A Resolution of the Fisher Effect Puzzle: A Comparison of Estimators.

A Resolu ion o he Fishe Effec Puzzle: A Compa ison o Es ima o s Eka e ini Panopoulou∗ Na ional Uni e si y o I eland, Maynoo h and Uni e si y o Pi aeus, G eece Feb ua y 2005 Abs ac This pape a emp s a esolu ion o he Fishe effec puzzle in e ms o es ima o choice. Using bo h sho - e m and long- e m in e es a es o 14 OECD coun ies, we ind ample e idence suppo ing he exis ence o a long- un Fishe effec in which in e es a es mo e one- o-one wi h in la ion. Ou esul s sugges ha he eason why he Fishe effec has no ound suppo in e na ionally lies on he es ima ion me hod. When he hypo hesis o a uni coefficien ela ing in e es a es o expec ed in la ionis es edwi hin heAu o eg essi eDis ibu edLag (ADL) amewo k, which is in a ian o he in eg a ion p ope ies o he da a, he Fishe effec easily su i es he empi ical e idence. Simila , bu less obus , esul s a e eached on he g ounds o he P e-Whi ened Fully Modi ied Leas Squa es (PW-FMLS) o he Johansen’s (JOH) es ima o s. JEL Classi ica ion: E40; E50; C12; C13; Keywo ds: Coin eg a ion Es ima o s; Fishe Effec ; ADL; DOLS; Small-sample p ope - ies Acknowledgmen s: Financial suppo om he G eek Minis y o Educa ion and he Eu- opean Union unde “H aklei os” g an is g ea ly app ecia ed. I am g a e ul o A. An zoula os, S. Kaly i is, G.Ha dou elis, D. Mallia opulos, M. Roche, M. Hu ley, N.Pi is, D. Thomakos, E. Tza alis and semina pa icipan s a he IIIS Minicon e ence on In e na ional Financial In e- g a ion, Na ional Uni e si y o I eland and he Uni e si y o Peloponesse o help ul sugges ions and commen s. The usual disclaime applies. ∗Co espondence o: Eka e ini Panopoulou, Depa men o Economics, Na ional Uni e si y o I e- land Maynoo h, Co.Kilda e, Republic o I eland. E-mail: [email protected]. Tel: 00353 1 7083793. Fax: 00353 1 7083934. 1 1 In oduc ion A as li e a u e is de o ed o he size o he esponse o nominal in e es a es o changes in expec ed in la ion, b oadly known as he Fishe effec .1The mone a y neu ali y implica ions o diffe en Fishe effec alues unde lie his long-s anding in e es in he opic. Mo e speci ically, long- un supe neu ali y o money is associa ed wi h a coefficien ela ing in e es a es o expec ed in la ion equal o one, while a alue below uni y implies subs an ial long- un non-neu ali ies. In his ein, he s a iona i y o he ex-an e eal in e es a e has some impo an implica ions. As sugges ed by he s anda d consump ion asse p icing model, eal in e es a es should ollow he pa e n o consump ion g ow h, which is clea ly a s a iona y a iable. Mo eo e , he neoclassical g ow h heo y based on dynamic op- imiza ion o a ep esen a i e economic agen implies ha he eal a e should be cons an in he s eady s a e, being p opo ional o he ep esen a i e consume ’s a e o ime p e e ence. Un o una ely he e is no consensus among economis s abou he ue size o he Fishe effec . The e a e se e al p oblems ha plague empi ical es i- ma es o he Fishe effec . Da by (1975) in oduced he effec o axes on he size o he Fishe effec . He a gued ha nominal in e es a es should inc ease by mo e han he inc ease in expec ed in la ion o compensa e deb holde s o a lowe a e - ax e- u n since in e es income is usually axed as o dina y income. In his case, we should ob ain a Fishe effec es ima e g ea e han one. A second p oblem is he gene ally unobse ed na u e o he expec ed in la ion a e. When ac ual ealized in la ion is used o p oxy expec ed in la ion an e o s-in- a iables bias is in oduced on he es ima e o he Fishe effec . Ano he issue in ol es he ime se ies p ope ies o he da a unde conside a ion when es ima ing a ela ionship like he Fishe effec . The only case ha s anda d leas squa es echniques a e alid is when he se ies a e second-o de s a ion- a y. In he e en o in eg a ed a iables, he only way o es ablish a heo e ical Fishe ela ionship is ia coin eg a ion echniques. Finally, e en when applying he app op ia e coin eg a ion me hods, se e e p ob- lems may a ise associa ed wi h he implemen a ion o coin eg a ion, such as he low powe o coin eg a ion es s o he pe o mance o he a ious es ima o s in small samples. C owde and Hoffman (1996) sugges ed ha he es ima o choice migh accoun o he con adic o y e idence in he li e a u e. Speci ically, he au ho s a - ibu e he diffe en conclusions eached in he li e a u e ega ding he ela ionship be ween in la ion and in e es a es o he diffe ences in he small sample p ope ies o he O dina y Leas Squa es (OLS), he Dynamic Leas Squa es (DOLS) and he Johansen’s (JOH) maximum likelihood es ima o s. Mo e ecen ly, Capo ale and Pi is (2004) show ha he es ima o s equen lyemployedinempi icals udies,namelyOLS and Fully Modi ied Leas Squa es (FMLS), a e he ones wi h he leas desi able small 1See e.g. Coo ay, 2003 and he e e ences he ein. 2 sample p ope ies. The inabili y o hese es ima o s o p o ide efficien es ima es in small samples is likely o be esponsible o he o e ejec ion o he Fishe hypo hesis. Speci ically, he au ho s show ha when he es ima o s wi h he bes p ope ies a e chosen, he e idence is s ongly suppo i e o he Fishe effec in he US. In his s udy, we use bo h sho - e m and long- e m in e es a es and p o ide in e na ional e idence on a long- un Fishe effec , i.e. ha in e es a es and in la ion mo e one- o-one in he long- un o 14 OECD coun ies. Using a a ie y o asymp o - ically efficien coin eg a ion es ima o s we a emp o explain he Fishe effec puzzle in e ms o es ima o choice. We a ibu e he sca ce e idence o an in e na ional Fishe effec in he li e a u e o he poo small sample pe o mance o he es ima o s employed so a . We pa icula ly ocus on wo ypes o coin eg a ion es ima o s ha a ise in he con ex o he Hend y-s yle Au o eg essi e Dis ibu ed Lag (ADL) models. The i s ype is usually e e ed o as he DOLS es ima o (see S ock and Wa son, 1993) and a ises om a s a ic coin eg a ion equa ion augmen ed by cu en and pas alues o he i s diffe ence o he eg esso . The second ype, he ADL es ima o (see Pesa an and Shin, 1999), is based on he p ojec ion o he coin eg a ion e o on he ull in o ma ion se , i.e. he cu en and pas alues o he i s diffe ence o he eg esso plus he pas alues o he coin eg a ion e o . In an ex ensi e Mon e Ca lo s udy, Panopoulou and Pi is (2004) highligh ed he po en ial pi alls o employing he DOLS es ima o as opposed o he ADL one in small samples o a wide a ie y o Da a Gene a ion P ocesses (DGPs). The au ho s showed ha he ADL es ima o , which u ilizes he exac p ojec ion o he coin eg a ion e o on he ull in o ma ion se , offe s a be e amewo k o es ima ing he coin eg a ion ec o han he DOLS es ima o ha u ilizes an app oxima e p ojec ion o he coin eg a ion e o on in o ma ion p o- ided only by he e o ha d i es he eg esso . To his end, he beha io o he ADL es ima o seems o be he limi ing one o he DOLS es ima o . Fo compa ison pu poses, we also include some o he commonly used coin eg a ion es ima o s, such as he OLS and he semipa ame ic FMLS es ima o o Phillips and Hansen (1990) and he Johansen’s maximum likelihood es ima o (1988, 1991). The layou o his pape is as ollows: Sec ion 2 p o ides a b ie li e a u e e iew on he Fishe effec and a discussion o he Fishe equa ion. Sec ion 3 ou lines he econo- me ic me hodology used in he empi ical analysis. Sec ion 4 p esen s es ima es o he Fishe equa ion ob ained by he ADL and DOLS es ima o s o bo h ou da ase s, along wi h es ima es ob ained om he OLS, FMLS and JOH es ima o s. Sec ion 5 summa izes he main indings o he pape . 2 B ie li e a u e e iew Ex an e eal in e es a es appea o be a key a iable when in es men - sa ings decisions and asse p ices de e mina ion a e conside ed. Thei long- un beha io is 3 o en analyzed in he con ex o he Fishe (1930) ela ionship, linking nominal a es o expec ed in la ion and equi ing ull adjus men o he o me o he la e . The impo ance o his adjus men p ocess s ems om he ac ha pe manen shocks o ei he in la ion o nominal a es should no be ansla ed in o pe manen dis u bances o eal a es hemsel es, which would be p oblema ic in he con ex o s anda d models o in e empo al asse p icing. Howe e , hus a he empi ical e idence has no been suppo i e o he Fishe ela ionship. Nume ous s udies ha e ound ha he slope coefficien in a eg ession o in la ion agains nominal a es is signi ican ly diffe en om one, a leas o e ce ain pe iods, (see e.g. Mishkin 1992 and E ans and Lewis, 1995). Fo mally, he ‘Fishe effec ’ can be exp essed as: i (m)=πe (m)+ e (m)(1) whe e i (m)is he m-pe iod nominal in e es a e a ime , πe (m)deno es he expec ed a e o in la ion om ime o +m,and e (m)is he ex-an e eal in e es a e. Assuming a ional expec a ions (see, e.g. Mishkin, 1992), ealized in la ion is linked o expec ed in la ion as ollows: π (m)=πe (m)+e (2) whe e e is a whi e noise p ocess, o hogonal o πe (m).I we u he assume ha he p ocess ollowed by he eal in e es a e is a whi e noise p ocess wi h a mean equal o , wea eable o es o heFishe effec in he con ex o he ollowing eg ession: i (m)= +θπ (m)+ν (3) The null hypo hesis o be es ed can ake he o m: Fishe hypo hesis holds ⇔(i) ν is I(0) and (ii) θ=1. The i s o hese condi ions, i.e. he condi ion ha i (m)and π (m)a e coin e- g a ed p ocesses is suppo ed by he bulk o empi ical e idence in he li e a u e. On he o he hand, when dealing wi h he second condi ion, es ima es o θappea o be signi ican ly diffe en om uni y, leading o he Fishe effec puzzle. Mishkin (1992) was one o he i s o sugges ha due o he appa en non- s a iona i y o nominal in e es a es and in la ion a possible sou ce o he low Fishe effec es ima es is he spu ious eg ession p oblem discussed by G ange and Newbold (1974). He co ec ly poin ed ou ha he Fishe ela ion should be ea ed wi hin he con ex o a coin eg a ed sys em, as in Engle and G ange (1987). Mishkin used he Engle-G ange OLS p ocedu e o es ima e he Fishe effec bu did no de i e any s ong conclusions due o he la ge s anda d e o s o he es ima ed pa ame e s. Subsequen s udies used mo e efficien es ima ion p ocedu es and gene ally ound 4 suppo o a long- un Fishe ela ion in he U.S. E ans and Lewis (1995) used he DOLS es ima o and C owde and Hoffman (1996) used he Johansen gaussian maxi- mum likelihood es ima o . C owde and Hoffmann (1996) sugges ed ha he es ima o choice migh accoun o he con adic o y e idence ga he ed so a . In pa icula , he au ho s a gue ha diffe ences in he small sample p ope ies o he OLS, DOLS and JOH es ima o s a e esponsible o he as ly diffe en conclusions eached in he li - e a u e abou he ela ionship be ween in la ion and in e es a es. Thei analysis, howe e , was much mo e limi ed han ou s as hey compa ed only h ee es ima o s in e ms o small sample bias. Mo e ecen ly, A kins and Coe (2002) ound e idence suppo ing he long- un Fishe effec o bo h Canada and he US using a a ie y o in e es a es and he ARDL bounds es de eloped by Pesa an e .al (2001) which is capable o es ing o he exis ence o a long- un ela ionship ega dless o he in eg a ion p ope ies o he unde lying se ies. Fahmy and Kandil (2003) con i med ha in la ion and in e es a es exhibi common ends in he long- un and mo e in a one- o-one ela ion a long ho i- zons, speci ically when he asse s’ ma u i y exceeds wo yea s. Thei da ase includes, excep o US, UK, Ge many and Swi ze land. Capo ale and Pi is (2004) employed i ually all a ailable single-equa ion es i- ma o s and allowed o al e na i e da a equencies along wi h s uc u al b eaks.2 The au ho s examined whe he (i) diffe ences in he es ima e o θ om one can be a - ibu ed o small sample bias and (ii) ejec ions o he null e lec he use o asymp o ic c i ical alues a he han he empi ical ones. They ound e idence in a o o bo h claims, which implies ha he Fishe hypo hesis su i es e en when less sa is ac o y es ima o s a e employed p o ided ha he empi ical c i ical alues a e used. Choosing he es ima o wi h he minimum bias and shi in he dis ibu ion o he associa ed -s a is ics, alid in e ence can be conduc ed in suppo o he Fishe iden i y. Howe e , hei s udy was con ined o he US, which is he coun y usually employed in empi ical s udies on he Fishe hypo hesis. The e is some e idence, hough, on he nominal in e es a es and in la ion ela ionship in o he indus ialized coun ies. Tes - ing whe he he Fishe ela ionship holds in e na ionally is o in e es since a necessa y, bu no sufficien , condi ion o eal in e es a es o be equalized in e na ionally is ha he Fishe ela ion holds in each coun y indi idually. Rose (1988) examined he in- eg a ion p ope ies o nominal in e es a es and in la ion o 18 OECD coun ies. He concluded ha in la ion does no appea o ha e a uni oo , while nominal in- e es a es do. By con as , Kous as and Se le is (1999) examined 10 indus ialized coun ies and es ablished ha he condi ions o meaning ul Fishe effec s, i.e. ha in la ion and in e es a es a e I(1) and coin eg a ed p ocesses, hold. The au ho s, 2These coin eg a ion es ima o s (mos o which a e asymp o ically efficien ) deal wi h he second o de effec s (long- un co ela ion and endogenei y effec ) p esen in he OLS asymp o ic dis ibu ion, ei he pa ame ically o non-pa ame ically. 5 howe e , we e no able o p o ide s ong e idence in suppo o he Fishe hypo hesis, i.e. o es ablish a uni coefficien . 3 Econome ic Me hodology In his sec ion, we conside wo asymp o ically efficien coin eg a ion es ima o s on which ou analysis is based, namely he ADL and DOLS es ima o s. The la e is a widely-used coin eg a ion es ima o sugges ed by Saikonnen (1991), Phillips and Lo e- an (1991) and S ock and Wa son (1993), while he i s de eloped by Pesa an and Shin (1999) is a ely employed in empi ical applica ions despi e i s supe io i y in many aspec s. Nex , we show how hese es ima o s a e de i ed and compa e hei p ope - ies. We also b ie ly discuss he OLS, FMLS and JOH es ima o s. To acili a e he discussion, we employ he Phillips iangula ep esen a ion o a coin eg a ed sys em. Le z and u be wo bi a ia e p ocesses, wi h z =[y ,x ]>and u =[u1 ,u 2 ]>. We u he assume ha u is a VAR(1) p ocess, d i en by e =[e1 ,e 2 ]>and he gene a ing mechanism o y is gi en by he sys em y =θx +u1 (4) ∆x =u2 (5) Ãu1 u2 !=Ãa11 a12 a21 a22 !Ãu1 −1 u2 −1!+Ãe1 e2 !(6) and Ãe1 e2 !˜NIID"Ã0 0!Ãσ11 σ12 σ12 σ22 !# (7) o =1,2,...T. Bo h eigen alues o he ma ix A=[aij],i,j =1,2a e assumed o be less han one in modulus, in o de o y and x o be I(1) a iables, and he coin eg a ion e o o be an I(0) p ocess. The long- un co a iance ma ix Ωand he one-sided co a iance ma ix ∆,needed o de ine he asymp o ic nuisance pa ame e s, a e gi en by equa ions (8) and (9), espec i ely Ω=(I−A)−1Σ(I−A>)−1(8) ∆=G(I−A>)−1(9) whe e Σdeno es he inno a ions co a iance ma ix o he VAR and Gis he uncondi- ional co a iance ma ix o u gi en by, ecG =(I−A⊗A)−1 ecΣ(10) 6 An ea ly esul by S ock (1987) shows ha he OLS es ima o o θob ained om (4) is supe -consis en , ega dless o he p esence o empo al and/o con empo aneous co ela ion be ween he eg ession e o , u1 ,and he e o ha d i es he eg esso , u2 .On he o he hand, in gene al, he asymp o ic dis ibu ion o he OLS es ima o o θ alls ou side he Local Asymp o ic Mix u e o No mals (LAMN) amily and con ains nuisance pa ame e s. The eason o he p esence o non-s anda d asymp o ics is ha in he p esence o con empo aneous and empo al co ela ion be ween he elemen s o u , wo ypes o second-o de asymp o ic effec s a e p esen in he limi ing dis ibu ion o he OLS es ima o (see Phillips and Lo e an 1991): The i s is he nuisance pa a- me e , ω12/ω22 ha desc ibes he “long- un co ela ion” effec , due o non-diagonali y o he long un co a iance ma ix Ω=[ωij],i,j =1,2.The second is he nuisance pa ame e δ21 =P∞ k=0 E(u20u1k) ha desc ibes he “endogenei y” effec . In o de o emo e he second o de effec s pa ame ically, we mus employ a new eg ession model whose e o e m is o hogonal o u2 and u2 −i,i=1,2,.... This can be done by employing he condi ional expec a ion o u1 ei he on he cu en and pas alues o u2 o on he cu en and pas alues o u2 plus he pas alues o u1 .The i s and second condi ioning in o ma ion se s esul in he DOLS and ADL es ima o s, espec i ely. Nex , we show how hese es ima o s a e ac ually de i ed, s a ing om he la e . 3.1 The ADL es ima o The ull sys em (4) and (5) wi h e o s speci ied by (6) - (7), implies he ollowing condi ional densi y o y : D(y |x ,z0 −1,λ 1)=N(θ1x +c1y −1+c2x −1+c3x −2,σ2 )(11) whe e λ1≡(θ1,c 1,c 2,c 3,σ2 )and θ1=θ+σ12 σ22 (12) c1=a11 −a21 σ12 σ22 (13) c2=a12 −σ12 σ22 (a22 +1−a21θ)−a11θ(14) c3=(a22 σ12 σ22 −a12)(15) σ2 ν=σ11 −σ2 12 σ22 (16) This condi ional model can be w i en as he ADL(q, ) eg ession, wi h o de s (q, )= (1,2): y =θ1x +c1y −1+c2x −1+c3x −2+ν (17) 7 The new e o e m, , is now o hogonal o u2 ,u −1,u −2,...and i s a iance is gi en by (16). In he con ex o he ADL(1,2) model he coin eg a ion pa ame e θis equal o he long- un mul iplie o y wi h espec o x , ha is θ=θ1+c2+c3 1−c1 (18) We can es ima e (17) by OLS and hen use (18) o ob ain an efficien es ima e o θ. Howe e , addi ional compu a ions a e equi ed o ob ain he a iance o his es i- ma e (see Bane jee e . al. 1993). A mo e con enien app oach, p oposed by Bewley (1979), ans o ms he model (17) in such a way ha a poin es ima e o θand i s a iance can be ob ained di ec ly. A e some algeb aic manipula ion, model (17) can be equi alen ly w i en as: y =δ0∆y +θx +λ0∆x +λ1∆x −1+η (19) whe e δ0=−c1 (1−c1)λ0=−c2+c3 (1−c1)λ1=−c3 (1−c1)η =1 (1−c1)ν Es ima es o he coefficien s and hei s anda d e o s can be ob ained by using he Ins umen al Va iables (IV) es ima o , wi h he o iginal ma ix o eg esso s, i.e. he a iables in (17), being he ins umen al a iables (see Wickens and B eusch 1988). This means ha he ADL es ima o o θis e y easy o apply since i in ol es only IV es ima ion echniques. 3.2 The DOLS es ima o The ADL model, de i ed abo e, may be hough o as a ising om p ojec ing u1 on he ull in o ma ion se B=(u2 ,u −1,u −2,...), ha is E(u1 |B)=σ12 σ22 e2 +a11u1 −1+a12u2 −1(20) As al eady men ioned, he second-o de effec s can be deal wi h by p ojec ing u1 on a subse o his se , namely A=(u2 ,u 2 −1,u 2 −2,...),A⊂B:The esul ing condi ional expec a ion in ol es an in ini e sum, E(u1 |A)= ∞ X i=0 βiu2 −i(21) whe e βia e unc ions o he pa ame e s in (6)-(7). This condi ional expec a ion does no admi a pa simonious ep esen a ion analogous o (20). On he o he hand, i allows o di ec subs i u ion o his exp ession in o (4), hus yielding he ollowing 8 model y =θx + ∞ X i=0 βi∆x −i+υ (22) whe e υ is, in gene al, a se ially co ela ed e o e m. In pa icula , υ ollows he AR(1) model υ =γ2υ −1+ε (23) whe e γ2is he MA coefficien in he ARMA (2,1) ep esen a ion o u2 .SimpleOLS applied o (22) yields he DOLS(p) es ima o o S ock and Wa son (1993), whe e p deno es he lag leng h o he i s diffe ences o he eg esso added o (22). The se ial co ela ion o υ does no aise any se ious p oblems in he es ima ion o θ,p o ided ha a consis en es ima o o he long- un a iance o υ is employed, such as he one p oposed by Newey and Wes (1987). Al e na i ely, he applica ion o Gene alized Leas Squa es (GLS) on (22), ensu es alid asymp o ic in e ences on θ.3In his case, he es ima o in use is he DGLS(p) one. In p ac ice, howe e , he second e m on he igh -hand side o (22) has o be eplaced by an app oxima ion in which he in ini e sum is unca ed a i=p.The esul ing model accommoda es a unca ion emainde ha is likely o inc ease he bias o he DOLS(p) es ima o o θ. This bias g ows wi h he pe sis ence o he coin e- g a ion e o . Inc easing he unca ion poin educes he DOLS bias, bu inc eases i s a iance. Mo eo e , es ima ing (22) by OLS is no easible i p is oo la ge compa ed o he sample size. Saikkonen (1991) speci ies an uppe bound o he a e a which p is allowed o inc ease wi h he sample size T, which is gi en by he condi ion p3/T →0. Ne e heless, his condi ion canno be used o de ine he op imal alue o p o any gi en sample size. On he con a y, he ADL es ima o does no accommoda e any unca ion emain- de and mo e impo an ly, yields consis en es ima es o he long- un coefficien s ha a e asymp o ically no mal i espec i e o whe he he unde lying eg esso s a e I(1) o I(0). Finally, i is easy o show ha he only case ha he ADL and DOLS es ima o s a e equi alen is his o a non-au oco ela ed e o in (4), which is a highly unlikely case in he case o mac oeconomic applica ions. Speci ically, he coin eg a ion e o is usually ound o exhibi a high deg ee o pe sis ence. 3.3 O he Coin eg a ion Es ima o s The OLS es ima o : This is he o dina y leas squa e es ima o applied o he s a ic equa ion (4). The Fully Modi ied Leas Squa es (FMLS) es ima o : Phillips and Hansen 3No e ha in he case o a linea eg ession which in ol es an I(1) s ic ly exogeneous eg esso , he OLS is asymp o ically equi alen o he GLS es ima o (see K ame 1986, Pa k and Phillips 1988). 9 imi a e he one o he DOLS class o es ima o s, while signi ican gains eme ge om he employmen o he p e-whi ened e sion o he FMLS es ima o . This es ima o pe o ms almos as well as he ADL one. On he o he hand, he pe o mance o JOH is a he ambiguous and leads o mixed esul s. The es ima es p oduced by his es ima o a e p obably biased upwa ds leading o es ima es ha in many cases exceed uni y signi ican ly. Re e ences [1]And ews, D.W.K. (1991), He e oskedas ici y and Au oco ela ion Consis en Co- a iance Ma ix Es ima ion. 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(1991), Asymp o ically efficien es ima ion o he coin eg a ing e- g essions, Econome ic Theo y,7,1,1-27. [35]S ock, J.H. (1987), Asymp o ic P ope ies o Leas Squa es Es ima o s o Coin e- g a ing Vec o s, Econome ica, 55, 1035-1056. [36]S ock, J.H. and M.W. Wa son (1993), A simple es ima o o coin eg a ing ec o s in highe -o de in eg a ed sys ems, Econome ica, 61, 783-820. [37]Wickens, M.R. and T.S. B eusch (1988), Dynamic Speci ica ion, he Long Run and he Es ima ion o T ans o med Reg ession Models, Economic Jou nal, 98, (Con e ence 1988), 189-205. 18 19 Appendix: Tables Table 1A: Es ima ion Resul s – Qua e ly sho - e m in e es a es Coun y Aus alia Belgium Canada Es ima o θ ˆ s.e ( θ ˆ) - es Ho: θ ˆ=1 θ ˆ s.e ( θ ˆ) - es Ho: θ ˆ=1 θ ˆ s.e ( θ ˆ) - es Ho: θ ˆ=1 OLS 0.411 0.107 -5.537 0.433 0.116 -4.873 0.598 0.118 -3.415 ADL(1,2) 0.721 0.272 -1.028 0.722 0.414 -0.671 0.959 0.199 -0.202 JOH 1.294 0.241 1.218 1.351 0.312 1.124 1.195 0.151 1.291 FMLS 0.499 0.190 -2.628 0.573 0.194 -2.204 0.677 0.138 -2.334 PW-FMLS 0.891 0.204 -0.532 0.971 0.373 -0.079 1.101 0.188 0.535 DOLS 1 0.510 0.121 -4.069 0.509 0.152 -3.235 0.695 0.126 -2.417 DOLS 2 0.563 0.130 -3.360 0.540 0.170 -2.704 0.756 0.132 -1.853 DOLS 3 0.584 0.136 -3.053 0.551 0.183 -2.456 0.786 0.134 -1.592 DOLS 4 0.592 0.141 -2.903 0.548 0.189 -2.389 0.799 0.136 -1.481 DOLS 5 0.597 0.146 -2.770 0.549 0.193 -2.337 0.810 0.135 -1.408 DOLS 6 0.603 0.151 -2.639 0.555 0.190 -2.340 0.813 0.134 -1.391 DOLS 7 0.616 0.155 -2.485 0.570 0.183 -2.350 0.819 0.133 -1.360 DOLS 8 0.629 0.157 -2.365 0.590 0.173 -2.379 0.823 0.133 -1.329 DOLS 9 0.647 0.160 -2.212 0.608 0.166 -2.360 0.835 0.133 -1.235 DOLS 10 0.669 0.162 -2.047 0.620 0.169 -2.244 0.843 0.135 -1.164 DOLS 11 0.692 0.162 -1.897 0.622 0.177 -2.138 0.854 0.137 -1.071 DOLS 12 0.713 0.161 -1.784 0.615 0.185 -2.078 0.862 0.140 -0.991 DOLS 13 0.732 0.160 -1.670 0.617 0.196 -1.959 0.875 0.141 -0.887 DOLS 14 0.754 0.159 -1.546 0.636 0.203 -1.796 0.886 0.142 -0.804 DOLS 15 0.772 0.157 -1.446 0.659 0.211 -1.614 0.895 0.143 -0.734 DOLS 16 0.792 0.156 -1.337 0.687 0.219 -1.426 0.905 0.143 -0.668 DOLS 17 0.811 0.153 -1.233 0.732 0.224 -1.197 0.916 0.142 -0.594 DOLS 18 0.832 0.152 -1.106 0.776 0.225 -0.994 0.923 0.140 -0.554 DOLS 19 0.847 0.152 -1.008 0.813 0.224 -0.835 0.927 0.136 -0.542 DOLS 20 0.853 0.152 -0.968 0.853 0.218 -0.675 0.927 0.133 -0.549 DGLS 1 -0.021 0.055 -18.589 0.095 0.057 -15.950 0.116 0.050 -17.871 DGLS 2 0.153 0.084 -10.139 0.228 0.083 -9.290 0.253 0.074 -10.034 DGLS 3 0.289 0.114 -6.244 0.411 0.108 -5.470 0.406 0.104 -5.735 DGLS 4 0.368 0.132 -4.798 0.368 0.125 -5.075 0.505 0.124 -3.999 DGLS 5 0.364 0.149 -4.259 0.160 0.149 -5.658 0.643 0.137 -2.609 DGLS 6 0.299 0.164 -4.268 0.101 0.165 -5.464 0.581 0.155 -2.702 DGLS 7 0.267 0.182 -4.035 0.056 0.179 -5.277 0.634 0.168 -2.185 DGLS 8 0.184 0.200 -4.076 0.113 0.190 -4.661 0.609 0.179 -2.181 DGLS 9 0.050 0.223 -4.259 0.205 0.201 -3.965 0.706 0.183 -1.613 DGLS 10 0.072 0.240 -3.868 0.325 0.211 -3.198 0.657 0.194 -1.769 DGLS 11 0.195 0.247 -3.263 0.401 0.223 -2.683 0.671 0.203 -1.623 DGLS 12 0.270 0.254 -2.876 0.320 0.233 -2.921 0.609 0.217 -1.807 DGLS 13 0.186 0.275 -2.962 0.179 0.240 -3.417 0.641 0.220 -1.628 DGLS 14 0.376 0.264 -2.361 0.126 0.251 -3.488 0.686 0.227 -1.383 DGLS 15 0.395 0.270 -2.238 0.006 0.267 -3.717 0.629 0.244 -1.520 DGLS 16 0.361 0.285 -2.242 -0.161 0.281 -4.128 0.640 0.254 -1.421 DGLS 17 0.366 0.294 -2.157 -0.255 0.301 -4.170 0.769 0.241 -0.961 DGLS 18 0.498 0.284 -1.772 -0.145 0.319 -3.584 0.837 0.239 -0.683 DGLS 19 0.612 0.278 -1.396 -0.271 0.347 -3.664 0.857 0.244 -0.586 DGLS 20 0.468 0.311 -1.710 -0.169 0.373 -3.135 0.783 0.262 -0.828 No es 1. The Newey and Wes (1987) me hod is employed in he DOLS(p) es ima o . 2. An AR(1) model is assumed o he e o s in he DGLS(p) es ima o . 20 Table 1B: Es ima ion Resul s – Qua e ly sho - e m in e es a es Coun y F ance Ge many I eland Es ima o θ ˆ s.e ( θ ˆ) - es Ho: θ ˆ=1 θ ˆ s.e ( θ ˆ) - es Ho: θ ˆ=1 θ ˆ s.e ( θ ˆ) - es Ho: θ ˆ=1 OLS 0.441 0.09 -6.185 0.444 0.095 -5.832 0.488 0.201 -2.544 ADL(1,2) 0.707 0.234 -1.249 0.787 0.366 -0.579 1.278 0.668 0.416 JOH 0.918 0.187 -0.440 1.575 0.157 3.671 1.535 0.854 0.626 FMLS 0.438 0.130 -4.336 0.526 0.157 -3.021 0.749 0.403 -0.621 PW-FMLS 0.627 0.228 -1.637 1.339 0.178 1.910 1.248 0.525 0.471 DOLS 1 0.475 0.094 -5.591 0.631 0.123 -2.995 0.687 0.260 -1.203 DOLS 2 0.492 0.098 -5.168 0.881 0.148 -0.805 0.820 0.269 -0.668 DOLS 3 0.500 0.104 -4.833 0.982 0.163 -0.109 0.840 0.312 -0.511 DOLS 4 0.499 0.110 -4.547 0.968 0.169 -0.192 0.773 0.330 -0.688 DOLS 5 0.505 0.116 -4.284 0.938 0.174 -0.355 0.795 0.310 -0.662 DOLS 6 0.507 0.120 -4.106 0.907 0.176 -0.528 0.814 0.307 -0.604 DOLS 7 0.512 0.122 -3.991 0.876 0.179 -0.693 0.816 0.314 -0.584 DOLS 8 0.521 0.123 -3.900 0.831 0.179 -0.948 0.904 0.307 -0.312 DOLS 9 0.530 0.122 -3.840 0.786 0.183 -1.169 1.047 0.320 0.148 DOLS 10 0.538 0.122 -3.780 0.749 0.191 -1.313 1.188 0.305 0.616 DOLS 11 0.547 0.123 -3.679 0.719 0.196 -1.430 1.237 0.305 0.777 DOLS 12 0.552 0.125 -3.590 0.669 0.193 -1.714 1.248 0.312 0.795 DOLS 13 0.551 0.125 -3.587 0.634 0.192 -1.910 1.318 0.302 1.054 DOLS 14 0.551 0.126 -3.581 0.617 0.195 -1.969 1.315 0.310 1.016 DOLS 15 0.556 0.128 -3.471 0.609 0.197 -1.987 1.294 0.315 0.932 DOLS 16 0.561 0.133 -3.307 0.579 0.198 -2.127 1.347 0.331 1.049 DOLS 17 0.563 0.139 -3.156 0.554 0.205 -2.181 1.358 0.313 1.142 DOLS 18 0.567 0.143 -3.035 0.529 0.213 -2.210 1.400 0.299 1.337 DOLS 19 0.577 0.145 -2.912 0.522 0.224 -2.135 1.498 0.283 1.760 DOLS 20 0.588 0.146 -2.824 0.504 0.231 -2.151 1.589 0.297 1.984 DGLS 1 0.272 0.073 -10.039 -0.045 0.042 -24.719 -0.167 0.263 -4.440 DGLS 2 0.410 0.096 -6.166 -0.057 0.078 -13.505 -0.307 0.429 -3.046 DGLS 3 0.584 0.114 -3.637 0.586 0.139 -2.980 0.865 0.577 -0.233 DGLS 4 0.501 0.128 -3.903 0.758 0.170 -1.422 1.112 0.577 0.195 DGLS 5 0.548 0.143 -3.165 0.772 0.195 -1.172 1.205 0.576 0.357 DGLS 6 0.503 0.155 -3.205 0.766 0.212 -1.103 1.208 0.579 0.360 DGLS 7 0.458 0.168 -3.232 0.867 0.230 -0.578 1.717 0.740 0.969 DGLS 8 0.477 0.175 -2.987 0.796 0.241 -0.849 1.673 0.714 0.942 DGLS 9 0.500 0.180 -2.784 0.716 0.244 -1.168 1.662 0.709 0.933 DGLS 10 0.476 0.189 -2.780 0.667 0.251 -1.328 1.664 0.689 0.964 DGLS 11 0.550 0.190 -2.369 0.753 0.261 -0.948 1.728 0.702 1.037 DGLS 12 0.637 0.195 -1.862 0.622 0.255 -1.482 1.676 0.746 0.905 DGLS 13 0.624 0.201 -1.871 0.541 0.252 -1.820 1.804 0.803 1.001 DGLS 14 0.565 0.210 -2.073 0.491 0.260 -1.957 1.913 0.849 1.075 DGLS 15 0.588 0.215 -1.916 0.520 0.267 -1.800 1.687 0.960 0.716 DGLS 16 0.609 0.218 -1.794 0.500 0.283 -1.766 1.985 1.014 0.971 DGLS 17 0.580 0.226 -1.857 0.475 0.294 -1.787 2.115 1.096 1.017 DGLS 18 0.550 0.237 -1.900 0.419 0.308 -1.885 2.431 1.227 1.166 DGLS 19 0.525 0.247 -1.922 0.440 0.322 -1.742 2.506 1.298 1.161 DGLS 20 0.480 0.263 -1.980 0.417 0.334 -1.746 2.441 1.200 1.201 No es 1. The Newey and Wes (1987) me hod is employed in he DOLS(p) es ima o . 2. An AR(1) model is assumed o he e o s in he DGLS(p) es ima o . 21 Table 1C: Es ima ion Resul s – Qua e ly sho - e m in e es a es Coun y I aly Ne he lands No way Es ima o θ ˆ s.e ( θ ˆ) - es Ho: θ ˆ=1 θ ˆ s.e ( θ ˆ) - es Ho: θ ˆ=1 θ ˆ s.e ( θ ˆ) - es Ho: θ ˆ=1 OLS 0.480 0.122 -4.252 0.415 0.084 -6.964 0.547 0.106 -4.255 ADL(1,2) 0.999 0.239 -0.003 0.902 0.209 -0.469 1.135 0.573 0.235 JOH 1.014 0.164 0.088 0.998 0.190 -0.009 1.425 0.196 2.164 FMLS 0.594 0.108 -3.758 0.524 0.140 -3.405 0.795 0.177 -1.155 PW-FMLS 0.772 0.182 -1.250 0.806 0.192 -1.006 1.245 0.220 1.105 DOLS 1 0.532 0.119 -3.937 0.505 0.099 -5.027 0.712 0.143 -2.012 DOLS 2 0.568 0.113 -3.820 0.546 0.109 -4.174 0.799 0.164 -1.226 DOLS 3 0.595 0.101 -4.011 0.566 0.114 -3.827 0.855 0.173 -0.844 DOLS 4 0.615 0.091 -4.231 0.579 0.114 -3.676 0.876 0.171 -0.724 DOLS 5 0.634 0.081 -4.497 0.587 0.112 -3.689 0.911 0.162 -0.550 DOLS 6 0.645 0.075 -4.706 0.598 0.108 -3.713 0.963 0.148 -0.249 DOLS 7 0.657 0.070 -4.885 0.610 0.105 -3.722 0.999 0.134 -0.010 DOLS 8 0.659 0.070 -4.842 0.620 0.101 -3.747 1.014 0.125 0.115 DOLS 9 0.662 0.073 -4.644 0.629 0.098 -3.776 1.035 0.123 0.282 DOLS 10 0.659 0.075 -4.557 0.642 0.096 -3.737 1.056 0.124 0.451 DOLS 11 0.657 0.076 -4.499 0.659 0.094 -3.625 1.068 0.125 0.544 DOLS 12 0.659 0.076 -4.512 0.673 0.092 -3.542 1.071 0.126 0.562 DOLS 13 0.664 0.075 -4.490 0.689 0.092 -3.404 1.077 0.124 0.619 DOLS 14 0.673 0.074 -4.414 0.708 0.092 -3.186 1.094 0.118 0.790 DOLS 15 0.677 0.074 -4.343 0.729 0.093 -2.924 1.111 0.112 0.990 DOLS 16 0.676 0.076 -4.276 0.740 0.093 -2.779 1.115 0.109 1.055 DOLS 17 0.673 0.076 -4.313 0.748 0.095 -2.653 1.121 0.106 1.141 DOLS 18 0.671 0.077 -4.271 0.755 0.097 -2.533 1.129 0.102 1.270 DOLS 19 0.669 0.079 -4.187 0.764 0.098 -2.407 1.142 0.098 1.450 DOLS 20 0.673 0.079 -4.149 0.774 0.098 -2.301 1.148 0.097 1.522 DGLS 1 0.161 0.059 -14.144 0.174 0.045 -18.455 -0.014 0.045 -22.728 DGLS 2 0.235 0.101 -7.577 0.360 0.055 -11.606 -0.014 0.069 -14.757 DGLS 3 0.445 0.135 -4.105 0.423 0.070 -8.289 0.017 0.108 -9.076 DGLS 4 0.577 0.151 -2.812 0.511 0.082 -5.938 -0.074 0.130 -8.248 DGLS 5 0.666 0.154 -2.170 0.471 0.099 -5.357 -0.172 0.150 -7.816 DGLS 6 0.663 0.165 -2.043 0.458 0.113 -4.785 -0.164 0.175 -6.646 DGLS 7 0.791 0.180 -1.164 0.508 0.126 -3.903 0.076 0.201 -4.601 DGLS 8 0.853 0.179 -0.821 0.536 0.139 -3.327 0.165 0.218 -3.836 DGLS 9 0.949 0.199 -0.259 0.450 0.153 -3.603 0.214 0.239 -3.292 DGLS 10 1.094 0.225 0.418 0.365 0.170 -3.729 0.265 0.263 -2.793 DGLS 11 1.054 0.238 0.227 0.463 0.176 -3.048 0.517 0.294 -1.644 DGLS 12 0.958 0.223 -0.189 0.433 0.187 -3.041 0.310 0.315 -2.189 DGLS 13 0.931 0.224 -0.310 0.382 0.200 -3.086 -0.039 0.320 -3.252 DGLS 14 0.942 0.239 -0.243 0.429 0.206 -2.773 -0.145 0.343 -3.335 DGLS 15 0.951 0.243 -0.204 0.636 0.198 -1.833 -0.094 0.389 -2.811 DGLS 16 0.966 0.228 -0.148 0.794 0.206 -0.999 -0.160 0.416 -2.791 DGLS 17 0.965 0.232 -0.150 0.808 0.218 -0.884 -0.221 0.447 -2.732 DGLS 18 0.955 0.250 -0.179 0.764 0.226 -1.044 -0.394 0.480 -2.906 DGLS 19 0.956 0.264 -0.168 0.791 0.235 -0.891 1.176 0.232 0.760 DGLS 20 0.995 0.297 -0.016 0.776 0.244 -0.921 1.222 0.227 0.976 No es 1. The Newey and Wes (1987) me hod is employed in he DOLS(p) es ima o . 2. An AR(1) model is assumed o he e o s in he DGLS(p) es ima o . 22 Table 1D: Es ima ion Resul s – Qua e ly sho - e m in e es a es Coun y Po ugal Sweden Swi ze land Es ima o θ ˆ s.e ( θ ˆ) - es Ho: θ ˆ=1 θ ˆ s.e ( θ ˆ) - es Ho: θ ˆ=1 θ ˆ s.e ( θ ˆ) - es Ho: θ ˆ=1 OLS 0.517 0.114 -4.255 0.579 0.077 -5.466 0.596 0.089 -4.501 ADL(1,2) 1.107 0.258 0.416 0.975 0.399 -0.063 0.860 0.209 -0.669 JOH 1.254 0.129 1.976 1.352 0.147 2.394 1.344 0.125 2.758 FMLS 0.716 0.157 -1.802 0.864 0.156 -0.867 0.776 0.149 -1.503 PW-FMLS 1.051 0.187 0.273 1.259 0.188 1.378 1.256 0.169 1.516 DOLS 1 0.651 0.124 -2.808 0.772 0.094 -2.437 0.742 0.100 -2.573 DOLS 2 0.866 0.119 -1.125 0.891 0.099 -1.095 0.858 0.105 -1.349 DOLS 3 0.906 0.099 -0.946 0.970 0.100 -0.303 0.913 0.118 -0.737 DOLS 4 0.921 0.090 -0.880 0.992 0.100 -0.077 0.915 0.121 -0.702 DOLS 5 0.914 0.091 -0.941 1.009 0.098 0.094 0.906 0.124 -0.762 DOLS 6 0.913 0.093 -0.943 1.042 0.092 0.457 0.892 0.128 -0.840 DOLS 7 0.913 0.094 -0.927 1.070 0.091 0.777 0.880 0.136 -0.887 DOLS 8 0.927 0.094 -0.785 1.071 0.092 0.771 0.874 0.139 -0.910 DOLS 9 0.935 0.094 -0.694 1.072 0.093 0.775 0.874 0.141 -0.897 DOLS 10 0.934 0.095 -0.701 1.075 0.096 0.783 0.884 0.137 -0.850 DOLS 11 0.933 0.096 -0.697 1.077 0.097 0.794 0.876 0.133 -0.934 DOLS 12 0.934 0.098 -0.671 1.078 0.099 0.784 0.848 0.130 -1.170 DOLS 13 0.944 0.098 -0.569 1.078 0.101 0.778 0.820 0.130 -1.388 DOLS 14 0.950 0.098 -0.508 1.083 0.102 0.809 0.807 0.132 -1.471 DOLS 15 0.947 0.101 -0.531 1.093 0.102 0.909 0.791 0.134 -1.554 DOLS 16 0.942 0.106 -0.553 1.103 0.100 1.026 0.788 0.141 -1.503 DOLS 17 0.947 0.109 -0.493 1.114 0.096 1.191 0.774 0.154 -1.467 DOLS 18 0.962 0.110 -0.344 1.124 0.091 1.371 0.759 0.170 -1.414 DOLS 19 0.981 0.110 -0.168 1.131 0.088 1.491 0.742 0.185 -1.396 DOLS 20 0.992 0.110 -0.074 1.143 0.083 1.719 0.737 0.197 -1.336 DGLS 1 -0.032 0.043 -23.845 -0.026 0.048 -21.275 0.075 0.048 -19.282 DGLS 2 -0.065 0.088 -12.078 -0.116 0.077 -14.520 0.020 0.078 -12.616 DGLS 3 0.093 0.159 -5.707 0.013 0.121 -8.185 0.383 0.120 -5.142 DGLS 4 0.352 0.188 -3.442 0.045 0.149 -6.431 0.624 0.145 -2.594 DGLS 5 0.460 0.199 -2.718 -0.127 0.164 -6.886 0.659 0.169 -2.020 DGLS 6 1.054 0.125 0.431 -0.018 0.185 -5.509 0.647 0.185 -1.908 DGLS 7 1.101 0.134 0.749 0.275 0.218 -3.329 0.553 0.200 -2.236 DGLS 8 1.128 0.141 0.912 0.363 0.247 -2.582 0.499 0.214 -2.345 DGLS 9 1.159 0.149 1.065 0.223 0.271 -2.868 0.471 0.224 -2.365 DGLS 10 1.170 0.157 1.083 0.960 0.221 -0.182 0.568 0.240 -1.800 DGLS 11 1.198 0.173 1.143 1.059 0.212 0.279 0.684 0.261 -1.209 DGLS 12 1.177 0.166 1.064 1.077 0.220 0.349 0.652 0.277 -1.258 DGLS 13 1.158 0.161 0.984 1.077 0.223 0.345 0.491 0.284 -1.792 DGLS 14 1.181 0.179 1.013 1.054 0.218 0.248 0.461 0.299 -1.802 DGLS 15 1.249 0.215 1.161 0.988 0.237 -0.051 0.364 0.306 -2.078 DGLS 16 1.194 0.208 0.934 0.037 0.396 -2.434 0.386 0.325 -1.890 DGLS 17 1.184 0.217 0.848 -0.043 0.419 -2.487 0.335 0.344 -1.934 DGLS 18 1.219 0.230 0.950 1.036 0.224 0.161 0.317 0.366 -1.866 DGLS 19 1.158 0.224 0.706 1.125 0.184 0.678 0.220 0.378 -2.065 DGLS 20 1.190 0.255 0.746 1.183 0.155 1.183 0.029 0.396 -2.455 No es 1. The Newey and Wes (1987) me hod is employed in he DOLS(p) es ima o . 2. An AR(1) model is assumed o he e o s in he DGLS(p) es ima o . 23 Table 1E: Es ima ion Resul s – Qua e ly sho - e m in e es a es Coun y UK US Es ima o θ ˆ s.e ( θ ˆ) - es Ho: θ ˆ=1 θ ˆ s.e ( θ ˆ) - es Ho: θ ˆ=1 OLS 0.416 0.052 -11.337 0.696 0.092 -3.301 ADL(1,2) 0.912 0.137 -0.645 1.053 0.197 0.267 JOH 1.092 0.105 0.874 1.451 0.174 2.599 FMLS 0.583 0.119 -3.503 0.802 0.149 -1.326 PW-FMLS 0.926 0.149 -0.493 1.218 0.165 1.322 DOLS 1 0.602 0.081 -4.933 0.783 0.100 -2.163 DOLS 2 0.691 0.090 -3.455 0.846 0.109 -1.414 DOLS 3 0.746 0.102 -2.493 0.872 0.114 -1.121 DOLS 4 0.748 0.101 -2.488 0.887 0.122 -0.931 DOLS 5 0.751 0.101 -2.472 0.900 0.129 -0.779 DOLS 6 0.764 0.097 -2.440 0.917 0.134 -0.618 DOLS 7 0.777 0.091 -2.461 0.930 0.140 -0.502 DOLS 8 0.781 0.088 -2.491 0.947 0.146 -0.363 DOLS 9 0.783 0.088 -2.478 0.962 0.148 -0.256 DOLS 10 0.779 0.089 -2.481 0.977 0.150 -0.156 DOLS 11 0.780 0.089 -2.478 0.990 0.154 -0.066 DOLS 12 0.780 0.089 -2.456 1.004 0.157 0.024 DOLS 13 0.781 0.090 -2.442 1.012 0.158 0.077 DOLS 14 0.781 0.090 -2.427 1.025 0.158 0.161 DOLS 15 0.781 0.090 -2.431 1.037 0.160 0.231 DOLS 16 0.783 0.090 -2.408 1.056 0.161 0.346 DOLS 17 0.786 0.090 -2.390 1.077 0.163 0.471 DOLS 18 0.783 0.092 -2.372 1.089 0.165 0.540 DOLS 19 0.779 0.094 -2.348 1.096 0.166 0.581 DOLS 20 0.775 0.096 -2.333 1.110 0.168 0.654 DGLS 1 0.041 0.036 -26.561 0.158 0.059 -14.185 DGLS 2 0.120 0.052 -16.974 0.357 0.094 -6.871 DGLS 3 0.460 0.075 -7.241 0.549 0.116 -3.900 DGLS 4 0.440 0.087 -6.462 0.616 0.133 -2.888 DGLS 5 0.396 0.096 -6.296 0.634 0.143 -2.560 DGLS 6 0.371 0.110 -5.738 0.718 0.152 -1.863 DGLS 7 0.578 0.121 -3.478 0.687 0.162 -1.936 DGLS 8 0.710 0.120 -2.413 0.737 0.170 -1.547 DGLS 9 0.835 0.118 -1.402 0.761 0.179 -1.339 DGLS 10 0.736 0.132 -1.996 0.746 0.192 -1.324 DGLS 11 0.712 0.146 -1.972 0.704 0.208 -1.423 DGLS 12 0.789 0.142 -1.491 0.827 0.214 -0.809 DGLS 13 0.800 0.146 -1.373 0.826 0.225 -0.772 DGLS 14 0.852 0.145 -1.020 0.877 0.233 -0.528 DGLS 15 0.892 0.151 -0.716 0.772 0.257 -0.887 DGLS 16 0.907 0.160 -0.584 0.718 0.277 -1.021 DGLS 17 0.890 0.161 -0.686 0.981 0.253 -0.074 DGLS 18 0.885 0.162 -0.709 1.075 0.257 0.291 DGLS 19 0.910 0.172 -0.524 1.025 0.270 0.092 DGLS 20 0.962 0.200 -0.191 1.026 0.279 0.092 No es 1. The Newey and Wes (1987) me hod is employed in he DOLS(p) es ima o . 2. An AR(1) model is assumed o he e o s in he DGLS(p) es ima o . 24 Table 2A: Es ima ion Resul s – Annual long- e m in e es a es Coun y Aus alia Belgium Canada Es ima o θ ˆ s.e ( θ ˆ) - es Ho: θ ˆ=1 θ ˆ s.e ( θ ˆ) - es Ho: θ ˆ=1 θ ˆ s.e ( θ ˆ) - es Ho: θ ˆ=1 OLS 0.251 0.185 -4.062 0.450 0.165 -3.345 0.574 0.151 -2.821 ADL(1,2) 1.166 0.353 0.469 0.761 0.356 -0.672 1.032 0.254 0.126 JOH 1.561 0.313 1.792 1.779 0.372 2.093 1.068 0.178 0.384 FMLS 0.368 0.170 -3.717 0.714 0.128 -2.241 0.900 0.215 -0.464 PW-FMLS 1.337 0.296 1.140 1.007 0.203 0.032 1.234 0.205 1.142 DOLS 1 0.314 0.197 -3.488 0.535 0.193 -2.415 0.661 0.141 -2.398 DOLS 2 0.507 0.160 -3.083 0.598 0.214 -1.879 0.734 0.144 -1.841 DOLS 3 0.623 0.172 -2.190 0.641 0.210 -1.713 0.826 0.148 -1.175 DOLS 4 0.687 0.178 -1.761 0.710 0.202 -1.434 0.856 0.132 -1.092 DOLS 5 0.745 0.173 -1.472 0.760 0.178 -1.344 0.882 0.107 -1.097 DOLS 6 0.814 0.149 -1.249 0.827 0.140 -1.238 0.909 0.082 -1.099 DOLS 7 0.898 0.125 -0.817 0.887 0.108 -1.043 0.932 0.080 -0.856 DOLS 8 0.955 0.106 -0.429 0.914 0.097 -0.890 0.961 0.089 -0.436 DOLS 9 1.019 0.090 0.209 0.949 0.089 -0.574 0.963 0.085 -0.438 DOLS 10 1.067 0.090 0.744 0.968 0.097 -0.334 0.964 0.089 -0.407 DOLS 11 1.106 0.083 1.284 0.962 0.119 -0.325 0.981 0.101 -0.193 DOLS 12 1.117 0.082 1.435 0.955 0.141 -0.321 0.989 0.104 -0.109 DOLS 13 1.125 0.097 1.286 0.924 0.171 -0.445 1.039 0.119 0.326 DOLS 14 1.144 0.117 1.230 0.911 0.197 -0.451 1.083 0.147 0.561 DOLS 15 1.146 0.153 0.954 0.856 0.215 -0.669 1.082 0.178 0.462 DOLS 16 1.151 0.154 0.981 0.781 0.211 -1.039 1.088 0.209 0.419 DOLS 17 1.176 0.160 1.098 0.820 0.235 -0.767 1.096 0.234 0.409 DOLS 18 1.192 0.165 1.162 0.883 0.254 -0.463 1.071 0.259 0.273 DOLS 19 1.271 0.182 1.491 1.030 0.312 0.097 1.110 0.333 0.330 DOLS 20 1.220 0.233 0.941 1.268 0.373 0.719 1.193 0.411 0.470 DGLS 1 0.174 0.058 -14.216 0.212 0.075 -10.572 0.234 0.083 -9.285 DGLS 2 0.298 0.089 -7.887 0.355 0.110 -5.882 0.441 0.110 -5.065 DGLS 3 0.315 0.115 -5.982 0.276 0.128 -5.635 0.579 0.130 -3.231 DGLS 4 0.388 0.137 -4.469 0.243 0.186 -4.079 0.633 0.161 -2.278 DGLS 5 0.385 0.161 -3.825 0.223 0.224 -3.479 0.700 0.163 -1.843 DGLS 6 0.448 0.174 -3.169 0.436 0.243 -2.327 0.791 0.173 -1.207 DGLS 7 0.659 0.174 -1.961 0.785 0.201 -1.071 0.859 0.160 -0.885 DGLS 8 0.808 0.143 -1.343 0.812 0.213 -0.886 0.916 0.104 -0.810 DGLS 9 0.955 0.104 -0.437 0.924 0.158 -0.480 0.925 0.101 -0.736 DGLS 10 1.050 0.079 0.634 1.046 0.163 0.284 0.971 0.125 -0.232 DGLS 11 1.110 0.075 1.472 1.088 0.175 0.501 0.988 0.131 -0.091 DGLS 12 1.113 0.082 1.378 0.971 0.189 -0.156 0.983 0.148 -0.116 DGLS 13 1.115 0.088 1.306 0.974 0.218 -0.122 1.058 0.163 0.358 DGLS 14 1.138 0.099 1.387 1.090 0.244 0.367 1.085 0.177 0.481 DGLS 15 1.141 0.105 1.337 1.036 0.268 0.133 1.088 0.197 0.448 DGLS 16 1.135 0.127 1.062 0.969 0.318 -0.099 1.126 0.241 0.523 DGLS 17 1.163 0.157 1.041 1.000 0.365 0.000 1.151 0.267 0.565 DGLS 18 1.170 0.192 0.885 1.015 0.456 0.033 1.196 0.334 0.586 DGLS 19 1.279 0.236 1.182 1.452 0.414 1.091 1.408 0.407 1.002 DGLS 20 1.334 0.267 1.252 1.912 0.414 2.205 1.579 0.530 1.092 No es 1. The Newey and Wes (1987) me hod is employed in he DOLS(p) es ima o . 2. An AR(1) model is assumed o he e o s in he DGLS(p) es ima o . 25 Table 2B: Es ima ion Resul s – Annual long- e m in e es a es Coun y F ance Ge many I eland Es ima o θ ˆ s.e ( θ ˆ) - es Ho: θ ˆ=1 θ ˆ s.e ( θ ˆ) - es Ho: θ ˆ=1 θ ˆ s.e ( θ ˆ) - es Ho: θ ˆ=1 OLS 0.334 0.151 -4.425 0.615 0.092 -4.196 0.551 0.054 -8.295 ADL(1,2) 0.767 0.283 -0.824 0.675 0.205 -1.587 0.686 0.127 -2.470 JOH 1.185 0.186 0.996 0.818 0.1383 -1.317 0.892 0.109 -0.993 FMLS 0.515 0.143 -3.397 1.136 0.277 0.490 0.833 0.156 -1.071 PW-FMLS 0.870 0.168 -0.772 1.622 0.303 2.052 1.047 0.158 0.299 DOLS 1 0.421 0.170 -3.398 0.645 0.098 -3.614 0.577 0.060 -7.064 DOLS 2 0.529 0.157 -3.002 0.662 0.119 -2.844 0.646 0.069 -5.138 DOLS 3 0.640 0.142 -2.541 0.613 0.130 -2.973 0.687 0.068 -4.588 DOLS 4 0.674 0.136 -2.392 0.574 0.147 -2.902 0.706 0.065 -4.554 DOLS 5 0.729 0.134 -2.032 0.604 0.151 -2.629 0.726 0.062 -4.440 DOLS 6 0.778 0.132 -1.687 0.618 0.144 -2.643 0.730 0.060 -4.520 DOLS 7 0.810 0.133 -1.424 0.653 0.145 -2.399 0.754 0.057 -4.337 DOLS 8 0.836 0.135 -1.218 0.705 0.131 -2.252 0.774 0.054 -4.195 DOLS 9 0.947 0.136 -0.389 0.766 0.119 -1.971 0.780 0.052 -4.208 DOLS 10 0.994 0.124 -0.049 0.813 0.135 -1.393 0.813 0.054 -3.446 DOLS 11 1.043 0.125 0.341 0.842 0.164 -0.963 0.842 0.056 -2.843 DOLS 12 1.082 0.134 0.614 0.811 0.200 -0.949 0.866 0.061 -2.188 DOLS 13 1.114 0.145 0.782 0.793 0.269 -0.768 0.864 0.075 -1.805 DOLS 14 1.105 0.147 0.715 0.847 0.322 -0.477 0.927 0.099 -0.732 DOLS 15 1.131 0.163 0.800 0.889 0.397 -0.281 0.884 0.119 -0.976 DOLS 16 1.131 0.161 0.814 0.852 0.480 -0.309 0.857 0.089 -1.611 DOLS 17 0.997 0.177 -0.020 0.769 0.474 -0.487 0.804 0.093 -2.116 DOLS 18 1.068 0.217 0.313 0.776 0.394 -0.569 0.806 0.094 -2.067 DOLS 19 1.178 0.227 0.784 1.149 0.248 0.599 0.727 0.124 -2.203 DOLS 20 1.478 0.255 1.872 1.141 0.216 0.652 0.755 0.164 -1.500 DGLS 1 0.147 0.063 -13.457 0.567 0.126 -3.436 0.319 0.087 -7.809 DGLS 2 0.255 0.089 -8.395 0.698 0.149 -2.036 0.367 0.108 -5.886 DGLS 3 0.392 0.117 -5.218 0.646 0.167 -2.128 0.534 0.110 -4.222 DGLS 4 0.372 0.140 -4.485 0.523 0.180 -2.651 0.612 0.104 -3.746 DGLS 5 0.441 0.171 -3.270 0.519 0.195 -2.464 0.683 0.095 -3.335 DGLS 6 0.639 0.184 -1.970 0.569 0.220 -1.965 0.675 0.095 -3.411 DGLS 7 0.695 0.191 -1.595 0.510 0.258 -1.896 0.699 0.081 -3.694 DGLS 8 0.777 0.134 -1.672 0.640 0.265 -1.361 0.738 0.071 -3.689 DGLS 9 0.857 0.143 -1.000 0.709 0.275 -1.058 0.751 0.070 -3.552 DGLS 10 0.891 0.173 -0.629 0.823 0.284 -0.625 0.795 0.069 -2.988 DGLS 11 0.968 0.146 -0.222 0.794 0.292 -0.706 0.820 0.074 -2.445 DGLS 12 1.028 0.132 0.212 0.769 0.318 -0.725 0.845 0.080 -1.952 DGLS 13 1.092 0.144 0.639 0.744 0.385 -0.665 0.844 0.092 -1.693 DGLS 14 1.060 0.175 0.343 0.730 0.420 -0.643 0.887 0.116 -0.976 DGLS 15 1.046 0.168 0.273 0.903 0.535 -0.181 0.863 0.099 -1.382 DGLS 16 1.104 0.196 0.530 1.017 0.578 0.030 0.834 0.110 -1.503 DGLS 17 1.049 0.247 0.200 0.976 0.500 -0.049 0.831 0.131 -1.296 DGLS 18 1.013 0.343 0.039 1.365 0.420 0.869 0.777 0.146 -1.532 DGLS 19 0.844 0.501 -0.310 1.590 0.571 1.035 0.759 0.188 -1.285 DGLS 20 1.108 0.533 0.202 1.273 0.526 0.520 0.928 0.191 -0.376 No es 1. The Newey and Wes (1987) me hod is employed in he DOLS(p) es ima o . 2. An AR(1) model is assumed o he e o s in he DGLS(p) es ima o .