= 1h =
interpret a finding of g>0 as implying that speculation is stabilizing and
a finding of g<O as implying that speculation is destabilizing.

Table 4 reports regression estimates of equation (5), using the
survey expected depreciation as the lefthand-side variable. The regression
error can be interpreted as random measurement error. Under the joint
hypothesis that the mechanism of expectations formation is specified
correctly and that measurement error is random, the parameter estimates are
consistent. It should be noted that the joint hypothesis is a particularly
strong assumption because the spot rate appears on the right-hani-side; if
a change in expected depreciation feeds back to affect both the
contemporaneous spot rate and any element of the regression error, then the
estimate of g will be biased and inconsistent. However this is not a
problem under our null hypothesis that expected depreciation is constant.

The findings are once again ordered by the length of the forecast
horizon. It is immediately evident that the shorter-term expectations --
one week, two weeks and one month -- all exhibit large and significant
bandwagon tendencies: that is, g <0. In the one-week expectations, for
example, an appreciation of 10 percent in one week generates the
expectation that the spot rate will appreciate another 2.4 percent over the
next seven days.

In contrast with the shorter-term expectations, the longer-term
results all point toward distributed lag expectations, the stabilizing case.

Each of the regressions at the 6 and 12 month forecast horizons estimate g


IFDP

NUMBER

279

278

277

276

275

274

273

272

271

270

269

268

267

- 28 -

international Finance Discussion Papers

TITLES

The Prospect of a Depreciating Dollar
and Possible Tension Inside the EMS

The Stock Market and Exchange Rate Dynamics

Can Debtor Countries Service Their Debts?
Income and Price Elasticities for Exports
of Developing Countries

Post-simulation Analysis of Monte Carlo
Experiments: Interpreting Pesaran's (1974)
Study of Non-nested Hypothesis Test Statistics

A Method for Solving Systems of First Order
Linear Homogeneous Differential Equations
When the Elements of the Forcing Vector
are Modelled as Step Functions

International Comparisons of Fiscal Policy:
The OECD and the IMF Measures of Fiscal
Impulse

An Analysis of the Welfare Implications of
Alternative Exchange Rate Regimes: An
Intertemporal Model with an Application

1985
(partial listing)

Expected Fiscal Policy and the Recession
of 1982

Elections and Macroeconomic Policy Cycles

Assertion Without Empirical Basis: An
Econometric Appraisal of Monetary Trends
in... the United Kingdom by Milton Friedman
and ‘Anna J. Schwartz

Canadian Financial Markets:
Proposal for Reform

The Government's

Was It Real? The Exchange Rate Interest
Differential Relation, 1973-1984

The U.K. Sector of the Federal Reserve's
Multicountry Model: The Effects of
Monetary and Fiscal Policies

AUTHOR (s)

Jacques Melitz

Michael K, Gavin
Jaime Marquez
Caryl McNeilly

Neil R. Ericsson

Robert A. Johnson

Garry Schinasi

Andrew Feltenstein
David Lebow
Anne Sibert

William H. Branson
Arminio Fraga
Robert A. Johnson

Kenneth Rogoff
Anne Sibert

David F. Hendry
Neil R. Ericsson

Garry J. Schinasi

Richard Meese
Kenneth Rogoff

Hali J. Edison


CA

o

- 24 -
several other variables such as the lagged spot rate, tne long-run

equilibrium spot rate, and the lagged expected spot rate.

(7) Investors could improve both their short-term and their long-term
forecasts by reducing the absolute magnitude of expected depreciation
toward zero. This finding of "excessive Speculation" would follow from the
result that expected depreciation is not zero together with the popular

hypothesis that the true spot process follows a random walk.


- 10 -
depreciation. Under the assumption of rational expectations, the future
spot rate realizations are viewed as noisy measures of investors’
expectations. This noise is assumed to be uncorrelated with the forward
discount, and therefore can be identified with the residual term in
equation (3). Table 2 reports estimates of equation (3), using ex post
changes in the spot rate as the lefthand-side variable.6 All of the

point estimates of b are less than zero, and most are significantly less
than one, The conventional approach would therefore seem to imply that
changes in the forward discount predominantly reflect changes in the risk ‘
premium,

Our alternative test of equation (3) uses the survey expected
depreciation on the lefthand side, in place of the actual spot rate change.
The existence of heterogeneous beliefs, the use of the median survey
response, and the lack of perfect synchronization, are reasons to suspect
that the surveys may also be noisy estimates of market expectations. Now
the error term in the regression equation may be interpreted as measurement
error in the surveys. We make the assumption that this measurement error
is random, which is analogous to the assumption of rational expectations
used in the conventional technique above, i.e., that the expectation error
is random.

611 of the regressions in this paper are estimated using OLS. The
Economost surveys, MMS one-month and three-month surveys, and the AMEX
twelve-month survey were conducted at intervals shorter than their
respective forecast horizons. This implies that the error term in equation
(2) is serially correlated even under the null hypothesis. Consistent
estimates of the standard errors were obtained by the usual method cf
moments procedure (see Hansen and Hodrick (1980), or Froot and Frankel
(1986) for a more detailed description). For additional information. on the

construction of the data sets used in this paper, see the appendix to
Frankel and Froot (1985).


16A -

*szoqoueted adaorzequtueu Tre we 4se89
szojowezed 7as022 FUFUCH TTP "UO 3S23

due 0} spuodsezioo §~yo *TaAST Queored T |YyR 3e soUROTITUBTS squesetded xxx “TeAaT Juaored ¢
ay ze soUROTITUBTS sjuesertdey yy “TOAST JUedTEd OT eyR 3e aoUROTZTUBTS sjueserdey *
‘uak ted szeTTOp JO suze} UT e1e sezeI ebueyoxe pejoedxe pue Tenjov

(€vso°0)
9b°0 9€ ELT ax LL°Z ZOST"O S8/ZT-18/9 YUqUOW ZT 3YSTWOUCO”T
(9L€0°0) ———
€s°0 9E PTT xxx T2°€ 80ZT°O S8/ZT-18/9 yaUOW 9 4ySTWOUCDR
(Z7S0°0)
evo 9E T6°T xx 79°T Z2pto .. S8/ZT-18/9 yqUOW € YSTWOUCOT
(ZLE0°0)
6T°0 ov €0°T vy SESO"0- v8/0T-€8/T YaUOW € SNW
(8S70°0)
TE*O rAd 2o°T * 66°T- TT60°0- 98/2-¥8/0T yzUuOW T SW
(L870°0)
T2°0 vv T2°T €s*t- byVLO"0- v8/0T-€8/T 4S2M Z SWN
(6zS0°0)
ov'o €s Te*t xx DEO2- 6872T°0- 98/2-08/0T 48°M T SW
2a aa (Z) ma 0= h seqed qes ejed
quaetToTyzj900

( (Qs - £ (9)s 1(1-3)9 DR + & = (9)S - [(T+3)8] | tuoT}eTOeAded pezoedxg_ AeaIns jo suoTssezbey SIO

(3)s - [ (9)8 ](1-3)a teTqetTzea Auepuedepul
SNOILVLOddxa AALLdIVIY
9 aTawL

98/TT/80


-3-

Another question, which would be of particular interest to
policy-makers if one were to conclude that exchange rates have been
undesirably unstable, is whether government intervention in the foreign
exchange market offers a way of affecting the exchange rate even in the
absence of a change in macroeconomic policy. The question of whether
intervention can have an effect, even if sterilized so as to leave the
money supply unchanged, is generally thought to depend on the question
whether yen and dollar assets are imperfect substitutes in investors’
portfolios. Under the special case in which assets are perfect
substitutes, investors will be willing to absorb indefinitely-large
quantities into their portfolios, as long as the assets pay the going rate
of return, with no effect on the price of the asset. The condition one
would like to test is uncovered interest parity: risk-neutral investors
drive the yen interest rate into equality with the dollar interest rate
corrected for expected depreciation.

Exchange rate expectations are crucial for each of these
important. questions, and for others as well. Measuring investors'
expectations is always difficult. Probably the most commonly-used measure
of expected depreciation is the forward discount, which arbitrage (in the
absence of barriers to capital flows) in turn equates to the interest
differential. But using the forward discount or interest differential
prejudges the question of perfect substitutability. The other common
approach is to assume that market expectations can be measured as the

mathemati.cal expectation of the realized exchange rate within the sample


- 22A -

*Se7eUTISS SjuSUIOW JO poy oul o1e SIOIIe prlepuejS ‘siojowered ydeorequTUOU TTe UO 4se3

due 0} spuodse1i0>9 .y “TeAeT JueoIed [ 9|y3 Je soOUeOTZTUSTS squUeserdey xxx “TOA8T Quooted ¢
Suz Fe soUrOTITUBTS sSqUeseidey xx “TeAeT WUSdOZEd OT ay We souRroTFTUBTS sjuaesoidey *

‘uak zed sieTTop Jo suze uy ore saqer eHueyoxa po oedxo pue Ten}o7w

(9TEZ°T)
¥x 66°6 89°0 9 wee SED S29E°S $8/8-9L/T YqUOW ZT xeuy
(TETE*T) .
xxx ST°ET 8e°0 6% #x SE°T TT60°E $8/2T-18/9 U3IUOW ZT YSTWOoUCDT
(O€P9°T)
« STV 9r°0 L #x 6L°2 VOLS $8/8-9L/T U;UON 9 xeUTY
(Teps*T)
¥* T2°S zy" ve wx VS°Z LS8o°y $8/2T-18/9 UqUOW 9 YSTUIOUCD|
(vTE9°T)
wax T9°S 8r°0 gE wee S8°T SSSO"y $8/2T-18/9 UIUOW € 3STUIOUCDT
(9sze°e)
ae VED TT"O SY €0°T STEr'e v8/0T-€8/T UaUON € SW
(OSTO*ET)
Lez T0°O (44 se°o PLLS*Y 98/2-¥8/0T YaUOW T SHIN
O=q ‘0=e ua aq O=q 23 q sojed yes ejed
3593 a WUSTOTIJE0o
( (a)s - (4)F ) 4 + © = (T+9)8 - [(14+9)8] 2 tsr012q TeuoTaeIoedxa Kearns IO suoTssazhay so

(3)8 - (4)3 teTqeTrea quepuedepur
NOILWINOAdS AAISSHOXA JO SLSAL
Tl TavL

98/TT/80


14A -

*szejowered ydeo1e,uTUOU TTe UO 4s03

due oy spucdseiioo .y  *TeAeT quecred [ ey3 3e eouRoT;TUBTS squeserdeY xxx “TOAST JUsoIed ¢
9y} 3e soUeOTJTUHTS Squesetdey xy ‘“TeAeT Ueored OT 943 3e SOUROTJTUBTS squUesoidey *
‘uek ted sIeTTOp Jo sue, uT ere sajzer ebueyoxs pejzoedxe pue Tenjoy

(Z0LT°0)

€y°o L #* 6S°7 tbo S8/8-9L/T YRUOW ZT xeuy
(¥990°0)

sL°o 9€ Ty°T axe ST°S Teve’o $8/2T-18/9 UIUOW ZT 3STWOUCDg
(v2TT"0)

ep°o L VN wx 65°72 L067°0 $8/8-9L/T yqUOW 9 xXeUy
(1T0S0°0)

8s°o0 9E Lo°T wen OS°E €8LT°O $8/ZT-18/9 UIUCW 9 3STWOUCDy

(€ZS0°0) —_____

sv°o 9€ sort wax ELS 62yT°0 S$8/2T-18/9 YaIUOW € FSTWOUDD|
(TEZ0°0)

os*o oF T2°T #ex 00°E- y690°0- v8/0T-€8/T Y3UOW € SW
(9€70°0)

9n°0 (42 9L°T wax LL°T- 802T°0- 98/2-¥8/0T Y3UOW T SNH
(97S0°0)

£€°0 Lad ZETT xx 80°7- SETT°0- b8/0T-€8/T 43°M 2 SWW
(060°0)

€L°0 €s BL°T wax 88°0- T6EZ*O- 98/2-b8/0T 439M T SWW

wu aq (Z)ma 0=6 33 65 Jes eqed

JueToTsyaoo
( (4)s - (T-3)s )6 + & = (3)8 - [(143)8] 2 suoT}eTOsIdeq pejoedxy AeaIns Jo suotsseibey sIo

(3)8 - (1-3)S teTqeTzea juepuedepur
SNOILVLOadXa AALLVIOdVaLXa
v ATavL

98/TT/80


-19-
of the true spot process behaves in the same way, i.e., whether
expectations are rational. One way to proceed would be to re-estimate each
of tke models given in equations (5)-(8), only now using realized
depreciation as the lefthand-side variable. The hypothesis that
expectations are rational would imply that these regressions should yield
coefficients that are statistically indistinguishable from those obtained
earlier using the surveys on the lefthand side. A more direct way to test
the same hypothesis is to regress the difference between the survey
expectation and the actual future spot rate, the survey prediction error,
on each set of regressors in equations (5)-(8). Under the null hypothesis
that expectations are rational, this prediction error should be purely
random (conditionally independent of all information available at time t)
and therefore should be uncorrelated both with the righthand-side variables
and with past errors. We test whether the coefficients are jointly zero.
Table 7 reports regressions of the survey prediction errors on
the nost recent change in the spot rate. The estimated F statistics give
some evidence of systematic expectational errors: five of the nine data
sets reject the joint hypothesis that both the constant and slope
coefficients equal zero. In view of the discussion in the previous
sect:.on, an inspection of the slope coefficient, g, can help us to
determine whether investors place the correct weight on the lagged spot
rate. A finding of g,>0 would indicate that expectations are
"insufficiently" extrapolative: investors give too much weight to the
lagged spot rate and too little weight to the contemporaneous spot rate

relative to what is rational. Conversely, a finding of g,<0 would indicate


- 16 -
Table 5 presents tests of equation (4). Estimates of changes in 8

were calculated using CPI's to measure changes in the relative price levels
in tne United States and Japan, under the assumption of purchasing power
parity (PPP). Once again, there is strong evidence that shorter-term
expectations are formed in a manner different from longer-term expectations.
The shorter forecast norizons all yield estimates of tnat 9 are negative,
additional evidence that shorter-term speculation may be destabilizing.
Indeed, the 1-week data suggest that the contemporaneous deviation from the
long-run equilibrium is expected on average to grow by 3 percent over the
subsequent seven days. In other words, short-term expectations are
explosive. What about the longer-term horizons? In Frankel and Froot
(1985) we found a highly significant speed of regression at the longer-term
horizons. The longer-term estimates of 0 in Table 5 do not, however,
exhibit regressivity for the yen that is as highly significant. Only the
American Express 12-month data, which is available as far back as 1976,
shows an estimate that is significant even at the 10 percent level. It may
be that relative CPI's are not the appropriate indicator of the equilibrium
yen, dollar rate. It has been suggested that due to rapid productivity
growth in Japan, Japanese producers gain in international competitiveness
even to the extent that PPP is observed to hold. Marston (1986)
demonstrates that even though estimates of real exchange rate changes using
CPI show real appreciation of the yen against the dollar over the last
decade, estimates using manufactured goods prices give a very different

answer. 9

The final specification we consider is adaptive expectations. In

9Se2 also Krugman (1986) and Johnson and Loopesko (1986).


- 23-
V. Conclusions
(1) The survey data on exchange rate expectations appear to contain new
information about market expectations which is not apparent from either ex
post spot rate changes or the forward discount. Our measures show that,
despite the large swings in the value of the yen in the 1980s, the surveys

consistently called for a large appreciation of the yen against the dollar.

(2) These measures of expected appreciation are also substantially in
excess of the forward premium. An implication is that investors were
willing to accept a lower expected rate of return on dollar asset;s than on

comparable assets denominated in yen.

(3) Contrary to what is commonly assumed in most models in which
sterilized foreign exchange intervention is effective, variation in the
forward discount does not reflect a Statistically significant degree of

variation in the risk premium.

(4) Variation in the forward discount primarily reflects, instead of

changes in the risk premium, changes in expected depreciation.

(5) The expectations given in the short-term surveys exhibit bandwagon

effects, which could imply that short-term speculation is destabilizing.

(6) Expectations at longer-term horizons, in contrast, appear to put less

than full weight on the contemporaneous spot rate and positive weight on


-12-
exogenous downward trend during the 1981-85 period, as it would under the
hypothesis that internationalization was causing investors around the world
to become more willing to hold yen. (Figure 1 shows, on the negative axis,
the risk premium on dollars, i.e., the forward discount or interest
differential minus the expected appreciation of the yen.) In all cases,
however, we can reject the hypothesis of perfect substitutability, a=0 and
b=1 jointly. In other words, the risk premium does show up in the constant
tern.

To summarize, in Table 3, as in Table 1, it appears that. the ex
post depreciation may be a very poor measure of expected depreciation.
Table 3 provides evidence that changes in the forward discount reflect
primarily changes in expected depreciation rather than changes in the risk

premium.

IIIl. Models of Expected Depreciation

The results from the first three tables suggest that there is
information on expectations in the surveys which is not contained in either
realized spot rates or forward rates. We may thus gain new insigtts by
using this data source to reexamine several old formulations of exchange
rate expectations that are standard to the literature.7

A general framework for testing various specifications of
expectations is to model expectations of the future spot rate as giving
some weight to the contemporaneous spot rate as well as some weight to

other variables in investors' information set. In each case below, our

TThe tests reported in this section are similar to those reported in Frankel
and Froot (1985) for the dollar against five other currencies. But they
did not include the results for the shorter-term forecast horizons.


-7A-

To'9

028:

667k

C(1+9)8]a-(4)F
wOIWaad
‘SIa
(2)-(e)

es'y

PLP

Lo°b

eo°T

YN

VN

INnOoSIa
CuVMuOT
(e)

gg°ct

o
oy
a

OP's
as.
~-((1+9) 813

ViVd ASAUNS

(a)

ge + 80°O- Té
!
Be H es°c 9E
ge ' Led se
Ly : 06 °2- Lv
VE 1 SS°LZ vb
Lo 1 €2°b- Lb
es 1 6E°VS 29
H (4)s
N 1 -(1+9)s N
SONVHO
TWOLOV
(1)

(umuue zod qu

e0red

poyfied eydues 12aA0

ALVA NAA/$ FHL JO
NOILVIOGadad CHLOGUXH AO SHANSVAWN SNOIUVA

T

STqeL

%

S8/ZI-18/3

S$8/ZT-138/9

$8/EI-18/9

¥8/dT-€8/T

ye/0T-e8/T

98/c-¥8/0T

)

e12ae

LSINONOOE

LSINONOOE

LSINONOOT

Sk

SHR

zOunoSs
AGAENS

ZT

SHLNO}

SHLNOR 3

°

SHLINOR

HLNOW T

2
M
ti
fa
ol

NOZTUO
LSVOTHOT

98/F1/80


*saqeUT Ase squUaUOW Jo poyjou oTe Sore prepueys  “srejowered ydeorequTUOU TTR UO 3S93

a ue 03 spuodserz109 =,Yy *TaAeT JuUedred T oyR 32 aouRoTJTUBTS squesetdey xxx “TOAST QUedIed ¢
uy 3e BoUROTITUBTS SqUeseIdey xx ‘TOAST QusoIed OT 94; We eouroTsTUubts squeseidey *

‘uak red sieTTOp Jo suite} uy ere sajer ohueyoxs poqoedxe pue Tenjov

(L8T0°2)
eS°T 8Tt°o 9 ent LOLB°Z $8/8-9L/T yaqUOW ZT xeuy
(009L°0) - —_—____
xxx LOR sto 6% pert 9bv6°0 S$8/Z2T-18/9 YAUOW ZT 3S TwoUoog
1 (92Te°T)
a * GS°E zo L xx LS°Z BTLE°E $8/8-9L/T YAUOW 9 xXeUly
a
N (2026°0) —_—_____
1 exe EV°S py'o ve ax VOT €87p°? $8/2T-T8/9 yqUoW 9 YSTWOUCDT
(L88°0) ——_
ax SEE Te*o 9€ xx €0°7 8T66°0 S8/2T-18/9 YIUOW € 3STWOUCDT
(Z9LL°0)
xxx 627°S oc"o Sv * 86°T 90bS°T v8/0T-€8/T yaUuOW € SNH
(¥98L°0)
ax 82°E oT°o oy 66°0 86LL°0 98/2-¥8/0T YuaUOW T SW
o=a ‘0=e8 za aa q sozed yes eed
3803 4 queTOTZJe0o
{ (aye E(qtea}sig } a4 Pe = (t+2)s - [(t4+3)s] q tsz071a Teuotzejoedxg Aearns Jo suotsseizbey so

(a)s - [(1+3)8]a teTqeTzeA Quepuedepul
NOILWINOGdS AAISSHOXA JO SLSAL
OT FIAVL

98/TT/80


- 19C -

*SeREWT{se Bue JO POUZSW SAE Szczzs PIcPUeIS *ezaqaumred adeazeiqutuou TTR uO 3893

4 ue 03 spucdsezz0D 4k ‘TOAST QueoXed T ey3 Je SoURDTFTUBTS squesoTdod xxx “TOAST quooted ¢
9Y2.3e DoUROTZTUSTS sQuoserdey xx “T2AeT quaoied oT ey} 3e eoUROTZTUBTS squeserzdey *

eusk zed sieTTop jo suze} ut ore sozer ebueyoxe pe zoedxe pue TenjoV

(SLTE*0)

0£°0 Iz = V6°T- TLT9°0- $8/Z1-18/9 yauoW ZT 3STUOUCOE
(T69€°0)

se°t 00°0 62 8t°o 8990°0 $8/2T-18/9 yqUoW 9 YsTWOUCDT
(s86T'0)

ze" €€ we 90°% 880P'0 S8/ZT-18/9 yaUOM € STWOUCDT
(6962°0)

Wz 10°O 6 vE'O- OTOT"0- y8/0T-€8/T yquoW ¢ SHH
(6TSZ°0)

0€'2z 10°0 €€ 62°0- 22L0°0- 98/2-¥8/0T yauoW T SHH
(1TyT"0)

vet so°o vy 89°0 1960°0 y8/0T-€8/T 4294 7 SHH
(TSeT"0)

zs"0 To"0 vs £270 90£0°0 98/2-¥8/0T 499M T SHH

o='R‘o=e aq o='h yes e3ed

4803 4 QuseTOTZZe00

( (ays - ( (aps Tt-3)a A+ ® = (THs - {(14+3)8] @ 2820223 yeuoTze,oedxq Aearns Jo suotsserbex SIO

(a)s - ( (a)s ](1-3)a teTaeTzea Juepuedepul
SNOILVLOdXa AALLAvGW NI SvId
6 Fav.

98/TT/80



-5-

In section 2 we relate expected depreciation as measured by the
surveys to the forward discount, in order to test the hypothesis of
perfect substitutability. In section 3 we investigate some standard models
of expectations formation--distributed lag, adaptive, and regressive
expecta‘sions. In each case one motivation is to see if expectations are
stabilizing, versus the alternative of static or even bandwagon
expectations. In each case a second motivation, which we pursue in section
4, is to test whether the expectations formation process is similar to the
process describing the mathematical expectation of the actual spot rate,
that is, whether the expectations are unbiased conditional on the
particular information set. Included here is a test of the proposition
that investors would do better in forming their expectations if they put
more weight on the contemporaneous spot rate and less weight on other

variables. Finally in section 5 we briefly summarize our findings.

II. The Forward Discount: Risk Premium or Expected Depreciation?

Our first question is whether investors treat assets denominated
in yen and dollars as perfect substitutes. If positions in different
currencies were perfectly substitutable, investors would be indifferent
between holding open positions in foreign assets and selling the assets
forward, This would imply that the forward discount exactly equals the

expected depreciation of the currency:

GQ) As = fd
ttk t


-y-
period, conditional on some particular information set. But this approach,
too, prejudges much.

This paper proposes a third measure, survey data on exchange rate
expectations, to answer various questions of interest regarding the
yen/dollar market. The data come from three sources. The American Express
Bank Review surveys 250-300 central bankers, private bankers, corporate
treasurers, and economists once a year, with some surveys going bac< to

1976. The Economist's Financial Report has conducted telephone surveys of

currency traders and currency-room economists at 14 leading interna:ional
banks each six weeks since June 1981. Money Market Services, Inc. (MMS),
has also been surveying approximately 30 currency traders by telephone
every two weeks since January 1983, and every week since October 1934.
These data are discussed and analyzed in Frankel and Froot (1985) and Froot
and Frankel (1986).3 The results reported in the present paper are new,

in two respects. First, they focus exclusively on the yen/dollar rate,
where the earlier two papers examined simultaneously the yen, pound, mark,
French franc, and Swiss france. Secondly, they distinguish between
short-term expectations on the one hand--at horizons of one week, two weeks
or one month--as reported in the MMS survey, and long-term expectations on
the other hand-~at horizons of six months or twelve months--as reported in
the other two surveys. The short-term and long-term expectations turn out

to behave very differently.

3The first paper investigates how investors form expectations from t:he
contemporaneous spot rate and other variables. The second paper
investigates the standard regression equation of exchange rate changes
against the forward discount. Both papers include tests of the proposition
that the expectations measured in the survey are unbiased.


-13-
null hypothesis will be that of static expectations: investors place a
weight of one on the contemporaneous spot rate and a weight of zero on the
other information, so that expected depreciation is zero. The alternative
hypothesis depends on the precise variable chosen to represent the "other"
information. Suppose, for example, that investors assign a weight of g to
the lagged spot rate and a weight of 1-g to the current spot rate in

forming their expectations of the future spot rate:

e
(4) Stag 7 (Irs) st B5e_y,

where St is the logarithm of the current spot rate. Subtracting s_ from
both sides we have that expected depreciation is proportional to the

most recent change in the spot rate:

(5) ASP ax = 78 (3,78, 1)

We term the model in equation (5) extrapolative expectations. If
investors place positive weight on the lagged spot rate, so that g is
positive, then equation (4) says that investors' expected future spot rate
is a simple distributed lag. On the other hand, if investors tend to
extrapolate the most recent change in the spot rate, so that g is negative,
then equation (5) may be termed "bandwagon" expectations. In this latter
case a current appreciation by itself generates expectations of further
future appreciation. By defining "speculation" as the buying and selling

of yen in response to non-zero expected exchange rate changes, we can


-T-
First we look at simple averages over the sample period.
(Below we will consider variation over time.) In Table 1 we present the
time-series means for each set of survey data. The results are ordered by
length cf forecast horizon, from the shortest-term one-week expectations,
to the longer-term one-year expectations. The surveys cover a wide variet
of sample periods as well. In the first column, averages of actual
depreciation are reported. During the periods of the one-week and
one-month MMS surveys, from October 1984 to February 1986, the dollar
depreciated against the yen at an annual rate of 27.5 percent. During the
period covered by the three-month MMS surveys as well as the three, six and
twelve month Economist surveys, the rate of depreciation is much smaller.

Column (2) reports corresponding averages of the survey expected
depreciation. The time-series means of realized depreciation perform very
poorly as measures of the investors’ expectations reported in the surveys.
In contrast to the considerable swings in the sign and magnitude of average
actual spot rate changes, the survey consistently called for upward
movement:s in the value of the yen against the dollar. The expectations are
the same in sign, but larger in magnitude than the time-series averages of
the forward discount reported in column (3).

The last column in table 1 presents the risk premium on dollar-
denominated assets as implied by the surveys. Strikingly, during both
periods of appreciation and periods of depreciation the risk premium is
negative. Far from regarding the two assets as perfect substitutes,
investors appear to be willing to sacrifice the substantially higher

expected returns from holding yen in order to hold dollars. Indeed, the


-17-
this case, agents are hypothesized to form their expectation of the future
spot rate as a weighted average of the current spot rate and the lagged

expected spot rate:

e e
(8) Stake (1-Y) S, + YS.

Expected depreciation is now proportional to the contemporaneous prediction

error:

(9) A = ¥ (sf - 9).

s°
trk t

Table 6 reports estimates of equation (9). Once again, the
weight placed on the variable other than the contemporaneous spot rate, in
this case the lagged expectation, is sensitive to the forecast horizon of
the surveys. Shorter-term expectations again appear to be strongly
destabilizing, while the longer-term expectations are significantly
stabilizing. For example, the one-week data indicate that an unanticipated
appreciation of 10 percent by itself generates an expectation of
continued appreciation over the subsequent seven days of 1.3 percent. At
the other extreme, the Economist 12-month data suggest that an
unanticipated appreciation of 10 percent generates an offsetting
expectation of depreciation of 1.5 percent over the subsequent year.

The results of Tables 4, 5, and 6 suggest that in all three of
our standard models of expectations--extrapolative, regressive and

adaptive--short-term and long-term expectations behave very differently


International Finance Discussion Papers
Number 292

Revised: September 1986

SHORT-TERM AND LONG-TERM EXPECTATIONS
OF THE YEN/DOLLAR EXCHANGE RATE: EVIDENCE FROM SURVEY DATA

by

Jeffrey A. Frankel
Kenneth A. Froot

NOTE: International Finance Discussion Papers are preliminary materials
circulated to stimulate discussion and critical comments. References in
publications to International Finance Discussion Papers (other than an

acknowledgment that the writer has had access to unpublished materials)
should be cleared with the author or authors.


= 8 -
magnitudes are surprisingly large. In the three-month Economist data, for
example, respondents expected they could earn an additional 7.99 percent
per annum on assets denominated in yen compared with dollars. It is hard
to justify such large exchange risk premia using the theory of optimal
portfolio choice with conventional estimates of risk-aversion (Frankel
1985, and Mehra and Prescott 1985).

One explanation proposed for why investors were willing to hold
dollars at lower expected rates of return is that the United States
provided a "safe haven" from capital controls and other political risks
(for example, Dooley and Isard, 1985; but see Frankel and Froot, 1986).
Grounds for this argument seem especially lacking vis-a-vis the yen: Japan
was not directly involved in either the Latin American debt crisis or
concerns of "Europessimism", and the 1980s have been a period during which
Japanese financial markets have been steadily liberalized, if anything
reducing fears of prospective capital controls. Furthermore, only exchange
rate risk should in theory be relevant, not factors relating to the
political jurisdiction of Japan, because the spot and forward rates are
determined offshore in the Euromarket. But whatever the reason, table 1
suggests that investors distinguish between assets denominated in different
currencies, demanding a higher return on the yen than on dollars. This is
also clear in Figure l.

While the evidence so far indicates that a risk premium exists,
it is not necessarily evidence that the risk premium varies over time. The
proposition that the risk premium is time-varying rather than constant

comes out of most of the conventional empirical literature on the forward


uotTyeToerdde pezoodxe- qunoosTp preMI0j~ > untupad ystz - O
qeoi

Se—-I1f—-E2 vR-190-20 €a-320-90 e9—dad—-F1 ze-1dy—6t Te—Wty-Ez

no a
+ 2t-

J S

Ay ee

las V Fo
- g-—

- 7B -

eqeq AaAmg 4STwoUCSg WUOW-ZT

UVTIOW SHL ISNIWOW
T gana

mmune tad ywasted


-21-
was designed to test whether investors assign the correct weight to a
single element in their information set when predicting the level of the
yen/dollar rate. If, however, both expectations and the true spot process
depend on other unspecified infornation, then the above tests of
rationality are not necessarily the most enlightening nor the most powerful.
A more robust test would ask whether expectations assign too little weight
to the contemporaneous spot rate and (by default) too much weight to all
other variables in their information set. This test is performed by

regressing the survey prediction error on the survey expected de »reciation:

(10) Ss) +e

e e
s card (si, St

Stok” Stak ttk?

and testing the hypothesis that the coefficients are jointly zero. The
alternative hypothesis is that investors place too much (or too little)
weight on variables other than the contemporaneous Spot rate relative to
what is rational. Following Bilson (1981), we term this alternative
hypothesis "excessive speculation", because investors could improve their
forecasts by consistently reducing toward zero their expectations of
depreciation.

Table 10 reports our estimates of equation (10). Here we find
much more evidence of systematic expectational errors in the surveys. All
but one of the data sets reject the hypothesis that the constant and slope
parameter are jointly zero. Four of the seven estimates of b are also
statistically different from zero, so there is considerable evidence of

excessive speculation. Unlike the results of the preceding tests of


- 20 -
that expectations are "overly" extrapolative. Table 7 suggests that
predictions at the shorter forecast horizons tend to be overly
extrapolative, while those at the longer horizons are insufficiently
extrapolative. Such a pattern suggests that the contrast in Table 5
between the behavior of short-term and long-term expectations is too
extreme relative to what the actual process generating spot rate changes
would predict. Few estimates of 81, however, are significantly different
from zero. There is thus not enough evidence so far to conclude that, at
any of the reported forecast horizons, investors place too little or too
much weight on the lagged Spot rate relative to what is rational.

In Table 8 we test whether investors! expectations give the
correct weight to the long-run equilibrium spot rate, 3. Here the
results are surprisingly consistent across all of the forecast horizons:
expectations seem to be insufficiently regressive in that they give less
weight) to S, and therefore more weight to the contemporaneous spot rate,
than does the true process governing the behavior of the spot rate. In
Table 9 we perform the analogous test using lagged expectational errors on
the righthand side. In this case, the alternative hypotheses are that
expectations are either overly or insufficiently adaptive. As in Table Ty
the results in Table 9 do not suggest any clear tendency on the part of
investors to give too much or too little weight to the most recent
expectational prediction error.

The tests of rational expectations presented so far in Tables
1-9 are appropriate when we take as given the specific models of

expectations formation discussed in the previous section. Sach regression


-6-

where fd is the forward discount at term k (the log of tne current forward rate

minus the log of the current spot rate) and Asta is the log of the

k
expected spot rate k periods into the future minus the log of the current
spot rate. On the other hand, if investors need to be rewarded for

exposure to the additional risk of holding an open position in the foreign

currency, they will demand a risk premium in addition to the forwarc rate:

e k k.
(2) Ase, = fay - Ppp:

Because both expected depreciation, As®, and the risk premium,
rp, are unobservable, additional information or assumptions are required to
isolate them. If, for example, we were to assume that realized future spot
rates are unbiased measures of expected spot rates, then we could estimate
expected depreciation (and therefore the risk premium) from the time-series
of realized depreciation.4 A second method of identification would be
to assume the validity of a particular model of investor portfolio
optimization (such as Hodrick and Srivastava (1984) or Frankel (1982)) and
use it to obtain estimates of the risk premium. A third approach, the one
taken in this paper, is to employ survey data on expected depreciation.
While surveys of agents' expectations may in many contexts be less
desirable than data on their actual market behavior, the surveys are direct
estimates that do not require us to assume any particular model of expected

depreciation or of the risk premium.

4Perfect substitutability, or uncovered interest parity (which, given
covered interest parity, is an equivalent condition), is tested for Japan
versus the United States by Ito (1984) and McKenzie (1986).


- 15 -

to be significantly greater than zero.8 The Economist 12 month data,
for example, imply that a current 10 percent appreciation by itself
generates an expectation of 3.4 percent depreciation over the coning 12
months. Thus longer-term expectations feature a Strongly positive weight
on the lagged spot rate rather than complete weight on the contemporaneous
spot rate, and in this sense are stabilizing.

A second popular specification for the expected future spot rate
is that it is a weighted average of the current spot rate and the

long-run equilibrium spot rate, 3:

(6) = (1-0) 3, + 08,

ae
“tek t

or in terms of expected depreciation:

e -
(7) 8p, 7 9 (8 — 8)

If 0 is positive, as, for example, in the Dornbusch (1976) overshoot ing
model, the spot rate is expected to move in the direction of 3.

Expectations are therefore regressive. Alternatively, a finding of 0 < 0
implies that investors expect the spot rate to move away from the long-run

equilibrium,

8In Frankel and Froot (1986), we correct for the low Durbin-Watson
Statistics in similar regressions using five different currencies (and
those in Tables 6 and 7) using a three-stage least squares estimation
technique which allows for first order serial correlation in the residuals.
The technique is not repeated here since the corrected results obtained in
that paper are very similar to the uncorrected OLS estimates.


- 26 -

Hansen, Lars and Robert Hodrick, 1980. "Forward Rates as Optimal
Predictors of Future Spot Rates: An Econometric Analysis." Journal
of Political Economy, 88, October, pp. 829-853.

Hodrick, Robert and Sanjay Srivastava, 1984. "An Investigation of Risk and
Return in Forward Foreign Exchange." Journal of International Money
and Finance," 3, April, pp. 5-30.

» 1986. “The Covariation of Risk
Premiums and Expected Future Spot Rates." Journal of International
Money and Finance," 3, April, pp. 5-30.

Ishiyama, Yoshihide, 1985. "The Yen/Dollar Exchange Rate: Still a
Puzzle." U.S. - Japan Consultative Group on International Monetary
Affairs, Washington, D.C., Oct.

Ito, Takatoshi, 1984. "Use of (Time-Domain) Vector Autoregressions to Test
Uncovered Interest Parity." University of Minnesota, September.

» 1986. "The Intra-Daily Exchange Rate Dynamics and
Monetary Policies after G5." U.S. - Japan Consultative Group on
International Monetary Affairs, Oiso, Japan, July 11-13.

Johnson, Manuel and Bonnie Loopesko, 1986. "The Yen-Dollar Relationship:
A Recent Historical Perspective." International Finance Discussion
Paper Series No. 283, Federal Reserve Board, Washington, D.C., June.

Krugman, Paul, 1986. "Is the Japan Problem Over?" Conference on Trade
Frictions, NYU Center for Japan-U.S. Business and Economic Studies,
April. NBER Working Paper No. 1962, June.

Marston, Richard, 1986. "Real Exchange Rates and Productivity Growth
in the United States and Japan." American Enterprise Institute
Conference on Real-Financial Linkages, January. NBER Working Paper
No. 1922, May.

McKenzie, Colin, 1986. "Issues in Foreign Exchange Policy in Japan:
Sterilized Intervention, Currency Substitution and Financial
Liberalization." Ph.D. Dissertation, Australian National University.

Mehra, R. and E. Prescott, 1985. "The Equity Premium: A Puzzle," Journal
of Monetary Economics, 15, pp. 145-161.


IFDP
NUMBER

292

291

290

289

288

287

286

285

284

283

282

281

280

-27-

International Finance Discussion Papers

TITLES

1986

Short-term and Long-term Expectations of
the Yen/Dollar Exchange Rate: Evidence
from Survey

Anticipated Fiscal Contraction: The

Economic Consequences of the Announcement
of Gramm-Rudman-Hollings

Deposit Risk Pooling, Irreversible
Investment, and Financial Intermediation

The Yen-Dollar Relationship: A Recent
Historical Perspective

Should Fixed Coefficients be Reestimated
Every Period for Extrapolation?

An Empirical Analysis of Policy
Coordination in the U.S., Japan and
Europe

Comovements in Aggregate and Relative
Prices: Some Evidence on Neutrality

Labor Market Rigidities and Unemployment:
the Case of Severance Costs

A Framework for Analyzing the Process
of Financial Innovation :

Is the ECU an Optimal Currency Basket?

Are Foreign Exchange Forecasts, Rational?
New Evidence from Survey Data

Taxation of Capital Gains on Foreign

Exchange Transactions and the Non-neutrality

of Changes in Anticipated Inflation

Please address requests for copies to International Finance Discussion
Papers, Division of International Finance, Stop 24, Board of Governors of

the Federal Reserve System, Washington, D.C.

20551.

AUTHOR(s)

Jeffrey A. Frankel

, Kenneth A. Froot

Robert A. Johnson

Robert A, Johnson
Manuel H. Johnson
Bonnie E. Loopesko

P.A.V.B. Swamy
Garry J. Schinasi-

Hali J. Edison
Ralph Tryon

B. Dianne Pau.s
Michael K. Gavin
Allen B. Frankel
Catherine L. Mann
Hali J. Edison

Kathryn M. Dominguez

Garry J. Schinasi


- 194 -

*sajeuTASe SjUeUIOW JO poyjoW oe SIOIIe piepuejs ‘SAoejowered YdeorejuTUOU TTe UO 3S93

g@ ue 03 SpuodsertI0o ry “TeAeT QUeDTEd T |Yy} 3e BOUROTFTUBTS SQUeSeTdey xxx “TOAST JUdoTEd ¢
ay3 ze soURoTJTUBTS squesezdey xx “TOAST JUSdTEed OT S43 3e SOUROTITUDTS SqUSserdey *

‘ue Jed sie{T [Op JO suliej UT ere sozeI eHueyoxse pezoedxe pue Tenjoy

(vez0°T)
* VBE 8e°0 9 * LEZ L8zb°Z G8/8-9L/T yQUOW ZT xeuW
(O€LE*0)
xxx 89°S z0°0 6z €b°0- 88ST*0- S8/ZT-18/9 yQUOW ZT 3STWOUCDg
(8¥6S°0)
bez €£°0 L x ITZ 6bS2°T S8/8-9L/T yQUOW 9 xoUTY
(€09€°0)
Sz z0°0 ve €v°0 €€ST"O S8/ZT-18/9 yQUoW 9 3STWOUCDg
(s68T°0)
L8°T vT"O 9€ 22° €0€2°0 S8/ZT-18/9 yqUOW € YSTWOUODg
(LELT*O)
wx 8S°E L070 sv z8°0- ZEvT"O- ¥8/0T-€8/T uqUOW € SHH
(1297°0)
= 95°C €0°0 zy os*0- bRET*O- 98/Z-¥8/0T yquoW T SWW
(88ST°0)
~ €8°7 vT°O Sb €2°T- OS6T*0- ¥8/0T-€8/T 429M Z SHH
(8L€T°0)
8b°T 00°0 09 60°0- 8TT0°0- 98/Z-¥8/0T 422M T SWW
o=6 ‘0-2 28 aq 0=6 3 '6 jes eaed
3se3 4d queToTZya0o
( (a)s - (1-3)s 6 + & = (T43)8 - [(14+9)8] F #8077H TeuoTzeIOedxgZ Aeans Jo suotsseibey S10
(a)s - (1-3)S teTQeTIeA Juepuedepul
SNOLLVLOSdX AALLWIOAWYLXA NI SvId
<4 w1qwL

98/TT/80



-2-
the 3 per cent yen-dollar forward discount that prevailed in the early
1980s represented investors' expectations that the dollar would in the
future depreciate, presumably back toward some equilibrium level. One
implication is that investors acting on this expectation -- "speculators"
-- had a lower demand for dollars during the strong-dollar period than they
would have had acting solely on the basis of the interest differential or
other factors; in other words, speculation was stabilizing.

An alternative view is that the expected rate of depreciation is
much closer to zero than to the forward discount. Many empirical studies
have found that the rationally, or mathematically, expected rate of
depreciation is close to zero, i.e., that the exchange rate follows a
random walk so there is a prima facie case that the same is true of
investor expectations. If expected depreciation is zero ("static
expectations"), then there is no stabilizing effect in the form of
speculators selling a currency when it is strong. A more extreme view is
that there is a bandwagon effect: at each point during the 1980-84 period,
the appreciation of the dollar against the yen generated expectations of
further future appreciation, notwithstanding the fact that the dollar was
selling at a forward discount against the yen. It would follow from this
view that speculators --again, defined as investors acting on the basis
of expectations of exchange rate changes-- drove the yen/dollar rate to a
higher level than would have otherwise prevailed. It would follow that
speculators have exaggerated the reverse swing in 1985-86 as well. Whether
expectations are stabilizing or destabilizing in this sense is one of the

questions examined in this paper.


- 10A -

*sa}eUT Se SjUSWOU! JO PoYyoU oe SloIZe piepueIS ‘sie eUeIed ydeore,UTUOU TTe UO 3se3

a ue 03. spuodsezI0> «ay *TeAeT QueorEd T oy} Je SoUROTFTUBTS squesordey «yy “TOAST Jueored ¢
ay} Fe soURDTFTUBTS sjueserdoy yx “TeAeT JUedTed OT ey} 3e SOUROT;ZTUDTS squeserdey =,
suok rod szeTTOp Jo suite} uT ore sozer sHueyoxe pojoedxe pue [enjoy

(06SE°T)

xe S9°8 y9°0 9 ax VOR 798h°b- $8/8-9L/T YqUOW ZT xeuly
(esseT)

wee SZ°ET se°o 62 x 02°2- LTSO°2- S8/2T-18/9 UAUOW ZT 3STWOUOCDT
(9209°T)

=» 8E°0 9¥°0 L * 6L°7- LLLY*Ee- $8/8-9L/T YAUOW 9 xoUy
(ZOSL°T)

ae DEE zy-0 ve ee 8S°7- OLOS*E- $8/ZT-18/9 YaUOW 9 3STWIOUCD|
(s98s°T)

* 90°E op°o 9€ ae LUO SSZ76°2- S8/2T-18/9 YAUOW € 3STUIOUCD”
(LEE6°Z)

ax SPE 62°0 sv 06°T- OZLS"b- v8/OT-€8/T yaUOW € SW
(6Z€0°€T)

* VS°Z 80°0 cA 06°0- SSL9°OT- 98/7-¥8/0T yIUOW T SWW

sojed 3es B3eC
queToTsze00

( (a)8 - (8)3 ) a+ & = (9)8 - (149)8 tsebueYyD eWeY Jods Jo suoTssezbeY STO

(Q)s - (4)3 teTqetTzea quepuedepul
SWIG LNNODSIC CavMdoOd AO SLSAL
zz FIavL

98/TT/80


=
oo
I

*siojouered ydeorequTuou TTe uo 4saq

@ ue 03 spuodsazi0> ,y “TeASeT QUsoTEd T 943 Ye sOUkOTITUBTS SqueseIdey xxx “TOAST QUedIZEd ¢

ay 3e sOUROTJTUBTS Squesetdey yy ‘“TeAeT JuadIed OT oY} 3e dOUROTJTUSTS sqUaserdoy *

‘uaA red sie[Top jo suze} ut ere sejzer ehueyoxe pejoedxe pue [enjoy
(SZT0°O) (T8Te"0)

y09"0 ¥S"0 90°0 L 02°0 TO°T 9LT0°O SL°0- T29L°0 $8/8-9L/T YqUOW ZT xoury

(0600°0) (6pLT°0) ——__

000°O ¥Z°ZET Tro 9€ 00°2 GL°S STSO"O vo°Tt T2st°t S8/ZT-18/9 UIUOH ZT FSTWOUOo,
(0800°0) (¥S97°0)

Z2p°0 86°0 z0°0 L set°0 6€°0 TE€00°0 Le°o 8860°T $8/8-9L/T yUOW 9 xeuly
(9500°0) (s907°0)

000°O SZ°T2T ?@T°0 9€ Sh°T 6e°9 9S€0°0 60°T pS@Z°T $8/2T-18/9 YUOW 9 YSTWOUCO,
: (0900°0) (LTvp°O)

000°0 br°2z Ez°0 9€ T6°T 88°T €1T0°O so°T 667L°T $8/Z1-18/9 yqUOW € JSTWOUCDT
(¥¥00°0) (sepp'o)

000°0 T9°SS zL°0 OF O2°T Lerk Lze0°0 axe 78°9- ZOvT*T- y8/0T-€8/T yaquoW € SNH
(T€00°0) (7¥66°T)

€00°0 8s°9 8s°0 ty 9T°t 6v°E 60T0°0O wax 9S°E- 7860°9- 98/7-v8/0T yqUOW T SHH

T= 33 soqed 38s e3eC

aa (7
ya queToTzze0o quaToTzZ3e00

( (a)s - (2)3.) + & = (3)8 - [(143)8] @ tuoTIeTOeAded pe_oedx” Aearns jo suoTsseibex STO

(a) - (4)3 teTqeTzea quepusdeput
ALITIGVENLILSGNS Loadad JO SLSaL
€ FIavL

98/TT/80


Short-term and Long-term Expectations
of the Yen/Dollar Exchange Rate: Evidence from Survey Data

by

Jeffrey A. Frankel
Kenneth Froot!

1. Introduction

With most of Japan's restrictions on international capital flows
recently removed, the yen is now properly thought of as subject to the
asset-market model of exchange rates: the demand for yen versus dollars
resporids instantaneously to the expected rates of return on the two assets.
The most evident component of variation in recent years has been interest
rates. The differential between U.S. and Japanese interest rates can be
used to explain the increased demand for dollars and the sharp appreciation
of the dollar against the yen from 1979 to 1984, and the subsequent
reversal in 1985-86.2 But the other major determinant of the expected
return differential, the expected rate of future appreciation of the yen,
is much less easily observed than interest rates.

One view is that the expected rate of depreciation can be

measured by the discount in the forward market. According to this view,

\This paper was written while the authors were participants at the National
Bureau of Economic Research 1986 Summer Institute and while they were
Visiting Scholars at the International Finance Division, Board of Governors
of the Federal Reserve System, Washington, D.C. 20551. They would like to
thank in addition to these institutes, the Sloan Foundation, the Institute
of Business and Economic Research at U.C. Berkeley, and the National
Science Foundation (under grant no. SES-8218300) for research support.
Views expressed are those of the authors.

2Many papers discuss the role of the interest rates in determining the
yen/dollar exchange rate, especially since the 1979-80 liberalization.
Four examples are Amano (1986), Ishiyama (1985), Ito (1986), and Johnson
and Loopesko (1986).


- 25 -
References

Amano, Akihiro, 1986. "Japan's External Imbalance and Exchange Rates."
U.S. - Japan Consultative Group on International Monetary Affairs,
Oiso, Japan, July 11-13.

Bilson, John, 1981. "Profitability and Stability in International Currency
Markets." NBER Working Paper No. 664, April.

Dooley, Michael and Peter Isard, 1985. "The Appreciation of the Dollar:
An Analysis of the Safe-Haven Phenomenon," International Monetary Fund
DM/385/20, April.

Fama, Eugene, 1984. "Forward and Spot Exchange Rates," Journal of
Monetary Economics, 14, pp. 319-338.

Frankel, Jeffrey, 1982. "In Search of the Exchange Risk Premium: A
Six-Currency Test Assuming Mean-Variance Optimization," Journal of
International Money and Finance, 1, pp. 255-274.

__» 1985. "The Dazzling Dollar." Brookings Papers on
Economie Activity, 1, pp. 199-217.

Frankel, Jeffrey and Kenneth Froot, 1985. "Using Survey Data to “est Some
Standard Propositions Regarding Exchange Rate Expectations." NBER
Working Paper No. 1672. Revised as IBER Working Paper No. 86-11,

University of California, Berkeley, May 1986. Forthcoming, American
Economic Review.

, 1986. "The Dollar as a Specu!.ative
Bubble: A Tale of Fundamentalists and Chartists," NBER Working
Paper No. i354, March. First half in Marcus Wallenberg Papers in

International Finance 1, 1. Second half forthcoming in Economic
Record.
Froot, Kenneth and Jeffrey Frankel, 1986. "Interpreting Tests of Forward

Discount Bias Using Survey Data on Exchange Rate Expectations," NBER
Working Paper No. 1963, June.

Fukao, Mitsuhiro, 1982. "The Risk Premium in the Foreign Exchange Market,"
Discussion Paper Series No. 12, The Bank of Japan, May.

_ 1985. "The Effectiveness of Coordinated Intervention,"
p. 16-63 in T.Hosomi and M. Fukao A Second Look at Foreign Exchange
Market Interventions, Japan Center for International Finance Study,
No. 3, April.

__ and Takashi Okubo, 1984. "International Linkage of
Interest Rates: The Case of Japan and the United States,"
International Economic Review, 25 1, Feb.



-18-
from one another. Longer-term expectations consistently appear ta be
stabilizing, while shorter-term forecasts seem to have a destabilizing
nature. Within each of the above tables, it is as if there are actually
two models of expectations operating, one at each end of the spectrum of
forecast horizons, and a blend in between.

It may be that each respondent is thinking to himself or herself,
"I know that in the long run the exchange rate must return to the
equilibrium level dictated by fundamentals. But in the short run I will
ride the current trend a little longer. I only have to be careful to watch
for the turning point and to get out of the market before everyone else
does." If this is the logic of the typical investor, then he is acting
irrationally; it is not possible for everyone to get out before everyone
else. But so far we have not presented any evidence that the actual spot
process behaves differently from investors' expectations. We consider such

evidence in the following section, 10

Iv. Rationality of the Survey Expectations
Now that we have a sense for the behavior of the survey expected

depreciation, we turn to an analysis of whether the predictable conponent

10one possibility is that the MMS short-term survey is picking up
predominantly the expectations of floor traders, people who buy and sell
currency on a short-term basis, and that the other two, longer-term,
surveys are picking up predominantly the expectations of investors who have
a longer-term perspective. Under this interpretation, it may be tnat the
traders have developed the habit of ignoring economic fundamentals in their
expectations formation, rather going with time series trends (as in
“chartism" or "technical analysis"), and that the latter group pay3 more
attention to fundamentals. The chartist/fundamentalist dichotomy and its
implications for the determination of the value of the dollar in the 1980s
are pursued in Frankel and Froot (1986).


ABSTRACT

Three surveys of exchange rate expectations allow us to measure
directly the expected rates of return on yen versus dollars. Expectations
of yen appreciation against the dollar have been (1) consistently large,
(2) varlable, and (3) greater than the forward premium, implying that
investors were willing to accept a lower expected return on dollar assets.
At short-term horizons expectations exhibit bandwagon effects, while at
longer-term horizons they show the reverse. A 10 percent yen appreciation
generates the expectation of a further appreciation of 2.4 percent over the
following week, for example, but a depreciation of 3.4 percent over the
following year. At any horizon, investors would do better to reduce the
absolute magnitude of expected depreciation. The true spot rate process

behaves more like a random walk.


- 22 -
rationality, our estimates here are uniformly positive and do not appear
related to the length of forecast horizon. In every case we are also
unable to reject the hypothesis that b=1, which would imply that the
expectations contain no useful information at all as to the future spot
rate, i.e., that the spot rate follows a random walk.

We mentioned earlier the possibility of measurement error in the
survey data. In any of the regression equations where the expectations
variable appears only on the lefthand side, namely the cases of
extrapolative expectations (Tables 4 and 7) and regressive expecations
(Tables 5 and 8) random measurement error does not impair the regression
estimates. But in the case of adaptive expectations (Tables 6 and 9), as
well as in the present case of excessive speculation (Table 10), he
expectations variable appears also on the righthand side of the equation,
so that measurement error would affect the estimates.

When the issue of possible random measurement error in these
regression equations is addressed the results are qualitatively unchanged.
In the test for excessive speculation we can eliminate the problem of
measurement error (so long as it is random) by using the forward discount
as the righthand-side variable. Table 11 again shows systematic
expectational errors: investors could do better by routinely betsing

against the forward discount.11

\1see Froot and Frankel (1986) for further explanation. In the case of
estimating adaptive expectations, we would argue that the bias introduced,
though nonzero, is small, because the variance of actual spot rate changes

is approximately 10 times larger than the variance of expected depreciation
(Table 3, ibid.).


19B -

*Sogeut{so syududu JO Poyjou oxe S1017e prepuUeIS *saxojouezed 3deorequtuou [Te uo 4s03

4 ue 03 Spuodsezz10S 2H“ T8AeT Queozed [ ey3 3e soUROTZTUBTS squeserdey x¥y “TOAST queored ¢

- . Oy Qe soUROTZTUSyTS squeserdey xx “TOAST queosed oT ou} 3e soUeOTZTUBTS squeserdoy *
so . *wek ted SxeTTOP JO sutez UT ere SeZeT eHueyoxs pejoedxe pue Tenjo7

, (4065 "0)

L0°0 00°0 9 vT"O- 6080°0- $8/8-9L/T yquoOW ZT xeUy
(920€°0)

wee C6°TD = 99°0 62 wae 72°0- 166z°T- $8/ZT-18/9 yqUOW ZT 3STUOUCDT
: 7 (sSzz°0)

99°0 L0°0 L 08°0- 608T"0- $8/8-9L/T yQuoW 9 xoUTy

. (ogte 0) —_____

eee TOL ss‘0 ve eww VETE- S€90°T- - $8/2T-T8/9 yqUOW 9 4STUOUCOT
; , (ZE6T"0)

Bez zo 9€ Ls? T= OvOE*0- $8/ZT-T8/9 yaqUoW € ySTWOUCOT
; (94770)

wee €5°9 6£°0 sv we BE°7- 9L59°0- b8/0T-€8/T yquoW € SHW
. (SPTT"0)

@s°t z0°0 Le vp0- Z0S0°0- 98/2-¥8/0T yQUoW T SWW
(10L0°0)

wax €9°L €s°0 sy aux TZ'E- 0S2z"0- v8/0T-€8/T 420M 7 SHH
(46Z0°0)

6670°0- 98/7-¥8/0T 422M T SHH

queToTZJe0o

(143)8 - “[(14398] a tsa0rsg [euopQeGoedxg Asaatis ¥o SUCT

dda umtiqirtnba ung buot
(3)s - (3)8 teTQeTTea Juepuedepul
SNOILVLOSdXa AAISSTNOTA NI SVIG
8 aTavL

98/11/80


-9-
market, as well as the theory of optimizing investors, and is also a
property of models in which sterilized foreign exchange intervention has
important effects.

Thus we would also like to know whether changes in the forward
discount indicate a changing risk premium. The degree to which changes in
the forward discount reflect changes in the risk premium can be inferred

from a regression of expected depreciation on the forward discount:

(3) Ase

k k
tok 7 ot BEd + ©

tek

The null hypothesis in equation (3) is that assets are perfect substitutes,

i.e., a=0 and g=1. The coefficient, 8, converges in probability to:

e

b= cov (As tek’?

k k
fd.) / var (ta)

= 1- [ cov (ek, rat) / var (tak 3].

A finding that g is near zero or less than zero is evidence that changes in
the forward discount reflect changes in the risk premium, while a finding
that 8 is near one is evidence that such changes in the forward discount
reflect something else, namely equivalent changes in expected
depreciation.>

The conventional approach to testing equation (2) uses ex post

spot rate changes to infer the behavior of the unobservable market expected

5rama (1984), Hodrick and Srivastava (1984, 1986) and Froot and Frankel
(1986) discuss whether changes in the forward discount primarily reflect
changes in the risk premium or in expected depreciation.


-W-

Though the two approaches are analogous, there are several
reasons to prefer the surveys to the actual spot rate data in tests of
equation (3). The first is that, under the hypothesis that both actual
spot rates and the surveys contain only the market expectation plus purely
random noise, the noise element in actual spot rate changes turns out to be
much larger than the noise element in the surveys. In Froot and Frankel
(1986, table 3) we report estimates of the variances of actual ard survey
expected spot rate changes and find that the former is greater by a factor
of 7 to 10. This implies that, for any given sample, a more precise
estimate of b may be obtained by using the surveys. A second reason to
prefer the surveys is that they free us from imposing the restriction that
there are no systematic prediction errors in the sample, a proposition that
we would like to be able to test rather than impose. Such systenatic
errors, which the conventional technique must assume away, could occur
because of a failure of rational expectations, or because important events
which affect expectations did not happen to occur a representative number
of times in the sample (the "peso problem"), rendering the ex post
distribution of spot rate changes a biased estimator of the ex ante
distribution.

Tests of equation (3) using the survey data on the left-hand side
are reported in table 3. In each of the seven data sets the est:mates of b
are greater than those in table 2. In most cases we cannot reject the
hypothesis that b equals one. In other words, we cannot reject the
hypothesis that the survey risk premia reported in table 1 do not; vary over

time. There is not even much sign that the risk premium on yen had an