Stock Prices and the Monetrary Model of Exchange Rate: An Empirical Investigation.

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