STOCK RETURNS AND INFLATION: AN ARDL ECONOMETRIC INVESTIGATION UTILIZING PAKISTANI DATA

Transcription

1 89 Pakisan Economic and Social Review Volume 45, No. (Summer 2007), pp STOCK RETURNS AND INFLATION: AN ARDL ECONOMETRIC INVESTIGATION UTILIZING PAKISTANI DATA MUHAMMAD SHAHBAZ AKMAL* Absrac. According o heory here esablishes he relaionship beween sock marke prices and inflaion, his sudy invesigaes wheher his holds for Pakisan, over he period I examined he concerned relaionship aking ino accoun he exisence of srucural break over he considered ime episode. The empirical pracice uilizes ARDL, co-inegraion echnique in said conjuncion o deec he long run and shor run affecs beween involves variable by Error Correcion Approach (ECM). The resuls suppors he hypohesis ha socks hedges agains inflaion in log run bu no in shor, while black economy promoes he sock marke prices o heave boh in long run as well as in shor run. I. INTRODUCTION The inflaion rae in Pakisan has moved from 9.25 o 2.9 percen from 99 o 995. The owering raes of moneary enlargemen, low rae of economic growh in hree ou of he five years and adjusmen in adminisered prices conribued o he relaively high raes of inflaion. The expansion in money during 994 was mainly on he accoun of accumulaion of ne asses han domesic credi creaion. So, build up of foreign reserves had become necessary because of a draw down of reserves in he previous years. Thus he reason for he increase in money supply in 994 was qualified very differen. In 2004, inflaion came down o 8.44 percen and again creeping up o 0. percen in December 2006, in he main ime urn over on share prices have gone up from $ USA (millions) in Sepember (2003) o 90.8 $ USA (millions) in January (2005) only in Karachi Sock Exchange while marke *The auhor is Research Officer a Social Policy and Developmen Cenre, Karachi (Pakisan).

2 90 Pakisan Economic and Social Review capializaion rose $ USA (millions) from in he same period. Finally, general price index also rose from o from Sepember (2003) o January (2005) meaning ha here is an upward rend in Karachi sock exchange. Excep for a urn down in Sepember and Ocober 2003, share prices coninual heir rising rend hrough mos of he firs en monhs of fiscal year (FY) 2004, wih he Karachi Sock Exchange (KSE)-00 index peaking a 5,62 on 9 h April Subsequenly, equiy prices declined amid flucuaions, and he KSE-00 index fell o 5,297 on 30h June For he year as a whole, he index rose by 55.2 percen. Seady exchange rae, low ineres raes, higher economic growh, improved corporae profiabiliy, and improvemen in relaions wih India were he key facors conribuing o cheerfulness in he sock marke in (fiscal year FY) 2004 (Sae Bank, 2005). Theoreical and empirical research has shown ha he moneary policy can significanly aler he course of real economic aciviy in he shor-erm, alhough in he long-erm he impac of increase in excess money supply is only creaion of inflaion (Clarida e al., 999). As he objecive of he moneary policy was achieved and growh had, in fac, oversho he arge generaing inflaionary pressures he Sae Bank of Pakisan (SBP), he cenral bank, in July 2004 onwards had o shif he gear and moved more decisively o ackle inflaion (Riazuddin, 2005). In order o conain inflaionary pressures in he economy, SBP pursued igh moneary policy hroughou FY (2006). However, insead of increasing he discoun rae, Sae Bank of Pakisan (SBP), focused more on draining excess liquidiy from he iner-bank money marke. As a resul, shor-erm ineres raes remained close o he discoun rae (Sae Bank, 2006). Concluding, he Karachi Sock marke followed upward and downward flucuaions from 97 o 2006, wih flucuaions especially in 2002 and 2006 under he shade of economic reforms. The generalized Fisher hypohesis predics ha equiy socks, which represen claims agains he real asses of business, may serve as a hedge agains inflaion. 2 Wheher socks Economic reforms in Pakisan sared in 99, a srucural package by IMF. 2 Socks are said o provide a hedge agains inflaion if hey compensae invesors compleely (and no by more) for increases in he general price level hrough corresponding increases in nominal sock reurns, hereby leaving real reurns unaffeced. Tha is, socks hedge agains inflaion if heir real value or purchasing power is immune o changes in he general price level (Olesen Jan, 2006).

3 AKMAL: Sock Reurns and Inflaion 9 also provide a hedge agains inflaion empirically has been sudied exensively in he lieraure, see, e.g., Fama and Schwer (977), Gulekin (983), Boudoukh and Richardson (993), Ely and Robinson (997) and Barnes e al. (999). Wih he only excepion of Ely and Robinson (997), cf. below, he lieraure has based is inference on reurn regressions where nominal sock reurns are regressed on inflaion and possibly furher explanaory variables such as real producion growh and changes in a relevan discoun rae measure. The inflaion hedge hypohesis is hen pu o a es by esing wheher he coefficien o inflaion is significan and equal o. 3 In such a case, invesors would sell financial asses in he exchange for real asses when expeced inflaion is definie. Then, sock prices in nominal erms should fully effec he expeced inflaion and he relaionship beween hese wo variables should be posiively correlaed. While Bodie (976) argued ha equiies are a hedge agains inflaion rae due o he fac ha hey represen a claim o real and, hence, he real change on he price of he equiies should no be effeced. In his siuaion, firms are able o predic heir profi margins and since equaliies are claims no on curren bu also on fuure earnings, which confirms ha sock marke operaes as a hedge agains inflaion, a leas in long run. Lieraure suppors he evidence ha posiive relaionship beween nominal sock reurns and inflaion over he long horizons. The relaionship beween nominal socks reurns and inflaion in he Unied Kingdom is relaive posiive, a finding consisen wih generalized Fisher hypohesis (Firh, 979; Gulekin, 983; Boudhouch and Richarson, 993). Boudhouch and Richarson (993) concluded ha i is possible o recover a posiive associaion beween hese wo variables, however, he coefficien on inflaion in long run horizons regression is 0.46, below he expeced coefficien if he Fisher effec is held. Ioannidis e al. (2004) found evidence of posiive 3 Some sudies frame he es in erms of real raher han nominal sock reurns, esing wheher inflaion has a significan influence on real sock reurns; see, for insance, Fama (98) and Kaul (987). A survey of he lieraure including a deailed accoun of he empirical resuls is provided by Frennberg and Hansson (993). The laer sudy a he same ime represens an excepion in he lieraure as he auhors conclude ha Swedish socks provide a hedge agains inflaion even a fairly shor horizons (down o one monh). Anoher survey of he lieraure can be found in Sellin (998). He concludes, Socks seem o be a good hedge agains boh expeced and unexpeced inflaion a longer horizons (Sellin 998, p. 25). However, his conclusion is based on an imperfec hedge definiion, which allows sock prices (or reurns) o respond more han proporionaely o shocks o he general price level (or o inflaion).

4 92 Pakisan Economic and Social Review relaion beween inflaion and sock marke reurns in Greece beween 985 and Kessal (956) concludes ha unexpeced inflaion increases he firm s equiy value if he firm is ne debor. The general conclusion is ha socks do no hedge agains inflaion in shor run (invesmen horizons less han -2 years), where inflaion usually urns ou o have insignifican effec on sock reurns. In fac, a shor horizons he esimaed relaion beween nominal sock reurns and inflaion may even be negaive, see, e.g., Fama and Schwer (977) and Gulekin (983). There is some evidence of a significan posiive relaionship on longer horizons (more han 2 years) bu ofen wih a coefficien differen from so ha he inflaion hedge is no perfec, cf. Boudoukh and Richardson (993). Hence, he hedge hypohesis comes closer o receiving suppor a longer horizons bu he evidence is sill weak. Lieraure also provides suppor for negaive relaionship beween sock nominal reurns and inflaion in long run. Fama (98) found ha here is negaive associaion beween sock reurns and inflaion rae. The negaive correlaion exiss due o he associaion beween inflaion and fuure oupu. Spyrou (200) suggesed ha here exiss a negaive correlaion beween sock marke reurns and he level of inflaion in Greece for he period 990 o 995. Some sudies esablished mixed resuls abou he relaionship beween sock marke reurns and inflaion. Mark (200), found he mixed empirical evidence on he concerned issue. Amidhud (996) repored negaive correlaions beween sock prices and inflaion in shor run which followed by posiive associaion in he long period of ime. The main focus of his effor is on he relaionship beween inflaion and sock marke reurns in shor run as well as in long run. The basic quesion we aemp o give an appropriae answer hrough he analysis of he above relaionship is wheher he sock marke has been a safe place for invesors in Pakisan from 97 o 2006 (June). This empirical analysis is invesigaed by means of an ARDL co-inegraion as well as shor run causal coefficiens. The remaining par of paper is organized as: secion II presens model, mehodology and daa descripion, secion III repors on empirical esimaion, while secion IV presens a brief summary wih some concluding remarks. II. MODEL, METHODOLOGY AND DATA On he basis of heory of correlaion beween sock marke reurns and inflaion, I developed he model for empirical invesigaion as given follows: LSMI = δ 0 + δ LSMI ( ) + δ 2 LCPI + δ 3 LBL + μ ()

5 Where AKMAL: Sock Reurns and Inflaion 93 LSMI = Log of sock marke price index LCPI = Log of consumer price index LBL = Log of share of black economy (under-ground economy) μ = Error erm The daa of concerned variables has been obained from Monhly Saisical Bullein of Sae Bank of Pakisan and Economic Survey of Pakisan (Various issues). 4 In he ime series realizaion is used o draw inference abou he underlying sochasic process. So o draw inference from he ime series analysis, saionariy ess become essenial. A saionary es, which has been widely popular over he pas several years, is uni roo es. In his sudy Augmened Dickey Fuller (ADF) es applied o esimae he uni roo. ADF es o check he saionariy series is based on he equaion of he below given form: Δy = β + β + δ y + α Δy + ε 2 m i = Where ε is a pure whie noise error erm and Δy = (y y 2 ), Δy 2 = (y 2 y 3 ) ec. These es deermine wheher he esimaes of δ are equal o zero. Fuller (976) provided cumulaive disribuion of he ADF saisics, if he calculae-raio (value) of he coefficien δ is less han τ criical value from Fuller able, hen y is said o be saionary. 5 ARDL APPROACH FOR INTEGRATION Now, I employed he newly proposed auoregressive disribued lag (ARDL) approach for Co-inegraion (Pesaran and Shin, 995, 998; Pesaran e al., 996; Pesaran e al., 200). More recen sudies have indicaed ha he ARDL approach o co-inegraion is preferable o oher convenional coinegraion approaches such as Engle and Granger (987), and Gregory and Hansen (996). One of he reasons for preferring he ARDL is ha i is 4 Daa of black economy has been aken from Social Policy and Developmen Cener, Repor No. 65, raio of coefficien δ is always wih negaive sings.

6 94 Pakisan Economic and Social Review applicable irrespecive of wheher he underlying regressors are purely I(0), purely I() or muually co-inegraed. The saisic underlying his procedure is he familiar Wald or F-saisic in a generalized Dickey-Fuller ype regression, which is used o es he significance of lagged levels of he variables under consideraion in a condiional unresriced equilibrium error correcion model (ECM) (Pesaran, e al., 200). Anoher reason for using he ARDL approach is ha i is more robus and performs beer for small sample sizes (such as in his sudy) han oher co-inegraion echniques. The ARDL approach involves esimaing he condiional error correcion version of he ARDL model for variable under esimaion. The Augmened ARDL (p, q, q 2, q k ) is given by he following equaion (Pesaran and Pesaran, 997; Pesaran and Shin, 200): where k ' α ( L, p) y = α + β i ( L, p) xi + λw + ε (2) =,..., n i= α ( L, p) = α L α L... α L 2 β i ( L, qi ) = β i + β il + β i2l β 2 2 p p iq qi L i =,2..., k i y is an independen variable, α is he consan erm, L is he lag operaor such ha Ly = y, w is s vecor of deerminisic variables such as inercep erm, ime rends, or exogenous variables wih fixed lags. The long-erm elasiciies are esimaed by: φ = i i q β i(, q) β io+ β i β = α (, p) α α... α 2 p i =,2,..., k (3) Where pˆ and qˆ, i =, 2,, k are he seleced (esimaed) values of pˆ and i qˆi, i =, 2,, k. The long run coefficiens are esimaed by: q k λ( p, q, q2,..., ) π = (4) α α 2... α p

7 AKMAL: Sock Reurns and Inflaion 95 Where ˆ( λ pˆ, qˆ ˆ ˆ, q2,... qk ) denoes he OLS esimaes of λ in he equaion (2) for he seleced ARDL model. The error correcion model (ECM) linked o he ARDL ( pˆ, qˆ qˆ qˆ, 2,... k ) can be obained by wriing equaion (2) in erms of lagged levels and he firs difference of y, x, x 2,, x k and w : Δy ' λδw = Δα α o p j= α jδy k (, p) EC + β io i= k q i= j= β Δx ij Δx i i, j + + ε where ECM is he error correcion model and i is defined as follows: ECM ' = y α β x λw (6) i i x is he k-dimensional forcing variables which are no co-inegraed among hemselves. ε is a vecor of sochasic error erms, wih zero means and consan variance-covariance. The exisence of an error-correcion erm among a number of coinegraed variables implies ha changes in dependan variable are a funcion of boh he levels of disequilibrium in he co-inegraion relaionship (represened by he ECM) and he changes in he oher explanaory variables. This ells us ha any deviaion from he long run equilibrium will feed back on he changes in he dependan variable in order o force he movemen owards he long run equilibrium (Masih and Masih, 2002). The ARDL approach involves wo seps for esimaing long run relaionship (Pesaran e al., 200). The firs sep is o invesigae he exisence of long run relaionship among all variables in he equaion under esimaion. The ARDL mehod esimaes (p + ) k number of regressions in order o obain opimal lag lengh for each variable, where p is he maximum number of lags o be used and k is he number of variables in he equaion. The second sep is esimae he long run and shor run coefficiens of he same equaion. We run second sep only if we find a long run relaionship in he firs sep (Narayan e al., 2004). This sudy uses a more general formula of ECM wih unresriced inercep and unresriced rends (Pesaran e al., 200): (5) Δy p ' ' π yy y + π yx. xx + ψ iδz + w ΔX + i= = co + c + μ (7)

8 96 Pakisan Economic and Social Review where c 0 0 and c 0. The Wald es (F-saisics) for he null hypohesis π yy π. x ' H : π 0, H yx : π = 0, and alernaive hypohesis H o yy = o yx. x π yy π. x ' : π yy 0, H yx : π yx. x 0 ineres in above equaion is given by: hypohesis is correspondingly saed as: H. Hence he join null hypohesis of he H o o = = H H π yy o π yy I H I H π yx. x o. π yx. x, and alernaive The asympoic disribuions of he F-saisics are non-sandard under he null hypohesis of no co-inegraion relaionship beween he examined variables, irrespecive of wheher he variables are purely I(0) or I(), or muually co-inegraed. Two ses of asympoic criical values are provided by Pesaran and Pesaran (997). The firs se assumes ha all variables are I(0) while he second se assumes ha all variables are I(). If he compued F-saisics is greaer han he upper bound criical value, and hen we rejec he null hypohesis of no co-inegraion and conclude ha here exiss seady sae equilibrium beween he variables. If he compued F-saisics is less han he lower bound criical value, hen we canno rejec he null of no coinegraion. If he compued F-saisics falls wihin he lower and upper bound criical values, hen he resul is inconclusive; in his case, following Kremers e al. (992) and Bannerjee e al. (998), he error correcion erm will be a useful way of esablishing co-inegraion. The second sep is o esimae he long-run coefficien of he same equaion and he associaed ARDL error coercion models. III. EMPIRICAL INTERPRETATIONS Before I proceed wih he ARDL bounds es, I esed for he saionariy saus of all variables o deermine heir order of inegraion. This is o ensure ha he variables are no I(2) saionary so as o avoid spurious resuls. According o Ouaara (2004) in he presence of I(2) variables he compued F-saisics provided by Pesaran e al. (200) are no valid because bounds es is based on he assumpion ha he variables are I(0) or I(). Therefore, he implemenaion of uni roo ess in he ARDL procedure migh sill be necessary in order o ensure ha none of he variable is inegraed of order 2 or beyond. I employed ADF dickey-fuller es o obain he order of inegraion of each variable as resuls shown in Table, which indicaes ha wo variables LSMI and LCPI are I(), alhough LBL is inegraed a I(0). The ambiguiies in he order of inegraion of he variables lend suppor o he use of he ARDL bounds approach raher han one of he alernaive co-inegraion ess.

9 Variables AKMAL: Sock Reurns and Inflaion 97 Level ADF es saisics TABLE Uni-Roo Esimaion Lags s Difference es saisics LSMI ** LCPI * * LBL *** 4 Lags NOTE: *, **, *** significan a percen, 5 percen and 0 percen level of significance. Afer finding inegraing order of all variables, he wo-sep ARDL Coinegraion (see Pesaran e al., 200) procedure is implemened in he esimaion of equaion () for Pakisan uilizing annual daa over he period In he firs sage, he order of lag lengh on he firs differenced esimaing he condiional error correcion version of he ARDL model for condiional equaion is usually obained from unresriced vecor auoregression (VAR) by means of Schwarz Bayesian Crieria and Akaike Informaion Crieria which is 2 based on he minimum value (AIC) 6 as shown in Table 2. The resuls of he bounds esing approach for Co-inegraion show ha he calculaed F-saisics is which are higher han he upper level of bounds criical value of 7.52 a he percen level of significance, implying ha he null hypohesis of no Co-inegraion canno be acceped and here is indeed a Co-inegraion relaionship among he variables in his model. Having found a long-run relaionship, I applied he ARDL mehod o esimae he long run and he shor run elasiciies (see Pesaran e al., 200 and Pesaran and Shin, 999 for deails). The oal number of regressions esimaed following he ARDL mehod in he condiional equaion is (2 + ) 3 = I used AIC for lag lengh selecion. 7 As can be seen from Table 2, alhough he resuls of he F-es changes significanly a lag order, suppor for co-inegraion is less. F-es saisics is highly sensiive wih he lag order; here is srong evidence for co-inegraion because our calculaed F-saisics is greaer han is criical value when second lag is imposed.

10 98 Pakisan Economic and Social Review Lag order Akaike Informaion Crieria TABLE 2 Schwarz Crieria Log Likelihood F-Saisics for Coinegraion * Shor run Diagnosic Tess Serial Correlaion LM Tes = ( ) W-Heeroscedisiciy Tes = ( ) Ramsey RESET Tes = (0.7345) Jarque-Bera Tes =.096(0.6238) NOTE: * represening he significan level a % level of significance while criical value is 7.52 respecively. Long-run coefficiens of he variables under invesigaion are shown in he Table 3. To es he impac of inflaionary pressures on sock marke prices, I regressed, he naural-log of he sock marke price index on linear erms for he measure of inflaionary pressures (consumer price index) and lag dependen variable because sock marke prices are also affeced by heir previous rend. TABLE 3 Esimaed Long Run Coefficiens Using he ARDL Approach Dependen Variable: LSMI Variables Coefficien -values Prob-values Consan LSMI ( ) LCPI LBL R 2 = Adjused R 2 = Durbin-Wason sa =.5257 F-Sa (Prob-value) = (0.000)

11 AKMAL: Sock Reurns and Inflaion 99 Coefficien of inflaionary pressures represens ha socks are hedges agains inflaionary pressures (inflaion) in long run in he case of Pakisan and significan a 0 percen level of significance. While, previous rend of sock marke is also having posiive impac on he curren sock marke price significanly a percen significan level. Finally, and surprisingly black economy promoes he sock marke prices means more under ground economy (black economy), here will be a rising rend in sock marke prices in long run significanly. TABLE 4 Error Correcion Represenaion for he Seleced ARDL-Model (2,, ) Dependen variable: ΔLSMI Variables Coefficien -values Prob-values Consan ΔLSMI ( ) ΔLCPI ΔLBL CR ( ) R 2 = Adjused R 2 = Durbin-Wason sa = 2.02 Akaike info crierion = Schwarz crierion = F-saisic = 3.48 (0.02) Afer esablishing he long run relaionship beween sock marke prices and inflaionary pressures in he case of Pakisan as discussed in Table 3. Table 4 gossips he shor-run coefficien esimaes obained from he ECM version of ARDL model. The ECM coefficien shows he speed of adjusmen of variables reurn o equilibrium and i should have a saisically significan coefficien wih negaive sign. The error correcion erm CE( ), which measures he speed of adjusmen o resore equilibrium in he dynamic model, appears wih negaive sign and is saisically significan a 5 percen level, ensuring ha long run equilibrium can be aained. Bannerjee e al. (998) holds ha a highly significan error correcion erm is furher proof of he exisence of sable long run relaionship. Indeed, he has argued ha esing he significance of CE, which is supposed o carry a negaive coefficien, is relaively more efficien way of esablishing Co-inegraion.

12 00 Pakisan Economic and Social Review The coefficien of CE( ) is equal o (.4) for shor run model respecively and imply ha deviaion from he long-erm inequaliy is correced by (4) percen over he each year. The lag lengh of shor run model is seleced on basis of Akaike Informaion Crieria (AIC). Shor run dynamics resuls also provide evidence ha lagged sock marke price is associaed posiively wih curren sock price a percen level of significance. Inflaionary pressure (consumer prices) is also having posiive impac on sock marke prices bu no significan which, explains ha, sock marke reurns are no hedge agains inflaion in shor run because inflaion usually urns ou o have an insignifican effec on sock reurns. Coefficien of black economy (underground or unregisered economy) also affecs he sock marke prices posiively and significanly in shor span of ime. Diagnosic ess for serial correlaion, normaliy, heeroscedisiciy and funcional form are considered, and resuls are shown in Table 2. These ess show ha shor-run model passes hrough all diagnosic ess in he firs sage. The resuls indicae ha here is no evidence of Auocorrelaion and ha he model passes he es for normaliy, and proving ha he error erm is normally disribued. Funcional form of model is well specified and here is no exisence of whie heeroscedisiciy in model. The presence of heeroscedisiciy does no effec he esimaes and ime series in he equaion are of mixed order of inegraion, i.e. I(0) and I(), i is naural o deec heeroscedisiciy (Shresha, 2005). Finally, when analyzing he sabiliy of he long-run coefficiens ogeher wih he shor run dynamics, he cumulaive sum (CUSUM) and he cumulaive sum of squares (CUSUMsq) are applied. According o Pesaran and Shin (999) he sabiliy of he esimaed coefficien of he error correcion model should also be empirically invesigaed. A graphical represenaion of CUSUM and CUSUMsq is shown in Figures and 2. Following Bahmani-Oskooee (2004) he null hypohesis (i.e. ha he regression equaion is correcly specified) canno be rejeced if he plo of hese saisics remains wihin he criical bounds of he 5% significance level. As i is clear from Figures and 2, he plos of boh he CUSUM and he CUSUMsq are wih in he boundaries and hence hese saisics confirm he sabiliy of he long run coefficiens of regressors ha affec he sock reurns in he counry. The sabiliy of seleced ARDL model specificaion is evaluaed using he cumulaive sum (CUSUM) and he cumulaive sum of squares (CUSUMsq) of he recursive residual es for he srucural sabiliy

13 AKMAL: Sock Reurns and Inflaion 0 (see Brown e al., 975). The model appears sable and correcly specified given ha neiher he CUSUM nor he CUSUMsq es saisics exceed he bounds of he 5 percen level of significance (see Figures and 2). 20 FIGURE Plo of Cumulaive Sum of Recursive Residuals CUSUM 5% Significance The sraigh lines represen criical bounds a 5% significance level..6 FIGURE 2 Plo of Cumulaive Sum of Squares of Recursive Residuals CUSUM of Squares 5% Significance The sraigh lines represen criical bounds a 5% significance level.

14 02 Pakisan Economic and Social Review IV. CONCLUSIONS AND POLICY IMPLICATIONS In his paper he impac of inflaion and black economy on sock marke prices was invesigaed in he case of Pakisan by employing he ARDL for long run and Error Correcion Mehod (ECM) for shor run dynamics. Resuls suppors he hypoheses ha socks reurns are hedges agains inflaion in long run bu no in shor run, while, under-ground economy (black economy) promoes he sock prices o ge higher in long run as well as in shor run. Applicaion of CUSUM and CUSUMsq ess confirm he sabiliy of long run esimaes of sample period. For policy implicaion, governmen should regularize he share of black economy hrough sock markes.

15 AKMAL: Sock Reurns and Inflaion 03 REFERENCES Amihud, Y. (996), Unexpeced inflaion and sock reurns revised Evidence from Israel. Journal of Money Credi and Banking, Volume 28, pp Anari and Kolari (200), Sock prices and inflaion. Journal of Financial Research, pp Bahmani-Oskooee, M. and A. Nasir (2004), ARDL approach o es he produciviy bias hypohesis. Review of Developmen Economics J., Volume 8, pp Bannerjee, A., J. Dolado and R. Mesre (998), Error-correcion mechanism ess for co-inegraion in single equaion framework. Journal of Time Series Analysis, Volume 9, pp Barnes, M., J. H. Boyd and B. D. Smih (999), Inflaion and asse reurns. European Economic Review, Volume 43, pp Bodie (976), Common socks are Hedge agains inflaion. Journal of Finance, pp Boudhouch and Richarson (993), Sock reurns and inflaion: A longhorizon prospecive. American Economic Review, pp Crosby, M. (2005), Sock Reurns and Inflaion. mimeo. Ely, D. P. and K. J. Robinson (997), Are socks a Hedge agains inflaion? Inernaional evidence using a long-run approach. Journal of Inernaional Money and Finance, Volume 6(), pp Engle, R. F. and C. W. J. Granger (987), Co-inegraion and errorcorrecion. Fama, E. F. (98), Sock reurns, real aciviy, inflaion and money. American Economic Review, Volume 7(4), pp Firh (979), The relaionship beween sock marke reurns and raes of inflaion. Journal of Finance, Volume 34, pp Frennberg, P. and B. Hansson (993), Sock reurns and inflaion in Sweden: Do socks Hedge agains inflaion? Working Paper # 25, Deparmen of Economics, Lund Universiy. Gulekin (983), Sock marke reurns and inflaion. Journal of Finance, pp

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