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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*)

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