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March 1982
Vol. 64, No. 3

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3 Monetary Policy and Stock Returns:
Are Stock Markets Efficient?

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13 Monetary Policy and Short-Term Real
Rates of Interest
20 Central Banks’ Demand for Foreign Reserves
Under Fixed and Floating Exchange Rates

The Review is published 10 times per year by the Research Department o f the Federal Reserve
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Monetary Policy and Stock Returns:
Are Stock Markets Efficient?
LAWRENCE S. DAVIDSON and RICHARD T. FROYEN
.^ ^ .N efficient m arket is one that quickly processes
all relevant information. For exam ple, if m onetary
policy affects stock returns, then an efficient stock
m arket rapidly digests and incorporates all news
about m onetary policy. C onsequently, past policy
actions will have little value or explanatory pow er in
understanding current stock returns. Previous tests
of stock m arket efficiency have exam ined the rela
tionship betw een the tim ing of the growth of money
and stock returns. Although several early studies
found th at stock returns lagged b eh in d m oney
growth — evidence of stock m arket inefficiency —
the results of recent studies have supported the
efficient m arket hypothesis .1
The purpose of this article is to provide further
evidence on the tim ing of the relationship betw een
m onetary policy changes and stock returns by esti
m ating m odels that express stock returns as func
tions of anticipated and unanticipated m onetary
policy m easures. T hese m odels extend previous
work in several directions. First, past studies gen

erally have divided m oney growth into anticipated
and unanticipated com ponents in a m echanical or ad
hoc fashion .2 We com pare these results with esti
m ates of anticipated m oney growth m easured by the
fitted values of previously estim ated m onetary
policy reaction functions. This enables us to d eter
m ine w h eth er the efficient m arket findings are
robust across differing aggregates and decom po
sitions of m onetary policy into anticipated and un
anticipated com ponents.
Second, previous studies focused on the rela
tionship betw een m oney growth rates and stock
returns. But, during m uch of the period covered by
th ese studies, the F ed eral R eserv e’s short-run
(month-to-month) operating target was the federal
funds rate. Therefore, in addition to estim ating rela
tionships betw een stock returns and m oney growth
rates, we estim ate m odels relating stock returns and
both anticipated and unanticipated m onetary policy
actions using the federal funds rate. Again, antici
pated and unanticipated policy actions will be de-

Lawrence S. Davidson, an associate professor of business eco
nomics and public policy at Indiana University, is a visiting
scholar at the Federal Reserve Bank of St. Louis. Richard T.
Froyen is an associate professor of economics at the University of
North Carolina.
1Examples of studies that indicated a lag in the adjustment of stock
returns to changes in m oney growth rates are: M ichael J.
Hamburger and Levis A. Kochin, “Money and Stock Prices: The
Channels of Influence,” Journal o f Finance (Decem ber 1971),
pp. 1045-66; Michael W. Keran, “ Expectations, Money, and the
Stock Market,” this Review (January 1971), pp. 16-31; and Beryl
W. Sprinkel, Money and Stock Prices (Richard D. Irwin, Inc.,
1964). Recent studies that support the market efficiency pos
tulate include: Michael S. Rozeff, “ Money and Stock Prices:
Market Efficiency and the Lag in Effect of Monetary Policy,”
Journal of Financial Economics (September 1974), pp. 245-302;
John Kraft and Arthur Kraft, “Determinants of Common Stock

Prices: A Time Series Analysis,"Journal of Finance (May 1977),
pp. 417-25, and “Common Stock Prices: Some Observations,”
Southern Economic Journal (January 1977), pp. 1365-67; R. V. L.
Cooper, “Efficient Capital Markets and the Quantity Theory of
Money,” Journal o f Finance (June 1974), pp. 887-908; Richard J.
Rogalski and Joseph D. Vinso, “Stock Returns, Money Supply
and the Direction ofCausality, "Journal of Finance (September
1977), pp. 1017-30; James B. Kehr and David Leonard, “M one
tary Aggregates, the Stock Market and the Direction of Causal
ity. ” Journal o f the Midwest Finance Association (1980), pp.
47-57; and J. Ernest Tanner and John M. Trapani, “Can the
Quantity Theory be Used to Predict Stock Prices — Or Is the
Stock Market Efficient?” Southern Economic Journal (October
1977), pp. 261-70.
2Rozeff, “Money and Stock Prices,” for example, assumes that
anticipated money growth in a given month depends on money
growth in the past three months.

FEDERAL RESERVE BANK OF ST. LOUIS

rived from an em pirical reaction function in which
the federal funds rate is the d ependent variable.
Third, we extend the tim e period in earlier studies
through 1977. This allows us to exam ine the m one
tary policy/stock return relationship in both a period
o f low stable inflation (1954-65) and one of higher
and more variable inflation and m oney growth (196677).
Finally, for the period from 1974 through 1976, we
estim ate m odels that relate weekly stock returns to
the anticipated and unanticipated com ponents of
weekly m oney growth. Most previous work on this
topic used quarterly or m onthly data .3 Estim ates
w ith w eekly data provide a finer test of the efficient
m arket hypothesis.

DO STOCK RETURNS LAG OR
LEAD MONETARY POLICY?
Several recent studies of the relationship betw een
m oney growth rates and stock returns have found
that fu tu re m oney growth rates affect current stock
returns. Thus, stock returns appear to lead m oney
growth rates .4 O ther studies, however, do not find
such effects .5
T he finding that stock prices lead m oney growth
has been interpreted in several different ways. O ne
interpretation is that stock prices are a causal in
fluence on m oney growth. However, as Rozeff points
out, w ithin the general equilibrium setting of finan
cial markets, it is arbitrary to single out stock returns
as a causal variable .6 Rather, the evidence that future
m oney growth rates affect current returns m ay be a
reflection of the influence of other variables on both
stock prices and m oney growth, w ith stock prices
adjusting m ore quickly and, th erefo re, lead in g
m oney growth rates.
Another interesting interpretation of this finding is
provided by the “reversed causation with accurate
anticipations” m odel .7 In this m odel, causation runs
3One recent exception is Neil G. Berkman, “On the Significance
of Weekly Changes in M l,” New England Economic Review
(May/June 1978), pp. 5-22.
4See, for example, Rozeff, “ Money and Stock Prices;” Kraft and
Kraft, “Determ inants of Common Stock Prices;” and Rogalski
and Vinso, “Stock Returns, Money Supply and the Direction of
Causality.”
5See, for example, Kehr and Leonard, “ Monetary Aggregates, the
Stock Market and the Direction of Causality.”
6See Rozeff, “ Money and Stock Prices.”
7See Rozeff, “ Money and Stock Prices,” pp. 275-76.

MARCH 1982

from currently anticipated m oney growth to stock
returns. The apparent effect of future m oney growth
reflects the accurate anticipations of future m oney
growth by the market. It is theseaccurate predictions
of future m oney growth that affect current stock
returns.

SPECIFICATION OF THE MODELS
This section describes two sim ple m odels of
equity return determ ination. T obin’s theoretical
m odel of the financial sector stressed the im portance
of the return on capital as the link betw een the real
and financial sectors .8 His m odel established a po
tential causal connection betw een the exogenous
variables of the com m odities and financial markets
and the return on equities (ow nership claims on the
capital stock). The first of the two m odels presented
here is a sim ple version of T obin’s, originally esti
m ated by Rozeff .9 This m odel stressed the linkage
betw een m onetary aggregates and the equity return.
It im posed the additional restriction that only un
anticipated changes in the growth rate of m oney (gu)
cause unanticipated m ovem ents in the equity return

(Ru).

R ozeff s “predictive m onetary portfolio” m odel
relates the unanticipated current return on equities
(R“) to past u nan ticipated changes in m onetary
growth rates, that is,
(1) Rtu = f(gt1-l,...,gt1n-) + €„
w here R }1 is the unanticipated m ovem ent in the
equity return, defined as the actual return (Rt) m inus
the expected return conditioned on all available past
inform ation (E [R t/B t-i]). U n an ticip ated m oney
growth in period t-i, gt-i, is m easured as the change
in the m oney growth rate betw een t-i and t-i-1. The
error term , et, is assum ed to be a norm ally distrib
uted random variable w ith a m ean o f zero and
a constant, finite variance. Rozeff assum ed that the
expected value of the nom inal eq uity retu rn is
constant (E[Rt/Bt_i] = Co) and the m onthly em pirical
counterpart of the predictive m odel is:
16

(2) Rt = C 0 + 2 a; gi'j + e2t,
i= l
w here Co and ai are param eters to be estim ated.
8James Tobin, “A General Equilibrium Approach to Monetary
Theory,” Journal o f Money, Credit, and Banking (Februarv
1969),'pp. 15-29.
9See Rozeff, “Money and Stock Prices,” pp. 255-66.

FEDERAL RESERVE BANK OF ST. LOUIS

To evaluate the relative im portance of the m ost
recent m onetary information, Rozeff also estim ated
the nonpredictive m onetary portfolio m odel. In this
m odel, the contem poraneous m oney surprise is
added; the lag on the m onetary surprises starts at
zero instead of one:
16
(3) R, = C0 + 2 a; g"i + e3t.
i=o

A final variant of this model assum es that m arket
participants form expectations of future changes in
m onetary growth. If these expectations are at least
unbiased, then future m onetary growth rates would
cause changes in current equity returns. Rozeff’s
em pirical nonpredictive m onetary portfolio m odel
with anticipations adds eight leads (negative lags)
to equation 3 :10
16
(4) Rt = Co + 1 a; g“j + e4t.

i= - 8
To test w hether past inform ation about unex
pected m onetary growth influences current stock
returns, we exam ine the statistical significance of the
lagged unanticipated m oney growth terms in the
predictive m odel (equation 2). If the stock m arket is
efficient, the coefficients on the lagged term s should
be equal to zero ( a j = 0 , i = l,...,n). An F-test is used to
test this hypothesis; an F-value significantly greater
than 1.0 w ould suggest that the stock m arket was in
efficient, since past inform ation w ould affect current
stock returns.
On the other hand, a significant F-value for a
sim ilar test of the coefficients in the nonpredictive
m odels (equations 3 or 4) does not indicate m arket
inefficiency. The finding that only current m onetary
growth affects returns sim ply establishes the im por
tance of m onetary variables in equity return deter
m ination. If future, but not past, m oney growth
affects cu rren t returns, this suggests a forwardlooking propensity of the m arket w hich also is not
inconsistent w ith an efficient market.
The second m odel of equity returns considered
here is referred to as the Fam a approach .11 In this
10Future values of unanticipated money growth should not cause
current stock market returns to change. However, the exact
interpretation of gtu+i is not unambiguous. It could be rein
terpreted as the perfectly correct anticipated future change
in money growth. In that case, it would be an indicator of the
forward-looking propensity of the market.
“ This approach is set out in Eugene F. Fama, “Short-Term In
terest Rates as Predictors of Inflation,” American Economic
Review (June 1975), pp. 269-82.

MARCH 1982

m odel, the nom inal return on stocks (Rt) is assum ed
to be com posed of the real return (rt) and a prem ium
for expected inflation (7rt) — a Fisher effect for stock
returns:
(5) Rt = rt + TTt.

From equation 5, w e can write the expected value of
the nominal return conditioned on inform ation
available from period t-1 (Bt-i), as
(6) E(Rt/B,.1) = E(rt/Bt_i) + E(fft/Bt,1).

If we assum e a constant real m ean of stock returns
(c0), we can rew rite equation 6 as
(7) E(Rt/Bt.,) = c0 + E ^ /B n ).

Since E(Rt/Bt-i) is equal to the actual nom inal return
on stocks (Rt) minus its unanticipated com ponent
(Rt1), we can transform equation 7 into an expression
for the actual nominal stock return:
(8) Rt = c„ + Ri' + E(7rt/B,.1).

Equation 8 then can be converted into a rela
tionship betw een money growth and nom inal stock
returns if we express (as in equation 1) the unan
ticipated com ponent of stock returns as a function of
unanticipated changes in m oney growth and if, fur
ther, we express the expected inflation rate as a
function of expected m oney growth. W ith these as
sum ptions, our expression for nom inal stock returns
becom es
(9) Rt = c0 + f(g“, g“i,...,g“.ni)
+ h(gt*, gt*i,...,gt*.m2) + vt,

w here gt is the expected rate of growth of the m oney
stock, and h is the function relating expected m oney
growth to expected inflation. T he em pirical counter
part to equation 9 used in our estim ation is
ni
n2
(10) Rt = c0 + 2 b;
i=0

+ 2 d, g*,_j + vt,
j =0

w here various lag lengths and several different
m easures of anticipated and unanticipated m oney
growth are em ployed.
Additionally, one test uses the federal funds rate
rather than a m onetary aggregate as the m onetary
policy variable. The effects of this substitution on
the theoretical interpretation of ourm odels of equity
return are discussed below.
Using the Fam a (or Fisher) m odel of stock returns,
we can also test for m arket efficiency. M arket effi
ciency im plies that lagged unanticipated changes in
5

FEDERAL RESERVE BANK OF ST. LOUIS

money growth rates would not affect current stock
returns (bj = 0 for i > 0 in equation 10). In the Fam a
approach, however, lagged anticipated changes in
m oney growth rates m ight affect current stock re
turns through an effect on expected future inflation.
This result w ould not violate m arket efficiency; it
w ould sim ply be an elem ent of E(Rt/Bt-i) and would
not provide a basis for any profitable trading rules .12
This effect of anticipated m onetary policy on stock
returns is another channel by w hich m onetary policy
may affect stock prices — even in an efficient m arket
— an effect w e test for in the following section.

ESTIMATES OF THE MODELS

MARCH 1982

policy variables to last-day-of-the-m onth activity.
Changes in the average m onthly value w ould appear
to be the proper m easure of the shift in m onetary
policy from month to month. We relate this to the
cum ulative change in stock prices for the month.
This does m ean, how ever, that w hile the dependent
and independent variables pertain to the same tim e
period, they w eight daily observations w ithin the
tim e period differently. O ur tests w ith weekly data
therefore provide more intra-m onth precision.

Unanticipated Money Growth and Stock
Returns: Alternative Specifications o f the
Basic Models

Five sets of m odel estim ates are presented. In all
five, the m easure of the nom inal equity return is the
percentage change (m easured from the last business
day in each m onth or week) in the overall index of all
stock prices on the New York Stock Exchange .13
T hese tests em ploy a variety of m onetary policy
m easures .14 These include: 1) percentage changes in
actual, anticipated and unanticipated M l and the
m onetary base, and 2 ) anticipated and unanticipated
values of the federal funds rate.
The policy m easures in all the tests, except those
with w eekly data, are changes in average m onthly
values. Returns are changes betw een the last busi
ness day of each m onth. This specification relates the
cum ulative stock price change from the end of one
m onth to the next to the average month-to-month
change in the m onetary policy variable. As a result,
the stock return variable is m ore sensitive than the

The m odels in equations 2-4 specify that unan
ticipated m oney growth affects the unanticipated
stock return. Rozeff’s tests m ake the following two
explicit assum ptions:

12See Rozeff, “Money and Stock Prices,” p. 260.
13An alternative measure includes dividends, but because its
variance is so dom inated by stock price changes, it performs
almost identically to the index which contains only prices. This
alternative measure is not used in our tests.
14These measures of monetary policy each have limitations lor the
testing of the efficient market hypothesis. Tests of this hypoth
esis must distinguish betw een information which is currently
known and used by market participants and that which is not. In
fact, we do not know what information was available to and used
by these agents. In this research, we have limited the monetary
policy measures to those listed above. We have not tried narrow erorbroaderm easures of money like nonborrowed reserves
or M2, nor have we used seasonally unadjusted versions of M l
or the monetary base. Our tests have selectively em ployed both
revised and initially announced seasonally adjusted versions ol
M l. Since seasonally adjusted data are revised several times, it
would seem preferable to use the initially announced numbers
since those were the ones available to market participants.
Furtherm ore, Courtenay C. Stone and Jeffrey B. C. Olson, “Are
the Preliminary Week-to-Week Fluctuations in M l Biased?”
this Review (Decem ber 1978), pp. 13-20, have shown with

weekly data that the revised seasonally adjusted series is largely
independent of the unrevised series and therefore is a poor
proxy for that data. Our weekly aggregate tests, therefore, em
ploy the unrevised growth rates of seasonally adjusted M l.
This use of initially announced data is not without drawbacks.
For example, since initial announcements have been shown to
be unreliable indicators of how money is performing, market
participants may either ignore seasonally adjusted data or they
may modify it. One useful modification would discount the
announcem ent with what agents think is the true seasonal ad
justment. If they do this correctly, then they are using what turns
out to be the actual revisions. If they use seasonal adjustment
factors that are different from the true ones, they are using an
unobservable series. Our monthly aggregate tests use the re
vised, seasonally adjusted growth rates of M l.
The monetary reaction function tests do not rely totally upon
either revised or unrevised data. For example, the consumer
price index and the unemployment rate, which are used to
predict the monetary base, are not regularly revised. However,
the monetary base itself, like M l, is revised frequently. Finally,
the tests with the federal funds rate have no data revision prob
lems since this series is not revised.

i) Rtu = Rt - Cn, and
ii) gi1 = gt - gt-i-

The unanticipated return is a deviation from a m ean
(Rt - Co), w hile the unanticipated m oney growth rate
is a first difference (gt - gt-i). This section compares
the results based on these assum ptions w ith two
alternative specifications. T he first of these we call
the differenced model:
iii) R“ = Rt - R n,
iv) gi1 = gf- gt_i.

The second is called the m ean deviation model:

FEDERAL RESERVE BANK OF ST. LOUIS

MARCH 1982

Table 1
Sum m ary Statistics for Lead-Lag M oney Growth (g) and Equity Return (R) M odels1
_______________1 9 5 4 — 1 965______________ _____

Lag (lead)
M od e l

s p e c ific a tio n

M ixed
2
3
4

16 to 1
16 to 0
16 to (9)

D iffe re n c e d
2
3
4
M ean D e via tio n
2
3
4

__________ 1 9 6 6 — 1977______________

N um ber of
s ig n ific a n t
c o e ffic ie n ts
F

Lags

Leads

1.382
1.296
1.488

.149
.150
.250

1.78
1.79
1.92

2
1
1

—

16 to 1
16 to 0
16 to (9)

1.849*
1.888*
1.285

.178
.192
.214

2.83
2.83
2.85

0
0
0

—

16 to 1
16 to 0
16 to (9)

1.748*
1.649
1.720*

.170
.172
.267

1.80
1.82
1.95

4
4
1

—

0
2

0
0

0
1

N u m b e r of
s ig n ific a n t
c o e ffic ie n ts
F

Lags

.889
.859
2.790*

.100
.103
.381

1.80
1.83
1.87

0
0
3

1.480
1.720
2.990**

.147
.177
.386

2.90
2.88
2.84

0
0
0

1.150
1.070
2.940**

.119
.119
.384

1.85
1.86
1.91

0
0
2

Leads

N ote: In all cases th e d e p e n d e n t va ria b le s are som e tra n s fo rm o f th e e q u ity re tu rn , R. R2 is th e a d ju ste d c o e ffic ie n t o f d e te rm in a
tio n . F is th e F-value, and DW is th e D u rb in -W a tso n s ta tistic. A * (**) im p lie s re je c tio n o f th e n u ll h y p o th e sis at th e 95% (99%)
level. T h e n u ll h y p o th e sis states th a t th e e stim a te d c o e ffic e n ts o f th e in d e p e n d e n t va riab le s eq u al zero. T he L eads c o lu m n s
in c lu d e th e c o n te m p o ra n e o u s term s.
'D a ta are m o n th ly o b s e rva tio n s.

on past m onetary information are never significant,
nor are they ever significant as a group. In this
vi) gtu = gt - go,
period, the effect of future m oney is highly sig
tripling the explanatory pow er of the esti
w here Co and go are the sam ple-period means of R nificant,
m
ated
m
odels.
and g, respectively.
In the earlier period, there are no unam biguous
Sinee the original Rozeff specification mixes d e differences among the m odels. The R 2 reveals rela
viations from m eans (Rt - Co) with first differences tively equal explanatory power. T he differenced
(gt - gt-i), we refer to this as the m ixed m odel. None of m odel shows a statistically significant effect of the 16
the three versions inherently makes more sense than lags of m oney growth, yet no single coefficient is
the others. Our intent here is to see how sensitive the statistically significant. This m odel exhibits a high
original specification is to these m inor changes.
degree of autocorrelation; therefore, the F-tests
should be interpreted w ith caution .15 T he m ean
Table 1 provides estim ates of the original em deviation m odel also shows an apparent significant
pirical specifications of the three models: the mixed effect of past m oney growth in the early period.
model, given by equations 2, 3 and 4, and the modi However, w hen future terms are added to the equa
fied specifications w hich we term the differenced tion, the num ber of lagged significant coefficients
model and the mean deviation model. The estim ates falls to only one. As a whole, these results offer no
in the table cover two subperiods, 1954-65 and 1966- clear rejection of stock m arket efficiency. The effects
77.
of future m oney growth on stock returns are also
robust w ith resp ect to the type of specification
The results in table 1 offer no clear rejection of changes we have made.
Rozeffs specification. All three models explain m ore
of the variance of equity returns w hen current or 15As is well known, autocorrelation leads to a bias in the standard
future m oney growth is included in the regressions.
error of the regression. With negative autocorrelation, the direc
In the 1966-77 tim e period, individual coefficients
tion ot the bias could be positive or negative.
v) RJ1 = Rt - Co,

FEDERAL RESERVE BANK OF ST. LOUIS

MARCH 1982

Table 2
R eaction Function Estim ates of U nanticipated M onetary
Policy (§ 1 , § 2 ) and Equity Returns (1954:7 to 1972:3)1

In d e p e n d e n t
v a ria b le

S“
9“

N u m b e r of
s ig n ific a n t
c o e ffic ie n ts

Lag (lead)
M odel

s p e c ific a tio n

2
3
4

16 to 1
16 to 0
16 to (9)

2
3
4

16 to
16 to
16 to

1
0
(9)

Lags

.655
.621
.946

.051
.051
.117

1.78
1.78
1.87

0
0
7

.896
.969
2.660**

.068
.078
.271

1.79
1.83
1.95

0
0
0

Leads

___
0
7

—
0
3

1See note, ta b le 1. Data are m o n th ly o b se rva tio n s.

Unanticipated Monetary Base Growth
and Stock Returns: Estimates
Employing Monetary Reaction Functions
The basic m ixed m odel is retained in this section,
but two different proxies for unanticipated m onetary
policy actions (gu) are tried. In these tests, we as
sume that agents are rational and act as if they know
the appropriate function guiding m onetary policy.
Table 2 presents the results of estim ating equa
tions 2, 3 and 4 using two different proxies for unan
ticipated m oney growth. The first of these, denoted
gi, comes from Froyen’s m onetary policy reaction
function for the m onetary b ase .16 This function,
w hich we assum e is used to forecast future growth
rates of the m onetary base, relates the latter to past
values of the Federal R eserve’s assum ed goal vari
ables: the unem ploym ent rate, inflation rate, balance
of paym ents and the outstanding governm ent debt
held by the public. The estim ated function is used to
predict the level of the m onetary base.
If Mt is the prediction of the monetary base based
on the estim ated reaction function, then we can
define the anticipated monetary base growth rate as 17
gl.t = (Mt* - Mt*i) / Mt.i.
16See Richard T. Froyen, “A T estofthe Endogeneity of Monetary
Policy "Journal of Econometrics (July 1974), pp. 175-88.
' ’Alternatively, we tried a variant of this form where
g 3,t = (M; - M ul/M ,.,.
The results w ere not different enough to w arrant further
discussion.
Digitized for 8FRASER

Therefore, a first proxy for unanticipated m one
tary base growth is
gi'.t = gi,t - gt-

The second proxy for unanticipated growth (g 2,t)
is based on a sim ple third-order autoregressive
process sim ilar to the specification used by Rozeff:
g2,t = g2,t — gt,

w here
ga.t = «<> + < iig t.i + d o g t.j + «3gt-3-

The results in table 2 again support the efficient
m arket hypothesis. There is no clear evidence that
past unanticipated m onetary base growth signifi
cantly affects current stock returns using any of the
proxies tested here. W hile there are num erous sig
nificant lag coefficients in the g“ equation, they are
not significant until leads are added, and even then
the F-value is not significant. W ith regard to the
effects of future m onetary base growth on current
stock returns, the pattern of the results in table 2 is
interesting. W hen anticipated m onetary base growth
is m easured by the sim ple autoregressive specifica
tion, and future “ u nan ticipated ” m onetary base
growth is taken to be m oney growth that cannot be
predicted with that specification, g 2 t, our results
show a significant effect for these future terms. H ow
ever, for the proxy constructed on the basis of the es
tim ated m onetary policy reaction function,g*i t,
future unanticipated m onetary base growth has no
significant effect on current stock returns.

MARCH 1982

FEDERAL RESERVE BANK OF ST. LOUIS

Table 3
A nticipated vs. U nanticip ated M onetary B ase Growth and
Equity Returns (1954:7 to 1972:3)1
N u m b e r of
s ig n ific a n t

Lag

Anticipated
variable

coefficients

specification
gu

—

.969

.078

1.83

—

9*1

—

.621

.051

1.78

—

1.014

.081

1.85

.614

.054

1.80

1.001

.113

1.83

.890

.102

1.85

1See no te, ta b le 1. Data are m o n th ly o b se rva tio n s.

These estim ates are presented in table 3. We use
the same proxies for unanticipated m oney growth
and, in this case, the corresponding m easure of an
ticipated m onetary base growth, as for the estim ates
in table 2. The table is divided into three parts: The
first two lines include only unanticipated m onetary
base growth. T he second two add only the concur
rent anticipation of m onetary base growth. The third
pair allows up to six months lagged values of antici
pations of future m onetary base growth. In each of
these, unanticipated m onetary policy has the current
as w ell as 16 lagged values.
The results are not inconsistent with the efficient
m arket hypothesis, since unanticipated m onetary
base growth, current or lagged, has no significant
effect on stock returns. According to equation 9,
how ever, anticipated m onetary base growth should
have a positive effect on stock returns, if there is a
constant expected real return and if anticipated
m onetary base growth affects money growth and,
thereby, anticipated inflation. Our results do not
show this effect and w ould seem to indicate that the
expected real return on stocks is negatively affected
Anticipated and Unanticipated
by
expected inflation that results from anticipated
Monetary Base Growth and
m
onetary
base growth. This follows since the ex
Stock Returns
pected real return declines w ith anticipated infla
We discussed previously the Fam a version of the tion, unless there is an offsetting increase in the
m odel (equation 9), w here both anticipated and un nom inal return .18
anticipated values of m onetary policy should affect 18Fama uses a general equilibrium approach and concludes that
equity returns. In this section, w e again use m one real returns vary with expectations of future real economic ac
tary policy reaction functions to differentiate antic tivity. He also argues that apparent correlations betw een real
stock returns and expected inflation or money growth rates are
ipated and unanticipated policies. The m odel tested
spurious. See Eugene F. Fama, “Stock Returns, Real Activity,
here is the em pirical specification of the Fam a m odel
Inflation, and M oney,” American Economic Review (Septem
ber 1981), pp. 545-65.
given by equation 1 0 .
O ne interpretation of these results is that future
“ unanticipated” m onetary policy actions based on
the autoregressive proxy are not in fact unanticipated.
Inform ation other than past m onetary base growth —
information that is available to the public and, if the
reaction function specification is correct, informa
tion that does affect future m oney growth — may
enable the public to correctly anticipate such future
m onetary base growth. Since the prediction of the
reaction function already incorporates such avail
able information, the public cannot forecast future
unanticipated m onetary base growth as m easured by
reaction function residuals; therefore, these future
residuals do not affect current stock returns. O ur
results then are consistent with Rozeff’s “reversed
causation with correct anticipations” m odel, w here
the apparent effect of future m onetary base growth
on stock returns reflects the public’s correct forecasts
of future m onetary base growth on the basis of cur
rently available information.

FEDERAL RESERVE BANK OF ST. LOUIS

MARCH 1982

Stock Returns and the Federal
Funds Rate

federal funds rate. The results ofthese tests are given
in table 4.

If the m onetary authority pegs the federal funds
rate, the m oney supply becom es endogenous, and
changes in the setting of the rate may be taken as an
exogenous variable. In practice, the federal funds
rate may change for reasons other than policy, es
pecially over short intervals. C onsequently, these
tests may reflect not only how efficiently the m arket
absorbs infonnation about m onetary policy but also
the im pact of other inform ation em bodied in m ove
m ents in the federal funds rate. N evertheless, they
are useful in ascertaining how changes in the federal
funds rate are internalized by the m arket during a
period w hen the expressed policy was to m aintain
that rate w ithin a narrow range.

The results of estim ating equations 2, 3 and 4 are
shown in part A of the table. T hese results, using the
interest rate as a m easure of m onetary policy, are less
favorable to the efficient m arket hypothesis than our
estim ates using m onetary aggregates. As can be seen
from the first two lines of the table, lagged values of
the unanticipated portion of the federal funds rate
(lagged errors in forecasting the m onetary author
ity’s funds rate setting) appear to affect stock returns
significantly. This evidence supports the view that
stock returns lag monetary policy — even though our
results in the previous section w ould indicate that
stock returns do not lag money growth. T he addition
of current or future federal funds rate prediction
errors does not increase the explanatory pow er of the
equation (see estim ates of equation 4 in the table).

In the m odel with m onetary aggregates, antici
pated inflation was approxim ated by anticipated
m onetary growth. It is less appropriate to think of
anticipated changes in the federal funds rate as a
proxy for anticipated inflation. However, changes in
the anticipated federal funds rate that signal changes
expected in financial m arkets will still provide im
portant information in efficient markets. The tests in
this section rem ain, therefore, as tests of m arket
efficiency. T hey do, how ever, have less explicit
theoretical developm ent that explains exactly how
m onetary policy affects stock returns.
To split m ovem ents in the federal funds rate into
anticipated and unanticipated com ponents, we use
the m onetary policy reaction function estim ated by
Abrams, Froyen and W aud in w hich the federal
funds rate is the dependent variable .19 T he fitted
values from the estim ated reaction function provide
a m easure of the anticipated federal funds rate (RFt).
The unanticipated portion of the federal funds rate
(RFU) is sim ply the actual federal funds rate minus
the anticipated rate. T he m odels we estim ate using
the federal funds rate as a m easure of m onetary
policy again are those given by equations 2, 3, 4 and
1 0 , w here th e unanticipated (gu) or anticipated
m onetary policy variables (g*) are now in terms of the

In part B of the table, w e report estim ates of the
m odel that allows both anticipated and unantici
pated m onetary policy to affect stock prices. O ur
estim ates indicate that lagged values of both unan
ticipated and anticipated m onetary policy as m ea
sured by the federal funds rate have significant
effects on stock returns. Both here and in p artA ofthe
table, all the significant coefficients on the federal
funds rate variables are negative (the signs of these
coefficients are not reported in the table). This
accords w ith the conventional expectation that a
tightening of monetary policy, as m easured by an
increase in the federal funds rate setting, lowers
stock prices and, hence, stock returns. In part B, as in
part A of the table, how ever, the finding that past
available inform ation significantly affects stock
returns raises questions about m arket efficiency.

This is not to say that the results in table 4 directly
contradict the efficient m arket hypothesis. O ne in
terpretation of these results that is potentially con
sistent w ith the efficient m arket view is that the
federal funds rate is a determ inant of the expected
real return on stocks, which is not a constant. W ith
this interpretation, the excess return on stocks w ould
still be independent of past available inform ation,
the condition for an efficient market. Still, the results
19The anticipated federal funds rate is a function of 1) consistent in table 4 do suggest the possibility that w hile the
forecasts of future values of the unem ploym ent rate, the infla m arket efficiently absorbed data on m onetary ag
tion rate and external balance variables and 2 ) lagged values of
deviations of actual M l from its target values. See Richard K. gregates, information carried by observations on the
Abrams, Richard Froyen and Roger N. W aud,“Monetary Policy federal funds rate was not im m ediately reflected in
Reaction Functions, Consistent Expectations, and the Bums stock p rices and, h en ce, affected fu tu re stock
Era "Journal of Money, Credit, and Banking (February 1980),
returns.
p p . 30-42.

FEDERAL RESERVE BANK OF ST. LOUIS

MARCH 1982

Table 4
A nticipated vs. U nanticip ated M onetary Policy
(The Federal Funds R ate) and Equity Returns (1 9 71 :7 - 1 976:6)1
A. Unanticipated Federal Funds Rate (RFU)

M od e l

Lag (lead)
s p e c ific a tio n

2
3
4

16 to 1
16 to 0
16 to (9)

N u m b e r of
s ig n ific a n t
c o e ffic ie n ts
F
2.237*
2.097*
1.580

Lags

Leads

.254
.243
.206

1.75
1.73
1.59

4
4
4

—
—
0

B. Anticipated (RF*) and Unanticipated (RFU) Lead Values and Lags of the Federal Funds Rate
N u m be r of
s ig n ific a n t
c o e ffic ie n ts

Lags
(leads)
RFU

RF*

RFU

RF*

9
9
9
9
9

—

2.661*
3.355*
3.677*
3.058*
3.150**

.223
.309
.440
.332
.387

1.76
2.00
2.08
2.02
2.08

2
3
2
4
3

—
1
2
0
2

0
6
(3)
3 to (3)

1See note, ta b le 1. Data are m o n th ly o b se rva tio n s.

Tests with Weekly Money Stock Data
E arlier tests that split m oney growth into antici
pated and unanticipated com ponents are redone
using w eekly data. T he m easures of anticipated and
unanticipated w eekly m oney growth are taken from
Naylor .20 The tim e period for these tests is August
1974 to March 1977.
As noted, the use of weekly data provides a finer
test of possible lead-lag relationships b etw een
money growth and stock returns. Data on the m oney
supply generally were announced during our sample
period on Thursday afternoons. Therefore, we as
sume an injection of m onetary information occurs
Thursday, w hich is new inform ation to Friday’s
stock m arket transactions. By m oving to a w eekly
m odel, we better capture these events. All m oney
stock data used are the values originally announced
on the Thursday of each w eek. T he equity returns
are derived from the stock prices recorded at m arket
closing on the next day, Friday.
20Naylor’s

forecasts are from a 52-week autoregressive scheme.
This model is re-estimated one week at a time over the entire
sample period and generates one-week-ahead forecasts. For
details, see John A. Naylor, “ Do Short-Term Interest Rate Ex
pectations Respond to New' Information on Monetary' Growth?”
Southern Economic Journal (January 1982), pp. 754-63.

T able 5 presents the sum m ary data from our
w eekly regression tests. The top of the table (part A)
reveals that up to 16 lags and nine leads of unantic
ipated m oney growth explain very little o f the vari
ance in w eekly stock returns. None of the individual
coefficients are statistically significant at the 5
percent level of confidence. The F-values suggest
that none of the three lag specifications leads to a
rejection of the null hypothesis of m arket efficiency.
The bottom half of table 5 (part B) specifies past
values of both anticipated (gl) and unanticipated
m onetary growth (g") as determ inants of the w eekly
equity returns. Adding six past weeks of anticipated
m onetary growth im proves the explanatory pow er of
the equation (with 16 lags of unanticipated money),
doubling the R 2 to .166. The m ain contribution in
statistical significance comes from the current value
of gi with less added by the one week lag (t-value
equal to about —1.7). The signs of the estim ated
coefficients are negative, im plying an inverse rela
tionship betw een anticipated m oney growth and
equity returns .21
21This finding would agree with the federal funds rate results if
expectations of increased monetary growth are at least partially
caused by earlierbelow -targetgrow th. In this case, both higher
expected money and higher federal funds rates would correlate
with future falling stock returns.
11

MARCH 1982

FEDERAL RESERVE BANK OF ST. LOUIS

Table 5
A nticipated and U nanticipated M onetary Growth and
Equity Returns (1974:8 - 1977:3)1
A. Unanticipated Money Growth (gu)
N u m b e r of
s ig n ific a n t
c o e ffic ie n ts

M odel

Lag (lead)
s p e c ific a tio n

Lags

Leads

2
3
4

16 to 1
16 to 0
16 to (9)

.947
.897
.890

.084
.085
.115

2.02
2.02
2.03

0
0
0

—
0
0

B. Anticipated (g*) and Unanticipated Money Growth (gu)
N u m b e r of
s ig n ific a n t
c o e ffic ie n ts

Lags
gu

g‘

16
16
16

—
0
6

.897
1.179
1.302

.085
.115
.166

2.02
2.03
2.04

0
0
0

1
1

'S e e no te, ta b le 1. Data are w e e kly o b se rva tio n s.

Overall, the results of w eekly data indicate that
inform ation about m oney growth is quickly reflected
in stock prices, as one w ould expect if the m arket is
efficient.

CONCLUSIONS
The results of our study can be sum m arized as
follows: Estim ates of the relationship betw een stock
returns and m oney growth rates, using m onthly data,
support the notion that stock m arkets are efficient.
E ven from w eek to w eek, the m arket seem s to
quickly u tilize th e m ost recent inform ation on
m onetary aggregates. O ur estim ates of the relation
ship betw een stock returns and m onetary policy
actions as m easured by the federal funds rate, how
ever, suggest a possible violation of the conditions
for m arket efficiency.
On the question of w hether stock returns lead
m oney growth, our results indicate that w hen antic
ipated m oney growth is a fitted value from a reaction
function, future unanticipated m oney growth does
not significantly affect current stock returns. But
w hen future changes in m oney growth rates are
based only on past m oney (using a third-order auto
regressive schem e), th ey do significantly affect
returns. This finding supports the hypothesis that
the m arket uses inform ation other than past m oney
growth rates (information em bodied in the reaction
Digitized for 1FRASER
2

fu n ctio n p red ictio n ) to fo recast fu tu re m oney
growth and that such anticipations affect current
stock returns.
This research has uncovered very little about how
one can use m onetary policy information for profit in
the stock market. Information about aggregates is
quickly assim ilated by markets. T he m onthly esti
mations show little effect of anticipated or unan
ticipated aggregates (base or M l) upon stock returns.
T he w eekly tests suggest that stock returns tend to
fall w ithin a week after the m arket anticipates a rise
in the w eek’s m onetary aggregate. T he most useful
information seem s to come from the m onthly federal
funds rate. We found that increases in that rate
tended to lower stock returns over a six- to ninem onth period. Since the federal funds rate is an
im perfect indicator of m onetary policy, this finding
may say little about how m onetary policy affects
stock returns. It does, how ever, reveal that for our
1971-76 sam ple period, m onths w hen the federal
funds rate fell w ere followed by periods of rising
stock returns. H ad m arket participants been aware of
this relationship, they m ight have profited by it.
Since the expressed policy of the Federal Reserve
today allows the federal funds rate to float w ithin a
w ide band, there is no indication that this relation
ship continues. The relationship betw een m onetary
growth or m ovem ents in the federal funds rate and
stock returns in the post-O ctober 1979 period is a
subject for future research.

Monetary Policy and Short-Term
Real Rates of Interest
R. W. HAFER and SCOTT E. HEIN

T e x t b o o k d escrip tio n s of the ch ann els of
m onetary policy’s im pact on the economy usually
outline a two-step procedure: “The first is that an
increase in real balances generates a portfolio dis
equilibrium — at the prevailing interest rate and
level of income, people are holding more m oney
than they want. This causes portfolio holders to
attem pt to reduce their m oney holdings by buying
other assets, thereby changing asset yields. In other
w ords, the change in the [real] m oney supply
changes [real] interest rates. The second stage of the
transm ission process occurs w hen the change in
interest rates affects aggregate dem and .” 1
The rational expectations literature, how ever, has
raised serious questions about this description,
especially the first stage w herein an increase in real
m oney balances lowers expected real interest rates.
Shiller, for example, draw ing from previous work
in rational expectations, hypothesizes that the ex
pected real interest rate is unaffected by changes in
m onetary policy .2
W hile Shiller found little support for this hy
pothesis, other recent em pirical work supports it.
Fama, for instance, is unable to reject the hypothesis
that the expected real rate on short-term financial
assets was constant over m uch of the post-Accord
period in the U nited States .3 This hypothesis is even
•Rudiger Dornbusch and Stanley Fischer, Macroeconomics
(McGraw-Hill, 1978), p. 120.
2Robert J. Shiller, “Can the Fed Control Real Interest Rates?” in
Stanley Fischer, ed., Rational Expectations and Economic
Policy (The University of Chicago Press, 1980), pp. 117-56.
Shiller also outlined two other (non-exclusive) hypotheses:
(1) the Fed can affect real rates only through unexpected policy
moves and (2) Fed policies known far enough ahead of time
have no effect on real rates. These hypotheses are not as stringent
as the hypothesis considered in this paper.
3Eugene F. Fama, “Short-Term Interest Rates as Predictors of
Inflation,” American Economic Review (June 1975), pp. 269-82.

stronger than Shiller’s. It holds that m onetary ac
tions, as w ell as everything else, have had no system
atic effect on expected real interest rates.
This article re-evaluates the evidence suggesting
that the expected (ex ante) real interest rate on short
term financial assets is constant. Evidence is pro
vided that allows us to reject this hypothesis for the
1955-79 period. Follow ing this, data are exam ined to
determ ine w hether evidence supports the typical
textbook description in w hich changes in expected
real interest rates are associated w ith changes in real
m oney growth.

THE FRAMEWORK OF ANALYSIS
C onsider first the relationship betw een nominal
interest rates and inflation expectations em bodied
w ithin the so-called Fisher relationship ,4
(1) it = rf + P f,

w here it is a nom inal (or market) rate of interest (the
rate m easuring how many dollars m ust be repaid in
the future for a given dollar loaned today), rf is the
expected real interest rate (the rate m easuring how
“The belief in a positive relationship betw een expected inflation
and nominal interest rates has a long history in economics.
Henry Thornton recognized the relationship as early as 1811.
Alfred Marshall also acknowledged the link during the latter
half of the 19th century. Even so, the intensity with which
Irving Fisher examined the relationship during his career has
resulted in the distinction of equation 1 being dubbed the
“ Fisher equation.” See Henry Thornton, “Two Speeches of
Henry Thornton, esq. on the Bullion Report, May 1811,” in
F. A. v. Hayek, ed.,An Enquiry into the Nature and Effects of the
Paper Credit o f Great Britain (1802), (August M. Kelley, 1962),
pp. 323-62; Alfred Marshall, “Remedies for Fluctuations of Gen
eral Prices (1887),” in A. C. Pigou, ed., Memorials o f Alfred
Marshall (Kelley & Millman, Inc., 1956) pp. 188-211; and Irving
Fisher, The Theory o f In terest (Kelley & Millman, Inc., 1954),
especially Chapter 2.
13

FEDERAL RESERVE BANK OF ST. LOUIS

many more goods can be obtained in the future by
foregoing consum ption today) and P® is expected
inflation (the rate at w hich the dollar price of goods
is expected to rise.) Equation 1 represents a hypothe
sized equilibrium relationship. It posits thatchanges
in observed nom inal rates of interest fully reflect
changes in expected inflation, holding the expected
real rate constant . 5 In other words, nom inal rates
and expected inflation are positively related and,
ceteris paribus, move on a one-to-one basis.
The foundation for this equilibrium relationship
is the view that investors have two possible invest
m ent opportunities: they can invest either in capital
goods that produce a future stream of consum ption
goods or in financial assets denom inated in m onetary
terms. Investm ent in capital goods is expected to
produce rf percent more consum ption goods per
year than the am ount of consum ption goods original
ly given up to produce the capital good. To make the
return on investing in the capital good com parable
to the alternative investm ent (the financial asset),
the value of the future stream of consum ption goods
m ust be translated into dollar terms. This is accom
plished by adding the expected rate of change in the
dollar price of consum ption goods (Pf) to the rate of
increase of consum ption goods (rf). The right-hand
side of equation 1 , therefore, represents the ex
pected dollar return from investing in a capital good.
In equilibrium (and w ithout differential tax rates),
the dollar return from investing in capital goods
should equal the dollar return from investing in fi
nancial assets, m easured by the nominal interest rate,
it- Equation 1 thus states that an individual should
not find the dollar yield on financial assets any dif
ferent from the expected dollar yield on capital
goods. We stress that equation 1 is an equilibrium
condition: not only are the financial and capital
goods m arkets hypothesized to be individually in
equilibrium , but any differential in the expected real
yields in these two m arkets is arbitraged away.
In its present form, equation 1 cannot be exam ined
em pirically because the two variables on the righthand side, the expected real rate of interest and
inflation expectations, are not directly observable.
W hile there are many observable nom inal interest
rates on financial assets, there are no reliable aggre
gate m easures of either the expected real yield on
5This equilibrium relationship also should include the crossproduct term rf Pf. Like most empirical analyses of this relation
ship, we ignore this term, assuming that the magnitude of the
variable is sufficiently small.
Digitized for14
FRASER

MARCH 1982

capital goods or the expected future inflation rate .6

IS THE EXPECTED REAL RATE OF
INTEREST CONSTANT?
To test the relationship specified by equation 1,
one can make two assum ptions: First, assum e that
the expected real interest rate is a constant, such that
(2) rf = r.

Second, to circum vent the problem of m easuring
inflation expectations, assum e that next p eriod’s
actual inflation (Pt+i) is equal to w hat is currently
expected (at tim e t), plus a random disturbance ju,t+i,
w here /u,t+i is independent and distributed N(0, cr2):
(3) Pt+i = Pf + Mt+i-

This relationship specifies that one-period-ahead
inflation forecasts are unbiased; on average the actual
inflation rate over the next tim e period will be the
expected rate.
Substituting equations 2 and 3 into 1 yields
(4) it = r + Pt+i - nt+1.

This equation can be arranged to test em pirically
the hypothesis that today’s interest rate accurately
predicts tom orrow’s inflation as follows:
(5) Pt+i = - r + /3oit + Mt+i-

Assuming that financial m arkets are efficient, we
would expect to find /3o not to be statistically differ
ent from unity and the estim ated constant term to be
negative. If the estim ated coefficient (3o is not statis
tically different from unity, the proposition that
current interest rates fully reflect the m arket’s antici
pations of the future inflation rate cannot be rejected.
Similarly, if the estim ated constant term is negative,
the expected real rate of return is then positive as
suggested by the underlying economic theory. M ore
6Some researchers have attem pted to investigate the relationship
by using directly observed inflation expectations data generated
from Joseph A. Livingston’s biannual survey of economists. See,
for example, William E. Gibson, “Interest Rates and Inflationary
Expectations: New Evidence,” American Economic Review
(December 1972), pp. 854-65; David H. Pyle, “Observed Price
Expectations and Interest Rates,” Review o f Economics and
Statistics (August 1972), pp. 275-80; Kajal Lahiri, “ Inflationary
Expectations: T heir Form ation and Interest Rate Effects,”
American Economic Review (March 1976), pp. 124-31; Thomas
F. Cargill,“Anticipated Price Changes and Nominal Interest
Rates in the 1950’s,” Review o f Economics and Statistics (Au
gust 1976), pp. 364-67; John A. Carlson, “ Short-Term Interest
Rates as Predictors of Inflation: Comment,” American Economic
Review (June 1977), pp. 469-75; and Douglas K. Pearce, “Com
paring Survey and Rational Measures of Expected Inflation:
Forecast Performance and Interest Rate Effects,” Journal o f
Money, Credit and Banking (November 1979), pp. 447-56.

MARCH 1982

FEDERAL RESERVE BANK OF ST. LOUIS

Table 1
Em pirical Estim ates of Equation 51
C o e ffic ie n t

1/1955-IV/1979

1/1955-IV/1959

1/1960-IV/1969

1/1970-IV/1979

Ordinary Least-Squares Estimates
C o n s ta n t

-0 .5 8 0
(1.46)

2.686
(3.10)

—1.496
(2.65)

1.393
(1.42)

1.056
(13.49)

-0 .0 4 1
(0.13)

1.073
(7.97)

0.840
(5.61)

■R2

0.646

-0 .0 5 5

0.616

0.439

1.630

1.190

1.116

1.750

1.02

1.63

1.92

1.09

Generalized Least-Squares Estimates
-0 .1 2 6
(0.20)

2.584
(2.68)

-1 .4 9 6
(2.65)

1.586
(1.15)

0.957
(8.00)

-0 .0 0 1
(0.00)

1.073
(7.97)

0.797
(3.93)

0.389

-0 .0 5 6

0.616

0.270

1.424

1.169

1.116

1.573

2.21
0.504

2.15
0.190

1.92
0.000

2.04
0.455

C o n s ta n t

1R2 re p re se n ts th e c o e ffic ie n t o f d e te rm in a tio n a d ju ste d fo r de g re e s o f fre e d o m , SE is th e re g re s
sio n s ta n d a rd e rro r, DW is th e D u rb in -W a tso n test s ta tis tic and p is th e e stim a te o f th e a u to c o rre
la tio n c o e ffic ie n t. A b s o lu te va lu e o f t-s ta tis tic s a p p e a r in parentheses.

over, th e existence of serial correlation in the
residuals w ould deny the assum ption em bodied
in equation 3 and, consequently, w ould lead to a
rejection of the hypothesis specified in equation 5 .7
Previous em pirical studies generally have not
explicitly considered the tem poral stability of the
expected real rate w ithin this framework. The con
stant term in equation 5 represents the estim ate of
the (negative value of the) expected real rate of
return. The above theoretical foundation for this
specification suggests that, in addition to being nega
tive, this term is statistically tim e-invariant. Thus, a
test of the tem poral stability of the constant term is
also a test of the constancy of the expected real
interest rate.
Table 1 presents estim ates of equation 5 for vari
ous periods. The inflation data used to estim ate equa’Fama tested and rejected the hypothesis that the expected real
rate was linearly related to expected inflation. Critical examina
tions of Fama’s results are found in Carlson, “Short-Term Inter
est Rates as Predictors of Inflation” ; Douglas Joines, “Short-Term
Interest Rates as Predictors of Inflation: Comment,” American
Economic Review (June 1977), pp. 476-77; and Charles R.
Nelson and G. William Schwert, “Short-Term Interest Rates as
Predictors of Inflation: On Testing the Hypothesis that the Real
Rate of Interest is Constant,” American Economic Review (June
1977), pp. 478-86. Also, see Eugene F. Fama, “Interest Rates and
Inflation: The Message in the Entrails,” American Economic
Review (June 1977), pp. 487-96.

tion 5 are based on quarterly observations of the
GNP deflator, expressed as annual rates of change .8
Since the GNP deflator provides an average m easure
of prices over the quarter, the quarterly average
three-m onth Treasury bill rate is used as the nominal
interest rate m easure.
C onsider first the results obtained by estim ating
equation 5 over the full sam ple period, 1/1955IV/1979. T he constant term is negative (although
not significantly different from zero), and the coef
ficient on the interest rate variable is not statistically
different from unity as suggested by the theory.
U nfortunately, th e low D urbin-W atson statistic
provides evidence of first-order serial correlation .9
8The GNP deflator is used to avoid recent problems with the con
sumer price index. For a discussion of problems with this index,
see Alan S. Blinder, “ The C onsum er Price Index and the
M easurem ent of Recent Inflation,” Brookings Papers on Eco
nomic Activity (2:1980), pp. 539-65.
9Eugene F. Fama and Michael R. Gibbons, “ Inflation, Real
R eturns and C apital Investm ent,” W orking Paper No. 41
(Graduate School of Business, University of Chicago, 1980), also
find evidence of serially correlated disturbance terms when
quarterly data are employed. In addition, in that study as well
as in his “ Stock Returns, Real Activity, Inflation, and Money,”
American Economic Review (Septem ber 1981), pp. 545-65,
Fama drops the assumption that the expected real rate of interest
is constant. Both studies estimate the inflation/interest rate rela
tionship assuming that the expected real rate is a random walk.
15

FEDERAL RESERVE BANK OF ST. LOUIS

This result, by itself, is enough to reject the frame
work in equation 5 .10 Focusing solely on the con
stancy of the expected real rate, how ever, the
accom panying estim ation problem can be corrected
by u sin g g en eralized least-sq uares estim atio n.
T hese results appear in the low er half of table 1.
The full sam ple results reported there again indi
cate that next period’s rate of inflation does mirror,
one-for-one, a rise in today’s interest rates. M ore
over, the constant term rem ains insignificantly dif
ferent from zero.
Table 1 further reports estim ation results for sub
periods arbitrarily truncated at the end of each
decade. If the expected real rate of interest is tem
porally invariant, the constant term s in these sub
periods should not differ statistically. Yet, as the
table im m ediately shows, they do differ significant
ly across the various subperiods shown. In fact, the
estim ated constant term is positive and significant
in the first subperiod (late 1950s), w hile not different
from zero in the last decade (1970s). It has the
anticipated negative sign only in the decade of the
1960s. M oreover, the coefficient on the interest rate
variable is not statistically different from zero in the
late 1950s, even though theory suggests that it should
equal unity. Thus, the coefficient estimates, as well as
summary statistics such as the R2 and the standard
errors of the equation, vary substantially across sub
periods, irrespective of the estim ation technique
used.
T he statistical significance of the variation in the
constant term (the estim ate of the ex ante real
in terest rate) can be investigated by in clu ding
dum m y variables for possible shifts in the intercept.
Thus, equation 5 was re-estim ated with two dum m y
variables: D1 equal to 1 for I/1955-IV/1959 and
D2 equal to one for I/1960-IV/1969. E stim ating
such an equation w ith ordinary least squares again
yielded residuals that w ere significantly autocorre
lated. To improve hypothesis testing, the equation
was estim ated using a generalized least-squares
routine to correct for assum ed first-order autocorrela
tio n .T he I/1955-IV /1979 estim atio n resu lts are
(absolute value of t-statistics in parentheses):
(5') P,+i = 1.40 - 0.88 D1 - 1.88 D2 + 0.83 i,
(1.62) (1.19)
(3.46)
(6.51)
~R- = 0.55 SE = 1.37 DW = 2.07 p = 0.35
10For market efficiency, past values of the disturbance, since they
are past inflation forecast errors and are therefore known, should
provide no additional help in assessing future inflation beyond
that already incorporated in market interest rates. See Fama,
“ Short-Term Interest Rates,” p. 273, for a discussion of this
aspect.
Digitized for16
FRASER

MARCH 1982

T hese results support the previous subperiod
findings: the estim ated real interest rate is signifi
cantly positive only in the 1960s. The point estimates
of the expected real interest rate for the 1950s, 1960s
and 1970s, respectively, are —0.52, + 0.48 and —1.40.
W hile the point estim ates for the 1950s an d th e 1970s
are negative, they are not significantly different
from zero. On the other hand, the positive point
estim ate for the 1960s is significantly different from
zero. Thus, the hypothesis that the expected real
interest rate has been constant over the past 25 years
m ust be rejected.

EX POST REAL RATES:
FURTHER CONSTANCY TESTS
Equation 4 can be rew ritten as
(6) it - Pt+i = r - /ut+1.
This equation states that the ex post real rate should
equal a constant (the ex ante real rate), m inus a w hite
noise random error term .11 A feel for the statistical
variation in the real rate can be obtained by plotting
its behavior for our sam ple period. Chart 1 shows the
quarterly ex post real rate for the I/1955-IV/1979
period and its m ean values for the I/1955-IV/1959
(-0.03), I/1960-IV/1969 (1.21) and I/1970-IV/1979
(—0.39) subperiods. If equation 6 holds forthe whole
period, the m eans across subperiods should be
equal, since the expected value of the disturbance
term in each subperiod is zero.
Tests for equality of the ex post real interest rate
m eans across the subperiods provide another inves
tigation ofthe constancy hypothesis. Such tests again
lead to a rejection of this hypothesis. The t-statistie,
“ This measure of the ex post real rate is somewhat different from
that used by others. Many take the difference between today's
interest rates and today’s inflation rate as an ex post real rate
measure. Theory suggests, however, that the preferable mea
sure is the difference betw een today’s interest rates and tomor
row’s inflation.
In the test subsequently developed and others which follow,
interest rates are assumed to adjust one-for-one with inflation
expectations, a hypothesis that can be rejected in equation 5'.
The reader should be cautioned that there are counter theo
retical arguments and some empirical evidence to suggest that
the nature of the U.S. tax system has invalidated this rela
tionship, with interest rates rising more than one-for-one with
an increase in inflation expectations. For theoretical discus
sions, see Michael R. Darby, “The Financial and Tax Effects of
Monetary Policy on Interest Rates,” Economic Inquiry (June
1975), pp. 266-76; and Martin Feldstein, “ Inflation, Income
Taxes, and the Rate of Interest: A Theoretical Analysis,”
American Economic Review (Decem ber 1976), pp. 809-20. For
empirical evidence on the matter, see John A. Carlson, “Ex
pected Inflation and In terest R ates,” Economic Inquiry
(October 1979), pp. 597-608.

FEDERAL RESERVE BANK OF ST. LOUIS

MARCH 1982

C h a rt l

Short-Term Ex Post Real Rate of Interest

used to test w hether the m ean ex post real rate for interest to m onetary policy? After all, the textbook
the latter half of the 1950s is equal to that of the description of m onetary policy’s transm ission m ech
1960s, is 3.67, sufficiently large to reject the null anism relates changes in the real rate to changes in
hypothesis at the 5 p ercen t significance level. real money balances. In particular, it m aintains that
Further, the t-statistie used to test the equality of an increase in real m oney balances lowers expected
m ean ex post real rates in the 1960s relative to the real rates, at least tem porarily.
1970s is 4.86, again allowing rejection of the null
hypothesis of constant real interest rates at the 5
The previous framework, linking ex post and ex
percent level. Thus, if one accepts the propositions ante real rates, can be used to address this issue. If
that interest rates move in direct proportion with inflation expectations are unbiased and financial
expected inflation and that inflation expectations are m arkets are efficient, then the ex post real rate
unbiased, one m ust reject the constancy of the ex (it — Pt+i) is equal to the ex ante real rate (rf),
ante real interest rate over the subperiods investi m inus a random disturbance term (fit+i) capturing
gated.
unexpected inflation:
(7) it - P t+i = rf - /xt+i.

MONETARY POLICY AND
THE EXPECTED REAL RATE

T hese findings suggest that the real interest rate
has not been constant over the past 25 years. In this
light, is there any evidence that links the real rate of

The typical textbook relationship can be repre
sented as
(8) rj = fio + f3\ (Mt/Pt) + Pi (Mt_i/Pt_i) + ... + €t,

w here M is the nom inal m oney stock, P is the price
17

FEDERAL RESERVE BANK OF ST. LOUIS

level and e is a random error term. This relationship
represents the hypothesis that the expected real rate
is related to real m oney balances. Since nothing in
m acroeconom ic theory indicates how long it takes
for changes in m onetary policy to have an effect,
lagged real balances are included in an effort to
capture em pirically the dynamics of the process.
Theory does suggest, how ever, that some of the
coefficients should be significantly negative. W hile
it is im possible to estim ate equation 8 because of a
lack of observations on r'r', equation 7 indicates that
we have a close approximation in the ex post real
rate. Com bining equations 7 and 8 , we get
(9) it - P, + 1 = /30 + /3j (M,/ P t) + /3-2 (M u / P, i) + ... + e,

- fJ-t+iEquation 9 was estim ated initially by arbitrarily
trying 10 lags on real m oney balances in the relation
ship. Regardless of the sam ple period considered,
how ever, the only coefficients that w ere statistically
different from zero in any consistent fashion were
those for the contem poraneous and first-lagged real
m oney balances. Thus, results including only these
two variables are reported.
Estim ates of equation 9 over the full sam ple peri
od (I/1955-IV/1979) and most subperiods provide
evidence of significant first-order autocorrelation in
the residuals. Consequently, the relationship was reestim ated using a generalized least-squares tech
nique to correct for this problem . The resulting fullsam ple coefficient estim ates and summary statistics
are (absolute value of t-statistics in parentheses ):12
(10) it - Pl +1 = 5.00 - 0.89 (M/P), + 0.8.3 (M/P)m
(1.73) (2.68)
(2.48)
R = 0.07 SE = 1.37 DW = 2.14 p = 0.56 F(2,97) = 4.95

W hile the variation in the ex post real rate ex
plained by the equation is small, it is statistically
significant. M oreover, the coefficient estim ates are
consistent w ith the textbook transm ission m echa
nism. An increase in real m oney balances is asso
ciated w ith a statistically significant, contem po12Money (M/P) is measured (in billions of 1972 dollars) by the
adjusted monetary base for all results reported here. Thus, the
empirical results indicate that a $ 1 billion increase in real
balances will reduce the real interest rate by 89 basis points in
the current period. This decline is offset, however, by an 83
basis-point increase in the real rate in the subsequent period.
We also tried the M l measure and obtained similar results.
Digitized for18
FRASER

MARCH 1982

raneous decline in short-term real rates during this
period. Further, the results are consistent w ith the
long-run policy ineffectiveness of increasing real
balances to reduce real interest rates .13 The coef
ficient estim ate for real m oney balances lagged one
period is significantly positive and is not statistically
different from the absolute value of the coefficient on
contem poraneous real m oney balances. This finding
indicates th at a cu rren t increase in real m oney
balances w ill be associated w ith a current decline in
real rates, but followed by a rise in real rates of equal
size at tim e t+1. This suggests that m onetary au
thorities, to the extent that they can change real
balances, cannot permanently affect real rates of
interest.
W hile earlier evidence show ed that the ex post
real rate (it — Pt+i) behaved differently across
subperiods, there is little evidence to suggest that
its relationship to real m oney balances has changed
over the period. For exam ple, a conventional Chow
test evaluating a hypothesized break in the relation
ship at IV/1969 yields a calculated F-statistic of
F(3,94) = 0.39, w ell below the 5 percent critical
value of 2.70. Thus, the regression coefficients are
not statistically different before or after IV/196914
Changes in real balances have the same statistical
effect on real interest rates across the sam ple period.
Finally, it is appropriate to note that the estim ated
relationship im plies a positive relationship betw een
the volatility in real m oney balances and the volatil
ity in real interest rates. If the frequency of change in
real m oney balances increases, the estim ated rela
tionship im plies an increase in the frequency of
change in real interest rates. The evidence pre
sented here suggests that m ore stable real m oney
growth, even over periods as short as a quarter, will
produce a m ore stable pattern of real interest rate
m ovem ents .15
I3We do not mean to suggest that monetary authorities can con
trol real money balances over long periods of time. On this
point, see Denis S. Karnosky, “Real Money Balances: A Mis
leading Indicator of Monetary Actions,” this Review (February
1974), pp. 2-10.
14In addition, we tested the hypothesis that the variance of the
error term was larger in the 1970s than in the earlier period. The
calculated F-statistic (with 37 and 57 degrees of freedom,
respectively) was 1.44, less that the 5 percent critical value of
1.59. Thus, the hypothesis of equal variance across these two
periods cannot be rejected.
15An interesting investigation into the effects of monetary policy
on both short- and long-term real interest rates is provided in
Dean W. Hughes and Duane Weimer, “The Impact on Business
Investm ent of the Federal Reserve System’s Operating Proce
dures,” Federal Reserve Bank of Kansas City Economic Review
(February 1982), pp. 14-25.

FEDERAL RESERVE BANK OF ST. LOUIS

CONCLUSION
This article has provided evidence counter to the
hypothesis that the expected real rate of return on
short-term financial assets was constant over the
period 1955-79. If such a hypothesis w ere valid,
m onetary policy w ould be pow erless in affecting
real econom ic activity through the conventional
transm ission m echanism . W hile rejecting the con
stancy hypothesis, this article also provides evi
dence consistent w ith conventional m acroeconomic
theory w hereby increases in real m oney balances
tem porarily lower expected real rates. This effect is
contem poraneous on a quarterly basis. W hile such
an effect is significant, it is relatively small and

MARCH 1982

is offset in the following quarter by an identical
rise in ex p ected real rates. T h us, th e re is no
evidence of a long-run effect running from changes
in real m oney balances to changes in real interest
rates. Finally, the evidence presented here suggests
that more volatile short-run real m oney growth is
likely to produce more volatile real interest rate
fluctuations. Thus, contrary to recent claims, stable
m oney growth and stable interest rates are hardly
inconsistent policy objectives .16
16For another view, see Bryon Higgins, “Should the Federal
Reserve Fine Tune Monetary Growth?” Federal Reserve Bank
of Kansas City Economic Review (January 1982), pp. 3-16.

Central Banks’ Demand for Foreign
Reserves Under Fixed and
Floating Exchange Rates
DALLAS S. BATTEN

TJL HE international m onetary system has experi

enced significant changes during the 1970s. The
m ost dram atic of these has been the transformation
from a system of pegged exchange rates to one in
w hich central banks m ake no institutional com
m itm ent to m aintain a particular exchange rate.
D espite this change, central banks have been un
willing, in general, to allow their exchange rates to
be co m pletely m ark et-d eterm in ed and, co n se
quently, continue to hold foreign reserves. The
prim ary focus of this article is to analyze central
banks’ dem and for foreign reserves in light of this
institutional change.
C entral banks generally are thought to hold stocks
of foreign reserves so their econom ies can avoid
incurring the costs of adjusting to every international
im balance that w ould be transm itted to the dom estic
econom y through changes in exchange rates. In par
ticular, before March 1973, central banks partici
pating in the Bretton Woods Agreem ent w ere com
pelled to hold foreign reserves because they were
com m itted to intervene in foreign currency markets
w hen the value of their currencies m oved outside a
predeterm ined range.
It was commonly believed that the dem ise of the
Bretton W oods A greem ent and the concom itant
greater flexibility of exchange rates w ould reduce
central b an k s’ in terven tio n in foreign currency
m arkets and, consequently, reduce their dem and for
foreign reserves. T hat is, since perhaps the single,
m ost im portant reason for holding reserves had
dim inished, central banks w ould not be expected to
hold such large stocks of foreign reserves as they had
under the fixed exchange rate system. In spite of this
expectation, how ever, central banks have continued
to m aintain sizable stocks of reserves since March
The author would like to thank John Bilson, Michael Bordo and
Ed Ray for their comments on an earlier draft.
Digitized for
2 0FRASER

1973. This observation has led researchers to con
clude that central banks have not changed appre
ciably their dem and for reserves w ith the transition
from a fixed to a floating exchange rate system .1
This conclusion, though potentially accurate, is
founded on a framework of analysis in w hich foreign
reserves are considered by central banks as a very
special type of asset — one held solely to enable
them to interven e in foreign currency m arkets.
H ow ever, there is an alternative fram ew ork for
analyzing central bank behavior that predicts that,
even if all countries had adopted a com pletely cleanfloating exchange rate system in 1973, central banks
w ould have continued to hold a variety of financial
assets, some of which w ould have been classified as
foreign reserves under the previous fixed exchange
rate system. This article investigates w hich of these
com peting frameworks better explains central bank
behavior since March 1973.

TWO MODELS OF CENTRAL BANK
BEHAVIOR
To analyze w hether or not central bank behavior
has changed significantly since the introduction of
flexible exchange rates, the dem and for reserves
based on the intervention motive is com pared with
an alternative one developed w ithin an asset-choice
'See, for example, Jacob A. Frenkel, “ International Reserves:
Pegged Exchange Rates and Managed Float,” in Karl Brunner
and Allan H. Meltzer, eds., Public Policies in Open Economies,
Camegie-Rochester Conference Series on Public Policy, sup
plem ent to the Journal o f Monetary Economics, Volume 9 (1978),
pp. 111-40; H. Robert Heller and Mohsin S. Kahn, “The Demand
for International Reserves Under Fixed and Floating Exchange
Rates,” International Monetary Fund Staff Papers (December
1978), pp. 623-49; Nasser Saidi, “The Square-Root Law, Un
certainty and International Reserves Under Alternative Re
gimes, "Journal o f Monetary Economics (May 1981), pp. 271-90.

FEDERAL RESERVE BANK OF ST. LOUIS

fram ework .2 Only if the former explanation outper
forms the latter for the floating period can one con
clude that the changes in behavior since 1973 have
been relatively m inor and inconsequential.
The first m odel is the standard one based on the
derived dem and for foreign reserves for purposes of
intervening in foreign exchange markets. Since this
m odel has appeared frequently in the literature, its
characteristics are only briefly d escrib ed .3 T he
second m odel is based on asset-choice behavior and
has not been applied, until now, to the analysis of
foreign reserve dem and. In this m odel, foreign re
serves are treated as one of several assets that appear
in a bank’s portfolio and are held for the general
conduct of m onetary policy.

The Intervention Model
The central bank intervention m otive has been
thoroughly investigated. E arlier studies typically
have em ployed an optim izing approach in deter
m ining the dem and for foreign reserves. O ne pro
cedure is to find the stock of reserves at w hich the
marginal costs of holding them equal the m arginal
benefits of using them to in terv en e in foreign
currency m arkets (i.e., the avoidance of costs asso
ciated w ith the dom estic economy having to adjust to
each external shock). A second procedure is con
ducted in term s of w elfare m axim ization under
uncertainty. In particular, a central bank’s dem and
for foreign reserves is the result of its m aximizing a
2See Russell S. Boyer and David Laidler, “A Comment on the
Frenkel Paper,” in Brunner and Meltzer, eds., Public Policies in
Open Economies, pp. 141-43.
3Examples of this and similar models include Peter B. Clark,
“Demand for International Reserves: A Cross-Country Anal
ysis,” Canadian Journal o f Economics (November 1970), pp.
577-94; Peter B. Clark, “Optimum International Reserves and
the Speed of Adjustment, ’’Journal o f Political Economy (March/
April 1970), pp. 356-76; T. J. Courchene and G. M. Youssef, “The
D em and for International R eserves,” Journal o f Political
Economy (August 1967), pp. 404-13; Jacob A. Frenkel, “The
Demand for International Reserves by Developed and LessDeveloped Countries,” Economica (February 1974), pp. 14-24;
Frenkel, “International Reserves: Pegged Exchange Rates and
M anaged Float” ; H. Robert H eller, “Optimal International
Reserves,” Economic Journal (June 1966), pp. 296-311; H eller
and Khan, “The Dem and for International Reserves Under Fixed
and Floating Exchange Rates” ; F. Steb Hippie, The Disturbance
Approach to the Demand fo r International Reserves, Princeton
Studies in International Finance No. 35 (Princeton University
Press, 1974); Milton A. Iyoha, “ Demand for International Re
serves in Less-Developed Countries: A Distributed Lag Speci
fication,” The Review of Economics and Statistics (August 1976),
pp. 351-55; Michael G. Kelly, “The Demand for International
Reserves,” The American Economic Review (September 1970),
pp. 655-67; and Saidi, “The Square-Root Law, Uncertainty and
International Reserves.”

MARCH 1982

societal welfare function which is a positive function
of the expected level of real incom e and a negative
function of its variability. Since the holding of for
eign reserves diverts resources away from dom estic
uses, the larger the stock of reserves, the lower the
expected level of real income. However, if no re
serves are held, the dom estic econom y w ould have
to adjust to every external shock, resulting in more
real income variability.
Em ploying the intervention motive w ithin this
framework, previous studies have identified four
major determ inants of reserve dem and: the vari
ability of international paym ents and receipts, the
propensity to import, the opportunity cost of holding
reserves and a scale variable m easuring the size of
international transactions (usually the value of
imports). The variability of receipts and paym ents
m easures the likelihood that external disequilib
rium w ill occur, in d u cin g th e cen tral bank to
intervene in foreign currency markets in order to
m itig ate th e im p act of th is d iseq u ilib riu m on
dom estic markets. The larger the variability of a
country’s receipts and paym ents, the more suscep
tible is that country to external disequilibrium ;
consequently, the larger is the optim al stock of
reserves desired for purposes of intervention.
There are two possible rationales for including the
propensity to im port as a determ inant of reserve
dem and. First, the average propensity to im port can
be considered a m easure of the degree of openness
in an economy, thus indicating the degree to which
the economy is vulnerable to an external disequilib
rium. A second, alternative rationale stems from
the Keynesian m odel of an o p en econom y in which
an external d iseq u ilib riu m could be corrected,
w ithout changing the exchange rate, by a change in
output in proportion to the foreign trade m ultiplier.
This output cost of adjustm ent could be avoided if
the central bank used its stock of foreign reserves to
finance (or to sterilize) the disequilibrium . Since this
output cost is directly related to the size of the
foreign trade m ultiplier, and since this m ultiplier is
inversely related to the m arginal propensity to
im port, the output cost of not holding sufficient
reserves necessary to avoid this adjustm ent and,
thus, the central bank’s dem and for reserves, m ust
also be inversely related to the marginal propensity
to import. Because the m arginal propensity to import
is difficult to m easure, most studies have substituted
the average propensity as a proxy. However, if the
average propensity to im port is em ployed both as a
proxy for the marginal propensity and as a m easure of
21

FEDERAL RESERVE BANK OF ST. LOUIS

openness, the sign of its im pact on reserve dem and is
ambiguous.
Since central banks do not hold an infinite stock of
foreign reserves, there m ust be some cost associated
with holding them . Conceptually, from society’s
point of view, holding foreign reserves represents an
allocation of scarce resources away from dom estic
uses. Presum ably, for every dollar invested in its
stock of foreign reserves (through its central bank),
society foregoes a dollar of dom estic capital forma
tion. C onsequently, a rate of return on dom estic
capital is the appropriate m easure of the opportunity
cost to society of its central bank’s stock of foreign
reserves. On the margin, the optim al stock of re
serves is that level at w hich the cost of holding
reserves equals the m arginal benefits provided by
that stock of reserves. Few studies have included
explicitly a m easure of opportunity cost. Moreover,
those that have included it have not found it to be
em pirically significant .4 The hypothesized reason
for the overall poor perform ance of this variable is
the strong positive relationship betw een it and the
supply of reserves. In particular, the higher the
opportunity cost of holding reserves, the higher also
the dom estic rate of return on financial capital which
motivates capital inflows and, ceteris paribus, in
creases the supply of reserves. As described below,
interest rate differentials are em ployed as an attem pt
to circum vent this problem .
Finally, the scale variable and the dem and for
foreign reserves should be positively related. In fact,
if the value of international transactions is used as
the scale variable, the elasticity of reserve dem and
with respect to the value of international transac
tions should be betw een 0.5 and 1.0 .5

An Asset-Choice Model
In form ulating an asset-choice m odel of central
bank behavior, foreign reserves are treated sim ply as
one type of asset in a central bank’s portfolio held to
enable the central bank to conduct dom estic m one
tary policy. It is assum ed that the prim ary objective
4See,

for example, Courchene and Youssef, “The Demand for
International Reserves ’; Iyoha, “ D em and for International
Reserves in Less-Developed Countries” ; Kelly, “The Demand
for International Reserves” ; and Saidi, “The Square-Root Law,
Uncertainty, and International Reserves.”
5See E rnst B altensperger, “The Precautionary D em and for
Reserves,” The American Economic Review (March 1974), pp.
205-10; and J. H. G. Olivera, “The Square-Root Law of Precau
tionary Reserves,” Journal o f Political Economy (September/
October 1971), pp. 1095-1104.

MARCH 1982

of m onetary policy is to provide an econom ic en
vironm ent conducive to the stable, noninflationary
growth of real output. To this end, the central bank
affects the level of commercial bank reserves (and,
subsequently, the m oney supply) through activity in
governm ent securities and foreign currency m arkets
and by making loans directly to the banking sector.
C onsequently, to conduct m onetary policy ad e
quately, its portfolio should contain at least three
assets: foreign reserves, governm ent securities and
claims on com mercial banks.
A central bank typically confronts two types of
econom ic phenom ena — expected and unexpected
— to w hich it makes policy responses. In light of this,
the specific m odeling of the portfolio decision
making process of a central bank involves separating
its assets into two categories: com m itted and un
com m itted assets. In response to its anticipations of
prospective events, a central bank commits a portion
of its portfolio so that it can pursue its m onetary
policy objective w ithin this “expected” econom ic
environm ent.
However, since a central bank also is faced with
unanticipated econom ic events to which it may wish
to respond, it m ust hold additional reserves to enable
it to respond to these “unexpected” occurrences (or
shocks) as well. T hese “precautionary” reserves may
or may not be used for the conduct of m onetary
policy in any specific period, w hile the com m itted
portion, is, by definition, fully involved in the
monetary control process. C onsequently, a central
bank is concerned only with the yield (cost) on the
potentially idle, precautionary portion. That is, a
central bank’s dem and for the assets that form the
com m itted com ponent is hypothesized to be insensi
tive to their relative yields, w hereas the com position
of the precautionary (or uncom m itted) reserve com
ponent is hypothesized to be sensitive to changes in
relative asset yields.
To formalize this discussion of central bank b e
havior, assum e that a central bank (subject to certain
constraints) desires to m axim ize its “ ability” to
respond to unanticipated events. It accom plishes
this by maximizing the uncom m itted portion of its
portfolio .6 This can be sum m arized with the fol6A model assuming a wealth-maximizing objective of the U.S.
Federal Reserve System has been shown to be a better predictor
of Fed behavior than the traditional model of the Fed as an
automaton reacting only to political pressures. See Mark Toma,
“Inflationary Bias of the Federal Reserve System: A Bureaucratic
Perspective,” unpublished manuscript (California State Uni
versity, Northridge, 1981). Consequently, applying a similar
assumption to other central banks is not without precedent.

FEDERAL RESERVE BANK OF ST. LOUIS

lowing objective function:
(1) F(xi,...,xn) = II (xk - y k)
k=l
w here Xk
= asset k’s maturity value at the end of
the time period,
7k
= the committed or required value of
asset k,
xk — -yk = the uncommitted or precautionary
value of asset k,
/8k
= asset k’s share of the uncommitted
portfolio,
and

2 /3k =
k=l

The resulting system of asset-dem and equations is
as follows :8
£k /
(3) xk = n + Vk [TA j= i

k = 1, ., n

It is clear from equation 3 that a central bank’s
dem and for each asset in its portfolio has two primary
com ponents. The first is the required or com m itted
portion (yk), which is determ ined regardless of yields.
The second, or precautionary, com ponent is the
7A11 assets

are assumed to mature in one period, but longer-lived
assets could be included without a substantive change in the
analysis. Also, since the issue investigated here is a central
bank’s allocation of a given portfolio among various assets, the
determination of the size of the portfolio in any time period (TAt)
is not considered. For some insights into this question, see Toma,
“ Inflationary Bias of the Federal Reserve System.”
8More formally, the system of demand equations represented by
equation 3 is derived by setting up the Lagrangean function and
maximizing it with respect to each asset as follows:

(x2 - 72 )

(Xj +1 “ 7j + l)

1 + rk
= the yield on asset k w ithin the period,
= the present value of the assets in the
portfolio.7

— = (x i - y i)
fix,

ft+l

ft -1 -

- (xj.i

(x„ - 7n)

- 7j-i)

ft-1

fti

Xvj = 0

= ft (xj - 7j) 1 F - Avj = 0 or

(l') L = n (xk - n )
k=l

(2')

(2) TA = 1 vk xk,
k= l
i'k
TA

rem ainder of its b alan ce sh eet (TA — £ yj vj)>
j= l
w hich the bank allocates to the various assets (in
proportions denoted by /3k) according to relative
yields in a m anner that m aximizes its objective
function .9

ft (Xj - 7j)

which the central bank maximizes subject to the
following balance sheet accounting constraint:

where vk

MARCH 1982

X (TA

2
k=l

Vk Xk)

(3') - = f t (x i-7 j)
Solving (3') for /3j yields:
(4') 13, = Kv>(xJ - y Q .
F
Since 2 y8k = 1,
k
(5') 2 ft = p 2 vj (xj - 7j) = 1
j
J

= p (2 Vj Xj - 2 Vj y j )
j
j
X
= p (TA —2 Vj -yj) from (2) in the text or
j
(6') “ = TA - 2 Vj yj = T-(xj - yj) from (3’).
j
Solving (6’) for Xj yields:
(7') xj = yj +

(TA - 2 Vj yj)
J

which is the system represented by (3) in the text. It can be shown
that the own-price elasticity of demand for asset j is
( S ')

f xv -

- 1

yj(i-ft)

and that the Allen partial elasticity of substitution between assets
i and j is

(9')

xj - y s

Xj - y j

For (xk — yk) > 0, all assets are Hicksian substitutes.
9The value of yk is determ ined by those variables that influence
each country’s monetary policy decisions (e.g., economic activ
ity, unemployment, inflation). Certainly, interest rates may be
included in this group of determinants. However, since yk is
estimated, the hypothesized interest insensitivity of a portion of a
central bank’s portfolio can be easily tested. Specifically, if yk is
statistically significant, the hypothesis that a central bank holds a
portion of its portfolio for reasons other than relative yields
cannot be rejected. Also, the hypothesis that any part of the
portfolio is sensitive to changes in interest rates can be tested by
testing the statistical significance of /3k•
23

FEDERAL RESERVE BANK OF ST. LOUIS

MARCH 1982

ESTIMATION OF THE MODELS
The Intervention Model

The rationale for this is that central banks hold most
of their foreign reserves in the form of U.S. dollars.
Instead of holding idle balances of dollars, central
banks
typically invest their reserves in some short
T he functional form of central bank dem and for
term
asset
in order to m aintain a relatively high d e
foreign reserves for the purpose of exchange m arket
gree
of
liquidity;
hence, the ratio (or log difference)
intervention is a familiar o ne :10
m easures the net foregone yield. C onsequently, an
(4) In Rit = a0 + a; In Mit + a2 In mit + a3 In crit
appropriate yield on invested foreign reserves is a
short-term in terest rate on d ollar-d en om in ated
+ a4 In rit + uit,
assets .12
where Rit = the sum of country i’s holdings of gold,
The sam ple em ployed consists of seven coun
convertible foreign exchange, SDRs and
reserve position in the IM F at the end of tries for the tim e period 1/1964 to IV/1979.13 The
time period t,
countries in clu d ed are D enm ark, F rance, W est
G erm any, Japan, th e N eth erlan ds, N orw ay and
Mit = imports of i during t,
Sweden. The U nited States is not included because
m it = i’s average propensity to import during it is considered to be the prim ary supplier of foreign
t (Mit/GD Pit),
reserves. The data set consists of a pooling of crosso"it = the trend-adjusted variance of i’s stock of section and tim e-series observations.
foreign reserves in t,
The possibilities that country-specific variation
rit = i’s opportunity cost of holding foreign may be present and that a lagged adjustm ent process
reserves during t,
may exist are provided for in the following assum ed
autoregressive error structure:
uit = error term.

(All variables denom inated in domestic currency units are
converted into U.S. dollars using the end-of-period ex
change rate.)

The use of imports as a scale variable and the average
propensity to im port as an indicator of openness
have been discussed above. The trend-adjusted vari
ance of country i’s stock of foreign reserves is a proxy
for the variability of international receipts and ex
penditures. It is calculated using a m ethod sim ilar to
Frenkel’s .11
The m easure of opportunity cost em ployed is the
ratio of the discount rate in each country to the threemonth Eurodollar deposit rate. For a given portfolio
of assets, the discount rate represents a m easure of
the foregone earnings of central banks as a result of
holding assets in the form of foreign reserves; the
three-m onth Eurodollar deposit rate is a m easure of
the income earned from invested foreign reserves.
10See,

for example, Frenkel, “International Reserves”; and Heller
and Khan, “The Demand for International Reserves Under
Fixed and Floating Exchange Rates.”
11 Frenkel, “International Reserves,” p. 136. O ur measure of vari
ability is actually Frenkel’s divided by the num ber of degrees of
freedom (14 in this case); i.e.,
t -1
,

CTit =

2 (Rim - Rim-1 m =t-15,

V i m ) 2/

14,

where r)im is the slope of a linear time-trend equation esti
mated over the period t-15 to t-1.
Digitized for24
FRASER

(5) uit = pi uit_i + eit,
where pf = autocorrelation param eter for country i,
eit = white noise random error.

Including a separate autocorrelation param eter for
each country captures the country-specific variation
12The discount rate is em ployed because, even though it is not
market-determined, its movement closely parallels market rates
in the countries in the sample. Also, since most of the central
banks studied use interest rates as a mechanism of monetary
control, the discount rate reflects conditions in the respective
credit markets. Government securities markets are not suffi
ciently developed in all of the countries to be able to use an
interest rate from that market. The Eurodollar deposit rate is
used as the yield on foreign reserve stocks even though other
currencies are held as foreign reserves and even though some
central banks have refrained generally from investing in the
Eurodollar market directly. The justifications for this are: (a) the
U.S. dollar is still the major reserve currency, comprising 66 to 75
percent of the foreign reserves held by central banks, (b) some
central banks do invest directly in the Eurodollar market while
others invest indirectly using the Bank for International
Settlements as an intermediary and (c) the major alternative to
the Eurodollar market is the market for U.S. Treasury bills.
However, since the three-month Eurodollar rate and the threemonth Treasury bill rate move very closely together, they
yield virtually identical results when em ployed individually
in the estimation of both the intervention and the asset-choice
models. Finally, the ratio has been criticized as simply a proxy
forthe forward discount orprem ium on the currencies included.
However, when the covered ratio is substituted for the un
covered one, no significant qualitative changes occur.
13The sample period extends to IV/1980 for Japan, W est Germany
and the Netherlands. Gross domestic product data were not
available for the other countries in the sample for this extended
period.

FEDERAL RESERVE BANK OF ST. LOUIS

MARCH 1982

Table 1
Estim ation of Intervention M odel
1/1964-11/1973

111/1973-IV/19791

P a ra m e te r

E stim a te

S ta n d a rd
e rro r

ao
ai
a2
a3
a4

- .5 2 5
.883*
- .6 1 4 *
.064*
- .0 7 3

.420
.066
.072
.023
.060

E stim a te

S ta n d a rd
e rro r

1.102*
.644*
- .2 8 9 *
.113*
- .2 1 7 *

.503
.069
.070
.038
.055

C o u n try

D e n m a rk
F rance
G erm any
Japan
N e th e rla n d s
N orw ay
S w eden

.94
.94
.83
.92
.92
.90
.96

.89
.78
.93
.93
.54
.88
.74

N
RM SE
R 2 b e tw een a ctu a l
va lu e s and p re d ic te d
values

= 259
= .118

= .96

N
RM SE
R 2 b e tw e en a ctual
values and p re d ic te d
va lu e s

= 187
= .141

= .87

1The sa m p le p e rio d e xte n d s to IV/1980 fo r Japan, W est G e rm a n y and th e N e th e rla n d s.
"S ig n ific a n tly d iffe re n t fro m ze ro at th e 5 p e rc e n t level.

and also provides a m eans of introducing dynam ic the Sm ithsonian Agreem ent, that is, betw een the
behavior into the m odel .14
second and third quarters of 1973.16
Finally, the date ofthe switch from fixed to floating
The results obtained from estim ating the solution
exchange rates m ust be identified. Since the data are of equations 4 and 5 over the two tim e periods in
pooled, it is extrem ely difficult to identify the break dicated above are reported in table 1. Several dif
point as occurring at a specific point in time. It is ferences in the estim ated relationships for the two
likely the switch occurred over different intervals for periods are apparent. First, the im port elasticity (ai)
each country an aly zed .15 E xperim entation w ith in the fixed exchange rate period is significantly
various breakpoints around the March 1973 collapse larger than that in the floating rate period. In fact, the
of the Sm ithsonian Agreem ent yielded no single im port elasticity in the fixed period is not statistically
quarter as the most likely break point for all of the different from one, w hich indicates that central bank
countries in the sample. C onsequently, the break is holdings of foreign reserves do not exhibit econ
simply assum ed to coincide with the actual failure of omies of scale during that period. Second, the mag
nitude of the response to changes in variability (as) is
14For further explanation, see John F. O. Bilson and Jacob A.
Frenkel, “Dynamic Adjustment and the Demand for Interna
tional Reserves,” NBFR Working Paper No. 407 (November
1979), pp. 1-4; and H eller and Khan, “The Demand for Inter
national Reserves Under Fixed and Floating Exchange Rates,”
p. 631. As pointed out by H eller and Khan, when equation 5 is
substituted into equation 4, the result is observationally equiv
alent to an adaptive-expectations or an error-learning process.
15This is supported by Frenkel, “International Reserves,” pp.
122-25; and Saidi, “The Square-Root Law, Uncertainty and
International Reserves,” pp. 280-83.

16This choice is generally supported by Frenkel, “ International
Reserves,” pp. 124-25, and by Heller and Khan, “The Demand
for International Reserves Under Fixed and Floating Exchange
Rates,” pp. 637-39. The selection of the break point is also
constrained by the necessity to choose the same break point for
each model so that the performance can be compared over
identical sample periods. Also, for each model, the hypothesis
that the estimated parameters before this point are equal to
those after this point is rejected at the 5 percent confidence
level.
25

FEDERAL RESERVE BANK OF ST. LOUIS

larger under floating than under fixed rates. This is
som ewhat paradoxical since one m ight expect that
the increased exchange rate flexibility during the
floating rate period would serve as a buffer and,
consequently, reduce central banks’ response to
changes in variability .17
Third, the sensitivity of central banks’ reserve
holdings to interest rate changes under fixed rates
(a.4) is insignificant, a result sim ilar to that of other
studies .18 Alternatively, under floating rates, central
banks are found to respond in a significant and con
ceptually consistent m anner to changes in interest
rates. W hen com pared with those of previous studies,
these results suggest that an interest rate differential
is a better m easure of the opportunity cost of holding
reserves. Finally, a com parison of the intercepts (ao)
suggests that central banks are holding larger stocks
of foreign reserves, on average, in the floating rate
period than they did in the fixed rate period, indi
cating that they have actually added to their stocks
during the floating period.

The Asset-Choice Model
To estim ate the system of asset-dem and equations
represented by equation 3, it was assum ed that
norm ally distributed random errors enter additively
with zero m ean and constant variance. As a result of
introducing a random com ponent in this m anner, the
sum of the error term s across all equations in the
system m ust equal zero if the system is to be con
sistent .19 This restriction on the error structure, by
introducing linear dependence across equations, has
at least two im portant im plications for estim ation.
First, single-equation estim ating techniques are in
appropriate. Efficient estim ation requires the use of
a system technique. Second, the covariance matrix of
the entire system is singular. Because of this, a full17Frenkel,

“International Reserves,” p. 120, also obtained this
result; however, Saidi, “The Square-Root Law, Uncertainty and
International Reserves,” p. 285, found smaller responses to
changes in variability in the floating-rate period.
18See footnote 4.
19For the system of asset-demand equations represented by equa
tion 3 to be consistent, the value of the estimated portfolio must
equal the value of the actual portfolio. This condition implies
that the error terms across all n asset-demand equations must
sum to zero. That is, the error terms across equations are linearly
dependent and thus, by definition, correlated. It could also be
argued that, for this analysis, the demands for assets are cor
related regardless of the consistency condition. In particular, if
the impact of foreign exchange market intervention upon the
domestic money supply is sterilized (e.g., through an offsetting
sale or purchase of government securities), then foreign ex
change holdings and government security holdings are neces
sarily negatively correlated.
Digitized for26
FRASER

MARCH 1982

inform ation technique cannot be em ployed on the
entire system of n asset-dem and equations sim ul
taneously because the inversion of this covariance
matrix is required during the estim ation process.
Consequently, only n-1 equations can be estim ated
sim ultaneously.20
The countries and tim e periods em ployed here are
identical to those used in estim ating the intervention
m odel. The assets of the central banks of these
countries are aggregated into three categories: for
eign reserves, claims on governm ent and claim s on
com mercial banks. The interest rates used for these
asset groups are the three-m onth Eurodollar deposit
rate (for foreign reserves), short-term governm ent
bond yield in country i (for claims on governm ent)
and the discount rate in i (for claims on commercial
banks). The three-m onth E urodollar rate is used
here for the same reason it was used in the estim ation
of the intervention m odel. Also, a dynam ic specifi
cation is em ployed to capture lagged adjustm ent of
the com m itted param eters (yu) by allow ing them to
vary over time. This dynam ic feature is introduced
into the system by assum ing that the com m itted
level of each asset is a function of the total holding of
that asset during the previous tim e period as follow s:
(6)

yv t =

Xkt-i,

w ith 0 =£ 9\r s; 1 for all k. T h e p aram e ter 0^ reflects a
p ro p ortio n al relatio n sh ip b e tw e e n th e co m m itted
level o f asset k in th e cu rre n t p erio d to th e total
h o ld in g o f th a t a ss e t in th e p re c e d in g p e rio d .
F inally, th e d ate of th e sw itch from fixed to floating
exchange rates is th e sam e as in estim atin g th e in
terv en tio n m odel.

Substituting equation 6 into equation 3 and recog
nizing that n = 3 in this case, the resulting system of
asset-dem and equations is as follows:
(7.1) x iit = Hi x u m + —'lBi- t (T' A it - . 3X , Oj x jin vjit)/ + ulit
J=1
(7 .2 ) X2it

(7 .3 )

X2 iM

(T A it v 2it '

x3jt =

x 3it-i + —

+ —

V 3 it

(T A it -

Xjit.i Vjit)

u 2it

Xjit.i Vjit) +

u3it

J=1
.

J=1

20Robert A. Poliak and Terence J. Wales, “Estimation of the
Linear Expenditure System,” Econometrica (October 1969),
pp. 611-28. They prove that if a full-information, maximumlikelihood estimation procedure is employed, the estimated
param eters are invariant to w hichever n -1 equations are
included.

FEDERAL RESERVE BANK OF ST. LOUIS

MARCH 1982

Table 2
Estim ation of A sset-C hoice M odel
1/1964-11/1973
P a ra m e te r2
01
tt2
t>3
01
02
03

E stim a te

III/1973-IV/19791

S ta n d a rd
e rro r

.987*
.893*
1.005*
.536*
.326*
.138*

.022
.032
.017
.048
.035
.041

RM SE o f e q u a tio n 7.1 = .697
R2 b etw een a ctu a l and
p re d ic te d va lues fo r
e q u a tio n 7.1
= .98

E stim ate
.983*
1.001*
.897*
.261*
.213*
.526*

S ta n d a rd
e rro r
.011
.018
.049
.038
.047
.058

RM SE o f e q u a tio n 7.1 = 1.404
R2 b e tw een a ctu a l and
p re d ic te d va lues fo r
e q u a tio n 7.1
= .99

'T h e sa m p le p e rio d e xte n d s to IV/1980 fo r Ja p a n, W est G erm any and th e N e th e rla n d s.
2The s u b s c rip ts 1, 2 a nd 3 re fe r to th e th re e asset c a te g o rie s, fo re ig n reserves, cla im s on g o v e rn
m en t and cla im s on c o m m e rc ia l banks, resp e ctive ly.
'S ig n ific a n tly d iffe re n t fro m ze ro at th e 5 p e rc e n t level.

other hand, the estim ated com m itted param eters for
claims on governm ent (6 2 ) and for claims on com
m ercial banks (6 3 ) have changed significantly with
1
v jit
the change in regim es .22 Furtherm ore, the p er
1 + r,jit
centage of their discretionary portfolio that central
ijit = the yield on asset j in country i from be banks held in the form of foreign reserves (/3i) fell
ginning to end of time period t,
significantly from the fixed to the floating period.
TAit = the value of i’s portfolio at beginning The sensitivity of the dem and for foreign reserves to
of period t,
changes in interest rates (as m easured by the abso
lute value of the price elasticity of dem and) also fell
= error term.
.jit
from .563 in the fixed rate period to .289 in the
Table 2 presents the results of estim ating the above floating rate period. N onetheless, the fact that this
system om itting equation 7.3 .21 A full-information, percentage is statistically significant in both periods
m axim um -likelihood technique is used to obtain indicates that reserve holdings are at least partially
efficient estim ates.
sensitive to changes in interest rates.
All param eter estim ates are statistically significant
Taken together, the changes in 91 and /Si over the
and w ithin conceptually acceptable ranges of values. two periods shed some light on why H eller and Khan
As before, differences betw een tim e periods, but consistently overpredict central bank dem and for
also across assets, are readily apparent. In particular, foreign reserves during the floating period .23 In their
the estim ated com m itted param eter for foreign re m odel, central banks hold foreign reserves solely to
serves (fli) is relatively constant across tim e periods, intervene in foreign exchange m arkets. A lterna
indicating that central banks have not altered the tively, in the asset-choice m odel, intervention is
com m itted portion of their foreign reserves in the simply one of several m otives (where the com m itted
move from fixed to floating exchange rates. On the param eter m easures the dem and for reserves for
where jit

the value of country i’s holding of asset
j at the end of time period t,

21Except for ^3 and its variance, all parameters and their variances
are estimated directly. Since 2 f3y = 1, 03 = 1 — 0i — 02 and
k
Var ((83) = Var (/3i) + Var ((82) + 2 Cov (/3i, 02 ). The same results
as those reported were obtained when either equation 7.1 or 7.2
(instead of 7.3) was deleted.

22Even though 63 in the fixed period and 62 in the floating period
are greater than 1 (the conceptual limit of each), neither is
significantly greater than 1 in a statistical sense.
23H eller and Khan, “The Demand for International Reserves
Under Fixed and Floating Exchange Rates,” pp. 639-43.
27

FEDERAL RESERVE BANK OF ST. LOUIS

MARCH 1982

Table 3

Table 4

Partial Elasticities of Substitution

R esidu al-V arian ce Estim ates

Assets

1/1964-11/1973

F o re ig n reserves
and cla im s
on g o v e rn m e n t

.116

F o re ig n reserves
and c la im s on
c o m m e rc ia l banks

.031

C la im s on g o v e rn m e n t
and c la im s on
c o m m e rc ia l banks

.065

111/1973-IV/19791
.028

Level
L o g -le ve l
.076

.094

'T h e s a m p le p e rio d e xte n d s to IV/1980 fo r Japan, W est
G e rm a n y and th e N e th e rla n d s.

purposes of intervention ).24 Even though this rela
tionship appears to be relatively stable across tim e
(in the asset-choice model), overlooking the sig
nificant decline in the percentage of the precau
tionary portfolio held in the form of foreign reserves
by basing predictions on a interven tio n m odel
should lead to an overprediction of reserve dem and,
ceteris paribus.
O ne final question remains to be answ ered: Are
the assets in central banks’ portfolios close substi
tutes for each other? To answ er this question, partial
elasticities of substitution are calculated for each of
the asset pairs over each tim e period. Since these
elasticities are functions, inter alia, of the com m itted
and uncom m itted levels of each asset, the elasticities
reported are evaluated using the m ean holdings of
the relevant assets (table 3). Given the relatively
high estim ated values of the com m itted param eters,
it is not too surprising to find that none of the assets
are close substitutes.

Predictive Abilities o f the Two Models
T he ultim ate test of a structural m odel is how well
it predicts behavior. This section compares the pre
dictive abilities of the two m odels described above.
24One may infer that, since the asset-choice model does not ex
plicitly contain explanatory variables that represent the in
tervention motive, it is fundamentally mis specified. However,
the estimation of the asset-choice model clearly indicates that
the foreign reserve demands of central banks are sensitive to
yields on other assets in their portfolio. Since the intervention
model ignores these explanatory variables, it is also funda
mentally misspecified. Consequently, future research should
be directed at combining the features of both of these models to
specify correctly a central bank’s demand for foreign reserves.
Digitized for 28
FRASER

1/1964-11/1973

111/1973-IV/19791

.788
.0139

4.577
.0199

.486
.0144

1.970
.0167

Intervention model

Asset-choice model
(E q u a tio n 7.1)
Level
L o g -le ve l

1The sa m p le p e rio d e xte n d s to IV/1980 fo r Ja p a n, W est
G e rm a n y and th e N e th e rla n d s.

Two m ethods of com parison are em ployed: T he first
is the residual-variance criterion d evelop ed by
Theil 25 The use of the residual-variance criterion
involves calculating a residual-variance estim ate
(error sum of squares divided by degrees of freedom)
for each m odel and selecting the m odel w ith the
sm allest residual variance .26 Since the intervention
m odel is estim ated in log-level form and the assetchoice m odel is not, the residual-variance estim ates
from the two m odels are not directly com parable. To
m ake these estim ates com parable, eith er the re
siduals of the estim ated intervention m odel have to
be transform ed from logarithms to levels or the re
siduals of the estim ated asset-choice m odel have to
be transform ed from levels to logarithm s .27 Table 4
presents the results of both of these transform ations.
Except for the logarithm ic specification estim ated
over the fixed rate period, the asset-choice m odel
appears to outperform the intervention model.
T hese results, how ever, m ust be qualified. The
residual-variance m ethod presupposes that one of
the specifications is the correct one, a som ewhat
presum ptuous supposition. Also, in this case the two
25Henri Theil, Principles o f Econometrics (John Wiley and Sons,
Inc., 1971), pp. 543-45, 553-54.
26The selection of the specification with the smallest residual
variance is justified by the following proposition: if the correct
specification has uncorrelated disturbances with zero mean and
constant variance and if the explanatory variables are non
stochastic, the residual-variance estim ator of the correct
specification has an expectation that is never larger than that of
an incorrect specification. See Theil, Principles o f Econo
metrics, p. 543.
27This transformation is accomplished by converting the actual
and the predicted values from the level (logarithmic) specifi
cation into logarithms (anti-logs), calculating the sum of squared
deviations of the predicted value from the actual, then adjust
ing for degrees of freedom.

FEDERAL RESERVE BANK OF ST. LOUIS

m odels com pared are non-nested; that is, the m odels
have separate sets of explanatory variables such that
one m odel cannot be obtained from the other. Con
sequently, the conventional use of summary statis
tics and F-tests to discrim inate am ong alternatives
can be m isleading and even inappropriate .28
The second m ethod is an extension of the Cox test
developed by Pesaran and D eaton .29 This procedure
for testing non-nested hypotheses is not subject to
either of the above qualifications necessary for in
te rp re tin g the resu lts of th e resid u al-v arian ce
m ethod. In particular, Pesaran and D eaton’s pro
cedure does not em ploy a single m aintained (null)
hypothesis. (No m odel is considered a priori to be
the correct one.) The alternative m odels are anal
yzed one at a time. O ne by one, each is assum ed to be
the correct one.) The alternative m odels are ana
lyzed one at a time. O ne by one, each is assum ed to
be the correct model (null hypothesis); the alternative
has been observed. T he notion of absolute goodness
of fit plays no role in this procedure. In fact, the
possibility exists that all com peting m odels may be
rejected. This is not the case for conventional testing
procedures .30
The test statistics calculated w ith the intervention
m odel and equation 7.1 of the asset-choice m odel,
respectively, as the null hypothesis are reported in
table 5 .31 U nder the null hypothesis, this test statistic
is asym ptotically distributed as a norm al random
variable with zero m ean and unit variance. The rp28See M. H. Pesaran, “On the General Problem of Model Selec
tion,” The Review o f Economic Studies (April 1974), pp. 153-71.
29D. R. Cox, “Tests of Separate Families of Hypotheses,” in
Proceedings o f the Fourth Berkeley Symposium on Mathe
matical Statistics and Probability (University of California
Press, 1961), pp. 105-123; M. H. Pesaran and A. S. Deaton, “Test
ing Non-Nested Nonlinear Regression M odels,” Econometrica
(May 1978), pp. 677-94.
30A necessary condition for the use of this test is that both models
explain the same dependent variable. In this case, the first
equation of the asset-choice model explains the quantity of
reserves dem anded while the intervention model explains the
logarithm of the quantity of reserves demanded. Consequently,
to perform the Cox test, the anti-log of the intervention model
(i.e., a non-linear, Cobb-Douglas-type function) is estimated
using a maximum-likelihood procedure. The resulting pre
dicted values and e stimated parameters are essentially identical
to those obtained from a least-squares estimation of the loglinear functional form.
31The test statistic (C) is defined as:

where To = s I n --------;-------------------------------------------- ,
°o +

“ g(0Ao)]'[f(<£o - g(<?>Ao)]

MARCH 1982

Table 5
Statistics for Testing H ypotheses
Involving N on-N ested M odels
Ho: In te rv e n tio n m o d e l
H a : A sse t-ch o ice m od e l (E q u a tio n 7.1)
T est sta tis tic

Period
1/1964-11/1973

-1 8 .3 6 *

111/1973-IV/19791

-2 2 .6 2 *

Ho: A sse t-ch o ice m o d e l (E q u a tio n 7.1)
H a : In te rve n tio n m odel
T est s ta tis tic

P e riod
1/1964-11/1973

- 0 .8 5

111/1973-IV/19791

- 0 .7 5

1T he sa m p le p e rio d e x te n d s to IV /1980 f o r Ja p a n , W est
G e rm a n y and th e N e th e rla n d s.
‘ S ta tis tic a lly d iffe re n t fro m z e ro at th e 5 p e rc e n t level.

suits are unam biguous. W hen confronted w ith the
"data and the asset-choice m odel as an alternative, the
intervention m odel m ust be rejected. Alternatively,
the asset-choice m odel cannot be rejected. This
conclusion is invariant across sam ple periods. W hile
the rejection of the intervention m odel for the float
ing rate period is not unexpected, it is certainly
interesting that this m odel is also rejected for the
fixed rate period. This result confirms that the assetchoice m odel provides a m ore general explanation of
central banks’ dem and for reserves than does the
intervention m odel.

SUMMARY AND CONCLUSION
The purpose of this article has been to compare
central bank behavior before and after the m ove
m ent to floating exchange rates w ithin the fram e
work of two alternative m odels of a central bank’s
dem and for foreign reserves. In the first m odel,
sample size,
estimated variance of the model under
H0,
estimated variance of the model under

Ha,

f($o) - g(cf>Ao) = the residuals from an auxiliary esti

Var (T„)

mation of the model under H a using
the predicted values from the model
u n d e r Ho as th e d e p e n d e n t
variable,
the variance of To as defined in
Pesaran and Deaton, “Testing NonN e ste d N o n lin e a r R e g re ss ion
M odels,” p. 687.

FEDERAL RESERVE BANK OF ST. LOUIS

foreign reserves are treated as a special type of asset,
one dem anded solely to enable a central bank to
intervene in foreign currency markets. T he second
m odel considers foreign reserves to be the same as —
and also to be held for the same reasons as — any
other asset w ithin a central bank’s portfolio.
The estim ation of the asset-choice m odel as an
alternative to the intervention m odel yielded several
interesting results. First, a central bank’s dem and for
foreign reserves is sensitive to relative changes in
the yields of the assets in the portfolio. Second,
central banks consider foreign reserves as substi
tutes to other assets in their portfolio. Third, the
decrease in the percentage of the uncom m itted
portfolio com posed of foreign reserves is identified
as a possible reason for the usual overprediction of
reserve dem and by the intervention m odel in the

MARCH 1982

floating rate period. Finally, and m ost im portantly,
the asset-choice m odel consistently outperform s the
intervention m odel.
Since the testing procedure em ployed could lead
to the rejection of both m odels, the fact that the
asset-choice m odel cannot b e rejected in eith er
sam ple period is an extrem ely robust result. The
im plication is sim ply that, regardless of exchange
rate regim e, central banks hold foreign reserves for a
w ide variety of purposes — not ju st for intervention
in foreign exchange m arkets. C onsequently, the
in v estig atio n of w h eth er or n ot cen tral b an k s’
general behavior has changed with the m ovem ent to
a system of floating exchange rates w ithin the
framework of the intervention m odel appears to be
m isdirected. Investigation should focus on the
argum ents, instead of the param eters, w ithin the
dem and function.