract. By off­
setting an initial buy or sell order prior to the delivery
date, it is possible to trade in Treasury bill futures
contracts with far less money than the $1 million face
value of each contract.
Prices in the Treasury bill market are quoted on a
discount basis, that is, at a price lower than the face
value, and prices in the Treasury bill futures market
are also quoted on a discount basis. The interest earned
on a Treasury bill, if held to maturity, is the difference
between the purchase price and the face value (or par
price). Prices in the Treasury bill futures market are
quoted in terms of the IMM (International Monetary
Market) Index, which represents the difference be­
tween the Treasury bill yield (discount) on an annual
basis and 100 (face value or par).2 For example,
Table I shows the futures price and yield quotations
for Treasury bills on March 14, 1977, as published by
The Wall Street Journal. The March 1977 futures price
at the close of trading (the settlement price) was
95.39, so that the interest rate (yield on a discount
basis) on the March 1977 contract was 4.61 percent
(100 — 95.39).
-Opportunities in Interest Rates, pp. 27-29.

commodity at a future date provide market partici­
pants with information as to the expected pattern of
future spot prices of this commodity. This is because
information relating to the future state of the market
for a particular commodity is utilized by market par­
ticipants when determining the price at which they
are willing to buy or sell futures contracts.
If a trader projects that a commodity’s price will
be different in the future than at the present time,
he will buy or sell contracts for delivery of the com­
modity at some future date as if his projection were
correct. Any trader who has better information about
future spot prices than other market participants (or
feels that he does) can attempt to make profits by
trading on this information, with the result that such
information is quickly incorporated into the prices of
futures contracts. Thus, the interaction of all traders
in the futures market provides price quotations which
embody the market’s expectations of the future spot
prices that will prevail on various delivery dates.
Page 3

FEDERAL RESERVE BANK OF ST. LOUIS

In the case of the futures market in Treasury bills,
the yields on futures contracts indicate the pattern of
interest rates expected by market participants to pre­
vail in certain months in the future, given currently
available information. Any expectation of future in­
terest rates, however arrived at, utilizes information
about the current and expected values of variables
that are thought to influence the behavior of interest
rates. Such variables include measures of the current
and future state of the economy, the supply and de­
mand for credit, and the course of monetary and
fiscal policy. The futures market in Treasury bills
serves the role of a processor of this information. As
new information about the course of key factors
influencing interest rates becomes available, it is
rapidly reflected in futures market prices.4
The expected interest rate for any date in the
future which is embodied in the yield on current
futures contracts is not necessarily the interest rate
that will prevail at that future date. Market partici­
pants in the futures market do not have a crystal
ball that foretells the future perfectly. Their decisions
to buy or sell contracts are based on the information
available at th e presen t tim e. As new information be­
comes available, market participants may very well
revise their expectations. The effect of new informa­
tion — such as a change in the announced monetary
targets, new budget projections, revised projections
of the strength of economic activity, new pricing
policies by O PEC, and so on — is reflected in changes
in the prices of (and yields on) futures contracts.
Consequendy, ch an g es in market expectations can be
identified by shifts in the pattern of yields on futures
contracts (futures rates). Sharp declines or increases
in futures rates can be identified as changes in the ex­
pected level of future interest rates. Thus, a compari­
son of the quotations on futures contracts at two dif­
ferent points in time provides information on whether
4This discussion does not imply that the Treasury bill futures
market satisfies the “efficient market” hypothesis. In an “effi­
cient market”, all available information is utilized immediately
by traders (and potential traders), new information is avail­
able to everyone at the same time, and new information is
immediately incorporated into market prices and yields. The
discussion in the paper implies only that some of the avail­
able information is utilized by traders (or potential traders),
and that new information which is utilized is quickly reflected
in futures prices. This allows for information costs and imperfect
information among market participants. For a general discus­
sion of the “efficient market” model, see Oldrich A. Vasicek
and John A. McQuown, “The Efficient Market Model,” Fi­
nancial Analysts Journal ( September - October 1972), pp. 7184. For a theoretical treatment, see Eugene F. Fama, “Effi­
cient Capital Markets: A Review of Theory and Empirical
Work,” Journal of Finance (May 1970), pp. 383-417; or
Richard Roll, The Behavior of Interest Rates: An Application
of the Efficient Market Model to U.S. Treasury Bills (New
York: Basic Books, Inc., 1970).
4
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1977

market expectations have changed with regard to the
future level of short-term rates. One implication of
this is that it may be possible to assess the effect of
a change in monetary or fiscal policy on market
expectations of future short-term interest rates.

Futures Rates and Expected Spot Rates
One way of looking at the price and yield quota­
tions on Treasury bill futures contracts in Table I
is to interpret the yields on each futures contract as
a market estimate of the three-month Treasury bill
rate that is currently expected to prevail in each
delivery month. Thus, the market’s expectation on
March 14, 1977, was that the three-month bill rate
would be 5.23 percent in June of this year, and would
increase another 126 basis points by December to 6.49
percent. In comparison, the three-month bill rate on
March 14, 1977, for currently traded three-month
bills, was about 4.57 percent.
However, such use of the Treasury bill futures
rates is subject to some reservations. The main ques­
tion is whether the futures rates are unbiased esti­
mates of the market’s expectations of future interest
rates. According to the “normal backwardation”
argument of Keynes and Hicks, futures p rices are
downward-biased estimates of expected future spot
prices.5 This implies that even if future spot prices
are expected to remain the same as the current spot
price, the futures price will be below the expected
spot price by an amount equal to a risk premium.
This premium is considered to be a return to specu­
lators for assuming the risk of possible future price
fluctuations, and is larger for delivery dates which
extend further into the future. This implies, in turn,
that the price of the futures contract will tend to
rise (the yield will fall) as the delivery date ap­
proaches, provided there is no change in market
expectations.
In terms of futures markets in Treasury bills, the
theory of “normal backwardation” implies that yields
on futures contracts are u piv ard -biased estimates of
expected future interest rates (since prices and yields
of securities are inversely related). Accordingly, the
interest rate on three-month Treasury bills expected
to prevail as of some future delivery date is less than
the yield quoted on the futures contract for that
5John Maynard Keynes, A Treatise on Money: The Applied
Theory of Money, vol. II (New York: Harcourt, Brace and
Company, 1930), pp. 142-47; and J. R. Hicks, Value and

Capital: An Inquiry into Some Fundamental Principles of
Economic Theory, 2nd ed. (Oxford: Clarendon Press, 1946),

pp. 136-39.

FEDERAL RESERVE BANK OF ST. LOUIS

JUNE

1977

Table 1

FUTURES
Delivery
M onth

P R IC E S

FOR

U .S. T R E A S U R Y

BILLS O N
Price

O pen

High

Low

C lo se *

MARCH

14,

1977

Y ie ld **
Change* *

( Discount)

Yield
C h an ge *

March 19 77

9 5 .3 7

95.4 0

9 5 .3 7

95.39

+

-01

4.61

—

.01

June 1 9 7 7

94.7 3

94.84

94.71

9 4 .7 7

+

.03

5.23

—

.03

September 1 9 7 7

94.1 0

94.1 6

94.05

94.1 0

+

.01

5.90

—

.01

December 1 97 7

93.52

93.5 6

93.4 6

93.51

—

.01

93.05

9 3 .1 7

93.04

93.13

.01
.08

6.49

March 1978

+
+

6.87

-

.08

June 1978

92.6 6

92.75

92.6 6

92.6 6

7.34

♦Closing price is the settlement price.
♦♦Based on the closing (or settlement) price. Price and yield changes are the changes from the previous day.
Source: The Wall Street Journal, March 15, 1977

delivery date.6 In addition, if yields on futures con­
tracts are higher for later delivery dates than for
earlier delivery dates, it is not certain that the ex­
pected future spot rate is higher for the later deliv­
ery dates than for the earlier delivery dates. This is
because a larger risk premium is included in the
yield associated with the later delivery dates. Only if
the difference between the yields for an earlier and
later delivery date exceed the difference between
their risk premia can one conclude that the expected
future spot rate is higher for the later delivery date.
One implication of this line of reasoning is that
gradual declines in futures rates cannot necessarily
be identified as declines in market expectations of
future spot rates, since the yields on futures contracts
tend to fall as the delivery date approaches. How­
ever, sharp declines indicate a change in expectations,
as do increases in futures rates, provided the risk
premia are constant or change very little (which is
generally assumed by the theory).
If these risk premia could be easily estimated,
market expectations of future interest rates could be
estimated from quotations on futures contracts. Unfor­
tunately, this is not the case. In addition, other ana­
lysts dispute the “normal backwardation” argument
and claim that futures prices are u n b iased estimates
of expected future spot prices.7 The issues surround8Hicks used the “normal backwardation” argument of the
futures market in his development of the liquidity preference
theory of the term structure of interest rates. See Hicks,
Value and Capital, Chapters XI and XIII. In the literature
on the term structure, market expectations of future interest
rates have been examined using the implied forward rates
which are embodied in the yield curve. These implied for­
ward rates are theoretically equivalent to futures rates.
7For discussions of the issues involved and some empirical
evidence in support of normal backwardation, see Hendrik S.
Houthakker, “Normal Backwardation,” in Value, Capital, and
Growth: Papers in Honour of Sir John Hicks, ed. James N.
Wolfe (Edinburgh: Edinburgh University Press, 1958), Chap­
ter 7, and “Can Speculators Forecast Prices?” The Review of
Economics and Statistics (May 1957), pp. 143-51. For evi­
dence against the theory of normal backwardation, see Lester



ing this question of unbiasedness are not within the
scope of this paper, but some observations on the
matter can be made.
Even if futures rates are biased estimates of mar­
ket expectations, the bias will not be very large,
judging from the estimates of risk premia embodied
in the yield curve.8 Furthermore, the bias, if it exists,
is expected by most theorists to be consistent over
time, rather than being subject to large fluctuations.
Consequently, even though futures rates may not be
entirely accurate as point estimates of market expec­
tations, it may be possible to make rough estimates
of expected future interest rates.

Trading Volume
Another issue bearing on the usefulness of the
futures rates involves the amount of trading which
occurs in each contract. Generally, it is thought that
the larger the amount of trading in a security, the
more representative the price and yield quotations
G. Telser, “Futures Trading and the Storage of Cotton and
Wheat,” Journal of Political Economy (June 1958), pp. 23355. Telser argues that prices of futures contracts are solely
market expectations of future spot rates and contain no risk
premia.
8Since such premia in the Treasury bill futures market will be,
at most, for three-month bills eighteen months in the future,
the bias in the yields on futures contracts will not be very
large. This is due to the fact that the premia, according to
the liquidity preference theory, increase with term-to-maturity
for such Treasury bills. Thus, the premia associated with
three-month bills to be issued six months from today are
expected to be smaller than the premia associated with threemonth bills to be issued one year from today. Estimates of
these premia have generally been less than 50 basis points.
See J. Huston McCulloch, “An Estimate of the Liquidity
Premium,” Journal of Political Economy (February 1975),
pp. 95-119; Roll, The Behavior of Interest Rates, p p . 98-99;
and Edward J. Kane and Burton G. Malkiel, “The Term
Structure of Interest Rates: An Analysis of a Survey of Interest-Rate Expectations,” The Review of Economics and Sta­
tistics (August 1967), pp. 345-55.
The existence of a bias in the futures rates can be tested
by investigating whether, with constant expectations, the
prices of futures contracts rise (yields fall) as the delivery
date approaches.
Page 5

FEDERAL RESERVE BANK OF ST. LOUIS

JUNE

1977

Table II

AVERAGE

D A IL Y T R A D I N G V O L U M E

BY M O N T H

Contract Delivery Month

Month
Traded
January 1976
February 1976
March 1976
April 1976
May 1976
June 1976
July 1976
August 1976
September 1976
October 1976
November 1976
December 1976
January 1977
February 1977
March 1977
April 1977

March
1976

June
1976

128.95
58.89
27.46

36.79
41.53
182.39
141.76
92.00
26.47

Septembe r December
1976
1976
18.11
21.74
71.17
120.43
224.45
230.14
242.43
60.73
19.67

4.88
12.71
29.83
39.00
84.60
87.55
258.57
273.50
185.43
119.71
59.30
31.88

............. ...... ...... ...................................... ................... ..................
September December
June
March
June
March
September
1977
1977
1977
19 77
1978
1978
1978

Total
All
(Issues)

188.72
134.86
7.84
5.00
17.37
27.36
43.05
68.64
107.62
290.71
345.65
236.43
216.67
79.32
36.59

318.69
306.19
7.58
10.45
18.43
11.50
39.81
160.57
315.40
294.81
398.48
415.05
350.91
232.65

7.71
2.32
4.00
27.71
67.75
122.95
301.33
242.26
386.04
518.45

6.05
2.41
3.10
15.19
20.35
36.90
74.71
88.05
174.09
523.25

2.00
4.29
22.55
17.67
35.14
17.21
50.74
172.10

3.86
8.26
27.13
75.75

27.67
42.85

426.00
381.97
576.24
419.09
361.62
618.19
831.00
740.64
1030.19
850.16
1053.17
1565.05

Source: International Monetary Market Division of Chicago Mercantile Exchange

will be of the market value of the security.0 In the
case of Treasury bill futures contracts, this suggests
that contracts with low trading volume are not rep­
resentative of the market value of these contracts,
and, hence, are not representative of market expecta­
tions. However, the issue is more complicated than
this.
As can be seen from Table II, trading in any par­
ticular futures contract is low when it is first traded,
increases over time, but then is again low as its
delivery date approaches. For example, trading in the
futures contract for delivery in March 1977 can be
examined by reading down the appropriate column
in Table II. This issue was first traded in March
1976, and the average daily volume of trading was
only 7.84 contracts. By November 1976, trading in­
creased to over 345 contracts per day. But after
January 1977, with less than two months to the
delivery date, trading declined below 100 contracts
per day.
As the delivery date approaches, trading volume
generally declines because there is greater certainty
as to what the spot rate will be on the delivery date.
That is, traders tend to agree as to the future market
value of three-month Treasury bills (their expecta­
tions become homogeneous) when the delivery date
is near. Consequently, there is less risk of interest
rate fluctuations to be hedged against and less likeli­
hood that profits can be made from trading, so that
less trading occurs. In this case, the futures rates do
9This line of reasoning underlies, in part, the construction of
the Treasury Department’s yield curves, which give greater
weight to the yields of some actively traded issues.
Page
6



reflect the market valuation of the contracts, even
though there is little trading.
However, a lack of trading may also be indicative
of a case where market participants have ill-defined
expectations of future interest rates and their expec­
tations are so diffuse that traders’ bid or asked
prices are not matched up with each other. In this
case, there is little trading because there is great
uncertainty as to the range in which the future spot
rate will fall. It is possible that this case applies to
the futures rates associated with contracts for deliv­
ery in fifteen to eighteen months, such as the March
1978 contract which was first traded in September
1976 (T ab le I I ) .
On the other hand, when market participants have
well-defined but heterogeneous expectations of future
spot rates, trading activity is likely to be large. In this
case, traders tend to agree as to the range in which
the future spot rate will fall, but disagree as to the
exact value. Market participants perceive that there
is greater risk of interest rate fluctuations to be hedged
against, and that profits can be made from trading.
Bid and asked prices on contracts for the delivery
date match up over a larger number of traders, and
trading volume is larger.
Therefore, the extent to which the yields on futures
contracts for particular delivery dates accurately reflect
the market value of these contracts, and market expec­
tations of future interest rates, depends upon the
distribution of the expectations of traders. It is not
simply a matter of the amount of trading in each
contract.

FEDERAL RESERVE BANK OF ST. LOUIS

The volume of trading also reflects on the Treasury
bill futures market as a whole. The volume of trading
in futures contracts compares quite favorably with
the volume of trading in the spot market for Treasury
bills. The total volume of trading in the Treasury bill
futures market was relatively light during the first
two months of trading after its opening on January
6, 1976. But beginning in March 1976, trading in­
creased substantially to an average daily volume of
about 318 contracts (T ab le I I ) . W ith each contract
representing $1 million of three-month bills, this
trading represented the daily exchange of $318 mil­
lion of Treasury securities in the futures market. In
contrast, the average daily volume of trading by se­
curities dealers in the spot market for all outstanding
Treasury bills (approximately forty different issues)
was $6.76 billion during March 1976. These figures
average out to a daily volume of roughly $64 million
for each Treasury bill futures market issue (five
issues were traded in March 1976), compared to
about $169 million for each outstanding Treasury bill
issue in March 1976.

MARKET EXPECTATIONS OF
SHORT-TERM INTEREST RATES
SINCE JANUARY 1976
The pattern of yields on Treasury bill futures con­
tracts since the initiation of trading on the Interna­
tional Monetary Market is shown on a daily basis
in Chart I. Examining the movement of these yields
provides some insight into the adjustment of market
expectations of future short-term interest rates to new
information about the state of the economy and the
future supply of and demand for credit. The chart
shows that die yields on all of the futures contracts
being traded during any particular time period follow
the same pattern of movement to a remarkable
degree.
During the first quarter of 1976, market expecta­
tions of the future level of the three-month Treasury
bill rate increased as the economy experienced a 9.2
percent annual rate of growth in Real Gross National
Product (G N P ). W ith the economy growing at such
a rapid pace, market participants apparently antici­
pated a continuation of this upswing in economic
activity during the remainder of the year, although
not at so fast a pace. This expected strength in eco­
nomic activity was translated into anticipations of
increased demands for short-term credit, with a con­
sequent rise in interest rates. During March 1976, the
yield on the September 1976 futures contract was
generally above 6.50 percent, while the currently



JUNE

1977

traded three-month Treasury bill yielded about 5
percent.
The yields on futures contracts declined during
April 1976, but by May yields had returned to roughly
the same levels as were recorded in March (C hart
I ) . During most of April 1976, newly available data
indicated moderating pressures on the credit market
and expectations of future levels of interest rates were
revised downward. For example, the yields on the
September 1976 futures contract during April were
close to 6 percent, down from about 6.5 percent in
March. Data on the money stock ( M l ) that became
available in the first half of April showed that the
money stock had grown at a 2.9 percent rate over
the first quarter of 1976, well below the FO M C ’s an­
nounced target ranges for M l growth.10 Most market
participants apparently did not anticipate any nearterm tightening in monetary policy actions, and
viewed the growth of money as being consistent with
a continued gradual reduction of the longer-run infla­
tionary impact of policy actions. The preliminary
GNP data available in mid-April continued to show a
slowing in inflation and a strong surge in real output
growth. Business loan demand at commercial banks
remained weak and Treasury financing requirements
were running well below earlier estimates.
Beginning in late April 1976, however, there were
several developments that acted to change market
expectations. On April 22, market participants became
aware that there had been a very sharp surge in M l
in early April (money stock data is reported with a
one-week lag ). Data available in May indicated
that the money stock was rising very rapidly, ex­
panding at nearly a 17 percent annual rate in April
and then at a 5.7 percent rate in May. On May 3 it
was announced that the FO M C had voted at its April
meeting to lower the upper band on the long-run
growth of M l from 7V2 to 7 percent.11 The Federal
Reserve moved to a more restrictive policy, and this
was made apparent to market participants by a steady
rise in the Federal funds rate from about 4.78 per­
cent in the week ended April 23 to 5.02 percent in
the week ended May 14. Then, at its May 18 meet­
ing, the FO M C voted to adopt a Federal funds range
of 5 - 5 % percent, compared to a 4% - 5% percent
range at the April meeting. By the week ended May
28, the Federal funds rate had risen to an average of
10Albert E. Burger and Douglas R. Mudd, “The FOMC in
1976: Progress Against Inflation,” this Review (March 1977),
pp. 2-17.
11Ibid. Rates of growth of the money stock used in this paper
are the originally reported figures, not the subsequently re­
vised figures.
Page 7

’■
ti
p
OQ

<t>

00

Y i e l d s o n T r e a s u r y Bi ll F u t u r e s C o n t r a c t s 11
Ja n u a ry 1976 - April 1977

L I A ll y i e l d s a r e o n a d i s c o u n t b a s is.




S o u r c e : In t e r n a t io n a l M o n e t a r y M a r k e t D iv is io n

FEDERAL RESERVE BANK OF ST. LOUIS

5.50 percent. As this new information about the
course of monetary developments became available,
market anticipations of future levels of interest rates
returned by late May to about the same level as was
recorded in March 1976.
The expected increase in credit demand failed to
appear, GNP growth remained moderate, the inflation
rate declined, and the unemployment rate increased
during the summer of 1976. Growth of the money
stock fell to about a 3 percent rate from May to
September. Yields on futures contracts and the spot
rate on three-month bills both declined slowly from
late May until early October,12 when the yields on
futures contracts fell quite sharply. This sharp decline
was reversed in late October when yields increased
almost to their early September levels. This reversal
in expected yields was also associated with incoming
monetary data that indicated a sharp surge in the
rate of growth of the money stock. From September
to October, M l increased at a 15.5 percent annual
rate.
Indicators of the strength of economic activity con­
tinued to decline during the last quarter of 1976, as
did the rate of inflation, and market interest rates on
all types of securities continued to decline. In the last
half of November, market expectations of future
interest rates declined sharply. After the surge in
M l growth during October, the money stock was
little changed during November. But the Federal
funds rate declined from about 5 percent in early
November to about 4.75 percent in early December,
which, in turn, was interpreted by market partici­
pants as indicating that the Federal Reserve had
adopted a somewhat less restrictive policy. During
November, yields on futures contracts fell 50 basis
points or more. W ith pessimism about the “pause” in
the economy mounting, yields on futures contracts
for Treasury bills continued to fluctuate around these
lower levels until the end of the year.
The increase in expected future interest rates in
early January 1977 coincided with the new Adminis­
tration’s announcement of a stimulative fiscal pack­
age. At the same time, data on the economic indi­
cators for November were revised upward and a
strong showing of some of the indicators for Decem­
ber was reported. Furthermore, monetary actions were
no longer moving toward a further reduction in the
12Under the “normal backwardation” hypothesis, this gradual
decline in futures rates may not reflect a gradual decline in
market expectations of future spot rates. Instead, such a
gradual decline over time is consistent with constant market
expectations of future spot rates, since if “normal backwarda­
tion” holds, futures rates tend to fall (futures prices rise)
as the contract delivery date approaches.



JUNE

1977

Federal funds rate, contrary to the initial expectations
of many market analysts. As a result, yields on futures
contracts increased to their levels of mid-October
through early November.
From early January through March 1977, yields on
futures contracts were relatively stable. During April,
when the Administration’s rebate program was can­
celled and the energy program was announced, fu­
tures rates fluctuated sharply. As new information on
the state of the economy and on future supplies and
demands for credit becomes available to market par­
ticipants, the expected future interest rates that are
embodied in the yields on future contracts for U.S.
Treasury bills will be revised. Movements in the levels
of these yields will, therefore, provide a significant
indicator of revisions of market expectations of future
short-term interest rates.

SUMMARY AND CONCLUSIONS
The Treasury bill futures market provides a means
for hedging against interest-rate risk. Speculators are
allowed the opportunity of making profits in this
market in return for bearing the risk of future interest
rate fluctuations. In addition, futures markets provide
information about the expected future pattern of
prices. In doing so, indications of changes in market
expectations of future short-term interest rates can be
obtained. Although exact estimates of the expected
level of future spot rates may not be obtainable from
futures rates without adjusting for a risk premium, an
approximation of the level is possible.
If it can be shown that futures rates are unbiased
estimates of expected future interest rates, the data
from the Treasury bill futures market could be very
useful in a number of ways. Policymakers would be
able to readily assess the effects of policy changes on
market expectations of future interest rates. Econ­
omists and other researchers would have o b serv a b le
values for market expectations of interest rates, in­
stead of having to use proxy variables for such ex­
pected rates. Analyses of the portfolio behavior of
financial intermediaries, investment decisions of firms,
and the term structure of interest rates are among
the many areas of research which would be aided by
the use of such data. In addition, analysts who fore­
cast interest rates would be able to compare their
estimates of future interest rates against the market’s
expectations. Since market expectations of interest
rates are an important factor in many economic rela­
tionships, the information on expectations contained
in the Treasury bill futures market will be of increas­
ing interest to businessmen, financial managers, pol­
icymakers, and other economic analysts.
Page 9

Energy Resources and Potential GNP
ROBERT H. RASCHE and JOHN A. TATOM

X H E dramatic change in supply conditions for
energy resources since 1973 had a substantial effect
on the productive capabilities of the U.S. economy.
Higher prices of energy resources, relative to the
prices of labor and capital resources, resulted in a loss
of economic capacity and higher output prices. It has
been estimated that four to five percentage points of
both the higher price level and reduction in national
output in 1974 were due to the increased scarcity of
energy resources entailed by the quadrupling of
O PEC petroleum prices.1
The loss of national output because of energy mar­
ket developments was a permanent loss. The energy
price revision reduced the effective supply of re­
sources available. Thus, the rate of output achievable
by fully utilizing the nation’s resources, the “potential”
output of the economy, was lowered.
Conventional methods of measuring the economy’s
potential have focused primarily upon the availability
and productivity of la b o r resources. More recently
such efforts have also attempted to account for the
availability and productivity of ca p ita l resources. Es­
timates of potential output which consider the rela­
tionship of only capital and labor resources to national
output are not well suited to the task of accounting
for the effects of changes in the availability or cost of
energy resources. Nevertheless, the Council of Eco­
nomic Advisers (C E A ) has recently pointed to evi­
dence which indicates that a permanent drop in the
productivity of U.S. capital and labor resources may
have occurred after 1973. The CEA suggests that this
drop is due to the higher cost of energy resources.2
A direct route to estimating potential output, which
accounts for the supplies of labor, capital, and energy
resources under conditions of full utilization, is pos­
sible. Such an approach shows that a preoccupation
with the supply of energy resources in measuring po­
tential output is not important prior to 1973. Only
!See Robert H. Rasche and John A. Tatom, “The Effects of
the New Energy Regime on Economic Capacity, Production,
and Prices,” this Review (May 1977), pp. 2-12.
2See Council of Economic Advisers, Economic Report of the
President, 1977, pp. 55-56.
Page
10



small year-to-year changes in the relative scarcity of
energy occurred before 1973. The effect of such
changes was minor and capable of being captured by
the trend growth of productivity of labor and capital.
However, such a direct approach also demonstrates
the fundamental importance of accounting for energy
in measuring potential output after 1973. W hen
energy is included in the production relationship link­
ing resources to output, the effect of the increased
scarcity of energy is seen to be of the magnitude of
our earlier estimates which were based upon eco­
nomic theory and more indirect evidence.
Aside from clarifying the recent performance of the
U.S. economy relative to its potential, estimates of
potential output which account for energy resources
have important implications for economic and social
prospects. Potential output measures which do not
include the loss due to the change in the world energy
market overstate the gains in output achievable by
full utilization of resources. Consequently, such meas­
ures, in addition to endorsing impossible short-term
growth possibilities, foster an inflationary bias in ef­
forts to achieve an unattainable potential output. Also,
unrealistically high estimates of potential output im­
ply corresponding overestimates of the tax revenues
associated with full resource utilization. Thus, federal
budget planning tends to have a greater bias toward
deficits.

THE DEVELOPMENT OF MEASURES
OF POTENTIAL GNP
The Original CEA Estimates
The notion of potential GNP, the output rate pro­
duced when the economy fully utilizes its resources,
was first developed by the Council of Economic Ad­
visers in 1962.3 The original estimates of potential
GNP were based on three simple statistical approaches
3See Council of Economic Advisers, Economic Report o f the
President, 1962, pp. 49-56, and Arthur M. Okun, “Potential
GNP: Its Measurement and Significance,” American Statisti­
cal Association, 1962 Proceedings of the Economic Statistics
Section, pp. 98-104, also reprinted in his The Political Econ­
omy of Prosperity, (Washington, D.C.: Brookings Institution,
1970).

FEDERAL RESERVE BANK OF ST. LOUIS

JUNE

1977

C h o rt I

" O l d C E A ” P o te n tia l G N P a n d A c t u a l O u t p u t

L a te st d a t a p lotted : 1 9 7 6

S o u r c e s : U .S. D e p a rtm e n t o f C o m m e rc e a n d C o u n c il of E c o n o m ic A d v is e r s

developed by Okun that related the unemployment
rate to actual real GNP. The estimates assumed that
full utilization of resources occurs when the unemploy­
ment rate for the civilian labor force is four percent,
that is, the economy operated at its potential in mid1955. The original estimates assumed that potential
output grew at an annual trend rate of about 4.5 per­
cent from 1947 to 1953, and at about a 3.5 percent
rate from 1953 to 1962.4
The original estimates achieved widespread recog­
nition. The simple device of relating departures of
the unemployment rate from four percent to the
“gap” between actual and potential output facilitated
the popular discussion of both economic goals, such
as full employment and growth, and fiscal policy.
W ith regard to the latter, the notion of a high-employment Federal budget was developed and used
to indicate the state of the budget deficit or surplus
under high-employment economic conditions as well
as the magnitude of fiscal efforts required to move the
economy to a four percent unemployment rate.
Since these original estimates, the CEA has recog­
nized that various forces, particularly demographic
4See Okun, “Potential GNP,” pp. 101-02.



factors, can change the trend rate of growth of re­
sources and, hence, potential output. Consequently,
the CEA has from time to time adjusted the trend rate
of growth used to update their data series for potential
output. From 1952 through 1962, the CEA uses the 3.5
percent trend rate of growth derived by Okun. This
trend rate was raised to 3.75 percent for the period
from 1962 through 1968 and further increased to four
percent from 1969 through 1975. Because of a slow­
down in the rate of growth of the labor force, the CEA
reduced the trend rate of growth of potential GNP
after 1975 to 3.75 percent. This series is referred to
below as the “old” CEA estimate and is shown in
Chart I along with actual GNP.5
Okun indicated in his original work that his analysis
skipped over important links between changes in the
unemployment rate and output, and in an often
quoted passage he concluded:
Still, I shall feel much more satisfied with the esti­
mation of potential output when our data and our
analysis have advanced to the point where the esti­
5For a full description of the old estimate see the note in
U.S. Department of Commerce, Bureau of Economic Analysis,
Business Conditions Digest (September 1976), p. 95 and the
discussion in issues of the CEA Economic Report since 1962.
Page 11

FEDERAL RESERVE BANK OF ST. LOUIS

mation can proceed step-by-step and where the cap­
ital factor can be taken explicitly into account.6
Since 1962 several studies have attempted to improve
upon the original work. The major efforts attempted
to account for capital resources and for the interaction
between actual output and prospective potential out­
put. The major development has been to use an ap­
proach based upon an aggregate production function.7
However, until recently no serious problems have been
detected with the old CEA estimates.8

The “New” CEA Potential Output Series
More recently, studies of potential output have in­
dicated some major departures from old estimates.
In addition to the slowdown in the long-term growth
of the labor force pointed out by the CEA in the fall
1976 revision of the growth trend, a study by Data
Resources, Inc., suggests a further slowdown since
1973 because of a substantial decline in the growth of
the capital stock.9 More importantly, the CEA itself
has pointed out an apparent slowdown in productivity
growth since 1966. Clark has developed a new poten­
tial output series for the CEA which is based, to an
extent, on production function estimates rather than
simple trends.10 These new estimates imply a growth
rate of potential output of about 3.5 percent in the
6Okun, “Potential GNP,” p. 104.
7A few of the major studies are: Edwin Kuh, “Measurement
of Potential Output,” American Economic Review (Septem­
ber 1966), pp. 758-76; Lester C. Thurow and L. D. Taylor,
“The Interaction Between the Actual and the Potential Rates
of Growth,” The Review of Economics and Statistics (N o­
vember 1966), pp. 351-60; Stanley W. Black and R. Robert
Russell, “An Alternative Estimate of Potential GNP,” The
Review of Economics and Statistics (February 1969), pp.
70-76; and Benjamin M. Friedman and Michael L. Wachter,
“Unemployment: Okun’s Law, Labor Force, and Productiv­
ity,” The Review of Economics and Statistics (May 1974),
pp. 167-76.
8For example, see the discussion by George M. vonFurstenberg,
“Comments on Estimating Potential Output for the U.S.
Economy in a Model Framework,” Achieving the Goals of the
Employment Act of 1946 — Thirtieth Anniversary Review,
U.S. Congress, Joint Economic Committee, 94th Cong. 2nd
sess., December 3, 1976, pp. 26-28. He points out that more
elaborate “supply-orientecf models” are valuable for improv­
ing understanding, but estimates from them are not “demon­
strably more reliable” than the old official estimates. He also
notes that the usefulness of the old CEA potential output
estimates “would be unaffected by anyone showing, for in­
stance, that potential is consistently one percent larger or
smaller than officially estimated” (p. 2 8 ).
9See Roger Brinner, “Potential Growth to 1980,” Otto Eckstein

et. al., Economic Issues and Parameters of the Next 4 Years,

(Lexington, Massachusetts: Data Resources, Inc., Economic
Study Series, 1977), pp. 9-17.
10See the CEA, Economic Report, 1977, pp. 45-57 and Peter
K. Clark, “A New Estimate of Potential GNP,” Council of
Economic Advisers, unpublished memorandum, January 27,
1977.
Digitized forPage
FRASER
12


JUNE

1977

late 1960s and early 1970s. These new estimates
are in agreement with projections made in 1972 by
William Nordhaus.11
In two respects the new CEA series on poten­
tial output represents a major departure from the
methods used to compute the old series. First, poten­
tial output now is viewed more as high-employment
output rather than being linked to a four percent un­
employment rate. The new CEA estimates are based
on explicit considerations of participation rates and dif­
ferential high-employment unemployment experiences
of different age-sex groups. The high-employment
benchmark of a four percent civilian labor force un­
employment rate in mid-1955 is preserved, but the
new series is based on explicit estimates of the revi­
sion in the high-employment benchmark over time
due primarily to changes in the composition of the
labor force. The second major departure is an at­
tempt to account more explicitly for capital resources
in the estimation of productivity and potential output.
However, the new estimates of the CEA do not take
into account a further one-time reduction in produc­
tivity and potential output which their analysis indi­
cates occurred in 1974 and which they suggest may be
a permanent change due to the energy price shock.12
A comparison of the new and old series is presented
in Chart I I for the period 1952-1976. Until 1967, the
two CEA potential output series are very similar. The
new CEA estimates show potential output to be about
one percent lower from 1952 to 1967, but growing at
roughly the same rate. After 1967 the new estimates
fall short of the old series by a growing amount. By
1976 the new estimate of $1363.6 billion is only 95.9
percent of the old estimate of $1421.2 billion.13 The
bulk of the $57.8 billion reduction is attributed to a
slowdown in the growth of labor productivity and an
increase in the full-employment unemployment rate.
As noted above, the CEA has suggested that pro­
ductivity fell further in 1974, so that by 1976, poten­
tial output may be $30 billion lower than their own
new estimates. These new estimates, like those of
D ata Resources, Inc., mentioned above, assume a
n See William D. Nordhaus, “The Recent Productivity Slow­
down,” Brookings Papers on Economic Activity (3 :1 9 7 2 ),
pp. 493-545.
12While the Economic Report discusses the new estimates,
neither the old nor new series have been published in the
monthly publication of the Bureau of Economic Analysis,
Business Conditions Digest, since October 1976.
13See CEA, Economic Report, 1977, p. 55. All potential output
measures are in constant (1 9 7 2 ) dollars throughout this
article.

JUNE

FEDERAL RESERVE BANK OF ST. LOUIS

1977

C h a rt II

R a tio o f " N e w

L a te st d a t a plotted: 1 9 7 6

C E A ” to " O l d C E A ” P o te n tia l G N P

S o u r c e : C o u n c il o f E c o n o m ic A d v ise rs

Cobb-Douglas production function with only labor
and capital resources and assume output elasticities
of one-third for capital and two-thirds for labor.
Thus, neither estimate is able to capture fully changes
in productivity of labor and capital resources due to
reductions in potential energy usage associated with
a higher relative price of energy resources.

the E-H study is similar to that used here, the conclu­
sions are markedly different. These differences result
from serious data problems and a specification error in
their demand for energy. Since their study has such
a similar methodology and reaches such different re­
sults, a full critique is contained in Appendix I.15

The production-function approach to the estimation
of potential output taken in this article accounts
explicitly for energy resources. The potential output
measures draw heavily upon the recent work involved
in the new CEA measures of potential output, specifi­
cally by using their estimates of the potential labor
force and the full-employment unemployment rate.

ACCOUNTING FOR ENERGY IN AN
AGGREGATE PRODUCTION FUNCTION

One recent study, that of Eckstein and Heien (E -H ),
has attempted to account for energy effects on poten­
tial output through the aggregate production func­
tion.14 The E-H results indicate, however, that in
recent years potential output is much higher than the
old CEA estimates. W hile the methodology used in
14Albert J. Eckstein and Dale M. Heien, “Estimating Potential
Output for the U.S. Economy in a Model Framework,”
Achieving the Goals of the Employment Act of 1946 —
Thirtieth Anniversary Review, U.S. Congress, Joint Eco­
nomic Committee, 94th Cong., 2nd sess., December 3, 1976,
pp. 1-25.



The first step in a production-function approach to
measuring potential output is the estimation of an
1“Another study which includes energy price developments in
an estimate of potential output is that by Jacques R.
Artus, “Measures of Potential Output in Manufacturing
for Eight Industrial Countries, 1955-78,” International Mon­
etary Fund Staff Papers (March, 1977), pp. 1-35. Like
Clark’s study he finds an energy price impact using a
dummy variable approach instead of explicitly incorporat­
ing the energy price. Since his study includes seven
countries he is forced by data limitations to impose several
arbitrary constraints which raise serious questions about the
meaningfulness of his coefficient estimates. Relaxing the con­
straint that the effect is the same across countries, his esti­
mate of the energy price impact is that U.S. potential
manufacturing output fell 2.7 percent in 1974 which is
below both Clark's estimate of 4.2 percent for the private
business sector and our earlier estimate of five percent which
is confirmed below. Ignoring the other constraint problems,
it may be noted that his estimate is not significantly different
from ours given its relatively large standard error.
Page 13

JUNE

FEDERAL RESERVE BANK OF ST. LOUIS

aggregate production function. The approach taken
here follows the usual practice with one major ex­
ception: energy resources are considered as an inte­
gral part of the production function. This is in con­
trast to the usual practice of estimating the functional
relationship between output and only labor and
capital resources. The latter approach implicitly as­
sumes that changes in the stock and flow of energy
resources are captured by movements in the capital
stock and need not be explicitly taken into account.
The measure of output for which a production func­
tion is estimated is the output of the private business
sector. Real GNP includes, in addition to the out­
put of the private business sector, gross output orig­
inating in the rest of the world, the output of the
general government sector, output imputed to owneroccupied dwellings, and output of households and
nonprofit institutions. For estimating potential real
GNP these components of actual GNP are simply
added to potential real output of the private business
sector.
Actual real output in the private business sector
depends upon the employment of capital and labor
services as well as energy resources. The production
function may be written as
(1)

1977

the Federal Reserve Board index of capacity utiliza­
tion times the capital stock in place at the beginning
of each period.17 The annual capital stock measure is
the constant dollar (1972) net stock of fixed nonresidential equipment and structures.18 A comparable
data series on energy use in the private business sec­
tor could not be found. However, the rate of energy
use in the private business sector is presumably that
demanded and the demand for energy is determined
completely by the production function and the rela­
tive price of energy.
If firms in the private business sector maximize
economic profits, they employ energy at a rate where
the value of the additional product obtained from
employing more energy equals its price. The demand
for energy from equation ( 1 ) is
(2)

E = y Y

/

-

)

\

B

where PF is the price of energy and PB is the price
of output of the private business sector.19 Equation
(2 ) can be used for the energy input in the production
function so equation ( 1 ) may be found by estimating
i
(3)

Y = ( A* ert L “

P “ y)

l 'y

Y = A e " L “ K'i Ey

where Y is output, L is labor measured in manhours,
K is the effective flow of capital services, E is the
flow of energy resources, and t is time. The other
terms in equation (1 ) are estimated statistically. The
A term is essentially a scaling factor, r is the trend
rate of growth of output due to technological change,
and a , |3, y are the output elasticities of the respec­
tive inputs. The estimated production function was re­
stricted by requiring that the sum of the exponents
a , p, y equal unity. The basic implications of such a
“Cobb-Douglas” production function are constant re­
turns to scale and partial elasticities of substitution of
unity.18
The output and manhours data for the private busi­
ness sector are those prepared by the Bureau of
Labor Statistics of the U.S. Department of Labor. The
effective services of capital are found by multiplying
16Constant returns to scale means that equal proportionate
changes in each of the resources employed causes a propor­
tionate change in output. This is a common assumption em­
ployed in estimating production functions, especially at such
a highly aggregated level. Unit partial elasticities of substitu­
tion have also been employed in earlier studies, although al­
ternative production function specifications exist which relax
this constraint.
Page
14



where A* is another scaling factor and P is the rela­
tive price of energy (P E/PB). The relative price of
energy is measured by the ratio of the wholesale price
index for fuel, related products, and power to the
implicit price deflator for the output of the private
business sector.
The credibility of the assumed Cobb-Douglas pro­
duction function is, of course, purely an empirical
matter that can be subjected to statistical testing. The
assumption implies relatively high price and output
elasticities of demand for energy and unit partial
elasticities of substitution between energy and capital
17In a previous paper, “The Effects of the New Energy Re­
gime,” we discussed the possible biases of the FRB capacity
utilization index in recent years as a result of changes in the
relative price of energy, when it is viewed as a measure of
utilization of economic capacity. In the present context, we
need a measure of utilized capital. When this index is
viewed as such a measure, there is no reason to believe that
the change in the relative price of energy has introduced a
systematic measurement bias.
18See John C. Musgrave, “Fixed Nonresidential Business and
Residential Capital in the United States, 1925-75,” Survey of
Current Business (April 1976), pp. 46-52.
19The marginal product of energy from equation ( 1 ) is y Y /E ,
so the profit-maximizing employment of energy occurs where
PE = (v Y /E ) PB.

FEDERAL RESERVE BANK OF ST. LOUIS

or labor.20 There is, however, some evidence that
these properties apply to the U.S. economy. An output
elasticity of demand for energy of unity in the long
run for at least the United States, Japan, and Western
Europe is supported by a number of studies.21 Using
cross-sectional data and the trans-log production func­
tion, Griffin and Gregory have demonstrated that for
nine industrial nations the production function has
partial elasticities of substitution of energy for capital
and labor that are constant and unity.22 Most impor­
tantly for the purpose at hand, the assumption of a
Cobb-Douglas production function cannot be rejected
with the data examined.
Recent studies of productivity suggest that in esti­
mating an aggregate production function it is impor­
tant to account for qualitative changes in manhours
and for productivity differences in capital due to the
increasing importance of mandated pollution-abatement capital expenditures.23 Attempts to control for
skill differences by including variables for the com­
position of the labor force by age were unsuccessful
except for the 16 - 1 9 age group; a negative effect of
the share of the latter group on productivity was not
statistically significant when the estimation was ad­
justed for autoregression. Clark’s gross capital stock
data are adjusted for pollution-abatement capital. Use
of his series produced results essentially identical to
those found using the gross nonresidential stock of
business capital (constant 1972 dollars). Thus, no
attempt is made to adjust the net nonresidential stock
of business capital for pollution-abatement capital.24

JUNE

1977

Table 1

An

A ggre gate

P ro d u c tio n

Function w ith

E n e rgy

(A n nu al Data 1 9 4 9 -7 5 )
In Y =

1.7134 +
(1 1 .7 1 )

.7371 In I +
(1 2 .0 1 )

- . 1 3 6 3 In P +
(-5 .6 6 )
F
S.E.

=

.96

=

.0093

.26 2 9 In K
(4.28)

.0185 t
(9.67)
D.W. =
p

=

1.45
.63

Values in parentheses are t-statistics.

the ratio of output to capital and manhours to capital.
The hypothesized negative effect of the relative price
of energy is statistically significant.
The estimates of the output elasticities of the pro­
duction function, based on the equation in Table I,
are presented in the Table II. The output elasticity of
the energy resource is 12 percent which is consistent
with the Griffin and Gregory estimate of the cost
share of energy and energy price elasticity of demand
for capital.25 The latter estimates have been used to
show that capacity in manufacturing fell five percent
in 1974 due to the 45.3 percent rise in the nominal
price of energy from the end of 1973 to the end of
1974. The estimate also supports the assumption that
the manufacturing result is representative of the effect
of the energy price change on the private business
sector.26 The estimated standard error of the estimate
of y is 2.12 percent.27

20The potential biases introduced by assuming a Cobb-Douglas
production function and some indications of their absence
are discussed in Appendix II.
21See, for example, Joseph A. Yager and Eleanor B. Steinberg,
“Trends in the International Oil Market,” Higher Oil Prices
and the World Economy: The Adjustment Problem , ed.
Edward R. Fried and Charles L. Schultze (Washington,
D.C.; Brookings Institution, 1975), pp. 246-47, and the ref­
erences cited in their footnote 45.

The estimate of the output elasticity of labor in
Table I is very close to the usual estimate of labor’s
share of income as well as being approximately equal
to labor’s average share of cost in the private busi­
ness sector over the period of estimation. The aver­
age share of labor in the private business sector
over the sample period is 66.37 percent. A test for
the differences between the estimated output elastic­
ity and the sample period average labor share yielded
a t-value of 0.2914. Thus, the hypothesis that the esti­
mated output elasticity of manhours is equal to labor’s
share can n ot be rejected.

22See James M. Griffin and Paul R. Gregory, “An Intercountry
Translog Model of Energy Substitution Responses,” The
American Economic Review (December 1976), pp. 845-57.

Since the relative price of energy changed dramati­
cally in 1974 and 1975, the production function in

The production function (3 ) estimated with annual
data for the period 1949-75 is given in logarithmic
form in Table I. The equation was estimated with the
constant-retums-to-scale restriction imposed by taking

23See, for example, Clark, “A New Measure of Potential
Output.”
24No doubt pollution-abatement capital investment will be­
come an increasingly important factor for such studies in the
future. Thus, the problems of measuring such investment
will also become more pressing. The unimportance of the
adjustment now is due only to its small size to date. For
example, in Clark’s estimates the pollution-abatement capi­
tal stock is only about two percent of the gross fixed non­
residential capital stock by 1975.



25See Griffin and Gregory, “An Intercountry Translog Model,”
pp. 849-52.
26See Rasche and Tatom, “The New Energy Regime,” p. 5 and
pp. 10-12.
27Formulas for computing the variance of the restricted paramaters ( a , |3, y ) may be found in Jan Kmenta, Elements
o f Econometrics, (New York: The Macmillan Company,
1971), p. 444.
Page 15

FEDERAL RESERVE BANK OF ST. LOUIS

JUNE

Table II

1977

Table III

E stim ate s o f O u t p u t E la sticitie s —

T he C o b b - D o u g l a s

A c c o u n t in g fo r E n e r g y

P ro d u c tio n

Function

W it h o u t E n e r g y
(A n nu al Data)

Sam ple periods

1 9 4 9 -7 5

1 9 4 9 -7 3

Labor ( a )

6 4 .9 %

Capital (|3)

(5 .1 6 % )

(6 .9 3 % )

(y)

12 .0 %

11 .7 %

(2 .1 2 % )

(6 .0 8 % )

(3.1) 1 9 4 9 -7 3 : In Y =

Energy

Time Trend (r)

5 8 .9 %

1.0168 + .6968 In I + .3032 In K
(1 5 .1 5 )
(1 2 .4 8 )
(5 .4 3 )

(5 .1 6 % )

(6 .9 3 % )

+

2 3 .1 %

2 9 .4 %

1 .6 %
(0 .1 6 % )

.96
.00 8 5

(3.2 ) 1 9 4 9 -7 5 : In Y =

1 .2 %

Table I was reestimated over the period ending in
1973 to assess the impact of the large price change on
the estimates. The estimates of the output elasticities
for the earlier period are also given in Table II. The
estimates are practically the same as those for the
longer period, especially for energy.28 Thus, it does
not appear that the importance of energy resources
in the production function estimate is due to the
dramatic energy developments which have occurred
since 1973.
The importance of accounting for energy and its
relative price in estimating production relationships is
illustrated by the equations in Table III. A standard
Cobb-Douglas production function omitting energy is
estimated for the two periods 1949-73 and 1949-75.
The first equation, for the period prior to the large
rise in the relative price of energy, performs about the
same as the equation in Table I which includes energy
in the production function. W hen 1974 and 1975
are included to estimate the second equation, how­
ever, the simple production function performs much
worse. The standard error of the second equation is
more than 50 percent larger than that for the earlier
period and almost 50 percent larger than that given in
Table I.29 The omission of energy from production
function studies prior to 1974 would appear to be a
28The estimated standard error of a is 6.93 percent, so a 95
percent confidence interval for the restricted estimate of
labor’s share contains the sample average share of 66.2 per­
cent for 1949-73.
28For the sake of comparison it may be noted that the stand­
ard error of the equation in Table I over the shorter period,
1949-73, is .82 percent, about the same as for the first
equation in Table III. Also, before the Cochrane-Orcutt
adjustment, the coefficients of the Table III equations are
not as stable. For example, the manhours coefficient drops
significantly from 62 percent for the 1949-73 period to 47
ercent for the 1949-75 period. Such a significant change
oes not occur in the production function estimates which
include energy, nor was there a noticeable change in the
labor share data for 1974-75 in private business sector data.

D.W. =
p =

R2 =
S.E. =

1.58
.84

1.0729 + .7048 In L + .29 5 2 In K
(9 .7 4 )
(9 .0 2 )
(3 .7 8 )
+

(0 .2 1 % )

Values in parentheses are standard errors.

16
Digitized forPage
FRASER


R2 =
S.E. =

.0171 t
(7.9 6 )

.01 4 6 t
(4 .9 8 )

.91
.01 3 5

D .W =
p =

1.92
.86

Values in parentheses are t-statistics.

minor problem, if indeed it is a problem at all.30 After
the dramatic change in energy prices, explicit con­
sideration of energy resources and the relative price
of energy resources is required to obtain stable esti­
mates of U.S. production relationships.31

AN ESTIMATE OF POTENTIAL OUTPUT
The production function estimates can be used to
estimate potential output in the U.S. economy when
supplemented with assumptions concerning the fullemployment availability of resources. The stock of
capital available during a period is essentially the
same regardless of whether the economy operates at
its potential. The utilization rate of capital, however,
varies with economic conditions. Consequently, esti­
mations of potential output for the private business
sector and the economy as a whole requires some es­
timate of the utilization rate that would prevail at
potential output. Quarterly estimates of the Federal
Reserve Board index of capacity utilization in manu­
facturing since 1948 indicate that the 87.7 percent
utilization rate of capital achieved in late 1973 has
been exceeded in only two prior peak periods, dur­
ing the Korean W ar and the Vietnam War, when it
was about 90 percent. During mid-1955, a bench­
mark year for original studies of potential output,
30The unimportance of accounting for energy in some earlier
estimates of the production function is due to its high corre­
lation with time trends and capital. For example, from 1948
through 1970 a trend decline of the relative price of energy
of 1.33 percent per year accounts for over 95 percent of its
variation with a standard error of two percent.
31When the energy price is excluded from the production
function, a Chow test on the additional observations,
1974-75, indicates structural change at a one percent sig­
nificance level. At this significance level, equality of the
coefficients of the production function including the energy
price cannot be rejected when these observations are added.

FEDERAL RESERVE BANK OF ST. LOUIS

the index was 87.5 percent. 32 This latter rate is used
here as the assumed full-employment capital utiliza­
tion rate.
The flow of manhours at the potential output rate
depends upon both the size of the “potential labor
force” and the supply of hours per worker at potential
output. Clark’s recent study provides annual estimates
of the potential civilian labor force. The estimates are
based upon the population and labor force participa­
tion rate of each of eight age-sex groups adjusted for
cyclical effects. Clark has also estimated a full-em­
ployment unemployment rate annually since 1948
which is equivalent to a four percent unemployment
rate in 1955. These estimates are based upon the
relationship between the unemployment rate for each
of the eight age-sex groups and: 1 ) the unemploy­
ment rate of adult males (age 25-54) and 2) the
relative size of the potential group in the potential
labor force .33 An annual series for potential civilian
employment is obtained by adjusting the potential
labor force for the full-employment unemployment
rate. Potential employment in the private business
sector in each period is the difference between poten­
tial civilian employment and actual employment out­
side the private business sector, principally in
government.
Hours per worker in the private business sector at
potential output is estimated in a fairly standard
manner.34 Hours per worker varies cyclically as well
as secularly. Hours per worker at potential output,
adjusted for Clark’s full-employment unemployment
rate, is estimated using the postwar relationship in
Table IV, which treats hours per worker as a function
of the unemployment rate and a time trend. Potential
manhours is the product of the estimated potential
hours per worker and potential employment in the
private business sector.
The relative price of energy at potential output is
assumed to be the actual relative price. Until 1974 it
is conceivable that moving from a smaller output to
potential output in any period would have raised this
relative price. However, since any change of this type
would have probably been quite small given the small
variance in this relative price in the postwar period
through mid-1973, and since the coefficient of the
32See Richard D. Raddock and Lawrence R. Forest, “New
Estimates of Capacity Utilization: Manufacturing and Mate­
rials,” Federal Reserve Bulletin (November 1976), pp.
892-905.
33See Clark, “A New Measure of Potential GNP,” pp. 14-22.
34For example, see Black and Russell, “An Alternative Estimate
of Potential GNP,” pp. 70-76.



JUNE

1977

Table IV

H o u rs p e r W o r k e r in the

P riv ate B u sin e ss Se c to r

(A n nu al Data 1 9 4 8 -7 5 )
In H P W =

.8125 — .0 0 3 0 U - .0 0 4 0 t
(1 6 9 .2 7 ) (3 0 .0 0 )
(4 0 .0 0 )

HPW =
U =
t —
R2 =
S.E. =

hours per worker
unemployment rate
time

.97
.0062

D.W. =

.55

Values in parentheses are t-statistics.

relative price is not large, it is unlikely that the as­
sumption has any noticeable impact on the estimates
of potential output.
The production function and the assumptions above
provide an estimate of potential output in the private
business sector .35 Potential real GNP is found by
adding the actual component of output outside the
private business sector. The annual estimates of poten­
tial real GNP from 1952 to 1976 are shown in Chart III
along with the old CEA series .36 Unlike both the new
and old estimates of the Council of Economic Ad­
visers, the series is not smoothed. The average annual
rate of growth of the series from 1952 to 1975 is 3.4
percent. This is slightly lower than the 3.6 percent
average rate of growth in the new CEA series or the
3.7 percent in the old series for the same period.
The estimate of potential output is virtually identi­
cal to the old CEA estimates in their benchmark year
1955 as well as in 1969-70. Chart IV shows the ratio of
the estimated potential GNP to the old CEA measure
of potential output. Except for the early and mid1950s and 1969-70, the old CEA estimates show the
economy with greater potential than the estimates
here. The chart indicates that the old CEA measure
grows more rapidly in the late 1950s and early 1960s,
but that this is compensated for by a lower estimate
of potential output growth in the late 1960s.37 Chart
3“The exponential of the estimate of the logarithm of potential
output is a biased estimate of potential output. An exact
correction for this bias is derived in Dan Bradu and Yair
Mundlak, “Estimation in Lognormal Linear Models,” Amer­
ican Statistical Association Journal (March 1970), pp. 198211. The bias correction factor was computed for the esti­
mates of potential output presented here. In no case was the
correction more than .1 billion dollars.
:!,1The equations necessary to construct quarterly potential
output employing the same methodology are presented in
Appendix III.
37Black and Russell, “An Alternative Estimate of Potential
GNP,” p. 74, also found that the Council overstated the
trend growth in the late fifties. The fairly constant percent­
age from 1963-65 in Chart IV is also in agreement with
Black and Russell’s claim that the Council estimate of
growth was about right in this period.
Page 17

JUNE

FEDERAL RESERVE BANK OF ST. LOUIS

1977

E stim a te s o f P o te n tia l G N P

P ercentages indicate c o m pounded annual rates of chan ge in our estim ates of Potential G N P .
Latest d a ta plotted: 1976

Source: C oun cil of Economic Ad vise rs

IV also indicates that, according to our estimates, a
four percent trend rate of growth is slightly too high
for the period 1969-71 and about right for 1971-73.


Page 18


After 1973, the ratio plummets as the old trendbased estimates of potential output are unaffected by
energy developments.

C h art IV

R a tio o f E stim a te d P o te n tia l G N P to " O l d C E A ” P o te n tia l G N P

FEDERAL RESERVE BANK OF ST. LOUIS

As indicated in Chart II, the new CEA measures of
potential output are about 99 percent of the old
measures until 1967. Thus, the new CEA series shows
potential output to be smaller than the estimates here
from 1952-59 and from 1968-73. The new official
CEA estimates do not account for energy price de­
velopments so they are higher than the production
function estimates for 1974-75. However, when the
additional productivity shift discussed by the CEA is
taken into account, their new estimate of potential
output for 1974 and 1975 is not much different from
those presented in Chart III.

JUNE

Table V

An A ggre gate

For comparison purposes, a potential output series
was estimated as before using the production function
in Table V. The comparison is essentially the same as
that discussed above without the shift term T2. The
ratio of the estimated potential output, with and
without the slowdown in productivity growth, to new
CEA potential output is shown in Chart V. The new
38The principal source cited by Clark, “A New Estimate of
Potential GNP,” for the productivity slowdown is the study
by J. R. Norsworthy and L. J. Fulco, “Productivity and
Costs in the Private Economy, 1973,” Monthly Labor Re­
view (June 1974), pp. 3-9. The reason given by Norsworthy
and Fulco is a slowdown in the shift of labor from the agri­
culture sector. The slowdown in the shift appears to' be
contradicted by more recent evidence. See Robert Reinhold,
“Decrease in Farm Population Accelerates: Figures Show a
14 percent Decline from 1970-75,” New York Times,
April 15, 1977, p. A14.



P ro d u c tio n Function w ith E n e r g y a n d

A S h ift in the T re n d R ate o f G r o w t h A ft e r 1 9 6 6
(A nnu al Data 1 9 4 9 -7 5 )
In Y =

1.5 6 1 6 +
(9 .9 3 )

+

.7405 In I +
(1 1 .5 5 )

.0202 t (9 .0 3 )

.2595 In K (4 .4 1 )

.10 8 3 In P

(-4 .2 1 )

.00 4 7 T2

(-2 .1 8 )

0; 1 94 9 — 6 6
1 , 2 ........ 9; 1967, 1968, . . . . 1975
R2 =
S.E.

A primary difference, besides excluding energy con­
siderations, between the new CEA potential output
series and that presented in Chart III is a produc­
tivity slowdown in 1967. The new CEA series includes
such a slowdown and it is estimated that the trend
rate of growth falls 25 percent after 1966. The timing
of this shift appears to be arbitrary and its size ap­
pears to be quite large given the reasons cited.38
Nonetheless, such a shift is statistically significant
when a variable intended to capture such an effect
is added to the equation in Table I. Moreover, the
size of the reduction in the trend rate of growth
agrees with the estimates of the CEA. The estimated
equation is presented in Table V. It may be noted
that the equation implies a significant output elas­
ticity of energy of 9.8 percent and an output elasticity
of manhours of 66.8 percent. Given the size of the
standard errors of the coefficients, it does not appear
that the inclusion of the productivity shift parameter,
T2, significantly affects the results indicated in Tables
I and II. The only major differences between the
equation in Table V and the equation in Table I are
the differences in the trend rate and the slight im­
provement in the standard error.

1977

=

a =
(S.E. =

.97

D.W. =

.00 8 9

p

6 6 .8 %

js =

6 .6 3 % )

Values in
indicated.

parentheses

(S.E. =
are

2 3 .4 %
6 .6 3 % )

t-stastitics,

=

y =
(S.E. =

except where

1.54
.41
9 .8 %

2 .3 2 % )
otherwise

CEA estimates are lower than our estimates of poten­
tial output before 1959 and in 1968-73. Like the old
CEA estimates, the new CEA estimates indicate a
higher rate of growth of potential output until the
mid-1960s and a lower rate of growth of potential
from 1965-69. The new CEA rate of growth of poten­
tial output from 1969-73 is in agreement with the
energy based estimate. Finally, like the old CEA
estimates, the new CEA estimates show a higher rate
of growth of potential output in 1974-75.

THE IMPLICATIONS OF NEW
ESTIMATES OF POTENTIAL OUTPUT
Regardless of the historical pattern of the alterna­
tive estimates of potential output, the new CEA esti­
mates and those presented here have similar implica­
tions for the recent and near term performance of the
economy. Table V I shows the potential output meas­
ures for 1973-76 from the old series, the new series,
and those estimated using the equation in Table I and
shown in Chart III.39 Both of the new estimates show
that the economy was much closer to potential output
in 1973 than the old CEA series, indicates. More
importantly, both new series show a substantially
slower growth of potential output in recent years,
compared to the old series and, thus, a substantially
smaller gap between actual and potential output in
1976.
Our estimate of potential output also supports the
CEA’s recent suggestion that energy price develop39The conclusions from Table VI would be unaffected by using
the production function in Table V since the potential meas­
ures for 1973-76 are essentially the same on either basis.
Page 19

JUNE

FEDERAL RESERVE BANK OF ST. LOUIS

1977

C h a rt V

R a t io of E s tim a t e d P o t e n t ia l G N P * to " N e w

C E A ” P o t e n t ia l G N P

P e rc e n t
1 0 3 1--------

P e rc e n t
11 0 3

—

R a tio
for P ro d u c tiv ity Shift

________ To
1952

1953

1954

1955

1956

1957

1958

1959

1960

1961

1962

1963

1964

1965

1966

1967

1968

1969

1970

1971

1972

1973

1974

1975

1976

*T h e s o lid lin e is b a s e d u p o n a i e stim a te o f p o te n tia l o u tp u t f ro m T a b le V . The d a s h e d lin e is b a s e d u p o n o u r e st im a t e of p o te n tia l o u tp u t from T a b le I.
S o u r c e : C o u r :il o f E c o n o m ic A d v i s e r s

L a te st d a t a p lo tte d : 1 9 7 6

ments reduced potential output by an additional $30
billion by 1976.40 W hen this effect is subtracted from
the new CEA estimate for 1976, the result is within
one percent of our estimate of potential output.41
Our estimate of potential output suggests that in
1975, the economy failed to produce about 7 percent
40The $30 billion reduction is a “conservative” estimate. Clark,
“A New Measure of Potential Output,” shows a 4.2 percent
reduction in productivity in the private business- sector which
implies potential output measures for 1975 and 1976 of
$1,273.7 billion and $1,318.9 billion, respectively. These
estimates are even closer to our estimates derived from the
Table I equation and given in Table VI.
41A regression of the relative price of energy on the time
trend variables used by Clark, “A New Measure of Potential
Output,” shows why the estimates agree so well in recent
years. The coefficients, with t statistics in parentheses, for
the quarterly time variables are: .0034 (2 0 .7 ) for a time
trend for 1948 through 1975; .0036 (5 .6 ) for a time trend
beginning in the first quarter of 1967; and .4823 (2 3 .0 ) for
a shift variable which takes values of .25, .5, .75 from the
first through the third quarter of 1974, and one after that.
The adjusted R2 of this equation is .92 and the standard
error is 3.5 percent. The first trend reflects the historical
decline of 1.33 percent in the relative price of energy from
1948 to the end of the 1960s. The shift term beginning in
1974 shows a rise of 48 percent in the relative price, 35.4
percent of which occurred from the fourth quarter of 1973
to the fourth quarter of 1974. Such a shift in the relative
price of energy shows how Clark’s shift of potential private
sector output down by 4.2 percent can be associated with
the energy price. The coefficient of Clark’s shift variable
(.4823) in the energy price regression times the energy
rice coefficient in Table I (.1363) yields a permanent
ecline in potential output of 6.6 percent, about 50 percent
larger than Clark’s 4.2 percent.
Digitized for Page
FRASER
20


of its potential output due to the recession. In contrast
the old and new CEA estimates suggest that the gap
was about 13 percent and 10 percent, respectively.
More importantly, the gap fell to 4.5 percent of poten­
tial output in 1976 while the CEA estimates indicate
it only fell to 11 or 7 percent of potential output. On
the basis of the old CEA series, the worst loss of
potential output, prior to the 1973-75 recession, oc­
curred in 1958 when the gap was about 6.5 percent of
potential. Thus, both CEA estimates imply the econ­
omy performed very poorly relative to potential out­
put in 1976. In contrast, a 4.5 percent shortfall of
actual from potential output is about the same as the
performance indicated by our historical series for
1960-61 or 1971.
The gain in output to be achieved by moving to a
fully-employed economy is substantially smaller than
Table VI

T h re e M e a s u r e s o f P o te n tia l O u tp u t
(Billions of 1972 Dollars)

O ld CEA
1973
1974
1975
1 97 6

$ 1 2 6 5 .4
1315.9
136 8.6
1421.2

New CEA

Production
Function
(Table 1)

Actual G N P

$1 228.2
1271.7
131 6.9
136 3.6

$ 1 2 4 9 .2
1257.8
1283.8
132 4.6

$1 235.0
1214.0
1 1 9 1 .7
12 6 4 .6

FEDERAL RESERVE BANK OF ST. LOUIS

JUNE

either the old or the new CEA measures indicate.
Attempts to expand demand and production to such
unattainable levels in the near term would conse­
quently accelerate inflation. The period of time over
which output may grow at a given rate faster than
the growth rate of potential output is correspond­
ingly smaller. The rate of growth of potential out­
put will constrain actual output growth much earlier
than the old measure suggests. Also, at the output
rate achieved at full employment, Federal tax re­
ceipts and budget surpluses will be smaller than the
higher measures of potential indicate. Thus, a goal
of a balanced budget at full employment will require
more effort than either of the CEA estimates indicate.

CONCLUSIONS
Since 1962 estimates of potential output have be­
come popular and important sources of information
for policy formulation. The early estimates, and until
recently the official estimates, focused upon labor
resources only. New estimates by the CEA have at­
tempted, to some extent, to account explicitly for the
importance of capital resources and a production
function. The CEA has also suggested that t:iergy
developments are an important factor affecting the
productivity of fully-employed resources.
Using a production function which accounts ex­
plicitly for capital and energy resources, an alterna­
tive measure of potential output has been developed.
The production function estimates support the argu­

1977

ment that the new energy regime imposed in 1974
permanently reduced potential output by about four
percent. The production function estimates show that
failure to account for energy prior to 1973 is not
critical, but that serious inconsistencies arise when the
sample period is extended to include recent years.
Until 1973 the historical series for potential output
developed here tends to conform more to the old
CEA series than the new series. After 1973, however,
the new CEA estimates adjusted for the magnitude of
their suggested decline in productivity are very close
to our estimates. Thus, while our estimates cast some
doubt on the historical accuracy of the new CEA
estimates, they support the CEA’s suggestion that
energy price developments after 1973 reduced poten­
tial output.
The implications of the new CEA estimates and
those presented here are of great significance for the
full-employment and growth prospects of the econ­
omy. Attempts to achieve an unattainable potential
output rate through stimulative policy will not only
fail, but will add to inflationary pressures. Also, there
is little prospect for an extended period of growth at
rates higher than the rate of growth of potential out­
put (about 3.5 percent per year). The gap between
potential and actual output will tend to close within
two years, even with the moderate growth of actual
output achieved in 1976. Finally, at full employment,
existing tax and spending policies will result in a
much larger budget deficit than higher measures of
potential output indicate.

APPENDIX I
An Analysis of the Eckstein-Heien Model for
Determining Potential Output1

In a recent study for the Joint Economic Committee,
Eckstein and Heien (E -H ) have estimated an annual
1Albert J. Eckstein and Dale M. Heien, “Estimating Potential
Output for the U.S. Economy in a Model Framework,”
Achieving the Goals of the Employment Act of 1946 — Thir­
tieth Anniversary Review, U.S. Congress, Joint Economic
Committee, 94th Cong., 2nd sess., December 3, 1976,
pp. 1-25.



model which they use to construct an alternative to the
official C EA potential output series. Since their analy­
sis purports to introduce the im pact of energy price
changes on potential output, and since the conclusions of
their analysis are remarkably different from those re­
ported here, this appendix attempts to analyze the rea­
sons for the different conclusions.
Page 21

FEDERAL RESERVE BANK OF ST. LOUIS

The first difference involves the choice of data series.
E-H choose to study the private nonfarm sector of the
economy. This differs from the private business sector as
defined in the text, in that the E-H measure excludes the
farm sector of the economy, and includes the imputed
output to owner-occupied housing and output originating
in households and non-profit institutions. They also choose
to use raw materials as the third factor of production in
their estimated production function, in contrast to the
energy input concept employed above. In practice this
difference should not be too important, since 88 percent
of the weight in their Laspeyres index of raw materials
comes from the crude oil, refined petroleum products,
natural gas and coal components of their index. The
wholesale price index of energy used above measures
just these components plus electrical power, so the cor­
relation of the two input measures should be very high.
E-H estimate a three factor Cobb-Douglas production
function on annual data from 1950-74. The estimated
output elasticities in their function can be compared with
those implied by the production function which is re­
ported above. All three estimated elasticities are essen­
tially identical in both studies. In addition, the estimated
coefficient on the time variable is almost exactly the
same in both equations. The differences in the conclu­
sions of the two studies, therefore, cannot be attributed
to differences in the underlying production function, the
central relationship in both analyses.
E-H present a 12 equation model, while the analysis
above explicitly involves only one equation. For the pur­
poses of constructing potential output, the elaboration in
their 12 equations is somewhat misleading. They use the
assumption that four percent unemployment is the ap­
propriate rate of labor force utilization at which to con­
struct potential output. With this assumption, their model
can be characterized by three distinct blocks: 1 ) an
employment block consisting of the labor force participa­
tion equations and the various identities defining em­
ployment, labor force and unemployment, 2 ) a wageprice block consisting of the equations for the wage rate
in the private nonfarm economy and the price of output
in the private nonfarm economy, and 3) an output block
consisting of the production function, a derived demand
equation for raw materials, and an equation for the aver­
age hours per worker.
Under the assumed “full-employment” conditions, the
employment block is completely independent of the rest
of the model. The size of the male labor force is ex­
pressed solely as a function of exogenous variables, so it
is also an exogenous variable for purposes of the model.
The female labor force is a function of exogenous vari­
ables, other variables within the employment block of the
model, and lagged variables from other blocks of the
model. The various identities in this block relate vari­
ables defined within the block to exogenous variables.
Therefore, it is possible to solve this subset of their
equation system for the total private nonfarm employ­
ment as a function of only exogenous variables. Private
nonfarm employment can affect variables in both the
wage-price block and the output block.
Digitized forPage
FRASER
22


JUNE

1977

The wage-price block is affected by two exogenous
variables, the price of raw materials and the full-employ­
ment unemployment rate. It is also affected by the em­
ployment block and the output block, since these parts
of the model determine employment and output which
affect unit labor costs. Unit labor costs are specified as
an important influence in the determination of private
nonfarm wages.
The output block is affected by the exogenous capital
stock and exogenous capacity utilization rate. It is af­
fected by the employment block through employment
in the private nonfarm sector which enters into the
aggregate production function. Furthermore, the only
link between the wage-price block and the output block
is through the relationship for the average number of
hours per worker, which depends on the real wage rate.
This relationship is not particularly strong, since the
elasticity of the average number of hours per worker with
respect to the real wage rate is only .2 , but it explains
why E-H obtain a positive relationship between raw
materials prices and potential output.
In the E-H model, an increase in raw materials price
directly affects the price of output in the nonfarm sector.
A higher price level in turn causes higher wages, but the
increase is less than proportional, so the real wage rate
falls in response to the increase in raw materials prices.
Real wages have a negative impact on the average num­
ber of hours per worker, so hours per worker rise in re­
sponse to the increase in raw materials prices. But total
private sector employment in the model is exogenous at
potential output as discussed above, so total manhours
rise in response to the increase in raw materials prices.
The net effect is an elasticity of real output with respect
to raw materials prices in the E-H model of .02. The small
magnitude of this elasticity illustrates the weakness of
the interrelationship of the price-wage equations of the
model with the output equation through the average
hours equation.
If E-H had assumed, as do the authors of other studies
of potential output, a fixed number of hours per person
at full employment, then the link between the wageprice block and output block in their model would be
broken. Their potential output model would then consist
only of two equations; the production function and the
demand for raw materials equation, supplemented by
exogenous assumptions on the magnitude of manhours
supplied at potential output. Under these circumstances
their analysis would imply that there is no effect of
changes in raw materials prices on potential output. In
practice, their analysis effectively implies such a conclu­
sion since the price elasticity reported above is so close
to zero.
The two equation model which is so closely approxi­
mated by the E-H model is exactly the two equation
model which is implicit in the analysis presented above.
The aggregate production function, with the relative
price of energy as one of the right hand side variables,
is derived by substituting the demand equation for
energy under the assumption that the real price of energy

FEDERAL RESERVE BANK OF ST. LOUIS

JUNE

inputs is exogenous. Recall that the estimates of the
production function parameters are essentially the same
for the two studies. Therefore, the difference in the re­
sults obtained must be attributable to differences in the
explicit or implicit demand functions for energy inputs.
The problem with the E-H model is that the demand
functions for both labor and raw material inputs are
misspecified. Such demand functions normally would be
expected to be consistent with the first-order conditions
for cost minimization and/or profit maximization. In the
case of the Cobb-Douglas production function, this im­
plies that the input demand functions must be log-linear.
Yet both the demand function for raw materials and the
demand function for labor services in the E-H study are
specified as linear functions. This probably accounts for
the insignificance of the estimated coefficient of the
relative price term in the raw material demand equation
which E-H report in the text, but not in the equations of
the model.

1977

The approach used in this study implicitly assumes
that both the output elasticity and the price elasticity of
the demand for energy are one, and that the functional
form of this equation is log-linear. If this were not the
case, then the output elasticities derived from the pro­
duction function parameter estimates should be biased.
Three pieces of evidence suggest that this is not the case.
First, the estimated output elasticity of labor services
conform quite closely to the share of labor in total income
as it should under the constant-returns-to-scale restric­
tion. Second, the estimated output elasticity of energy
inputs conforms almost exactly with the estimates from
cross-section time series data of several countries, includ­
ing the United States obtained by Griffin and Gregory.
Third, as mentioned above, the estimated output elas­
ticity of energy (as well as of other resources) obtained
in this study are almost identical to those obtained by
E-H even though they used a measure of the quantity of
raw materials input in estimating the production func­
tion directly.

APPENDIX II

Equation (2) constrains both the output and price
elasticities of energy demand to unity. Consider the
unconstrained hypothesis for the energy demand curve:
In E = 80 + 8j In Y - S2ln (PE/PB) + e

If this is substituted in the Cobb-Douglas production
function:
I n Y = a + a l n L + /3l nK + ' y l n E + u
w here a + /3 + y -

1, the result is:

[In Y - In K] = /3j + 0 2 [In L - In K]
+

In (Pe/P B) + 0 4 In K +

7€ + U

1 - 8 ,7
80 y
w here /3. = (1 - S,y

-y S2
1 - 8. y

ft, = (-

1 - 8j y

—1 + a + (3 + 5, y

(----------------------— )
1 - 8, y

Therefore, if the output elasticity of energy demand,

8 i, were not unity, the specification which has been esti­
mated would have an omitted variable, In K, which
would be correlated with at least one of the included



regressors, (In L-ln K ), so all of the estimated regression
coefficients (P’s) would be biased.
If the price elasticity of energy demand, 62,^ is not
unity, then the estimated regression coefficients (P’s) are
not biased, but the output elasticities which we have
derived from the regression coefficients are biased. Our
estimates^ of the output elasticities for labor and energy
are a* = ^2/(1 — $ 3) and y #= ^ / (1 — P3), respectively.
The unbiased estimates of these output elasticities are
y = y [-

1 + ( / - l)(l - 8„)

-] and a = n ° [-

1 - 8,

2
Consequently, if 62 < 1, our estimate of the output elas­
ticity of energy is biased downward and our estimate
of the output elasticity of labor is biased upward. The
consistency of our estimates of the output elasticities
with estimates from other sources and the consistency of
the output elasticity with the labor share data, suggests
that biases from these sources are not substantial. Even
if the output elasticities were biased because the price
elasticity of energy demand was less than unity, the
biases would not affect our potential output computa­
tions, since these are Jaased on the unbiased estimated
regression coefficients (P’s).
Page 23

APPENDIX III
A quarterly series for potential GNP can be constructed
using the same method and data when some additional as­
sumptions are made concerning the data. The principal
data problems involve quarterly estimates of the capital
stock and potential employment or manhours.

Quarterly data on the stock of capital are found by
prorating the annual year-end changes in the net stock of
fixed nonresidential equipment and structures over quar­
ters using quarterly rates of investment in nonresidential
fixed investment as the weights. Clark’s annual data on
the potential labor force are assumed to be for the
second quarter of each year and a linear interpolation is
used for other quarters. To find potential manhours, a
quarterly estimate of hours per worker is obtained such
as that contained in Table IV. The quarterly potential
hours per worker is found by using Clark’s full-employ­
ment unemployment rate for the respective years in the
equation
(1 )

In H PW =.8120 - .0033 U - .0010 t
(346.6) ( - 7 . 0 8 )
( - 5 0 .7 5 )
R2= .97
D.W. = .31
S.E. = .0062




which is estimated for the period from the second quar­
ter of 1948 through 1975.

The quarterly production function comparable to the
annual estimate in Table I, (II/1948-IV/1975) is
(2 )

In Y = 1.5974 + .7192 In L 4 - .2808 In K
(14 .2 0 ) (20.85)
(8 .1 4 )
- .1 1 6 4 In P + .0045 t
(- 5 .6 4 )
(15.00)
R2 = .98

D.W. = 1.90

S.E. = .008

p = .80

The estimated coefficients are essentially the same as for
the equation in Table I. The estimated output elasticities
and trend growth term are (standard errors in
parentheses)
a = 64.4% (3.08%), P = 25.2% (3.08% ),
y = 10.4% (1.85% ), f = .4% (.03% ).