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(12 noon) -0.043 -0.016 -0.097 -0.035 -0.117
Tuesday 9/6/87 -0.075 -0.064 -0.247 +0.032 -0.192
(12 noon)
Source: Taylor (1989), Table 3.
arbitrage that ensures CIP. This is in part reflected in the fact that if one
bank for a forward quote it calculates the forward rate it will offer by usin
relationship. That is to say it checks on the values of rf, r,$ and S, and then qu
F , calculated as


where the bid-offer distinction has been ignored. Looking at potentially profit
using data on which market-makers may have undertaken actual trades is clear
way of testing CIP. However, many early studies of CIP used the logarithm
mation and ran a regression:


The null of CIP is
Ho:a=O, b = l
and if there are transactions costs these may show up as a # 0. Since (r$ - rf)r
nous then 2SLS or IV rather than OLS should be used when estimating (12.8)
these regression tests of CIP have a number of acute problems. The regression
do not distinguish between bid and offer rates and do not explicitly (or care
account of transactions costs. Also if the logarithmic form is used then (12.8)
approximation. In early studies the rates used are not sampled contemporane
these reasons these regression tests are not reported (see Cuthbertson and Ta
and MacDonald (1988) for details).


1 . UNCOVERED INTEREST PARITY AND FORWARD
22
UNBIASEDNESS
With perfect capital mobility (i.e. foreign and domestic assets are perfect
instantaneous market clearing, zero transactions costs) and a zero risk premiu
neutrality) then the uncovered speculative return is zero:
- S,-1 - d,-l =0
s;

where d,-l = r,-1 - r:-l, the uncovered interest differential and s, = In S,. Equa
holds if the spot market is ‘efficient’ and hence eliminates knowable oppor
supernormal profit (providing there is a zero risk premium). Assuming RE, s
hence:
+ +
S, = st-1 d,-1 U,

Equation (12.10) has the testable implication that the current spot rate depend
previous period’s spot rate and the uncovered interest differential, with a unit
on each variable. The orthogonality property of RE implies that no other varia
at time t - 1 or earlier should influence sf (other than sf-l and d,-l).
effective rate (July 1972-February 1980) found that the interest rate coeffic
included as independent variables, have unit coefficients; but lagged values of
in the exchange rate and a measure of credit expansion are also significant.
RE forecast error ur is not independent of all information at time t - 1 or ear
joint hypothesis of zero risk premium and the EMH fails; similar results we
for the E/$ rate. Cumby and Obstfeld (1981) using weekly data (July 1974-Jun
six major currencies against the dollar found that lagged values of the depende
(sf - st-l - d f - l ) of up to 16 weeks are statistically significant for all six
The RE forecast error is therefore serially correlated, contrary to part of the
hypothesis.
+
Our interim conclusions concerning the validity of UIP RE is that not all
the maintained hypothesis hold and this may be due either to a (variable) risk
or a failure of RE or risk neutrality.

Testing FRU
First some stylised facts. A graph of the 30-day forward rate F and the actu
led by 30 days Sr+l for the $/DM(using weekly data) is shown in Figure
obvious that the broad trends in the $/DMactualfiture spot rate are picked
current forward rate. This is the case for most currencies since the root m
of the prediction error, Sr+l - F f , is of the order of 2-2.5 percent against


.4907



1
WDM




-
.3128

24 February 19
5 January 1973

Figure 12.1 Forward Rate (30 Days) and Spot Rate (Led Four Weeks): Dollar-De
Source: Frankel (1980). Reproduced by permission of the Southern Economic Journal
by Fo
l/aF-D dEGZ7
- -
n
n
Deutschmark 2.10 2.12
1.
French franc
2. 2.21 2.09 -11
Pound sterling 2.18 2.23
3.
Italian lira 2.53
4. 2.76 -1
Swiss franc
5. 2.5 1 2.61
-1
Dutch guilder 2.10 2.0
6.
Japanese yen
7. 1.84 1.84
Source: Frankel (1980), Southern Economic Journal, April.
Date Period: weekly data 5 July 1974-4 April 1978 (193 data points).


for the currencies shown in Table 12.2. This is particularly true for those cur
experience a trend in the exchange rate (e.g. Japan and the UK). The four-week
in the spot rate in column 2 of Table 12.2 is about 2-2.5 per cent for most
The forward market does not predict changes in the spot rate at all accurately
For example, only 2 percent of the changes in the $/DMrate are predic
forward rate (column 3). In some cases this percentage is negative indicati
forward rate is a worse predictor than the contemporaneous spot rate. The la
these prediction errors does not necessarily imply a failure of market efficien
alternative predictors of S t + l , given information at time t , may give even larg
errors.
It is clear from Figure 12.1 that a regression of St+l on F , will produce
serially correlated residuals since F , provides a run of under- and overpredicti
If the $/DMfuture spot rate S,+l is lagged one period, the solid line would
right and would nearly coincide with F , . Hence the current forward rate ap
more highly correlated with the current spot rate than with the future spo
suggests that variables or news that influence S , also impinge upon F , .
If the forward market conforms to the EMH and speculators are risk neutr
forward rate is an unbiased predictor of the (logarithm of the) expected futur
sp, 1 If we incorporate an additive risk premium rp, and invoke RE then
*




+k+l
= $+I
Sf+1

Risk neutrality implies r p , = 0. The risk premium is the expected profit ma
speculator and may also capture any transactions costs (e.g. manpower costs)
with the forward contract. RE implies:
Er(ut+l IQ) = 0
which includes the assumption that u,+l is serially uncorrelated. The simplest
to make concerning the risk premium is that it consists of a positive consta
‘white noise’ random element v,:
+
r p , = a vt
of the form:
+ Bft + v A + Er+l
=a ˜
sr+l

where At is a subset of the complete information set available at time t. If t
true we expect a < 0, /3 = 1, y = 0 and Er to be serially uncorrelated. 121 may
relevant economic variables including values of the lagged dependent variab
or lagged forecast errors ( S t - ft-1). A slightly weaker test of the EMH assu
+
+
and tests for p = 1 in the regression st+l = a Bfr E r , which excludes A,.
There is an important econometric point to be made here. E t + l in the
equation (12.18) is equal to uf+l - vr, but vr influences the risk premium rp,
equation (12.13). Hence Er+l and f, in equation (12.18) are correlated, and OL
inconsistent estimator. This is the so-called ‘errors in variables’ problem in eco
‘Correct’ (i.e. asymptotically unbiased) estimates may be obtained using an in
variables technique such as 2SLS. (A correction to the covariance matrix an
dard errors because of the presence of heteroscedasticity can be made usin
estimator.)
Alternative formulations of the unbiasedness property to equation (12.18)
times used. For example, unbiasedness also implies that the forward premiu
(f - s) is an unbiased predictor of the future change in the spot rate. Subtract
both sides of (12.13) and using (12.14):


B = 1 and that
A test of unbiasedness is then a test of a = y1 = 0, is whi
Er
the regression:
+ Y1Ar + Er+1
+ B(f - s)r
Asr+l = a
Some early studies used the ‘levels version’ (12.18) of the unbiasedness
However, if sf+l and fr are 1(1) the usual test statistics in (12.18) are invalid.

-
equation (12.20) we see that if (s, f ) are 1(1) but st+l and fr are cointegrated
+
tegration parameter (1, -l), that is st+l = fr Et+l with Er+l I ( 0 ) then the v
(12.19) are I ( 0 ) . The latter carries over to (12.20) if the variables in At are eith
I(1) but cointegrate among themselves or if y1 = 0. In general (12.20) is to b
to (12.18) under the assumption of cointegration between s and f , since the er
stationary and hence the usual test statistics are valid,

Early Tests
Frankel (1982a) reports a regression of the change in the spot rate Asr+l on t
premium/discount (f - s)t and other variables known at time t (e.g. Asr). He
to reject the null hypothesis that a = y1 = 0, @ = 1 and E t is not serially corr
equation (11.27)). However, the ‘power’ of this test is rather low since on
accept the joint hypothesis a = y1 = B = 0. The latter result should come as
since we noted that the forward premium/discount explains little of the change
for the set of currencies will be contemporaneously correlated (i.e. E(Eif,E j t ) #
Zellner’s (1971) seemingly unrelated regression procedure (SURE) yields mo
estimates of the standard errors of the parameters a and j?. For example, M
using a SURE estimator, finds that for quarterly data over the period 1972(1)-
six major currencies against the dollar only sterling and the Canadian dollar pa
hypothesis that a = 0, B = 1. Rejection of the null hypothesis appears to be
to a # 0 rather than /?# 1, and is more severe when Zellner’s estimation meth
compared with the more favourable results in his OLS regressions. However
does not address econometric problems associated with the non-stationarity o
Notwithstanding the above empirical results, the balance of the evidence
single equation studies is that there is a strong negative correlation between t
premium and the subsequent change in the exchange rate (e.g. Fama (1984)
and Roghoff (1983)). In fact the coefficient on the forward premium fp, =
often nearer -1 than the ‘unbiasedness value’ of +l. This could be due to a
rational expectations or of risk neutrality. Following Fama (1984) we now m
assumption of RE while relaxing the assumption of risk neutrality to see if the
be the cause of the ‘failure’ of FRU.


12.3 FORWARD RATE: RISK AVERSION AND RATIO
EXPECTATIONS
Risk averse speculators in the forward market will require compensation
premium payment) for holding a net forward position in foreign exchange. H

fr = rpr + $+I


- sr, fpr = fr - s t , and rpr is an ad-hoc a
where = Ersr+l, As;+1 =
premium which may be time varying. Under RE equation (12.22) becomes:
fr - S t + l = r p , - Er+l
where Er+l = st+l - s:+l is the RE forecast error. Suppose we now assume a v
‘model’ for the risk premium, namely that it depends (linearly) only on t
premium fpr:
rpt = 81 + BlfPr
Under the null of RE but with a time varying risk premium given by (12.24
substituting (12.24) in (12.23) (Fama, 1984):


If the risk premium depends on the forward premium then we expect /?I
however, that equation (12.25) embodies a rather restricted form of the ris
+ B2fPr +
- st = 82 &t+1
St+l


We expect /32 = 1 for unbiasedness and a time invariant risk premium im
constant. After some tedious algebra (see Appendix 12.1) Fama (1984) is ab
that the difference between B1 and 82 is given by:

>I/ var<fpt>
- 8 2 = [var(rpt>- var(As;+,
B1

- var (expectations)]/ var( f p f )
= [var (risk premium)

A positive value for (/I1 - 82) indicates that the variance of the risk premium
than the variance of expectations about s;+˜. However, it can be seen from (12
rp, is highly variable then the forward premium will be a poor predictor of th
change in the spot rate and this is what we find in the usual ‘unbiasedness sing
regression’ (12.26). Therefore 81 - 82 provides a quantitative guide to the rela
tance of the time variation in the risk premium under the maintained hypo
RE holds.
Studies of the above type (e.g. Fama 1984) which estimate equations (
(12.26) usually find that 8 - 8 2 is positive. The latter usually arises becau
1
cally 8 2 is less than zero while is usually positive. Fama (1984) finds
- 82 of 1.6 (for Japanese yen) to 4.2 (for Belgian francs). Fama’s result
indicates that variations in the forward premium cause variations in the ris
(see equations (12.22), (12.24) and (12.25)) while 8 2 < 0 implies that unbiase
not hold (see equation (12.26)). Thus the overall conclusion from this work is
the null of RE, the FRU proposition fails because the (linear additive) risk
‘highly’ time varying.
It is worth repeating that a limitation of the above analysis is that the poten
varying risk premium r p , is assumed to depend only on the time varying forwar
fpr. Also the risk premium is an ad-hoc linear addition in equation (12.13)
based on any well-founded economic theory.
The weakness of the above analysis is that it assumes that RE holds s
violation of the null hypothesis is attributed to a time varying risk premium
require is a method which allows the failure of FRU to be apportioned between
of RE and variations in the risk premium.

Forward Rate: The Separation of RE and Risk Using Survey Data
+
As we have seen the joint null of ‘FRU R E + risk neutrality’ is rejected
number of empirical studies (using a variety of regression techniques). By us
data on agents’ expectations of the future spot rate, Frankel and Froot (1986)
one can apportion the rejection of the null between that due to a failure of R
due to a failure of risk neutrality. Consider the usual forward premium regres

+ Bfpt + E f + l
Ast+1 = a
It is easy to show that
P = 1 - BRE- SRN
where




and


Under the assumption of RE, the forecast error E ˜ + I is independent of the info
S 2 r and hence of f p r so that /?RE = 0. Also, regardless of how expectations
then under FRU the expected rate of appreciation will equal the forwar
fpt, so that cov(A$+,, f p f ) = 1 and hence ˜ R = 0 (i.e. risk neutrality holds)
N
risk neutrality hold then /?RE = SRN 0 and hence from (12.30), B = 1, as
=
expect.
we can construct a data series for Et+l =
If we have survey data on
along with the sample analogues of SRE and SRN. The latter provide evide
importance of the breakdown of either RE or risk neutrality in producing the re
First, let us remind ourselves of some problems, outlined in Chapter 5, t
using survey data to test economic hypotheses. The first question that arises
the data is qualitative (e.g. respondents answer ‘up’, ‘down’, or ‘same’) or q
(e.g. respondents answer ‘the exchange rate for sterling in 91 days will be 2
If qualitative date is used then the different methods which are used to transfo
yield different quantitative results for Hence we’can have different sets of q
data purporting to measure the same expectations. Also, if we have quantitativ
may be either for individuals or for averages (or median value) over a group of i
In principle, RE applies to an individual’s expectations and not to an average
a set of individuals.
There is also the question of whether the respondents are likely to gi
thoughtful answers and whether the individuals surveyed remain as a fixed
change over time. Also, when dealing with the FRU proposition the individua
of s;+˜ must be taken at the same time as fr (and st). Finally there is the
whether the horizon of the survey data (on exactly matches the outturn
sr+l. These problems bedevil attempts to draw very firm conclusions from stu
on survey data. Different conclusions by different researchers may be due to su
differences’ in the survey data used.
Let us return to the study by Frankel and Froot (1986, 1987, 1989) who use q
survey data on US respondents. They calculate SRE BRN and using (12.3
and
that B # 1 (in fact is negative) and that this is primarily attributed to a fa
(i.e. B R E is non-zero). This broad conclusion holds over five (main) currencie
horizons of 1, 3 and 6 months, for data from the mid 1970s and 1980s. MacD
namely that the failure of p # 1 is mainly due to ˜ R # 0. However, this eviden
N
weak since for three out of the four exchange rates studied RE = BRN= 0 a
one case is /?RN > 0. In fact, BRN = 1.4(t = 0.15) for the sterling effective ra
difficult to interpret results using the effective rate since this is a ‘basket’ of
(each of which has a set of bilateral forward rates).
On balance then there appears to be fairly strong evidence based on regres
survey data (in particular see Froot and Frankel (1989)) that
the forward premium is a biased predictor of subsequent changes in the exc
0

most of the bias is due to systematic forecast errors and very little to va
0

the risk premium
the average risk premium is non-zero but it is time invariant and in partic
0

not vary with the forward discount
The failure of RE may be due to the fact that agents are ‘irrational’ and th
make systematic forecast errors. However, it could equally be due to the fact
take time to learn about new exchange rate processes and while they are lea
make systematic errors because they do not know the true model. This lear
persist for some time if either the fundamentals affecting the exchange rate are
changing or if the influence of noise traders on the market varies over time. A
there may be a ‘Peso problem’ and a failure of FRU may occur even when
rational in the general sense of the word - namely they are doing the best the
the information available.


12.4 EXCHANGE RATES AND NEWS
A prominent feature of the movement in bilateral exchanges is their extreme
Weekly changes are extremely volatile with monthly and quarterly changes less
empiricism tell us that ‘news’, for example new money supply figures or ne
the current account position, can lead foreign exchange dealers to buy and sell
and influence spot and forward rates. Newspaper headlines such as ‘Dollar fa
of unexpectedly high money supply figures’ are not uncommon. The implicat
that if the published money supply figures had been as expected the exchange
have remained unchanged. It is the ‘new information’ contained in the mon
figures that leads FOREX dealers to change their view about future exchange r
to buy and sell ‘today’ on the basis of this ‘news’. On the other hand, expec
that are later confirmed may already be incorporated in the current exchange
implication of an efficient market. For example, another headline might be ‘Exc
improves as President announces lower monetary targets for the future’. The
here is that expected future events may influence the exchange rate today.
We shall use the term ‘news’ as a shorthand solely for unexpected events
in this section is to examine whether the above commonsense notions conc
behaviour of the foreign exchange market may be formally incorporated in the
Two stylised facts about exchange rate volatility have a bearing on the an
follows. We have noted that the predicted change in the exchange rate, gi
forward premium f p , , gives a poor forecast of As,+l on a month-to-month
variance of the actual change in the spot exchange rate can often exceed t
forward discount by a factor of 20 (Frankel, 1982a). This suggests that t
exchange rate changes As,+l are due to ‘new information’ which by definitio
have been anticipated and reflected in the forward discount f p , which preva
previous period.
Second, contemporaneous spot and forward rates move very closely to
example, for the $/E, $/DM $/yen exchange rates the correlation between t
and
poraneous spot rate and one-month forward rate exceeds 0.99 and correlatio
the corresponding percentage changes in spot and forward rates exceed 0.9
three currencies.

Direct Tests of the News Hypothesis in Spot and Forward Markets
Our first problem is how to measure news or unexpected events. There are
approaches, one using survey data on expectations, another public forecasts an
RE and regression analysis.
Expectations data exist for prices, inflation and output for a number o
countries. Data on interest rate expectations are also available for the US (
et a1 (1985)). Usually, but not always, data on expectations are qualitative. How
are methods for transforming the data into a quantitative figure for expectatio
and Parkin, 1975 and Pesaran, 1987).
Whether we think that economic fundamentals influence the exchange ra
on our model of exchange rate determination. However, given a time serie
data on expectations of relevant variables, E,-IX,, the unexpected or ‘news’ v
simply given by ( X , - E , - l X , ) . Public forecasts of X , (from, for example,
Bank, Treasury or City forecasters) can be used in a similar manner to form
representing ‘news’.
If neither survey data on expectations nor forecast data are available, we ca
pseudo expectations series E,- 1X, and ‘news’ variables ( X , - E,-IX,) using
analysis. For any variable X , we can assume agents make a forecast of X,
values of X , itself and past values of other relevant economic variables 2,:

x, = e l ( w , - l+ e 2 ( ˜ ) ˜+rE,- l
where & ( L ) are polynomials in the lag operator. Equation (12.33) can be v
reduced form of a ‘complete’ economic model. After estimating (12.33) the
X , can be taken as a proxy for agents’ expectations, E,-1X,. The residual fro
namely i?,, measure of the surprise of news about X t , so gf is a proxy for ( X ,
is a
Let us now turn to a general representation of models of the exchange rat
designate :
+
st = BXr
a white noise error). For example, in some monetary models, X , includes rela
supplies, relative real output and relative interest rates (see Chapter 13). Fro
and (12.35):
+ + + +
/?’(X, - E t - l X f ) w, = s news 0,
St = sp :
where sf = E,-lsf. Thus the forecast error (s, - s f ) is composed of an un
random component 0, and unexpected changes (‘news’) in the fundamental v
that determine s,. If expectations are rational, (X, - E,-IX,) will be orthogona
lated) with any other variables (at t - 1 or earlier), and with error term w f .
Equation (12.36) can only be made operational if we have a model for
relationship between s, and X , should come from some relevant economic
practice there may be several competing hypotheses about the determinants
of the hypothesis that ‘news’ influences the spot (or forward) rate is always te
with a hypothesis about the determination of the equilibrium expected excha
and the expectations generating equation (12.33). Hence, different researcher
different models for s: and E,-1X, often obtain different results when testing
hypothesis.
Perhaps the simplest and most straightforward models of the determination of
risk neutrality and RE. UIP with a constant risk premium rp implies s an :
mined by:
+ +
s = sf-l df-l r p
:

+ CIP) then sf is given by:
If we assume FRU (or UIP

+ rp’
s = f ,-I
:

Substituting the above expressions for sf in equation (12.36) we obtain:
+ B ’ K - E,-lXf 1 +
- Sr-1 - dl-1) = r p
(Sf Of

= rp‘ + y’(Xt - Er-1X,) + w,
- fr-i
sr

+
The above equations may be viewed as models embodying UIP RE and F
respectively, but where one is attempting to explain some of the RE foreca
terms of surprises in specific economic variables X,.If the EMH in the spot an
markets holds then one would expect /? and y to be non-zero and for any varia
at time t - 1 or earlier to have zero coefficients when added to either of these
If one uses a specific economic model based on fundamentals then s: in
replaced by the appropriate economic variables PX,. For example, in moneta
of exchange rate determination X , would include relative money supplies in th
and foreign country (see Chapter 13). In this case economic theory would in
‘sign’ one would expect on and hence on the surprise variables ( X , - E,-I
regression (12.36).
The main problem with studies of this type is that there is no general agr
a theory about the economic ‘fundamentals’ that determine the expected (eq
exchange rate . Hence there is no agreement on what variables to include as
:
s
an important news item in one period may not be viewed as important at an
period, suggesting that the coefficients /3 and y may not be statistically signi
all subsamples of the data and may appear unstable over time.
It follows from the above that these ‘news regressions’ are unlikely to
insights. In general, the news items (e.g. surprises in interest rates, money s
prices) that are found to be statistically significant (e.g. Frenkel (1981), Copela
still leave much of the variation in the dependent variable in equation (12.3
or (12.40) unexplained - that is there is still a lot of ‘noise’ or ‘news’ in exc
movements which is not explained at all.
Often in these studies lagged news items (e.g. ( X + l - E r - 2 X t - l ) ) are fo
significant. This is a refutation of RE since these lagged forecast errors are kno
t - 1. Such results are indicative of market inefficiency.


PESO PROBLEMS AND NOISE TRADERS
12.5
In previous sections we have noted that the simplifying assumptions of risk neu
RE are not consistent with the empirical results on FRU and speculation in the s
via the UIP relationship. This section examines two reasons for the apparen
failure of these relationships and the high volatility exhibited by the spot rate
shown how the Peso problem can complicate the interpretation tests of the EM
and forward markets. Second, a study of chartists, a particular form of noise tr
FOREX market allow us to ascertain whether their behaviour might cause d
exchange rate movements and nullify the EMH.

Peso Problem
The apparent failure of the EMH in empirical tests may be illusory because
known as the Peso problem. The Peso problem leads the researcher to measu
tions incorrectly, hence forecasts may appear biased and not independent of i
at time t.
The Peso problem arises from the behaviour of the Mexican peso in the
Although the peso was on a notionally fixed exchange rate against the US doll
consistently at a forward discount for many years, in anticipation of a devaluat
eventually occurred in 1976). Prima facie, the fact that the forward rate for th
persistently below the outturn value for the spot rate (in say three months’ tim
persistent profitable arbitrage opportunities for risk neutral speculators.
The Peso problem arises from the fact that there could be unobservable
unquantifiable) events which may occur in the future, but in our sample of
actually do occur. It is completely rational for an investor in forming his e
to take account of factors that are unobservable to the econometrician. How
event never occurs in the sample of data examined by the econometrician, th
erroneously infer that the agent’s expectations are biased. Hence the econome
believe that he has unearthed a refutation of RE but in fact he has not. This is
holds and US and Mexican interest rates are always equal and constant, then
= sr
mt+1

where s, is measured as dollars per peso. If the Mexican government’s fixed
rate policy is entirely credible (call this ‘regime 1’) and has been adhered to fo
of years then s,‘+˜ = s,+l = sf for all time periods in regime 1. Hence under
credibility’ expectations are correct in all time periods.
Now suppose that Mexican investors begin to think the government’s comm
fixed exchange rate has weakened and that there is a non-zero probability n th2
will be devalued and a probability (1 - n2) that it will remain ‘fixed’. Call
‘partial credibility’. A rational investor would then have an expectation given

+ (1 - n2)s,+1
(2) (1)
= n2s,+1
&t+l




sLi)l = exchange rate under the fixed exchange rate, regime 1, s (2)˜ = new
where ,+
(2) (1)
rate under the devaluation, regime 2, that is sf+l > s,+˜ = s:’). Suppose, how
during the ‘partial credibility’ period the Mexican government does nut alter th
rate. The outturn data will therefore be s:˜ = s:’), the existing fixed parity. H
!
)
survey data collected over this partial credibility period (which accurately
Etst+l),will not equal the (constant) outturn value sj’)


The ex-post forecast error in the ‘partial credibility’ period using (12.42) is

= s y - E,s,+1 = Q(S, - s,+l) < 0
(2)
(1)
ii++l


where we have used s$)l = st(l). Hence the ex-post forecast error, which is ob
we have survey data on expectations, is non-zero and biased. Also if sj’) var
then a regression of G++1 on the actual exchange rate s;” will in general yield
coefficient. The latter coefficient will equal n2, if is constant over the sam
and may be ‘close to’ n is:
2 f! varies only slightly over time (i.e. some omitte
bias will ensue). Hence we have an apparent refutation of the informational
assumption of RE because the forecast error is not independent of informati
t. Notice that even if n2, the probability of the unobserved event, is small th
the forecast error @,+I can still appear large if the potential change in s und
regime is thought to be large (i.e. s!’) - s is large).
!
:
)
˜
Now let us consider the problems caused when we try to test for FRU. If inve
a devaluation of the peso is likely then s$l1 > s!’) and hence from (12.43) w
E,s,+l > sj’) (remember that sf is in units of pesos per US dollar and hence a
in ‘s’ is a devaluation of the peso). Under FRU and risk neutrality, specula
spot rate (i.e. peso at forward discount).
Suppose we had a longer data set which included a period when the Mexic
ment announced a fixed exchange rate but that agents then believe that this
rate might be abandoned in favour of a revaluation of the peso. The above anal
again apply but in this ‘favourable partial credibility period’ (regime 3) the
forecast errors ii˜:would now be positive (and not negative as under regime
with a long enough data set where ‘unfavourable’ and ‘favourable’ unobser
occur equally often, our data set would conform to the RE postulates of unbias
errors and forecast errors that are independent of Qf.
The Peso problem therefore arises because one is testing a hypothesis with
data set, in which there are unobservable yet non-random variables (i.e. the
of changes in government policy). Thus the average of the outturn values for
an accurate representation of agents’ true expectations. The RE assumption
+4+l
= E&+l
Sf+l

where u,+l is random around zero, does not hold in the ‘short’, partial credibili
The only way one can in principle get round the Peso problem when investig
is to use accurate survey data on expectations to test Etsf+l = fr. However, i
analysing survey data has its own problems. It is possible that Peso problem
prevalent and in any actual data set we have, they do not cancel out. Peso pro
involve an equal frequency of positive and negative ‘events’ with probabilities
of shifts (d’) - d i ) )that just exactly cancel out in the data set available to the
seems unlikely. Clearly a longer data set is likely to mitigate this problem b
not irradicate it entirely. However, for advocates of RE, the apparent failure
statistical tests can always be attributed to ‘hidden’ Peso problems.

Noiser Traders
If one were to read the popular press then one would think that foreign exchan
were speculators, par excellence. In the 1980s, young men in striped shirt
primary coloured braces were frequently seen on television, shouting simultan
two telephones in order to quickly execute buy and sell orders for foreign
The obvious question which arises is, are these individuals purchasing and sell
exchange on the basis of news about fundamentals or do they in fact ‘cha
If the latter, the question then arises as to whether they can have a pervasive
on the price of foreign exchange. As we have seen there have been a large
technically sophisticated tests of market efficiency in the foreign exchange mar
terms of spot speculation (UIP) and speculation in the forward market (FRU)
there has been remarkably little work done on the techniques used by actu
exchange dealers and whether these might cause movements in exchange rates
not related to news about fundamentals. An exception here is the study by
Taylor (1989a) who look at a particular small segment of the foreign exchan
and undertake a survey of chartists’ behaviour. Chartists study only the price m
in the market and base their view of the future solely on past price changes
example, they might use moving averages of past prices to try and predict fu
They may have very high frequency graphs of say minute-by-minute price
and they attempt to infer systematic patterns in these graphs. Consider, fo
the idealised pattern given in Figure 12.2 which is known as ‘the head and
reversal pattern’. On this graph is drawn a horizontal line called ‘the shoulder
pattern reaches point D, that is a peak below the neckline, the chartist would
signals a full trend reversal. He would then sell the currency believing that it
in the future and he could buy it back at a lower price. As another exampl
Figure 12.3, the so-called ‘symmetric triangle’ indicated by the oscillations
on the point at A. To some chartists this would signal a future upward moveme
the interpretation of such graphs is subjective. For chartists as a group to in
market, most chartists must interpret the charts in roughly the same way, other
chartists would do would be to introduce some random noise into prices but
It is well known that chartists also use survey data on ‘market sentiment’. Fo
if ‘sentiment’ is reported to be optimistic about the German economy, the ch
well try and step in early and buy DMs.
The data set on which the Allen and Taylor study is based is rather small.
was conducted on a panel of chartists (between 10 and 20 responded every
the period June 1988-March 1989. They were telephoned every Thursday
for their expectations with respect to the sterling-dollar, dollar-mark and
exchange rates for one and four weeks ahead, yielding about 36 observations
per currency. The survey also asked the chartists about the kind of information
in making their forecasts and who the information was passed on to (e.g. actu
It was found that at the shortest horizons, say intra-day to one week, a
90 percent of the respondents used some chartist input in forming their exc




-
Time
Figure 12.2 Head and Shoulders. Source: Allen and Taylor (1989b).
Time
Figure 12.3 Symmetric Triangle. Source: Allen and Taylor (1989b).

expectations. As the time horizon lengthens to three months, six months o
the weight given to fundamentals increases and 85 percent of the responde
that over these longer horizons ‘fundamentals’ were more important than cha
However, the chart analysis was always seen as complementary to the ana
on fundamentals and therefore it is possible that chart analysis influences exc
even at these longer horizons.
If one looks expost at the accuracy of the chartists’ forecasts taken as a w
Figure 12.4 for the DM/$, four-week ahead forecasts are fairly typical of the
other currencies. In general Allen and Taylor find:
There is a tendency for the forecasts to miss turning points. On a rising
0

market the chartists’ expectations underestimate the extent of the rise or f
Prediction errors are noticeably greater at the four-week horizon than at th
0

horizon. Individual chartist’s forecasts for four-week ahead predictions ar
unbiased but they are biased for the one-week ahead predictions.
For all the chartists taken as a whole, they correctly predict the change in th
0

rate over one-week and four-week horizons approximately 50 percent of th
is what one would accept if their forecasts were purely due to chance.

However, the above result for all chartists neglects the possibility that individu
might in fact do well and do consistently well over time. In fact there are di
forecast accuracy among the chartists and there are some chartists who are sys
‘good’. However, one cannot read too much into the last result since the tim
the survey is fairly short and in a random sample of individuals one would alw
that a certain percentage would do ‘better than average’ (e.g. 5 percent of the p
Again taking chartists as a whole, Allen and Taylor assess whether they
alternative methods of forecasting. For example, some alternatives examined a
based on the random walk and ARIMA forecasts or forecasts based upon a
exchange rates, the interest rate differential and the relative stock market pe
1.90

1.85

1.80

1.75

1.70



, ˜
Sept Oct Nov Dec Jan Feb Mar
Aug
July
1*65

- -Median, .---.High/Low Forecast
Actual,
Actual rate plotted at time t, forecast plotted at t+4

Figure 12.4 Deutschmark: Four Weeks Ahead Chartist Forecasts. Source: Allen
(1989b)

The results here are mixed. However, few individual forecasters (apart from
‘M’) beat the random walk model. In most cases the ARIMA and VAR fore
worse than predictions of ‘no change’ based on a random walk and often mo
failed to beat these statistical forecasting models. However, overall there is n
it. All of the statistical forecasting methods and the chartists’ forecasts had app
the same root mean squared errors for one-week and four-week ahead forecas
balance, the random walk probably doing best. However, there were some ch
chartist ‘M’) who consistently outperformed all other forecasting methods.
Since Allen and Taylor have data on expectations they can correlate change
tations with past changes in the actual exchange rate. Of particular interest
chartists have bandwagon expectations. That is to say when the exchange rat
between t - 1 and t, does this lead all chartists to revise their expectations upw
and Taylor tested this hypothesis but found that for all chartists as a group, b
expectations did not apply. Thus chartist advice does not appear to be intrinsic
bilising in that they do not over-react to recent changes in the exchange rate.
Taylor also investigate whether chartists have adaptive or regressive expectati
are essentially mean reverting expectations and there were some chartists wh
mated this behaviour. Thus chartists may cause short-run deviations from fun
Overall the results seem to suggest there are agents in the market who make
forecasting errors but there appears to be no bandwagon or explosive effect
behaviour and at most chartists might influence short-run deviations of the exc
from fundamentals. The Allen and Taylor study did not examine whether char
casts actually resulted in profitable trades, they merely looked at the accuracy o
forecasts. However, a number of studies have been done (Goodman, 1979, 198
1980 and Bilson, 1981) which have looked at ex-post evaluations of forecastin
models based on fundamentals, in forecasting the future spot rate.

12.6 SUMMARY
For the topics covered in this chapter the main conclusions are:
Riskless arbitrage opportunities in the FOREX market sometimes do app
tively long horizons (one year) but for the most part there are no large
profitable opportunities and covered interest parity holds.
Evidence suggests that UIP and FRU do not hold but one cannot concl
that this is due to a failure of the assumption of risk neutrality or RE.
conclusion might be that rejection lies more with the assumption that age
at all times.
The addition of explicit variables to proxy ‘news’ does not appear to a
deal to the predictability of the future change in spot rates given either
differential (UIP) or the forward discount (FRU).
Because of a presumption of frequent and possibly substantial government i
in the forward and spot markets, Peso problems are likely to be present
they are virtually impossible to quantify and this makes it difficult to interp
the ‘negative’ results when testing UIP and FRU do imply a rejection of
Noise traders probably do influence spot rates but such behaviour, based
from chartists’ expectations, are likely to have only a short-run impac
floating spot rates and chartists’ behaviour is unlikely to be destabilising
dently of other traders’ behaviour.
Hence, no definitive results emerge from the tests outlined in this chapter on the
of forward and spot rates and this in part accounts for governments switching
stance with regard to exchange rates. Sometimes the authorities take the vie
market is efficient and hence refrain from intervention while at other times th
the market is dominated by (irrational) noise traders and hence massive inte
sometimes undertaken. A ‘half-way house’ is then provided when the authori
that rules for concerted intervention are required to keep the exchange rate wi
nounced bands, as in the exchange rate mechanism of the European Monetary
logical development of the view that free market exchange rates are excessiv
and that governments cannot prevent fundamental and persistent misalignm
move towards a common currency, as embodied in the Maastricht Treaty fo
countries.


APPENDIX 12.1 DERIVATION OF FAMA’S DECOMPO
OF THE RISK PREMIUM IN THE FORWARD MARK
If we include an additive time varying risk premium rp, in the FRU hypothesis we o

f = rpt + s;+,
t
and (la) and (1b) become

ft = rpr + sr+1 - E,+1
+ ASf+l - Ef+1
f P t = rp,
Assume that rp,+l depends linearly on the forward premium

+ 8lfPt
rpr+1 = 61

Under null hypothesis of RE, FRU and a time varying risk premium we have from (3

(ft - Sr+l) = 61 + 81fPf - E,+1
null hypothesis of FRU + RE but with a constant
Now consider the 'usual' risk prem

+ 82fPr + E f + l
= 62
b+l

For unbiasedness we require p 2 = 1 and a constant risk premium implies 82 = -rp, =
Under their respective null hypotheses OLS provides consistent estimators of p
equations ( 5 ) and (6):

corn - I/ W f p , )
= s + 1 fPf
B1 r1

8 2 = cov(As1+17 fPf I/ W f P r 1
ft - s,+l from (3a) and for fp, from (lb) in equation (7):
Substitute for


Under RE, the forecast error &,+I is independent of inforination at time t including rp,
is independent of &,+I under RE. Hence (9) reduces to



Equation (2), the RE condition, may be rewritten



where As,+l = sf+l- s, and - AS^+^ from
= $+, s,. If we now substitute for
fp, from (lb) in equation (8) we obtain:

8 = cov(As;+',, + Ef+17 rp, + A.s;+;,)/var(fp,)
2
is independent of rp, and As;+l hence:
Under RE, &,+I


82 = [cov(rpf, As;+l 1 + var(As;+, )]/ W f p ,
Substracting (13) from (10) w e then obtain (12.27) in the text
13 I
I
The Exchange Rate and
Fundamentals
There are a large number of alternative models based on ‘economic fundam
have been used to analyse movements in the spot exchange rate. This chapte
sketches only the main ideas. It is probably correct to say that monetary
their various forms have dominated the theoretical and empirical exchange
ture and we discuss a number of these such as the flex-price and sticky-price
models and the Frankel real interest rate model. As we shall see these m
been far from successful in explaining movements in exchange rates. Indee
no consensus among economists on the appropriate set of economic fundam
influence exchange rates and this in part is why policy makers have soug
exchange rate movements by cooperative arrangements such as Bretton Woo
ERM in Europe (and in the latter case to consider proposals for a move towards
currency). The flex-price monetary model (FPMM) concentrates on the current
the capital account and assumes prices are flexible and output is exogenously
by the supply side of the economy. Under floating rates the FPMM model
close relationship between rapid monetary growth and a depreciating exchang
vice versa) - which, for example, is broadly consistent with events in Ital
Germany and Japan in the first half of the 1970s and in some Latin American c
the 1970s and 1980s. In fact, in terms of its predictions the text book Munde
model under the assumption of a full employment level of output yields sim
to the FPMM.
Unfortunately, the FPMM failed adequately to explain the large swings
exchange rate (or competitiveness) that occurred in a number of small, open
such as those of the UK, the Netherlands and Italy in the second half of
and early 1980s. The FPMM takes ‘money’ as the only asset of importance
ignores other asset flows in the capital account of the balance of payments
recognise the importance of capital flows, which have obviously increased
gradual dismantling of exchange controls, we have to address the question of ex
Speculative short-term capital flows respond to relative interest rates between th
and foreign country but also depend upon expectations about exchange rate m
The sticky-price monetary model (SPMM) invokes the rational expectations hy
deal with exchange rate expectations and it is usually assumed that capital acc
are perfectly mobile. Price adjustment in the goods market is slow and is det
A recurring theme in the exchange rate literature concerns the response of th
rate to a change in domestic interest rates. The FPMM model predicts that a d
ensues after a rise in domestic interest rates, while the SPMM model yield
site conclusion. The real interest rate monetary model (RIMM) clarifies thi
rate-interest rate nexus and also yields insights into why exchange rate movem
to be ‘excessively’ volatile.
Finally, a defect in the SPMM is its implicit assumption of the perfect sub
of domestic and foreign assets and failure to analyse explicitly the stock flow
arising from current account imbalances. This is remedied in the portfolio bal
of exchange rates (PBM).


13.1 FLEX-PRICE MONETARY MODEL
The FPMM model relies on the PPP condition and a stable demand for mone
The (logarithm) of the demand for money may be assumed to depend on (the lo
real income, y, the price level, p , and the level of the (bond) interest rate, r .
a similar ‘foreign’ demand for money function. Monetary equilibria in the do
foreign country are given by:
ms= p+c$y-Ar
ms*= p* + +*y* - A*r*

where foreign variables are starred. In the FPMM model the domestic inte
exogenous - a rather peculiar property. This assumption implies that the dome
rate is rigidly linked to the exogenous world interest rate because of the ass
‘perfect capital mobility’ and a zero expected change in the exchange rate.
output is also assumed fixed at the full employment level (the neoclassical su
then any excess money can only influence the ‘perfectly flexible’ domestic
one for one: hence the ‘neutrality of money’ holds.
Equilibrium in the traded goods ‘market’ (i.e. the current account) ensues w
in a common currency are equalised: in short when PPP holds. Using lower
to denote logarithms, the PPP condition is:
s=p-p*

The world price, p * , is exogenous to the domestic economy, being determi
world money supply. The domestic money supply determines the domestic
and hence the exchange rate is determined by relative money supplies. Alg
substituting (13.1) and (13.2) into (13.3) gives

+ $*v* + Ar - A*r*
- -
s = (ms mS*) c$y

Possible transmission mechanisms underlying (13.4) are (i) an increase in th
money supply leads to an increased demand for foreign goods (and assets),
rise in domestic prices via the Phillips curve. This is followed by a switch t
cheap foreign goods causing downward pressure on the domestic exchange
probably (i) that is closest to the spirit of the FPMM price-arbitrage approach
It is worth noting that the effect of either a change in output or the dome
rate on the exchange rate in the FPMM is contrary to that found in a Keyne
A higher level of output or lower domestic interest rates in the FPMM mode
increase in the domestic demand for money. The latter allows a lower dom
level to achieve money market equilibrium, and hence results in an apprecia
exchange rate (see, for example, Frenkel et a1 (1980) and Gylfason and Helliw
Now, a rise in nominal interest rates may ensue either because of a tight mone
or because of an increase in the expected rate of inflation, n.The Fisher hypot
that real rates of interest \I/ are constant in the long run:

r=Q+n

Adding this relationship to the FPMM of equation (13.4) we see that a high ex
of domestic inflation is associated with a high nominal interest rate and a d
in the domestic exchange rate (i.e. s has a ‘high’ value). Thus the interest rat
rate relationship appears somewhat less perverse when the Fisher hypothesis
the FPMM model to yield what one might term the hyperinfiation FPMM
terminology arises because r is dominated by changes in 7˜ in hyperinflations
Germany in the 1920s). This is all very well but one might be more disposed
rate of depreciation (i.e. the change in s ) as depending on the expected rate
as in the Frankel (1979) ‘real interest’ model discussed below.
The FPMM as presented here may be tested by estimating equations of the
for the exchange rate or by investigating the stability of the PPP relationsh
demand for money functions. As far as equation (13.4) is concerned it worked
well empirically in the early 1970s floating period for a number of bilatera
rates (see Bilson (1978)), but in the late 1970s the relationship performed
than for countries with high inflation (e.g. Argentina and Brazil). The increas
mobility in the 1970s may account for the failure of the FPMM model. Alth
are difficulties in testing the PPP relationship it has been noted that it too does
to hold in the latter half of the 1970s (see also Frenkel (1981)).


13.2 STICKY-PRICE MONETARY MODEL (SPMM
In the latter half of the 1970s the FPMM ceased to provide an accurate de
the behaviour of exchange rates for a number of small open economies. Fo
in the UK over the period 1979-1981 the sterling nominal effective exchan
the rate against a basket of currencies) appreciated substantially even thou
money supply grew rapidly relative to the growth in the ‘world’ money supply
more startling, the real exchange rate (i.e. price competitiveness or the term
appreciated by about 40 percent over this period and this was followed by an eq
the FPMM failed to explain this phenomenon adequately. Large volatile swings
exchange rate may lead to large swings in net trade (i.e. real exports less real im
consequent multiplier effects on domestic output and employment. The SPMM
an explanation of exchange rate overshooting (Dornbusch, 1976) and short-r
in real output, as occurred in the very severe recession of 1979-1982 in th
SPMM is able to resolve the conundrum found in the FPMM where one o
counterintuitive result that a rise in domestic interest rates leads to a deprecia
domestic currency. In the SPMM if the rise in nominal rates is unexpected
constitutes a rise in real interest rates the conventional result, namely an appr
the exchange rate, ensues.
Like the FPMM the SPMM is ‘monetarist’ in the sense that the neutrality o
preserved in the long run by invoking a vertical neoclassical supply curve for
equivalently a vertical long-run Phillips curve). However, PPP holds only in th
and hence short-run changes in the real net trade balance are allowed. Key e
the SPMM are the assumption of a conventional, stable demand for money fu
uncovered interest parity. Agents in the foreign exchange market are assum
(Muth) rational expectations about the future path of the exchange rate: they im
act on any new information and this is what makes the exchange rate ‘jump’ a
frequent changes. In addition, in SPMM the capital account and the money ma
in all periods, but the goods market, where prices are sticky, does not. It is this co
of ‘flex-price’ and ‘fix-price’ markets that can produce exchange rate oversho


13.3 DORNBUSCH OVERSHOOTING MODEL
We now look at a simplified account of the Dornbusch (1976) model beginn
description of the main behavioural assumptions, followed by an analysis of
of a tight monetary stance on the economy. (For a detailed account see Cuthb
Taylor (1987).)
The uncovered interest parity (open-arbitrage) relationship expresses the co
equilibrium in the capital account. Foreign exchange speculators investing abroa
+
return of r* p percent, where r* = foreign interest rate and p = expected ap
of the foreign currency (depreciation in the domestic currency). With perf
mobility and risk neutrality, equilibrium in the capital account requires:
r==r*+p
Expectations about the exchange rate are assumed to be regressive. If the actu
below the long-run equilibrium rate, S, then agents expect the actual rate to ri
the long-run rate; that is, for the spot rate of the domestic currency rate to de
the future:
o<oti
p=e(s-s)

where s and S are in logarithms. This expectations generating equation may be
consistent with rational expectations in that the regressive formula allows expe
In the goods market, aggregate demand (AD) is given by

+ p * ) - or + yy + y’
AD = 6(s - p

The first term represents the impact of the real exchange rate on net trad
the second ( - o r ) the investment schedule, the third ( y y ) the consumption fu
expenditure effects on imports and the final term ( y ’ ) exogenous demand fact
government expenditure. The ‘supply side’ is represented by a vertical long-r
curve: the rate of inflation responds to excess demand in the goods market; p
slowly to equilibrium (0 < Il < l),

+ p * ) - or + yy + y’ - 71
p = n ( A D - 7 ) = n[8(s - p
7 is the full employment level of output.
where

Flexible Prices: Long Run
Consider a reduction of 1 percent in the money supply. If prices are perfectly fle
of 1 percent in the price level will restore money market equilibrium (with an
level of interest rates). In addition, if the exchange rate appreciates by 1 perce
exchange rate remains constant and real aggregate demand continues to match
supply. In the long run, the interest rate is unchanged and therefore real
is unchanged and uncovered interest parity still holds. It follows from the
(immediately after the ‘long-run’ appreciation), the exchange rate is expected
constant in the future. Thus, as prices in the SPMM are not sticky in the lon
after a monetary contraction the exchange rate will be higher in order to mai
competitiveness (PPP).

Fixed Prices: Short-Run Overshooting
In contrast, now assume prices and output are sticky in the short run. Wit
‘sticky’, a decrease in the money supply requires a rise in the bond rate, r
the money market (dr = -(l/A)drns, equation (13.8)). The rise in r causes
capital inflow, which can be arrested only if the domestic exchange rate is e
depreciate, thus re-establishing uncovered interest parity. According to equatio
expected depreciation of the domestic currency requires the actual spot rate im
to appreciate above its long equilibrium value; hence the exchange rate ‘ove
long-run value.
It is useful to present a simplified account of the mathematics behind
Because of the vertical Phillips curve, output is fixed in the long run and the
of money implies d p = dm. As PPP also holds in the long run, d3 = d p = d
a bar over a variable indicates its long-run value). Turning to the short run,
and y are fixed so that any short-run disequilibrium in the money market is t
adjustments in r:
d r = -dms/A
From the expectations equation (13.7) and using (13.12) above, the short-run
the exchange rate is:
ds = ds - d p / 8 = [1+ (Oh)-’]dms

+
Since 8h > 0 the initial change in the spot rate of [ l (8h)-’]drns exceed
long-run change: dS = d d .
It is clear that ‘overshooting’ is in part due to the restrictive channels thro
monetary policy is forced to operate. Initially all adjustment in the money m
the interest rate and only in the long run does the price level equilibrate the mo
and the interest rate return to its original level. Although it is not immediate
from the above analysis, the assumption of risk neutrality is of equal importa
respect. Note that, in contrast to the prediction of the FPMM, the response of th
rate to the interest rate is as one might intuitively expect: an unanticipated j
interest rate (consequent on a fall in the money supply) leads to an apprecia
domestic currency.


13.4 FRANKEL REAL INTEREST DIFFERENTIA
MODEL (RIDM)
Frankel(l979) provides a general model for analysing the impact of changes in
rate on the exchange rate and he refers to this as the ‘real interest differential
provides a Dornbusch relationship with respect to the nominal interest rate (
and a hyperinflation FPMM with respect to the expected rate of inflation (
Also, the exchange rate may overshoot its long-run equilibrium value.
Frankel ’s model assumes uncovered arbitrage but modifies the Dornbusc
tions equation for the exchange rate by adding a term reflecting relative expec
inflation (n - n*). expectations equation is
The


and uncovered interest parity yields
se - s = r - r*

The expected rate of depreciation (se - s) depends upon the deviation of the
rate from its equilibrium value, which as we know gives Dornbusch-type
addition, if s = 3, the expected rate of depreciation is given by the expecte
differential between the domestic and foreign currency: as we shall see this term
hyperinflation FPMM results. Frankel asserts that the expectations equation is
expectations generating mechanism per se but it may also be shown to be cons
rational expectations. (We do not deal with this aspect.)
Combining equations (13.14) and (13.15) and rearranging we have
s - s = ( 1 / 8 ) [ ( r- n) - (r* - n*)]
its long-run level (7 - 7*),given by relative expected inflation, that the ‘curren
rate appreciates above its long-run equilibrium level (S - s > 0).
We now assume that PPP holds in the long run and with the usual demand
functions (with @ = @*, h = A* for simplicity) we obtain an expression for th
exchange rate (as in the FPMM model):
+
--
s = p - p* = - m* - @(Y - Y*) h(r - T;*)

+ h ( n - n*)
= (rn - f i * )- @(Y - jj*)
where we have used F - T;* = n - n* (the ‘international Fisher effect’ which is
the hyperinflation FPMM). The crucial elements in the Frankel model are the e
equation (13.14) and the distinction between the short-run and long-run dete
the exchange rate. Substituting for S from (13.16) in (13.17) we obtain Frankel’s
form’) exchange rate equation:
m* - @(? ?*) - (l/O)(r - r * )+ [ ( l / O ) + h ) ( n- 71*)
-
s = rn - -
-
= m - m * - @(Y - ?*I + a ( r - r * ) + p(n - n*)
˜
where a = -(l/@ and = ( l / @+ A. We can now characterise our three
models in terms of the parameters a and p.
It is evident from Table 13.1 that in the Frankel model we obtain a Dorn
result (as/ar < 0) if interest rates increase while inflation expectations remai
This situation is likely to correspond to an unanticipated change in the mo
which has an immediate impact on interest rates (to ‘clear’ the money ma
not immediately perceived as permanent and hence does not influence II. O
hand, an equal increase in the nominal interest rate, r, and inflationary exp
+
cause a depreciation in the exchange rate ( p a > 0) - a FPMM-type result
adding an ancillary assumption to the Dornbusch-type model, namely equati
an anticipated increase in the money supply is likely to lead to an expecte
tion and (the Frankel model then predicts) an actual depreciation. Implicitly
model highlights the possible differential response of the exchange rate to anti
unanticipated changes in the money supply and interest rates.

Table 13.1 The Frankel Real Interest Rate Model
Model Parameters
< 0, B I 1 > IQ1
S
Frankel > 0;
Q

FPMM =0
> 0,?!/
Q
FPMM-hyperinflation = 0, >0
Q
< 0, p
Dornbusch-SPMM =0
Q




The Portfolio Balance Model
The current and capital account monetary models which have been the sub
of the preceding sections make at least two important simplifying assumption
portfolio balance model (PBM) is determined, at least in the short run, by
demand in the markets for all financial assets (i.e. money, domestic and foreign
the PBM a surplus (deficit) on the current account represents a rise (fall) in n
holdings of foreign assets. The latter affects the level of wealth and hence
demand for assets which then affects the exchange rate. Thus, the PBM is an
dynamic model of exchange rate adjustment which includes behavioural inte
asset markets, the current account, the price level and the rate of asset accumu
reduced form equations used in testing the PBM therefore include stocks of a
than money. For example, domestic and foreign bonds and stocks of overseas
by domestic and foreign residents (usually measured by the cumulative curre
position) influence the exchange rate.

A General Framework
The above models can be presented in a common framework suitable for empir
by invoking the UIP condition as a key link to the ‘fundamentals’ in each mo
this, note that the UIP condition in logarithms is:
- s, = rr - r:
E,s,+l
Now assume that some model of the economy based on fundamentals z, impl
interest differential depends on these fundamentals:
r, - r: = yfzr
From the above:
= m t + 1 - YfZf
Sf

and by repeated forward recursion and using the law of iterated expectations
fl-1


i=O

+
Hence movements in the current spot rate between t and t 1 are determin
sions to expectations or ‘news’ about future fundamentals Z r + j . In this RE
exchange rate is volatile because of the frequent arrival of news. The funda
in equation (13.22), vary slightly depending on the economic model adopte
flex-price monetary model FPMM we have
- p: = (rn - m*),- a ( y - y*If + /?(r- r*lt
st = p t
substituting for r - r* from the UIP condition and rearranging we have
+ P)lzr + “(1 + B)I&Sr+l
=[ W
3,

where z, = (rn - rn*)t - a ( y - y * ) f . By repeated forward substitution
Pt - PI-1 = axt
and excess demand is high when the real exchange rate depreciates (i.e. st in
+ P: - p r )
Xr = q 1 ( s t
Using UIP and the money demand equations this gives rise to a similar form
except that there is now inertia in the exchange rate:
00

+
= e1St- <1
6 2 ˜ t1-zt+ j
i (@1,@2)
st

j=O

where zr depends on current and lagged values of the money supply and outp
The portfolio balance model (PBM) may also be represented in the form
noting that here we can amend the UIP condition to incorporate a risk prem
depends on relative asset holdings in domestic B, and foreign bonds BT.
+ f(Br/B:)
rt - r: = ErSr+1 - sr
The resulting equation (13.29) for the exchange rate now has relative bond
the vector of fundamentals, zt.
Forecasts of the future values of the fundamentals Zt+j depend on informa
t and hence equation (13.29) can be reduced to a purely backward looking
terms of the fundamentals (if we ignore any implicit cross-equation RE restri
this is often how such models are empirically tested in the literature as w
below. However, one can also exploit the full potential of the forward terms
which imply implicit cross-equation restrictions, if one is willing to posit an
of forecasting equations for the fundamental variables. This is done in Cha
the FPMM to illustrate the VAR methodology as applied to the spot rate in t
market.


13.5 TESTING THE MODELS
As one can see from the above analysis, tests of SPMM involve regressions of t
on relative money stocks, interest rates, etc. and tests of the PBM also include
stocks. If we ignore hyperinflation periods, then these models have not proved
in predicting movements in bilateral spot rates, particularly in post 1945 dat
the models do work reasonably well over short subperiods but not over the wh
Meese (1990) provides a useful ‘summary table’ of the performance of such
estimates a general equation which, in the main, subsumes all of the above th
+ a l ( L ) ( m- m*), a 2 ( L ) ( y- y*)t + a3(L)(r- r*)t + a4(L)(n -
+
st = a0



where F = stock of foreign assets held by domestic residents and F* = stock
assets held by foreign residents. Meese (1990) repeats the earlier tests of
mean square forecast errors from (13.30) with those from a benchmark prov
‘no-change’ prediction of the random walk model of the exchange rate. It is
Table 13.2 that the forecasts using the economic fundamentals in (13.30) are
worse than those of the random walk hypothesis.
Meese (1990) dismisses the reasons for the failure of these models based on
tals as mismeasurement of variables, inappropriate estimation techniques or e
variables (since so many alternatives have been tried). He suggests that th
such models may be due to weakness in their underlying relationships such
condition, and the instability found in money demand functions and the mountin
from survey data on expectations that agents’ forecasts do not obey the axioms
expectations. He notes that non-linear models (e.g. chaotic models) that invo
changes (e.g. Peso problem) and models that involve noise traders may pr
insights into the determination of movements in the spot rate but research in
is only just beginning.
A novel approach to testing monetary models of the exchange rate is p
Flood and Rose (1993). They compare the volatility in the exchange rate and i
fundamentals for periods of ‘fixed rates’ (e.g. Bretton Woods, where permitte

a b l e 13.2 Root Mean Square Error (RMSE) Out-of-Sample Forecast Statistics -
1980 through June 1984 (44 Months)
Exchange Horizon Random Mod
Rate (Months) Walk 1
3.1 3.1
1
6 7.9 8.4
12 8.7 11.1
1 3.5 3.3
6 7.0
7.8
12 9.0 7.5


RMSE Out-of-Sample Forecast Statistics - November 1976 through June 1981 (56 M
Exchange Horizon Random Forward M
Rate (Months) Walk Rate 1
log(DM/$) 1 3.22 3.20 3.65
6 8.71 9.03 12.03
12 12.98 12.60 18.87
log(yen/$) 1 3.68 3.72 4.11
6 11.58 11.93 13.94
12 18.31 18.95 20.41
(a) Model 1: Equation (13.30) with a5 = 0. Model 2: Equation (13.30) with all parameters fre
Both models are sequentially estimated by either generalised least squares or instrumental
a correction for serial correlation. RMSE is just the average of squared forecast errors fo
three prediction horizons.
Source: Meese (1990).
floated. For nine industrialised (OECD) countries, Flood and Rose find th
the conditional volatility of bilateral exchange rates against the dollar alters d
across these exchange rate regimes, none of the economic fundamentals e
marked change in volatility. Hence one can legitimately conclude that th
fundamentals in the monetary models (e.g. money supply, interest rates, inf
output) do not explain the volatility in exchange rates. (It is worth noting, howe
latter conclusion may not hold in the case of extreme hyperinflations where th
in relative inflation rates (i.e. fundamentals) across regimes might alter subst
A more formal exposition of the Flood and Rose methodology in testing
may be obtained from equation (13.4) with @ = @*, h = A* and substituting
from the UIP condition
+
Sf = TF, h(s;+l - Sf)

where TF, = (m - m*)t - +(y - y*), is ‘traditional fundamentals’. Equa
defines ‘virtual fundamentals’ (VF) as VF, = st - h ( r - r*)r. Now, under
equation (13.4), we expect the variability in virtual fundamentals VF, to
variability in traditional fundamentals TFt. To obtain a time series for TF, and
requires is a representative value for the structural parameters of the demand
function h and 4. As reported above, Flood and Rose find that while the
VF increases dramatically in the floating rate period, the volatility of funda
changes very little. (This result is invariant to reasonable values of E, and 4 an
when they consider the SPMM.) Flood and Rose speculate that since few mac
variables undergo dramatic changes in volatility, which coincide with changes
rate regimes, then it is unlikely that any exchange rate model based only o
fundamentals will prove adequate. For nine OECD countries, they also c
average monthly variance of the exchange rate over successive two-year hor
against the variance of various macroeconomic variables. They find that
correlation between a2(S)and either the variability in the money supply or in
or FOREX reserves or stock prices and only a rather weak negative correlati
variance of output. Hence in moving from a floating exchange rate regime to
the reduced volatility in the exchange rate is not reflected in an increase in
other macroeconomic variables. (A similar result is found by Artis and Taylo
European countries which moved from a floating rate into the Exchange Rate
in the 1980s.) The balance of the argument on fixed versus floating based o
evidence would seem to favour some kind of target bands rather than a p
regime. The evidence also suggests that there is some change in the trading b
agents when there is a move from flexible to ‘fixed’ rates (e.g. do noise trad
to other ‘unrestricted’ speculative markets? does the credibility of the fixed
play an important role in influencing expectations and hence trading activity?

Rational Bubbles
We noted in Chapter 7 that there are not only severe econometric difficultie
for rational bubbles but such tests are contingent on having the correct equilib
bubble term results in an equation for the spot rate of the form:
00

+ PI-’ + BO[(P + ˜)/B)I‘
sr = (1 ˜ / ( 1 P)Eizr+i
+
i=O

where 2, = set of monetary variables and Bo = value of bubble at t = 0. The
bubbles is Ho: BO = 0. However, if the 2, variables are a poor representation
fundamentals then the estimate of Bo may be different from zero, as it is the
candidate left to help explain the dependent variable. Testing Bo = 0 in (13
problematic because of the ‘exploding regressor’ problem. However, the test
(1987a) avoids the latter problem and provides a test for any form of bubb
stochastic or deterministic.
Meese (1986) uses the FPMM as his maintained fundamentals model fo
exchange rate (1973-1982) and rejects the no-bubbles hypotheses. West (19
second type of West (1988a) test and augments the FPMM of Meese to inc
demand errors which may pick up other potential ‘fundamentals’. He finds
presence of bubbles for the $/DM rate (1974-1984).
The Peso problem poses an additional difficulty when testing for bubbles in
exchange market. It is widely believed that the monetary authorities frequentl
in the FOREX market and that the authorities often try and mitigate large swi
and) nominal exchange rates (e.g. Plaza and Louvre agreements in the 198
participants are likely to form expectations of such events and these expe
unlikely to be measured correctly by the econometrician. The latter, couple
poor performance empirically of exchange rate models based on fundament
that there is little one can say with any degree of certainty about the presence o
of rational bubbles in spot exchange rates.

Random Walk Reappears
The failure of structural models of the spot rate led researchers to fall back on
parsimonious statistical representations. To a reasonable approximation, dai
exchange rates follow a martingale
- s,-1 = 0
E,-lS,

where the forecast error q, = S, - E,-1S, has a non-constant variance (Baillie
slev, 1989 and Baillie and McMahon, 1989). Hence the model is:
+ rlr
= Sr-1
Sr

and the time varying variance of q, denoted of seems to be well approxim
autoregressive structure of the form
+ alor-l+ a2qr-1
2 2
=a0
0
:

which is known as a GARCH(1,l) process (see Chapter 20). In a recent s
(1995) has re-examined the usefulness of ‘fundamentals’ in explaining chan
- sr = J k -k @k(st - zr)
Si+k


Mark finds that the R2 in the above regression and the value of /?k incre
horizon k increases from 1 to 16 quarters. (He uses quarterly data on the
against the Canadian dollar, Deutschmark, yen and Swiss franc, 1973- 1991.
of-sample forecasts at long horizons ( k = 16) outperform the random walk f
and Swiss franc. The above ana!ysis is not a test of a ‘fully specified’ mone
but demonstrates that ‘monetary fundamentals’ may provide a useful pred
exchange rate, over long horizons (although not necessarily over short hor
above exchange rate equation is a simple form of error correction model, w
correction term (s - -fiis model is re-examined in the context of coin
Chapter 15. Ciearly, if one is looking for a purely statistical representatio
also consider non-linear models (e.g. Engel and Hamilton (199(ijj, neural ne
Trippi and Turban (1993)) and chaos models of the exchange rate. Below
discuss the latter.


13.6 CHAOS AND FUNDAMENTALS
The RE hypothesis when applied tomodds of speculative prices and return
an Euler equation which can contain an exogenous bubble term (De Grauwe e
The model is therefore not fully self-contained because we need to select
either with or without the bubble and this choice is not determined by the
requires and ad-hoc assumption using information which is exogenous to the
there is, in a sense, an ad-hoc element in RE models; they are not ‘complete
the expectations process.
RE models of the exchange rate attribute the volatility in the spot rate to
of new information or news. However, using high frequency data the study b
(1989) finds that most exchange rate movements appear to occur in the absenc
able news. Ad4 to this evidence from cointegration studies that for many curr
is no long-run (cointegrating) relationship between the spot rate and economic
tals (e.g. Boothe and Glassman (1987) and Baillie and Selover (1987)) then m
on fundamentals begin to look rather weak. There is also evidence that at sho
(e.g. one month) the spot rate is positively autocorrelated whereas at long
there is significant negative serial correlation (Cutler et al, 1989) which is i
NT with extrapolative predictions at short horizons and with fundamentals mo
inant at !onger horizons. Finally, there is evidence using survey data that expe
not rational and they may exhibit bandwagon effects at short horizons with m
sion at !onger horizons (Frankel and Froot, 1988 and Takagi, 1991). Also, F
(1989) demonstrate that the chain rule of RE doesn’t apply, in that the forwa
of expectations over short horizons do no: equal those for the equivalent lon
An eclectic view of the evidence on exchange rate behaviour therefore
numberrof anomalies relative to the central paradigm of a model based o
fundamentals in which ait agents use RE. Models of chaos suggest that appar
non-linearities rather than in applying RE to such models (which analyticall
very difficult because the mathematical expectations operator cannot evaluate
such as E ( x , / y , ) which appear in the non-linear systems).
The spirit in which we approach models of chaos is one where we hope the
to provide alternative insights into the somewhat anomalous behaviour of th
rate (and other asset prices) rather than provide a complete theory of such m
This section examines the contribution that chaos theory can make in acc
the empirical results discussed earlier, which seem to indicate a failure of fu
in explaining movements in the spot rate and for an apparent failure of RE
efficiency. The work of De Grauwe et a1 (1993) is used extensively to sh
specific illustrative chaotic model can provide a starting point, at least, into t
anomalous behaviour of the FOREX market. This is done using the sticky-p
tary model (SPMM) to determine the equilibrium exchange rate as viewed b
money (SM) and is combined with the model of heterogeneous expectation
traders (NT) and SM presented in Section 8.3 which provides further non-li
the model. The model gives rise (under certain parameter values) to chaotic
of the exchange rate. It is then possible to show that the simulated exchange
from this chaos model:
approximates a random walk
0

yields a regression in which the forward premium is a biased predictor o
0

change in the exchange rate
yields a regression of the exchange rate on fundamentals (i.e. money suppl
0

the economic fundamentals provide a poor predictor of future movem
exchange rate.

All of the above empirical results are observed in the real world data and
chaotic model is at least capable of mimicking the behaviour of real world
FOREX market. The final part of this section briefly outlines the results of som
chaos and for the presence of non-linearity in relationships in the FOREX ma

Sticky-Price Monetary Model
We have already discussed this model so we can be brief. In the long run th
rate is governed by PPP
s; = p;/pf"

where P: is the domestic steady state price level. Changes in the real exchang
to changes in real (excess) demand (i.e. net trade) and hence in the rate of in



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