Centralizing information improves market efficiency more than increasing information: Results from experimental asset markets

1 Cen alizing in o ma ion imp o es ma ke e iciency mo e han inc easing in o ma ion: Resul s om expe imen al asse ma ke s* I án Ba eda-Ta azonaa, 1 , Gianluca G imaldaa, c, And ea Mo one a, b, Simone Nuzzob, And ea Teglioa aLEE & Economics Depa men , Uni e si a Jaume I, Cas ellón, Spain b Dipa imen o di Economia, Managemen e Di i o d’imp esa, Uni e si à degli S udi di Ba i, Aldo Mo o, I aly c Ins i u ü Wel wi scha , Kiel, Ge many Abs ac We s udy he ela ionship be ween ma ke e iciency and he dis ibu ion o p i a e in o ma ion in expe imen al inancial asse ma ke s. T ade s ecei e impe ec signals o e he eal alue o an asse . Agen s can sha e hei in o ma ion wi hin a ela i ely small – compa ed o ma ke size - g oup o agen s. Bo h he numbe o signals and he way hese a e alloca ed among agen s a e manipula ed in ou expe imen al ea men s. In wo ea men s signals a e e enly dis ibu ed among agen s. In wo o he ea men s one g oup o ‘quasi-inside ’ agen s ecei es mo e signals han all o he g oups. In he baseline condi ion no signal is dis ibu ed. We show ha cen alizing in o ma ion unambiguously achie es highe ma ke e iciency han sp eading in o ma ion e enly. Fu he mo e, inc easing he amoun o in o ma ion has no e ec on e iciency ei he when in o ma ion is symme ic o when i is asymme ic. We a gue ha wo complemen a y mechanisms d i e hese esul s. Fi s , ha ing mo e p i a e in o ma ion ex an e induces ade s o ely on hei own signals, educing he expec ed bene i s o sha ing in o ma ion. Second, he p esence o quasi-inside being common knowledge p omp s agen s o ex ac mo e in o ma ion om ma ke p ices a he han hei own p i a e signals. This leads o swi in o ma ion agg ega ion. Key wo ds: Expe imen al Ma ke s; In o ma ion Agg ega ion; Ma ke Coope a ion * Financial suppo by Uni e si a Jaume I (p ojec P1.1B2015-48) and he Spanish Minis y o Economics and Compe i i eness (p ojec s ECO2013-44409-P and ECO2015-68469-R) is g a e ully acknowledged. 1 Co esponding au ho : LEE & Economics Depa men , Uni e si a Jaume I, 12071 Cas ellón, Spain. E-mail add ess: i an.ba [email protected]. 2 In oduc ion The capaci y o ma ke s o e icien ly agg e ga e p i a ely dispe sed in o ma ion has been a cen al opic in economics since Adam Smi h and on Hayek. In he con ex o inancial ma ke s, Fama (1965) de ines a ma ke as e icien whene e p ices " ully e eal" he in o ma ion dispe sed in he ma ke . In ui i ely, e iciency can be achie ed becau se ade s owning p i a e in o ma ion on he eal alue o an asse – so-called “inside s” - will seek o p o i whene e p ices do no ully embody hei own p i a e in o ma ion. I ma ke s a e e icien , inside s’ p i a e i n o ma ion is in he long un wo hless and inside s canno ealize highe gains han o he ade s. In he sho un, unin o med ade s can y o in e he exis ence o inside in o ma ion om he obse a ion o ading ac i i y, in o de o also ealize p o i s. This can ei he accele a e he p ocess o con e gence owa d he equi lib ium, o d i e i as ay i unin o med ade s a e mis aken i n hei in e ences, as he li e a u e on in o ma ional cascades demons a es (Bikhchandani e al., 1998). The expe imen al li e a u e has ex ensi ely examine d he condi ions a which inancial ma ke s achie e e iciency (see he nex sec ion o a e iew). Howe e , his is no mally done in se ings whe e agen s a e ei he ully in o med o no in o med, and ha e no connec ions wi h o he s. In his pape we gene alize on bo h o hese condi ions. We allow o all agen s o ha e impe ec in o ma ion and o some agen s – whom we call “quasi-inside s” - o ha e close- o-pe ec in o ma ion. We a y he o e all amoun o in o ma ion a ailable in he ma ke an d he way his is dis ibu ed among agen s. In pa icula , in a wo-by- wo desi gn, i n o ma ion is ei he equally dis ibu ed among ade s o is unequally dis ibu ed. In he la e case, “quasi-inside s” ecei e a highe amoun o in o ma ion han o he agen s. Mo eo e , he o e all quan i y o in o ma ion is also modi ied ac oss ou expe imen al condi ions. Secondly, we in oduce a simple ne wo k s uc u e in ou inancial ma ke s. Each agen is connec ed wi h wo o he agen s and each has he op ion o sha e hei own p i a e in o ma ion wi h he wo o he agen s i n hei g oup. The impo ance o ne wo ks in inancial ma ke s has been s essed bo h he o e ically and empi ically. Acco ding o Abou la ia, (1997), inancial ma ke s a e embedded in o a as and dense ne wo k o cus oma y codes o conduc s, mu ual expec a ion s o app op ia e beha io , and us among i ndi idual agen s. In ac , some accoun s s ess ha he b eakdown in he ne wo ks o us among inancial agen s played a majo ole in p ecipi a ing a nd 3 agg a a ing he 2008 inancial c isis (Ki man, 2010; Anand e al., 2013). Acco ding o his iew, inancial ma ke s may sha e some cha ac e is ics wi h s anda d ma ke s o goods, whe e social no ms and us ne wo ks can ca use he ac ual ma ke p ice o depa om he Wal a sian p ice (G ei , 1993). The e ec o us ne wo k in inancial ma ke s is a la gely unexplo ed issue. We a e he i s , o he bes o ou knowledge, o examine i expe imen ally. Ou main esea ch ques ion is whe he and how he amoun , dis ibu ion, and he sp eading o in o ma io n h ough he ne wo k, i nc ease ma ke e i ciency. Excep o he baseline c ondi ion whe e no a gen ecei es any in o ma ion, in all o he expe imen al condi ions all agen s ecei e some noisy signals on he undamen al alu e o he asse . Such signals only e eal he eal alue o he asse wi h 70% p ob abili y. We conside wo cases whe e each agen is ei he alloca ed he same numbe o signals as all o h e s o whe e some “q uasi-inside s” a e endowed wi h a la ge numbe o signals. The o e all numbe o signals dis ibu ed in he m a ke be o e an sac ions i s also manip ula ed ac oss expe imen al condi ions. Ou amewo k enables us o s udy wo di e en mechanisms o he di usion o in o ma ion in he ma ke . The i s is wha we call a “leade ship mechanism”, whe e i is common knowledge ha one g oup o quasi-inside s wi hin he ma ke owns ex an e mo e in o ma i e signals han all o he g oups. In some cases quasi-inside s can expec o know he eal alue o he asse wi h p obabili y g ea e han 95% 2 . We expec ha his mechanism will ha e impo an consequences on “in o ma ion di sclosu e” (see nex sec ion) and hus on ma ke e iciency. On he one ha nd, quasi-inside s will p esumably y o gain om hei in o ma ional ad an age, and hei ading ac i i y should, ce e is pa ibus, d i e he asse p ice in he di ec ion o he undamen al alue as e han i n o he cases. On he o he hand, les s in o med ade s may pay mo e a en ion o he p ice adjus men s wi hin h e ma ke , because he p esence o quasi- inside s should make hem awa e o he possi bili y ha p ices mo e in he di ec ion o he undamen al as e han in o he cases. The second channel is wha we call a “coope a ion mechanism”, whe eby agen s can sha e hei p i a e signal(s) wi hin g oups o med by h ee membe s, a nd can in 2 The e m “inside ” no mally ch a ac e izes ade s who know wi h p o babili y one he eal alue o he asse . S ince in ou s udy ade s h a ing in o ma ional ad an age can ne e be absolu ely ce ain o he eal alue o he asse , we p e e o call h em “quasi-inside s”. See also sec ion 2. 4 u n ecei e he in o ma ion sha ed by he o he wo membe s o hei g oup. This is done be o e ading s a s, so agen s can access he ma ke wi h a la ge numbe o pe capi a signals, i o he s in hei g oup ha e decided o sha e. In he coope a ion mechanism, in o ma ion is he e o e mul iplied i agen s decide o sha e. I coope a ion does occu , we expec ha ansac ions will become mo e in o ma i e and, in agg ega e, p ices may inco po a e he a ailable i n o ma ion. Manipula ing he quan i y o signals owned by quasi-inside s makes i possible o specula e o e he ela i e s eng h o hese wo ac o s. Ou expe imen al design includes a baseline condi ion whe e no in o ma ion is a ailable o agen s, and ou ea men condi ions ha a y bo h he amoun and he concen a ion o signals. In o ma ion is e enly dis ibu ed among agen s in wo o such ea men s,, bu he o al numbe o signals is ipled in one ea men compa ed o he o he . Tha is, in one ea men each agen ecei es one signal, while in he o he ea men each agen ecei es h ee signals. In wo o he condi ions in o ma ion is une enly dis ibu ed be ween one g oup o quasi-inside s and h ee g oups o non- inside s. In hese wo condi ions he o al numbe o si gnals is kep cons an . This enables us o e alua e he impac on e iciency o modi ying he dis ibu ion o signals om e en o une en. In o de o be e app ecia e he ele ance o each o he wo mechanisms illus a ed abo e, we d aw on wo di e en p ice benchma ks. The i s is he “Bayesian p ice”. This is he p ice ha would esul i all ade s agg ega ed he in o ma ion a hei disposal a ionally – namely, acco ding o he Bayes ule – a e ade s ha e decided whe he o sh a e hei signals wi hin hei g oup o no . Mo e p ecisely, indi idual Bayesian p ices a e compu ed o each ade , and he ma ke Bayesian p ice is calcula ed as he a i hme ic mean o such indi idual p ices. The second no ion is wha we call “Fama-ma ke e iciency”, and d aws on he idea se ou a he beginning o he pape ha p ices should inc o po a e all he in o ma ion p esen in he ma ke . Fo Fama-e iciency we do no conside signals being sha ed in he “ coope a ion s a ge”, bu we only conside he in o ma ion a ailable be o e such a s age. He e we compu e wha we call he “Fama-e icien ” p ice as ha esul ing om he assump ion ha each agen knew he whole in o ma ion p esen in he ma ke . We ind ha he “leade ship mechanism” unambiguously b ings abou mo e e iciency han he "coope a ion mechanism”. In e es ingly, we a lso ind ha inc easing 5 he quan i y o signals does no necessa ily lead o app eciable gains in e iciency. In pa icula , e iciency is no highe in he symme ic ea men ha ing h ice as many signals as he al e na i e symme ic ea men . Likewise, e icie ncy is no highe in he asymme ic ea men h a ing o e all wice as many signals as he al e na i e asymme ic ea men . None heless, he wo asymme ic ea men s b ing abou app eciably mo e e ici ency han he symme ic ones. We specula e ha he main d i e o hi s esul is non-inside s ex ac ing in o ma ion om ma ke p ices mo e ac i ely han in symme ic ea men s. Ou s udy is o in e es o he heo e ical issue o whe he ma ke s a e capable o e icien ly agg ega ing and dissemina ing p i a e in o ma ion. We inno a e on p e ious li e a u e (see n ex sec ion) by gene a lizing he s anda d a mewo k in he wo di ec ions men ioned abo e. Tha is, we allow o all agen s o ecei e impe ec signals, compa ing cases o equal dis ibu ion o he in o ma ion and unequal dis ibu ion. We also in oduce a ne wo k s uc u e whe eby agen s can sha e hei p i a e in o ma ion. We belie e ha ou s udy is al so ele an o policy issues. In es iga ing how ma ke e iciency is a ec ed by inc easing in o ma ion o sp eading i mo e e enly, and how in o ma ion sp eads wi hin ne wo ks, a e all impo an ques ions o he op imal managemen o inancial ma ke s. Bo h in no mal imes bu , e en mo e so, in imes o “c isis”, inancial au ho i ies may decide o elease addi ional pieces o in o ma ion o s abilize ma ke s. Ou expe imen al e ide nce may help unde s and how o do his op imally. The emain de o he pape is o ganized as ollows. I n he nex sec ion we p esen a e iew o ele an li e a u e and in he hi d sec ion he expe imen al design. In sec ion 4 we p esen he me hodology o he analysi s, hen in sec ion 5 we epo he esul s ob ained. Sec ions 6 discu sses he esul s and 7 conclude. 2 Rela ed Li e a u e Expe imen al s udie s dealing wi h in o ma ional e iciency a e ypically di ided in o h ee ypes. The i s one is he dissemina ion o in o ma ion om iden ically in o med agen s - no mally e e ed o as “inside s” - o unin o med ade s (Plo and Sunde , 1982). The second s and includes s udies abou in o ma ion agg ega ion among ma ke pa icipan s wi h less han pe ec i n o ma ion (Plo and Sunde , 1988). The hi d on e ocuses on h e simul aneous equilib ium in asse and in o ma i on ma ke s 6 (Sunde , 1992). Theo e ically, he i n o ma ion agg ega ion p ocess can be expec ed o be mo e sluggish in achie ing ma ke e iciency han he dissemina ion one. In he dissemina ion case inside s’ ansac ions elease unambi guous signals abou he alue o he asse , a leas w hen h e p esence o inside s is com mon knowledge. Con e sely, in h e agg ega ion case he p oce ss o e ie ing in o ma ion is by cons uc ion subjec o e o s. Consequen ly, making i n e ence on he ue s a e o he wo ld is mo e p ob lema i c in he la e case. Comp ehensi e ecen su eys on ex pe imen al inancial ma ke s can be ound in No ussai and Tucke ( 2013), and Mo one and Nuzzo (2016). Hayek (1945) and Mu h (1961) a gued ha ma ke s ne e ail in agg ega i ng he a ailable i n o ma ion. In a pionee ing wo k, Plo and Sunde (1988) s udied in o ma ion agg ega ion in h ee di e en ly designed ma ke s and showed ha his is no gene ally he case. In pa icula , while he p ice mechanism e icien ly agg ega ed he dispe sed in o ma ion bo h in ma ke s whe e pa icipan s aded a comple e se o A o w-Deb eu secu i ies and in ma ke s whe e ade s had iden ical payo s uc u es, agg ega ion ailed in single secu i y ma ke s whe e ade s we e paid di e en di i dends upon he ealiza ion o unce ain y. T he au ho s explain ed his esul a guing ha ade s canno in e he con ingen s a e o he ma ke om o he agen s’ ading beha io when hei payo s uc u es di e . Fo sy he and Lundholm (1990) ound ha , in spi e o he e ogeneous di idend s uc u es in incomple e ma ke s, in o ma ion was co ec ly agg ega ed whene e he di idend dis ibu ion was common knowledge among ade s and he su bjec s had p e iously expe ienced he ad ing ins i u ion. O he s ud ies ound e en mo e nega i e esul s on he c apaci y o ma ke s o agg ega e in o ma ion unde mo e gene al condi ions han he ones c onside ed in p e ious s udies. O'B ien and S i as a a (1991) s howed ha , e en wi h uni o m an d common di idend dis ibu ions, ma ke s did no manage o agg ega e he dispe sed in o ma ion i some elemen s o complexi y (mul i-pe iod asse s, no common knowledge abou in o ma ion dis ibu ion) a e in oduced in he ma ke design. Noe h e al. (1999) ound ha in o ma ion agg ega ion migh be hinde ed by he exis ence o “in o ma ion aps”. In pa icula , misal igned pa e ns, in which ac ions a e based on w ong belie s a bou o he s’ in o ma i e se , can esul in in o ma ion no being co ec ly e ealed in o p ices. B andouy e al. (2000) p o ided u he e idence a bou p ice o ma ion, asymme ic in o ma ion and ade s’ beha iou , in he con ex o asymme ic and possibly misleadi ng in o ma ion in a (double-auc ion) s ock ma ke . 7 They ound ha asymme ic in o ma ion eleased i s e ec in o he ma ke only when i is common knowledge among ma ke pa icipan s. Plo e al. (2003) ound ha in o ma ion agg ega ion s ic ly de pends on he en i onmen complexi y. Wh ile he compe i i e equilib ium ( a ional expec a ions model) is e y likely o hold in simple con ex s, p i a e in o ma ion based models a e gene ally mo e accu a e in mo e complica ed en i onmen s. In a ma ke whe e in o ma ion abou he in insic alue o an asse is cumu la i ely dis ibu ed among ade s, Hube e al. (2008) p o ed he exi s ence o a wide ange o le els o in o ma ion o which acqui ing addi ional in o ma ion di d no p oduce hi ghe gains. A posi i e ela ion sh ip be ween in o ma ion and highe p o i s was de ec ed only o e y high in o ma ion le els. Among he s udies ha analyzed he impac o inside in o ma ion, Scho e and Yo ulmaze (2009) ound ha eleasing in o ma ion o some inside s helped o dec ease he a e o bank un s in an expe imen o e banking c isis. A s we shall see, we ob ain a simila esul in he con ex o inancial ma ke s, as h e p esence o inside s aises e iciency (see sec ion 4). Simila ly o he s udies dealing wi h in o ma i on agg ega ion, in ou expe imen al ma ke s all agen s a e only impe ec ly in o med on he undamen al alue o he asse . No ade is gi en enough in o ma ion o know wi h ce ain y he u u e alue o he asse . No ne heless, we in oduce wo majo no el ies. Fi s , in wo o ou expe imen al condi ions “quasi-i nside s” ecei e a la ge numbe o signals han o h e s. Al hough we can no , s ic ly speaking, alk abou a p ocess o dissemina ion o in o ma ion, we a e none heless in e es ed in s udying he impac on ma ke e iciency o cen alizing in o ma ion in he hands o ew agen s. Second, di e en ly om all p e ious s udies, in ou design ade s a e gi en he chance o sha e hei in o ma ion se wi h he o he membe s o hei g oup be o e ading begins. We expec ha us and ecip oci y may p o e ele an mo i a ions as ound in he li e a u e s udying s anda d coope a ion p oblems (Feh and Fischbache , 2002). In ac , g ou p a achmen and social iden i y may also play a ole (B ewe , 2008). The p esence o quasi-inside may ei h e induce a s onge sense o iden i y in g oups o non-quasi-in side s, o a heigh ened pe cep ion o he un ai ness o he p ocess (Feh and Schmid , 1999; T au ma nn, 2009; K awczyk, 2011). In bo h cases we would expec g oups o less-in o med ade s o inc ease coope a ion in compa ison wi h symme ic ea men s. This would lead o smoo hing he in o ma ion dis ibu ion he e ogenei y 8 and o inc easing he low o in o ma ion among ade s 3 . To he bes o ou k nowledge, ou pape is he i s s udying in o ma ion agg ega ion in a amewo k whe e coope a ion, ecip oci y and leade ship all ma e o agen s’ choices and p ice dynamics. 3 Expe imen al Design 3.1 Gene al Design We un 27 independen expe imen al ma ke s whe e a o al o 324 agen s aded a gene ic inancial asse . Each age n was p o ided wi h 1000 okens and en uni s o asse . Each oken was wo h 0,02 Eu os. A he end o he ading pe iod, he asse paid an unce ain di idend D, wh ich c ould be wo h en okens o ze o okens, depending on wo equally likely s a es o he wo ld. A he beginning o he pe iod, agen s ecei ed pa ially in o ma i e signal(s) on he undamen al alue o he secu i y. Be o e ading s a ed, in wha we call he sha ing s age, each ade independen ly decided whe he o no o e eal he signal(s) o he o he wo membe s o he g oup o no . We designed ou ea men s in addi ion o a baseline condi ion w he e no agen ecei ed any in o ma ion. In ea men 1 (T 1) all agen s ecei ed one signal; in ea men 2 (T2) basic-in o med agen s ecei ed one signal and quasi-i nside agen s ecei ed h ee signals; in ea men 3 (T3) all agen s ecei ed h ee signals; in ea men 4 (T4) basic-in o med agen s ecei ed one signal and quasi-inside agen s ecei ed nine signals. Th ee ma ke s we e un o he baseline condi ion, while six ma ke s we e un o each o he ou ea men s. This design allows us o conside se e al in a ian s o ea men s compa ison. T1 and T2 di e because o he p esence o qua si-inside s bu p ese e he amoun o in o ma ion gi en o basic- in o med agen s. T3 and T4 di e because o he p esence o quasi-inside s agen s bu p ese e he o al amoun o in o ma ion in he ma ke . T1 and T3 do no include quasi-inside s agen s b u di e in he amoun o in o ma ion gi en o basic-in o med agen s. T2 and T4 bo h include quasi-inside s bu di e in he amoun o addi ional in o ma ion gi en o hem. 3 In a companion pape , we s udy in de ail how sensi i e he p e- ade coope a ion mechanism is o he p esence o quasi-in side s. 9 Each ma ke included 23 ading pe iods, h e e o which we e ial pe iods while all o he 20 ensuing pe iods we e paid o . The expe imen was p og ammed in z-T ee (Fischbache , 2007) and was un a he Labo a o y o Expe imen al Economics (LEE) o Uni e si a Jaume I (Cas ello n, Spain). Ins uc ions a e epo ed in he App endix G. 3.2 S a e o in o ma ion In all cases excep he baselin e, ade s ecei ed pa ially in o ma i e signal(s) on he u u e alue o he asse di idend be o e ading s a ed. Signals we e no 100% eliable. Assuming ha he ue di idend o be paid a he end o he pe iod was en (ze o), he p obabi li y o ge ing a signal indica ing ha he di idend would be en (ze o) was p. (1 – p) was he e o e he p obabili y o ge ing a p i a e signal indica ing ha he di idend would b e en ( ze o) while he ue alue o he di idend was ins ead ze o ( en). In o he wo ds, p was he p obabili y ha he signal e eals he ue alue o he di idend, while 1-p is he c omplemen a y p obabili y ha he signal indica ed a w ong alue o he di idend. We se p e qual o 70%. The alue o p was common knowledge among subjec s. A he beginning o he expe imen al session, in ea ch ma ke 12 ade s we e andomly assigned o ou di e en g ou ps, each composed by h ee ade s. The g oup composi ion was ixed h oughou he session. Be o e ading began, subjec s wen h ough a sha ing s age, in which hey simul aneously decided whe he o no o sha e hei signal(s) wi h o he s in hei g oup. In o ma ion sha ing could only occu wi h componen s o he same g oup. Mo eo e , i one ade decided o sha e he in o ma ion, all his o he signal(s) would be sha ed wi hin he g oup. No dec ep ion when sha ing signals was allowed. T ea men T1 T2 T3 T4 Baseline Panel A Ex-An e Numbe o signals dis ibu ed o “basic in o med” ade s 1 1 3 1 - Numbe o signals dis ibu ed o “quasi inside ” ade s - 3 - 9 - 16 Al e na i e Hypo hesis 1(a): Keeping cons an he o al numbe o signals, p ices exhibi a signi ican close con e gence o he e icien p ice when in o ma ion is uni o mly dis ibu ed. Al e na i e Hypo hesis 1(b): Keeping cons an he o al numbe o signals, p ices exhibi a signi ican close con e gence o he e icien p ice when quasi-inside agen s a e p esen in he ma ke , i.e. when in o ma ion is cen alized. As a second s ep, conside ing hose cases in which quasi-inside agen s a e p esen in he ma ke (T2 and T4), we es whe he an inc ease in he numbe o quasi- inside s’ pe capi a signals imp o es he con e gence owa d he e icien p i ce. Indeed, in T2 and T4, while basic in o me d agen s we e p o ided wi h one signal each, quasi- inside agen s ( h ee subjec s who belong o he same g oup) we e gi en h ee an d nine signals each espec i ely. The e o e, we o mula e hypo hesis 2 and i s al e na i es. Hypo hesis 2: O he hings being equal, when quasi-inside agen s a e p o ided wi h h ee signals each, p ices exhibi he same de ia ion om he e icien p ice as when quasi-inside agen s a e p o ided wi h nine signals each. Al e na i e Hypo hesis 2(a): O he hings being equal, when quasi-inside agen s a e p o ided wi h h ee signals each, p ices exhibi a signi ican close con e gence o he e icien p ice han when hey a e p o ided wi h nine signals each. Al e na i e Hypo hesis 2(b): O he hings being equal, when quasi-inside agen s a e p o ided wi h nine signals each, p ices exhibi a signi ican close con e gence o he e icien p ice han when hey a e p o ided wi h h ee signals each. Finally, conside ing he cases whe e in o ma ion is uni o mly dis ibu ed among ade s (T1 and T3), we es whe he inc easing he numbe o signals in he ma ke impac s on ma ke e iciency. This can be es ed because each agen is p o ided wi h one and h ee signal(s) in T1 and T3, espec i ely. Ou hi d hypo hesis and i s al e na i es a e s a ed below: Hypo hesis 3: When in o ma ion is uni o mly dis ibu ed and ade s a e p o ided wi h one signal each, p ices exhibi he same de ia ion om he e icien p ice as when ade s a e p o ided wi h h ee signals each. 17 Al e na i e Hypo hesis 3(a): When in o ma ion is uni o mly dis ibu ed, p ices exhibi a signi ican close con e gence o he e icien p ice when ade s a e p o ided wi h one signal each. Al e na i e Hypo hesis 3(b): When in o ma ion is uni o mly dis ibu ed, p ices exhibi a signi ican close con e gence o he e icien p ice when ade s a e p o ided wi h h ee signals each. 5 Resul s 5.1 In o ma ion sha ing We i s analyze how ade s use he op ion o sha e hei p i a e in o ma ion; secondly we p esen esul s on ma ke ou comes. Figu es 1 and 2 illus a e how subjec s use he coope a ion mechanism. They epo he a e age numbe o signals s ha ed in each o he six ma ke s comp ising a gi en ea men o basic in o med agen s’ (Figu e 1) and quasi-inside agen s (Figu e 2). Figu e 1: In o ma ion sha ing by basic-in o med agen s Figu e 2: In o sha ing by quasi -inside s agen s We i s compa e in o ma ion s ha ing pa e ns in T1 and T3, whe e no quasi- inside agen is p esen . Th oughou ou desc ip i e analysis, we conside each ma ke as yielding one independen obse a ion. Indeed, since he same g oup o people wi hin a ma ke in e ac o e se e al pe iods, wi hin-g oup obse a ions a e se ially in e dependen . This p ope y makes i sui able o conside each g oup (ma ke ) as an independen obse a ion, e.g. 0.2 .4 .6 .8 1 1 2 3 4 T ea men In o Sha ing (%) Median Line Only basic in o med agen s included In o ma ion sha ing o e ea men s 0.2 .4 .6 .8 1 42 T ea men In o Sha ing (%) Median Line Only quasi inside s included In o ma ion sha ing o e ea men s 18 by compu ing he mean (m edian) o he a iable o in e es o e he pe iods comp ising a gi en ma ke (see F e che e, 2012). We no e ha ade s coope a e signi ican ly less in T 3 ( wo- ailed k-sample median es : N = 6; Pea son chi squa e = 5.33; P = 0.021. See also Table A1, Appendix A). This is likely he conseq uence o ade s’ ini ial in o ma ion se being la ge in T3 compa ed o T1. Agen s can hus be mo e con iden in T3 han T1 ha hei in o ma ion s e is su icien o i ndica e he ue s a e o h e wo ld. In o he wo ds, he expec ed bene i s om coope a ion is lowe in T3 han T1, hence he incen i es o sha e in o ma ion a e also lowe . We a lso ind ha he le el o in o ma ion sha ing among basic in o med age n s does no signi ican ly change when quasi- insi de agen s a e in oduced in he m a ke , as can be seen in he com pa ison be ween T1 - agen s p o ided wi h one signal each - and T2 - basic in o med and quasi-inside agen s p o ided wi h one and h ee signals each, espec i ely - ( wo- ailed k-sample median es : N = 6; Pea son chi squa e = 0.00; P = 1.000. See also Table A2, Appendix A) and be ween T1 and T4 - basic in o med and quasi-inside agen s p o ided wi h one and nine signals each espec i ely – ( wo- ailed k-sample median es : N = 6; Pea son chi squa e = 0.00; P = 1.000. See also Table A3, Appendix A). Fu he mo e, mo ing om T2 o T4, he median pe cen age o basic in o med ade s sha ing hei in o ma ion se swi ches om 57.22% o 63.61%. Ye , his di e ence is no s a is ically signi ican ( wo- ailed k-sample median es : N = 6; Pea son chi squa e = 0.00; P = 1.000. See also Table A4, Appendix A). Finally, no signi ican di e ence ( wo- ailed k-sample median es : N = 6; Pea son chi squa e = 1.33; P = 0.248. See also Table A5, Appendix A) eme ges be ween quasi-insid e s’ in o ma ion sha i ng beha io in T2 and T4, al hough i is appa en om Figu e 2 ha sha ing is lowe in T4 ha n T2. This beha io p esumably ollows he same easons as he d op in sha ing o basic in o med agen s in T3 ela i e o T1. Tha is, a highe numbe o ini ial signals o each agen educes hei need o coope a e wi h o he s. Ou conjec u e (s ee sec ion 2) ha p ocedu al un ai ness in he asymme ic ea men s may ha e led o s onge “g oup spi i ” in basic-in o med agen s is hus discon i med by he da a. As ound in a companion pape , hough, some o he iden i y e ec s, which a e no ele an o he p esen pape , seem none heless o eme ge. 5.2 Ma ke E iciency 5.2.1 Gene al O e iew 19 Figu es 5-8 epo he box-plo s o he RMSE dis ibu ion o e ach o he benchma k p ices in each ea men . These g aphs pool RMSE o e pe iods and ma ke s. A mo e de ai led o e iew can be ound in Figu es B1, B2, B3, B4, and B5 in Appendix B . The e we show he ac ual e olu ion o he aded p ices in ela ion o he benchma k p ices, b oken down by ma ke and pe iod. Fi s , we no e a clea di e ence be ween he baseline condi ion and all o he ea men s. The unin o med and di idend p ice RMSE dis ibu ions a e shi ed downwa d and upwa d, espec i ely, in compa ison o all o he ea men s. Th ough he use o a Tobi eg ession analysis (see Appendix C, Model C1), we ind ha he unin o med p ice RMSE in he baseline is signi ican ly lowe han ha compu ed in each o he o he ea men s (P < 0.00 1 in all he ou pai wise compa isons). On he con a y, we ind ha he di idend p ice RMSE dis i bu ion in he baseline condi ion is signi ican ly highe wi h espec o ha compu ed in each o he o he ea men s (P < 0.05 in all he ou pai wise compa isons). This p elimina y analy sis shows ha when no in o ma ion is p esen in he ma ke , ade p ices emain signi ican ly close o he unin o med p ice and u he away om he di idend p ice han when some in o ma ion is p esen in he ma ke . In pa icula , we no e h a his di e ence is mo e p onounced o he unin o med p ice han he di idend p ice. I is ela i ely easie o ma ke s wi h in o ma ion o depa away om he unin o med p ice han o come close o he undamen al in compa ison o ma ke s wi hou in o ma ion. In ac , ade p ices in he baseline condi ion exhibi a andom walk p ocess a ound he expec ed alu e o he di idend dis ibu ion, and in n o case p ices each he di idend alue (see Figu e B 5, Appen dix B). We e mploy a Tobi eg ession model (see Appendix C, Model C2) o assess whe he , when no in o ma ion is in he ma ke , he dis ance be ween ade p ices and he unin o med p ice i s lowe han he dis ance be ween ade p ices and he undamen al alue o he asse . This i s he s anda d assump ion in ma ke s wi h no in o ma ion, and i is, no su p isingly, con i med in ou case (coe . = -4.18; P < 0.001). This p elimina y e idence e nsu es ha agen s we e able o exploi he a ailable in o ma ion and aded a p ices ha we e u he away om he unin o med p ice and close o he undamen al asse alue han in he baseline. 20 Figu e 5: RMSE Dis ibu ion, Unin o med P ice Figu e 6: RMSE Dis ibu ion, Bayes P ice Figu e 7: RMSE Dis ibu ion, E icien P ice Figu e 8: RMSE Dis ibu ion, Di idend Among he ea men s wi h in o ma ion, we no e some endency o he uni o med p ice RMSE o inc ease as we mo e om T1 o T4, and co espondingly ( hough less ma kedly so) o he di idend p ice RMSE o dec ease as we mo e om T1 o T4. This may signal ha he combina ion o adding in o ma i on and cen alizing in o ma ion helps agen s o ade a p ic es ha a e close o he unda men al. Ne e heless, we no e no clea pa e n wi h espec o ei he he Bayes RMSE o he Fama-e icien p ice. We conjec u e ha his appa en lack o ea men di e ences in he Bayes and Fama-e icien RMSE may be due o lea ning e ec s. Lea ni ng may occu because agen s upda e hei decisi on-making ules as hey accumula e ading expe ience. Agen s c an imp o e hei abili y o in e in o ma ion om he o he ade s’ ac i i y o e he cou se o 20 pe iods. Agen s may also upda e hei coope a ion s a egies o e ime, hus also a ec ing h e way ma ke s sp ead i n o ma ion. In ac , ime se ies plo s in Appen dix B ypically exhibi p oximi y o unin o med o Bayesian p ice s in ea ly pe iods, and p oximi y o he Fama-e icien p ice in he la e pe iods o he session. Fo ins ance, in ma ke 1 om ses sion 2 and T2 (see appendix B, Figu e B2), unin o med ades domina e he i s h ee pe iods, p ices hen con e ge o he Bayes p ice in 012345 RMSE Unin o med P ice Baseline T ea men 1 T ea men 2 T ea men 3 T ea men 4 02468 RMSE Bayes P ice T ea men 1 T ea men 2 T ea men 3 T ea men 4 02468 RMSE E icien P ice T ea men 1 T ea men 2 T ea men 3 T ea men 4 0246810 RMSE Di idend P ice Baseline T ea men 1 T ea men 2 T ea men 3 T ea men 4 21 pe iods om ou o nine, and p ices ack he e icien eq ui lib ium p ice o all la e pe iods. This sugges s a pa e n whe eby agen s ade as i hey we e unin o med in he ea lies pe iods, p ocess hei own p i a e in o ma ion in in e media e pe iods, and e en ually man age o co ec ly pool he in o ma ion dispe sed in he ma ke in he inal pe iods. Lea ning may hus be ele an no only o accoun o indi idual beha io bu also o i s impac on ma ke pe o mance. Fo hese easons, we spli ou desc ip i e esul s in o he i s and second block o en pe iods in each ma ke 5 and epo on he benchma ks pe o man ce a es o e he ou ea men s. We iden i y o each p e iod o each ma ke which benchma k p ice is bes able o app oxima e he ac ual an sac ion p ices. Mo e p ecis ely, we selec he benchma k p ice wi h he lowes RMSE alue om ac ual p ices 6 . Essen ially, in each ea men we coun how many imes a gi en benchma k bes app oxima es ou da a. Table 2 epo s he pe cen ages o each b enchma k being selec ed as he one wi h he lowes RMSE. Pe o mance Ra es Unin o med P ice Bayes P ice E icien P ice Di idend T ea . 1 Fi s Hal 45.00% 45.00% 10.00% 0.00% T ea . 1 Second Hal 45.00% 38.33% 16.67% 0.00% T ea . 2 Fi s Hal 43.33% 46.67% 10.00% 0.00% T ea . 2 Second Hal 21.67% 28.33% 50.00% 0.00% T ea . 3 Fi s Hal 50.00% 50.00% 0.00% 0.00% T ea . 3 Second Hal 35.00% 46.67% 18.33% 0.00% T ea . 4 Fi s Hal 43.33% 48.33% 8.33% 0.00% T ea . 4 Second Hal 15.00% 38.33% 46.67% 0.00% Baseline Fi s Hal 100.00% / / 0.00% Baseline Second Hal 100.00% / / 0.00% 5 Box-Plo s a e epo ed in Appendix D. 6 In case o ies be ween RMSE o wo o mo e benchma ks, we selec he leas e icien benchma k. This is on he o ne hand he mos conse a i e c i e ion o ou analysis and on he o he hand pe mi s pe o mance a es o always sum up o 100%. 22 Table 2: Benchma k pe o mance a es, g oup ed by ea men and i s o second blo ck o en pe iods. Fi s , we no e ha he Di idend p i ce has ne e he lowes RMSE, deno ing he di icul y o ade s o achie ing he undamen al p ice. Wi h ega ds o he h ee o he benchm a k s, in T1 he unin o med and he Bayes p ices a e he bes pe o ming benchma ks in bo h he i s and he second 10 - block pe iods, wi h a pe o mance a e o 45% and 45%, espec i ely, in he i s 10-block pe i od, and o 45% and 38.33% in he second 10-block pe iod. The e icien p ic e ma ginally i mp o es om a pe o mance a e o 10% in he ea ly pe iods o a pe o mance a e o 16.67% in la e pe iods. T ading in T1 is hus s ill p edominan ly unin o med o based on p i a e in o ma ion. In T2 he unin o med and he Bayes p ices a e he b es pe o ming ones in ea ly pe iods (wi h a pe o mance a e o 43.33% and 46.67% espec i ely). Ne e heles s, when we mo e o la e pe iods he e icien p ice becomes he b es acked benchma k (wi h a pe o mance a e o 50%). I is pa icula ly in e es ing o no e how unin o med ades dec ease om 43.33% o 21.67% and e icien ades inc ease om 10% o 50% when mo ing om ea ly o la e pe iods. This e idence shows ha , o e ime, ade s imp o e h ei abili y o in e and agg ega e he in o ma ion dis pe sed in he ma k e . In T3 esul s a e ema kably simila o T1. Bo h he unin o med and he Bayes p ices pe o m be e in accoun ing o ou da a han he e icien p ice in bo h ea ly and la e pe iods. I n pa icula , in he second en- ound block, he Bayes p ice is he bes ac ked bench ma k wi h a pe o mance a e o 46.67%. I is ema kable ha , in spi e o he numbe o ini ial signals being ex an e h ee imes as high in T3, we obse e ma ke p ices o ha e he same le els o p oximi y o he e icien p ice and he B ayes p ice as in T1. This is no due o he ac ha he ex pos numbe o signals is si mila in he wo ea men s. As Table 1, Panel B, shows, agen s in T3 ha e a signi ican ly (Mann Whi ney U es : N 7 = 6; z = -2.882; P < 0.0039) la ge amoun o in o ma ion (5 .90 signals pe capi a) han in T1 (2.18 signals pe capi a). The ex pos a io o numbe o signals is 2.70, which is less han he ex an e a io o 3:1 bec ause agen s sha ed on a e age less in T3 han T1. The bad pe o mance o he e icien p ice sugges s ha ade s a e mainly conce ned wi h p ocessi ng hei own p i a e in o ma ion han yi ng o in e o he s’ in o ma ion h ough he obse a ion o p ice signals. 7 Ma ke a e ages o he ex-pos signals dis ibu ion a e used o accoun o wi hin ma ke co ela ion. 23 Finally, benchma ks in T4 pe o m simila ly o T2. While he unin o med and he Bayes p ices exhibi he highes pe o man ce a es in ea ly pe iods (43.33% and 48.33% espec i ely), he e icien p ice pe o ms be e in la e pe iods (wi h a pe o mance a e o 46.67%). E en in his case i is ema kable how he e icien p ice pe o mance a e swi ches om 8.33% o 46.67% mo ing om ea ly o la e pe iods. He e again we no e ha in spi e o a la ge numbe o signals being a ailab le in T4 compa ed o T 2 bo h ex an e - in a p opo ion o 2:1 - han ex pos - in a p opo ion o 1.9:1 (Mann Whi ney U es : N 8 = 6; z = -2.892; P < 0.0038) – he pe o mance in e ms o e iciency appea o be i ually he same. 5.2.3 Econome ic Analysis In his sec ion we pe o m a ho ough ec onome ic analysis o ou hy po heses and o he conjec u es ha eme ged om he desc ip i e analysis. Fo his pu pose we use he ollowing Tobi eg ession model: 𝑅𝑀𝑆𝐸𝑖,𝑡 =𝛼+∑𝛽𝑖 𝑛 𝑖=1 ∙𝑀𝑘𝑡𝑖+𝛾∙𝑃𝑒𝑟𝑖𝑜𝑑+∑𝜃𝑗 𝑘 𝑗=1 ∙𝑋𝑖,𝑗+𝜀𝑖,𝑡 The RMSE index o ac ual ade p ices wi h espec o a gi en p ice benchma k is he dependen a iable o he model. Ou co a ia es include a dummy a iable 𝑀𝑘𝑡𝑖 o each o n ma ke s bu one ha is omi ed. In his way we con ol o bo h possi ble hydiosinc acies ac oss ma ke s and o he clus e ing o ou da a a he ma ke le el. 𝑃𝑒𝑟𝑖𝑜𝑑 is a end a iable cap u ing he ime e ec ; and 𝑋 𝑖,𝑗 is a ec o o d emog aphics and a i udinal a iables 9 ha a e a e aged a he ma ke le el. We es o ea men e ec s pe o ming Wald es s o e he di e e nce be ween he sums o ma ke dummy coe icien s belonging o di e en ea men s. Tha is, o es o he null hypo hesis o absence o di e ences be ween wo ea men s, we conside he null hypo hesis: 8 Ma ke a e ages o he ex-pos signals dis ibu ion a e used o accoun o wi hin ma ke co ela ion. 9 A de ailed d esc ip ion o he demog aphics and a i udinal a iables is epo ed in he no e below Table E1 (Appendix E). 24 𝐻0: 𝑍𝑟,𝑠 ≡∑βi, 𝑛𝑟 i=1 −∑βi,s 𝑛𝑠 i=1 =0 whe e and s iden i y he ma k e s associa ed wi h wo di e en ea men s. 𝑛𝑟 and 𝑛𝑠 a e he numbe s o ma ke s belonging o ea men and s. Ou design includes six ma ke s o each ea men . 𝑛𝑟 and 𝑛𝑠 a e he e o e always equal o six, excep o he ea men o which he omi ed ca ego y o he model belongs (T ea men 1). No e ha he possibili y ha 𝑛𝑟>𝑛𝑠 o compa isons in ol ing T ea men 1 does no a ec he es ima ion o ou pai wise c ompa isons, since he omi ed ca e go y coe icien is implici ly ze o. Since ou desc ip i e analysis highligh ed he p esence o di e en p i ce pa e ns be ween he i s and second hal ma ke pe iods, we un he econome ic model bo h in he i s and he sec ond block o en pe iods as well as o e he en i e se o ma ke pe iods. All he eg ession ou pu s a e epo ed in Appendix E; all he ea men s pai wise compa isons a e a ailable in Appendi x F. He e we mainly oc us on he esul s de i ed om he s econd block o en pe iods. Resul 1: Hypo hesis 1 is ejec ed. We ind ha , keeping in o ma ion cons an ex an e (36 signals in he ma ke ), when quasi-inside agen s a e ac i e in he ma ke (T4), ac ual p ices exhib i a signi ican ly close con e gence o he e icien p ice wi h espec o he case in which in o ma ion is uni o mly dis ibu ed (T3) (𝑍𝑇4,𝑇3 = -4.40; P = 0.014). The e o e , keeping cons an he quan i y o in o ma ion in he ma ke , a cen alized in o ma ion dis ibu ion in which some agen s a e p o id ed wi h mo e in o ma ion gua an ees mo e e iciency han a uni o m in o ma ion dis ibu ion in which all subjec s ecei e he same amoun o in o ma ion. Resul 2: We canno ejec Hypo hesis 2. We ind ha , o he hings being equal, when quasi-inside ade s a e gi en nine signals (T4), ma ke e iciency is no signi ican ly highe han when quasi-inside agen s a e p o ided wi h h ee signals each (T2) (𝑍𝑇4,𝑇2 = -0 .79; P = 0.710). I n o he wo ds, when i n o ma ion is pola ized, p o iding quasi-inside agen s wi h a g ea e numbe o pe -capi a signals does no signi ican ly inc ease ma ke e iciency. Resul 3: We canno ejec Hypo hesis 3. When in o ma ion is uni o mly dis ibu ed, swi chi ng om a ma ke whe e subjec s a e p o ided wi h one signal each 25 (T1) o a ma ke whe e h ee signals a e eleased o each subjec (T3) does no lead o a signi ican inc ease in he ma ke e iciency le el (𝑍𝑇3,𝑇1 = -1.58; P = 0.384). We conjec u e ha he common knowledge ha in o ma ion is uni o mly dis ibu ed leads subjec s no o ecognize he p esence o an in o med ma ke leade and, as a consequen ce, no o ocus on he o he s’ ading ac i i y. In ac , he sign o he coe icien indica es ha he con e gence o he e icien p ice is highe in T1 han in T3. This is ema kabl e, as he numbe o ini ial signals is h ee imes highe in T3 han in T1 (keeping ixed he uni o m dis ibu ion in bo h ea men s). We conjec u e ha he g ea e amoun o in o ma ion in T3 makes ade s mo e con iden in being able o co ec ly o ecas he asse di idend and makes hem less p one o use he ma ke ading ac i i y as an in e ence ool. On he con a y, when p o ided wi h only one in o ma i e signal (as in T1), ade s ocus mo e on he ma ke ac i i y o imp o e hei chance o p ope ly in e ing he asse undamen al alue and, consequen ly, ma ke e iciency is imp o ed. Wi h ega d o he e maining be nchma ks, we ind ha addi ional in o ma ion is no disca ded bu is somehow p ocesse d by ade s. This is e iden om he inc eas ing pa e n o e ea men s o he unin o med p ice RMSE in la e pe i ods. In o he wo ds, mo ing om T1 o T4, as he quan i y o in o ma ion ( o al numbe o signals) inc eases, p ices de pa om he unin o med p ice. This end is in place in all he pai wise compa isons (𝑍𝑇1,𝑇2 = -4.93; P = 0.00; 𝑍𝑇1,𝑇3 = -3.89; P = 0.000; 𝑍𝑇1,𝑇4 = - 8.29; P = 0.000; 𝑍𝑇2,𝑇4 = -3 .80; P = 0.0 01; see Table F8, Appen dix F) bu on e (𝑍𝑇2,𝑇3 = 0.40; P = 0.717; see Table F8, Appendix F). In e es ingly, e en i no signi ican , he sign o he Wald es 𝑍𝑇2,𝑇3 appea s o con adic he ule “mo e in o ma ion less noise ”. Indeed, al hough in T3 ade s ecei e wice as many signals as i n T2, p ices come close o he unin o med p ice when only basic-in o med agen s a e ac i e in he ma ke (T3) 10 . Cohe en ly wi h ou esul s on he e icien p ice, we also ind ha e en k eeping iden ical he amoun o in o ma ion wi hin he ma ke (i.e. in T3 and T4), asymme ic in o ma ion dis ibu ions p oduce lowe noise ha n h e case in which in o ma ion is ins ead symme ically sp ead ou (𝑍𝑇3,𝑇4 = -4.21; P = 0.000; see Tab le F8, Appendix F). 10 In e es ingly, when in o ma ion is ins ead asymme ically dis ibu ed, doubling he o e all amoun o signals leads p ices away om he unin o med p ice (𝑍𝑇2,𝑇4 = -3.80; P = 0.001) 32 APPENDIX A T1 T3 To al Obse a ions Lowe han he median 1 5 6 G ea e han he median 5 1 6 To al 6 6 12 Pea son chi-squa e (1) = 5.3333 P = 0.021 Table A1: Median es on in o ma ion sha ing ( eamen s 1 and 3) T1 T2 To al Obse a ions Lowe han he median 3 3 6 G ea e han he median 3 3 6 To al 6 6 12 Pea son chi-squa e (1) = 0.0000 P = 1.000 Table A2: Median es on in o ma ion sha ing ( ea - men s 1 and 2), only basic-in o med included T1 T4 To al Obse a ions Lowe han he median 3 3 6 G ea e han he median 3 3 6 To al 6 6 12 Pea son chi-squa e (1) = 0.0000 P = 1.000 Table A3: Median es on in o ma ion sha ing ( ea - men s 1 and 4), only basic-in o med included T2 T4 To al Obse a ions Lowe han he median 3 3 6 G ea e han he median 3 3 6 To al 6 6 12 Pea son chi-squa e (1) = 0.0000 P = 1.000 Table A4: Median es on in o ma ion sha ing ( ea - men s 2 and 4), only basic-in o med agen s included T2 T4 To al Obse a ions Lowe han he median 2 4 6 G ea e han he median 4 2 6 To al 6 6 12 Pea son chi-squa e (1) = 1.3333 P = 0.248 Table A5: Median es on in o ma ion sha ing ( ea - men s 2 and 4), only quasi-inside s agen s included 33 APPENDIX B 0246810 0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400 Time P ice Di idend Unin o med P ice Bayes P ice E icien P ice T1-S1-M1 0246810 0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400 Time P ice Di idend Unin o med P ice Bayes P ice E icien P ice T1-S3-M1 0246810 0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400 Time P ice Di idend Unin o med P ice Bayes P ice E icien P ice T1-S3-M2 34 Figu e B1: T ade p i ces in T ea men 1 0246810 0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400 Time P ice Di idend Unin o med P ice Bayes P ice E icien P ice T1-S3-M3 0246810 0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400 Time P ice Di idend Unin o med P ice Bayes P ice E icien P ice T1-S10-M1 0246810 0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400 Time P ice Di idend Unin o med P ice Bayes P ice E icien P ice T1-S10-M2 35 0246810 0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400 Time P ice Di idend Unin o med P ice Bayes P ice E icien P ice T2-S2-M1 0246810 0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400 Time P ice Di idend Unin o med P ice Bayes P ice E icien P ice T2-S4-M1 0246810 0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400 Time P ice Di idend Unin o med P ice Bayes P ice E icien P ice T2-S4-M2 36 Figu e B2: T ade p i ces in T ea men 2 0246810 0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400 Time P ice Di idend Unin o med P ice Bayes P ice E icien P ice T2-S4-M3 0246810 0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400 Time P ice Di idend Unin o med P ice Bayes P ice E icien P ice T2-S4-M4 0246810 0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400 Time P ice Di idend Unin o med P ice Bayes P ice E icien P ice T2-S9-M1 37 0246810 0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400 Time P ice Di idend Unin o med P ice Bayes P ice E icien P ice T3-S5-M1 0246810 0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400 Time P ice Di idend Unin o med P ice Bayes P ice E icien P ice T3-S5-M2 0246810 0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400 Time P ice Di idend Unin o med P ice Bayes P ice E icien P ice T3-S5-M3 38 Figu e B3: T ade p ices in T ea men 3 0246810 0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400 Time P ice Di idend Unin omed P ice Bayes P ice E icien P ice T3-S8-M1 0246810 0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400 Time P ice Di idend Unin omed P ice Bayes P ice E icien P ice T3-S8-M2 0246810 0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400 Time P ice Di idend Unin omed P ice Bayes P ice E icien P ice T3-S8-M3 39 0246810 0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400 Time P ice Di idend Unin o med P ice Bayes P ice E icien P ice T4-S6-M1 0246810 0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400 Time P ice Di idend Unin o med P ice Bayes P ice E icien P ice T4-S6-M2 0246810 0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400 Time P ice Di idend Unin o med P ice Bayes P ice E icien P ice T4-S6-M3 40 Figu e B4: T ade p i ces in T ea men 4 0246810 0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400 A P ice Di idend Unin o med P ice Bayes P ice E icien P ice T4-S6-M4 0246810 0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400 Time P ice Di idend Unin o med P ice Bayes P ice E icien P ice T4-S7-M1 0246810 0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400 Time P ice Di idend Unin o med P ice Bayes P ice E icien P ice T4-S7-M2 41 Figu e B5: T ade p ices in he baseline condi ion 0246810 0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400 Time P ice Di idend Unin o med P ice Baseline-S11-M1 0.00 2.00 4.00 6.00 8.00 10.00 0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400 Time P ice Di idend Unin o med Baseline-S12-M1 0.00 2.00 4.00 6.00 8.00 10.00 0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400 Time P ice Di idend Unin o med Baseline-S12-M2 48 Table E2 con d. T4S6M3 0.329 0.531 0.442* (0.364) (0.338) (0.248) T4S6M4 -0.681* -0.138 -0.334 (0.400) (0.337) (0.253) T4S7M1 -0.112 -0.543 -0.223 (0.613) (0.349) (0.361) T4S7M2 0.421 0.240 0.439 (0.527) (0.537) (0.365) age_ma ke _mean 0.0938 0.0130 0.0596 (0.0706) (0.0615) (0.0480) deg_ma ke _mean 0.370 -0.856 -0.170 (0.602) (0.627) (0.417) exp_ma ke _mean -0.403** -0.263 -0.265** (0.200) (0.170) (0.126) in_ma ke _mean 0.213 0.119 0.132 (0.276) (0.286) (0.194) u _ma ke _mean -0.313 0.0487 -0.0907 (0.252) (0.283) (0.187) gende _ma ke _mean -0.323 -0.212 -0.247 (0.318) (0.292) (0.227) Cons an 1.143 3.057* 1.538 (1.897) (1.736) (1.301) Obse a ions 240 240 480 Pseudo R2 0.0734 0.162 0.0826 No es: The Bayes P ice RMSE is he Dependen Va iable. See No es o Table E1 o a iables’ de ini ion. 49 Table E3: Reg ession analysis o Tobi model o p ice con e gence owa d he Unin o med P ice VARIABLES Pe iods 1_10 Pe iods 11_20 Pe iods 1_20 pe iod 0.0472*** 0.0526*** 0.0508*** (0.0159) (0.0193) (0.00665) T1S3M1 0.336 -0.832*** -0.276 (0.426) (0.235) (0.306) T1S3M2 0.0687 -0.116 -0.0985 (0.265) (0.265) (0.207) T1S3M3 0.836*** 0.730** 0.686*** (0.274) (0.354) (0.228) T1S10M1 1.173*** 0.267 0.672** (0.336) (0.416) (0.315) T1S10M2 1.010** 1.698*** 1.282*** (0.412) (0.511) (0.334) T2S2M1 0.621** 1.582*** 1.123*** (0.312) (0.342) (0.246) T2S4M1 0.180 1.566*** 0.846*** (0.322) (0.381) (0.279) T2S4M2 0.230 1.507*** 0.866*** (0.332) (0.314) (0.249) T2S4M3 0.282 1.108** 0.684** (0.307) (0.428) (0.279) T2S4M4 -0.205 0.980** 0.388 (0.317) (0.383) (0.275) T2S9M1 -0.0160 0.486 0.158 (0.284) (0.323) (0.211) T3S5M1 0.919*** 0.204 0.480* (0.279) (0.286) (0.245) T3S5M2 0.982*** 0.213 0.510* (0.352) (0.391) (0.298) T3S5M3 0.755** 1.852*** 1.214*** (0.298) (0.421) (0.277) T3S8M1 0.196 1.574*** 0.839*** (0.236) (0.388) (0.262) T3S8M2 0.471** 0.842*** 0.649*** (0.237) (0.249) (0.185) T3S8M3 0.917*** 2.138*** 1.507*** (0.269) (0.322) (0.248) T4S6M1 1.335*** 2.092*** 1.685*** (0.332) (0.394) (0.268) T4S6M2 1.001*** 1.882*** 1.372*** (0.229) (0.357) (0.226) 50 Table E3 con d. T4S6M3 1.571*** 2.541*** 2.058*** (0.263) (0.228) (0.194) T4S6M4 0.488 2.015*** 1.197*** (0.307) (0.306) (0.256) T4S7M1 1.110*** 1.000*** 1.047*** (0.386) (0.372) (0.284) T4S7M2 1.209*** 1.504*** 1.274*** (0.244) (0.371) (0.218) age_ma ke _mean 0.00693 0.0325 0.0446 (0.0503) (0.0598) (0.0404) deg_ma ke _mean 0.648** 0.950*** 0.881*** (0.300) (0.351) (0.262) exp_ma ke _mean 0.228** 0.182 0.171* (0.110) (0.142) (0.0981) in_ma ke _mean 0.215 0.278 0.165 (0.172) (0.231) (0.148) u _ma ke _mean 0.283 0.158 0.307* (0.177) (0.262) (0.163) gende _ma ke _mean -0.387* -0.261 -0.202 (0.214) (0.283) (0.193) Cons an -0.397 -1.637 -1.605* (1.167) (1.483) (0.940) Obse a ions 270 270 540 Pseudo R2 0.194 0.241 0.177 No es: The Unin o med P ice RMSE is he Dependen Va iable. See No es o Table E1 o a iables’ de ini ion. 51 Table E4: Reg ession analysis o Tobi model o p ice con e gence owa d he Di idend P ice VARIABLES Pe iods 1_10 Pe iods 11_20 Pe iods 1_20 pe iod -0.0691** -0.0655* -0.0728*** (0.0301) (0.0357) (0.0118) T1S3M1 -0.00707 -0.396 -0.117 (0.777) (0.515) (0.478) T1S3M2 0.434 -0.903* -0.129 (0.549) (0.460) (0.362) T1S3M3 -0.413 -1.469* -0.893 (0.794) (0.816) (0.579) T1S10M1 -0.789 -1.371* -1.116* (0.869) (0.721) (0.586) T1S10M2 -1.510** -2.065** -1.756*** (0.639) (1.023) (0.623) T2S2M1 -0.665 -2.528*** -1.652*** (0.533) (0.565) (0.402) T2S4M1 -0.157 -2.226*** -1.216** (0.614) (0.689) (0.488) T2S4M2 -1.231** -1.861** -1.605*** (0.528) (0.883) (0.532) T2S4M3 -0.538 -1.953** -1.277** (0.574) (0.779) (0.496) T2S4M4 -0.707 -1.937*** -1.311*** (0.451) (0.647) (0.409) T2S9M1 -0.374 -1.127* -0.763* (0.504) (0.605) (0.406) T3S5M1 -0.564 0.00251 -0.152 (0.496) (0.554) (0.406) T3S5M2 -0.625 -0.0954 -0.310 (0.814) (0.690) (0.540) T3S5M3 -1.084* -1.802* -1.354** (0.586) (0.927) (0.562) T3S8M1 -0.651 -2.906*** -1.693*** (0.432) (0.626) (0.395) T3S8M2 -0.589 -2.075*** -1.358*** (0.487) (0.502) (0.362) T3S8M3 -1.130** -3.409*** -2.218*** (0.518) (0.517) (0.383) T4S6M1 -1.191** -3.401*** -2.280*** (0.574) (0.557) (0.427) T4S6M2 -0.643 -2.192*** -1.422*** (0.580) (0.749) (0.484) 52 Table E4 con d. T4S6M3 -0.951** -3.004*** -1.991*** (0.396) (0.643) (0.398) T4S6M4 -1.032** -2.364*** -1.684*** (0.460) (0.587) (0.383) T4S7M1 -0.600 -2.494*** -1.557*** (0.814) (0.653) (0.550) T4S7M2 0.197 -1.264* -0.459 (0.581) (0.755) (0.481) age_ma ke _mean 0.153 -0.132 -0.0195 (0.101) (0.103) (0.0709) deg_ma ke _mean -0.113 0.460 0.0887 (0.621) (0.648) (0.472) exp_ma ke _mean -0.273 -0.299 -0.217 (0.236) (0.248) (0.172) in_ma ke _mean 0.326 -0.179 0.104 (0.397) (0.437) (0.288) u _ma ke _mean -0.217 -0.527 -0.378 (0.374) (0.431) (0.287) gende _ma ke _mean 0.288 0.201 0.0636 (0.421) (0.480) (0.325) Cons an 2.011 10.08*** 6.809*** (2.341) (2.445) (1.642) Obse a ions 270 270 540 Pseudo R2 0.0491 0.0806 0.0640 No es: The Di idend P ice RMSE is he Dependen Va iable. See No es o Table E1 o a iables’ de ini ion. Appendix F 53 Wald es s o e he di e ence be ween he sums o ma ke dummy coe icien s belonging o di e en ea men s. In o de o es o he null hypo hesis o absence o di e ences be ween wo ea men s, we c onside : 𝐻0: 𝑍𝑟,𝑠 ≡∑βi, 𝑛𝑟 i=1 −∑βi,s 𝑛𝑠 i=1 =0 whe e and s iden i y he ma ke s associa ed wi h wo di e en ea men s. 𝑛𝑟 and 𝑛𝑠 a e he numbe s o ma ke s belongi ng o ea men and s. Ou de sign includes six ma ke s o e ach ea men . 𝑛𝑟 and 𝑛𝑠 a e he e o e always equal o six, excep o he ea men o which he omi ed ca ego y o he model belongs (T ea men 1). No e ha he possibili y ha 𝑛𝑟>𝑛𝑠 o compa isons in ol ing T ea men 1 does no a ec he es ima ion o ou pai wise compa ison s, since he omi ed ca e go y coe icien is implici ly ze o. Wi h e e ence o each pai wise compa ison, ables om F1 o F12 epo he s a is ics 𝑍𝑟,𝑠 as well as he ela ed p- alu e in b acke s (*** p<0.01, ** p<0.05, * p<0.1). In p a icula , each pai wise compa ison has o be ead sub ac ing he colu mn a iable om he ow a iable, e.g. T1 – T2, T1 – T3, T1 – T4, T2 – T3, and so on. Table F1: Pai wise compa isons o Rmse E icien P ice ac oss ea men s in pe iods om 1 o 10 Rmse E icien P ice in Pe iods 1_10 T1 T2 T3 T4 T1 -0.16 (0.938) -1.44 (0.444) -2.34 (0.238) T2 -1.28 (0.446) -2.18 (0.292) T3 -0.90 (0.617) T4 54 Table F2: Pai wise compa isons o Rmse E icien P ice ac oss ea men s in pe iods om 11 o 20 Rmse E icien P ice in Pe iods 11_20 T1 T2 T3 T4 T1 2.02 (0.300) -1.58 (0.384) 2.81 (0.136) T2 -3.60* (0.068) 0.79 (0.710) T3 4.40** (0.014) T4 Table F3: Pai wise compa isons o Rmse E icien P ice ac oss ea men s in pe iods om 1 o 20 Rmse E icien P ice in Pe iods 1_20 T1 T2 T3 T4 T1 1.39 (0.327) -1.37 (0.296) 0.63 (0.647) T2 -2.77** (0.031) -0.76 (0.613) T3 2.01 (0.120) T4 55 Table F4: Pai wise compa isons o Rmse Bayes P ice ac oss ea men s in pe iods om 1 o 10 Rmse Bayes P ice in Pe iods 1_10 T1 T2 T3 T4 T1 0.39 (0.771) -0.17 (0.871) -1.41 (0.199) T2 -0.57 (0.671) -1.80 (0.200) T3 -1.23 (0.292) T4 Table F5: Pai wise compa isons o Rmse Bayes P ice ac oss ea men s in pe iods om 11 o 20 Rmse Bayes P ice in Pe iods 11_20 T1 T2 T3 T4 T1 -5.90*** (0.000) -2.11** (0.023) -3.38*** (0.000) T2 3.79*** (0.002) 2.52* (0.057) T3 -1.27 (0.192) T4 56 Table F6: Pai wise compa isons o Rmse Bayes P ice ac oss ea men s in pe iods om 1 o 20 Rmse Bayes P ice in Pe iods 1_20 T1 T2 T3 T4 T1 -2.63*** (0.005) -1.32* (0.073) -2.47*** (0.001) T2 1.31 (0.162) 0.16 (0.867) T3 -1.14 (0.138) T4 Table F7: Pai wise compa isons o Rmse Unin o med P ice ac oss ea men s in pe iods om 1 o 10 Rmse Unin o med P ice in Pe iods 1_10 T1 T2 T3 T4 T1 3.07*** (0.001) 0.06 (0.939) -2.17** (0.013) T2 -3.14*** (0.000) -5.62*** (0.000) T3 2.47*** (0.002) T4 57 Table F8: Pai wise compa isons o Rmse Unin o med P ice ac oss ea men s in pe iods om 11 o 20 Rmse Unin o med P ice in Pe iods 11_20 T1 T2 T3 T4 T1 -4.93*** (0.000) -3.89*** (0.000) -8.29*** (0.000) T2 0.40 (0.717) -3.80*** (0.001) T3 -4.21*** (0.000) T4 Table F9: Pai wise compa isons o Rmse Unin o med P ice ac oss ea men s in pe iods om 1 o 20 Rmse Unin o med P ice in Pe iods 1_20 T1 T2 T3 T4 T1 -1.10 (0.168) -1.96** (0.011) -5.39*** (0.000) T2 -1.13 (0.138) -4.56*** (0.000) T3 -3.43*** (0.000) T4 64 A he end o e ach pe iod you will be shown you indi idual gain s in he las pe iod, and you accumula ed gains, al so he a e age gains in you g oup, he a e age gains in you ma ke and he a e age gains o he membe s o he ype B g oup.