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FED RAL RESERVE BANK
OF SAN FRANCISCO

.....CONOMIC
R VIEVV

SPRING 1878

The Federal Reserve Bank of San Francisco’s Economic Review is published quarterly by the
Bank’s Research and Public Information Department under the supervision of Michael W. Keran,
Vice President. The publication is edited by William Burke, with the assistance of Karen Rusk
(editorial) and William Rosenthal (graphics). Editorial Committee members for this issue are
Larry Butler (chairman), Herbert Runyon and Michael Bazdarich.
For copies of this and other Federal Reserve publications, write or phone the Public Information
Section, Federal Reserve Bank of San Francisco, P.O. Box 7702, San Francisco, California
94120. Phone (415) 544-2184.

Information and Market Efficiency

Introduction and Summary

II.

Using T-Bill Futures to Gauge
Interest Rate Expectations

III.

IV.

5
William Poole

GNMA Futures: Stabilizing orDestabilizing?
Kenneth C. Froe wise

Public and Private Sector Information
in Agricultural Commodity Markets

Michael Gorham

Practical Monetarism and the Stock Market

Kurt Dew

eluding in the concept of a policy plan an understanding of the policy adjustments required by
certain contingencies.
Poole notes that today's futures rate is not an
especially accurate forecast of "tomorrow's" spot
rate, so that its policy significance ought not to
be exaggerated. However, policymakers' own
forecasts of interest rates are not very accurate
either. "Unless policymakers have solid evidence
that their own forecasts are more accurate than
market forecasts, they cannot afford to ignore
the T-bill futures market."
Kenneth Froewiss analyzes another new type
of market
the futures market in the financial
instruments of the Government National Mortgage Association (GNMA). This market was inaugurated in late 1975 by the Chicago Board of
Trade, but it is the result of several earlier developments dating back to the late 1960's. The first
was the mortgage industry's attempt to devise a
hedging mechanism to protect itself from unforeseen interest-rate fluctuations. The second was
GNMA's introduction of a new
- the
pass-through certificate - to attract more investors to the housing market.
Froewiss' empirical results suggest that the
GNMA spot market has
its
mance in the period since futures
began
in those securities. "The spot market has become
more efficient in processing new information; it
has shown less purely random
variability;
and it has become more closely integrated with
the rest of the bond market. Futures trading is
not necessarily responsible for any of those beneficial developments, but it
has not had a
destabilizing effect on
prices of
GNMA certificates.
Froewiss argues that these conclusions have a
wider reference than to the GNMA market
alone. Financial futures markets are still in their

Markets provide consumers and producers
with information-the prices at which they can
buy and sell-which they need to make rational
economic decisions. Economists judge market
performance both by the reliability of the information conveyed and by the efficiency with
which market participants utilize that information. The four articles in this issue examine questions of the quality of information and the
efficiency of its use in various specific markets Treasury bills, GNMA futures, commodity markets and the stock market.
William Poole applies such an analysis to the
market for Treasury-bill futures which began
trading in early 1976. The evidence suggests that
the T-bill futures market is closely linked to the
spot market in bills, at least for the nearest futures maturity. Unexploited arbitrage opportunities between the two markets rarely exist.
In Poole's view, the existence of the explicit interest-rate forecasts provided by the futures market emphasizes the need for policymakers to
understand why discrepancies arise between
market forecasts and their own interest-rate
forecasts. "If, at some point in time, rates in the
bill futures market are based on forecasts of a
strong and/or more inflationary economy than
projected by policymakers, and if the market is
correct, then there is a danger that policymakers
will determine a more expansionary policy than
is appropriate for the needs of the economy."
Market interest-rate forecasts also may reflect
forecasts of policies that are different from those
that policymakers are actually planning. Consequently, policymakers should make their plans
known and ensure that announced policy plans
are realized. However, this raises the question of
how adjustments may be made in response to
changing economic conditions. Poole sees no easy
solution to this dilemma, except perhaps by in-

infancy, so that more and more of them are likely
to be established. "The results of this study of
GNMA futures suggest that we have nothing to
fear and potentially much to gain from the further development of these markets."
Michael Gorham, in a third paper, discusses
the development of information in commodity
markets. Most market participants rely upon
some source or sources of information to enhance
their decision-making abilities, obtaining this information from both the public and private sectors. Gorham explores the relationship between
public- and private-market information, with
particular emphasis on a specific market with a
large component of public-sector information the market for agricultural commodities.
Gorham shows how public information both
destroys and creates opportunities for providers
of private-sector information. He then measures
the private sector's response to these new opportunities in the case of three major agricultural
commodities with highly-developed spot and futures markets. His analysis indicates that private-information sources correctly forecast
public-sector announcements for soybeans, but
not for corn and wheat.
For technical reasons, the quality of both types
of information generally improves during each
individual crop year. However, over longer periods, public-sector information has improved in
quality, whereas the private sector's forecasting
ability has lagged behind. Gorham does not find
this surprising. "The public sector, unlike the private sector, is not constrained by considerations
of profitability when adopting improved methods
of forecasting or expanding its survey activities
although of course it is subject to certain budget constraints." The U.S. Department of Agriculture thus has been better situated than the
private sector to improve its forecasting ability.
Kurt Dew, in a final paper, considers the information provided by the stock market as a means

of analyzing changes in monetary-policy behavior. He poses the question - "Are changes in
policy procedures only differences in style or
does monetary policy now affect the economy in
a substantially different way than it did in the
1960's?" Utilizing the theory of efficient markets, he answers by saying that the Federal Reserve's response to money growth has changed,
and as a result, the economic impact of a temporary deviation of money growth from trend has
actually been reversed.
Dew makes the case that the Fed today raises
interest rates in response to undesirably rapid
money growth, whereas it did not do so in the
1960's. This change in response is revealed indirectly, through an analysis of the stock market's
response to the money supply. He points to evidence that the stock market today (unlike the
1960's) responds negatively to an increase in the
money supply. He then bolsters his conclusion
with the proposition that the stock market is an
efficient forecaster of the future economic impact of a change in the money supply, which impact in turn depends on the Federal Reserve's
policy reaction.
Dew argues that the new emphasis on the monetary aggregates has in fact altered the structure
of the economy, and that most econometric models of the monetary-transmission process are misspecified as a result. He questions the naive interpretation of the portfolio-adjustment theory
namely, that an excess demand or supply of money precedes changes in long-term interest rates
and equity values, which changes in turn influence levels of real economic activity. Dew's empirical work instead indicates that stock prices
and interest rates primarily reflect anticipated
trend rates of money growth. "Thus, according to
a more accurate interpretation of portfolio theory, past rates of money growth affect current
real economic activity only if they affect forecasts of future money growth."

William Poole'

term, premiums is examined. Studies of the term
structure of interest rates have generally found
that longer-term securities on average have higher yields than shorter-term securities. This finding is of importance in its own right, but it also
implies that a term premium must be subtracted
from a futures rate if that rate is to be interpreted
as the market expectation of the future spot rate
at the maturity of the futures contract. This rather technical issue is treated at some length, because it is of great importance in assessing the
significance of yields in the futures market.
From evidence presented in previous studies of
the term structure, and from new evidence on the
futures market, it is argued that part of the observed term premiums may reflect transactions
costs rather than risk aversion. The conclusion
reached is that, since transaction costs in the futures market are almost non-existent, it is probably not necessary to make any allowance for
term premiums when using futures rates to
gauge market expectations of future spot rates.
In the last section, the policy implications of
market interest-rate forecasts are explored. The
major issue concerns the significance of differences between market forecasts and policymakers' forecasts of interest rates.

Trading in three-month Treasury-bill futures
began on January 6, 1976. Six contracts were
traded originally: March, June, September, and
December of 1976, and March and June of 1977.
When each contract matured, trading began in a
new contract dated three months beyond the
most distant contract previously traded. More
recently trading has been conducted in eight contracts.
The details of this market and its uses in various types of hedging, speculative, and tax-motivated transactions have been fully described
elsewhere. 1 The purpose of this paper is to provide an analysis of the link between the futures
market and the spot market in Treasury bi!ls of
varying maturities, and to examine the policy
significance of the interest-rate expectations incorporated in the T-bill futures.
In the first section of the paper, it is shown that
the spot and futures Treasury bill markets are
closely linked in practice; profitable arbitrage
opportunities between the two markets rarely exist, at least for the nearest futures maturity traded at any given point in time. (Only this maturity
is examined in this paper.)
In the second section the issue of liquidity, or

I. Relationships Between Spot and Futures T-Bill Markets
At the present time, eight contracts are traded
in the Treasury-bill futures market. In August,
1977, for example, trading was conducted in futures for September and December, 1977;
March, June, September and December of 1978;
and March and June of 1979. Government security futures other than bills are also available.
When yields on these securities get out of line

with yields in the futures market, profitable riskfree arbitrage transactions are possible.
Only for short maturities, however, is it possible to find a perfect match of maturities in the
spot and futures markets. For example, from
March 24 through June 22, 1977, spot bills due
June 23 and September 22 and June futures provided instruments with exactly matching maturities. Settlement on the June futures took place on
June 23, and required delivery of the September
22 bill-a 91-day bill on June 23-on all June
futures contracts still open. If held to maturity,

*Professor of Economics, Brown University. The empirical
work in this paper was conducted while the author was Visiting Scholar at the Federal Reserve Bank of San Francisco in
Summer 1977: The views expressed are the responsibility of
the author and do not necessarily retlect those of the Bank.

an investment in the combination package of the
June 23 spot bill and a long position in June futures had identical characteristics to an investment in the September 22 spot bill. The two
investments should, therefore, have identical
yields-except for possible differences in transactions costs should the investor desire to sell out
before maturity. The yield differences are limited, however, by the possibility of arbitrage between the two markets.
Arbitrage opportunities for futures maturities
other than the nearest one are not quite risk-free
because the maturities do not quite match. For
example, between December 23, 1976 and
March 22, 1977, arbitrage involving June 1977
futures had to be based on bills dated September
20 and June 23; the September 22 bill was not
issued until March 24.
In studying the completeness of arbitrage, we
may limit the investigation to the nearest maturity futures contract, so as to avoid the need for
extra assumptions concerning arbitrage when
maturities do not quite match. In examining arbitrage, we may proceed as if the spot bill yields

are fixed; the problem is the determination of the
range of bill futures yields such that risk-free arbitrage profits are possible considering the explicit transactions costs involved. The range will
be defined in terms of an upper critical point,
FU, above which substitution of the short spot
bill and a long futures position for the long spot
bill will be profitable; and a lower critical point,
FL, below which substitution of the long spot bill
and a short futures position for the short spot bill
will be profitable. Although we will be determining upper and lower critical points for the futures
rate given the spot bill yields, we could just as
well have determined upper and lower critical
points for either spot bill given the yield on the
other bill and the futures yield.
In the derivations below it is assumed that bills
are infinitely divisible, and all calculations are
per $100. In fact, the discreteness of bills and of
futures contracts-each futures contract is for
$1 million face value of bills-prevents arbitrage
from being profitable precisely at these critical
points. However, the critical points derived under the perfect divisibility assumption provide

Chart 1

6.20
6.00
5.80
5.60
5.40

5.20
5.00
4.80
4.60
4.40
4.20

JAN

FEB

March Futures

June Futures
1976

September Futures

benchmarks against which the market may be
judged with respect to the exhaustion of arbitrage opportunities.
Suppose that an n+91-day bill is owned, where
n is the number of days to the maturity of the
nearest futures contract. If the futures yield is
high enough, the investor can raise his rate of return over the n+91-day horizon by selling the
n+91-day bili and using the proceeds to buy an
n-day bill and a long position in a futures maturing in n days. What futures yield will be high
enough to make this substitution profitable?
Each n+91-day bill is worth P~+91 t at time
t, where pb is the dealer's bid price-the price at
which investors other than dealers can sell the
bill. By the definition of the banker's discount
yield-the quotation method used in the bill
market-we have
Rb
P bn+91,t = 100 - n+91
360
n+91,t
where Rbis the bid yield, in percent, on the
banker's discount basis. In the arbitrage transaction being examined, enough n+91-day bills are
sold to buy the n-day bills required to provide the
cash needed in n days to settle the maturing long
futures position. The cash requirement at time t
also includes the futures market commission$60 per contract-and the futures market margin requirement-$1500 per contract. Since
each contract is for $1 million face value of bills,
Percent

the commISSIon and margin amount to only
$0.006 and $0.15, respectively, per $100 of face
value. 2
Working backwards, in n days the amount
needed to settle the long position in the futures
market will be
91
where
Fn t
qn t = 100 - 360'
,
Fn,t is the yield at time t on the futures contract
maturing in n days. However, when the futures
contract matures, the $1500 per contract margin
will be returned, and so the net cash requirement
per $100 in n days is qn,t - 0.15.
Each n-day bill will be worth 100 upon maturity in n days; thus a (qnt, - 0.15)/100 fractional
n-day bill must be purchased at time t to provide
the cash needed at time t+n. For investors other
than dealers, the purchase price of an n-day bill
is the dealers' asked price, P~,t' which is related
to the asked yield by a
n
a
Pn,t = 100- 360 Rn,t·
Thus, the cash needed at time t is that required to
buy the fractional bill at the price of P ~ ,t per
bill plus the amount needed for the futures contract margin requirement and commission, or
$0.15 and $0.006 per $ i 00. Thus, the totai cash
requirement at time t is
( qn,\
P~,t + 0.15 + 0.006.
The cash requirement at time t is to be raised
by selling a fractional part, X, of the n+91-day

Og.15 )

Chart 2

5.80
5.60
5.40
5.20
5.00
4.80
4.60
4.40
4.20
4.00

December Futures

June Futures

March Futures

1977

1976

bill already owned. If this fraction is less than
one, then the arbitrage operation will be profitable. The purchase of the n-day bill and the futures contract package will produce $100 in
n+91 days. Simply holding the n+91-day bill
will also produce $100 in n+91 days. Thus, if the
arbitrage transaction requires that a fraction less
than one of the n+91-day bill be sold, then the
fraction I-X of an n+91-day bill will be a riskfree arbitrage profit.
From these considerations, the fraction, X, of
n+91-day bills selling at price pb
sold
n+91,t
must be such that

ceeds invested on maturity in a 91-day bill. The
yield on a 91-day bill is, of course, unknown before the bill is issued, but the investor can (if desired) lock in a known yield by buying a bill
futures contract. He can also lock in that yield
implicitly by buying an n+91-day bill, provided
he is willing to lock in the package combination
of the equivalent of an n-day bill and the 91-day
bill to be issued at time t+n.
From a similar line of reasoning, the lower
critical point may be defined. A risk-free arbitrage opportunity exists if
(2)

X pb
n+91,t

(qn,t - 0.15)pa + 0.15 + 0.006.
100
n,t

Dividing through by p ~+91 ,t defines X; arbitrage is profitable if X < I, or in yield terms,
(I)

n
a)- I [n+91 b
Fn,t> ( 1-36000Rn,t
~Rn+91,t
n,t

n,t

< (1 36000 Rn,t)

-1 [n+91

~ R n + 91 ,t

b
360
n
b
Rn,t - 9T (0.006) - 1 (0.0015 Rn,t

)J .

The right-hand side of (2) defines the lower critical point for profitable arbitrage.
The critical points defined by (1) and (2) have
been calculated from daily data for the period
from January 6, 1976 to June 23,1977, and plotted as solid lines in Charts 1 and 2. 3 The futures
quotes are plotted as dots in the charts.
The charts suggest that profitable arbitrage
opportunities rarely exist, and when they exist
are small in magnitude. This finding is especially
significant because only explicit costs were included in the calculation of the arbitrage
points-no allowance was made, for example, for
the labor time of the arbitrageur-and perfect
divisibility was assumed.
Two other features stand out in the charts.
First, there appears to be a tendency for the futures rate to fall closer to the lower than the upper arbitrage point, especially in the first month
plotted for each contract. Second, there seems to
be a tendency for the futures rate to fall in the
last month of trading for each contract. These
observations are directly related to the nature of
term premiums in interest rates for securities of
various maturities.

_~ R a + 360 (0.006) +~ (0.0015 R a )l.
91

Fn,t

The right-hand side of the inequality (l) defines
the upper critical point for profitable arbitrage.
The expression has been written so that the components due to explicit transactions costs in the
futures market-the terms involving 0.006 and
a.0015-may be clearly identified.
It may also be noted that without the two futures market transaction-cost terms, the righthand side of (1) defines the implicit forward rate
of interest in the term structure calculated from
the bid yield on the n+91-day bill and the asked
yield on the n-day bill. In the example being discussed, the implicit forward rate is the rate of interest that would have to be earned on a 91-day
bill to be issued at time t+n, so that the total
yield over n+91 days would be the same on an
n+91-day bill and on an n-day bill with the pro-

II. Term Premiums and Bid-Asked Spreads4
The existence of term premiums had been widely
assumed, and so recent empirical findings have
seemed to confirm the theoretical expectation
that risk aversion would cause longer-term secu-

It is now generally agreed that longer-term securities have systematically higher yields than
shorter-term securities, the differences being labled "term premiums," or "liquidity premiums."

Table 1

rities to sell at higher yields on the average than
shorter-term securities.
To this author's knowledge, however, the relationship of transactions costs to term premiums
has never been carefully investigated. The data
used in previous studies of the term structure
have consisted either of points drawn free-hand
through yield observations-the Durand and
Treasury Bulletin yield curves-or means of bid
and asked yields. Given the significant size of
bid-asked spreads-especially for short-term securities-it is clear that transactions costs need
to be examined carefully.
The second and third columns of Table I suggest that transactions costs may be related to estimated term premiums. These two columns are
reproduced from Tables 5-3 and 6-12 in Richard
Roll's study of the Treasury bill market.5 (The
other column in Table 1 will be discussed later.)
The sharp drop in Roll's estimated marginal
term premium-the average difference between
the one-week implicit forward rate m weeks in
the future and the one-week spot rate realized in
m weeks-between the 13- and 14-week maturities appears to be suspiciously related to the
sharp increase in the mean spread between the
same two maturities. Before discussing this issue
further, however, a review of some of the a priori
arguments concerning term premiums will prove
helpful.

Bid-Asked Spreads and Term Premiums
Weeks to
Maturity

I
2

Mean
Spread a

.2336
.1762

Term Premium
Marginal b
Average C

0
.00704

0
.00352

.1486

.0555

.0208

.1288

.168

058

.1121

.291

104

.0993

.323

.141

.0893

.347

.170

.0813

.383

.197

.0753

.445

.224

.0695

.427

.245

.0649

.396

.258

.0580

.414

.271

.0424

.562

.294

.0843

.0403

.276

.0835

.0696

.262

.0831

.142

.254

.0822

.175

.250

.0810

.189

.246
.247

.0788

.256

.0762

.262

.248

.0734

.296

.250

.0710

.305

.252

.0681

.310

.255

.0620

.328

.258

.0555

.365

.262

26
.0415
NA
NA
NA: Not Available.
a Weighted (by number of observations) averages of mean
spreads for March, 1959-December, 1961 and January,
1962-December, 1964 reported in Roll, R., The Behavior of
Interest Rates. Table 5-3.
b For March, 1959-December, 1964, from Roll, Table 6-12.
c For maturity m, mean of marginal term premiums for maturities 1, 2, ... , m.

As a matter of arithmetic, a given change in
yield to maturity produces a larger change in the
price ofa longer-term security than in the price
of a shorter-term security. As a matter of fact,
long-term yields do not fluctuate as much as
short-term yields, but the relative variability of
long-term and short-term yields is such that the
prices of long-term securities nevertheless fluctuate more than the prices of short-term securities;
thus, the capital values of long-term securities
are subject to more interest rate risk. If we assume that investors are risk averse, we would expect that the average yield on long-term
securities will have to be higher to compensate
investors for the greater risk.
Another argument suggesting the probable existence of term premiums depends on transactions costs. Consider the situation faced by a firm
that temporarily has excess cash which it will

need in m days. The firm could buy an m-day
Treasury bill, which would mature just when the
cash was needed. 6 Alternatively, the firm could
buy a longer-term security and then sell it in m
days. A firm that is not risk averse would compare the yield on the m-day bill with the expected
yield over m days from buying an n-day bill,
where n is larger than m, and selling it after m
days. This yield would have to be calculated from
the asked price of the n-day bill and the expected
bid price of an nom bill in m days.
Letting Pk,t be the price at time t of a bill with
k days to maturity, the continuously compound11

Since bid-asked mean yields have typically
been employed in term structure studies (including Roll's), (6) is in a form that relates the present argument to previous work. The typical
finding that short-term rates are on the average
below long-term rates is consistent with (6) provided that the yield differential is not excessive
compared to the spread. The average difference
between the yield to maturity on an m-week bill
and the yield on a one-week bill is the average of
the marginal term premiums for maturities 2, 3,
... , m. This average term premium, calculated
from Roll's estimates of marginal term premiums, is reported in Table 1. Using these estimates of average term premiums for various
maturities and the estimated spreads in Table 1,
inequality (6) is found to hold for maturities of 1,
2, 9, 10, 11, and 12 weeks but not for maturities
of three through eight weeks.

ed yield to maturity is
100 - log Pk,t).
The expected continuously compounded holdingfrom
an n-day bill at
the asked price

and selling it m days later at

the expected bid price

Pg~m,t+m

(log

Pg~m,Hm-log P~,t)
n-m b*
- I l l Rn-m,t+m

The firm needing cash in m days will buy an mday bill rather than an n-day bill if R;h t >
nH~ t. Using the definition of the bid-~sked
yield 'spread Sk on a bill with k days to maturity
as the difference between the bid and asked
yields, this
the expression
n-m
a*
m ) (Rn-m,t+m

>~
m

(3)

It is interesting to note that Roll found the hypothesis of market efficiency well-supported except for maturities of 4 to 8 weeks. 8 For these
maturities yields seem to be too lo\v, on the aver=
age. We may conjecture, however, that the apparent anomaly would disappear with a fuller
accounting of transactions costs.

+ S~_m ,Hm)'

A particularly convenient interpretation of inequality (3) arises for n == 2m. In this case, we
have
(4)

R;h,t >

A few numbers will provide a feel for the magnitudes involved. From inequality (6), the yield
on a four-week bill is too low by about 10 basis
points according to Roll's evidence. (A basis
point is .01 percent.) Comparing the two sides of
inequality (3) and using the fact that R~ == R m
-1/2 Sm' this 10 basis point discrepancy makes
the right-hand side of (3) larger than the lefthand side by about 20 basis points. The firm with
cash to invest for four weeks could, therefore,
have a 20 basis points advantage on the average
from investing in an eight-week bill (which
would be sold after four weeks) rather than in a
four-week bil1. 9 These yields, however, are all expressed at annual rates. The yield advantage per
four weeks is only 4/52 of 20 basis points, or
about $154 per million of invested funds. It is
easy to imagine that the extra transactions costs
from buying an eight-week bill and selling it four
weeks later as compared to simply buying a fourweek biil and holding it to maturity would exceed
$154 per million of funds invested.

2R~m,t - (R~,Hm + S~,Hm)·

Suppose interest rates on particular maturities
are not expected to change so that R;h* t+m =
R;h t, and suppose that bid-asked spr~ads for
, maturities are constant over time so that

S~,Hm == Sm. 7 Then we can write (3) as
(5)

R;h , t >

Letting
a
== Rk,t + 2

R~m
L,t

Sm .

1
2

Sk,t,

(5) may be written in terms of yields defined as
the means of bid and asked yields.
(6)

Rm,t> R2m,t -

S2m·

The analysis of the transaction-cost effect in
12

depressing yields on very short-term bills is, however, only indirectly relevant to the issue of the
size of term premiums in bill futures-market
quotes. We need to know whether the term premium should be subtracted in order to interpret
the futures quotes as reflecting market expectations of future spot rates on three-month bills;
the fact that a one-week bill has an average yield
below that on a 13-week bill is not directly relevant to this issue.
The transaction-cost argument suggests that
yields on very short-term bills could be depressed
without there being any noticeable impact on
longer-term bills. For example, in comparing the
yield from holding a 13-week bill to maturity
with the yield from holding a 26-week bill for 13
weeks, the bid-asked yield spreads are small
enough, and the 13-week holding period long
enough, so that there is little room for the average I3-week bill yield to fall below the average
26-week bill yield. From inequality (6) and the
mean spread on 26-week bills (Table 1), the effect would be only two basis points.
Nevertheless, the transaction-cost effect on
very short-term bills can affect term premiums
(as estimated in previous studies) because of the
way in which implicit forward rates are calculated. To understand the argument, consider first
the expression defining the implicit forward rate
of interest on a 13-week loan to begin m weeks in
the future, calculated from the yields to maturity
on spot bills with m and m+ 13 weeks to maturity. Using continuously compounded yields,
(7)

m+I3
13 r m,t = (-1-3-) Rm +13,t -

1
= RI +13

The third line in equation (8) is derived from the
definition
-Lk

13 r m,t =

= -k1 L

j=1

L·
J.

Each Lj. it may be recalled, is the marginal term
premium-the amount by which the implicit forward rate on a one-week loan to mature k weeks
in the future exceeds the realized spot rate on a
one-week loan maturing k weeks in the future.
The summation term in (8) contains 13 Lj's. If
the Lj's were nondecreasing so that Lj+ 1 :> Lj,
then

,,~+13 L.:> l ,,13 L· =
13LJ=m+IJ-13Lj=I J

13-

In this case the implicit forward rate I3rm,t
would be an upward biased estimate of R13 =
RI + L13·
Roll's estimates of the Lj, however, are not nondecreasing for all j. When the summation term in
(8) is calculated using Roll's estimates it is found
that 13rm is an upward biased estimate of RI3
for m from 1 to 7 weeks but a downward biased
estimate for m from 8 to 12 weeks. The maximum size of the downward bias is about four basis points and the maximum size of the upward
bias is about two basis points. While the size of
the upward bias is very small based on Roll's estimates, the phenomenon may help to explain the
appearance in .the charts of a decline in the implicit forward rates underlying the arbitrage
points in the last month of trading of a futures
contract.
McCulloch provides another term-structure
study of direct relevance to this issue. 1o Using
somewhat different estimation methods than
Roll and a sample period from March 1951 to
March 1966, McCulloch reports estimates of the
term premium attached to implicit forward 13week rates various periods in the future (Table
2). If these estimates are taken at face value, 10
to 20 basis points should be subtracted from implicit forward rates for I3-week bills one or more
months in the future to obtain market expecta-

~ Rm,t,

where 13rm,t is the implicit forward rate as of
time t on a 13-week loan to begin in m weeks and
Rk,t is the yield to maturity on a spot bill with k
weeks to maturity. On the average, the yield on a
k-week bill exceeds the yield on a one-week bill
by the average term premium Ik Thus, on the
average we have
(8)

.L m+I3
j=m+l Lj.

m+I3
13 )(Rl +L m +13)

~~ (RI + L m )
=Rl + ( m+I3)[ +13 - J!L I
13
m
13 m
13

Table 2

per and lower arbitrage points are also reported,
although it is obvious from the charts that the
futures rate almost always lies between the two
arbitrage points.
A test of the statistical significance of the re~
suits in Table 3 is reported in Table4. The test
has been confined to the first 20 observations in
each of the periods listed in Table 3, since there is
much more interest in market forecasts of the bill
rate a few months in the future than in forecasts
a few weeks in the future. For the first 20 trading
days in each period, the difference between the
futures rate and the implicit forward rate was
calculated; the means and standard deviations of
these differences appear in Table 4 along with
the statistic for testing the statistical significance
of the mean difference. The mean difference is
negative for all periods. Using a one-tailed t-test,
the mean differences for the first, second, and
fourth periods are significant at the .001 level,
the third period at about the .02 level, the fifth
period at almost the .05 level, and the last period
at about the .15 level. From these results for the
individual periods, it is obvious that, in the
pooled sample for the six periods combined, the
mean is statistically different from zero at a very
high level of statistical significance.
The evidence suggests that yields on very short
maturities are depressed by the existence of
transaction costs. Investors depress the return on
very short-term bills when they attempt to obtain
a return on balances invested for only a few
weeks' time. The return is apparently slightly
lower than can be explained by the bid-asked
spreads on longer-term bills, but not by much.

McCulloch Estimates of Term Premiums
in 13-week Implicit Forward Rates
Term Premium
Bill to be
Issued in:

Free Form
Estimates

ExponentialF orm
Estimates

I month

0.10

0.Q9

2 months

0.15

0.14

3 months

0.17

6 months

0.16
0.12

9 months

0.11

0.22

I year

0.13

0.22

2 years

0.12

0.22

0.21

tions of future spot rates on 13-week bills.
These estimates of term premiums are above
those relevant for the bill futures market if the
argument on transaction costs is accepted, because transaction costs affect implicit forward
rates calculated from spot bills of varying maturities but not the bill futures market. If this argument is correct, quotes in the futures market
should generaliy be below the corresponding implicit forward rates.
This hypothesis was tested by calculating the
.mean futures rate and the mean implicit forward
rate over the three-month period preceding the
maturity date of the six futures contracts maturing between January, 1976 and June, 1977 (Table 3).11 In every case the mean of the rate on a
given futures contract is below the corresponding
mean of the implicit forward rate calculated
from bid-asked mean rates. The means of the up-

Table 3
Means of Futures Rates, Implicit Forward Rates,
and Arbitrage Points for Selected Periods
Implicit Forward Rate

Arbitrage Point

Asked
-

lower

Upper

5.13

5.02

5.50

5.38

5.32
5.69
5.57

Futures
Contract

Futures
Rate

BidAsked
Mean

5.17

5.21

3/24/76-6/23/76

March 1976
June 1976

5.10
5.48

5.54

5.57

6/24/76-9/22/76

Sept. 1976

5.45

5.49

5.42

5.34

4.95

4.98

4.92

4.84

5.05

4.85
5.11

4.87

4.82

4.73

4.96

5.12

5.10

4.99

5.23

Period

1/6/76-3/17/76

9/23/76-12/22/76

Dec. 1976

5.42
4.84

12/23/76-3/23/77

March 1977

4.82

June 1977

5.05

3/24/77-6/22/77

Bid

Table 4

Futures and Implicit Forward Rates
(Differences, first 20 observations each period)
116176-

3/24176-

6/24176-

9/23176-

12/23176-

3/24/77-

Differences

3/17176

6/23176

9/22176

12/22/76

3/23/77

6/22/77

Mean, X

-0.1345

-0.0505

-0.0285

-0.1590

-0.0405

-0.0205

0.0788

0.0511

0.0584

0.0397

0.1079

0.0894

7.63

4.42

2.18

17.9]

1.68

1.03

Standard
Deviation, S
Test
Statistic,

IX/sJ2o I

tures market can, therefore, be interpreted for all
practical purposes as the market's unbiased estimates of the future spot rates on 13-week bills.
The policy significance of this finding will now be
explored.

The term premiums involved, however, do not in
any event extend very far into the yield structure.
Beyond maturities of about 13 weeks, the average term structure is essentially flat.
Quotes on the nearest maturity in the bill fu-

Policy Implications of T-Sill Futures
ty of these futures were 4.97,5.32,5.01, and 4.25
percent, respectively. For a more recent example,
on September 30, 1976 the futures rates for December, 1976, March, June, September, and December, 1977, and March, 1978 were 5.37, 5.71,
6.07, 6.44, 6.77, and 7.10 percent, respectively,
whereas the realized spot rates were 4.25, 4.52,
5.00, 5.85, 5.96, and 6.22 percent, respectively.
If the findings in the previous section apply to
all futures maturities, then the differences between the futures rates and the realized spot
rates over the last two years reflect genuine expectational errors rather than term premiums attached to the futures rates. A variety of
interpretations of these expectational errors is
possible.
One starting point would be a hypothesis concerning the relationship between economic activity and inflation on the one hand and the spot bill
rate on the other. .It is generally argued that
higher levels of economic activity add to the demand for funds to finance business inventories,
purchases of consumers' durables, and so forth,
and so tend to raise interest rates. Higher rates of
inflation also tend to raise interest rates. Expectational errors, therefore, could have occurred if

The evidence discussed above shows that for
the nearest bill futures maturity there is a close
correspondence between the futures rate and the
implicit forward rate calculated from spot rates.
If this finding also applies to the other bill futures maturities-and in this section it will be assumed that the finding does apply to all
maturities-then it is clear that the opening of
the bill futures market did not provide policymakers with much new information. Nevertheless, the futures rates, by displaying investors'
expectations of future spot rates on 13-week bills
explicitly, have focused attention on these expectations in a way implicit forward rates never did.
Since the start of trading in bill futures in January, 1976 the rates on more distant futures have
always been higher than the rates on near futures; investors have been expecting spot bill
rates to rise over time. As of this writing-early
April, 1978-realized bill rates have been almost
always below prior expectations as measured by
rates on the more distant futures contracts. For
example, on January 30, 1976 the futures rates
for March, June, September, and December,
1976 were 4.89, 5.33, 5.64, and 5.86 percent, respectively.12 The realized bill rates on the matmi15

economic activity and the inflation rate had been
below investors' anticipations. This explanation
seems not very satisfactory, however, because the
performance of the economy over the past two
years has, if anything, been slightly stronger than
earlier forecasts had suggested likely.
Another possible explanation of expectational
errors emphasizes the influence of government
policy on interest rates. In the short run, accelerated money growth probably tends to depress interest rates, and slower money growth to raise
interest rates. If money growth is higher than anticipated, interest rates will tend to be lower than
anticipated. Similarly, since government budget
deficits require financing, smaller-than-anticipated budget deficits will tend to lead to lowerthan-anticipated interest rates. Interpretation of
the interest-rate effects of monetary policy is
complicated, however, by the fact that higher
money growth in the long-run raises the rate of
inflation and, therefore, raises interest rates. It is
not known exactly where the dividing line in time
lies between the short-run effect of depressing interest rates and the long-run effect of raising interest rates.
The explanation for recent expectational errors
that emphasizes errors in anticipating government policy fits the facts better than the explanation based on the performance of the economy.
Money growth on the Ml definition was higher
in 1976 than in 1975, and higher in 1977 than in
1976; on the M2 definition, money growth was
higher in 1976 than in 1975, but lower in 1977
than in 1976. 13 And the total government-budget
deficit-federal, state and local government
combined-has been lower than anticipated by
many observers because of below-budget federal
spending and surprisingly large state-and-local
budget surpluses. 14
A third explanation-one consistent with
much recent discussion-is that the demand for
money may have declined over the past several
years. Especially on the M 1 definition, money
growth in 1975 and 1976 was much slower than
would have been anticipated given the observed
changes in income and interest rates. Or, viewed
another way, interest rates were much lower than
would have been anticipated given the observed
growth in M 1 and income. From the point of

view of a bill futures market participant in early
1976, theconcensus forecast for income growth
and· the Federal Reserve's announced money
growth targets implied, from the existing evidence on money demand relationships, higher interestrates than were in fact realized.
While this brief discussion mayor may not be a
correct analysis of the interest rate expectational
errors of the past two years, it serves to introduce
the nature of the problem faced by policymakers
in interpreting the interest rate forecasts incorporated in T-bill futures rates. The key problem
faced by policymakers is that of assessing the significance of market interest rate forecasts that
differ from the policymaker's own forecasts.
Suppose, for example, that T-bill futures rates
are higher than policymakers' forecasts of future
interest rates. One possibility is that the market
is anticipating a higher level of economic activity
and/or a higher inflation rate than policymakers
are anticipating. It is especially important to consider this possibility, because the market forecasts incorporated in bill futures rates reflect
more than simply the interest-rate guesses of
speculators. Firms may enter the biU futures
market on the basis of their anticipated cash
flows arising, for example, from the expected effects of current plans or commitments to accumulate inventories.
This type of activity in the bill futures market
is similar to that in commodity futures markets;
the wheat futures price, for example, reflects expected demands for wheat by bakeries and supplies of wheat by farmers. Trading in this
market, therefore, reflects the impact of current
decisions-bread supply commitments by bakeries and planting decisions by farmers-that
will affect wheat supplies and demands and,
therefore, wheat prices in the future.
If policymakers' forecasts of interest rates below those in the bill futures market do reflect
mistaken forecasts by policymakers of the future
strength of aggregate demand, then their decisionsmay provide for a more expansionary policy
than is appropriate. The accuracy of the economic forecasts available to policymakers is not so
high that the possibility that high futures rates
are forecasting higher levels of economic activity
and/or higher inflation can be ignored.
16

An even more troubling possibility, though, is
that rates in the bill futures market may reflect
anticipations concerning policy decisions that do
not reflect actual policy plans. Failure of policy
decisions to ratify private anticipations concerning policy then falsifies one of the assumptions
under which business decisions are made and
leads to less appropriate business decisions than
would otherwise be the case.
To avoid private expectational errors, policymakers must provide clear information, through
formal announcements or otherwise, concerningprospective policies. And if statements concerning policy intentions are to be believed,
policymakers must in fact determine policy in accordance with those announced intentions. If
policies typically do not reflect previously announced policy intentions, then statements of
policy intent will simply not be believed. Business
planning will be subject to unnecessary uncertainty, but so also will policy planning. To interpret current economic data in such a situation,
policymakers will have to guess what businessmen are guessing the policymakers will do.
An apparently easy solution to this problem
would be for policymakers to make clear announcements of their policy plans and then to ensure that these plans are realized. Under this
approach, however, policy could not be adjusted
in a flexible and timely manner when economic
conditions change unexpectedly. The policy dilemma is clear. To encourage sound and sensible
business planning, policymakers need to make
their plans clear and must realize their plans to
retain credibility. But policy plans should, presumably, be adjusted from time to time to reflect
changing economic conditions.
Different policy analysts place differing degrees of emphasis on the relative importance of
realizing policy plans and of retaining policy
flexibility. Unfortunately, there is no simple way
of determining how to strike a balance between

those two goals. What can be done, though, is to
broaden the concept of the announced policy
plan by making clear the nature of the policy responses to be expected under specified conditions. It is well understood, for example, that the
Federal Reserve will intervene heavily to stabilize money markets disrupted by a spectacular
bankruptcy such as the Penn-Central failure in
1970, even if such intervention produces a temporarysurge in money growth far above what
had been planned.
But it is important to distinguish between specific intervention of this type and a more generalized intervention to cushion interest-rate
increases. An excellent example of the benefits of
not cushioning interest-rate increases occurred in
April 1977, when M 1 increased at a 20-percent
annual rate (since revised to 14 percent). That
episode raised fears in the markets that the Federal Reserve was permitting money to expand at
a rate far above its announced policy intentions.
By permitting short-term interest rates to rise
sharply at that time-the 13-week bill rate went
from 4.57 percent in the week ending April 1 to
5.06 percent in the week ending May 27-the
Federal Reserve convinced the markets that
money growth would not be permitted to continue at clearly excessive rates.
While the rate on 13-week bills was rising in
May 1977 rates on the more distant bill futures
fell. Comparing weekly average rates for the
week ending April 1 to weekly average rates for
the week ending May 27, the September 1977 futures went from 5.88 to 5.65, the March 1978 futures from 7.03 to 6.62, and the September 1978
futures from 7.83 to 7.22. In this situation, expanding the rate of money growth even further to
hold down the rate on 13-week bills might very
well have led to heightened fears of future inflation which would have raised rates in the futures
market.

IV. Summary and Conclusions
will determine a more expansionary policy than
is appropriate for the needs of the economy.
Market interest-rate forecasts may also reflect
for~castsof poliGies that differ from those that
policymakersare actually planning. This possibility emphasizes the importance of policymakers making their plans known and
maintaining credibility by ensuring that announced policy plans are realized. However,
strict adherence to policy plans makes it difficult
for policy to be adjusted flexibly in response to
changing circumstances.
While there is no easy solution to this dilemma,
the problems raised can be eased by including in
the concept of a policy plan an understanding of
the policy adjustments required by certain contingencies. For example, permitting temporarily
high money growth to cushion market disruptions caused by a major bankruptcy, such as the
Penn-Central failure, need not imply that longrun plans for money growth will not be realized_
Although the accuracy of the bill futures rates
as predictors of future spot rates was not discussed in detail, it is clear that futures rates, even
if unbiased, are not especially accurate forecasts.
For this reason the policy significance of these
interest rate forecasts ought not to be exaggerated. However, the policymakers' own forecasts of
interest rates are not very accurate either. Unless
policymakers have solid evidence that their own
forecasts are more accurate than market forecasts, they cannot afford to ignore the T-bill futures market.

The evidence reviewed in this paper demonstrates that the Treasury-bill futures market is
closely .linked to the spot market in Treasury
bills. Unexploited arbitrage opportunities between the two markets rarely exist.
A key question is whether term premiums must
be subtracted from T-bill futures rates to convert
those rates into market forecasts of future spot
rates on Treasury bills. A review of evidence on
term premiums from previous studies suggests
that very short-term bills trade at lower yields
than longer-term bills on the average but that
much, and perhaps all, of the average yield differential probably reflects the extra transactions
costs from selling longer-term bills before maturity compared to holding very short-term bills to
maturity. Because transactions costs in trading
bill futures are so very small, futures rates were
hypothesized to be slightly lower than the forward rate implicit in the yields on spot bills of
various maturities. This hypothesis is supported
by the evidence presented in this paper.
What is the policy significance of the new market in Treasury bill futures? The existence of
these explicit market interest-rate forecasts emphasizes the need for policymakers to understand
the reasons for discrepancies between their own
interest-rate forecasts and market interest-rate
forecasts. If, at some point in time, rates in the
bill futures market are based on forecasts of a
stronger and/or more inflationary economy than
projected by policymakers, and if the market is
correct, then there is a danger that policymakers

FOOTNOTES
cash or securities to be withdrawn from the margin account. Because the amounts involved are so small, these considerations
would have a negligible effect on the arbitrage calculations presented below and so are ignored.
3. The data base consists of closing bid and asked yields on
bills, and closing futures quotes-all from the Wall Street Journal.
4. This section is somewhat technical and may be skipped by
the reader primarily interested in the policy implications of the
bill futures market.
5. Richard Roll, The Behavior of Interest Rates (New York: Basic Books, 1970).
6. Treasury bills, of course, do not mature every day. The firm
wanting to invest in a maturing bill would have to select the existing bill with maturity best matching the firm's predicted cash
needs. The following analysis ignores the fact that purchase of a
bill with more than m days to maturity permits the firm to keep its

1. See, for example: Albert E. Burger. Richard W. Lang, and
Robert H. Rasche, "The Treasury Bill Futures Market and Market
Expectations of Interest Rates," Federal Reserve Bank of St.
louis Review, June, 1977; Wallace H. Duncan, "Treasury Bill
Futures-Opportunities and Pitfalls," Federal Reserve Bank of
Dallas Review, July, 1977; Paul L. Kasriel, "Hedging Interest
Rate Fluctuations," Business Conditions (Federal Reserve
Bank of Chicago), April, 1976; and Linda Snyder, "How to Speculate on the World's Safest Investment," Fortune, July, 1977.
2. The calculations discussed below are based on the assumptions that the $60 commission is paid when the futures position
is taken and that the $1500 margin is put up in cash. In fact, the
commission may in some cases be paid when the futures position is covered and the margin requirement may be satisfied by
putting up interest-bearing securities. In addition, futures price
fluctuations may lead to a requirement that additional cash or
securities be added to the margin account or may permit some

funds invested right to the day its cash needs arise, since an
existing bill can be sold on any business day.
7. Rather than interpreting equation (4) as applying to a time
when rates are not expected to change, the rates in (4) may be
interpreted as the means of the rates over a long sample period
in which there is no overall trend in the level of rates. The means
of R~, t+m and R~,t differ only by virtue of one observation at
each end of the sample.
8. See Roll, p. 116.
9. That the holding period yield advantage is greater than the
discrepancy in yields to maturity can be seen readily from the
fact that the yield to maturity, Rn, on an n-week bill is the weighted average of the yield over the first m weeks and the yield over
the remaining n-m weeks. II the latter yield is below R n, then the
former yield must be above Rn.

Journal of Political Economy, 83 (February, 1975),95-119.
11. The yields in Table 3 are bankers' discount yields. The implicitforward rates were calculated with due regard for discounting considerations.

12. The two longer futures contracts, March and June 1977,
were not actively traded in the first several months after the futures market opened.
13. Measuring money growth from December of one year to December of the next, M 1 growth was 4.1 percent in 1975,6.1 percent in 1976, and 7.7 percent in 1977, while M2 growth was 8,5,
11.4, and 9.2 percent, respectively.
14. See Edward M. Gramlich, "State and Local Budgets the Day
after It Rained: Why Is the Surplus So High," in Arthur M. Okun
and George L. Perry, eds., Brookings Papers on Economic Activity, 1978:1, 191·214.

10, J. Huston McCulloch, "An Estimate olthe Liquidity Premium,"

Kenneth C. Froewiss'
On any list of the most controversial sectors of
the U.S. economy, surely futures markets, financial markets, and the housing market would appear near the top. The housing sector has been
the intended beneficiary of a wide variety of public programs. Financial markets have long been
subjected to a myriad of government regulations.
And futures markets have had to fight repeated
attempts to legislate them out of existence.
The Chicago Board of Trade established a
unique link among these three sectors in October
1975 when it inaugurated a futures market in the
financial instruments of the Government National Mortgage Association (GNMA). This
agency had designed its "pass-through" certificates-mortgage-backed bonds guaranteed by
GNMA-in order to help the housing industry
by attracting more investors to the mortgage
market. Most economists would argue that the
institution of futures trading in G N MA certificates should further that goal. Economic theory
suggests that futures trading arises in markets
characterized by large price variability and that
it helps to reduce that variability.1 By contrast,
many non-economists believe that futures trading is a cause of greater price variability rather
than a response to that variability. Business
Week referred recently to " ... the charge that
futures markets themselves increase the volatility of commodity prices and that speculators are
the chief culprits behind wild swings, often pushing prices in directions that are unwarranted by
underlying economic conditions."2
If the establishment of a GNMA futures market increases the variability of GNMA spot
prices, a number of investors might find GNMA
certificates less attractive. Futures trading in
GNMA's would then be at odds with the goal of
increasing the liquidity of the mortgage mar-

ket-a market in which GNMA securities are
playing an increasingly important role. At the
end of 1977, G N MA-back securities accounted
for almost $44 billion of the $650 billion outstanding debt on one-to-four-family homes. 3
There have already been charges that the "explosive growth" of the G N M A market has led to
speculative excesses. 4 Presumably, the growth of
a futures market will encourage even more speculative activity in this market. The purpose of
this article is to determine whether futures trading in GNMA certificates has stabilized or destabilized GNMA spot prices. This question is
important to policymakers charged with aiding
the housing market as well as to those responsible
for regulating futures trading. Furthermore, the
question has implications for the other financial
futures markets now in existence: Treasury bills,
Treasury bonds, and commercial paper. The
Wall Street Journal has noted government officials' concern that speculative activity in financial futures could disrupt the bond market.5
Consequently, should the development of these
futures markets be encouraged or discouraged?
As in the case of the GNMA's, the answer partly
depends on the extent to which futures trading
affects spot prices.
A related and equally important policy issue is
whether banks and thrift institutions should hold
financial futures only for use in hedging activities. However, this article will not attempt to address that question.
Section I discusses the motivations which led to
the development of the GNMA futures market.
Section II examines the theoretical basis for the
belief that speculation will tend to stabilize rather than destabilize prices. Section III presents
the results of alternative empirical tests of the effect of G N MA futures on the spot market. Section IV summarizes the principal findings, which
support the position that futures trading has had,
if anything, a stabilizing influence on the spot
prices of GNMA certificates.

'Economist, Federal Reserve Bank of San Francisco. The author wishes to thank Ladan Amir-Aslani for her assistance
with this study. Data were kindly provided by the Chicago
Board of Trade and the First Boston Corporation, neither of
which necessarily concurs with the views presented here.

I. Development of the GNMA Futures Market
The G N MA futures market is the result of two
separate developments, both dating back to the
late 1960's. The first was the mortgage industry's
attempt to devise a hedging mechanism to protect itself from unforeseen interest-rate fluctuations. The second was GNMA's introduction of
a new security to attract more investors to the
housing market.

between the two groups is that the latter deals in
a homogeneous commodity for which it is easy to
set standards, while the former deals in a "commodity" (i.e., mortgages) which varies tremendously in quality and in exact specifications. This
lack of homogeneity among mortgages was one
of the greatest obstacles to the establishment of a
mortgage-futures market. 9

Mortgage hedging6
The possibility of unforeseen price changes
makes holding inventories of any good a risky
business. Since many people are willing to pay a
price to exchange risk for certainty, organized
futures markets exist so that holders of inventories can hedge against the risks of price
changes.! For example, when a warehouse purchases grain, it may simultaneously enter into a
futures contract to lock in the price at which it
can sell that grain at a later date.
Until the 1960's, futures trading in the United
States was concentrated in grains and the soybean complex. But during the next decade, futures contracts were added in a number of other
"commodities," ranging from plywood to pork
bellies. And just when the exchanges began looking for new markets to enter, real-estate investors
began discussing the feasibility of a futures market to hedge against interest-rate risk.
Actually, economists at a much earlier time
had used the analogy between the markets for financial instruments of varying maturities and
the commodity futures markets to explain the
term structure of interest rates. S But now people
were beginning to discuss the practical problems
of setting up an interest-rate futures market.
They were motivated to do so by the sharp rise in
interest rates in 1969, and by the resulting losses
incurred by fixed-income security holders in general and by mortgage lenders in particular.
Mortgage bankers and mortgage-originating
savings-and-Ioan associations stand to lose money if interest rates rise between the time at which
they commit their funds and the time at which
they sell the mortgages. Their situation is exactly
analogous to that of the grain elevator which
temporarily holds wheat bought from farmers
before selling it to millers. The biggest difference

GNMA certificates
At the same time that the real-estate community was attempting to find a way to hedge mortgage-interest risks, the Government National
Mortgage Association-created by the Housing
Act of 1968 as part of the Department of Housing and Urban Development-was attempting to
help the housing market by making mortgages
more attractive to all types of investors. lO Both
groups faced the same key problem: the lack of
homogeneity across mortgages. Many investors,
lacking the necessary ability to gauge the quality
of particular mortgages, tended to avoid the secondary mortgage market. Individual investors
were further dissuaded by the large volume of
funds which would be '1eeded to purchase a reasonably well-diversified portfolio of mortgages.
As a result, the secondary mortgage market
lacked the depth of, say, the secondary government-bond market. During periods of high interest rates, whenever thrift institutions tried to sell
mortgages out of their portfolios to offset deposit
outflows, they were forced to accept unfavorable
terms because of the thinness of the secondary
market. In view of this problem of raising funds,
they found it difficult to continue making new
mortgage loans during tight-money periods.
The GNMA modified pass-through certificates represented a means of easing this difficulty.11 Introduced in early 1970, these certificates
enable an individual investor to purchase a share
in a pool of FHA/VA insured mortgages, with
payment of the interest and principal guaranteed
by GNMA. The originator of the mortgagestypically a mortgage banker or savings and loanpackages them into a pool of at least $1 million
and turns them over to a custodial bank. All of
the mortgages must bear the same face rate of
interest and have roughly the same maturity
21

date. GNMA may then issue secunties In
amounts as small as $25,000 on the pool.
The coupon rate on the securities is 50 basis
points less than that on the underlying mortgages. (Yield quotations on the securities are
based on the assumption of prepayment in the
12th year.) The issuer of the securities receives
44 basis points as a management fee-for collecting the monthly mortgage payments, "passing-through" the payments to the security
holders, and for dealing with any delinquent
loans or foreclosures. Even if the issuer does not
receive all of the monthly payments due him, he
remains responsible for seeing that the security
holders get their full payments on time. (It is this
feature that gives rise to the name "modified"
pass-through security.) GNMA itself guarantees
timely payment to the security owners in the
event of a default by the issuer, for which service
it receives 6 basis points.
GNMA securities therefore have three levels
of guarantees. The underlying mortgages are all
FHA- or VA-insured. The issuer of the securities
guarantees payment of principal and interest
whether or not he receives his payments on time.
And GNMA stands behind his guarantee with
the full faith and credit of the U.S. Government.
Thus, GNMA securities allow an investor with
no specialized knowledge of mortgages to participate in the secondary mortgage market with
virtually no fear of default risk.

for conversion into a GNMA certificate, he
might negotiate with, say a life insurance company regarding the price at which he will sell that
security at some specified future date. Such forward contracts became increasingly common as
mortgage lenders attempted to hedge against interest-rate risk-but they did not constitute a futures market.
A forward contract is an agreement between
two individuals, tailored to their particular
needs. A futures contract is a standardized
agreement, traded on an organized exchange, in
which the exchange itself is the opposite party in
every contract. Telser and Higinbotham express
the difference as follows:
"In a forward contract, the actual identity
of the buyer and seller is important. Neither has recourse in case of dispute to a
third party other than a court of law. The
validity of the forward contract depends on
the good faith of the two parties themselves. A futures contract has a third party,
the organized exchange or its designated
representative, that guarantees the validity
of the contract and will enforce the
terms."13
With contracts standardized and with the entire exchange standing behind each agreement,
futures contracts are much more liquid instruments than forward contracts. As a result, the
transactions costs involved in divesting oneself of
a futures contract are generally less than for a
forward contract. The greater expense of finding
a buyer for an individually-tailored forward contract tends to limit the sale of such contracts to
individuals who actually plan to take physical
possession of the underlying commodity. But futures-market participants also include a large
number of speculators who are willing to incur
the price risks of buying and selling futures contracts but who never want to take or to make delivery. Because of the presence of these
speculators, futures markets have a greater
breadth than forward markets, with consequent
expanded possibilities for hedging.
Nonetheless, futures markets often evolve out
of forward markets. In the case of GNMA securities, this evolutionary process was aided by the
passage of the Commodity Futures Trading

Forwards and futures
The introduction of GNMA certificates not
only helped to broaden the secondary mortgage
market; it also suggested a solution to the problem faced by those attempting to create a mortgage futures market. Rather than deal directly in
mortgages, market participants might trade
GN MA securities of some designated denomination. Indeed, several years before the approval of
organized futures trading, the market developed
informal forward trading in GNMA securities. 12

Forward trading and futures trading are not
the same thing, despite a number of similarities.
Whenever two people agree now to the terms of a
transaction which will take place sometime later,
forward trading can be said to exist. For example, when a mortgage banker begins the monthslong process of assembling a pool of mortgages
22

1977, over four times the level of a year earlier. 14
But the futures market, not surprisingly, has by
no means replaced the forward market. The two
markets typically coexist during the early stages
of development of a futures market, and they
may coexist indefinitely.
A number of recent articles have described
how the GNMA futures contract may be used
for hedging. 15 The question here, however, is not
the usefulness of GNMA futures to individual
hedgers, but rather the impact-if any-of futures trading on the spot market. Has the futures
market been "too successful" in attracting speculators, so that they, rather than hedgers, dominate the setting of futures prices? To determine
how much truth there is in that popular fear, let
us take a look, first, at the economic theory of
speculation, and second, at the empirical evidence in the case of GNMA futures.

Commission Act of 1975, which provided the legal basis for the establishment of a formal interest-rate futures market. In October of that year,
trading in GNMA futures contracts began on
the Chicago Board of Trade.
Each contract confers the right to buy or sell a
GNMA certificate with $100,000 in principal
balance and an 8-percent coupon at some specified future date. (Actual delivery may be made
using certificates with another coupon rate, in
which case the principal balance is adjusted accordingly.) It is currently possible to enter into
contracts up to almost three years into the future.
Trading in GN MA futures has grown very rapidly. In 1977, over 422,000 contracts changed
hands, compared to less than 129,000 during
1976, the first full year of trading. Open interest
in GNMA futures (the number of contracts outstanding) rose to almost 21,000 by the end of

II. The Economics of Speculation
low, and capital requirements are small-at least
compared with the costs of actually purchasing
goods on the spot market and holding them in inventory.

Basically, although speculation usually occurs
in markets characterized by a relatively large
amount of price variability, it is the result not the
cause of that variability. This view was succinctly expressed by John Stuart Mill over a century
ago:
"These dealers [speculators] naturally
buying things when they are cheapest, and
storing them up to be brought again into
the market when the price has become unusually high; the tendency of this operation
is to equalize price, or at least to moderate
its inequalities... Speculators, therefore,
have a highly useful office in the economy
of society; and (contrary to common opinion) the most useful portion of the class are
those who speculate in commodities affected by the vissicitudes of the seasons."16
Speculation, of course, can occur apart from
the existence of futures markets. In the above
quote, Mill described the behavior of speculators
who deal only in the spot market. But as we noted
earlier, organized futures trading tends to encourage speculation. Speculation in futures markets can be carried out without any need to
handle the commodities involved. Moreover,
transactions costs in futures markets are very

Consequently, if speculation is socially beneficial, and if futures markets lead to more speculation than would otherwise occur, we may
conclude that futures markets are useful to society as a whole, over and above their benefits to
individual hedgers. Furthermore, their existence
may help to reduce price fluctuations in ways
other than those described by Mill. They may do
so by improving inventory and production decisions-specifically, by providing information on
the likely course of prices in months to come. 17
Holbrook Working has gone so far as to say that,
"Today, the fact that futures trading provides
central market prices established in open competitive bargaining may deserve to be regarded
as the chief merit of futures markets from the
standpoint." 18
what if speculators forecast badly? Might
they not then affect prices perversely, increasing
their variability and reducing their usefulness as
a source of information to direct the allocation of
resources? Milton Friedman, in an often-quoted
passage dealing with foreign-exchange specula23

permanently a small body of successful
speculators; and the existence of this body
of successful speculators will be a sufficient
attraction to secure a permanent supply of
this floating population."21

tion but applicable to any commodity, argued
that any such tendencies could not persist for
long:
"People who argue that speculation is generally destabilizing seldom realize that this
is largely equivalent to saying that speculators lose money, since speculation can be
destabilizing in general only if speculators
on the average sell when the currency is low
and buy when it is high."19
Presumably, such speculators would be speedily
eliminated from the market, leaving only those
with superior foresight.
However, Friedman was careful to add a qualification, which is less often quoted: "A warning is
perhaps in order that this is a simplified generalization on a complex problem."20 Friedman himself conceded the possibility, earlier suggested by
Kaldor, that destabilizing speculation might persist if a small body of professional speculators
made money while a continually changing group
of amateurs regularly lost larger sums. The successful speculators would still be the ones with
superior foresight, but they would use their forecasting skills to predict the psychology of other
speculators. As Kaldor argued:
"In such circumstances, even if speculation
as a whole is attended by a net loss, rather
than a net gain, this will not prove, even in
the long run, self-corrective. For the losses
of a floating population of unsuccessful
speculators will be sufficient to maintain

In Kaldor's scenario, it is profitable for professional speculators to act in a destabilizing manner-buying even when they consider prices to
be too high in terms of non-speculative underlying trends-as long as they believe that they will
be able to sell at even higher prices to other speculators. When the psychology of the market
changes, the hapless amateurs are left with the
goods, which they must sell at a loss. These unsuccessful speculators are then eliminated from
the market, but a fresh group is always available
to support the next speculative boom.
Other economists have also attempted to argue
that destabilizing speculation can be profitable. 22
But the possibility described by Kaldor, in which
speculators devote their efforts to outwitting
each other, probably best accords with the popular suspicions about futures markets. These suspicions are buttressed by what Abba Lerner
refers to as "... the hostility which people who
have to work hard for their living often develop
against the mysterious gains that speculators
make in offices while dealing in goods which they
would not even recognize. "23 Let us consider
whether, in the specific case of GNMA futures,
there is any factual basis for this anti-speculative
attitude.

III. Empirical Evidence
Statistical tests for the effects of GNMA futures trading on GNMA spot prices face a fundamental limitation. We may be able to
determine whether the behavior of spot prices
has been different (in some suitably-defined
way) since the start of futures trading, but we
may never be able to ascribe such differences
definitely to the existence of a futures mar
They may merely reflect any of a numbe
changes which have occurred in the economy
since futures trading began.

some in the present context. Since October 20,
1975-the beginning of GNMA futures trading-the course of the U.S. economy in general
and of financial markets in particular has
changed considerably from what went before.
But in addition, the GNMA pass-through is itself a relatively new financial instrument, so that
the development of the GNMA futures market
has coincided with the maturation of the GNMA
spot market. As a result, any claims that changes
in the spot market were caused by the establishment of a futures market would have to be accompanied by even more than the usual
qualifications.

This problem is, of course, common to many
economic studies, but it is particularly trouble-

Graphic analysis
With those warnings in mind, let us analyze the
actual behavior of spot GNMA prices during the
periods before and after futures trading began.
(Chart I. Incidentally, the months immediately
surrounding the start of futures trading have
been omitted to remove any transitory disturbances associated with the opening of the new
market.) Clearly, the average level of GNM.A.
prices has been higher, and the variability about
that average has been lower, since futures trading began. But it would surely be wrong to attribute those spot-market changes primarily to the
futures market.
The broad movements in the level of spot prices
are more reasonably explained as the normal
market response to changes in the prices of longterm debt instruments which substitute for
GNMA's in investor portfolios. Indeed, recent
prices of GNMA's have roughly paralleled the
prices of long-term government bonds. However,
while it would be wrong to attribute the reduced
variability in the level of GNMA spot prices to
futures trading, it would similarly be unfair to

blame futures trading for the wider swings in
spot prices which would undoubtedly accompany
another period of widespread greater variability
in bond prices. The effects of futures tradingfor good or ill-must be sought elsewhere.
One likely place to look would be the behavior
of the changes in spot prices. Thus, while the
overall trend in spot GNMA prices will be dominated by the overall movements in bond prices,
futures trading might reduce the short-run variability in spot prices about that trend. It could do
this by providing market participants with more
information, in the form of instantly available
price quotations on futures contracts, determined through competitive bidding in a centralized market. Armed with this additional
information, investors in the spot market should
be able to move prices more rapidly to their equilibrium values, thereby reducing the purely random movement in those prices.
An examination of the first differences in the
weekly GNMA price series appears to bear out
this hypothesis (Chart 2). The variability of the
differences has declined markedly since the com-

Chart 1

GNMA SPOT PRICES

104

1973 -1975 Period

104

102

100

1976 -1977 Period

84FMAMJ J A SON D J FMAMJJASOND
1977
1976

J J A SON D
1973

mencementof futures trading, especially when
the sharp price movements of January 1977 are
excluded. The graphical evidence, then, suggests
that futures trading inGNMA's may have reduced the random variability in spot prices. But

before drawing this conclusion, we should test
statistically to determine whether the reduction
in·. the week-to-week movements inGNMA
prices again merely parallels a more <general
market trend.

Table 1
Responsiveness of GNMA Prices to Changes
in Bond-Market Prices
Percentage Change in
Government Bond Prices

Standard

Durbin-

Error

Watson

May 30, 1973December 28, 1977

0.646
(15.1 )

0.00541

May 30, 1973-

0.637

0.00709

1.65

October 15, 1975
October 22,1975-

(8.97)
0.00302

2.37

Sample Period

December 28, 1977

0.658
(16.7)

(Numbers in parentheses are t-statistics. None of the constant terms were significant, and were therefore not reported.)

Regression results
Our test involves regressing the weekly percentage changes in spot GNMA prices on the
weekly percentage changes in the prices of tenyear U.S. Government bonds, which serve as a

proxy for "the bond market." (The ten-year maturity was chosen because it approximates that of
GNMA certificates, which are usually assumed
to have an average life of 12 years.)24 The coeffi-

Chart 2
FIRST DIFFERENCES OF GNMA SPOT PRICES

1973-1975 Period

-2

-3

1976 -1977 Period

-2

J JA SON 0 J

-3 F M AM J J A SON 0 J F M A M J J A SON 0

1973

1976

1977

of the random movements around the systematic
trend. The time-series approach seeks to explain
the systematic component of GNMA prices solely in terms of the past history of those prices.
An analysis of the autocorrelation structure of
GNMA spot prices suggests that the series could
be adequately represented as a second-order autoregressive process, i.e., current prices can be
explained by the prices of last week-GNMA
(-I)-and the week before-GNMA (-2)plus a constant term (Table 2).
As in Table I, F-tests indicate no statistically
significant difference (at the five-percent level)
between the coefficients in the two sub-periods,
but they indicate a sigificantly smaller standard
error of the regression in the second period (at
the one-percent level).29 We can thus infer that
the systematic movements ofGNMA prices have
followed the same pattern in the period after as
in the period before futures trading-as evidenced by the unchanged coefficients-but that
the random fluctuations in spot prices have been
reduced significantly.
In a final test, we regress the percentage weekly change in spot prices on the previous week's
percentage change (Table 3). In this case, the coefficient on the lagged percentage price change is
significant on the first sub-period but not in the
second. In other words, a knowledge of how
GNMA prices moved last week no longer conTime-series analysis
tains useful information as to how they will move
As a check on these regression results, a Boxthis week. All new information affecting GNMA
Jenkins analysis was utilized to measure the imprices is rapidly incorporated into the current
pact of GNMA futures trading. 28 As above, it is
market price rather than absorbed by the market
assumed that futures trading has a negligible imslowly over several weeks. In the language of
pact on the level of GNMA prices-broad marcapital-market theory, the GNMA market has
ket forces cause the systematic movements in the
become more "efficient" since futures trading
spot price, but futures trading can affect the size
began. 30
Table 2
Time Series Analysis of Spot GNMA Prices

cient of the latter variable provides a measure of
the variability of GNMA prices relative to the
variability of bond prices generally. If the coefficient rises significantly after the beginning of futures trading, one could argue that futures
trading tends to destabilize spot prices, increasing their relative variability and hence making
GNMA's a riskier asset.2 5
The coefficient on the market index appears
roughly constant in both the period before and
the period after the beginning of futures trading.
The standard F-test for the equality of coeficients confirms this impression (at the five-percent level of significance).26 Therefore, the
evidence in Table I suggests that futures trading
has not made GNMA's more risky.
The standard error of the regression was much
smaller in the second sub-period than in the first.
Again, this impression is supported by the appropriate F-test, which indicates that (at the onepercent level) the standard error is significantly
less in the later period. 27 Since a greater proportion of the week-to-week variance in GNMA
prices can be explained by the movement of other
bond-market prices following the start of futures
trading, it appears that the GNMA market has
become more integrated over time with the rest
of the capital market.

Sample Period

May 30, 1973December 28, 1977
May 30, 1973October 15, 1975
October 22, 1975December 28, 1977

Constant

GNMA

GNMA(-2)

3.48

1.20

-0.238

(2.44)

(18.5)

(-3.70)

4.06

1.22

-0.261

( 1.98)

(13.1 )

(-2.84)

6.26

1.07

-0.139

(2.24)

(11.6)

(-1.54)

(Numbers in parentheses are t-statistics.)

Standard

Durbin-

Error

Watson

0.707

2.05

0.844

2.05

0.526

2.06

Table 3
Time Series Analysis of
Percentage Weekly Change in GNMA Prices
Sample Period

May 30, 1973December 28, 1977

lagged Percentage

Standard

Durbin-

Constant

Change in Price

Error

Watson

-0.00016

0.224

0.0075

2.04

0.0091

2.03

0.0056

2.04

(-0.32)

May 30, 1973-

-0.00053

October! 5, ! 975

(-0.61)

October 22, 1975-

0.00024

December 28, 1977

(0.47)

(3.46)
0.246
(2.66)
0.153
( 1.66)

(Numbers in parentheses are t-statistics.)

IV. Summary and Conclusions
The empirical results presented in this paper
all suggest that the GNMA spot market has improved its performance in the period since futures trading began in those securities. The spot
market has become more efficient in processing
new information; it has shown less purely random price variability; and it has become more
closely integrated with the rest of the bond market. It is impossible to say with certainty how responsible futures trading has been for any of
these beneficial deveiopments. But it seems clear

that futures trading in GNMA certificates has
not had a destabilizing effect on spot market
prices.
The significance of this conclusion extends beyond the GNMA market. Financial futures markets are still in their infancy. Proposals for still
more of them are constantly being made. The results of this study of GNMA futures suggests
that we have nothing to fear and potentiaiiy
much to gain from the further development of
these markets.

FOOTNOTES
1. See. for example, the discussion by B.A. Goss and B.S. Ya10. Winfield A. Boileau, "GNMA Pass Through," in Investment
mey in their introductory essay in The Economics of Futures
Opportunities, The GNMA Story, Mortgage Bankers AssociTrading, ed. Goss and Yamey (New York: John Wiley and Sons,
ation (1977), pp. 5-9.
1976), pp. 29-32.
11. For a general discussion of governmental programs to aid
2. "Stability in a Swin9ing Market," Business Week (August 8,
the secondary mortgage market, see Peggy Brockschmidt, "The
1977), p. 70.
Secondary Market for Home Mortgages." Federal Reserve Bank
3. Federal Reserve Bulletin (February 1978), p.A41.
of Kansas City Monthly Review (September-October 1977). pp.
11-20.
4. "A Fever of SpeCUlation Afflicts Ginnie Mae," Business Week
(July 18, 1977), p. 28.
12. The forward market is described in Thomas C. Miller,
5. "Interest Rate Futures Gain Popularity," Wall Street Journal
"Growth, Acceptance to Improve Liquidity of GNMA Security,"
(February 2, 1978), p. 1.
Investment Opportunities, The GNMA Story, Mortgage Bank6. This section draws heavily on the article by Richard L. Saners Association (1977), pp. 19-22.
dor, "Trading Mortgage Interest Rate Futures," Federal Home
13. Lester Telser and Harlow Higinbotham, "Organized Futures
Loan Bank Board Journal (September 1975), pp. 2-9.
Markets: Costs and Benefits," Journal of Political Economy
7. Futures markets exist for other reasons than merely to acco(October 1977), pp. 969-1000. Also, Gray, p. to.
modate "hedging" in the narrow sense of risk avoidance in which
14. These figures have been taken from various issues of the
that term is commonly used. See Holbrook Working, "Economic
Interest Rate Futures Newsletter of the Chicago Board of
Functions of Futures Markets," in Futures Trading in liveTrade.
stock-Origins and Concepts, ed. Henry Bakken (Madison,
15. For example, Neil A, Stevens, "A Mortgage Futures Market,"
Wisconsin: Mimir Publications, Inc., 1970), pp. 29-41. Also RogFederal Reserve Bank of S1. Louis Review (April 1976), pp. 1219.
er W. Gray, The Feasibility of Organized Futures Trading in
Residential Mortgages, FHLMC Monograph NO.3 (November
16. John Stuart Mill, Principles of Political Economy (London,
1974), p. 6.
1848), Book 4, Chapter 2, Section 4. as quoted in Goss and Ya8. John R. Hicks, Value and Capital (London: Clarendon Press,
mey, p. 30.
1946), pp. 144-147; Paul H. Cootner, "Common Elements in Fu17. "Stability in a Swinging Market," Business Week (August 8,
1977), p. 71.
tures Markets for Commodities and Bonds," American Econom18. Working, p. 47.
ic Review (May 1961), pp. 173-183.
19. Milton Friedman, "The Case for Flexible Exchange Rates,"
9. Gray (p. 13) notes some offsetting advantages of mortgages
over commodities, such as lack of storage and transportation
Essays in Positive Economics (Chicago: University of Chicago
problems.
Press, 1953) p. 175.

is well below the critical value of 3.04. See Jan Kmenta, Elements of Econometrics (New York: Macmillan, 1971), p. 373.
27. The F-statistic for a reduction in the standard error across
the two samples is the ratio of the two sums of squared residuals, ~ach divided by the respective degrees of freedom. The calculated F-value is 2.39, compared to the critical value of 1.59.
28. George E. P. Box and Gwilym M. Jenkins, Times Series
Analysis (San Francisco: Holden-Day, 1970).
29. The calculated F-value for the test of equality of coefficients
is 2.31, which is below the critical value of 2.65. The calculated
value for the test of reduction in standard error is 2.57, which is
greater than the critical value of 1.59.
30. See Eugene F. Fama, "Efficient Capital Markets: A Review of
Theory and Empirical Work," Journal of Finance, (May 1970).
Although the regressions presented in Table III show that past
movements in GNMA prices formerly contained information useful for predicting future movements in those prices, it is not necessarily the case that profitable arbitrage possibilities existed
during the first sub-period. Transactions costs may have been
too high for investors to exploit the predictive content of past
price movements. The futures market, by reducing the costs of
taking a short position, may have allowed investors to exploit
the information in past prices. This interpretation of the results in
Table 3 was suggested by Kurt Dew.

20. Friedman, p. 175.
21. Nicholas Kaldor, "Speculation and Economic Stability," Review of Economic Studies (1939-40), pp. 2-3. An alternlltive
model involving two groups of speculators has been suggested
by Fred Glahe, "Professional and Nonprofessional Speculation,
Profitability, and Stability," Southern Economic Journal (July
1966), pp. 43-48.
22. See the discussion (and references) in Robert M. Stern, The
Balance of Payments (Chicago: Aldine Publishing, 1973),
pp.77-89. Also, Jorg Schimmler, "Speculation, Profitability, and
Price Stability," Review of Economics and Statistics (February 1973), pp. 110-114.
23. Abba Lerner, quoted in Goss and Yamey, p. 32.
24. All of the regressions presented in this article were also run
for subsamples which omitted the months immediately surrounding the start of futures trading. Similarly, they were run using different proxies for the market index. The qualitative results were
not different for any of these alternatives.
25. For a full discussion of this approach to measuring an asset's risk, see Michael C. Jensen, "The Foundations and Current
State of Capital Market Theory" in Studies in the Theory of
Capital Markets, ed. Jensen (New York: Praeger, 1972), pp. 343.
26. The F-value calculated for these regressions is 0.085, which

Michael Gorham'

When we examine the decision-making of participants in any market, we see that most participants rely upon some source or sources of
information to enhance the value of their decisions. We also notice that relevant information in
many markets is available from both the public
and the private sector. The public/private information mix varies widely over markets. In some,
such as the markets for air conditioners, shoes,
calculators and pre-EPA automobiles, there is
virtually no public-sector information. In others,
such as the markets for labor, financial instruments and agricultural commodities, the public
sector plays a very large role.
The purpose of this paper is to explore the rela-

tionship between public- and private-market information, with particular emphasis on a specific
market with a large component of public-sector
information-the market for agricultural commodities. First, we show how public information
both destroys and creates opportunities for providers of private-sector information. We then
measure the private sector's response to these
new opportunites in the case of three major agricultural commodities with highly-developed spot
and futures markets. Our analysis indicates that
private-information sources correctly forecast
public-sector announcements for soybeans, but
do not do so for corn and wheat.

Relationship Between Public and Private Sector Information
commodity emerges from the traditional world
of subsistence agriculture and is bought and sold
in the market. In developed economies, this may
happen when a new commodity or service is created, such as microwave ovens, calculators, stock
options or kiwi fruit.
As a market emerges, so too do information
providers. In some cases, market participants
may conduct their own information search
through discussions with other market participants; thus the information providers and the information users become one and the same. This
would tend to be true of very small markets. In
other cases, a distinct set of private-sector information providers may arise. Some may simply be
existing firms which expand to cover a new market, while others may be new firms. In either
case, resources are organized to provide information to a new market when it is profitable to do
so. Private-sector information expands until the
cost of providing the last unit of information is
just equal to its price-or value, when market
participants generate their own information.

In order to discuss the interaction of public and
private information, it is useful to construct a
model of an information sector. In doing so, however, it is not necessary that all the real-world circumstances be exactly duplicated. Basically, the
model involves the development of a commodity
market, the emergence of private firms supplying
information to market participants, and the entry of public-sector information providers-due
to the public sector's belief that an inadequate
supply of information is available from the private sector. Finally, the model includes a readjustment by private firms to the new presence of
the public sector.
Private-sector entry
A market for a particular commodity or commodity group emerges at some point in time. In
developing countries, this may happen when a

*Economist, Federal Reserve Bank of San Francisco. The author gratefully acknowledges the research assistance of Pat
Weber.

mation through surveys, the value of the information would have to exceed any inconvenience
costs before market participants would have any
incentive to request it.

Public-sector entry
This equilibrium amount of private information is provided until the public sector makes its
entry. If the public sector is assumed to aim at
maximizing social welfare, specifically with regard to the use of information as a public good,
then it would be likely to consider available information inadequate whenever the private sector is
left to do the job on its own. The public sector
thus would "decide" to undertake the task of creating the appropriate information. 1
However, public servants may be just as interested in their own survival as in social welfare. In
a democracy, high-level public servants are either elected by the populace or serve at the pleasure of those who are so elected. If a large voting
bloc wants the public sector to provide information to some particular market, public officials
would be likely to pay attention because of their
own interest in re-election. Their willingness to
grant such requests would depend upon the voting strength (or campaign support) of the interests affected, but also upon their own ability to
justify to others the social subsidy involved in the
public provision of the information in question.
In the case of agriculture, the farm sector's political power could be expected to generate demands for publicly-provided information on
commodity markets, with this situation being
justified to the rest of society on the grounds of
its contribution to a stable supply of food at stable prices.
One caveat is in order. Not all participants in
all markets would benefit from the public provision of market information. Some participants
who benefit from a less-than-competitive market
might suffer if broadly available information
made that market more competitive. Where freely-supplied market information provides a positive value to market participants, those participants would have an incentive to ask for it.
But where the government obtains market infor-

II.

Private-sector response
When government provides market information, it disrupts the equilibrium in the production
of private information. To the extent that the
free (or low-cost) government information substitutes for existing private-sector information,
private providers may be forced to change their
product or to leave the business entirely. But at
the same time, new opportunities can arise from
these private firms. They can provide analysis
and prescription-in other words, translate government statistics into specific market advice in
the form of market letters. They can also sell information predicting what the next package of
government information will say. Good predictions are valuable to people who want to profit by
taking positions in advance of any price change
induced by the next release of government information.
This last stage could be characterized as a market with a mature information sector-one
which has reached a second stage of equilibrium
incorporating both private- and public-sector information flows. With the completion of the external shock from the public sector, any new
adjustments will probably be relatively minor.
There will always be commodity-market changes
which induce further changes in its associated information sector. There will also be technological changes in the information industry itself.
These may arise from developments in theoreticalor applied statistics, such as those which led
agricultural officials to adopt new sampling techniques during the early 1960's or from innovations in engineering, such as the remote sensing
devices which allow satellites to "photograph"
the midwestern corn crop or the Brazilian coffee
crop.

Information in the Market for Agricultural Commodities

The public sector probably accounts for a
greater share of total market information in agriculture than in any other market except finance.
And despite continuing minor changes, the information sector in agriculture can appropriately be
characterized as mature. The public sector began

providing information .to these markets over a
century ago: and t~e prIvate secto: has generally
completed Its adjustment to thIS goverm-r:ent
role. At this point, it would be usefUl. to consI~er
the institutional background to the ~nformatlOn
sector associated with these commodIty markets.
31

ers- such as large grain companies, food-processing firms, and food-brokerage firmsgenerate substantial amounts of internal information as a means of identifying emerging market opportunities as quickly as possible. Because
of the difficulty of measuring this type of market
information, the tests performed in the next section of this article must be indirect rather than
direct.
Private-sector firms, again, may complement
the USDA both in the collection and the analysis
of raw data. There might appear to be little opportunity for private firms in the area of data collection since the USDA collects data on
practically every variable of interest to market
participants, but these firms still play an important role by filling a time gap. USDA information is published at regular intervals-weekly,
monthly, quarterly, or annually-but important
developments often occur between reporting
dates and thereby affect the profit prospects of
market participants. Some firms develop interim
estimates by conducting limited field surveys,
but most develop these estimates by evaluating
the effects of weather, disease or pest developments on the most recent USDA estimates of
crop production.
Private firms similarly play an important role
by filling an analysis gap. While the USDA provides some useful analysis in its Situation Reports, it does not usually predict price
movements, nor does it provide market participants with advice on the positions they should
take in the market. This type of analysis gap is
filled by a number of market letters and services,
each of which is generally aimed at a different
audience of farmers, merchants, or speculators.

Public-sector information
The U.S. Department of Agriculture (USDA)
provides virtually all the public-sector information relevant to the nation's agricultural markets.
(However, the Department of Commerce and
the Federal Reserve provide information on related economic conditions, and farm officials in
individual states generate data on local agricultural markets). The USDA publishes production, price and other data for all major (and
many minor) crop and livestock products. Most
of this information is available free of charge,
and it is widely used by farmers, merchants, and
other market participants.
One of the most useful USDA series is the
monthly Crop Production Report, which contains harvest forecasts for a number of major
crops. Early in the year, farmers are asked how
much acreage they intend to plant to each crop,
and those planting intentions are compiled for
each major crop by state. After the planting season, Department representatives count the plants
growing in a systematic sample of all U.S. farms.
Because of the comprehensiveness and predictive
accuracy of these surveys, USDA announcements of expected crop production are generally
taken as scripture by market participants.
Private-sector information
The private sector tends to complement rather
than substitute for the public sector, reflecting
the fact that the latter already provides a vast
amount of free and high-quality information. In
the private sector, it is useful to distinguish between the information that market participants
generate for sale to others in the market. Some
firms generate information in the form of market
letters and market-information services, but oth-

III.

Measuring the Performance of the Private Information Sector

The agricultural-information sector is mature
in the sense that it has already incorporated both
a public-sector entry and a private-sector response. But how successful has the private sector
been in filling the analysis gap and the time gap
that remain after the public sector has done its
job? We cannot answer in the case of the analysis
gap, which is not amenable to quantitative testing, but we can make an estimate in the case of
the time gap. Fortunately, we can do so without

inspecting private-firms' actual predictions. This
is doubly fortunate because private-sector subscriber information is often difficult or costly to
acquire-and frequently difficult to evaluate because of being presented in qualitative rather
than quantitative terms-while much other private forecast information is simply impossible to
acquire because of being prepared only for confidential internal documents.

Nature of test
The test consists of examining the effects of
USDA output forecasts on specific commodity
prices. If USDA announcements are fully anticipated by market participants, they should not affect market prices, but if they are surprises, they
should cause prices to jump one way or the other.
Thus, from observing the movement of market
prices in response to USDA announcements, we
can infer how well the private-information sector
forecasts those announcements. (Chart 1).
The USDA typically makes monthly forecasts
of the coming harvest of wheat, corn and soybeans from midsummer through November each
year. County surveys of crop conditions are conducted around the first of the month, and are
then sent to Washington and kept in a doublelocked box until the compilation of the official
estimates around the tenth of the month. On that
day, compilers work behind locked and guarded
doors until the state and national totals are tabulated and inspected by a representative of the
Secretary of Agriculture. That individual takes
the approved report directly to the USDA press
room, where it is released immediately. In other
words, utmost secrecy surrounds the preparation
of production estimates for crops which are traded heavily in commodity markets.
If the USDA were the only source of information, a unique price could be associated with any
given crop-production forecast, and prices would
change only after a monthly announcement
changed the previous forecast. In other words,
the world might look something like Chart 1. But
when other reliable information is available the

market-price path will appear more jagged during the month and the announcement effect on
prices will be more moderate. In the extreme
case, private-sector information may become so
well developed that the USDA will never offer
any surprises and the announcement effect on
prices will be zero.
In order to estimate this announcement effect,
we examine the monthly production forecasts
and associated market prices for three commodities (corn, wheat and soybeans) for the 1970-77
period. The announcement effect is represented
by the coefficient "b" in the following basic equation:
%LlP = a + b%LlQ
(I )
where %LlQ is the percentage change between
the current month and the previous month in the
USDA harvest forecast, and %LlP is the percentage change in the market place between the day
of and the day following the announcement.
(Price is measured by the closing futures' price of
the post-harvest contract, which is December for
wheat and corn and January for soybeans.) Since
the USDA announcement is always made at 3
p.m. EST, after the close of all spot and futures
markets, this information should be fully captured by the change in the price between the
close of the market on the announcement day
and the same time on the following day. Also, to
take account of the ceilings imposed on daily futures' price movements, the terminal price used
in the %LlP figure is the closing price on the first
post-announcement day on which the limit was
not reached.
Some asymmetry is involved in using daily
price changes on one side of the equation and
monthly quantity changes on the other. However, an example will demonstrate the appropriateness of our test. Assume that a wheat-crop
forecast is made on the 10th of July, and that the
market accepts this as the best available at that
time. As the month progresses and rainfall becomes lighter than expected, private-information
providers will adjust the July USDA forecast
downward. To the extent that this downward adjustment is off the mark and the market is surprised by the new USDA forecast of August 10,
the surprise will show up only in the August 11
price change. Thus, since we are simply trying to
estimate the degree to which the market is sur-

Chart 1
USDA AS SOLE SOURCE OF CROP INFORMATION

Market price

Announcement affect

USDA production
estimate

SON
Time (months)

changes in the corn harvest. Note that while the
magnitude of the announcement effect is roughly
the same for wheat and corn, the effect for corn is
much more statistically significant. 3
Much of this difference can· be explained by
technical differences among crops. Soybeans are
a very hardy crop, so that month-to-month
changes in temperature and rainfall affect yields
to a relativeiy minor extent. Corn and, to a lesser
extent, wheat yields are much more affected by
environmental changes. In fact, the variability of
soybean yields is roughly only half that of corn or
wheat (Table 1). The ranking of the crops by
variability of yield parallels their ranking by the
private sector's output-forecasting performance,
which suggests that the technical difficulty of the
task is the primary factor determining the private sector's ability to forecast changes in USDA
estimates.

prised by the USDA forecast adjustment, this
test is appropriate. If, on the other hand, we were
trying to estimate an elasticity of demand, we
would need to use the same time period for both
price and quantity, and the test used here would
not be appropriate.
A recent unpublished paper by Pearson and
Houck2 uses a non-parametric chi-square test to
examine the hypothesis of an inverse relationship
between USDA forecast adjustments and associated market-price changes. For the 1963-75 period, they found that forecast changes and market
prices moved in opposite directions for corn, soybeans, and spring wheat, but not for winter
wheat. The current paper extends the Pearson
and Houck tests by 1) using regression analysis
for estimating the magnitude of the announcement effect, 2) expanding the sample period
from 12 to 28 years, and 3) testing for changes in
the announcement effect through the crop season
and over time.

Table 1
Per-Acre Crop Yields, 1966-76a )
(Bushels per Acre)

Announcement effect?
We obtain the following results from estimating Equation 1 (t values in parenthesis):
%LlPs

= -.632 -.004% Soybeans
(2.43) (0.05)

%LlP w = .028 -.202% Wheat
(0.10) (1.56)

%LlPc = .078 -.236% Corn
(0.31) (3.01)

Mean

R2 = .000
DW = 1.97
SER = 2.36
n = 84
R2 = .029
DW = 2.07
SER = 2.48
n = 84

Standard
Deviation

Coefficient
of
Variation

.072

Soybeans

25.52

1.83

Wheat

27.94

3.36

120

Corn

75.12

12.71

.169

a) Yield data taken from USDA. Agricultural Statistics
1977

Variation over crop season
As the crop season progresses, the uncertainty
associated with crop estimates decreases. Cropproduction estimates are based upon: 1) an estimate of planted acreage, and 2) an estimate of
yield per acre. While good acreage estimates can
be obtained early in the season, initial yield estimates are subject to change during the course of
the season. As the season progresses, yield estimates involve fewer assumptions and therefore
become less uncertain. Consequently, both the
public and private sectors should do a better forecasting job as the season progresses. Indeed,
throughout the past 28 years, the accuracy of the
USDA forecast improved and the variation in
the forecast error fell as the season advanced.
(Table 2).

R2 = .079
DW = 1.68
SER = 2.60
n = 107

While the explanatory value of the equations is
quite low, all of the coefficients carry the expected sign, which implies that price moves in the opposite direction from quantity. However, the
relationship is highly significant only for corn,
while it is weakly significant for wheat and essentially zero for soybeans. This suggests that the
private market does a very good job anticipating
changes in the soybean forecast, a somewhat
poorer job anticipating changes in the wheat harvest and a considera bly poorer job in anticipating
34

Table 2
Accuracy of and Variation in
USDA
Forecast, 1950-77

the 28 annual observations, can be seen in the upper right hand corner of Table 3. Altogether, no
consistent increase or decrease in the announcement effect is apparent over the crop season. This
suggests that the private sector does indeed improve its forecasts at roughly the same rate as the
private sector. However, since forecast improvements over the crop season are due almost exclusively to an easier forecasting environment, it
might be expected that all forecasters would find
themselves improving at about the same rate.

Forecast/post-harvest estimate
July

August

Sept.

Oct.

.990

.996

.997

.996

.999

1.031
1.032
1.035
Variation in Forecast Error a

1.040

Soybeans
Wheat
Corn

.993

NOli.

.997

.080

.043

.034

.027

.023

.010

.016

Corn

.084

.077

.076

.077

a) Measure of variation

= ~~

Soybeans
Wheat

.044

m i= I

(forecasti-final
final

Vari.ation over ti.me

The USDA has taken a number of steps to improve the accuracy of its forecasts, and these
measures have led to a gradually improved forecast ever since 1929. 4 Even within the shorter
1950 to 1977 period under consideration in this
paper, the accuracy of USDA forecasts has improved considerably, as is evident from the
shrinking variation in the forecast error displayed in Table 4. The only exception is a decline
in the forecasting accuracy for soybeans as we
move from the late 1960's into the commodityturbulent early 1970's.

While summary statistics similar to those in
Table 2 cannot be constructed for private-sector
forecasts (for reasons explained above), the private sector's improvement through the crop season can be measured in an indirect fashion. If
this sector improves its forecast at roughly the
same rate as the public sector we would expect to
find no systemetic change in the announcement
effect over the crop season. If, on the other hand,
it lags behind the public sector's performance, we
would expect to find an increasingly significant
announcement effect over the crop season.
To test this hypothesis, we estimated Equation
I separately for each monthly change. For example, the announcement effect for the July/ August change in the corn forecast, estimated with

Variation

1950·56

Soybeans

Wheat

-.218 (I.I

Aug./Sept.

c
-.011 (0.12)

Sept./Oct.

-.051 (0.25)

-.935 (0.77)

Oct./Nov.

-.008 (0.03)

July/Aug.

186 (0.78)

1957-63

1964-70

Error
1971-77

Soybeans

.076

.037

.033

.042

Wheat

.037

.025

.024

.022

Corn

.137

.075

.054

.043

a) Measure of variation used here is the same as that in
Table 2.

Table 3
Announcement Effect As
Crop Season Progresses a
Month of
Change

Table 4
in the USDA Forecast
Through Time, 1950-77a

But has the private sector kept pace with these
public-sector improvements? In a test similar to
the one above, Equation I was estimated for each
of four 7-year periods, with the results reported
in Table 5. With only a single exception, the announcement effect grew increasingly larger and
more significant over time-that is, market participants became increasingly surprised over
time. This suggests that the private sector lagged
behind the public sector in improving its forecast.
This might have been expected. Unlike the
forecast improvement over the crop season,
which is attributable to environmental changes,
improvements over time are generally attribut-

Corn

-.061 (0.99)
-.443 (2.16)
+.028 (0.18)
- .550 (2.85)

a) Announcement effects are estimates of "b" in Equation I.
calculated for each crop and for each monthly change.
Each estimate is based upon 28 observations for the 28
years of the sample.
b) t·values in parentheses
c) No soybean-crop estimate prepared for July.
d) October/November changes were too small to use for estimation.

able to actions taken by the forecasting agent itself. Because some improvements may be too
costly to be adopted by private firms (since they
may not stimulate a commensurate rise in revenues), the public sector adoption of such improvements would tend to enhance its forecast
accuracy relative to the private sector. Examples
might be a move to larger sampling frames or
more intensive physical counts within each
frame. Thus, due to the profitability constraint in
the private sector, a well-endowed public sector
agency like the USDA might be expected to improve its forcastsat a more rapid rate than the
private sector, thus generating larger announcement effects over time. (A more formal and technical presentation of this interpretation can be
found in the Appendix.)

Table 5
Announcement Effect Over Time a
Period

Soybeans

Wheat

Corn

1950-56

.021 (0.45)

.003 (0.08)b

-.017 (0.31)

1957-63

-.134 (1.34)

-.016 (0.31)

-.147 (1.45)

1964-70

-.315 (2.31)

-.198 (1.27)

-.229 (2.14)

1971-77

.214 (0.63)

-.972 (1.63)

- .918 (2.60)

a) Announcement effects are estinlates of "b" in Equation i

for each crop, for each of four time periods. Corn equations are based upon 35 observations (5 months x 7 years);
wheat and soybean equations are based upon 28 observations (4 months x 7 years).
b) t-values in parenthesis

IV. Conclusion
This paper was designed to explore the relationship between the provision of public and private information to participants in commodity
markets. We emphasized particularly the market
for agricultural commodities, since this is a market with a large component of public-sector information.
Whenever public information is considered reliable, its release would be expected to have a significant impact on the market. However, market
participants have an obvious incentive to predict
such public announcements, since this is equivalent to predicting a movement in prices. In a
mature information sector, private information
providers would become fairly adept at making
such predictions, so that we would expect to find
a fairly weak public-announcement effect. In our
test, however, we found that the private information sector did a good job of prediction only for

soybeans. Corn and, to a lesser extent, wheat still
have significant announcement effects.
For technical reasons, public-sector information generally improves in quality over the crop
season-and the same appears to be true for private-sector performance. However, over time,
public-sector information has improved in quality, whereas the private sector's forecasting ability has lagged behind.
This should not be too surprising. The public
sector, unlike the private sector, is not constrained by considerations of profitability when
adopting improved methods of forecasting or expanding its survey activities-although of course
it is subject to certain budget constraints. Thus,
in response to constituents and other pressures,
the USDA has been able to improve its forecasting ability more rapidly than has the private
sector.

APPENDIX
The notion that an increasing announcement
effect suggests that the private sector lags the
public sector in increasing its forecast accuracy
has some intuitive appeal. However, a more formal demonstration of the conditions under which
diverging forecast accuracy leads to increased
announcement effects would make such a notion
more plausible.
Let G and P represent the forecast error of the

government and private sector respectively. Furthermore, let the government error be written as
a function of both the private sector error (to the
extent that both sectors make the same types of
mistakes) and its own unique source of error, E,
such that:
1)

= aP + E

where a > 0 to reflect the fact that both private
36

the improvement), then "a" falls. Note that 0 <
a < 1 since we assumed (1) that government and
private errors were positively correlated which
implies a > 0 and (2) that initially a~ =
which from equation 2 implies that a < 1. Now,
as a positive "a" approaches zero, the expected
difference in equation 3 grows and, thus, the announcement effect grows larger.
So, it is only an increase in government accuracy via a fall in "a" that is consistent with our interpretation in this paper. The question then
becomes whether the actual source of increased
USDA accuracy has been a fall in <T~ or a. For
one thing, private forecasters can sell their forecasts partly on the basis that they are good forecasts of yet-to-be-announced USDA forecasts,
thus allowing subscribers to take advantageous
market positions. This creates an incentive for
private forecasters to behave in a manner .that
keeps "a" as close to I and E as close to zero as
possible (in equation I). To the extent that they
are successful in this and that there is little E and
a lot of "a" for the public sector to reduce, most
of the reduction in the variance of the public sector forecast would likely come from reductions in
a. Futhermore, the government forecasts are
based upon surveys of farms, while the private
sector forecasts are based both upon farm surveys and the integration of secondary information on weather conditions, random media
coverage of the farm sector and so on. To the extent that USDA expands the size or quality of its
farm surveys beyond that allowed by profitability considerations in the private sector, this represents a fall in "a" and an increased
announcement effect. This is probably more
typical of what has taken place over the past several decades. (Note: This treatment was suggested by Patrick Weber.)

and public tend to make errors in the same direction, and both E and P have zero mean and some
positive variance, a~ and a~ respectively. Assume further that the covariance between P and
E is zero and that a is independent of both a~ and
a~. Now, the variance of the government error
can be written as a function of the variance of the
private error and the independent government
eHor

a2 = a2a2

ab,

+ a2

Let us take the case where the errors initially
have the same variance and then the variance of
the government error falls, while the variance of
the private error remains unchanged. There are
two ways in which the variance of the government error can decline according to equation 2.
Either "a" could fall which would mean that the
government began to rely less on the methods or
data it shared with the private sector, or a~ could
fall because of increased public sector reliance on
better techniques or data not available to the private sector.
The announcement effect could either increase
or decrease depending upon which of these two
factors, a or <T~, was responsible for the accuracy
of the government forecast. Since the size of the
announcement effect depends upon the expected
difference between the two errors, let us write the
square of that expected difference as
3) E(P-G)2 = (a-I)2<T 2 + a 2

Clearly, if the government increases its accuracy
by reducing the variance of the error unique to
the government, i.e., a~, then the expected difference expressed in equation 3 will also fall and
the announcement effect will decrease. If, on the
other hand, government accuracy increases because it improves on a technique used by both
sectors (while the private sector does not make

Economic Studies (November 1954). A recent merging of the
public·goods and economics-of-information literature can be
found in Bruce Owen, Jack Beebe and Willard Manning, Television Economics (Lexington, Mass: Lexington Books, 1974).
2. Daniel Pearson and James P. Houck, "Price Impacts of
SRS Crop Production Reports: Corn, Soybeans, and Wheat," unpublished manuscript, Department of Agriculture and Applied
Economics, University of Minnesota, April 1977.
3. The price effect of a change in the harvest forecast should
be rather sensitive to the amount of the commodity currently in
storage. The new harvest does not usually make up the total
supply, but simply adds to that supply-and price is determined
by the intersection of demand and total supply. Since stock levels changed considerably over the sample period, it seemed appropriate to control for these changes. Thus Equation 1 was
modified such that %.!.Q refers to the change in total supply,
where total supply equals July 1 stocks plus the harvest forecast. As might be expected, the size and significance of the coefficients and the fit of the equations improve modestly, though
the announced effect for soybeans remains essentially zero.
The new estimated equations are:

1.• Apub'ic gOod is one. whose cost of production is un<lffectedbythe number ofpeople who consume it. This is to be distinguished from a collective good, which (once produced) is
automatically consumed bY ali. (Public safety is. a collective
good.) Information, per se, is a pure public good, since the cost
of creating it is the s"mewhelheritis uSl>d by one or by "million
people. (Nolethat Whill> the me"sage is a public good,the medium-book, pamphlet or magazine __ isa private good.) The
problem with a public good is th<lt the private sector will not
price it at the m<lrginal cost of production-which is zero since
adding a new consumer costs nothing-but will r"ther charge
sOl11e price ""hiGh will Gover fiXl>dGostsand allo\Na pr()fil,ll is
gener<llly recognized that this is not'optimal, because (once producl>d) the information can be provided to. additional people i.e. social welf<lre can be incre<lsed-at no additional GOst.
While this suggests that government intervention may make so·
cietybetter off, it is by no means clear that it would.
The private sector can come fairly close to providing the optimal amount of information if it C<ln charge each consumer a price
equal to the value of the information to him or, more realistically,
if the cosf of creating the information becomes very small relative to the cost of disseminating it. In the latter case, the portion
of the price attributable to the public good (the message) approaches the optimal level of zero, while the bulk of the price
charged to the consumer is the price at the private good (the
medium). In the case of paperback books, information costs are
low relative to dissemination costs, and thus the private sector
may be pr()viding close to the optimal amount of information; in
the case of the National Income Accounts, production costs are
so great that the private sector would probably provide consid·
erably less than an optimal amount. Information on agricultural
markets probably lies somewhere between these two extremes,
but closer to the latter.
The classic article on the optimal level of a public good is Paul
Samuelson, "The Pure Theory of Public Expenditure", Review of

%.lP s = .629 -.013 %.lTotal Soy
(2.42) (0.15)

R' = .003

%.lP w = .020 -.356 %.lTotal Wheat
(0.07 (1.84)
%.lP c = .059 - .357 %.lTotal Corn
(0.24) (3.16)

R2 = .040
R2 = .086

4. A moderate improvement in USDA forecast accuracy over
the 1929-1970 period was discovered using different techniques than those in Table 4 by G. Gunnelson, W.D. Dobson, and
S. Pamperin, "Analysis of the Accuracy of USDA Forecasts,"
American Journal of Agricultural Economics (November
1972).

Kurt Dew'
Is today's monetary policy more effective than
2. If the Fed does respond differently, has the
change altered the structure of the national
the monetary policy of earlier decades? Since the
1960's, dramatic changes have occurred in both
economy in any significant way?
monetary policy procedures and the amount of
This article will utilize the developing theory of
information provided by the Federal Reserve to
efficient markets to show that the Fed's response
Congress and the public. Still, the language of
to growth in M I has changed, and as a result, the
economic impact of a temporary deviation of M I
both Fed critics and advocates is sometimes
from trend has actually been reversed. Section I
reminiscent of an earlier time. The new proceshows that the public record is inconclusive
dures, coupled with the not-so-new debate over
about the Fed's attempts to control money. Pubpolicy options, raise a question: are the procedurlic pronouncements of Federal Reserve officials
al changes only differences in style, or does monetary policy now affect the economy in a
suggest that the monetary aggregates are more
substantially different way than it did in the
important in the policy process now than before,
1960's?
but there is no explicit evidence that the behavior
The changes that led to the present policymakof the monetary aggregates changes policy deciing approach began in 1966, when the Fed began
sions. Furthermore, there is no shortage of criti"paying attention to the monetary aggregates."
cism of the Federal Reserve on the grounds that
the Fed continues to pay insufficient attention to
These procedures developed gradually between
money.
1966 and 1975, and the interested reader may
find detailed accounts of the development in sevIn Section II, the case is made that the Fed toeral sources [d. (2), (8), (I I)]. Finally, in
day raises interest rates in response to undesirMarch of 1975 Congress required the Federal
ably rapid money growth, whereas it did not do
Reserve to "... consult with Congress ... about the
so in the 1960's. This change in response is reBoard of Governors' and the Federal Open Marvealed indirectly, through an analysis of the
ket Committee's objectives about the rate of
stock market's response to the money supply.
growth or diminution of monetary and credit agThe conclusion is based on the evidence that the
gregates in the upcoming twelve months." (9)
stock market today (unlike the 1960's) responds
This Congressional Resolution solidified the
negatively to an increase in the money supplyFed's commitment to an approach that assigned
and the proposition that the stock market is an
great importance to the behavior of various meaefficient forecaster of the future economic imsures of the quantity of money. The Federal Repact of a change in the money supply, which imserve's new procedures have come to be called
pact in turn depends on the Federal Reserve's
"Practical Monetarism" by the financial press.
policy reaction.
Was the monetary policy of the early '60's,
Section III argues that the new emphasis on
when the Fed did not pay explicit attention to
the monetary aggregates has in fact altered the
money, really different in economic impact from
structure of the economy, and that most econothe practical monetarism of post-I 975, or were
metric models of the monetary-transmission prothe changes primarily cosmetic? This question
cess are mis-specified as a result. This section
may be subdivided:
raises questions about a naive interpretation of
I. Does the Fed actually respond to the behavthe portfolio-adjustment theory of the transmisior of the money stock in a way it did not in
sion of monetary policy-namely, that an excess
the 1960's?
demand or supply of money precedes changes in
*Economist. Federal Reserve Bank of San Francisco
39

long-term interest rates and equity values, which
changes in turn influence levels of real economic
activity. The empirical work presented here indicates that stock prices and interest rates primarily reflect anticipated trend rates of money

growth. Thus, according to a more accurate interpretation of portfolio theory, past rates of
money growth affect current real economic activity only if they affect forecasts of future money growth.

I. Recent History of Monetary Policy
By all accounts, the most important and most
controversial change in monetary policymaking
in the last several decades has been the increasing importance attributed to various measures of
money-in particular, the narrowly-defined Ml
measure (currency and demand deposits) and
the broader M2 measure (currency plus all bank
deposits except large negotiable CD's). According to the minutes of the Federal Open Market
Committee (FOMC), that key policymaking
committee clearly has paid greater attention to
the behavior of M lover time. The first such expression of interest occurred in 1966, when a
"proviso" clause was first included in the Directive, the document containing the monthly
instructions from the FOMe to its operating
arm, the System Open Market Account
(SOMA). An example of a Directive with a proviso clause was the December 1967 Directive (4):

emphasis on the aggregates. The February 1970
Directive, for example, put the financial community on notice that moderate growth in M 1 and
the other aggregates was an important FOMC
objective. However, the role of money in the new
procedure remained ambiguous. Thus, in his testimony before the Congressional Joint Economic
Committee on July 23, 1970, Chairman Burns
emphasized that changes in money growth sometimes would have little effect on subsequent
FOMC decisions.
"An impression seems to have prevailed in
some quarters that the Federal Reserve had decided to pursue fixed target rates of growth in
the monetary aggregates on a more or less continuous basis. This is a misreading of our intent. We believe that the nation would be illserved by a mechanical application of monetary rules. We know that large, erratic, and unpredictable short-run changes often occur in
demands for money and credit. One of the important functions of a central bank is to prevent
such short-run shifts from interfering with the

" ..., System open market operations until the
next meeting of the Committee shall be conducted with a view to moving slightly beyond
the firmer conditions that have developed in
money markets ... provided, however, that operations shall be modified as needed to moderate any apparently significant deviations of
bank credit from current expectations or any
unusual liquidity pressures. (emphasis added)"
The proviso clause was the first explicit FOMC
recognition of the need to pay attention to unanticipated behavior of the money and credit aggregates during the periods between meetings. But
even with that clause, it remained unclear exactly how the information on money included in the
Directive would feed into actions of the SOMA
and its Trading Desk. For several years, various
Directives mentioned growth in money and credit, but did not give the Desk instructions about
what to do should the aggregates go off course.
As a result of historical experience, such as the
undesirably rapid growth of money supply in the
last half of 1968, the FOMC came to place more

Chart 1

ro t - - - - - - - - - 7 < : : - - - - - - - - - - L M

'--------------:':---------Y
Yo

smooth functioning of money and capital markets. We have no intention of abandoning our
responsibilities in this area (3)."
By 1975, however, the Federal Reserve had
come to focus its stated policy intentions on the
monetary aggregates. The FOMC's quarterly
choice of growth rates for M I and M2 became an
index of FOMC policy intentions in the six to
twelve months following their selection.
The present FOMC Directive provides operating instructions to the SOMA in terms of "shortterm tolerance ranges," one for the M 1 and M2
monetary aggregates, and one for the Federalfunds rate. For example, in its July 19, 1977
meeting, the FOMC voted the following Directive:
"Specifically at present, it [the FOMe] expects the annual growth rates over the JulyAugust period to be within the ranges of 3V2 to
7'12 percent for Ml and 6V2 to 101;2 percent for
M2. In the judgment of the Committee such
growth rates are likely to be associated with a
weekly-average Federal funds rate of about 5%
percent. If, giving approximately equal weight
to M 1 and M2, it appears that growth rates
over the two month period will deviate significantly from the midpoints of the indicated
ranges, the operational objective for the Fedral
funds rate shall be modified in an orderly fashion within a range of 5V2 to 53)\ percent (5)."
The SOMA's basic task is to achieve, on a
weekly average basis, the "midpoint" of the
short-term tolerance range for the Federal-funds
rate. However, the appropriate SOMA response
to unanticipated growth in the monetary aggregates is still not spelled out explicitly in the Directive, although the desirability of some
response is certainly suggested.
The lack of an explicit link in the Directive between the aggregates target and the funds-rate
target, as well as occasional statements by Fed
officials, raises the question of whether the Federal Reserve actually responds more than before
to unintended growth in the monetary aggre-

Chart 2

rol-----.........:'r-----------Ms

L-

..L-

Mo
y

gates. Former Federal Reserve insiders sometimes suggest that the monetary aggregates are
not given much attention in practice. James
Pierce, former associate economist for the
FOMC, is quoted to this effect in the March 27,
1978, issue of Fortune magazine:
"...The Fed still conducts its business virtually
the same way it always has. When Congress
passed its 1975 resolution, it intended the Fed
to pay more attention to the growth of the monetary aggregates-Ml, M2, etc.-and less attention to stabilizing interest rates. Since 1975
the Fed has paid more and more lip service to
the monetary aggregates... (l0)"

II. Has the Fed's Behavior Changed?
In the economics textbooks, the Fed is described as having two options when implementing policy: I) control interest rates, or 2) control
the money stock. In reality, however, the second
option is not a simple one under the current institutional framework. The amount of money (M 1)
is jointly determined by the Fed, the commercial
banks and the public at large. Moreover, it is
partly estimated, rather than measured, by the
Fed, so the word "control" is not quite applicable.
A better description would be to say that the Fed
has the choice either of changing interest rates,
or of not changing them, in response to unanticipated behavior of the money stock. In this section
we argue that the Fed has recently "controlled"
the money stock to some degree-that is, the Fed
has changed its interest-rate plans in response to

unanticipated changes in M I-in ways that it
did not during the 1960's.
This argument is based upon the changes that
have occurred over time in money-stock market
relationships. Most economists agree that. the
stock-market response to M 1 is important evidence of M 1's impact on economic activity in
general, because the stock market is an efficient
market. That is, stock-market behavior reflects
accurate forecasts (rational expectations) of future economic activity. In the words of William
Poole, "The validity of the rational-expectations
(efficient market) hypothesis as applied to prices
in active auction markets has been extensively
tested. Numerous investigators have analyzed an
enormous amount of data using many different
statistical techniques, and no serious departure
Chart 3

ro I - - - - - - - - : : " : : - - - - - - - - - - L M

ro I--------::'<::-------""'=----Ms

from the predictions of the hypothesis has been
found (12)."
According to the efficient-market hypothesis,
all relevant available information affecting a
firm's future net revenues is accurately reflected
in its current stock value. With an efficient stock
market, the market's response to a change in the
money supply occurs as soon as market participants compute the economic inlpact of a change
in MI. In particular, an efficient stock market
would adjust for any change in Federal Reserve
response to M I growth.
We attempt to show here that the Federal Reserve, under certain circumstances, is the decisive factor in determining the economic effects of
a given change in M I. Next, we present evidence
of a reversal, since 1970, of the stock market's
response to M 1 changes. Since that turning
point, increases in the money supply have tended
to nave negative rather than positive impacts on
stock prices. This suggests a shift over time in

both the Fed's response and the economy's response to changes in MI.
Consider the standard IS- lM model of income
determination (Chart 1). Income (Y) and interest rates (r) are determined by joint equilibrium
of the markets for goods and services (IS) and for
money (lM). The IS curve represents various
equilibrium combinations of interest rates and
income in the market for goods and services. The
curve is negatively sloped to indicate that households and firms will purchase relatively mOre
goods and services if interest rates decline, other
things equal. The lM curve represents various
combinations of interest rates and income that
lead to equilibrium in the money market. It is
sometimes constructed with an upward slope and
sometimes horizontally, depending on the Fed's
behavior. In this case the lM curve is horizontal,
because the Fed controls interest rates over the
very short-run.
The short-run structure of the money market
Chart 4

Yo I - - - - - - - - - " l < - - - - - ' T - - - - - - LM

ro 1 - - - - - - - - - - - " , : - - - - - - - - " ' 1 < - - Ms

Y
y=y

I
Md

may be summarized by: 1) a standard moneydemand function, where money demand is directly proportional to nominal income and inversely related to interest rates; and 2) a
horizontal short-term money-supply function,
where the Federal Reserve implements policy by
choosing a particular level of the Federal-funds
rate and supplying the cash necessary to maintain this level. Chart 2 summarizes the money
market under these conditions, with equilibrium
interest rate ro and income Yo.
Consider first a policy where the Fed does not
respond to changes in the money supply. If there
were an unanticipated increase in the money supply, would income be permanently higher as a result? The answer depends on the source of the
increased money.
One possible source would be an upward shift
in the demand for money at old levels of income
(Chart 3). Such a change in money demand
would mean more money, an increase from M o

to M 1, but the IS-LM relationship would be unaffected and income and interest rates would be
unchanged.
A second possible source would be an increase
in money demanded due to an outward shift in
the IS curve (Chart 4). An unanticipated increase in money of this sort would tend to be associated with higher future income. Except in
those cases where the increased quantity of money is due to an upward shift in money demand,
there is a positive probability of greater future
income with a surprise increase in money. In Appendix I this proposition is demonstrated analytically.
Now suppose the Fed becomes sensitive to the
behavior of money under a policy of practical
monetarism. In this situation, an unanticipated
increase in the money supply would lead the Fed
to increase its funds-rate target. But if the source
of the increased money was a shift in the IS
curve, the increase in the funds-rate target would

Chart 5

3
r1 1 - - - - - - = : : . . , , - - - - - - - - - - - - L M 2 r1

LM1

1---~:--------------Ms2

~ I~",

15 2

~Md1

151

I
Yo
Y

Ms 1

'~d2
""
M

tend to offset the otherwise higher level of future
income (Chart 5). The chart shows (1) the initial
equilibrium, (2) the equilibrium after the surprise increase in the supply of money due to the
shift in the IS curve, and (3) the equilibrium at
old levels of income and higher interest rates
after the Fed responds to the unanticipated
change in money by raising the funds-rate target.
As our analysis suggests, the IS-LM: model
does not by itself lead to any single conclusion
about the future of interest rates and income following an unanticipated change in money, independently of Federal Reserve policy. The effect
of an increase in M I depends on whether or not
the Fed intends to offset this increase by returning to former money-growth rates. If the Fed
does not raise interest rates in this situation , an
increase in money will tend to result in more rapid income growth and unchanged interest rates.
If the Fed does respond to increased M I growth,
future income will remain unchanged and future
interest rates will tend to rise.
The effect of an increase in M I upon an efficient stock market depends upon the policy
choice made by the Federal Reserve. The efficient stock market equates the value of stock to
the discounted value of future net earnings of the
firm
Vt = Eo

EI
I

E2
(1

+ r)2

Chart 7

(present)

Ms.

growth will be an increase in the firm's net earnings. Thus, if the Fed does not respond to increased M I, the resulting higher income and
unchanged interest rates would lead to an increase in stock prices.
Next, consider the case where the Fed raises its
interest-rate targets in response to money growth
(Chart 7). Income and expected earnings would
not increase. Instead, the stock market would anticipate a rise in interest rates, which would tend
to raise the discount applied to future earnings
and to lower the value of stock. Thus, efficientmarket-determined stock values, like economic
developments, depend in the last analysis upon
the Fed's response to money growth. If the market expects the Fed to offset a given increase in
M I growth, the result would be lower stock values.
Chart 8

M1 and STOCK PRICES

+ i)

June 27 - December 27. 1968
Percent
Change
1.0

Chart 6

(forecast)

(present)

_______ YA~
MsA

~ P (stock) Y

(forecast)

Consider the case where the Fed sets its interest-rate targets independently of money growth
(Chart 6). In the short run, earnings depend on
demand-induced changes in aggregate spending.
Although policy-induced increases in aggregate
demand will eventually affect costs as well, the
initial effect of an increased rate of income

(present)

r (short)~

where
Vt = value of a share of stock at time t
Ei = earnings per share of stock at time (t
r = rate of interest

(forecast)

_______v-.

P(stock)A
- - - - - - r (short)- /
(forecast)

Most empirical studies of the subject, based entirely or predominantly upon 1960's data, have
found a positive correlation between changes in
the money supply and changes in stock prices.
Most of these studies have utilized monthly or
quarterly average behavior of the two variables,
but similar results have been obtained with weekly-cha.nge data for second-half 1968-specifically, the Federal Reserve's money data released
each Thursday after the stock-market close, and
the closing stock-price data released the following Friday (Chart 8). However, a completely different picture emerges when we compare the
same two variables in a more recent period, the
first half of 1977 (Chart 9). In this period, we
observe a negative rather than a positive relationship between money and stock prices.
To capture the entire effect of the monetary
impact on the stock market, we may have to take
account of microeconomic as well as macroeconomic effects. According to a micro approach, an
unexpected increase in current money balances
in an individual portfolio leads to an undesirably
high ratio of money to other assets. As a result,
savers attempt to reduce their holdings of other
types of assets so as to restore their money-earning assets ratios to preferred levels.
Changes in the money supply could have both
kinds of effects. Microeconomic effects, which
can occur at any time, involve market participants as they make portfolio decisions that directly affect stock prices and perhaps ultimately
the economy as a whole. Macroeconomic effects,
which occur only at one specific time, involve
market participants as they adjust their economic forecasts in response to new money data. The
microeconomic effects of money growth are always positive, while the macroeconomic effects
may be either positive or negative.
If the micro effects are dominant, then the behavior shown in the charts would represent only
irrelevant "announcement effects" and would be

Chart 9

M1 and STOCK PRICES
January 6 - June 30, 1977
Percent

Change

2.0

1.5

1.0

1977

dominated by the "actual effects" of the moneystock price relationship. But a separate statistical
analysis (Appendix II) supports the thesis suggested by the charts -- namely, that the inverse
macro relationship dominates the positive micro
relationship. This inverse relationship is evident
in the 1973-77 period, and especially in 1975-77.
The statistical evidence also suggests that, because of changing Federal Reserve behavior, the
market has reversed the macroeconomic effects
expected from unanticipated changes in MI.

III. Transmission of Money Growth to the Economy
What is the mechanism that transforms
changes in money into changes in the level of economic activity? Chart 10 indicates that changes
in money immediately affect stock prices and
long-term interest rates, because these changes
cause market participants to revise their fore-

casts of future income and interest rates.
If holders and prospective holders of long-term
bonds decide that short-term rates will rise more
than originally anticipated, they will bid up longterm rates as a means of arbitraging the higher
expected short-term yield. This change in short-

Chart 10

(present)

Chart 12

(present)

(forecast)

(future)

(present)

(forecast)

(present)

(future)

'--I
1

P(stockl'-'C

1
1.1
~V
1I r (short) 1
\
/
I r (I01lQ) _ 1
L __ -1
(present)

would be higher long rates and lower stock
prices, which in time would tend to reduce consumption and investment and therefore reduce
income.
The stock market's recent behavior casts doubt
on the idea that the portfolio-adjustment process
is primarily a response to a disequilibrium
amount of money in current portfolios. The evidence suggests that a change in the anticipated
rate of money growth is more important than
current monetary changes in explaining portfolio
adjustment. In the 1960's, an unexpected increase in money had a positive impact on the
stock values, because it suggested accelerated future money growth (due to accelerated future
GNP growth). In the 1970's, however, a similar
increase in money was contractionary, because it
meant slower future money growth (due to the
Fed's raising of interest rates at current GNP
growth rates).
If changes in anticipated future rates of money
growth are more important than current
changes, the emphasis should be on anticipated
future excess supplies. Then the substitution of
equities for money that would drive the system
into equilibrium would be a substitution of future
claims to money for current holdings of equity -in other words individuals would tend to buy equity on credit. Replacing a current excess supply
of money with a future excess supply would make
the inverse money-stock price relationship consistent with the portfolio-adjustment model.

(future)

term rate forecasts also would increase the discount on future corporate revenues and reduce
stock values.
Consider the 1960's-style response to a surprise
increase in MI (Chart II). Since market participants would expect the Federal Reserve to accommodate such unanticipated increases, the
result would be higher forecasts of income and
unchanged forecasts of interest rates. These forecasts would tend to push stock valuation upward,
and leave long term rates unchanged. The booming stock market stimulates consumer spending,
which leads to higher levels of income.
Next, consider the 1970's-style response to a
surprise increase in MI (Chart 12). Since market participants would expect the Fed to offset
such unanticipated increases, they would revise
their short-rate forecasts upward but leave income forecasts unchanged. The initial effects
Chart 11

(present)

(forecast)

(present)

(future)

'--I
I vA I P (stock) A--- d ...........
1
1./
vA
II r(s~rt) 1\
/
I r(long)
1_
L __ .-J

IV. Summary and Conclusions
The apparent reversal in the stock market's response to a change in money should ease the
Fed's attempt to reduce fluctuations in income.
In the case of an unanticipated decline in M 1,
market participants would expect the Fed to lower interest rates as a means of offsetting the asso-

ciated decline in income, and thus they would act
to push equity values upward and to reduce longterm interest rates. Rising stock values would increase net wealth and therefore increase consumption spending out of net wealth, thus
bringing about the beneficial effect on income
47

growth desired by the Fed. Similarly, long-term
rates would tend to fall in anticipation of the
Fed's intention to reduce future short-term rates.
This decline in long-term rates would increase investment expenditures, again moving the economy in the direction desired by the Fed.
However, the effect of efficient auction markets upon the economy can be a two-edged
sword. Suppose the Fed made an error the stock
market was aware of -- for example, by choosing
a "wrong" money growth target that led to a
higher growth in income than the Fed desired.
Market participants then would re-evaluate
firms' expected revenues, and stocks would appreciate in value. Likewise, traders would reduce
the levels of expected short-term interest rates,
bringing long-term rates down. Both results
would exacerbate the initial policy mistake and
lead to excessive growth in income.
The stock market thus can be a useful indicator
of the impact of monetary policy. If the actions
of policymakers are consistent with their desires,
the stock market should reflect this fact. In contrast, if their policy is more restrictive than desired, the results would be seen in an undesirably

weak stock market.
Most past studies of relationships between the
stock market and other economic variables have
focused upon past events that have affected present stock values. But if the stock market is efficient, this is not the right order of influence.
With an efficient market, the key influenceis the
future behavior of key economic variables -- or at
least the best available estimate of their behavIor.

As a consequence, the stock market can help
judge the future course of monetary policy.According to the evidence developed here, the Fed's
response to unanticipated behavior of MI has
changed substantially-so substantially, in fact,
as to reverse the earlier implication of how
changes in money growth would affect the average firm's future net income.
In addition, the market's response to M I has
an economic impact all its own. This helps the
Fed in achieving its goals when the Fed's estimate of future economic activity coincides with
the market's estimates. However, the market will
thwart the Fed's intentions when it thinks the
Fed's forecasts are mistaken.

APPENDIX I
In this appendix we derive the economic impact of unanticipated changes in the money supply under two different monetary-policy
procedures, using the IS-LM model:

base their initial income forecast, Yo, upon an IS
curve relationship and upon an LM curve relationship:

~Yo

yt = a o + a I rt + PlYt - I + et

~Yo =

mt = bo + blYt +bl t + P2 m t-1 + Ut
= nominal income in period t
= amount of money in period t
= interest rate in period t
= independent normally distributed random variables with mean zero and
variances (J~ and (Ja respectively.
First we consider a monetary policy which is
formulated independently of changes in M, so
that the course of future interest rates will not be
influenced by an unanticipated increase in the
money supply. Stock-market participants, knowing this, will assume future interest rates unchanged. In forming estimates of the unanticipated increase in current income associated
with the surprise increase in money, traders may

=0
bl -I ~mo

in order to minimize the variance, the two forecasts would be weighted according to the size of
the associated forecast errors:
Yo = q (0) + C2 (bI I ~mo)
where

(bI I )2(Ja
q=---'-----=-(bI I )2 (Ja + (J~
c2

(J2
e
(bI l )2 (Ja

+ (J~

After this inital period, the increased income associated with the unanticipated increase in money will result from the auto-correlation in income
implicit in the IS curve:
48

ture income by raising interest rates. This increase in interest rates is:

LlYi = PILlYi-I
So thatLlYi = p\ c2bli Llm o '
l
Since PI, c2, bi > 0,

Llfj = -a;;-I pi ,iYo
The resulting equations for changes in interest
rates and income associated with the unanticipated change in the money supply is:
1) ,iYo = C2bil Llm o

LlYi
Mi
- - >0 - - = 0
Llmo
' i1mo
.

Next, we consider a monetary policy where interest rates respond to unanticipated changes in
the money supply. The first-round effect of this
surprise change is the same as before. However,
the Fed is now using the minimum variance estimate of the current increase in income derived
above, and attempting to offset its effect on fu-

2) ,iYi =
i = 1,2, ...
1-1
3 ) Llfj = -a 1 c2 b ILlm o
c2' bi l > 0, ail < 0
4) ,iri =

i = 2, .. ,

APPENDIX II
where

This appendix contains a time-series analysis
of the impact of a given percentage change in the
money supply upon stock prices.

Et = earnings due to holding a share of
stock during the period from time
t-I to time t.
E = anticipated earnings due to holding a
share of stock at time t-I.
t-I Xt = vector describing the information
important to stockholders that is
learned between time t-I and time
t.
Given an efficient stock market, money-supply
changes also affect stock values to the extent that
they affect the "best" forecasts of real economic
variables. This means that money-supply behavior that does not change the economic forecast
also has no impact on the value of stock. While
money changes might affect real economic activity with a time lag, they would affectjorecasts of
future economic activity immediately, and so the
effect on the stock market would also be immediate. Similarly, the part of a change in the money
supply that was expected to occur would already
be included in current economic forecasts, and
hence would already be reflected in stock values
at the time it occurs. So only unanticipated money changes have any impact upon stock values.
Therefore, in an efficient stock market, changes
in stock values between, say, time t-I and time t
would not be related to:
1) money-supply changes that occur prior to
time t-I, and
2) money-supply changes that occur after time
t-I but are anticipated at time t-I.

A convenient way of expressing the value of a
share of stock, Vt, at any point in time is:
Vt =L(Ri - Ci)
i
(I
i

where Ri
Ci
r

= t, t +

1 (

+ r)

t-I

I, ...

= anticipated revenues in period i
= anticipated costs in period i
= the interest rate.

This in turn provides us with a formula for the
change in the price of a share of stock in a given
time period:
1

LlVt=LLl(Ri-Ci)(
t'
i
1 + r) - 1
-Dt
where Dt = dividends paid during period t.
That is, the change in share prices in any period t-I Llt is the change in the present value of
anticipated net revenues less the dividends paid
during the period.
Adding dividends to both sides:
Et = Dt + LlVt
I
= LLl
(R' - C") - - - - ; i l l (I + r) t -

= f (t-I Xd + E
49

Table 1
Structure of Autocorrelation (up to 20 lags)
ofM1 Percentage Change (monthly)
in Different Time Periods

In short, the only changes in the money supply
that potentially affect stock values are those that
are unexpected and occur during the same time
period as the change in stock values.
To develop an appropriate measure of the
change in stock values, we used an updated version of the Standard and Poor Index of the endof-the-month return to stock. (Ibbotson and Sinquefield, "Stocks, Bonds, Bills, and Inflation:
Year by Year Historical Returns (1926-1974),"
Journal of Business, Vol. 4a). It was then necessary to develop an appropriate measure of the
new information provided by M 1 during the
month in which stock values were affected-that
is, M 1 data available to financial-market participants at the time, rather than later revisions. For
this reason, M 1 data were based on last- Wednesday-of-the-month releases from the Federal Reserve Statistical Release H-6, Table 1.
In order to find the unanticipated change in the
money supply over a given time period, we first
had to develop some sort of estimate of the anticipated change in M]. If stock-market participants are rational, they would at least use all the
information provided by the past behavior of the
money supply itself. In other words, to the extent
that money growth follows predictable patterns,
past values are useful in forecasting the future
money supply. We use the standard Box-Jenkins
analysis to develop the information from past
money-supply behavior efficiently.
Since the basic hypothesis was that monetarypolicy techniques had shifted between the 1960's
and the 1970's (particularly after 1975), it
seemed logical to form different estimates of anticipated money for the different periods considered. Initially, three time periods were examined:
January 1960 - December 1969, January 1970 December 1976, and January 1973 - December
1976 (Table I). The table describes lags at which
significant autocorrelation existed between the
M 1 change in a given month and M 1 changes k
months in the past. (Significance was based on
one standard deviation of the asymptotic distribution of the autocorrelation term, under the null
hypothesis that inter-period changes in M 1 are
independent. With independence, autocorrelation terms are asymptotically normal with zero
mean and variance 1IN where N is the size of
the sample.)

Test statistic N·1 /2
Sample period:

.091
.109
.145
Jan. 1960· Jan. 1970· Jan. 1973 .
Dec. 1969 Dec. 1976 Dec. 1976

2
3
4
6
11
17
18
19

I
1
4
4
7
7
8
8
11
II
12
Significant
15
autocorrelations
14
17
at k =
15
17
19
Based on these results, we constructed the following equations (see Table 2) for the purpose of
estimating anticipated money. Q statistics indicate that an x-square test will permit acceptance
of the hypothesis that the residuals of the anticipated money series are uncorrelated. Thus, we
may reject the hypothesis that there is more information about the current change in M 1 contained in past behavior of M 1after the adjustment.
After forming monthly forecasts of M 1 change
based upon the information contained in past
money behavior, we subtract the forecasts from
the actual change to get some measure of the surprise change in MI. We can then compare the
unanticipated change to the change in stock
valuation to determine if there is a relationship
between the two variables. Most recent studies of
this relationship have been based upon data from
the 1960's and early 1970's. The evidence they
present is not conclusive, but they generally support the proposition that the market for stock is
efficient, according to the criterion that "old"
M 1 data has no identifiable effect on the stock
market. (See for example Rogalski and Vinso,
Journal of Finance. September 1977 for an examination of the efficiency with which the stock
market uses monetary data.) Our evidence on the
subject is also not conclusive, at least for the
1960-69 period. In that period, surprise changes
in the money supply apparently had some predictable relationship to changes in stock values in
future periods. However, later data show no such
relationship, and therefore support the efficiency
hypothesis (Table 3).
50

Table 2
Filter for M1 Change (percent) for 1960 - 1969

Equation Lag
Coefficient

2.
-0.10181

4.
0.09436

3.
-0.27571

Autocorrelations of Residuals
0.06
0.02 -0.02
I - 10
001
II - 20 -0.00 -0.05

0.00
-007

0.03

0.05
0.06

6.
-0.26240

0.01
0.13

-0.02
0.03

9.
-0.12015

0.03
-0.08

II.
-0.11795
Q
Statistics
0.00
0.999
0.10

7.091

Summary Statistics
Variance of Residuals = .1257x I0- 4 , degrees of freedom = 113
Durbin-Watson Statistic = 2.097
R2=.155
Filter for M1 Change (percent) 1970 - 1976

Equation Lag
Coefficient

4.
0.04699

0.16914

Autocorrelations of Residuals
I - 10 -0.02 -0.07
0.01
II - 20
0.03 -0.13
-0.06

-0.01
0.10

7.
0.19062

-0.02
-0.15

-0.03
0.08

8.
0.06291

0.02
0.18

0.08
-0.00

9.
-0.26921

-0.03
0.03

11.
-0.24289
Q
Statistics
-0.04
1.417
-0.05
9.466

Summary Statistics
Variance of Residuals = 0.0422x 10- 4 , degrees of freedom = 77
Durbin-Watson Statistic = 1.920
R2=.125
Filter for M1 Change (percent) 1973· 1976

Equation Lag
Coefficient

2.
0.31124

0.29351

4.
0.53073

5.
-0.37976

7.
0.04356

8.
-0.00996

Q
Autocorrelations of Residuals
I - 10 -0.04 -0.0 I
0.09 -0.10
II - 20

0.09
0.05

0.03
0.03

-0.02
-0.25

-0.09
-0.03

-0.00
0.20

007
-0.07

0.09
-0.05

Statistics
-0.01
1.466
-0.11
8.207

Summary Statistics
Variance of Residuals = 0.2729x I0- 4 , degrees of freedom = 41
Durbin- Watson Statistic = 1.964
R2 = 0.269

In all three periods, we found some indication of
a relationship between present stock prices and
future changes in the money supply, but the relationship was stronger after 1970. In the case of
the 1975 to 1976 residuals, significant relationships appear to exist between changes in the value of stock and unanticipated money and next
week's unanticipated money. This result is consistent with the hypothesis of an efficient stock
market that believes unanticipated increases in
the money stock have an adverse effect upon the
discounted net earnings of the average firm.

Other studies have found a significant relationship between changes in the stock values in a given week and unanticipated M I changes in
following weeks
a sort of reverse causality
running from the stock market to the money supply. One reasonable explanation for this behavior
is that stock-market participants can find available other (non-money) information useful in
forecasting future M I changes prior to the publication of M I data. In this case, changes in stock
values will tend to precede unanticipated
changes in the money supply, because market
participants are partly able to anticipate them.

Table <3
Correlations of Unanticipated/Monthly Percentage
Change inM1 with Monthly Percentage Change
in Stock Values at Various
Leads and Lags
I. January \960 - December 1969
a) contemporaneous correlation p = 0.117*
b) correlation between stock and M 1 i periods in the past

7
8
9
2
3
4
5
6
P = 0.11 1* 0.217* 0.034
0.090 -0.044 -0.053
0.005 0.077 -0.069
c) correlation between stock and M I i periods in the future
7
8
9
i=
1
2
3
4
5
6
-0.037 -0.366*
0.072
P = 0.061
0.025 -0.1 12*-0.003
0.014
0.017
*significant with critical value I/.JN = .096
II. January 1973 December 1976
a) contemporaneous correlation p = -0.107
b) correlation between stock and M I i periods in the past
7
8
9
i=
I
2
3
4
5
6
0.054 -0.146* 0.058
P = -0.091 -0.060 -0.192 * 0.215 * 0.159* 0.190*
c) correlation between stock and M I i periods in the future
7
8
9
i=
I
2
3
4
5
6
0.095
0.092 -0.195*
P = -0.417* -0.061 -0.124 -0.049 -0.132 -0.095
* significant with critical value I/.JN = .144

-0.121

x2
11.67

10
-0.042

19.02

10
-0.195*

9.39

10
-0.050

x2
13.18

I I 1. Residuals from January 1975 - December 1976 based on anticipated money series constructed using
January 1973 - December 1976 M I data.
a) contemporaneous correlation p = -.368*
b) correlation between stock and M I i periods in the past
5
6
i=
I
2
3
4
x2
0.188
P=
-0.115
-0.169
-0.059
0.135
0.003
1.958
c) correlation between stock and M I i periods in the future
4
5
6
i=
I
2
3
x2
p=
-0.461 *
-0.086
-0.232
-0.135
0.163
7.648
0.012
* significant with critical value I/.JN = .209

BIBLIOGRAPHY
1. Ando, Albert "Some Aspects of Stabilization Policies, The
Monetarist Controversy, and the MPS Model," International
Economic Review, Vol. 15, no. 3, October, 1974.
2. Axilrod, Steven and Beck, Darwin "The Role of Projections
and Data Evaluation with Monetary Aggregates as Policy Targets," in Controlling the Monetary Aggregates II: The Implementation, Federal Reserve Bank of Boston, September 1972.
3. Burns, Arthur, Testimony before Joint Economic Commillee,
July 23, 1970.
4. Federal Open Market Commillee, Minutes of Federal Open
Market Committee, 1967, P. 1480, December 12, 1967
meeting.
5. Federal Open Market Commillee, Federal Reserve Bulletin,
Vol. 63, no. 2, February 1977, pp. 138-139.
6. Friedman, Benjamin "Targets, Instruments and Indicators of
Monetary Policy," Journal of Monetary Economics, 1(1975), p.
443-473.

7. Keran, Michael "Expectations, Money, and the Stock Market," Review of the Federal Reserve Bank of SI. Louis, vol. 53,
no. 1, January, 1971, pp. 16-31.
8. Meek, Paul "Nonborrowed Reserves or the Federal Funds
Rate as Desk Targets -- Is There a Difference?" New England
Economic Review. March/ April 1975.
9. Monetary Policy Oversight, Hearings before Committee on
Banking, Housing and Urban Affairs, United States Senate,
February 25-26, 1975.
10. Pierce, James "Why the Fed Keeps Missing Its Monetary
Targets," Fortune Magazine, March 27, 1978.
1 L Poole, William "The Making of Monetary Policy: Descripiion
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1975.
12. _ _ , Rational Expectations in the Macro Model," Brookings Papers on Economic Activity, vol. 2, 1976, pp. 463·505.
13. Rogalski, Richard and Vinso, Joseph "Stock Returns, the
Money Supply and the Direction of Causality," The Journal of
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Full text of Economic Review (Federal Reserve Bank of San Francisco) : Spring 1978 : Information and Market Efficiency

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