-16-

calculation. In general the signs on all the coefficients seem somewhat
low.

It is the sign on the short term interest rate differential which
is crucial in distinguishing between the overshooting and the more
traditional monetary model. In all models in Table 2, the sign turns out
to be positive. This suggests the model conforms to the traditional
monetary description, a result not altogether uncommon. However from
casual empiricism one tends to associate an appreciation of the exchange
rate (a rise in the $/f rate) with a fall in interest rate differential
(a larger rise in UK interest rates). In examining the results more
closely it was found that a negative relationship is at times exhibited.
There is in fact a definite negative relationship between current changes
in the exchange rate and in lagged changes in the interest rate
differential. This result suggests there might be a problem of
simultaneity. To allow for this, the model was reestimated using an
Instrumental Variable Estimator. The results are reported in the fourth
row in Table 2. The size and sign of the coefficients remain much the
same, but the standard errors increase. The change in estimation
technique does not yield further insights on the problem.

In Table 3 the long run stationary state estimates are reported.
These results are derived as described in section III by setting ee, 5,
and z = Zit-j and solving for e’. A unit elasticity of prices with
respect to exchange rate is observed as predicted by the PPP hypothesis,
hence the weak condition is met. In addition to prices there are other
economic variables which influence the long run exchange rate. Three of

these additional variables--income, interest rates and wealth--indicate


———

-13-

conditions hold. According to much of the literature on PPP
(Officer(1976)) the last test is really the only true test of PPP. In
our experience the last test is rather stringent since most equations
fail this test. Consequently, we offer three tests of varying degrees of
stringency to be used when testing for PPP.
The tests stated below all refer to the reduced form coefficients,
the y's in particular, from equation (5). The tests are:
WEAK FORM TEST: This corresponds to the first condition
holding - prices and exchange rates are
proportional to each other, Yi2= -¥13= Yiae
SEMI-STRONG TEST: The weak test must hold and each country must exert
the same influence on the exchange rate. The
conditions on the other gammas are as follows:
YLFrY2s Y3="YusYs=-Ye¥7=-Yas Y9=-Y10
STRONG TEST: The semi strong test must hold however all the
gammas on all the variables excluding prices
and exchange rate must now equal zero i.e. y, 70
for i= 1,11. Only relative prices should
exert influence on the long run exchange

rate.

IV. Empirical Results:

The main concern of this section is to model the monthly changes
and to analyse the long run tendency of the dollar/pound exchange rate
from January 1973 to September 1979. In Graph 1 the log of the exchange

rate is plotted over the entire period. The large decline in the


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GOW ANLGNOH SIGNS: SaWL


-4-

where XE (ysw,i,b,p_))
L = lag operator
n = lag length
b = inflation rate (an argument added to equation 1)
(4)

The wealth term here represents total personal wealth and is included to

first difference operator

explain the allocation of wealth to money holdings. The long-term
interest rate, b, is used to proxy the inflation rate.

A similar money demand function for the foreign country is assumed:

n 1 1 '
+E oi Sky + Bay Xy + Bag (L)m

(3) al pps ae

' toe
where x; = (y ww yi 4b »P_y)

(') denotes foreign country

The formulation of these functions allow us to test for homogeneity
between money and prices; we need not assume (or impose) it. These money
demand functions are meant to be general. It has been argued that they
are more an econometric specification than an economic formulation.
However, this criticism can equally be applied to partial adjustment type
generalisations as well.

The purchasing power parity equation is embodied in (4)

n
a
(4) se =a +2 aga Ays + aa.¥e + dag +B, (Le
t 30 k=o 3ik “~it-k si" it-1 33 33


Table 3 LONG-RUN RESULTS

RISK e = 16.2 + (p-p') - 1.75y + 7.76(b - b') + 2.17%
WEALTH e = 18.08 + (p - p') - 1.98y + 8.64(b - b') + 2.821"
+ 1.94 = .376W!
t ' v
SIMPLE e = 5.52 - 1.48(m = m') + 4.91(b - b')

LONG INTEREST-RATE ELASTICITIES

b. b i
RISK «757 1.48 -378
WEALTH +844 1.617 =492

SIMPLE 479 +918 -



-19-

flexible prices in the short run and the tendency of the exchange rate
towards PPP is tested. In the synthesis model the assumption of bonds
being perfect substitutes is relaxed. Two restrictions which distinquish
between the models are monitored: i) the coefficient on the short-run
nominal interest rate differential and ii) the adjustment mechanism.

The main conclusion that emerges from the econometric
investigation is that the data supports the augmented monetary model.
All evidence point to the exchange rate and interest rates moving
together. Moreover, the adjustment mechanism is not monotonic and it
seems to be more complex than that described in the overshooting model.

The other general conclusion that emerges from this study is that
the long-run exchange rate does not support the PPP hypotheses. In the
first two economic models considered other factors influences the long-
run exchange rate and these factors have different weights assigned for
each country. In the simple monetary model, on the other hand, exhibits
a "semi-strong" tendency towards PPP, however, none of the results met
the rigorous requirements of PPP. This suggests a non-contant real
exchange rate and that goods are not perfect substitutes. No firm
conclusion can be made about bonds substitutability here since this is
not tested explicitly.

Lastly, a few words about the overall success of the economic
models. All three economic models explain the in-sample exchange rate
better than the univariate time series model. Furthermore, the simple
monetary model with a dummy for the 1976 sterling crises predicts over
the post-sample period using actual values for the predetermined
variables equally as well as the time-series model. This result we find
encouraging for exchange rate modellers. The method of starting with a

general model and testing for simplifications seems to work well.


-17-

that the long run exchange rate is influenced by different factors
asymmetrically. Hence PPP, rigorously defined, is rejected since only
the weak criteria is fulfilled.

On the whole, the model captures turning points well, though not
all of the magnitudes are correct. The forecasting performance of the
‘risk' model using actual values for predetermined variables, however, is
not as good as the univariate time series (i.e. .0085 to .0059). In two
months, May and June of 1979, the general model performed poorly, these
months correspond to period of political and economic turmoil in the
uK.20/

Two alternative models of exchange rate similiar to the general
model but imposing some initial exclusion restriction are now considered.
Again following the search procedure the final specifications for the
model where p=0 are reported in Table 4. It turns out that there are
only two restrictions to the previous model. The results and
interpretation of coefficients are similiar as before: a) interest rate
differential is positive, b) non-monotonic adjustment and c) PPP does not
hold in the long run (as reported in Table 3). We also note more change
in the coefficients as well as standard errors when using an IV
estimator.

The results of the simple model, reported in Table 5 vary somewhat
from the previous models: i) the coefficient on U.S. income is higher ii)
a lagged money velocity term is included and iii) the rate of change of
inflation is substituted for the change in inflation. However, as in the
other two models there is a positive coefficient on nominal interest rate
differential as well as a long run unit elasticity between prices and the

exchange rate. The other variables which influence the long run exchange

rate, money supply and bond rates, have identical coefficients for both


Table 1 Generalised Model, Equation (5), Coefficient Estimates

0 1 2
e - 341 .013
(.214) (.209)
P - 530 1.30
(1.87) (1.85)
p - -.727 -.587
(.81) (.68)
m -.204 -818 -.205
(.78) (.95) (.797)
y -.984 044 =.95
(1.11) (1.36) (1.16)
w 25 -.01 52
(.40) (.41) (.36),
i 1.35 .89 -.53
(.69) (.73) (.83)
b 45 -3.15 5.12
(3.10) (4.31) (3.75)
m -.43 -.63 1.20
(244) (.50) (.48)
y' -.60 .03 -.57
(.20) (.32) (.46)
w ; -.23 .037 -.20
(.29) (.30) (223)
b -.51 004 545
(.34) (.38) (.43)
OIL -.027 - -
(.035)
cA 4.2E-07 - -
(1.9E-06)
cal -7.96-06 - :
(9.9E-06)
CAE! -.001 - -
(1.004)
cae! -.05 - -
(1.04)
NYSE 242 - -
(.18)
FTSE -.04 - -
(.066)

RSS = .00103 NOBS = 69


-9-

The gap between the exchange rate and its equilibria value is
Proportional to the real interest rate differential-the term inside the

brackets. Substituting equation (10) in for the definition of é€ yields
(13) e=m-m' - gy + o'y' + ow + ow! - Uii- i') + (1 +A)(n tn)
6 6

This is the final equation for the overshooting model which corresponds
to Frankel (1979). Note the negative coefficient on the nominal interest
rate differential term is a distinquishing characteristic of this model.
Frankel (1983) extends this model by relaxing the assumption that bonds
are perfect substitutes. In this case the model is no longer said to be
strictly monetary; it is instead said to be a synthesis of the monetary
and portfolio models. In this model he assumes that there is only one
aspect in which domestic and foreign currency bonds differ - their
currency of denomination. The uncovered interest rate parity equation
(7) is modified to include a risk premium which is assumed to be a

8/

function of net supplies of bonds.—
(14) i =7i' = E(ae) +p
here p is a risk premium and according to Frankel (1983) p = (B,F)

where B,F are net supplies of bonds (domestic and foreign currency

denominated respectively).


References

Bilson, J.F.0. (1978), "The Monetary Approach to the Exchange Rate: Some
Empirical Evidence", IMF Staff Paper, Vol. 25, No. I,
pp. 48-75.

Davidson, J.E.H., D.F. Hendry, F. Srba and, S. Yeo (1978), "Econometric
Modelling of the Aggregate Time Series Relationship Between
Consumer's Expenditure and Income in the United Kingdom" Economic
Journal, 88, pp. 661-692.

Driskill, R.A. and S.M. Sheffrin (1981), "On the Mark: Comment" American
Economic Review, 71, pp. 1068-1074.

Dornbusch R. (1976) "Expectations and Exchange Rate Dynamics", Journal of
Political Economy, 84, pp. 1161-1176.

Edison, H.J. (1981) “Short-Run Dynamics and Long-Run Equilibrium
Behaviour in Purchasing Power Parity: A Quantitative
Reassessment", unpublished L.S.E. PhD Dissertation.

Edison, H.J. (198la) "The Rise and Fall of Sterling: Testing
Alternative Monetary Models of Exchange Rate Determination",
International Centre for Economics and Related Descipline
Discussion Paper 81/30.

Haache, G. and J. Townend (1981), "Exchange Rates and Monetary Policy:
Modelling Sterling's Effective Exchange Rate, 1972-1980 in W.A.
Eltis and P.J.N. Sinclair (ed) The Money Supply and the Exchange
Rate, Claredon Press, Oxford.

Frankel, J. (1979) "On the Mark: A Theory of Floating Exchange Rates
Based on Real Interest Rate Differentials", American Economic
Review, pp. 610-622.

Frankel, J. (1983) “Monetary and Portfolio-Balance Models of Exchange
Data Determination", in International Transmission of Economic
Disturbances Under Flexible Exchange Rates edited by J. Bhandari
and B. Putnam, MIT Press.

Frenkel, J. (1976) "A Monetary Approach to the Exchange Rate: Doctrinal
Aspects and Empirical Evidence", Scandinavian Journal of Economics,
78, No. 2, May pp. 200-224,

Haache, G. and J. Townend (1981), “Exchange Rates and Monetary Policy:
Modelling Sterling's Effective Exchange Rate, 1972 - 1980 in W.A.
Eltis and P.J.N. Sinclair (ed) The Money Supply and the Exchange ,
Rate, Claredon Press, Oxford.

Haynes, S.W. and J.A. Stone (1981) "On the Mark: Comment", American
Economic Review, 71, pp. 1060-1067.

Hendry, D.F. (1980) "The Simple Analytics of Single Dynamic Econometric
Equation", LSE unpublished.

Hendry, D.F. (1980a) “Predictive Failure and Economietric Modelling in
Macroeconomics: The Transactions Demand for Money", in P.A. Omerod
(ed.) Economic Modelling, Heinemann, London.


studies such as Frankel discussed how results changed when new
observations were added. When dividing our sample at various points in

time, we rejected the hypothesis that the periods were different by using
a Chow Test. :

21/ In assessing the property of his demand for money functions,
Goldfeldt (1973) also found that excluding wealth improved his models
prediction capabilities.

22/ In Rogoff and Meese (1982) none of the economic models were found to
consistently out forecast using realised values for the predetermined
variables the simple univariate time series model. Our results are not
inconsistent with these findings since most of the models we explicitly
examine do worse. We are more optimistic than Meese and Rogoff and for
that matter, Haache and Townend who claim that they have not found a
stable empirical relationship that can be used in forecasting. The
reason for this optimism is that the ecnometric methodology used here
helps in testing well-specified models. Thus, if we, as economist's, can
describe the exchange rate market more closely we may be able to find a
model that consistently out-performs a univariate time-series model.


~6-

(5) needs to be stressed. The difference between (4) and (5) is the
Presence of additional factors that explain short-run fluctuations in the
exchange rate, but which supposedly do not influence the long run
exchange rate. The lag structure can be justified in terms of costs of
adjustment or by time lags.

An important feature of this model is as in the traditional
(Bilson-Frenkel) monetary model that the expected sign on the short-term

interest rate differential is positive, i.e. 6, > 0, 85 <0. This

5
corresponds to the original negative coefficient in the money demand
equation. Thus, sterling appreciates when the interest rate differential
increases in favour of the U.S. In the next model the opposite result
holds. The difference stems from whether real interest rates are
considered constant or not. In the traditional model they are assumed to
be constant when nominal interest rates rise--due to higher price
expectations--the exchange moves with the interest rates. In the
overshooting model, real interest are variable with nominal interest
rates reflecting monetary policy.

The second model considered is the sticky price or "overshooting"
monetary model as described in Frankel (1979, 1983). The reduced form
equation of this model is a special case of euation (5). As in the first
model the assumption PPP is relaxed in the short run. An important
feature of this model is the distinction between the short and long run
and the role of expectations. Two distinquishing features of this model
are short-term nominal interest rate differentials are negatively related
to the exchange rate and that after a monetary shock there is monetonic
adjustment of the current exchange rate back to the long-run exchange
rate. Both of these features can be used to distinquish this model from

the first one. The long run predictions of this model and the


-5-

where y; = (p,p )

e = log of exchange rate (home currency/foreign currency )

explanatory variable (captures deviations from PPP)

This equation differs from the traditional monetary model only
insofar as it does not assume that prices adjust immediately to PPP
similar to Dornbusch (1976). The way (4) is written it is implicit that
the expected signs on the coefficients for p are negative. The exchange

rate may exhibit the tendency towards PPP, this is observed when

B33 = 83) = B aoe The variable Q is introduced to explain deviations

from PPP in the short run (or are transitory factors). If a is included

in the long run solution it also indicates that the exchange rate does
not converge to ppp,0/ Thus, PPP is not assumed to hold in the short run
due to sticky prices and imperfect substitutability of goods. Whether
PPP holds in the long run can be determined by analyzing the econometrics
results, i.e., it is not assumed or imposed.

Combining equations (2), (3), (4), and solving for current prices

the reduced form exchange rate equation is obtained.
+
ik Zitek * iter 7 Tag (Lee
where 247 (yy y's W w', i, i', by b', m, m', 9, Ply P'_))
Equation (5) says that the exchange rate, as the relative price of two

currencies, is determined by the supply and demand for money. The 6's

and y's are reduced-form coefficients. The general dynamic structure in


€
Whe

ssw

ecg

“

sum

1800

tna | ois



~8-

Note that symmetry on the coefficients is not assumed. Letting r= .' and
assuming as Frankel does that the nominal interest rate differential is
equal to the inflation differential in equilibrium, i-i'= a-1', then

equation (9) can be rewritten to define the long run exchange rate.
(10) @ =m ~ im - gy + o'¥' + ow + o'W' + X(n - w')

This equation illustrates the traditional monetary model of
exchange rate determination. The exchange rate is determined by the
relative demand for the two currencies. The money market is always in
equilibrium. A given increase in money supply leads to an equiportionate
rise in the exchange rate. Note the positive relationship between
interest rates, the long-term inflation rates in equilibrium, and the
exchange rate.

To derive the final short run exchange rate equation we assume as
Frankel does that the expected exchange rate change is a function of the
gap between the current spot rate and the long-run equilibrium rate, plus
the expected rate of change in the long run inflation differential

between the domestic and foreign countries.

(11) E(ae) = - e(e -e) +4 - a*

The parameter @ represents the speed of adjustment. Equation (11) is

combined with equation (7) to give

(2) ese -UGi - 9) - (i= 44)


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International Finance Discussion Papers
Number 224
dune 1983

THE RISE AND FALL OF STERLING: TESTING ALTERNATIVE MODELS OF EXCHANGE
RATE DETERMINATION

by

Hali J. Edison

NOTE: International Finance Discussion Papers are preliminary materials
circulated to stimulate discussion and critical comment. References in
publications to International Finance Discussion Papers (other than an
acknowledgment by a writer that he has had access to unpublished
material) should be cleared with the author or authors.


-11-

variables include actual current account, spot price of oil, stock prices
and unexpected current account. This set of variables, or a subset of
them, are thought to be useful in explaining risk and ultimately
movements in the exchange rate. Hooper and Morton (1982) in a model
similar to (15) have used current account and intervention figures to
account for risk. Note that the same set of variables used to model the
risk premium, y, is also used in equation (5) to model deviations from
PPP, Q.

Note that model 1, equation (5), is more general than even
Frankel's synthesis model under the assumption that the same set of
variables are used to explain » and 2. Equation (15) can be derived from
(5) by applying the following restrictions

i) se=0

ii) 8; = 0 for i =1, 13

= 0

Ti) v2 = 143

iv) n=l

YY Norns!

vi) - Ys = Y¢

vii) Y7 = - ¥g

These restrictions are quite numerous. The first four restrictions
relate to removing all the dynamics, it is assumed that the dependent
variable becomes the level of the exchange rate. The latter three
restrictions relate: to symmetry. This leads us to point out some of the
drawbacks of both the Frankel models and the technique he has employed to
test them. These criticisms, outlined briefly, are as follows:

(i) Since Frankel only uses contemporaneous variables this

increases the possibility of biased coefficient estimates.


-10-

With this additional assumption equation (13) can be rewritten to
synthesize many different versions of asset-market models, monetary as

well as portfolio.

ta '
mM-m - oy + oy + oW + oW

(15) e

— ZH) eG tare)
+ av)

Equation (15) represents the final version of the second model --a
synthesis of the overshooting and the monetary model a In many ways it
is used as a punching bag. It is useful in so far as it contains

individual competing models as special cases, for example:
1
i) If o =o = 0 and y = 0, then we obtain Frankel (1979).
1
ii) Ifo=o= =O and 3 +) = 0, then we obtain a Dornbusch
model.
'
iii) Ifo =o=y-=0 and
model.

t= 0, then we have a typical monetary
iv) If all the regressors on the right hand side are dropped except

for ae then we have the portfolio model.

When empirically implemented as in Frankel (1983) it suffers from
several drawbacks. Before turning to some of these drawbacks, two points
must be made. In the empirical work Frankel uses estimates for supply of
bonds by assuming that a good measure of net outside wealth is the stock
of government issued liabilities held by the public sector. We, however,
approach the risk term from a slightly different perspective (and perhaps

from a more naive one) by using a different set of variables y. These


5) Interest U.S.: Eurodollar Rates: 3 month rate quoted in London
at end of month (BE) (percent per annum).
Bond Rate: (Long-Term Rate) Average of daily
figures for bonds maturing or callable in 10
years or more U.S. Government (FRB).

U.K.: Euro-sterling Rates: 3 month rates end of month

percent per annum (BE).

Bond Rate: Long term bond rates (10 years or

more) on U.K. government stocks (BE).

6) Wealth U.S.: Quarterly Outstanding of Net Personal Sector
Financial Assets (Fed Flow of Funds).
U.K.: Net Wealth of Personal Sector: published by the
C.S.0. Studies in Official Statistics No. 35
(1965-75) and (FT-Feb 1978).

7) Stock Market Prices: New York Stock Exchange: Dow Jones Industrial
Averages 30 Stocks (SCB).
Financial Times Share Index: Index of
Industrial ordinary shares 1 July 1985 - 100.
(FS).

8) Current Account Data: U.S: Quarterly data on U.S. current account
in millions of dollars (FRB).

Trade balance: monthly trade balance based on averages in
millions of $ (OECD) exports--imports.

Forecast of current account: biannually produced by the OECD
(OECD/OutTook) in billions of $.

U.K.: current account: U.K. based in million of &
MD).
trade balance: monthly averages in millions of
£ (exports -imports )

Forecast of current account: As for the U.S. biannually
produced by the OECD six months in advance--
billions of $ (OECD/outlook).

9) Oil Price: Arabian crude 34° light spot market price in the
Rotterdam Market: Petroleum Intelligence Weekly.


APPENDIX I

THE DATA:

Notation
of
Sources

(SCB)
(FRB)
(OECD/0)
{oeco)
MD)
(ET)
(FS)
(BE)

Survey of Current Business (USA)
Federal Reserve Bulletin (USA)
Biannual Economic Outlook of OECD
Historical Data of OECD

Monthly Digest of CSO (UK)
Economic Trends (CSO-UK)
Financial Statistics (CSO-UK)
Bank of England Quarterly Bulletin

(all data are monthly and seasonally unadjusted unless otherwise noted)

1) Exchange Rate:

2) Prices:

3) Money:

4) Income:

Income:

U.S.:
U.K.:

U.Ke:

defined as the $/z rate. Reported for the
last working day of the month--the middle rate
(average of bid/ask spread) (BEQ)

Consumer Price Index (CPI) general base year
rescaled 1973 = 100 (SCB)

Retail Price Index (RPI) general--all items base
year rescaled 1973 = 100 (MD)

Ml in billions of dollars (FRB) average daily
M2 in billions of dollars (FRB) figures

Ml in billions of pounds sterling (BE)

TM3 in billions of pounds (BE) (total M3)
OCA: other currency in accounts in billions
of pounds (BE)

SM3: defined as: M3-OCA.

Income: Gross National Product in constant 1972
prices in billions of dollars--seasonally
adjusted (SCB) (QUARTERLY). Industrial
Production Index--monthly seasonally adjusted
(SCB). Retail Sales: monthly: seasonally
adjusted in billions of dollars (SCB).

Gross domestic income at factor costs (at 1975
Prices) seasonally adjusted quarterly data (ET).
Industrial Production: based 1975 = 100 monthly
seasonally adjusted (ET).

Value Retail Sales Index: monthly 1971 = 100
seasonally adjusted.


-7-

traditional model are the same hence we argue that the nomenclature
monetary remains applicable for this model as well 2/
The overshooting model retains the money demand function as in (1)

for both countries:
(1) m-p = gy --Ai + ow
(6) m'-p' = ty! - ati! +otw!

In the overshooting model domestic and foreign bonds are considered as
perfect substitutes as in the previous model. Portfolio shares are
infinitely sensitive to expected rates of return. This one-bond

assumption gives us the uncovered open interest rate parity condition
(7) i - i* = E(Ae)

where E(Ae) = the expected depreciation of domestic currency.
Unlike the first model this model assumes that the long-run

exchange rate will always equalise long run relative prices (PPP):

(8) e=p-p'
where bars over variables signify long run.

Relative prices are obtained by subtracting equation (1) from (6)

and solving for p - p'.

(9) p-p'=m-m' - gy + gty'+ ai - ATi! - ow + o'w!


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Footnotes

*This paper is a revised version of Edison (198la) and chapter 4 of my
dissertation. I would like to thank my colleagues at the LSE and in
particular my advisors; Meghnad Desai, David Hendry, and Stephen Nickell.
I would also like to thank my colleagues at the Fed, Richard Haas and
Peter Hooper, for helpful comments while revising this paper. This paper
represents the view of the author and should not be interpreted as
representing the views of the Board of Governors of the Federal Reserve
System.

1/ From the definition of the exchange rates quoted as the dollar/pound
rate, a rise in the exchange rate implies an appreciation of the pound
(or a depreciation of the dollar). Since both countries typically quote
the exchange rate in this form, we treat the U.K. as the "foreign"
country. Therefore, when we talk about, for example, a positive sign on
the interest rate differential with respect to the exchange rate we mean,
3e/a(i-i')>0 or that the equation conforms to the traditional monetary
model.

2/ We single out Frankel's models as alternative models since they
incorporate other models that are considered in the literature.

3/ A distinquishing feature of this model is that the added dynamics
are not derived by assuming rational expectations.

4/ In the first model, the risk term is in the model to explain why
there may not be goods arbitrage (goods substitutability) while in the
second model it is used to explain why assets are not perfect
substitutes. However, in the reduced form exchange rate equation, we do
not distinquish between these two assumptions.

5/ The three characteristics which highlight the model are:
~ a) PPP-goods are perfect substitutes

b) assets are perfect substitutes

c) real interest rates are constant

6/ Throughout this paper, we distinquish between short and long run. By
short run we mean transitory factors that may or may not effect the
outcome in the long-run equilibrium state. Hooper and Morton (1982)
assume in their paper that the long-run exchange rate is not constant and
that cummulated current account explains long-run deviations from PPP.

7/ Once again this model's long-run conditions embody most of the
‘important monetary model main characteristics a) PPP, b) asset
substitutability.

8/ In the estimation, the two terms, y and 9, are treated identically.
This enables us to use equation (5) as the general model with its
monetary attributes while equation (15) takes on portfolio balance type
characteristics.


-3-

traditionally static monetary model. Its components are similar,
uncovered interest rate parity is implicitly assumed, and in the reduced
form exchange rate equation the nominal interest rate differential is
positively related to the exchange rate. Therefore, we argue that the
model described here is monetary as opposed to monetarist since it
retains, in the long run, the characteristics of the traditional monetary
5/

model .—

The fundamental equation in the monetary approach is a money demand
function, such as:

(1) m=p + 6y - Ai + ow

where m

log of the domestic money supply

log of domestic price level

73
"

i = the domestic short term interest rate

o
au

money demand elasticity with respect to income

2X = money demand semi-elasticity with respect to the interest rate

mn

o = money demand elasticity with respect to wealth

which is derived from the stationary state relationship that % = KYM exp (-ai)
a Cagan-type money demand. This type of steady state relationship also forms
the basis of the generalised monetary model. In the generalised

model, however, it is assumed that there are both costs of adjustments

and time lags. Thus the conventional static money demand equation (1) is

generalised to include dynamics.

n

(2) A(m-p) =a + © ay, ax, + By. X; + B6,,(L)m
t 10 k=0 lik “it-k li “it-1 16


Or'0

0S"0

03°0

OL'O

08"0

06°0

00"

6LEI BL6l

L246} -

°

GLE) UAGWI1IdaS OL SLE) AMVANVE "JONVY -

9ZL61

“SLEL

vL6l

ay A=)

TUTTTTTTTTT TTT T TT TTT Ty

siaperii tial

qT

ALVa SSNVHOXA GNNOd/YVTIOd JO 907. -

k HdVuo


-15-

modifications are considered. The first of these two models sets 2=0 and
is referred to as monetary-portfolio model while the second model sets
2=0 and B,2=B29=0 and is referred to as the simple monetary model.
Before concluding estimates of a model based on equation (15) which is
the dollar/pound equivalent to Frankel's mark/dollar model are
presented.

In Table 1, coefficient estimates are reported for equation 5, the

general model. 1/

This model represents the maintained hypothesis. 11
subsequent models can be nested within this model where restrictions on
the coefficients can be explicitly tested. In Table 2 the final results

of restricting the ‘general risk' model are reported.28/

The dependent
variable in this ( and subsequent) models is the change in the log
exchange rate($/£). The first row includes all variables that are
Proposed to measure risk. None of them turn out to be significant or
with the expected sign.

The third row is the final specification of the general risk model
where the risk variables have been deleted except for changes in spot
price of oil. This variable is reported as it has been commonly argued
that sterling had become a haven of petrodollars- as the price of oil
goes up so does the demand for sterling. The sign reported in Table 2,
however, show results which are not consistent with this argument .29/

The coefficient on the sum of changes in money supply is .327,
significantly less than one. A one percent change in relative money
supply ceteris paribus leads to a .3 percent change in the exchange
rate. This result appears unfavourable to the overshooting model,

The change in wealth, which is actually modelled as the share of money

wealth, for statistical reasons, must also be considered in this


-2-

used to derive these other models are noted. Furthermore, both models
are shown to be special cases of the augmented monetary model. Two
restrictions are emphasised (i) the sign on the short term interest rate
differential and (ii) the dynamic properties--especially the overshooting
and monotonic adjustment mechanisms--portrayed in Frankel's models.

In Section IV the econometric results are discussed. In general,
the results tend to support the generalised ‘traditional' monetary model. ,
The short term interest rate differential coefficient is positive in all
the specifications considered, (i.e., ae/a(i - i')>0, where i, i’ are
the U.S. and U.K. nominal interest rates respectively. Furthermore, the
dynamics do not tend to indicate overshooting. Lastly, PPP does not

appear to hold in a strict sense, although prices and the exchange rate

are found to move proportionally in the long run.

II. Alternative Models of Exchange Rate Determination

The first model considered here is based on the traditional
monetary model as developed by Bilson (1978) and Frenkel (1976). It is
assumed that there are no barriers (such as transactions costs or capital
controls) restricting capital markets and that domestic and foreign bonds
are perfect substitutes in investors' demand functions. The analogous
assumption of no barriers in the goods market is relaxed (hence PPP does
not hold at all points in time). The common assumption of homogenous
demand for money function with respect to prices is also relaxed (at
least in the short run). It is, of course, a matter of debate how far
the monetary model can be adapted before it losses its essential

features. This general monetary model is the dynamic form of the


-18-

countries. This result is slightly more favourable to PPP but does not
meet the criteria of the strong test.

An inclusion of a dummy variable for the sterling crisis of 1976
enchances this model. In fact, the forecasting results are as good as
the univariate model 21/ This happens to be an uncommon result in many
studies 22/ Still it does seem as though there is some tradeoff between
complex models and more parsimonious models -- simpler models do better
especially during turbulent times because there are fewer explanatory
variables which can cause these models to break down.

Lastly we report two equations in Table 6 similiar to Frankel's
models corresponding to equations (15) and (13) respectively. Comparing
the results of equations with the results of the general model, we can
see that the exclusion restriction on the dynamics leads us to reject
equation 15 since the joint F test is 121. However, it is interesting to
note that estimating this model, ala Frankel, also leads to the positive
sign on nominal interest rates. The second row in Table 6 corresponds to
equation 13; it too can be rejected by the more general models. Both

equations are econometrically misspecified.

V. Conclusion

The purpose of this paper is to analyse the fluctuations in the
dollar/pound exchange rate and to assess the long-run tendencies of the -
exchange rate. Three asset market models of exchange-rate determination-
the augmented-monetary model, Frankel (1979) overshooting model, and
Frankel (1983), synthesis model--are outlined in section II. The
augmented-monetary model is a generalised version of the traditional
(Bilson-Frenkel) monetary model and econometrically encompasses the other

models considered. All of the models relax the assumption of perfectly


May 1983 Hali J. Edison*
The Rise and Fall of Sterling: Testing Alternative Models

of Exchange Rate Determination

I, Introduction

The purpose of this paper is threefold. Firstly, to model short
run fluctuations and analyse the long run tendencies of the dollar-pound
exchange rate over the current floating period.2/ Secondly, to point out
a number of shortcomings of existing models which have been proposed to
describe the behaviour of exchange rates (particularly Frankel (1979,
1983)2/but also Frenkel (1976), Bilson (1978), Dornbusch (1976).
Thirdly, to apply the econometric method of starting from a general model
and testing for simplifications as advocated by Hendry-Mizon (1978). and
Davidson et al (1978). One salient feature of this econometric approach
when modelling the exchange rate is that the hypothesis that the long-run
tendency of the exchange rate is towards Purchasing Power Parity,
henceforth PPP, can be tested. This test relates to the restrictions on
the estimated coefficients and is described in detail in section III.

The first model considered in section II is a general or
"augmented" monetary model ~ Its special attributes are that it relaxes
the assumption of fully flexible prices of the monetary model in the
short run by incorporating dynamics¢/ To be consistent with much of the
recent literature on exchange rate determination we single out Frankel
(1979), a variant of Dornbusch's model of "overshooting", and Frankel
(1983) "synthesis" model (of monetary and portfolio-balance models).

Both of Frankel's models embed other models. Some of the restrictions


Hendry, D.F. and G.E. Mizon (1978), "Serial Correlation as a Convenient
Simplification not a Nuisance: A Comment on a Study of the Demand
for Money by the Bank of England", The Economic Journal, 88, pp.
549-563.

Hooper, P and J.E. Morton (1982), Fluctuations in the Dollar: A Model of
Nominal and Real Exchange Rate Determination, Journal of
International Money and Finance, 1, pp. 39-56.

Meese, R.A. and K. Rogoff (1983), "Empirical Exchange Rate Models of the
Seventies: Do they fit out of sample? Journal of International
Economies.

Mizon, G.E. (1977) "Model Selection Procedures", in Studies in Modern
Economic Analysis edited by Artis, M.J. and A.R. ay, Bas
Blackwell, Oxford.

Mussa, M (1976) "The Exchange Rate, the Balance of Payments and Monetary
and Fiscal Policy under a Regime of Controlled Floating"
Scandinavia Journal of Economics, 78, pp. 229-249.

Officer, L.H. (1976) "The Purchasing Power Parity Theory of Exchange
Rates: A Review Article", IMF Staff Papers, 23, pp. 1-60.


9/ Equation (15) is identical to Frankel's equation (27), except that in
T[15) we have not spelled out what vy is, therefore, the structural
coefficients at this point differ.

10/ This is explained in more detail is Edison (1981) and Mizon (1977).

l1/ Haynes and Stone (1981) have pointed out this problem of imposing
the linear constraint of symmetry on variables. This is not a problem
related to Frankel alone, but also symptomatic of many studies in the
literature.

12/ Driskill and Sheffrin (1981) have also argued that the nominal
interest differential are endogenous.

13/ The use of long term bond rates is wide spread, but it is not
altogether clear whether it is the best way to model inflation.

14/7 As described in Mussa (1976).
15/ These tests are suggested in Hendry (1980).

16/ All of the equations estimated in this paper were done by using
David Hendry's computer program--G.I.V.E.--Generalised Instrumental
Variables Estimates.

17/ The number of lags is truncated at 2 when estimating the general
model in log levels. The reason for doing this is due to both data and
computational limitations (i.e., the number of degrees of freedom and the
dimensions of the computer package). The decision here had to be made
between truncating the lag or imposing untested restrictions on the
polynomial lag structure. Since both involve restrictions which can lag
to inconsistent estimates, the former method was followed as suggested in
Mizon (1977).

18/ The general model reported in Table 1 is in log levels. However, it
can be easily estimated with the dependent variable in difference from
where the regressors are in both levels and first differences.

19/ Haache and Townend (1981) discuss various ways North Sea oi] may
effect the exchange rate. Their results were quite positive when using
index of Saudi marker of crude. This is contrary to our result, however,
consist with their statement, pg. 225, “It is unlikely that the direct
and indirect effects of these changes can be easily captured
empirically.

20/ Three additional tests were carried out to test for
misspecification. They were a) a dummy for 1976 sterling crises, b)
seasonal dummies, and c) for structural break. The first test was
considered because it was thought that the relationship changed, no
statistical evidence for the "risk" model substantiated this hypothesis.
The results showed that the seasonal dummies were jointly insignificant.
The third test was considered to determine whether the data generating
Process was completely different in the earlier and later periods. Other


-12-

Using longer lags may induce inefficient estimates but this is
a small sacrifice as compared to inconsistent estimates
obtained when truncating the lags .20/

(ii) Imposing symmetry on ‘the coefficients, if invalid, also
biases coefficient estimates L/

(iii) Interest rates are endogenous in the overshooting model,
yet they are treated as though they were exogenous especially
when the model is estimated. 12/

(iv) The use of long term bonds as a proxy of inflation may be
incorrect introducing further error.t2/

(v) It must be noted that the assumptions used to derive
Frankel's final model, such as the money supply process and
the way expections are formed are restrictive,changing them

changes the final reduced for equation.24/

III. Testing for PPP
The long run assumption of purchasing power parity can be analysed

from (5). Setting e*=e and z".= Zz; for all k and i= 1,13 and

t-k i t-k
solving for e the econometric results can be compare with the original
theory. In the case of the exchange rate this is

(16) E=k?,

P
Three conditions are important in testing PPP. They are: (i)

proportionality between relative prices and the exchange rate (ii)
symmetry between the domestic and foreign country and (iii) the
requirement that K is a constant (but not necessarily unity). Following
these conditions three tests are considered corresponding to when

condition (i) holds, condition (i) and (ii) hold and when all three


-14-

exchange rate in 1976 is due to the sterling crisis, the upward trend -
an appreciation of the pound - occurring after the implementation of the
IMF package.

A simple exchange rate equation, a univariate time series model, is
examined first to monitor the success and to detect misspecification of
the economic model. Two key statistics are used to monitor the results:
(i) the residual sum of squares (RSS) and (ii) the sum of squared
forecast errors (fe). The objective is to test whether the economic
model fits and forecasts the data using realised predetermined variables
better than the time series model A5/ The results from this simple time-

16/

series estimation are:—

Ae, = -.0024 + .097 ae
(.003)  (.125)

2
NOBS=69 R= .009 RSS=.0507

t-1
(17)

2
Z 3(6)=2.67 Z,=7.75 Z5= .848 Jfe =.0059

where

2, The Lagrange Multiplier Test of (nyth order autocorrelation

4 The Chi-Square Prediction Test

5 Chow Test of Parameter Stability
rte? Sum of squared forecast errors.

The first economic model that is estimated is referred to as the
"risk" model, the case where p= and corresponds to the general model,

equation (5). Two further models also starting with a general model with