S ock P ices and he Mone a y Model o he Exchange Ra e:
An Empi ical In es iga ion
Simon B oome
Economics Depa men
Na ional Uni e si y o I eland Maynoo h
and
B uce Mo ley*
Economics G oup
Uni e si y o Wales Abe ys wy h
Oc obe 2003
*Add ess o co espondence: Economics G oup, SMB. Uni e si y o Wales Abe ys wy h,
Abe ys wy h, Ce edigion, SY23 3DB. E-mail: b m@abe .ac.uk. Tel. 0044 1970 622522.
S ock P ices and he Mone a y Model o he Exchange Ra e:
An Empi ical In es iga ion
Abs ac
This pape de elops an al e na i e e sion o he mone a y model o exchange a e
de e mina ion, which inco po a es a s ock p ice measu e. This model is hen es ed
using da a om Canada and he USA, applying he coin eg a ion and e o co ec ion
me hodology. In con as o many p e ious es s o he mone a y model, his e sion
p oduces e idence o coin eg a ion and s ock p ices ha e a highly signi ican e ec
on he exchange a e in bo h he sho and long un. In addi ion he es ic ed e sion
o he model ou pe o ms a andom walk in ou o sample o ecas ing.
(JEL Classi ica ion: F 32)
2
1. In oduc ion
Al hough he asse ma ke app oach o exchange a e de e mina ion domina es
heo e ical exchange a e modelling, a emp s o cons uc empi ical models based on
he asse app oach ha e me wi h limi ed success. This is especially ue o he
lexible p ice mone a y model, which was shown by Meese and Rogo (1983) o
p o ide in e io ou -o -sample o ecas s compa ed o a andom walk. Fu he mo e
a emp s o p oduce he alid long- un equilib ium ela ionship implied by he
mone a y model ha e gene ally me wi h mixed success, pa icula ly when he
implici es ic ions o he model a e applied. Fo example Meese (1986) and
McNown and Wallace (1989), ail o ind a alid long- un ela ionship o he
con en ional mone a y model1.
This pape de elops and es s a e sion o he mone a y model ha inco po a es s ock
p ices. The analysis is mo i a ed by ea lie wo k by F iedman (1988) and Boyle
(1990) ha shows how he demand o money is de e mined in pa by he le el o he
s ock ma ke . To da e he only a emp o es he ole o s ock p ices on he exchange
a e is Smi h (1992) who uses a Po olio Balance app oach2. We show ha including
he le el o he s ock ma ke p oduces a alid long- un equilib ium ela ionship and
co ec ly speci ied dynamic e o co ec ion model (ECM). The implici es ic ions
o he model a e hen examined and i is shown ha he ECM ou -pe o ms a andom
walk in ou -o -sample o ecas ing.
The emainde o he pape is as ollows. Sec ion 2 ou lines he heo e ical case o
including equi ies in he mone a y model and discusses he econome ic me hodology
3
used in he pape . Sec ion 3 desc ibes he da a se and p esen s he ime se ies esul s.
Sec ion 4 con ains he conclusions and conside s some implica ions o he in eg a ion
o capi al ma ke s.
2. S ock p ices and money demand
In he con en ional mone a y model he exchange a e adjus s o balance he
in e na ional demand and supply o mone a y asse s. The demand o money is
usually conside ed o be a unc ion o he le el o in e es a es and income. Howe e
he e is an inc easingly good case o including equi y p ices as sepa a e de e minan s
o he demand o money. In pa icula F iedman (1988) and Boyle (1990)3 p o ide
empi ical e idence desc ibing he ela ionship be ween money demand and he le el
o he s ock ma ke , including a speci ic lag s uc u e o he ela ionship, which due o
a di e en me hodology we do no a emp .
On he heo e ical side, F iedman (1988) sugges s ou possible channels h ough
which s ock p ices migh di ec ly e ec money demands. Fi s ly as s ock ma ke
luc ua ions end o ou weigh luc ua ions in income, s ock ma ke mo emen s a e
gene ally associa ed changes in he weal h o income and hence money o income
a ios. Secondly a ise in s ock p ices e lec s an inc ease in he expec ed e u n om
isky asse s ela i e o sa e asse s. The implied inc ease in po olio isk can be o se
by an adjus men away om o he isky asse s such as long e m bonds owa d sa e
asse s including money. Thi dly a ise in s ock p ices e lec s an inc eased le el o
inancial ansac ions and hus an inc ease in he demand o money. The abo e h ee
‘weal h e ec s’ all sugges a posi i e ela ionship be ween he le el o he s ock
4
ma ke and money demand. Howe e as he eal s ock p ice ises equi ies become
mo e a ac i e o in es o s causing a ‘subs i u ion e ec ’ om equi ies o money.
The ela ionship be ween equi y p ices, he demand o money and exchange a e is
he e o e an empi ical ques ion. As wi h F iedman (1988) we expec he weal h e ec
o domina e and hus we expec he demand o money and s ock p ices o be
posi i ely ela ed. To cap u e hese e ec s we inco po a e a s ock ma ke a iable
in o he s anda d money demand unc ion,
siypm





 (1)
Whe e m is he nominal demand o money, p is he p ice le el, y is he eal income
le el, i is he nominal a e o in e es and s is he eal le el o he s ock ma ke
( ollowing F iedman (1988), a ma ke index is used). All a iables excep he in e es
a e a e in loga i hms. Fo eign money demands a e gi en by,
****
* siypm

 (2)
Whe e * deno es a o eign a iable. I is assumed ha absolu e PPP holds, so ha ,
(3)
ppe

*
Whe e e is he log o he exchange a e, de ined as he domes ic p ice o o eign
cu ency. PPP is used only as a long- un equilib ium condi ion in his model, in he
sho un he e o co ec ion model allows de ia ions om PPP. The e idence on
5

PPP as a long- un equilib ium condi ion is gene ally posi i e (Cul e and Papell,
1999). S aigh o wa d ea angemen o (1) - (3) yields,
emmyyiis
      
   
01 2 3 4
()()()(
***
s
)
*
)
(4)
The mone a y app oach assumes ha domes ic and o eign bonds a e pe ec
subs i u es so ha Unco e ed In e es Pa i y (UIP) holds,
(5) ])|([ 1
* eIeEii  
Whe e is he a ional expec a ion o he exchange a e one pe iod in o he
u u e, condi ional on he cu en ly a ailable in o ma ion se . Deno ing he se o
o cing a iables as , subs i u ing
(5) in o (4) and sol ing o he exchange a e yields,
Ee I
(/
1
I
(
4

)])()([ 210   ssyymmX




j
IeE
IXE
e1
3
3
311 








Sol ing his equa ion by o wa d i e a ion gi es,

n
n
j
j
n
j
IeEIXEe 










 3
3
3
03
1
31
)|()]1/([)1(




6
Le ing ,
j
o assuming ha he solu ion is ee om a bi a y specula i e
bubbles gi es he o wa d-looking solu ion o he mone a y exchange a e4 (FLME),
(6)
)|()]1/([)1( 3
03
1
3 j
j
j
IXEe 


 

As in Campbell and Shille (1987) and Macdonald and Taylo (1993) he exchange
a e should be coin eg a ed wi h he o cing a iables . This is illus a ed by
sub ac ing om bo h sides o (6) o ob ain,
X
X










  ........
11
12
3
3
2
3
1
2
3
3
3
3 IXEIXEXXe






Rea anging in o i s di e ences yields,











  ........
11
12
3
3
2
3
1
2
3
2
3
1
3
3 IXEIXEXIXEXe






and,
 
























  ........
1
11 2
3
3
3
2
2
3
3
1
3
3 IXEIXEIXEXe






Which o all


j
gi es,
(7)
)|()]1/([ 3
13 j
j
j
IXEXe 


 

7
Unde a ional expec a ions he o ecas ing e o s a e s a iona y, hus i he o cing
a iables in a e I(1), hen he igh hand side o (7) mus also be s a iona y.
Consequen ly i is also I(1), hen he exchange a e mus be coin eg a ed wi h he
a iables . Thus a es o he FLME is o es o coin eg a ion
be ween he exchange a e and o cing a iables
X
mm
,,
e
yy s s
,,
**
and *
5 :
(8)
ussyy mme  *
65
*
43
*
210

Whe e is a andom e o e m and,
u






12345
  ,,
6
0
  
14 23 56
00,,,,,

The sign on he s ock ma ke di e en ial depends on he ela i e s eng hs o he
income and subs i u ion e ec , al hough as wi h F iedman (1988), he weal h e ec is
assumed o domina e, p oducing a nega i e ela ionship. Bahmani-Oskooee and
Soh abian (1992), p o ide a u he explana ion o why exchange a es and domes ic
s ock p ices a e nega i ely ela ed. They sugges ha an exogenous inc ease in
domes ic s ock p ices should esul in a ise in domes ic weal h. Acco ding o he
po olio app oach, he ise in weal h ough o acili a e an inc ease in he demand o
money and a ise in he in e es a e. Highe in e es a es should encou age a capi al
in low, inc eased demand o he domes ic cu ency, which esul s in an app ecia ion
o he domes ic cu ency. To ep esen dynamic ma ke adjus men s, we can ew i e
he equilib ium model o (8) as an e o co ec ion model (ECM) o gi e;
8
ssyymm
sbsbybybmbmbbe


1
*
65
*
43
*
21
*
65
*
43
*
210
][e-

(9)
Whe e all e ms mus be s a iona y, ha is in eg a ed o o de ze o, deno ed I(0), is
a andom e o e m wi h a ze o mean.

is he i s di e ence ope a o and he speed
o adjus men is gi en by

. Fo alues o

close o uni y, adjus men is e y apid,
wi h he disequilib ium being o ally elimina ed wi hin one pe iod o ime. Fo
10 

he dynamic adjus men pa h will be mono onically con e gen .
I he e is e idence ha he o eign and domes ic coe icien s sa is y he implici
es ic ions o he mone a y model, hen he ollowing es ic ed model is
subsequen ly es ima ed:
(10)
ussyymme  )()()( *
3
*
2
*
10

Whe e:
0 ,0 ,0 321




To ep esen dynamic ma ke adjus men s, we can again w i e he equilib ium model
o (10) as an e o co ec ion model (ECM) o gi e;
ussyymme
ssayyammaae


1
*
3
*
2
*
1
*
3
*
2
*
10
)]()()([(
)()()(

(11)
3. Empi ical Resul s
9
al hough mo e esea ch on he mone a y class o exchange a e models is s ill
equi ed.
End No es
1Ch ys al & Macdonald (1995) ind e idence o a alid long- un ela ionship using di isia money.
Choudh y & Lawle (1997) ind e idence o a long- un ela ionship o he es ic ed mone a y model
using Canadian/US da a o he 1950’s loa .
2 Ga in (1989) p o ides a nice heo e ical e sion o he s icky p ice mone a y model o exchange a es
in which s ock p ices ha e weal h e ec s on he demand o money and exchange a e.
3 This con as s wi h F iedman’s (1956) pape ha ela es money demand o he a e o e u n on
equi ies.
4 An ad an age o using he FLME, is ha i p oduces a model in which s ock p ices a e he
explana o y a iables along wi h income and money. I he con en ional mone a y model, wi h s a ic
expec a ions o F ankel eal in e es a e model had been used, bo h long and sho in e es a es would
ha e been inco po a ed in o he model, which could ha e p oduced p oblems o collinea i y be ween
he in e es a es and s ock p ice e u ns in he ECMs. In gene al he con en ional FLME (wi hou
s ock p ices) has no been widely used as i gene ally ails o p oduce e idence o a alid long- un
equilib ium ela ionship and is no a good p edic o o he exchange a e.
5 Tes ing o coin eg a ion be ween he exchange a e and o cing a iables is also a es o he
p esence o bubbles in he exchange a e. I coin eg a ion is ound and ce ain es ic ions p o ed o
hold, hen he specula i e bubble hypo hesis is ejec ed. Howe e his line o in es iga ion is beyond
he scope o his pape . Assuming UIP means he in e es a e di e en ial equals he expec ed a e o
dep ecia ion. In he absence o a bi a y bubbles, he a e o expec ed ep ecia ion is some unc ion o
expec ed mo emen s in undamen als and so equa ion (8) mus be ue.
16

17
6 Canada and he USA we e used as bo h coun ies ha e inancial sys ems based a ound inancial
ma ke s, a he han he banking sec o as in Ge many o F ance. The UK was no used as in 1982 i
changed he way in which i ’s main mone a y agg ega es we e calcula ed.
7 S ock ma ke indexes a e as ollows: US; S anda d and poo Composi e index; Canada; To on o s ock
ma ke composi e index.
8 Gi en ha he Johansen maximum Likelihood p ocedu e is essen ially a ec o au o eg ession
(VAR) based echnique, i is mo e app op ia e o p oduce he comple e ECM a he han a
pa simonious speci ica ion , in which he non-signi ican lags a e omi ed.
9 The esul s o he F ankel eal in e es model a e no included he e, as his model has been es ed on
Canada and he USA o e he 1950’s loa and he ecen loa in a numbe o o he s udies (Mcnown
and Wallace, 1989, Choudh y and Lawle , 1997). The un es ic ed F ankel eal in e es model did
p o ide e idence o coin eg a ion, howe e he es ic ions on he domes ic and o eign explana o y
a iables we e ejec ed, so he es ic ed e sion o his model was no es ima ed.
Re e ences
Bahmani-Oskooee, M., and Soh abian, A. (1992). “S ock P ices and he E ec i e
Exchange Ra e o he Dolla ”, Applied Economics, 24, 4 , 459-464.
Boyle, G. W. (1990), “Money Demand and he S ock Ma ke in a Gene al Equilib ium
Model wi h a iable Veloci y”, Jou nal o Poli ical Economy, 98, 5, 1039-1053.
Campbell, J.Y. and R.J. Schille , (1987), “Coin eg a ion and Tes s o P esen Value
Models”, Jou nal o Poli ical Economy, 95, 1062-1088.
Choudh y, T. and P. Lawle , (1997), “ The Mone a y Model o he Exchange Ra e:
E idence om he Canadian Floa o he 1950’s”, Jou nal o Mac oeconomics, 19, 2,
349-362.
Ch ys al, K. and R. Macdonald, (1995), “ Exchange a es, inancial inno a ion and
di isia money: he s e ling/dolla a e 1972-1990”, Jou nal o In e na ional Money
and Finance, 14, 493-513.
Cul e , S. and D. Papell, (1999), “Long- un pu chasing powe pa i y wi h sho - un
da a: e idence wi h a null hypo hesis o s a iona i y”, Jou nal o In e na ional Money
and Finance, 18, 751-768.
Diebld, F.X. and R.S. Ma iano (1995), “Compa ing p edic i e abili y”, Jou nal o
Business and Economic S a is ics, 13, 253-263.
F iedman, M. (1956). “The Quan i y Theo y o Money- a Res a emen ”, In S udies in
he Quan i y Theo y o Money, edi ed by M.F iedman. Chicago Uni . Chicago p ess.
F iedman,M. (1988). “Money and he S ock Ma ke ”, Jou nal o Poli ical Economy,
96 , 2, 221-245.
Ga in, M. (1989). “The S ock Ma ke and Exchange Ra e Dynamics”, Jou nal o
In e na ional Money and Finance, 8 , 2, 181-200.
18
Gonzalo, J. (1994), “Fi e Al e na i e Me hods o Es ima ing Long-Run Equilib ium
Rela ionships”, Jou nal o Econome ics, 60, 203-233.
G ange , C. W. J. (1986). “De elopmen s in he S udy o Coin eg a ed Economic
Va iables”, Ox o d Bulle in o Economics and S a is ics, 48, 3, 213-228.
G ange , C.W.J. (1988). “ De elopmen s in a Concep o Causali y”, Jou nal o
Econome ics, 39, 199-211.
Johansen, S. (1988), “S a is ical Analysis o Coin eg a ion Vec o s”, Jou nal o
Economic Dynamics and Con ol, 12 , 2, 231-254.
Johansen, S. and Juselius, K. (1990). “Maximum Likelihood Es ima ion and In e ence
on Coin eg a ion wi h Applica ions o he Demand o Money”, Ox o d Bulle in o
Economics and s a is ics, 52 , 2, 169-210.
Hend y, D.F. and J.A. Doo nik, (1994), “ Modelling Linea Dynamic Econome ic
Sys ems”, Sco ish Jou nal o Poli ical Economy, 41, 1-33.
Macdonald, R and Taylo , M.P. (1993). “The Mone a y App oach o he Exchange
a e: Ra ional Expec a ions, Long Run Equilib ium and Fo ecas ing”. In e na ional
Mone a y Fund S a pape s, 40, 1 , 89-102.
McNown, R., and Wallace, M. (1989). “Coin eg a ion Tes s o Long Run
Equilib ium in he Mone a y Exchange Ra e Model”, Economics Le e s, 31 , 3, 263-
267.
19
Meese, R.A. (1986). “Tes ing o Bubbles in Exchange Ma ke s: A Case o Spa kling
Ra es?”, Jou nal o Poli ical Economy, 94 , 2, 345-373.
Meese, R.A. and Rogo , K. (1983). “Empi ical Exchange Ra e Models o he
Se en ies: Do hey Fi Ou o Sample”, Jou nal o In e na ional Economics, 14,1,3-
24.
Pesa an, M. H. and Y. Shin, (1996), “ Coin eg a ion and he Speed o Con e gence o
Equilib ium”, Jou nal o Econome ics, 71, 117-143.
Smi h, C. (1992). “S ock Ma ke s and he Exchange a e: A Mul i-Coun y App oach”,
Jou nal o Mac oeconomics, 14 , 4, 607-629.
Table 1- The Augmen ed Dickey-Fulle (ADF) and Phillips-Pe on Tes o Uni oo s
ADF Tes Phillips-Pe on Tes
Va iables Tes o I(0) Tes o I(1) Tes o I(0) Tes o I(1)
E
CM1
UM1
CY
UY
CS
US
DM1
-2.586
0.688
-1.663
-2.485
-2.870
-0.824
1.502
-0.470
-3.007
-4.211
-2.213
-2.916
-2.767
-15.110
-15.272
-2.686
-2.590
1.000
-1.997
-2.656
-1.931
-0.942
2.089
0.051
-28.894
-25.294
-24.645
-12.527
-5.640
-17.471
-19.717
-20.287
20
DY
DS
-2.944
0.191
-3.704
-7.987
-1.922
0.464
-28.361
-18.292
No es:. E is he exchange a e, CM1 and UM1 a e Canadian and US M1 espec i ely, CY and UY a e
Canadian and US eal income espec i ely, CS and US a e Canadian and US eal s ock p ices
espec i ely, DM1, DY and DS a e he di e en ial be ween Canadian and US M1, eal income and eal
s ock p ices espec i ely. Fo each a iable he i s column o s a is ics es s he null hypo hesis ha he
se ies is I(1) agains he al e na i e ha i is I(0). The second column es s he null ha he se ies is I(2)
agains he al e na i e ha i is I(1). The c i ical alues o bo h hese es s a he 10% and 5% le els o
signi icance a e -2.56 and -2.89 espec i ely. The Phillips Pe on es uses 40 Ba le lags in each es .
Using he same es s wi h a end included does no ma e ially change he esul s.
Table 2- Johansen Maximum Likelihood Tes o Coin eg a ion o he Un es ic ed
and Res ic ed models.
Un es ic ed Model Res ic ed Model
Vec o s T ace Tes Eigen alue Tes T ace Tes Eigen alue Tes
0
 1
 2
 3
 4
 5
177.92*
127.41*
84.09
53.63
31.11
14.75
50.52*
43.31
30.47
22.51
16.36
9.80
78.00*
31.98
15.07
5.32
46.01*
16.92
9.75
5.32
21

 6 4.96 4.96
No es: C i ical alues o Johansen’s T ace and Eigen alue es s a he 95% le el o signi icance a e:
0; 147.27 and 49.32.
 1, 115.85 and 43.61.

2, 87.17 and 37.86.

3, 63.00 and 31.79.
 4, 42.34 and 25.42.
 5, 25.77 and 19.22.

6, 12.39 and 12.39 espec i ely. A * indica es
signi icance a he 5% le el. Fo he Res ic ed Model:

0, 63.00 and 31.79.
 1, 42.34 and
25.42.
 2, 25.77 and 19.22.
 3, 12.39 and 12.39. Bo h es s included seasonal dummy
a iables.
Table 3- No malised Equa ions o he coin eg a ing ec o s.
Un es ic ed Model Res ic ed model
Va iable Coe icien Signi icance Va iable Coe icien Signi icance
E
CM1
UM1
CY
UY
CS
US
-1.000
1.318
0.139
4.394
-6.360
-1.942
1.594
0.651
0.513
0.024
4.724*
5.904*
5.963*
1.866
CE
DM
DY
DS
-1.000
-1.015
0.858
-3.138
0.237
1.117
0.036
11.129*
22
No es: The signi icance o he coe icien s we e es ed using he LM s a is ic which es s he es ic ion
ha he coe icien is equal o ze o.( . A * indica es signi icance a he 5% le el.
(().
.

05
213841)
Table 4- Res ic ion Tes s on he coe icien s o he ollowing a iables
Null Hypo hesis Chi-squa e s a is ic
H1: CM1=1,UM1=-1
H3: CY=-UY
H4: CS=-US
H5: CM1=-UM1;
CY=-UY; CS=-US
0.372
1.412
0.144
4.312
No es: C i ical Values a e 3.84 and 7.815 (5%)
Table 5- E o Co ec ion Model Resul s o he Un es ic ed Model

E

CS U
S
Cons an
es 1
0.017 [0.305]
-0.004 [0.328]
-0.126 [0.607]
0.035 [0.736]
0.481 [2.529]*
-0.107 [2.452]*
E

CM
1
0.096 (0.619)
0.084 (0.343)
-0.090 (1.900)
1.022 (2.774)
-0.031 (0.938)
1.581 (8.594)*
UM1

CY

0.187 (0.645)
-0.318 (3.994)*
-0.478 (0.030)
1.161 (4.283)*
1.504 (0.191)
-0.001 (0.073)
UY

CS

0.324 (1.274)
0.147 (8.931)*
-1.606 (4.839)*
-0.068 (0.745)
-1.082 (1.236)
-0.376 (3.840)**
23
US

R
2
SC(12)
SC(6)
Rese
He e oskedas ici y
ARCH(12)
-0.103 (4.924)*
0.187
1.658
1.417
0.077
0.522
0.482
0.147 (0.131)
0.206
2.022
1.019
0.232
0.204
0.155
0.047 (0.026)
0.213
0.827
1.021
1.573
0.122
0.989
No es: es deno es he e o co ec ion e m;
R
2 is he coe icien o de e mina ion; DW is he Du bin-
Wa son s a is ic; SC(i) a e he i h o de es s o se ial co ela ion; ARCH(i) is Engle’s (1982) es o
he i’ h au o eg essi e condi ional he e oskedas ici y. These es s a is ics all ollow he F-dis ibu ion,
c i ical alues a e: F(6,222)=2.14, F(12,216)=1.80, F(1,227)=3.89. The alues in squa e b acke s
ep esen -s a is ics o he cons an and ec . The alues in o dina y b acke s ep esen Wald s a is ics,
which ollow a chi-squa e dis ibu ion, c i ical alue 3.842. All equa ions include seasonal dummies. A
* indica es signi icance a he 5% le el, ** 10% le el.
Table 6- E o Co ec ion Model o he Res ic ed Model

E
D
S
Cons an
es 1
0.003 (0.705)
-0.001 (0.678)
0.034 (4.112)*
0.147 (4.921)*
E

DM

-0.075 (0.418)
0.073 (0.545)
-0.691 (1.208)
0.035 (1.311)
DY

DS

0.061 (0.064)
0.101 (3.733)**
1.266 (0.253)
-0.129 (13.055)*
R
2
SC(12)
0.08
1.592
0.189
0.746
24
SC(6)
Rese
He e oskedas ici y
ARCH(12)
0.320
1.510
1.025
0.795
0.524
3.913
0.007
0.920
No es: See Table 4
Table 7- RMSE S a is ics o Fo ecas s using he Compe ing models
Models 3 Mon hs 6 Mon hs 9 Mon hs 12 Mon hs
Random Walk
Un es ic ed
Model
Res ic ed
Model
F ankel Model
0.010
0.013
0.009
0.011
0.017
0.017
0.016*
0.016*
0.017
0.018
0.016*
0.016*
0.016
0.017
0.015*
0.015*
No es: A * indica es a signi ican Diebold-Ma iano es s a is ic a he 5% le el. The
es uses he s anda d Newey-Wes adjus men , wi h Ba le weigh s and a lag window
o 2.
Figu e 1- Pe sis ence P o iles o he E ec o a Sys em Wide Shock on he
Coin eg a ing Vec o .
25