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FREDERIC S. MISHKIN
Universityof Chicago
Eicient-MarketsTheoryv
Implications for
Monetary Policy
EXPECTATIONShave come to the forefront in recent discussions of
macroeconomicpolicy. The theoryof rationalexpectations,initiallyde-
veloped by Muth,
asserts that both firms and individuals,as rational
agents, have expectationsthat will not differsignificantlyfrom
optimal
forecastsmade using all availableinformation.When rationalexpecta-
tions are imposedon macroeconomicmodels,some startlingobservations
emerge.Lucasfindsthat changesin policy affectthe parametersof many
behavioralrelations;thusthe use of currenteconometricmodelsto project
effects
of macro policy
can be misleading.'
Rational expectations,to-
getherwith the
"naturalrate hypothesis"of Friedmanand Phelps, lend
supportto the propositionthat a deterministicmonetarypolicy has no
effect on the outputof the economy.In these models only unanticipated
Note: I thank Andrew B. Abel, Dennis W. Carlton, Eugene F. Fama, Nicholas J.
Gonedes, Robert E. Lucas, Jr., Donald N. McClosky, Michael Mussa, A. R. Nobay,
Steven M. Sheffrin,Robert J. Shiller, and members of the Brookingspanel
for their
helpful comments. I also appreciate
the help
of Lawrence Fisher, who offered data
on long-term government bonds as well as advice, and Stephen Grubaugh, who
provided competent research assistance. This article benefited from comments made
at the Finance
and Money Workshops at the University of Chicago and the Money
Workshops at Harvard and Northwestern universities. The research has been sup-
ported in part by
the Social Science Research Council.
- Robert E. Lucas, Jr., "Econometric Policy Evaluation: A Critique,"in Karl
Brunnerand Allan H. Meltzer, eds., The Phillips Curve and Labor Markets, Carne-
gie-Rochester Conference Series
on Public Policy, vol.
1 (Amsterdam: North-
Holland, 1976), pp. 19-46.
0007430317810003-0707$00.2510C BrookingsInstitution
708 BrookingsPaperson EconomicActivity,3:
monetarypolicy affectsoutput, and there is some empiricalsupportfor
this proposition.
Several major objectionshave been raised against
rational expecta-
tions theory. The cost of obtainingand analyzinginformationmay be
quite high for many agents in the economy, and their use of rules of
thumbto formexpectationsin decisionmakingmightwell be appropriate,
even thoughthese expectationswould not be quite "rational."3In addi-
tion, the implicationsof certainrational-expectationsmodels-in particu-
lar, the so-called equilibriummodels of the businesscycle that include
both the naturalrate hypothesisand rational expectations-have been
criticizedas beinghighlyunrealistic.It has been arguedthatthesemodels
cannot explainthe persistenceof unemployment,and they are therefore
an inaccurate guide to the effects of policy.
Although
the existenceof rationalexpectationsin all marketsin the
economycanbe questioned,it seemssensiblethatbehaviorin speculative-
auctionmarkets,such as those in which bonds and commonstocks
are
traded,would reflectavailableinformation.As is discussedbelow, plau-
sible and less stringentconditionsare needed to demonstratethat, as a
useful approximationfor macroeconomicanalysis,bond and stock mar-
kets areefficient-that is, pricesin thesemarketsfully reflectavailablein-
formation.
When this concept is tested on bond and stock markets,as
Fama's survey
in support
of the efficient-marketstheory states, "con-
tradictoryevidenceis sparse."
Efficient-marketstheory has major implicationsfor the econometric
evaluationof policy
as well as for macro forecastingmethodology.6In-
- See Thomas J. Sargent and Neil Wallace, "'Rational' Expectations,the Opti-
mal
Monetary Instrument,and the Optimal Money Supply Rule," Journal of Politi-
cal Economy, vol. 83 (April 1975), pp. 241-54,
and Robert J. Barro,
"Unanticipated
Money
Growth and Unemployment in the United States,"American Economic Re-
view, vol. 67 (March 1977), pp. 101-15.
- See William Poole, "Rational Expectations in the Macro Model,"
BPEA,
2: 1976, pp.
463-505, and Robert J. Shiller, "RationalExpectationsand the Dynamic
Structure
of Macroeconomic Models: A Critical Review," Journal of
Monetary
Economics, vol. 4 (January 1978), pp.
1-44.
- Franco Modigliani, "The Monetarist Controversy or, Should We Forsake
Stabilization Policies?" American Economic Review, vol.
67 (March 1977), pp.
1-19.
- Eugene F. Fama, "EfficientCapital Markets:
A Review of Theory and Em-
pirical Work,"Journalof Finance, vol. 25 (May
1970), p. 417.
Poole
discussed some of these implications in his "Rational Expectations in
the Macro Model"; this paper extends some of Poole's analysis.
710 BrookingsPaperson Economic Activity,
3:
libriumexpected return
(or "normal"return), R*, is viewed as deter-
minedby factorslike risk
and the covarianceof Rt
with the overal mar-
ket return,the abovepropositioncan be statedin a slightlydifferent
way.
Efficient-marketstheory
impliesthat no unexploitedprofitopportunities
will exist in securitiesmarkets:at today'sprice,
market participants
can-
not expectto earna higherthannormalreturnby investing
in thatsecurity.
One important
attributeof the theory embodiedin 2 is that not all
participantsin the securities
marketshave to use informationefficiently.
Some marketparticipantscould even
be irrationalwithoutinvalidating
marketefficiency.
Equation
2 is analogousto an arbitragecondition.Arbitrageurs
who
arewilling
to speculatemayperceiveunexploitedprofitopportunities
and
purchaseor sell
securitiesuntil the price is drivento the point where
holds approximately.9Several
costs involvedin speculatingcould drivea
wedgebetweenthe left- and right-handsides of
Because
the collection
of information
is not costless, arbitrageurswould have to be compen-
satedfor thatcost and
othersincurredin theiractivities,as well as for the
risk they bear. Transactionand storage costs
would also affect 2. Yet
securities
have the key featureof homogeneity,for they are merelypaper
claims to income
on real assets. Transactionsand holding costs should
thus be negligible,while compensation
of arbitrageursand the cost of
informationcollection (especially
for the data on interestrates analyzed
here)
shouldbe quitesmallrelativeto the total valueof securities
traded.
Therefore,
the efficient-marketstheory of 2 is a close approximation
to
realityand could
be extremelyusefulin macroeconomicanalysis.
- An example
can be found in the capital-asset-pricingmodel of Sharpe
and
Lintner
discussedin Fama, "EfficientCapital Markets."
- Depending on the arbitrage condition,
2 may not always hold exactly. In-
deed, as Sanford
J. Grossman and Joseph E. Stiglitz have pointed out,
if 2 held
exactly, efficient-marketstheory would imply
a paradox.
See "Information and
Competitive
Price Systems,"American Economic Review, vol. 66 (May
1976), pp.
246-53. If all information were fully
reflected in a market according to 2, obtaining
information would have zero return. Thus the market
would not be able to reflect
this information
because it would be uncollected and hence unknown. The Gross-
man and Stiglitz argument does not, however,
deny the usefulness of efficient-
markets
theory for macroeconomic analysis. Even though their argument
implies
that information collection
must be compensated, the difference between the right-
and
left-hand sides of 2 would be negligible if the cost of collecting
a piece
of infor-
mation were small,
as it is for the data on interest rates discussed in this article.
FredericS. Mishkin 711
MARTINGALE IMPLICATIONS
Whetherthere are significant
correlationsbetween past information
andcurrentchangesin securitiespricesis the crucialissuein the empirical
tests and analysisof this article.The martingalemodel,whichis a special
case
of efficient-markets theory,
leads to hypotheses
about these corre-
lations.
Equation 2 impliesthat, if the excess return,R- R", is regressedon
any past availableinformation, 5t-l,
the coefficientson this past informa-
tion should be zero. A commonassumptionin tests of marketefficiency
is thatthe equilibriumreturn,R*,
is constantover time.
This thenimplies
that thereis no correlationbetweenthe actualretur, Rt,
andpast infor-
mation,
#t-,
If
0t-l
is takento be past returnson the security-that is,
0t-l
=
Rt-,
or Rt2,
and so
on-no serial correlation
of one-periodreturnsshouldbe
found. This
is the basic martingaleresult.
On the other hand, if
cP-,
in-
cludes variablesthat describeother informationthat was publiclyavail-
able in the past (or linearcombinationsof them), the generalresultis that
returnsare uncorrelatedwiththese variables,even thoughthey aregener-
ated outsidethe marketfor the security
in question.
In Fama'sterminol-
ogy,
tests of the serial correlationof returnsare "weakform" tests;tests
of the more generalproposition
are "semi-strongform"tests.
An examplemightclarifythe intuitionbehindthesemartingaleresults.
Assumethat the returnfor a securityover the comingperiodis positively
correlatedwith the volume of tradingin that securityat the beginningof
the period. Then if the tradingvolume were high today, a returnthat is
higherthan normalfor this securitywould be expected over the subse-
quentperiod.This implies a contradictionbecausean unexploitedprofit
opportunitywould now exist. Efficient-marketstheory indicatesthat in
this case the security
would have been immediately
bid up
in price until
the expected
returnwas equal
to the normal return,
and the positivecor-
relation between past trading
volume and the return from this security
would have disappeared.
One crucialpoint is centralto an understanding
of much of the
em-
pirical literatureon efficientmarkets.Even if the equilibriumreturn,
R*, is not constantover time, so long as its variationis small relativeto
other sourcesof variationsin returns,the correlationof Rt
and t
will
FredericS. Mishkin 713
modem, structuralmacroeconometricmodels view
monetarypolicy as
affectingaggregatedemand primarilythroughits effects on long-term
bond and stock markets. Incorporatingthe implicationsof efficient-
marketstheory into these models is thus crucialto an understandingof
monetarypolicy
and the formulationof appropriateprescriptionsfor
stabilizationpolicy.
Efficient-MarketsTheoryandtheTermStructureof InterestRates
Monetarytransmissionmechanismsfound in the literature,especially
those of structuralmacroeconometricmodels, focus primarilyon the
effects of monetary policy that operate through long-term securities
markets.
Most traditionalmechanismsin structuralmacro models emphasize
the effects of monetarypolicy on long-terminterest rates and on the
cost of capital.Changesin the latteralterspendingfor both businessand
consumerinvestment.Variantsof the cost-of-capitalapproachalso stress
the effects of the stock market on investment,either directly through
changesin the cost of capital,or throughthe ratio of the value of capital
to its replacementcost, the Tobin-Brainardq ratio. The stock marketis
also cited as a factor in consumerexpendituresthroughits effects on
wealth and the compositionof the householdbalancesheet.
The effect of credit availabilityon residentialhousingis the one sig-
nificant monetary transmissionmechanismthat does
not operate pri-
marily throughlong-termsecuritiesmarkets.Savingflows into and out
of institutionsissuingmortgagesare viewedas importantdeterminantsof
the residentialhousingcycle. Recentwork,however,findsthatthe effects
of creditavailabilityare
not as clear-cutas was previouslythought,espe-
- A more extensive survey of the literatureon monetary transmissionappears
in Frederic S. Mishkin, "EfficientMarkets Theory: Its Implications for Monetary
Policy," report 7809 (University of Chicago, Center for Mathematical Studies in
Business and Economics, February 1978). References to research on the monetary
transmissionmechanisms discussed here can be found in this working paper. Other
recent surveys are W. C. Brainardand R. N. Cooper, "EmpiricalMonetary Macro-
economics: What Have We Learned in the Last 25 Years?" American Economic
Review, vol. 65 (May 1975), pp. 167-75, and Franco Modigliani, "The Channels of
Monetary Policy
in the Federal Reserve-MIT-Universityof Pennsylvania Econo-
metric Model of the United States," in G. A. Renton, ed., Modelling the Economy
(Heinemann Educational Books for the Social Science Research Council, 1975),
pp. 240-67.
714 BrookingsPaperson Economic
Activity,3:
cially for single-familyhousing.In any case, the literatureon monetary
transmissionindicatesthatbehaviorin long-termbond andstockmarkets
is criticalto the
propertiesof macroeconomicmodels. The implications
of efficient-marketstheoryfor behaviorin these marketsshould thus be
examinedcarefully.
The link betweenmonetarypolicy andlong-termbond ratesand stock
prices in structuralmacroeconometricmodels can be characterizedas
follows. An actionby the FederalReserve,such
as a changein the dis-
count rate or unborrowedreserves,leads to a change in short-termin-
terest rates, usually throughsome kind of money-demandrelationship.
Changes
in short-term rates
are then linkedto long-termratesthrougha
term-structureequationin which the long-termrate respondsto a long
distributedlag on currentand past short-termrates.14In models with a
stockmarketsector (such as the MPSmodel), long-termratesthenaffect
the value of stocks
with a distributed lag.
The previous discussionof efficient-marketstheory leads to doubts
about the appropriatenessof these term-structureequations.First, it is
disturbingthat these equationsallow the predictionof changesin long-
term rates and stock prices from publicly availableinformationin the
past (in particular,interestrates). Second,the use of these equationsin
the contextof policy
evaluationis suspicious
because expectations
about
changesin policy have no role
in these equations.
I
now turn to a more
detaileddiscussionof the problemsthat arisein theseequations.
THE TERM-STRUCTURE EQUATION
The typicalequationlinkingshort-andlong-termratesis derivedfrom
the expectationshypothesis
of the termstructure.Let RL7 be the yield to
maturity
of an n-period
discountbond at time t,
and let rt be the one-
period short-term
rate at time t. Assume that there is a positive
but
constant liquidity premiumequal
to k. Using
the approximation
that
ln(1 + rt)
= rt, the expectationshypothesiscanbe characterizedby
RLt
k
(-n)
Et(rt
rt+,-),
- This is modeled either with the long-term rate regressed directly on current
and past
short-termrates or with a Koyck-typelag
mechanismin which the long-term
rate is regressed
on the current short-termrate and the long-term rate is lagged one
period.
716 BrookingsPaperson EconomicActivity,3:
and becausert+2 = rt+
ut+2 -XUl
(8) Et(rt+2) Et(rt+,)
t
More
generally,
(9) Ej(r1+j)
=
Et(rt+i)
-1- , rs
for i = 1, 2, 3, 4,.
Substituting
9 into equation
yields
(10) RL
=
k+ Irt+ (n-i) (?Lr)l
nr
n- I- X\
= k+ -t+
n
(? r'
n nl \I-A
or, equivalently,
n
+rt
+n -ic
(I 1)
RLt = k + n
E
X.irt,;.
n n
i_
A compelling
reason for the additionof an errortermis that market
participantshave informationon othervariablesbesides
currentand past
short-termrates. Thus, based on this information,their expectationof
futureu may not be
zero. The long-term
bond rate,RL', will reflectthese
expectationsand will fluctuatearoundthe
values given by 11 as
new in-
formationon these variablesis receivedby the market.In addition,an
errorterm, et,
should be added to 11 to alow for possible
shifts in the
liquiditypremium.17Thus
rt n-i
RL
n
ir,_. + et
n
n
Equation12,
whichuses a distributed lag
on currentandpast variables
to reflectexpectations,
can be used in empirical
workto provide
valuable
information.
For example,
estimatesof equations
like 12 strongly
indi-
cate that movements
in long-term
rates are heavily
influenced by
move-
ments in
short-termrates. However,
even though
these term-structure
equations
are useful as a summary
of average
historical experience
dur-
- This discussion does not imply
that eg is serially
uncorrelated.It is entirely
conceivable
that information on other variables relevant to expectationsof future u
is serially
correlated.Thus etmight
also be serially
correlated.
FredericS. Mishkin 717
ing the sample period, they can be viewed as structuralequationsonly
underextremely
restrictiveand highlyimplausibleassumptions.In terms
of the equationsystemabove,Xwouldhave to be an unvarying
structural
parameterbecausethe distributedlag coefficientsof rt will
be alteredby
any changein X, which reflectsthe time-seriesprocess of the short-term
rate.For example,
with a largerX,the shockto the short-termrateis less
persistentover time and the distributedlag
weighton the currentshort-
termrate is smaller,while the lag weights
on short-termrates furtherin
the past would be correspondinglyhigher.If X is close
to zero,
the time-
series processbecomessimilarto a randomwalk, and the weighton
the
currentshort-termrate approachesone, while past short-termrateshave
little
importance.In effect,X can be unvaryingonly if marketparticipants
assignedto every surprise
in short-termrates the same degree of per-
sistence (or samerate of decay) in the future,regardless
of any informa-
tion they had aboutthe sourceand significanceof the disturbance.
Realistically,changesin expectationsof policy ruleswould alterX and
hence the distributedlag weights
of 12. For example,if FederalReserve
policy were expectedto resultin a permanentloweringof
the short-term
rate by 100 basispoints, equation 3 would not predicta slow adjustment
while 12 could do so."
In policy
evaluation or forecasting, the estimated distributedlag
weightsof term-structure
equationsare assumedto be constantregardless
of whatpolicy changeis being evaluated
or anticipated.
Yet, as shouldbe
clearfromthe aboveexample,the invarianceof
the weights
is a dangerous
assumption.
The example
also can be used to clarifyinterpretationsof the impor-
tant work on the term structureby Modiglianiand Shiller.
They indi-
cate that,if expectationsare"rational,"an estimatedterm-structureequa-
tion should have coefficientsthat are consistent with the time-series
behaviorof variablessuch as short-termrates. This is equivalent,in the
above example,
to findingthat the X estimatedin 12 is no differentfrom
the Xof 5.
Their finding
that this conditionis met andthatthe termstruc-
tureis rational
does not imply,however,
that such a term-structureequa-
tion is invariantto policychanges
and can
be used as a structuralequation
- The point raised here is similar to that made by Lucas in his consumption
example describedin "EconometricPolicy Evaluation."
- Modigliani and Shiller, "Inflation, Rational Expectations, and the Term
Structureof Interest
Rates."
FredericS. Mishkin 719
would be a normal returnfor a security
with the risk characteristics of
long-termbonds-that is, there should be no unexploitedprofitoppor-
tunities.Givenreasonable measuresof Et(r
+1), it is unlikelythatthis effi-
cient-marketsconstraintwould be satisfiedbecause forecasts using an
equationsuch as 4 do not use all availablerelevantinformation.In gen-
eratingforecasts,the marketwill use informationfromdistributed lags of
past variables,and it will also be concernedwith subjectiveinformation,
such as whetheror not the mood in Congressis to pursueexpansionary
fiscal policy. As was discussed above, the existence of error terms in
equationssuch as 4 and 12 implies that past informationbesides short-
term rates is importantto expectationsof futureshort-termrates. Thus
when 4 is used to forecast RL" , it does not exploit informationem-
bodied in RLt, whichin an efficientmarketreflectsall availableinforma-
tion. The resultingforecastof RL7+1is less than optimalwhen compared
with RL' and will probablyimply the existenceof an unexploitedprofit
opportunity.
To ascertainhow seriousa violationof marketefficiencyis impliedby
one-periodforecasts with equationssuch as 4, a numberof experiments
have been conductedthat are akin to simulationexperiments.These are
not intendedto settle the issue of whetherfinancialmarketsare efficient,
but ratherto illustratethe propertiesof term-structureequationslike 4.
Using term-structureequations estimatedover several sample periods,
along with several measuresof Et
(rt+i), the implied,expectedquarterly
returnswere calculatedfor the mostrecentfive-yearperiodfor whichdata
are available.In the interestof conservingspace, only one experimentis
discussed below. (Other experimentsare discussedin note 32.) The re-
sults discussedin the text are by no means atypical,and, if anything,of
the results I explored,these tend to be among the least unfavorableto
term-structureequationsof the formof 4.
Modiglianiand Sutch23 have estimateda term-structure equation in
which the long-termgovernmentbond rate is a seventeen-quarterdis-
tributedlag on currentand past 90-day treasurybill rates,with the coeffi-
cients of past bill rates lying on a fourth-orderpolynomialwith an end-
point constraint.In the example discussedhere, this equationhas been
- In a similar way, simulation experiments with macroeconometric models
only illustrate the propertiesof these models and do not settle the question of what
the true structureof the economy is.
- Modigliani and Sutch, "Innovations"and "Debt Management."
720 BrookingsPaperson Economic Activity,3:
reestimatedover the 1964-76 period,24using the same polynomiallag
constraintsas Modiglianiand Sutchand a correctionfor first-orderserial
correlation.The governmentbond seriesuses yields fromtaxablegovern-
ment bonds callablein ten yearsor more,with bondschosenso that tax-
induceddistortionsfromcapitalgainsandestateprivilegesareminimized.
Both the bondyieldsandthetreasurybillratesareend-of-quarterfigures.
The reestimatedterm-structureequationusing ordinaryleast squares
is as follows, with the coefficienton
aut-
equal to the first-order serial
correlationcoefficient;standard errorsare in parenthesesas is the case
throughoutthe article.All interestrate variablesare expressedin frac-
tions-that is, a 6 percentyieldis 0.06.
(15) RGOVt
RTBt
16
Et
16
b = 0.9444,
R2 = 0.9450; Durbin-Watson= 2.12; standarderror = 0.0033;
where
RGOVt
= long-termgovernmentbond yield,end of quarter
RTBt
= treasurybill rate at end of quarter.
At first glance,
the term-structure equationlooks quite satisfactory.
The fit is good-the percentageof varianceexplainedis high and the
- The 1964-76 sample period has been used for all my empirical tests because
the need for forward rates in some of the empirical work requires that the sample
period begin no earlier than 1964. Whenever possible, I also conducted empirical
tests on the longer sample period from 1954-76. (Some of the results from the
longer sample period are reportedin the notes.)
- Lawrence Fisher supplied me with these bond data, which also include the
returns from holding these bonds. The data are described in Lawrence Fisher and
James H. Lorie, A Half Century of Returns on Stocks and Bonds: Rates of Return
on Investmentsin Common Stock and on U.S. TreasurySecurities,1926-1976 (Uni-
versity of Chicago, GraduateSchool of Business, 1977). The Board of Governorsof
the Federal Reserve System supplied me with the data
on prime commercial paper
and the 90-day treasurybill market yield for the last tradingday of the quarteron a
discount basis.
722 BrookingsPapers on EconomicActivity,3:
tationsfrom realizationsshouldbe seriallyuncorrelated.If this were not
the case, the expectationsmeasurecould clearlybe made more accurate
by using this informationon serial correlation,and this measurecould
not representexpectationsin an efficientmarket.Box and Pierce have
suggesteda so-calledQ statisticto test for serialcorrelation.28They find
that,for anunfilteredseries,
K
Q(K
=
T E rk,
k-I
where
T
= number of observations
Pk
= correlationbetweenthe seriesand its value
k
periods
earlier.
This Q(K)is distributed approximatelyas X2(K)underthe hypothesisHo
that
rl P2 =*** Pk-=.
For RTBt
over the 1964-76 period, Q(12) = 8.7 and Q(24)
= 22.0, while the critical Q
at 5 percentare 21.
and 36.4, respectively.
Thus the hypothesisthat the firsttwelve or twenty-fourautocorrelations
are zero cannot be rejected,and the forward-ratemeasurefor expecta-
tions meetsthe criterionimpliedby marketefficiency.
An alternativemeasureof expectationscan be obtainedfromthe time-
series process of the treasury
bill rate. Using
Box-Jenkinsidentification
procedures,an autoregressivemodel was estimatedover the 1964-
period29as
(19) RTBt
= 0.0096 + 0. RTBt&
RTBt,
RTBt..
Durbin-Watson
= 1.82.
- G. E. P. Box and David
A. Pierce, "Distribution
of Residual Autocorrela-
tions in Autoregressive-Integrated
Moving Average Time Series Models," Journal
of the American Statistical Association, vol. 65 (December 1970), pp. 1509-26.
The
Q-statisticsbelow were derived using Charles R. Nelson's ESTIMATE program.
- Significantheteroscedasticitywas present in the regression,so it is estimated
here with weighted least squares, using a proceduresimilar to that outlined below.
FredericS. Mishkin 723
Takingexpectationsof both sides of 19 yields an autoregressivemea-
sureof
E,(RTB
+,), whichis
ERARt+i
0.0096 + 0.7859 RTBt
RTBt&2-
RTBt4.
The Q(12) statisticfor
RTB,
is distributedas X2(9). For the
1964-76 periodit is 6.7, while the criticalQ at the 5 percentlevel is 16.9.
Furthermore,Q(24) = 10.7, whilethe criticalQ at 5 percentequals32.7.
Thus thereis no evidenceof serialcorrelationin the forecasterrors.
Based on 16 and either of the two measuresof E
(RTB,+,),
implied
one-periodquarterlyreturnsfrom holdinga long-termgovernmentbond
have been calculatedfor the 1972-76 period.Because these government
bonds are not consols, a formula more complicatedthan 14 generates
these returns,usinginformationon the maturitydate of each bond.
The implied expected returnsfrom 15, the term-structureequation
(shown
in table 1), illustratehow forecastsfromthis type of equationare
inconsistentwith marketefficiency.3'The impliedexpectedreturnsfluc-
tuate substantiallyand the violationof efficientmarketsis severebecause
it is quite implausiblethat normal returnsfor long-termbonds would
equal the implied returnsof table 1. Using either measureof expected
RTB, the quarterlyreturnson governmentbonds were 20 percent or
higherat an annualrate at the end of 1976, well above what can be con-
sidereda normalrate of returnfor this type of security.Expectedlosses
in nominaltermsappearfor somequartersof 1973 and 1974, but nominal
- The measure of autoregressive expectations suffers from the same problem
that arises for term-structureequations such as 4: the coefficients in the equation
are not invariant to a change in policy regime. The time-seriesprocess of the short-
term rate thus might change over time, and ERARt
might at times be a poor measure
of expectations. ERARt
also suffers from the disadvantage that it restricts itself to
information on past short-term rates, while the market may use other information
in generating its expectations.However, ERARt
is used in the above experimentbe-
cause it also shows that implied expected returnsfrom equation 15 are inconsistent
with market efficiency according to a number of expectations measures.
- Because of the way bond-pricing conventions reflect bond coupon payment,
there are some subtle technical issues in calculating bond returns that have been
allowed for in Fisher's data on bond returnsand in the calculations found here. The
Fisher series uses the average of
bid and asked prices in calculating returns, and
transactionscosts are not included in his calculations of quarterlybond returns.
Frederic S. Mishkin 725
returnscould never be negativewith the existenceof money,
a risk-free
assetwith a nonnegative return.
In summary,a typical term-structureequationis theoreticallyan in-
adequatestructuralequationin a macro model. More direct empirical
tests follow, which indicate that past information,
such as that used in
term-structure equations,is not particularlyhelpfulin predictingchanges
in long-term ratesor stock prices.This providesfurtherevidencethat the
use of theseterm-structureequationsshouldbe abandoned.
Testsof Efficient-MarketsTheoryfor BondandStockMarkets
The tests of marketefficiencyconductedin this section use quarterly
returnsfor the long-termgovernmentbonds discussed above and the
quarterly,value-weightedstock returnsof New York Stock Exchange
stocks compiled by the Universityof Chicago, Centerfor Researchin
SecurityPrices.33These returnsareexpressedin fractions.Otherinforma-
tion includes data on treasurybills and forwardrates discussedabove
and on the Moody'sAaa corporatebond rate.Because misleadingresults
can be obtainedfrom tests
with averageddata, all informationon security
- Using the same estimation proceduresas in 15, implied quarterlyreturnsfor
1972-76 analogous to those in table 1 are as follows:
Period of Serial
Equation estimation correlation Range (percent)
1 1964-76 Uncorrected -10.6 to 29.
2 1954-76 Corrected -3.6 to 23.
3 1954-76 Uncorrected -6. to 34.
4 1964-71 Corrected -51.4 to 178.
5 1954-71 Corrected -3.3 to 35.
The sum of the coefficientson the treasury
bill rates in these equations ranges from
0.99 to 1.31. All the term-structureequations discussedin this note are characterized
by
the same difficultiesas equation 15.
In the 1964-76 sample period, a change of
11 basis points in the long-term gov-
ernment bond rate correspondsto a 4 percentage point movement in the quarterly
bond return at an annual rate. Thus if the equilibriumreturnfor these bonds is taken
to be close to the return on 90-day bills, table 1 indicates that the long-term bond
rate predicted by 15 never differed from the efficient-marketsprediction for bond
yields by
more than 60 basis points.
Quarterly
stock returns have been computed for these data from the value-
weighted,monthly returns, with dividendsreinvested.
726 BrookingsPaperson EconomicActivity,3:
pricesis takenat a particularpoint in time." The bond and stock returns
are calculatedfrom securityprices at the beginningand the end of the
quarter.All tests are carriedout on the 1964-76 sampleperiod. (Addi-
tionaltestson longersampleperiods,whenthiswaspossible,arediscussed
in the notes.)
Particularattentionmustbe paid to possibleheteroscedasticityin these
tests.Heteroscedasticitydoes not lead to inconsistentparameterestimates,
but it does lead to inconsistenttest statistics.Because the test statistics
are of primaryinterest in the empiricalwork below, correctionsfor
heteroscedasticityaremadeif necessary.
Two types of efficient-markettests are conducted.Weak-formtests
analyzewhetherone-periodlong-termbond or stock returnsare serially
uncorrelated-the implicationof the martingalemodelof the firstsection.
Both the Q(K) statistic,whichjointlytestswhetherthe firstK autocorre-
lationsarezero, andtest statisticson individualautocorrelationsareused.
For semistrongform tests, the efficient-marketsmodel can be charac-
terizedby the followinglinearequation:
(21) Rs
R* +
#(Xt-Xt) + et,
where
e
= expected values conditional on all past publicly available
information
Rt = one-periodreturnon a securityfor the periodt - I to t
R*= equilibrium return
Xt
= a variable(or vectorof variables)relevant
to the pricingof the
security
for the period
t - 1 to t
= coefficient(or vectorof coefficients)
= white-noiseerror process.
The returnsin this equationdeviatefromthe equilibriumreturn only
when
newinformationis receivedby the market-that is, whenthereis a surprise,
Xt- X 0. Marketefficiencyimplies,therefore,that in a regression
equationof the form
N
(22) Rt= Rt
+ 3(X. -
Xe)
ED7$(Xg,
i-i
For example, security prices averaged over a quarterwill not follow a ran-
dom walk even though the price series can be characterizedas a random walk. See
Holbrook Working, "Note on the Correlationof First Differences of Averages in a
Random Chain,"Econometrica, vol. 28 (October 1960), pp. 916-18.
