The Relationship between Exchange Rates and Stock Prices: Studied in a Multivariate Model Desislava Dimitrova, The College of Wooster


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1 Issues n Poltcal Economy, Vol. 4, August 005 The Relatonshp between Exchange Rates and Stock Prces: Studed n a Multvarate Model Desslava Dmtrova, The College of Wooster In the perod November 00 to February 004, there was an unambguous upward trend n the U.S. stock market. Over the same perod, the U.S. dollar kept deprecatng aganst all major currences. Analysts kept tryng to predct when ths downward trend would come to an end based on the U.S. trade defct. Was not the exchange rate affected by the stock market nstead? In ths paper, I study f there s a lnk between the stock market and exchange rates that mght explan fluctuatons n ether market. I make the case that, n the short run, an upward trend n the stock market may cause currency deprecaton, whereas weak currency may cause declne n the stock market. To test these assertons, I wll use a multvarate, openeconomy, shortrun model that allows for smultaneous equlbrum n the goods, money, foregn exchange and stock markets n twocountres. Specfcally, I focus on the Unted States and the Unted Kngdom over the perod January 990 through August 004. Establshng the relatonshp between stock prces and exchange rates s mportant for a few reasons. Frst, t may affect decsons about monetary and fscal polcy. Gavn (989) shows that a boomng stock market has a postve effect on aggregate demand. If ths s large enough, expansonary monetary or contractonary fscal polces that target the nterest rate and the real exchange rate wll be neutralzed. Sometmes polcymakers advocate less expensve currency n order to boost the export sector. They should be aware whether such a polcy mght depress the stock market. Second, the lnk between the two markets may be used to predct the path of the exchange rate. Ths wll beneft multnatonal corporatons n managng ther exposure to foregn contracts and exchange rate rsk stablzng ther earnngs. Thrd, currency s more often beng ncluded as an asset n nvestment funds portfolos. Knowledge about the lnk between currency rates and other assets n a portfolo s vtal for the performance of the fund. The MeanVarance approach to portfolo analyss suggests that the expected return s mpled by the varance of the portfolo. Therefore, an accurate estmate of the varablty of a gven portfolo s needed. Ths requres an estmate of the correlaton between stock prces and exchange rates. Is the magntude of ths correlaton dfferent when the stock prces are the trgger varable or when the exchange rates are the trgger varable? Last, the understandng of the stock prceexchange rate relatonshp may prove helpful to foresee a crss. Khald and Kawa (00) as well as Ito and Yuko (004) among others, clam that the lnk between the stock and currency markets helped propagate the Asan Fnancal Crss n 997. It s beleved that the sharp deprecaton of the Tha baht trggered deprecaton of other currences n the regon, whch led to the collapse of the stock markets as well. Awareness about such a relatonshp between the two markets would trgger preventve acton before the spread of a crss. Next I revew lterature related to the hypothess and modelng approach of ths paper. In Secton II, I outlne the theoretcal background whch yelds the model presented n Secton III. The data and results are analyzed n secton IV. I. Lterature Revew Most studes that try to explan the fluctuatons of stock prces and exchange rates are nterested n fndng a hghfrequency, statstcal relatonshp between the two varables. The papers analyzed below pertan to my research n the followng way. Ajay and Mougoue (996) examne the short run relatonshp between stock and currency markets n the U.S. and U.K.,
2 whch are the countres of nterest n my paper. Ther results support my hypotheses about the expected sgns of the twoway relatonshp. Granger, Huang and Yang s (000) work further llustrates that the two markets can jontly affect each other. Hsng (004) and Zetz and Pemberton (990) develop models wth monthly data and smultaneously determned macroeconomc varables. Thus, ther approach s partcularly relevant to the one undertaken n my study. Ajay and Mougoue (996) nvestgate the shortand long run relatonshp between stock prces and exchange rates n eght advanced economes. Of nterest to me are the results on shortrun effects n the U.S. and U.K. markets. They fnd that an ncrease n stock prces causes the currency to deprecate for both the U.S. and the U.K., supportng the hypothess of my paper. Ajay and Mougoue explan ths as follows: a rsng stock market s an ndcator of an expandng economy, whch goes together wth hgher nflaton expectatons. Foregn nvestors perceve hgher nflaton negatvely. Ther demand for the currency drops and t deprecates. As to the currency effect on the stock market, the authors fnd that currency deprecaton leads to a declne n stock prces n the short run, also consstent wth my hypothess. The authors explan ths negatve relatonshp as follows: exchange rate deprecaton suggests hgher nflaton n the future, whch makes nvestors skeptcal about the future performance of companes. As a result, the stock prces drop. Ths hypothess s supported by data from the U.K. markets. Granger, Huang and Yang (000) research whether currency deprecaton led to lower stock prces or whether declnng stock prces led to deprecatng currences durng the Asan Crss of 997. The data on some of the Asan countres support the case of bvarate causalty. Stock prces are expected to react ambguously to exchange rates. The authors explan ths wth the effect of currency changes on the balance sheets of multnatonal companes. Deprecaton could ether rase or lower the value of a company, dependng on whether the company manly mports or manly exports. When the stock market ndex s consdered, the net effect cannot be predcted. The other hypothess s that the currency wll deprecate f the stock market declnes (contrary to my expectatonthat currency deprecates f the stock market s boomng). Ths s explaned as follows: n markets wth hgh captal moblty, t s the captal flows, and not the trade flows that determne the daly demand for currency. A declne n stock prces makes foregn nvestors sell the fnancal assets they hold n the respectve currency. Ths leads to currency deprecaton. In my study, t s reasonable to assume that n a perod of one to three months, trade flows (current account) also play a role n determnng the demand for currency. Therefore, the result observed here s contrary to what I expect because of the dfferent tme frame assumptons. Seven of the countres examned by Granger, Huang and Yang (000) showed a strong relatonshp between the two markets causalty was undrectonal n some cases and bdrectonal n others. Whenever the relatonshp was undrectonal, t was found to be negatve, regardless of whch the lead varable was. For four of the countres the authors found evdence of jont causalty. The drecton (postve or negatve) of the dual causalty could not be determned, nor could t be specfed whch the trgger varable was. The reason for the dsparty of results between the dfferent countres mght be the dfferent degree of the captal moblty, trade volume and economc lnks among them. Another reason could be an omtted varable bas for example nterest rates may have an nfluence on stock and currency markets.
3 Granger, Huang and Yang s (000) results mply that I should use a tme perod longer than daly tme span f I want to capture trade flows as a determnant of the exchange rate. The fndngs of Ajay and Mougoue (996) and Granger, Huang and Yang (000) support my hypothess that stock prces and exchange rates are jontly determned. Therefore, they can be ncluded as smultaneously determned varables n the same model. Both papers use a twovarable VAR model wth daly data. I beleve ths approach does not capture a sound theoretcal relatonshp. In that sense, my study dffers fundamentally as t vews the same relatonshp n the context of other varables and uses monthly data. The followng papers I revew address that ssue. Hsng (004) studes how fluctuatons of macroeconomc ndcators affect the output n Brazl n order to prescrbe monetary and fscal polcy. The artcle s especally pertnent to my study n ts consderaton of stock prces n a MundellFlemng model. It also uses monthly data, whch stll provdes a shortrun nsght, but captures more macroeconomc relatonshps than daly data. The author bulds upon the open economy MundellFlemng framework where net exports depend on the real exchange rate. The model s slghtly extended by ncludng varables whch research clams as relevant ol prces, domestc and external debt. Stock prces are also ncluded and they are expected to affect output through wealth and nvestment. Hsng (004) adopts a structural VAR model orgnally proposed by Sms (986), usng ths method allows for the smultaneous determnaton of several endogenous varables. Among the seven endogenous varables are output (Y), real nterest rate (RR), exchange rate (EX) and the stock market ndex (ST), whch are also the four endogenous varables n my model. The model conssts of seven equatons where each endogenous varable s expressed as a functon of ts own lag, the lags of the other sx endogenous varables, the two exogenous varables (whch are the same for all seven equatons), and a whte nose term. Hsng (004) uses the smultaneously estmated model to examne the followng relatonshp: (.) Y = f (REAL INTEREST RATE, BUDGET DEFICIT, EXTERNAL DEBT, DOMESTIC DEBT, REAL EXCHANGE RATE, STOCK MARKET, FOREIGN INTEREST RATE, OIL PRICES) Because all the presented results relate to the author's nterest n output, the conclusons about the relatonshp between stock prces and exchange rates are drawn qute ndrectly. To determne the sgn of the relatonshp, Hsng (004) ntroduces an artfcal shock to each varable. The response of output to a shock n exchange rates and stock prces s gven n Fgure. The author fnds a negatve relatonshp between stock prces and output n the ntal three to four months (Fgure below), whch turns nto an unambguous postve relatonshp after the fourth month. Hence, the shortrun effect s not consstent wth any expectatons.
4 Fgure : Impulse response results for stock prces and exchange rates The exchange rate ncrease (deprecaton) does cause a slght drop n output over the frst two months but overall, the relatonshp s postve and strengthens wth tme. Ths s consstent wth a longrun relatonshp between the exchange rate and the current account (a postve one). The author ponts out that ths result s contradctory to other studes. The observed effect vares wth a specfc country s relance on mports, the tme perod, and model specfcatons. In a country lke the U.S., whch reles on mports and runs a negatve trade balance, deprecaton wll have a negatve effect on the current account and output. The obtaned shortrun results are: a postve relatonshp between exchange rates and GDP and a negatve relatonshp between stock prces and GDP. Therefore, I can ndrectly deduce that the shortrun relatonshp between stock prces and exchange rates s postve. For output to reman constant, an ncrease n stock prces must be accompaned by an ncrease n the exchange rate. The study that I found closest to my research s the one by Zetz and Pemberton (990). The authors use a twostage least squares method to estmate a modfed open economy Mundell Flemng model wth flexble prces. In addton to the three endogenous varables n the standard model (output, nterest rates and exchange rates), they add a fourth varable to be determned wthn the system, prces. Thus, the general structure of ther smultaneous system of equatons s based on a smlar theoretcal framework as my study. The major dfference from Zetz and Pemberton s model s my assumpton of fxed prces mpled by my shortrun focus. Zetz and Pemberton (990) study longrun relatonshps and allow prces to vary by ncludng them as one of the endogenously determned varables. In the case of fxed prces, t s the exchange rate that acts as the adjustment varable to any fluctuaton n net exports. Therefore, my study does not nclude a prce varable. Because my study focuses on the relatonshp between exchange rates and stock prces, I ncorporate a stock prce varable, whch Zetz and Pemberton s model lacks. Stock prces are both an explanatory varable that affects output and an endogenous varable that s determned together wth output, nterest rates and exchange rates. Zetz and Pemberton (990) omt two varables that I have found mportant to nclude CC (margnal propensty to consume) and OP (ol prces). There s abundant theoretcal support that the margnal propensty to consume as well as ol prces are factors that affect domestc output (ncome). A varable the authors nclude and I fnd pertnent to my model s government defct. Ths varable captures the dfference between taxes and government spendng.
5 Regardng the exchange rate varable, I keep the nomnal exchange rate n the model, even though the authors use the real exchange rate. My assumpton of fxed prces permts ths, because under fxed prces changes n real and nomnal exchange rates are dentcal. The authors nclude a current account varable, whch s a quarterly measure of the cumulated real balance on goods and servces. The change n current account over one perod s fully determned by the change n net exports. Therefore, I use the change n net exports between the U.S. and the U.K. as a proxy for the change n the U.S. current account that s due to the change n U.S.U.K. trade flows. Furthermore, monthly data s avalable for net exports and not for the current account. The exstence of jont determnaton between stock prces and exchange rates s, n general, supported by the lterature. However, there s no ubqutous support for a partcular sgn of the relatonshp. The predomnant estmaton technque appears to be the vector autoregresson (VAR) model. Because of ts atheoretcal nature and hgh senstvty to varable choce and orderng, my study wll follow Zetz and Pemberton (990) n buldng a multvarate model, estmated usng the twostage least squares approach. II. Theoretcal Background In ths secton, I theoretcally justfy a postve lnk from stock prces to exchange rates. I argue that an ncrease n stock prces causes an ncrease n output through an ncrease n wealth and nvestment. Then, I make use of a MundellFlemng model wth Jcurve effect to tral out the mpact of hgher output on the exchange rate. Fnally, I outlne theoretcal support for the negatve mpact of exchange rates on stock prces. A. The effect of the stock market on exchange rates The effect of a stock prce ncrease on expendture s explaned by Mshkn (00) as follows. Frst, t leads to ncreased nvestment by frms. The value of a frm s equty ncreases as ts stock prce rses whle the prces of new equpment reman unchanged n the short run. As a result, nvestment s now relatvely cheaper and companes wll tend to nvest more. Hence, nvestment s a functon of stock prces: (.) I = f (R, SP)  where I s nvestment, SP s stock prces, and R s the borrowng/ lendng nterest rate, whch has a negatve mpact on nvestment because t makes nvestment fundng more costly. Second, an ncrease n stock prces wll affect postvely the value of fnancal assets held by households, leadng to an ncrease n household wealth and therefore consumpton. As people assocate hgher wealth wth lower probablty of fnancal dstress, they are lkely to hold more llqud assets. Ths means expendture on durables and housng wll rse as well. Thus, (.) C = f [MPC (Y T), W(SP)] where C s consumpton, Y s ncome, T s taxes, W s wealth, and MPC s the margnal propensty to consume, whch along wth dsposable ncome (YT) affects consumpton postvely.
6 The aggregate expendture of the economy (E) equals ncome (Y) n equlbrum and s defned by the dentty: (.) Y= E = C I G NX = C(MPC(Y T), W(SP)) I(R, SP) G NX  where G s government spendng and NX s net exports. I have ncorporated the stock prce effect nto the consumpton and nvestment patterns and thus obtaned an nvestmentsavngs (IS) relatonshp that depends on stock prces. Ths s the frst modfcaton I ntroduce nto the classcal open economy MundellFlemng model. The second way n whch I dverge from the standard model s by assumng a short run negatve relatonshp between the nomnal exchange rate and the current account. Ths assumpton s based on the nverse relatonshp between the exchange rate and the current account. Ths s typcal of the shortrun and s known as the Jcurve effect. The Jcurve effect (Fgure ) states that the mmedate effect of exchange rate deprecaton s to generate a current account defct, before t translates nto a surplus. Ths lag s estmated to last around sx quarters 4. Therefore, I can assume wthn a tme frame of fxed prces, there s an nverse relatonshp between the exchange rate and the current account. Current Account Surplus CA= PX E P M E deprecates at To Defct Tme 6 quarters Fgure : Jcurve effect
7 Therefore, the current account term n the balance of payments schedule has the followng characterstcs: (.4) CA = f (Y, E, Y*)   where Y s domestc ncome, Y* s foregn ncome, and E s the nomnal exchange rate defned as domestc per foregn currency After ntroducng these modfcatons to the model, t becomes 5 : (.5) BP = CA(Y, E, Y*) K (R R*) = (.6) IS: Y = C(Y, T, W(SP)) I(R, SP) G CA(Y, E, Y*) (.7) LM: MB /P = L (Y, R)  where CA s the current account defned as (.8) CA = NX = X P M P E. X s the amount of exports, M s the amount of mports, P s the prce level n home currency, whch s fxed n our shortrun model, MB/P s real money balances, K s the captal account, R s the domestc borrowng / lendng rate, and NX s net exports. All varables marked wth a star (*) pertan to the foregn country. Fgure below gves a graphcal representaton of the model.
8 R LM Ro* A BP IS Yo* Y Fgure : Open Economy MundellFlemng model The BP schedule represents the accountng dentty of the balance of payments account. It s the mechansm that equlbrates the nternatonal captal and goods markets. If a country has a negatve trade balance (current account), t has essentally borrowed money from abroad, whch would be consstent wth a postve captal account. Snce I assume hgh but mperfect captal moblty, the BP schedule s slghtly upward slopng. The LM locus represents possble equlbrum levels of ncome (Y) and nterest rates (R) n the domestc money market. It reflects the dea that hgher ncome ncreases the demand for money balances. For a fxed money supply by the central bank, money market equlbrum s consstent wth a hgher nterest rate. Therefore, the LM curve s upward slopng. The IS locus represents the equlbrum between savngs and nvestment n the economy. At lower nterest rates, borrowng s cheaper, companes wll nvest more, and hence expendture (whch equals output n equlbrum) wll be hgher. The IS locus s upward slopng. The three markets determne the equlbrum n the economy (pont A). Below I tral out the effect on the exchange rate after an ncrease n stock prces (Fgure 4).
9 R LM B BP R Ro* A BP IS IS Y Y Y Fgure 4: Reacton to a stock market shock An ncrease n stock prces wll ncrease the level of expendture for a gven nterest rate (rght shft of the IS schedule to IS ). The LM schedule s not affected by a change n stock prces. Thus, as a result of a postve shock to stock prces, the new domestc equlbrum s at pont B, hgher output and hgher nterest rates. Ths new equlbrum pont s above the BP curve whch ndcates that for a gven output level (Y), the nterest rate at B s hgher than the one consstent wth a balanced account. A hgher nterest rate attracts foregn captal flows (R>R* leads to hgher K n equaton.5). As a result the balance of payments account s n surplus (BP > 0). The adjustment n the captal account takes place relatvely quckly n markets wth hgh captal moblty. The new domestc equlbrum (B) also has a hgher ncome level (Y). Ths s consstent wth hgher expendture both domestcally and abroad, whch means mports ncrease and the current account deterorates (as can be seen through equaton.8). However, n the short run mports do not adjust as quckly as the captal markets. Therefore, the effect of a captal account surplus domnates the effect of a current account defct and, overall, the balance of payments account s n surplus. That s why pont B s above the BP curve. In order to reach nternatonal market equlbrum, adjustment n the balance of payments account takes place va the exchange rate when prces are fxed. The exchange rate rses (currency deprecates), the current account deterorates and the balance of payments s restored back to zero. An ncrease n the exchange rate s consstent wth an upward shft of the BP schedule (n Fgure 4 BP to BP ). A fnal equlbrum n all markets s reached at pont B (R, Y ) n Fgure 4. Ths new equlbrum s consstent wth a hgher expendture level, hgher nterest rates, hgher domestc exchange rate and hgher stock prces. The most mportant result of ths analyss s that an ncrease n stock prces s followed by currency deprecaton n the same country. B. The effect of the exchange rate on the stock market There are several ways n whch the exchange rate can affect the stock market.
10 Frst, a deprecatng currency causes a declne n stock prces because of expectatons of nflaton (Ajay and Mougoue, 996). (.9) RER = E P* P where RER s the real exchange rate Hgher nomnal exchange rate n the short run s consstent wth a decrease n the prce rato P*/P towards a long run equlbrum level, where the real exchange rate equals unty. A lower P*/P rato mples relatvely hgher domestc prces. Therefore, a deprecaton of the nomnal exchange rate creates expectatons of nflaton for the future. Inflaton s seen as negatve news by the stock market, because t tends to curb consumer spendng and therefore company earnngs. Second, foregn nvestors wll be unwllng to hold assets n currency that deprecates as that would erode the return on ther nvestment. In a case of USD deprecaton, nvestors wll refran from holdng assets n the US, ncludng stocks. If foregn nvestors sell ther holdngs of US stocks, share prces ought to drop. Thrd, the effect of exchange rate deprecaton wll be dfferent for each company dependng on whether t mports or exports more, whether t owns foregn unts, and whether t hedges aganst exchange rate fluctuaton. Heavy mporters wll suffer from hgher costs due to weaker domestc currency and wll have lower earnngs, thus lower share prces. Multnatonal corporatons based n the US wll have hgher ncome when the US currency deprecates. The ncome realzed by the foregn subsdary s converted nto dollars at the hgher exchange rate. Companes that have hedged adequately wll have ther earnngs and stock prce unaffected by a fluctuatng currency. The stock market, whch s a collecton of a varety of companes, wll tend to react ambguously to currency deprecaton. Last, on a macroeconomc level, a deprecated dollar wll boost the export ndustry and depress the mport ndustry. The mpact on domestc output wll be postve. Increasng output s seen as an ndcator of a boomng economy by nvestors and tends to boost share prces. Overall, the effect of exchange rates on stock prces s qute nconclusve as there s some support for both a postve and a negatve relatonshp. Based on Ajay and Mougoue s (996) work, I assume that the negatve lnk wll be predomnant. In the short run, t wll be the expectatons of nvestors that affect the stock market, rather than the fundamentals of the economy. Based on the dscusson above, I can specfy the factors that nfluence stock prces as follows: (.0) SP = f ( Y, INF, E )   where Y s output, INF s nflaton, and E s the exchange rate. Based on the theoretcal background outlned n ths secton, I next derve an emprcal model by makng reference to the study by Zetz and Pemberton (990).
11 III. Emprcal Model The operatonalzed model s specfed next. The sgns n front of the varables reflect the expected relatonshps dscussed earler. Table. summarzes what data s used to measure the varables, the unts of measurement, and the concept they capture *) ( ε β β β β β ε α α α α α = = E NX Q R R E (.) DF NX MB Q R (.) P ε θ θ θ θ θ ε φ φ φ φ ε δ δ δ δ ε γ γ γ γ γ γ γ γ = = = = E CPI MB Y S (.6) M E Q M (.5) X E YF X (.4) CC OP SP DF MB R Q Q (.) Y M X Q Y (.8) M X NX (.7) Identtes = = : where ε ε 6 are random error terms, s the tme perod wth =0 ndcatng the present perod; α β γ φ θ are the coeffcents to be estmated. The sgn before each of these coeffcents ndcates the sgn of the expected relatonshp. Consstent wth the theoretcal model, equaton. stems drectly from the LM locus, equaton. from the BP locus, equatons.,.4 and.5 represent the output of an open economy (see dentty.8) and thus represent the IS schedule presented earler. The addton of a stock market s represented by equaton.6, whch ncludes explanatory varables for the fourth endogenous varable stock prces. The theory dscussed earler and results presented n the revewed lterature support the ncluson of the stock prce (SP) varable as an endogenous one. Hence, t s determned smultaneously wth the other endogenous varables nterest rates (R), ncome (Y) and exchange rates (E). The smultaneous effect comes from the presence of the stock prce varable as an explanatory one n equaton. and from the fact that t s affected by factors lke output, nterest rates and exchange rates.
12 Table.: Defntons and varable measures Varable Concept Measured wth: Unts CC Margnal The Unversty of Mchgan's Index 966 = 00 Propensty to Consume Consumer Sentment Index CPI Inflaton Consumer Prce Index (CPI) Index 9884=00 Expectatons DF Government Federal budget defct/ Mllons of dollars ndebtedness surplus E Exchange rate U.S. / U.K Exchange Rate USD / GBP M Imports US mports from UK Mllons of dollars MB Money M monetary base Bllons of Dollars NX Net exports xm Mllons of dollars OP Ol prces Crude Ol WTI Spot Prce Dollars/ bbl FOB Q Domestc (ynx) Mllons of dollars expendture R Domestc Effectve Federal Funds Rate Percent nterest rate RF Foregn Bank of England base rate Percent nterest rate SP Stock prces Standard and Poor s 500 Index 944 = 0 Index X Exports US exports to UK Mllons of dollars Y Domestc US Industral Producton Index 997 =00 output Index YF Foregn output UK Index of Producton Index 00 =00 Equaton. regresses nterest rates (R) aganst the varables mpled by the LM schedule: domestc output (Q) and net exports (NX) comprse the total output of the economy (Y). The government defct (DF) s ncluded because Hsng(004) argues that hgher defct and debt levels wll lead for hgher borrowng cost for the government. Equaton. ncludes only the varables from the balance of payments schedule, as t was specfed n the prevous secton. Snce prces are fxed, t s the exchange rate that acts as the adjustment varable to net exports fluctuatons. In lne wth the Jcurve effect, I expect a negatve relatonshp between net exports (NX) and the exchange rate. I ntroduce a few addtonal varables nto equaton. CC(margnal propensty to consume) and OP (ol prces). Ther ncluson has the followng theoretcal support. The margnal propensty to consume affects domestc absorpton va prvate consumpton the hgher the margnal propensty to consume, the hgher the output. Ol prces have an nverse relatonshp wth output. Rsng ol prces lead to hgher costs, lower consumer spendng and lower producton by frms, hence lower output. Zetz and Pemberton (990) also nclude the government defct (DF) n ther equaton. Ths varable captures government spendng and taxes. Thus, n equaton. the government defct (DF ) along wth ncome (Y) account for the effect of dsposable ncome on consumpton. There s no need to nclude a dsposable ncome
13 varable, snce ts effect s already captured. Includng a dsposable ncome wll create perfect collnearty. Net exports (NX) s an endogenous varable n the system (determned by equatons.4 and.5). Its dependence on the exchange rate s justfed as follows: Wth dollar deprecaton (E ncreases), US goods appear cheaper to foregners and they are prone to consume more and US exports ncrease. Hence, the postve sgn n equaton.4. Smlarly I can argue that the US mports dfferental on the nomnal exchange rate s negatve. For the ncluson of the partcular varables n equaton.6, I reference Ibrahm(999), but exclude hs foregn reserves varable, whch s applcable to regmes of pegged exchange rates. I do keep hs nflaton varable, even though I have assumed fxed prces. Theoretcally, expectatons of nflaton affect the stock prces because nvestors take t as bad news. So, I use the percentage change n the CPI ndex as a leadng ndcator of nflaton expectatons, assumng that next perod s nflaton expectatons adjust to the observed nflaton for ths perod: [EXPECTED INFLATION t = INFLATION t ]. Thus I expect that hgher nflaton n the prevous month wll have a negatve mpact on the stock market n the current month. The most problematc specfcaton of ths model s the lag length. There s no consensus n the lterature on ths ssue. It s determned ether arbtrarly or through lengthy emprcal tests. Hsng (004) n a study of the Brazlan economy ncludes lag length of three months based on several crtera, whch he unfortunately does not dscuss. Another study by Ibrahm(999) on the relatonshp between macroeconomc varables and stock prces n Malaysa uses a fnal predcton error crteron. Ths s an econometrc estmaton tool whch determnes the lag length. The largest lag length s three months and s used for the stock prce varable. For the US UK case, I can argue that market effcency s hgher than n Brazl and Malaysa. Effcent markets help shocks travel faster through the economy, meanng that for US and UK the lag perod s lkely to be under three months. From an econometrc perspectve, t s better to nclude more varables than exclude relevant ones. Thus, based on the studes cted above and beng overly cautous, I use a lag of three months. The sample sze of 76 months allows ths wthout creatng a severe degrees of freedom problem. The model ensures that equlbrum s acheved at the same tme n the goods, money, foregn exchange and stock markets. Endogenous varables appear both as explanatory and dependant, whch makes the error terms correlated wth certan ndependent varables. For example, the error term of equaton. affects the dependent varable Q. Naturally, total output (Y) s affected as well because of dentty.8. The output varable (Y) then appears as explanatory n equaton.6 and affects stock prces (SP). Ultmately, the error term n equaton. s correlated wth the stock prce varable, whch also appears n equaton. as explanatory. The problem created s known as smultaneous equaton bas. A basc assumpton of the OLS estmaton s volated and the estmaton of the model requres the use of a smultaneousequaton econometrc model. The twostage least squares (SLS) method s approprate here. The two stage least square technque conssts of two stages of OLS regressons. Frst, each endogenous varable s expressed n terms of only exogenous varables n the model. Then the frst stage of the OLS regresson s run and thus estmates of all endogenous varables are obtaned. In the orgnal model, wherever an endogenous varable appears as explanatory on the rght hand sde, t s substtuted wth the obtaned estmate. The second stage can then be run. It entals an OLS regresson on each of the equatons n the orgnal model. However, the use of estmates n place of explanatory endogenous varables ensures that the smultaneous equaton
14 bas s elmnated. The product of the second stage s coeffcent estmates for the varables of the ntal model. Most recent studes, ncludng the ones revewed n the prevous secton of ths paper, use newer econometrc models such as vector autoregresson (VAR) after Sms(980) or structural vector autoregresson(svar) after Sms(986). However, there s lttle evdence that t s a superor estmaton technque, and s extensvely crtczed because of ts lmted theoretcal foundaton and hgh senstvty to order and omsson of varables (Cooley and LeRoy, 985 and Gannn, 99) 6. All data s tmeseres wth monthly frequency, seasonally adjusted, over the perod January 990 through August 004. The sample sze s 76 months. For the estmaton, I generate varables as percentage changes of the collected data. The exchange rate, federal funds rate, monetary base, US ndustral producton ndex and the CPI data are obtaned from the St Lous Federal Reserve 7 ; the UK Index of Producton data from The Offce for Natonal StatstcsUK 8. The UK nterest rate data was collected through the Bank of England 9. The S&P500 ndex tme seres comes from Yahoo Fnance 0. The US budget defct and consumer sentment ndex are acqured from EconStats. Imports and exports data comes from The US Census Bureau and crude ol prces from the US Department of Energy. IV. Data Analyss and Results Ths secton s structured as follows: frst I examne the propertes of the data and determne whether any econometrc problems exst; next I estmate the model usng a two stage least squares procedure; fnally I summarze and analyze the results. Tmeseres macroeconomc data s notorous for ts problematc nature as to meetng the classcal assumptons of OLS estmaton. Because the twostage least squares procedure s essentally an OLS estmaton performed twce, the valdty of the assumptons stll needs to be checked. I perform DurbnWatson tests for autocorrelaton, DckeyFuller tests for nonstatonarty. I analyze the correlaton matrx of the varables to detect sgns of collnearty and evaluate VIF statstcs to test whether multcollnearty s present. I plot the resduals for each of the sx equatons n the model n order to spot any pattern of nonconstant varance of the error term (heteroskedastcty). Because I use data n percentage changes, I do not expect to have any of these problems, as they seem to be common for data n levels. Fnally, I test for Granger causalty to see whether there s emprcal evdence for jont causalty between stock prces and exchange rates. A. Autocorrelaton A way to test for the presence of ths problem s to regress ε t = ρ ε t u t, where ε s the error term from the regressed equaton; ρ s a coeffcent whose value can be between [,], u s a random error term. A value of zero for ρ suggests no autocorrelaton. The RSTAT command n Shazam 4 gves an estmated value for ρ, and also a Durbn Watson test statstc (d), whch takes values wthn the nterval [0,4]. A value of d=0 corresponds to ρ= and perfect postve autocorrelaton; d=4, ρ= suggests perfect negatve correlaton; d=, ρ=0 s consstent wth no seral correlaton. Below I show the conclusons of a two sded Durbn Watson test wth a null hypothess of no autocorrelaton. Ho: ρ=0, d=
15 Table 4.: DurbnWatson test results 5 Equaton n Explanatory varables n equaton Round down to n=00 0 percent test d ρ Concluson D L.) R Accept Ho.) E Accept Ho.) Q Accept Ho.4) X Accept Ho.5) IM Accept Ho.6) SP Inconclusve D U In the case where the test s nconclusve for equaton.6 and where the DurbnWatson tables dd not provde accurate crtcal values, the values of ρ can be consdered closer to 0 than to the endponts of the nterval [, ]. Also, all DurbnWatson statstcs are closer to a value of than to any endpont n the nterval for d, [0, 4]. Overall, I conclude that the SLS model does not suffer from autocorrelaton. B. Nonstatonarty Nonstatonarty s a commonly observed problem wth tmeseres. It stems from the fact that the tme seres s not ndependent of tme. When a varable s not statonary, ts mean and varance are not constant over tme, and an observaton s correlated wth ts more recent lags. A number of studes, ncludng the ones revewed earler, found the data to be nonstatonary of unt root one I(), whch means that the value of the varable for the current perod s correlated wth the value of the varable n the prevous perod. To check for nonstatonarty, I use a DckeyFuller test, whch has the general form: Δx = φ x u, where x s any of the varables represented above, φ= ρ, t t t where ρ measures the lnk between x t and xt ( xt = ρ xt ut ) The tested hypotheses are: Ho: unt root one (data s nonstatonarty n levels, but frst dfference s statonary) φ=0, ρ = and H : φ<0, ρ<. Upon performng a ttest on φ, f the test statstc exceeds the crtcal value n absolute value, I reject null hypothess of nonstatonarty. Nonstatonary data creates fallacous correlaton between the varables. The result s nflated R and tstatstcs. The data I use for the regresson s n percentage change form: x p = x t x x t t Therefore, I test whether the tme seres n percentage changes are statonary over tme. Table 4. summarzes the test results for unt root one (frst dfference s statonary) at the 0 percent sgnfcance level.
16 Table 4.: DckeyFuller test results Varable Test 0 percent Concluson Stat crtcal value E Statonary R Statonary RF Nonstatonary MB Nonstatonary X Statonary IM Statonary Y Statonary Q Statonary YF Statonary DF Statonary CC Statonary SP Statonary OP Statonary CPI Statonary I was not able to reject the null hypothess of nonstatonarty only for two varables, MB (money base) and RF (foregn nterest rate). The latter result s surprsng and, theoretcally, there s no theoretcal reason why I mght observe t. If the two varables are contegrated, then the nonstatonarty of the two varables cancels out and they can be left as they are. To elmnate the nonstatonarty when there s no contegraton, frst dfferences can be taken. Ths has the major drawback of changng the meanng of the varables and losng nformaton about ther longrun trend. Studenmund (p.47) advses that frst dfferences should not be used wthout weghng the costs and benefts. I keep the varables as percentage changes and wll take account of the possblty that the money balances (MB) and foregn exchange rate (RF) coeffcents mght be nflated. C. Multcollnearty The correlaton matrx shows very low correlaton between pars of varables. The absolute value of most correlaton coeffcents s below 0.. Ths mght be related to the fact that the data s percentage changes, whch does not fluctuate as much as data n levels (mllons of dollars). An excepton s Corr(q,y)= By defnton, Q s a lnear functon of Y. I do not expect ths to cause a problem, because the two varables do not appear n the same equaton, nor do they appear as exogenous varables together. To test for multcollnearty, I regress each of the explanatory varables aganst all other explanatory varables. I run an OLS regresson for each of the thrteen varables. Each equaton has the form: X = α α X... α X u where u s a stochastc error and the varables X... X are the varables lsted below The Rsquared statstc and the Varance Inflaton Factor (VIF) for each equaton are lsted n Table 4. below.
17 Table 4.: Test for multcollnearty: auxlary regresson results Varable Auxlary R VIF 6 E R RF MB X IM Q YF DF CC SP OP CPI Based on the very low values of the Rsquared and the VIF for all the varables, I conclude that there s no multcollnearty. D. Heteroskedastcty Heteroskedastcty s a phenomenon usually observed n crosssectonal data, but I need to make sure that t s not present n my model. Heteroskedastcty volates the assumpton that the error term has constant varance. Because the standard tests may not be vald for a SLS model, I plot the error terms of each equaton as a way to observe whether they follow the requred homoskedastc pattern. Nonconstant varance of the error term wll show up as a dstnct fannng out pattern n the plot of the resdual aganst tme. The plotted error terms for each of the sx equatons n the model are ncluded n Appendx B. The plots of resduals seem to have an obvously stable varance around the zero mean. An excepton s the error term for equaton.4, where the varance of the resduals seems to slghtly reduce over tme. One possble way to adjust ths would be to measure all varables n per capta terms. However, I choose not to redefne the varables and be aware that the presence of slght heteroskedastcty n equaton.4 wll underestmate the standard errors and therefore may lead to nflated tstatstcs. I conclude that the rest of the resduals have homoskedastc propertes. E. Granger Causalty Test Lastly, I test whether the assumpton of jont causalty between the exchange rate and stock prce varables holds. Ths assumpton s derved analytcally from theory, and s backed emprcally by many studes, ncludng the ones revewed n Secton I. The Granger causalty test, after Granger (969) 7, checks for causalty between an explanatory varable and the dependent varable. I frst let the exchange rate be a dependent varable and test whether past values of stock prces mpact current values of the exchange rate. Ths s done by comparng the results of an Ordnary Least Squares Estmaton (OLS) on equaton (4.) and ts restrcted form (4.R) below.
18 (4.) E = α α E α E (4.R) E( R) = α α E (4.) SP = β β SP α E β SP (4.R) SP( R) = β β SP α E β SP α E β SP α SP 4 β SP ε 4 β E α SP 4 5 β E 5 α SP β E where E s the exchange rate, SP are stock prces, α and β are the coeffcents to be estmated, ε s a random error term, and (R) denotes the restrcted verson of the specfed equaton. The Fstatstc s calculated as follows: ε 6 ε F() = (RSS(R) RSS()) number of constrants on RSS() degrees of freedom() where F() s the test statstc for the equatons wth dependent varable ; R s the restrcted form equaton for varable ; RSS s the resdual sum of squares, or the amount of varance n the dependent varable that was not captured by the explanatory varables; the number of constrants n our case s for ether restrcted equaton; the degrees of freedom for the unrestrcted equatons are 65 (= 7 observatons 6 explanatory varables ). The null hypothess s that the varables on the rght hand sde do not Grangercause the varables on the left hand sde. A hgh F statstc s the result of hgher explanatory power of the unrestrcted equaton. If t exceeds the crtcal Fvalue for the specfed sgnfcance level, the null hypothess of no Granger causalty s rejected. The Ftest results for the equatons specfed above are: Null hypothess F statstc Crtcal F at 0 percent confdence 8 Concluson SP does not cause E SP does not cause E E does not cause SP E does not cause SP I conclude that causalty from past values of stock prces to current values of exchange rates and form past values of exchange rates to current values of stock prces does not exst. Ths s not consstent wth Ajay and Mougoue (996), who performed a smlar test for the same two countres over a dfferent tme perod. I beleve the nsgnfcance of the test s due to a poor data set and the transformaton of data nto percentage changes, whch elmnated a substantal part of the varance n the orgnal data. Next I proceed wth the estmaton of the model specfed n Secton III.
19 F. Estmaton Results The results of the twostage procedure are hghly dependent on the ft of the frst stage estmaton. If the ft s poor, the estmated endogenous varable wll not be a true proxy of the actual varable and therefore, the ft n the second stage of the SLS wll also have a poor ft. In the SLS technque, the R as well as the adjusted R statstcs have a lower bound of negatve nfnty nstead of zero, and therefore have dfferent nterpretaton. A negatve value usually ponts to poor explanatory power. Another typcal property of the SLS estmaton procedure s that t yelds negatvely based coeffcent estmates for small samples. The estmate of β s lkely to be smaller than the true β. Ths wll also cause the tstatstcs to be lower. As can be seen n Table 4.4, each of the equatons has a low standard error, as well as very low R and adjusted R statstcs. Table 4.4: Estmaton results Eq. Dependent R Adjusted R SE of the estmate Varable. R E Q X M SP I perform a twotal ttest on the estmated coeffcents at 0 percent confdence level wth a null hypothess Ho: β=0. Snce the number of degrees of freedom n each of the sx equatons s greater than 0, the tdstrbuton can be approxmated to normal. So, the crtcal value s.64. When the coeffcent passes the sgnfcance test, I nterpret ts value as the percentage change n the varable on the left hand sde that s caused by percent change n the varable on the rght hand sde that corresponds to the partcular coeffcent. Also, the ttest n general s sad to be not exact for the SLS estmators, but accurate enough n most crcumstances (Studenmund, 467). The estmated coeffcents wth tstatstcs n brackets are lsted below. An astersk ndcates a tstatstc hgher than the crtcal value and hence, statstcally sgnfcant coeffcent. The underlned coeffcents are the ones whose estmated sgn s dfferent form the theoretcally expected one. The obtaned tstatstcs are low n general. Ths may be consstent wth a small sample bas or bad ft of the reducedform equatons n the frst stage of the twostage process, whch further worsens the ft n the second stage. Ths would lead to hgh standard errors and lower tstatstcs. I do not observe hgh standard errors, thus the low tvalues seem to be due to low coeffcents. A reason for the low coeffcents mght be the fact that a lot of the varaton n the data was elmnated by takng percentage changes. (.) R = Q 6.58 MB 0.6NX 0.00 DF (.85)* (5.96)* (.45) (0.89) (0.9) (.) E = ( R R*) 0.6 Q NX 0.80 E (0.0) (4.7)* (0.70) (.)* (.47)*
20 Q = Q 0.045Q 0.5Q 0.0R 0.006R 0.00R 0.00 R (.6) (0.5) (0.40) (0.97) (0.64) (.4) (0.9) (0.5) (.) 0.MB 0.06 MB (0.66) (0.) (0.4) (0.86) (0.57) (0.04) (0.40) 0.00 DF 0.06MB 0.085SP 0.005SP 0.55MB 0.006SP 0.00 DF 0.00DF 0.06SP 0.0OP 0.00 DF 0.00OP (.) (.79)* (0.9) (0.7) (.60) (.55) (0.48) 0.006OP 0.005CC 0.0CC 0.006CC (0.95) (0.4) (.00) (0.6) (.4) (.5) X M = YF 0.45 YF (.07) (0.9) (0.) (.) (.5) (0.75) (0.67) E 0.7 E (.56) (0.67) 0.55 E = Q. Q 0.68 M (.47) (4.9) *.7YF.97 Q.698YF.45 Q 0.70 E 0.86 E 0.57 E E (0.07) (0.84) (.4) (.0) (0.6) (0.48) (0.) (0.4) 0.7 E (.6) SP = Y.9MB.805 CPI 0.6 E 0. E 0.54 E 0.6 E (.6) * (0.69) (.9) * (.4) (.57) * (.8) (.77) * (.5) Very few results are statstcally sgnfcant. Some of the few sgnfcant coeffcents are the ones for the exchange rate varables n the stock prce equaton (.6). The exchange rate n the current perod and two perods back has a sgnfcant, and as expected, negatve effect on stock prces. Ths means that a percent ncrease n the exchange rate (deprecaton) now causes a 0.6 percent declne n current stock prces. The effect seems to fade away wth tme, because a percent ncrease n the exchange rate would cause the stock prce to declne by 0.54 percent two months later. The coeffcents for the other perods appear to be postve, but they are not statstcally sgnfcant, hence I cannot say they are dfferent form zero. Regardng the effect of stock prces on exchange rates, most of the coeffcents are nsgnfcant. Hence, the best that can be done s to try to determne the sgn of the relatonshp. The sgn of the relatonshp s followed through the followng lnk: Eq.. Eq.. stock prces (SP) output (Y) exchange rates (E)
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