Predictability of stock returns and consumption-based CAPM: Evidence from a small open market

Transcription

1 Predicabiliy of sock reurns and consumpion-based CAPM: Evidence from a small open marke Auhor Li, Bin, Zhong, Maosen Published 2010 Journal Tile European Journal of Economics, Finance and Adminisraive Sciences Copyrigh Saemen 2010 EuroJournals Publishing, Inc. The aached file is reproduced here in accordance wih he copyrigh policy of he publisher. Please refer o he journal's websie for access o he definiive, published version. Downloaded from hp://hdl.handle.ne/10072/34569 Link o published version hp:// Griffih Research Online hps://research-reposiory.griffih.edu.au

2 European Journal of Economics, Finance and Adminisraive Sciences ISSN Issue 22 (2010) EuroJournals, Inc hp:// Predicabiliy of Sock Reurns and Consumpion-based CAPM: Evidence from a Small Open Marke Bin Li Griffih Business School, Griffih Universiy, Brisbane, QLD 4111, Ausralia b.li@griffih.edu.au Tel: Maosen Zhong Pureland Learning College, Toowoomba, Ausralia Absrac In his sudy, we use he condiional consumpion CAPM (CCAPM) wih he consumpion-wealh raio and/or he surplus consumpion raio o examine he predicabiliy of reurns in he Ausralian equiy marke. We also explore he relaionship beween expeced excess marke reurns in Ausralia and he ime-varying risk aversion associaed wih he world as well as local consumpion. Our sudy reveals ha he consumpion-wealh raio can predic he variaion of excess sock marke reurns a he inermediae horizons (from 1 year o 2 years); on he oher hand, he surplus consumpion raio can only predic excess sock marke reurns a he very shor horizon, one quarer ahead. We show ha hese wo sae variables are no muually exclusive, bu complemenary. As a small bu open marke, Ausralian marke s expeced reurns should be affeced by global price of consumpion risk. Our resuls show ha boh he world surplus consumpion raio and he world consumpion-wealh raio have predicive power for excess reurns in he Ausralian equiy marke over he long horizons. eywords: Consumpion-based CAPM, Consumpion-wealh Raio, Habi Formaion, Asse Pricing JEL Classificaion Codes: G12; G15 1. Inroducion Saring from Rubinsein (1976), Lucas (1978) and Breeden (1979), many auhors define equilibrium in he capial markes using consumpion variables. Under a number of assumpions, he asse reurns should be linearly relaed o he growh rae in aggregae consumpion as long as he parameer of he linear relaionship remaining consan over ime. Despie he heoreical soundness and simpliciy, he consumpion-based asse pricing model (CCAPM) is usually no easy o be explicily esimaed for he highly non-linear naure and non-separabiliy of consumpion uiliy among periods. GMM, iniiaed by Hansen and Singleon (1982), is a good ool for solving CCAPM empirical problems. However, esimaes from GMM always depend on he choice of insrumenal variables. Wih differen ses of insrumens, he esimaed resuls may differ significanly. The well-known weak idenificaion problem may also plague he reliabiliy of resuls (Sock and Wrigh 2000). When coming back o canonical Consumpion CAPM models, i has no performed well empirically (e.g. Mankiw and

3 149 European Journal of Economics, Finance And Adminisraive Sciences - Issue 22 (2010) Shapiro 1986; Breeden, Gibbons and Lizenberger 1989), and hey are rejeced boh on he U.S. daa (Hansen and Singleon 1982) and inernaional daa (Whealey 1988). In response o his, some auhors have modified he consumpion-based CAPM hoping o enhance he empirical performance of he model. Campbell and Cochrane (1999) inroduce a habi formaion variable surplus consumpion variable, which is he ime-varying consumpion in surplus o habi, o modify he opimal choices of consumpion over ime o explain he cyclical variaion in expeced reurns and volailiy. The habi formaion of Campbell and Cochrane (1999) is non-linear, slow-moving and exernal in response o he hisory of consumpion. They find ha due o he fac ha risk aversion is inversely relaed o surplus consumpion, a high level of consumpion exceeding habi should forecas low expeced sock marke reurns. Their model is infinie-horizon non-linear model. In ligh of his, Li (2001) argues ha he finie-horizon linear habi model also indicaes he inverse relaion beween expeced reurns and surplus consumpion, and i performs almos as well as Campbell and Cochrane s (1999) nonlinear habi model for he U.S. marke. The modified consumpion-based asse pricing model can no only explain U.S. sock marke reurns, bu also predic he inernaional sock marke reurns. Using quarerly daa of 17 naional indices from Morgan Sanley Capial Inernaional (MSCI), Li and Zhong (2005) invesigae he predicabiliy and he cross-secion of reurns from inernaional equiy markes under consumpionbased asse pricing model wih habi formaion. Their findings sugges ha he domesic and world s log surplus consumpion raios,, parly explains he reurns from mos of he developed equiy markes. Their cross-secional ess of CCAPM under habi formaion show ha he model performs slighly beer han he uncondiional world CCAPM and CAPM, he condiional world CAPM and a hree-facor inernaional model. Li, Lu and Zhong (2004) invesigae he predicabiliy of sock reurns from indusry porfolios of he U.S. marke using aggregae consumpion in surplus of habi. They find ha a considerable large amoun of predicabiliy of long-horizon indusry porfolio reurns are explained by he surplus consumpion raio and he ime varying beas and ime-varying marke risk premium associaed wih he surplus consumpion raio help explain he predicabiliy of long-horizon expeced reurns over half of he U.S. indusry porfolios. In a recen paper, Jacobs and Wang (2004) examine he significance of idiosyncraic consumpion risk for he cross-secional variaion in asse reurns. They find ha he cross-secional variance of consumpion growh and he rae of aggregae consumpion growh are boh significan pricing facors for asse reurns. The resuls sugges ha his wo-facor CCAPM ouperforms he CAPM and perform almos as well as he Fama-French hree-facor model. Furhermore, he recen sudies by Leau and Ludvigson (2001a, 2001b) explain ime series and cross-secional variaion of US porfolios reurns wih a log consumpion-wealh raio called cay, which is consruced as he residual from he shared rend among log consumpion (c ), log asse holding (a ) and log labor income (y ). Under he assumpion of a represenaive agen s binding ineremporal budge consrains, hey find here is coinegraion relaionship beween log consumpion, log asse holding and log labor income, and heir consruced log consumpion-wealh raio ( cay ) can predic U.S. sock marke excess reurns a shor and inermediae horizons. Moreover, cay can serve as he sae variable of CCAPM o explain cross-secional sock marke reurns and is performance can be compared o he Fama-French hree-facor model. cay can help forecas abou 9% of one quarer ahead excess marke reurns and explain abou 70% of he cross-secional reurns in U.S. daa wih he framework of Breeden s (1979) CCAPM and Jagannahan and Wang s (1996) Human Capial CAPM. The performance of cay is also evidenced in U.. and Japanese markes (Gao and Huang 2004). There are hree reasons for us o choose Ausralian equiy marke as a case sudy of reurn predicabiliy based on he consumpion-based CAPM. Firs, inernaional evidence of reurns

4 150 European Journal of Economics, Finance And Adminisraive Sciences - Issue 22 (2010) predicabiliy based on cay and in counries oher han he U.S. is limied, parly because of he unavailabiliy of reasonably good daa. These daa from Ausralia, however, are available o he auhors. Second, few sudies examine he predicabiliy of sock reurns based on boh sae variables, and cay. We argue in Secion 2 ha hese wo sae variables are heoreically no muually exclusive bu complimenary in explaining asse reurns. Third, in ligh of he incomplee marke risk sharing argumen (Li and Zhong 2005), asse reurns may be beer explained by boh domesic and inernaional prices of risks. The choice of he counry should ake ino consideraion of is openness o he global markes. Ausralia is a small bu open marke and is deemed an ideal case for our sudy. In his paper, we fill he gap of he lieraure and provide an empirical invesigaion of he predicabiliy and variaion of excess reurns in he Ausralian equiy marke using wo consumpion sae variables: he log surplus consumpion raio,, and he log consumpion-wealh raio, cay. Under he assumpion ha consumpion and dividends follow random walk processes in he habibased model, he marke risk premium should vary wih a single sae variable: he surplus consumpion raio. We use OLS regressions o examine he predicabiliy of hese wo sae variables for quarerly and long-horizon reurns in he case of Ausralia. Given he recen empirical evidence on he imporance of habi formaion and incomplee risk sharing in he inernaional markes, we also explore he relaionship beween expeced excess reurns in he Ausralian marke and he ime-varying prices of risks associaed wih he world as well as local surplus consumpion. Our empirical resuls provide inernaional evidence of reasonable predicive power of Campbell and Cochrane s (1999) surplus consumpion raio and Leau and Ludvigson s (2001a) consumpion-wealh raio. Moreover, our sudy adds a few new insighs abou he predicabiliy of aggregae sock reurns in he Ausralian equiy marke. We show ha he consumpion-wealh raio can predic he variaion of excess sock marke reurns a he inermediae horizons (from 1 year o 2 years); on he oher hand, he surplus consumpion raio can only predic excess sock reurns a he very shor horizon, one quarer ahead. Including boh surplus consumpion raio and consumpionwealh raio ino he regression yields higher adjused R 2, which suggess ha hese wo consumpion variables are no muually exclusive, bu complemenary. We provide he heoreical jusificaion in he conex of including boh sae variables of CCAPM. In addiion o he empirical analysis of ime-varying expeced reurns in he domesic seing, our exploraory invesigaion of CCAPM under incomplee inegraed marke reveals ha Ausralian asse pricing are deermined by boh he domesic and world s prices of consumpion risk. Boh he world surplus consumpion raio and he world consumpion-wealh raio, apar from heir domesic counerpars, have predicive power of excess reurns in he Ausralian equiy marke over long horizons. Overall, he inernaional version of CCAPM has more explanaory power han he domesic version of CCAPM. These findings sugges ha when esimaing Ausralian cos of equiy using CCAPM over he usual annual horizon, one would need o use cay as a scaling facor for a domesic version of CCAPM. The res of he paper is organized as follows: Secion 2 presens he heoreical developmen of he surplus consumpion raio ( ), he consumpion-wealh raio ( cay ) and he corresponding economeric models for esing. Secion 3 offers a deipion of he daa and is sochasic properies. I also conains a comprehensive discussion abou how several key variables are consruced. Secion 4 gives he empirical findings and relevan discussion. Secion 5 concludes his paper. 2. Model Developmen This secion firs presens he heoreical developmen of he surplus consumpion raio ( ) and he aggregae consumpion-wealh raio ( cay ) in he conex of CCAPM. Then we derive he

5 151 European Journal of Economics, Finance And Adminisraive Sciences - Issue 22 (2010) corresponding economeric models using hese wo sae variables under he hypohesis of compleely segmened marke. We also exend he economeric models o he assumpion of he parially inegraed marke Surplus Consumpion Raio Campbell and Cochrane (1999) presen CCAPM wih exernal habi formaion where a represenaive agen derives uiliy from he difference beween consumpion and a ime-varying habi level, and he model can capure much of excess sock reurns in he long horizon. We provide a concise inroducion of his model. Assume a represenaive agen ake he uiliy funcion as 1 γ ( C j j) 1 j + X + E δ, (1) j= 0 1 γ where C is he per capia real consumpion, X is he habi level, δ is he subjecive discoun facor, and γ is he uiliy curvaure parameer. Abel (1990) and Campbell and Cochrane (1999) sugges he level of habi X o be exernal. X is also assumed o depend upon a long hisory of aggregae consumpion and follows an infinie-horizon nonlinear formaion process (Campbell and Cochrane 1999). The surplus consumpion raio SCR, is defined by C X SCR < 1. (2) C SCR indicaes he sae of he economy. When SCR declines, consumpion C drops o he habi level X, and he economy is reaching recession and invesor risk aversion rises. On he oher side, rising SCR means ha curren consumpion exceeds X, and he economy is expanding, and invesor risk aversion decreases. Hereafer, we use uppercase leers o denoe variables a heir original scale, and lowercase leers o denoe he logs of he corresponding uppercase leers. Campbell and Cochrane (1999) sugges a heeroscedasic AR(1) process for he log surplus consumpion raio, log( SCR) : + 1 = (1 ϕ) + ϕ + λ( ) εc, + 1, (3) where φ is he habi persisen parameer, and λ ( ) is he sensiiviy funcion, and ε c, + 1 is he innovaion in consumpion growh. Campbell and Cochrane (1999) sugges ha we should use a large value of he persisence parameer in order o obain he predicive power of he log surplus consumpion raio. As in Li and Zhong (2005), we use φ = 0.90 in his paper 1. λ ( ) represens he condiional sensiiviy of SCR o C, and i is inversely relaed o he surplus consumpion raio SCR. When SCR falls, he sensiiviy funcion λ ( ) and expeced excess reurns rise. Consumpion growh is assumed independenly and idenically disribued (i.i.d.). Imposing hree condiions ha he risk-free rae is fixed, habi is predeermined a he seady sae, and habi moves non-negaively wih conemporaneous consumpion elsewhere, we can specify he sensiiviy funcion λ ( ) = max{0,(1/ SCR) 1 2( ) 1}, (4) where he seady sae is SCR = σ c γ /(1 ϕ), and σ c is he sandard deviaion of he unexpeced consumpion growh ε c, + 1. The resuling sensiiviy funcion λ ( ) is inversely relaed o he log surplus consumpion raio,. Following Campbell and Cochrane (1999) and Li, Lu and Zhong (2005), we choose curvaure parameer γ = 2 o compue he seady-sae value of. 1 Alernaive habi persisence values ( ϕ = 0.80, 0.95 ) do no aler any of he conclusions reached in his sudy.

6 152 European Journal of Economics, Finance And Adminisraive Sciences - Issue 22 (2010) Under he exernal habi formaion, Eq. (1) implies he ineremporal marginal rae of subsiuion of he represenaive invesor a ime + 1 is C 1S 1 M = ( ) CS. (5) Le R i, + 1denoe one plus he rae of reurn on asse i from ime o + 1, hen R i, + 1saisfies he Euler equaion of he following form: E[ M+ 1 Ri, + 1] = 1, (6) where E is he expecaion condiional on he informaion se as of ime. Under he assumpion of he joinly lognormally disribuion of asse reurns and consumpion growh, he Euler equaion (6) implies ha expeced excess reurns on any asse is e 1 2 E[ ri, + 1 ] = σi + γ[1 + λ( )]cov ( ri, + 1, Δc+ 1) 2. (7) In Eq. (7), σ is he Jensen s alpha, and he risk premiums on asse i are he price of risk, 2 i γ[1 + λ( )], imes he condiional covariance of he asse s reurns wih consumpion growh. The price of risk depends on he uiliy curvaure parameer γ and he sensiiviy funcion λ ( ). Given ha he expeced excess reurns are inversely relaed o, λ( ) is inversely relaed o he surplus consumpion raio, (Eq. (4)). Thus invesors require higher expeced reurns on asses when consumpion falls oward habi. Under he assumpion ha he condiional covariance of reurns wih consumpion growh is consan, linear approximaions o he sensiiviy funcions λ( ) imply ha he expeced excess reurn on asse i can be wrien as e E[ r ] = α + α i, 1 1z + β1 +, (8) where z is a vecor of informaion variables, is he log surplus consumpion raio and he slope coefficien β 1 is consan. Sensiiviy funcion λ ( ), according o Eq.(7), is posiively relaed o he expeced excess marke reurns, and is inversely relaed o λ ( ), so he coefficien β 1 is expeced o be negaive. Several informaion variables are included in he predicabiliy ess as moivaed by previous sudies [e.g. Ferson and Harvey (1998), Leau and Ludvigson (2001a), and Li and Zhong (2005)]. These informaion variables are dividend yield, dividend payou raio, derended shor erm governmen bond reurns, governmen bond erm spread. The model for expeced one-period reurns in Eq. (8) can be easily exended o a model for e e e e expeced reurns over muliple periods. Le ri, + k = ri, ri, ri, + kdenoe he cumulaive k = 1 excess sock marke reurns wih coninuous compounding over periods. If are highly persisen, hey should be able o predic muli-period reurns. We wrie expeced -period excess reurns as e E[ ri, + k] = α + α1 z + β1, (9) k = 1 where α1 is a vecor of consans and β1 are consan slope coefficiens 3. 2 See Li (2001) for deailed derivaion. 3 Similar o Campbell e al. (1997), if follows an AR(1) process wih an auocorrelaion coefficiens θ, hen he law of ieraed expecaions implies β = β (1 θ ) /(1 θ). 1 1

7 153 European Journal of Economics, Finance And Adminisraive Sciences - Issue 22 (2010) Assuming he growh raes of consumpion and dividends are i.i.d., expeced excess sock reurns are deermined by a single sae variable he surplus consumpion raio. Campbell and Cochrane (1999) and Li (2001) show ha expeced excess reurns should be negaively relaed o he sae variable because high (low) surplus consumpion a he business cycle roughs (peaks) are associaed low (high) invesor risk aversion, hus reducing (increasing) he required rae of reurns Consumpion-Wealh Raio Here we heoreically derive he aggregae consumpion-wealh raio cay ha provides useful condiioning informaion for asse reurns. Consider a represenaive invesor who invess his wealh in a single asse wih a ime-varying risky reurn R 4. We denoe W as aggregae wealh including human capial and household asse holding a ime, C as consumpion and R +1 is he ne reurn on he marke porfolio of all invesed wealh. For a complee-marke model where wealh includes human capial as well as financial asses, under he ineremporal budge consrain, he period-o-period aggregae wealh is W+ 1 = (1 + R+ 1)( W C). (10) Campbell and Mankiw (1989) derive he log consumpion raio from Eq. (10). In order o make he budge consrain funcion linear, we approximae i by aking firs order Taylor expansion (see Campbell and Mankiw (1989) for deails), resuling in Δ w+ 1 = w+ 1 w k+ r+ 1 + (1 1/ ρ)( c w), (11) where he parameer ρ is he average raio of invesed wealh, W-C, o oal wealh, W, and k is a consan. The wealh growh rae Δ w + 1 can be arranged in erms of consumpion growh rae and he change of log consumpion-wealh raio. Solving i forward recursively, we can ge a log-linear version of he infinie-horizon budge consrain i c w = E ρ ( r+ 1 Δc+ 1) (12) i= 1 Eq. (12) links he log consumpion-wealh raio wih fuure marke reurn and he fuure consumpion growh, suggesing ha a higher log consumpion-wealh raio a his period mus forecas eiher higher reurns on he marke porfolio a fuure periods or low fuure consumpion growh raes. Given ha aggregae wealh W is he sum of financial asse A and human capial H, he log linear approximaion of W is a convex combinaion of he log-linear approximaion of A and H, w ωa + (1 ω) h, (13) where ω equals he average share of asse holdings in oal wealh, A/W. If aggregae labor income Y can deibe he non-saionary componen of human capial H (see Leau and Ludvigson (2001a) for deails), hen we can obain he following relaionship beween log consumpion-aggregae wealh raio i, +, + + ] (14) c ωa (1 ω) y = E ρ ωr + (1 ω) r Δ c + (1 ω) z a i h i i i= 1 Assuming all erms on he righ-hand side of Eq. (14) are saionary, hen he lef-hand side mus also be saionary, implying c, a, y mus have coinegraion relaion wih a coinegraing vecor (1, -ω, ω -1). We now denoe cay as he lef side of Eq. (14), c ωa (1 ω) y. This equaion suggess ha as long as expeced fuure reurns on human capial r h,+i and consumpion growh c +i are no oo volaile, or if hey have high correlaion wih expeced fuure reurns on asses, hen cay should help forecas he expeced fuure asse reurns. 4 Individuals, usually in empirical research, are assumed o be aggregaed ino a single represenaive agen economy (see Campbell, Lo and Macinlay (1997), p.304).

8 154 European Journal of Economics, Finance And Adminisraive Sciences - Issue 22 (2010) Eq. (14) suggess ha cay has posiive linear relaion wih he excess sock marke reurn. To examine he implicaion of he single-sae-variable model for he predicabiliy of reurns on he marke porfolio, he regression equaion is as follows: e E [ r ] = α + α z + β cay, (15) i, e [ ] i, 1 where E r + is one-quarer ahead expeced excess sock marke reurns; α is a consan, a 1 is he vecor of consan slope coefficiens of insrumenal variables, and β2 is he consan slope coefficien. Accordingly, he model for expeced one-period reurns in Eq. (15) can be easily exended o a model for expeced reurns over muliple periods. If cay are highly persisen, hey should be able o predic muli-period reurns. We wrie expeced -period excess reurns as e E[ ri, + k] = α + α1 z + β2 cay, (16) k = 1 where α1 is a vecor of coefficiens and β A Unified CCAPM wih Boh Sae Variables are consan slope coefficiens. In his sub-secion, we show ha boh and cay are complemenary sae variables in he CCAPM. Ineremporal marginal rae of subsiuion m +1 in Eq. (5) can also be approximaed as follows (Leau and Ludvigson 2001b): m+ 1 δ{1 γgλ( ) γ( ϕ 1)( ) γ[1 + λ( )] Δ c+ 1}, (17) where is he log surplus consumpion raio; γ is he parameer of uiliy curvaure; g is he average consumpion growh rae; φ is he habi persisen parameer, and λ ( ) is he sensiiviy funcion; δ is he subjecive rae of ime preference. λ ( ) may be a funcion of unobservable variables, bu heir variaion should be capured by suiable proxies for ime-varying risk premia. Leau and Ludvigson (2001b) sugges ha consumpionwealh raio, cay, may be a good proxy because i no only capures represenaive agens expecaions of fuure reurns of marke porfolio bu also may play a role in linear facor models wih ime-varying coefficiens of CCAPM. Assuming λ( ) is a linear funcion of cay and, we may wrie an approximae form of he risk aversion as follows: λ ( ) * = a + b cay + d * 5. (18) Subsiue Eq. (18) ino Eq. (17), we have m δ{1 γg( a + b cay + d ) γ( ϕ 1)( ) γ(1 + a + b cay + d ) Δ c } (19) Unlike Leau and Ludvigson (2001b), we show ha cay and can be unified in he consumpion CAPM and may be used ogeher o predic reurns. Eq. (19) can be rewrien as m + 1 α + β1 + β2cay + β3δ c+ 1+ β4 ( Δ c+ 1) + β5 ( cayδ c+ 1), (20) where α is consan, β 1, β 2, β 3, β4 and β 5 are consan slope coefficiens. Eq. (20) implies ha excess sock marke reurns should have a linear relaionship wih boh he log consumpion-wealh raio, cay, he log surplus consumpion raio,. Thus he regression equaion can be expressed as 5 Such ha m = a + bz, where he scaling/condiioning variables z include boh cay and ha λ( ) is a linear (negaive) funcion of.. I can be demonsraed

9 155 European Journal of Economics, Finance And Adminisraive Sciences - Issue 22 (2010) E[ e ri, + 1] = α + β1 + β2cay, (21) where α is consan, β 1, β 2, β 3 and β 4 are consan slope coefficiens. Similarly, he regression equaion over long horizons can be expressed: e E[ ri, + k] = α + β1 + β2 cay, (22) k where α is a vecor of consans and β1 and β 2 are consan slope coefficiens. 2.4 CCAPM under Incomplee Marke Inegraion We now move o he derivaion of he inernaional version of he CCAPM wih he sae variables cay and/or. Sulz (1981a, b) argues ha if we assume inernaional marke are compleely inegraed and all he markes compleely share he consumpion risk, asse prices from all counries are deermined by one common sochasic discoun facor. On he oher hand, in a compleely segmened capial marke, asse prices from each counry should reflec heir own counries sochasic discoun facor. Ausralia is relaively small and open counry, so is asse pricing models should be deermined by he local as well as he world sochasic discoun facor. We consider CCAPM based on parial marke inegraion. Marke-based parial inegraion ess have been conduced by a number of researchers such as Chan e al. (1992) and Dumas e al. (2003). Li and Zhong (2005) poin ou ha, under he assumpion of parial marke inegraion, he consumpion-based model can be deibed as follows: e 1 2 e e E[ ri, + 1 ] = σi + φγ w[1 + λ( w)]cov ( ri, + 1, Δ cw, + 1 ) + (1 φ) γ[1 + λ( )]cov ( ri, + 1, Δ c+ 1) (23) 2 e 2 where E[ r i, + 1] is expeced excess local sock marke reurn; σ i is local variance of excess sock marke reurn; φ is he fracion of local counry s expeced reurns a ime ha are relaed o heir covariance wih world consumpion, if he marke is parially inegraed, 0 < φ < 1; γ w and λ( w ) are he parameer of he world consumpion curvaure and he world consumpion sensiiviy funcion, respecively; γ and λ ( ) are he parameer of he local consumpion curvaure and he local consumpion sensiiviy funcion, respecively; Δc w, + 1and Δc + 1 sand for world consumpion growh rae and local consumpion growh rae, respecively. In his paper, we use he U.S. consumpion variables o proxy for he world consumpion variables. Eq. (23) suggess ha expeced excess marke reurns are inversely relaed o he lagged world and local surplus consumpion raios. Linear approximaions o he sensiiviy funcion λ( w ) and λ( ) imply ha he expeced excess reurn on marke reurns can be wrien as E [ e ri, + 1] = α + α1z + β1ww + β1, (24) where w and represen he world and local log surplus consumpion raios, respecively, and z is a vecor of informaion variables. The slope coefficiens β 1w and β1are consans. Here, w is orhogonal o. The ime-varying Jensen s alpha, α 1 z, capures he ime-varying degree of inegraion and ime-varying condiional variances and covariance as well as he linear approximaion error in Eq. (24). Similarly, he model for expeced one-period reurns in Eq. (24) can be easily exended o a model for expeced reurns over muliple periods. If he surplus consumpion raios are highly persisen, hey should be able o predic muli-period reurns. We wrie expeced -period excess reurns as e E[ ri, + k] = α + α1 z + β1ww + β1, (25) k

10 156 European Journal of Economics, Finance And Adminisraive Sciences - Issue 22 (2010) where α1 is a vecor of consans and β w and β 1 are consan slope coefficiens. In addiion, expeced reurns a each horizon should be inversely relaed o he lagged world and local log surplus consumpion raios, β w <0 and β 1 <0 if βw and β 1 <0, respecively. In a similar manner, we can consruc he predicing equaion for reurns using world and local consumpion-wealh raios. One-quarer-ahead regression equaion is: E [ e ri, + 1] = α + α1z + β2wcayw + β2cay (26) Exending o -periods, expeced cumulaive excess reurns can be expressed as e [ E ri, + k] = α + α1 z + β2wcayw + β2 cay (27) k Wih he four sae variables, he economeric model akes he form: e E [ ri, + k] = α + α1 z + β1 + β1ww + β2cay + β2wcay w. (28) k = 1 3. Daa As discussed above, he key sae variables for reurn predicabiliy es are he log surplus consumpion raio and he log consumpion-wealh raio. This secion deibes how we compile he daa for hese key sae variables and oher financial daa. Our macroeconomic daa include household consumpion (non-durable goods and service), afer-ax labor income and ne household wealh. Our financial daa include AllOrd sock marke reurns, ASX/S&P200 sock marke reurns, dividend yield, earnings per shares, relaive shor erm bond rae, and erm spread beween long erm governmen bond and shor erm governmen bond. We also repor summary saisics of he variables and conduc uni roo es for macroeconomic variables and es heir coinegraion relaionship ey Sae Variables Macroeconomic daa usually only exis in lower frequency such as quarerly or annually. In Ausralia, Ausralia Bureau of Saisics (ABS) mainains a good record of macroeconomic daa. Our consumpion, wealh and labor income daa are consruced from he ime series spreadshees from AusSas Daabase 6. These variables are only available in quarerly or annually. For his paper, we use he daa daing back o he fourh quarer of 1976 (1976Q4) and unil he second quarer of 2004 (2004Q2), which yields 111 observaions. The daa used here are quarerly, seasonally adjused, real per capia daa, measured in dollar. See Appendix A for deailed deipion of how aggregae consumpion, wealh and labor income are consruced. We employed augmened Dickey-Fuller (1979) and Philips-Perron (1988) Uni Roo es in he series of household consumpion, labor income and ne household wealh. We find here is only one uni roo in each of hese hree series. Nex we move o es wheher here is any coinegraion relaionship among hese hree variables. To do his, we conduc wo kinds of coinegraion es: one is Phillips-Ouliaris (1990) residual-based coinegraion es, which is o discern wheher here is a leas one coinegraion vecor among hese hree variables; he oher es is a more popular one: Johansen s (1988, 1991) L-Max es and race saisics es, which will ell us he number of coinegraion vecors of he long-erm relaionship. Boh ess sugges here is only one coinegraion vecor among he hree variables. The resuls of Phillips-Ouliaris coinegraion es and Johansen coinegraion es are given in Panel A and Panel B of Appendix B, respecively. Coinegraion ess sugges ha here is a shared rend in consumpion, labor income and ne asse wealh. In order o examine he predicabiliy of sock marke reurns using cay, we should 6 These series can be rerieved a hp://

11 157 European Journal of Economics, Finance And Adminisraive Sciences - Issue 22 (2010) esimae he parameers of he coinegraion relaion. Due o endogenously deermined naure of c, a and y series, we use he single equaion procedure suggesed in Sock and Wason (1993) and use he dynamic leas squares (DLS) esimaes wih Newey and Wes (1987) o correc for any residual serial correlaion, k c = α + β a + β y + b Δ a + b Δ y + ε a y ai i yi i i= 1 i= 1 k. (29) Ordinary Leas Square (OLS) esimae of Eq.(29) produces he super-consisen esimae of βa and β y of coinegraion parameers (Leau and Ludvigson 2001). Adding leads and lags of he firs difference of ne asse wealh and labor income will capure he effecs of regressor endogeniy in he linear regression of consumpion on asse wealh and labor income. From DLS esimaion of Eq.(29), we can obain he esimaed rend deviaion cay c β a β y, where ha means esimaed a y parameer. Using quarerly daa from 1976Q4 o 2004Q2, we obain he esimaed coefficiens of he rend deviaion (Corresponding -saisics are given below in he parenhesis) of consan, ne asse wealh and labor income: c = a y (30) (3.06) (11.85) (2.29) Thus cay = c 0.405a 0.239y. Ausralia marke is an open bu small marke in he world. World business cycle should have some impac on Ausralian sock marke reurns. Thus, we add he world surplus consumpion raio and he world consumpion wealh raio as pricing facors for Ausralian sock marke reurns. However, i is hard o consruc he world consumpion-wealh raio due o he lack of world daa on household wealh. In his paper, we use he U.S. surplus consumpion raio and he U.S. consumpion-wealh raio o proxy for he world surplus consumpion raio and he world consumpion-wealh raio, respecively. This is because he U.S. plays a significan role in Ausralian foreign inward invesmen. The U.S. is he larges source of foreign invesmen in Ausralia, accouning for around one-hird of oal foreign invesmen in Ausralia. 7 The U.S. consumpion-wealh raio can be downloaded from he websie of Marin Leau 8, which provides quarerly daa from he fourh quarer of 1951 o he second quarer of The variables which are used o consruc U.S. consumpion-wealh raio - consumpion, labor income, household ne wealh are log real per capia daa. The U.S. surplus consumpion daa are consruced in he same manner as in Campbell and Cochrane (1999) Financial Daa For sock marke index, here are wo commonly used indices: AllOrd Index and ASX/S&P 200 Index. AllOrd Index is from he Cenre for Research in Finance (CRIF) daabase of he Ausralian Graduae School of Managemen (AGSM), which is daing back o December 1979 wih base index of 500 in ha monh. ASX/S&P 200 index is colleced from he bullein saisics of Reserve Bank of Ausralia (RBA) wih base index of 500 a December They are monhly daa, so we conver hem ino quarerly daa using he average value of he hree monhs in each quarer. AllOrd Index is he value weighed price index for he companies raded in Ausralian Sock Exchange (ASX) which should provide a beer proxy for nonhuman componens of household asse wealh han ASX/S&P 200 index. We ry sock marke reurns using boh AllOrd Index and ASX/S&P 200 index, and he empirical 7 See Ausralian Bureau of Saisics 2003 Publicaion, , Inernaional invesmen posiion, Ausralia: Supplemenary counry saisics. 8 Quarerly cay daa can be rerieved from Marin Leau s Webpage: hp://pages.sern.nyu.edu/~mleau/.

12 158 European Journal of Economics, Finance And Adminisraive Sciences - Issue 22 (2010) resuls are no sensiive o he ype of index used. We deflae he sock marke index by CPI o ge he real sock marke reurn. Sock marke reurns are log reurns: r = log(allord ) log(allord -1 ), (31) where AllOrd is he series of All Ord Index. The cross-secional 24 indusry index daa are also from AGSM CRIF daa base, which are adjused for franking credis, and share issues and reconsrucions. They daes back from December The prices given are he price relaives, so we conver hem back o he prices wih he base price of 1 in December To compue he quarerly reurns, we use he price of las monh of he quarer as ha quarer s price. The daa of he elecommunicaions indusry, only becomes available afer he second quarer of 1985, o obain he non-missing value daa, we use 1985Q2 o 2002Q3 as he esimaion period for he cross-secional regressions. For risk-free rae, we use he shor-erm 2-year governmen bond as a proxy. Quarerly and monhly 2-year governmen shor-erm bond yields are also available in IFS unil June Le us denoe r m as he log real reurn of he sock marke index, and r f as he log real reurn on he risk-free e rae, hen log real excess reurn on he sock marke is r = rm rf. The local informaion variables include log dividend yield, dp ; log dividend payou raio, de ; derended shor-erm governmen bond reurn, RREL ; governmen bond erm spreads, TRM. I is well documened ha hese informaion variables can forecas excess aggregae marke reurns over long horizons (e.g. Shiller 1984; Fama and French 1988; Lamon 1988; Campbell 1987; Fama and French 1989). The quarerly daa of he dividends yield and he dividend payou raio for he Ausrlian sock marke index is only available in recen years in he daabase. Forunaely, Shares magazine and is predecessors, SXJ and he Ausralian Sock Exchange Journal, mainain a good record of average dividend yields and PE raio of all he raded companies in he Ausralian Sock Exchange (ASX). We hand colleced he dividend yields and PE raios from January 1978 unil Augus Thus, dividend payou raio can be easily obained by dividend payou raio = dividend yields * PE raio / 100. (32) We also conver monhly daa o quarerly daa. Derending he shor erm Treasury bill rae is used by a number of researchers such as Campbell (1991) and Hodrick (1992) and Leau and Ludvigson (2001a) o predic he U.S. sock marke reurn. In ligh of his, we use he shor-erm governmen bond rae, which is 2-year governmen bond rae minus 12 monh backward moving average, o predic Ausralian sock marke reurns. Term spread, he difference of long-erm governmen bond yield and shor-erm governmen bond yield, is also added as informaion variable o predic he sock marke reurn. Term spread is 15- year governmen bond yield minus 2-year shor-erm governmen bond yield. For world informaion variables, we include he U.S. erm spread, Eurodollar rae, TRMW and he relaive REURO, whose empirical performances have been documened in Ferson and Harvey (1993) and Bekaer and Harvey (1995). The U.S. erm spread is obained from he Federal Reserve Bank of S Louis, compued as he U.S. 10-year bond yield minus he 3-monh U.S. bill rae. The relaive Eurodollar rae is obained from Inernaional Financial Saisics, calculaed as he hreemonh Eurodollar rae minus a one-year moving average. Preliminary regression resuls (no repored bu available upon reques) show ha among he four local informaion variables, erm spread dominaes he predicabiliy of excess sock reurns wih highly significan coefficiens a inermediae and long horizons. Oher informaion variables do no have significan forecasing power for excess reurns. Neverheless, we include all four informaion variables in our predicabiliy o be compaible wih previous lieraure. The world informaion variables have he predicive power for sock reurns on mos horizons.

13 159 European Journal of Economics, Finance And Adminisraive Sciences - Issue 22 (2010) Table 1: Summary Saisics r e dp e r + 1 de RREL TRM Δc + 1 Panel A: Correlaion Marix w cay cay w dp de RREL TRM Δc w cay cay w Panel B: Univariae Summary Saisics Mean Sandard Error Auocorrel aion e Noes: r + 1 is quarerly log excess reurn on AllOrd index; dp is he log dividend yield; de he log dividend payou raio; RREL is he relaive shor erm governmen bond rae; TRM is he governmen bond spread beween long-erm governmen bond and shor erm governmen bond; Δ c + 1 is he consumpion growh rae a ime +1; cay = c 0.405a 0.239y, where c is log consumpion, a is he log of household ne asse wealh, and y is log afer-ax labor income; cay w is he world consumpion-wealh raio; is he surplus consumpion raio of Ausralia, and w is he world surplus consumpion raio. The sample period is from he fourh quarer of 1979 o he second quarer of Summary Saisics Table 1 has wo panels: he correlaion marix and univariae summary saisics. The quarerly e variables include log excess reurn on sock marke index r + 1, log dividend yield dp, log dividend payou raiode, he derended shor erm governmen bond rae RREL, governmen bond erm spread TRM, consumpion growh rae Δ c + 1, he local surplus consumpion raio, he world surplus consumpion raio w, local consumpion-wealh raio cay, and he world consumpion-wealh raio cay w. The sample period is from he fourh quarer of 1979 o he second quarer of Panel A demonsraes ha excess reurn on he sock marke is negaively relaed he local surplus consumpion raio, bu posiively correlaed wih he local consumpion-wealh raio. The sign of he correlaion is consisen wih he heory we discussed in Secion 2. The sae variables, w, cay, and w cay are moderaely correlaed wih he four informaion variables, herefore, we orhogonalize he informaion variables o he sae variables in he following predicabiliy ess.

14 160 European Journal of Economics, Finance And Adminisraive Sciences - Issue 22 (2010) Panel B suggess ha relaive o he mean, he variaion of and cay is less han ha of all oher variables. Panel B also presens he auocorrelaion of he variables a lag 1. Excep excess sock marke reurn and consumpion growh rae, all oher variables exhibi higher auocorrelaion. The high persisence propery of he independen variables may be helpful for forecasing excess marke reurns over long horizons. 4. Predicabiliy Resuls 4.1. Single-Sae-Variable Forecasing Regressions Now, we move o examine he predicive power of and cay and oher informaion variables for he aggregaed sock marke reurns in long horizons. We follow Harvey (1989) o es he null hypohesis ha he condiional covariance in Eq. (7) is consan. Firs, we regress marke excess reurn on he informaion variables o obain residuals, hen we regress he produc of he regression residuals and consumpion growh on he informaion variables, and conduc he F-es. Our resul rejecs he null hypohesis, hus concluding ha he condiional covariance beween marke excess reurns and 2 consumpion growh is consan ( χ = 3.29, p value= 0.51). Table 2 repors he OLS regression esimaion resuls using single sae variable: he log surplus consumpion raio,, and he log consumpion-wealh raio, cay, and/or oher informaion variables as predicive variables. We run he following leas square regressions using full sample over he horizons spanning from 1 o 16. The dependen variable is cumulaive -period excess marke reurns: e r + k k = 1. The informaion variables are: he log dividend yield, dp ; he log dividend payou raio, de ; he relaive shor erm governmen bond rae, RREL ; he governmen bond erm spread, TRM. Panel A shows he resuls of he regression wih he sae variable bu wihou informaion variables; Panel B shows he resuls of he regressions wih boh he sae variable and informaion variables. Each informaion variable is orhogonalized o he sae variable by using he fied residuals from he regression of ha informaion variable on he sae variable. Table 2 also repors he adjused R 2, and Newey-Wes (1987) adjused - saisics o accoun for any residual serial correlaion. Newey-Wes adjused -saisics are placed in parenhesis under he esimaed coefficiens, and he adjused R 2 of he regression is placed in he square brackes below he -saisics.

15 161 European Journal of Economics, Finance And Adminisraive Sciences - Issue 22 (2010) Table 2: Single-Sae-Variable Forecasing Regressions Regression Regressors 1 2 cay 3 4 cay Regression Horizons Panel A: Wihou Informaion Variables (-2.724) (-1.178) (-0.407) (-0.012) (0.410) (0.915) (0.643) (0.748) [0.038] [0.012] [-0.007] [-0.011] [-0.008] [0.003] [-0.001] [0.018] (0.856) (1.432) (1.743) (2.154) (2.361) (2.532) (1.576) (0.819) [0.006] [0.047] [0.089] [0.139] [0.191] [0.236] [0.140] [0.032] Panel B: Wih Informaion Variables (-2.399) (-1.046) (-0.386) (0.021) (0.566) (1.644) (1.365) (1.523) [0.013] [-0.008] [-0.002] [0.014] [0.069] [0.195] [0.284] [0.386] (0.806) (1.313) (1.560) (2.007) (2.114) (2.090) (1.279) (0.475) [-0.024] [0.044] [0.119] [0.199] [0.225] [0.297] [0.364] [0.430] Noes: This able presens he resuls from he regression of he long horizon excess marke reurns on lagged variables. denoes he reurn horizon in quarers, spanning from 1 o 16. The dependen variable is he cumulaive excess marke reurns over period: e r + k k = 1. The sae variables are one-quarer lagged values of he following variables: log consumpion-wealh raio cay = c 0.405a 0.239y, where c is log consumpion, a is he log of household ne asse wealh, and y is log afer-ax labor income; and surplus consumpion raio of Ausralia,, which is derived from modified Campbell and Cochrane (1999) model. The informaional variables are: dp is he log dividend yield; de is he log dividend payou raio; RREL is he relaive shor erm governmen bond rae; TRM is he governmen bond erm spread, which equals 15 year governmen bond yield minus 2 year shor erm governmen bond yield. Panel A shows he regression resuls wih he sae variable bu wihou informaion variables; Panel B shows he regression resuls wih boh he sae variable and informaion variables. The informaion variables are orhogonal o he sae variables. Significan coefficiens a he 5% (10%) significance level are highlighed in bold (ialics) face. Newey-Wes adjused -saisics are placed in parenhesis under he esimaed coefficiens. The adjused R 2 of he regression is placed in he square bracke below he -saisics. The regression sample period is from he fourh quarer of 1979 o he second quarer of Regression 1 shows he explanaory power of he log surplus consumpion variable,, which is derived from modified Campbell and Cochrane (1999) model. Here, we use he parameer of he curvaure of risk aversion γ=2.0, as suggesed by Campbell and Cochrane (1999); he habi persisence parameer φ=0.90, he same value used by Li and Zhong (2005). The resul shows ha can predic excess marke reurns in he very shor horizon. A quarer 1, he esimaed coefficien is -0.05, Newey- Wes adjused -saisics is and can explain 3.8% of he variaion of he excess sock reurns. However, hardly has any predicive power of for excess marke reurns over inermediae and long horizons. The adjused R 2 a inermediae horizon is negaive and negligible over long horizons. The esimaed coefficien is no significan a 10% level. Our finding ha he esimaed coefficien of a shor horizons is negaive is consisen wih he heory. Under he assumpion of i.i.d of he growh raes of consumpion and dividends, Campbell and Cochrane (1999) and Li (2001) poin ou ha expeced excess sock reurns are deermined by a single sae variable he surplus consumpion raio, and expeced excess reurns should be inversely

16 162 European Journal of Economics, Finance And Adminisraive Sciences - Issue 22 (2010) relaed o he sae variable because high surplus consumpion a he business cycle roughs are associaed wih low invesor risk aversion, hus lowering he required rae of reurns. Regression 2 of Table 2 shows he forecasabiliy of log excess sock marke reurns over long horizon using cay as a single sae variable. The predicive power of cay is quie srong in he inermediae horizons (from 1 year o 2 year). The adjused R 2 has jumped monoonically from quarer 1 o quarer 8, parly because he reurns are overlapping reurns. A year 2, he predicive effec of cay on accumulaed excess reurns is quie large; he poin esimae of he coefficien on cay is abou 5.6. Newey-Wes adjused -saisics is 2.5 and cay can explain nearly 24% of he variaion of he accumulaed excess sock reurns. A shor horizons, cay has lile explanaory power, however, he esimaed coefficiens become marginally significan over hree quarers and R 2 jumps o 9%. In addiion, cay is losing explanaory power afer 2 years, and he coefficien, adjused -saisics, and adjused R 2 all fall. cay s low forecasing power a shor horizons may be driven by is marginal predicing power of fuure consumpion growh a shor horizons (he resuls are available upon reques). I is no surprising ha he coefficien of cay is posiive, which is in accordance wih he heory. As suggesed by Eq. (12), a higher log consumpion wealh raio a his period mus forecas eiher higher reurns on he marke porfolio a fuure periods or lower fuure consumpion growh rae. cay almos has no predicing power of consumpion growh (resul is no repored), hus, a higher log consumpion-wealh raio a his period mus forecas higher reurns on he marke porfolio a fuure periods. Therefore, consumpion rend deviaion should covary posiively wih excess sock reurns. Moreover, economic inuiion indicaes ha, when invesors expeced low fuure reurns on asses, hey will drop oday s consumpion emporarily below he long erm relaionship among consumpion, asse and wealh o secure fuure higher consumpion. Therefore, rend deviaion cay and excess sock reurns should have posiive covariance. In Panel B, four informaion variables: dp, de, RREL, TRM are orhogonalized o our key sae variables. Adding informaion variables o he regression equaions wih and cay, he regression resul is robus, as shown in Regression 3 and 4. However, adjused R 2 has risen significanly over inermediae and long horizons, which is mainly driven by he erm spread, TRM Two-Sae-Variable Forecasing Regressions Regression 1 shows he log surplus consumpion raio,, only predics excess sock marke reurn one quarer ahead. Regression 2 suggess he log consumpion-wealh raio, cay, can srongly predic variaion of excess sock marke reurn on he inermediae horizons. Eq. (22) gives he regression equaion over long horizons using facors, and cay. The resuls are shown in Regression 5 of Table 3. can sill only forecas one quarer ahead excess marke reurns, and i has no forecasing power beyond wo quarers ahead. cay can predic variaion of aggregae sock marke reurns over inermediae horizons. Compared o Regression 2, adding ino he regression equaion makes he coefficien of cay a year 3 significan a 5% significance level. Using boh of hem increase he explanaory power for variaion of excess sock 2 reurns, as R increases. Using boh cay and can predic 27.4% of variaion of excess sock reurns over 2 years horizon, which is 3.8% higher han he one using cay as a sole variable. A oher horizons, he fracion of he predicable variaion of excess sock marke reurns also rise.

17 163 European Journal of Economics, Finance And Adminisraive Sciences - Issue 22 (2010) In Regression 6 of Panel B, we add informaion variables ino regressors oher han and cay. The resul is robus; however, he adjused R 2 rises significanly over inermediae and long horizons, which is mainly driven by he erm spread, TRM Forecasing under Incomplee Marke Inegraion Ausralia is a small bu open marke. The expeced reurns on he Ausralian equiy marke should be affeced by he global price of consumpion risk. In his secion, we invesigae wheher aggregae sock marke reurns in Ausralia is affeced by he world consumpion fundamenals. Here, we use he U.S. log consumpion-wealh raio and he U.S. log surplus consumpion raio o proxy he world counerpars. Table 4 presens he resuls from he regression of he long horizon excess marke reurns on lagged variables under he assumpion of incomplee marke inegraion. The sae variables are he local consumpion-wealh raio, he local surplus consumpion raio, he world consumpion-wealh raio and he world surplus consumpion raio. Panel A shows he resuls of he regression wih he sae variables bu wihou he informaion variables; Panel B shows he resuls of he regression wih boh he sae variables and he informaion variables. Table 3: Two-Sae-Variable Forecasing Regressions Regression Horizons Regression Regressors Panel A: Wihou Informaion Variables (-2.923) (-1.056) (-0.150) (0.312) (1.088) (1.524) (1.313) (1.053) cay (0.681) (1.385) (1.816) (2.336) (2.889) (3.332) (2.187) (1.379) [0.037] [0.051] [0.080] [0.132] [0.201] [0.274] [0.171] [0.077] Panel B: Wih Informaion Variables (-2.769) (-1.019) (-0.148) (0.331) (1.042) (1.927) (1.666) (1.667) cay (0.635) (1.300) (1.646) (2.161) (2.355) (2.467) (1.418) (0.721) [0.030] [0.069] [0.117] [0.190] [0.220] [0.314] [0.362] [0.425] Noes: This able presens he resuls from he regression of he long horizon excess marke reurns on lagged variables. denoes he reurn horizon in quarers, spanning from 1 o 16. The dependen variable is he cumulaive excess marke reurns over period: k = 1 e r + k. The sae variables are one-quarer lagged values of he following variables: log consumpion-wealh raio cay = c 0.405a 0.239y, where c is log consumpion, a is he log of household ne asse wealh, and y is log afer-ax labor income; and surplus consumpion raio of Ausralia,, which is derived from modified Campbell and Cochrane (1999) model. The informaional variables are: dp is he log dividend yield; de is he log dividend payou raio; RREL is he relaive shor erm governmen bond rae; TRM is he governmen bond erm spread, which equals 15 year governmen bond yield minus 2 year shor erm governmen bond yield. Panel A shows he regression resuls wih sae variables bu wihou informaion variables; Panel B shows he regression resuls wih boh sae variables and informaion variables. The coefficiens and -saisics of he four informaion variables are no repored o save space. The informaion variables are orhogonalized o boh sae variables. Significan coefficiens a he 5% (10%) significance level are highlighed in bold (ialics) face. Newey-Wes adjused -saisics are placed in parenhesis under he esimaed coefficiens. The adjused R 2 of he regression is placed in he square bracke below he -saisics. The regression sample period is from he fourh quarer of 1979 o he second quarer of 2004.