Price Stability and Volatility in Markets with Positive and. Negative Expectations Feedback: An Experimental

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1 Pric Sabiliy and Volailiy in Marks wih Posiiv and Ngaiv Expcaions Fdback: An Exprimnal Invsigaion Pr Hmijr, Cars Homms, Jop Sonnmans and Jan Tuinsra Cnr for Non-linar Dynamics in Economics and Financ (CNDEF) School of Economics Univrsii van Amsrdam Rorssraa 11, 1018WB Amsrdam, Th Nhrlands May 2006 Absrac: Th voluion of many conomic variabls is affcd by xpcaions ha conomic agns hav wih rspc o h fuur dvlopmn of hs variabls. Hr w show, by mans of laboraory xprimns, ha mark bhavior dpnds o a larg xn on how h ralizd mark pric rsponds o an incras in avrag pric xpcaions. If i rsponds by dcrasing, as in commodiy marks, prics convrg quickly o hir quilibrium valu, confirming h raional xpcaions hypohsis. If h ralizd pric incrass afr an incras of avrag xpcaions, as is ypical for financial marks, larg flucuaions in ralizd prics ar likly. Kywords: mark bhavior, coordinaion, xpcaions fdback, xprimnal conomics JEL-cods: D02, G12, C92

2 2 A ky diffrnc bwn naural and social scincs is ha in social sysms individual xpcaions or blifs can affc h oucom. An invsor buys a sock ha h xpcs o go up in h fuur, a chip-manufacurr builds a nw producion faciliy bcaus sh xpcs ha dmand and hrfor prics will b high afr goods hav bn producd. Expcaions drmin bhavior of conomic agns and h acual mark oucom (i.., pric and radd quaniy, following from dmand and supply) is an aggrgaion of individual bhavior. Simulanously, conomic agns form hir xpcaions on h basis of mark hisory. Thrfor, a mark, lik ohr social nvironmns, has h propris of an xpcaions fdback sysm: pas mark bhavior drmins individual xpcaions ha, in urn, drmin currn mark bhavior and so on. Th srucur of an xpcaions fdback sysm can b characrizd as ihr posiiv or ngaiv. In dmand-drivn financial marks h fdback is posiiv and slf-confirming: if many agns xpc h pric of an ass o ris and hrfor sar buying h ass, aggrga dmand will incras, and so, by h law of supply and dmand, will h ass pric. Whn a majoriy of invsors xpcs marks o go down, his blif will b slf-fulfilling and h mark will go down. In supply-drivn commodiy marks h fdback is ngaiv: if many producrs xpc fuur prics o b high hy will incras producion. This lads o low prics and firms will, in hir disappoinmn, dcid o dcras producion only o find ha hy wr wrong again. To invsiga how xpcaions fdback affcs aggrga mark bhavior w dsignd xprimnal mark nvironmns ha diffr only in h sign of h xpcaions fdback bu ar quivaln along all ohr dimnsions. W compar hs marks wih rspc o h coordinaion of xpcaions and convrgnc o h mark quilibrium pric. Th diffrnc bwn posiiv and ngaiv xpcaion fdback sysms is rlad o h concp of, rspcivly, sragic complmns and subsius as inroducd by John Haliwangr and Michal Waldman (1985). Whn acions ar sragic complmns, raional

3 3 dcision-makrs br imia irraional individuals. This is h cas in h ass mark whr prdicing a pric clos o h prdicions of h ohr paricipans is mos profiabl. This coordinaion nhancs h impac of h irraional paricipans upon h ralizd prics and convrgnc o h quilibrium pric is unsur. In h ngaiv fdback marks raional dcision-makrs hav an incniv o prdic high (low) prics whn irraional individuals prdic prics blow (abov) h quilibrium pric. Hr acions ar sragic subsius: h impac of irraional individuals will b limid and convrgnc o h quilibrium pric mor likly. Coordinaion of prdicions will only ak plac afr convrgnc. Erns Fhr and Jan-Robr Tyran (2002, 2005) rpor on a rlad xprimn in which hy sudy h adjusmn of nominal prics afr an anicipad mony shock in a pric sing gam wih posiivly (complmns) or ngaivly slopd (subsius) racion curvs. Thy find much fasr convrgnc in h subsiu condiion, in lin wih our rsuls. 1 In Scion I w discuss wo wll-known xpcaions fdback modls from conomics and s ou h xprimnal dsign. Scion II dscribs h xprimnal rsuls and Scion III concluds. Th appndics conain a dscripion of h xprimnal insrucions and daild simaion rsuls of h individual prdicion sragis. I. Expcaions Fdback and Exprimnal Dsign Th mark wih ngaiv xpcaional fdback usd in h xprimn is basd on h classical cobwb or hog cycl modl (s Mordcai Ezkil, 1938, Marc Nrlov, 1958, Richard B. Frman, 1975, 1976, Gary A. Zarkin, 1985 and Paul R. Krugman, 2001). Is ky 1 Anohr rlad sudy concrning sragic subsius vrsus sragic complmns is Jan Pors and Sigrid Suns (2005). Thir focus, howvr, is mor on social bhavior han on convrgnc and coordinaion. Courno gams and Brand gams ar boh social dilmma siuaions (h Nash quilibrium is Paro-infficin), bu in Courno gams acions ar sragic subsius whil in Brrand gams hy ar sragic complmns. Pors and Suns dsign wo gams wih h sam Nash quilibrium, h sam social opimum and h sam absolu (bu opposi) slop of h racion curv. Thy find mor coopraion in h cas of sragic complmns han whn acions ar sragic subsius.

4 4 faur is a fixd producion lag, so producion dcisions by pric-aking firms ar basd on a forcas of h mark pric in h nx im priod. L D ( p ) b a nonngaiv and monoonically dcrasing dmand funcion and l ( ) S, b h nonngaiv supply funcion p h of firm h. Supply of firm h in h nx priod dpnds upon h xpcd pric, p,, for ha h priod by ha firm. Th scond ordr condiion for profi maximizaion implis ha S is a non-dcrasing funcion. Morovr, w assum ha all firms hav h sam supply funcion. In h modl qualiy bwn dmand and supply in ach priod is no rquird, bu in ach priod h mark pric is adjusd in h dircion of h xcss dmand, h rad gap islf bing absorbd by a hypohical mark makr. An incras of h pric forcas lads o incrasing producion, a dcrasing xcss dmand and hrfor a lowr mark pric. Th following pric-adjusmn formula was usd: (1) p p λ D( p ) S( p ) + ε. H = h, h= 1 Th xprssion bwn bracks rprsns xcss dmand, whr h mark makr uss dmand in priod -1 as a proxy for dmand in priod. W assum hr ar H supplirs, only diffring in h way hy form xpcaions. In h laboraory xprimn w ak H=6. Th mark makr adjuss h mark pric proporionally o h xcss dmand, wih a posiiv pric adjusmn cofficin λ. Th rm ε is a random rm, rprsning.g. small uncrainis in dmand; in h laboraory xprimn ε ~ N ( 0,1/ 4). In h cobwb ramn in h xprimn, h paricipans ac as advisors o h producrs in h mark, so hir individual pric xpcaions p, drmin aggrga supply. Th dmand funcion is akn h o b linarly dcrasing, D( p ) a bp ( p h ) sp S h, =, and h supply funcion is linarly incrasing,, =. No ha a linarly incrasing supply funcion can b drivd from h profi maximizaion problm of producrs wih a quadraic cos funcion.

5 5 For h laboraory xprimns w chos paramr valus s=1/6 and b=21/20, λ=1/b=20/21 and, for h inrcp of h dmand funcion, a=123. Th pric adjusmn rul hn bcoms: (2) p = ( 123 ) + ε, p whr 6 1 p = ph, is h avrag prdicion of h six paricipans in h xprimnal 6 h= 1 mark. Th scond mark in our laboraory xprimn consiss of a sandard ass-pricing modl (s Kih Cuhbrson, 1996, John Y. Campbll al. 1997, and William A. Brock and Cars H. Homms, 1998). Dmand of spculaors for a risky ass dpnds posiivly upon h ass s xpcd pric incras. Invsors can ihr invs in a risk-fr ass (.g. a govrnmn bond) wih a fixd gross rurn 1+r, or invs in a risky ass (.g. a sock) paying an uncrain dividnd y in ach priod. In his modl, xcss dmand for h risky ass lads o an incras in h ass pric, and an xcss supply o a dcras (s Avraham Bja and M. Barry Goldman, 1980). Sinc in h xprimn dmand was akn o b an incrasing funcion of h pric prdicions, as would b naural in h cas of a sock or som ohr financial ass, our ass pricing ramn was drivn by posiiv xpcaions fdback, which, o a crain xn, confirmd any ndncy in h paricipans' blifs abou fuur prics. As in h cobwb modl abov, a mark makr adaps prics in proporion o xcss dmand and h acual dvlopmn of prics is givn by (3) p ( p + y ( 1+ r) p ) H Eh, 1 s = p 1 + λ z + ε. 2 h 1 aσ = Excss dmand is givn by aggrga dmand, which consiss of h sum of individual dmand funcions of h radrs in h mark, minus h supply z s of shars of h risky ass,

6 6 assumd o b consan. Th xprssion for h dmand funcion is sandard and obaind from man-varianc maximizaion of nx priod s xpcd walh, whr a quals h cofficin of risk avrsion and 2 σ is h blif abou h condiional varianc of xcss rurns, hr assumd o b consan for all priods and all radrs. Each paricipan in h xprimn acs as an advisor o a radr (say a larg pnsion fund) informing hm of hir prdicions p,, h which h radr hn uss o calcula hr dmand funcion. Six paricipans form a group in h xprimn, i.. H = 6. To achiv symmry bwn h posiiv and ngaiv fdback ramn, w choos paramrs such ha hs ramns only diffr in h sign of h xpcaions fdback. Fixing paramrs valus a r = 1/ 20, σ 2 s a = 6, z = 1, λ = 20 / 21 and assuming ( y ) 4 E for all h and w g, for h posiiv fdback ramn, h following pric h, = adjusmn rul: (4) p = ( 3 + ) + ε, whr p and p p ar dfind as abov. As bfor, ε ~ ( 0,1/ 4) N is a random rm, rprsning.g. small random flucuaions in h supply of h risky ass. Th wo ramns ar prfc symmric opposis. On may asily chck ha h raional xpcaions quilibrium pric of (2) and (4) is p * = 60, and ha if all paricipans would forcas p h 60, hn p = 60 + ε. Boh pric sris (2) and (4) ar gnrad as a linar, = funcion of h avrag prdicions of six paricipans, h ralizaion of h random shocks is 2 Noic ha w hav chosn paramrs in boh ramns in such a way ha h dpndnc of p on p 1 cancls ou, and prics ar drmind by pric xpcaions alon. In his way w can isola h ffc of h xpcaions fdback, wihou any inrfrnc from pric fdbacks.

7 7 xacly h sam and h absolu valu of h slop of h rlaion bwn p and p is qual o 20 / 21 for boh ramns. Th only diffrnc bwn h ramns is h sign of his slop. No also ha p * = 60 is a sabl sady sa undr naïv xpcaions, p h, = p 1, sinc h absolu valu of h slop of (2) and (4) is givn by 20/21 and smallr han on. Thirn xprimnal marks of 50 priods wr crad, six wih ngaiv and svn wih posiiv fdback. In ach mark six sudns paricipad, who arn mor mony if hy prdic mark prics mor succssfully (h arnings in a priod ar basd on h quadraic rror of h prdicion). Evry priod h paricipans s h prviously ralizd prics and hir own prvious prdicions and hav o prdic h nx pric, wihou bing abl o obsrv ach ohr s prdicions. Thir paymn (on avrag abou 22 uro in approximaly 90 minus) was basd upon hir quadraic prdicion rror (s Appndix C for dails on insrucions). II. Aggrga Mark Bhavior and Individual Prdicion Sragis Rsuls ar shown in Figurs 1 (ngaiv fdback) and 2 (posiiv fdback). Each individual panl shows, for on xprimnal mark, h ralizd prics and h six im sris of individual prdicions. Two characrisics of h daa cach h y immdialy. Firs, in h ngaiv fdback mark prics nd o go hrough an iniial phas of high volailiy, naly convrging afrwards o h quilibrium pric 60, only o b disurbd occasionally by h impac of a misak by on of h group mmbrs. Allowing for an iniial larning phas, for all six ngaiv fdback marks avrag prics ar saisically no significanly diffrn a a 5% lvl from wha h raional xpcaions hypohsis prdics. Volailiy is no significanly diffrn a a 5% lvl from h volailiy undr raional xpcaions for h firs

8 8 (N1) and fourh (N4) mark. In conras, in h posiiv fdback marks, alhough h hrogniy of prdicions dcrass in a much shorr priod, a quick convrgnc o h quilibrium pric dos no occur. Rahr, mos groups show a slow oscillaory movmn around h quilibrium pric of 60, and com clos o i only in h vry long run. Avrag prics and volailiy in all posiiv fdback groups ar significanly diffrn a a 5% lvl from h pric and volailiy undr raional xpcaions. Scond, in boh ramns hr is lil disprsion bwn individual prdicions wihin xprimnal marks, which is paricularly rmarkabl for h non-convrging posiiv fdback ramn. Paricipans in h posiiv fdback ramn quickly coordina on a common non-quilibrium prdicion rul. Convrgnc of prics and coordinaion of xpcaions is dmonsrad in mor dail in Figur 3. Th uppr panl shows h mdian of h absolu diffrnc bwn h mark pric and h quilibrium pric of 60 for boh ramns. W find a much highr dgr of convrgnc o h quilibrium pric in h ngaiv fdback ramn afr priod wo (saisically significan a 5% in 44 of h 48 priods, Wilcoxon s). Coordinaion of xpcaions is masurd by h sandard dviaion of h individual xpcaions of h mark paricipans. Th lowr panl shows h mdian ovr 6 or 7 marks of hs sandard dviaions for ach priod. A low sandard dviaion implis a high lvl of consnsus among h paricipans abou h fuur pric. W find ha h sandard dviaion is highr (and hrfor coordinaion is lss) for h ngaiv fdback ramn in h arly priods 2-7 (saisically significan a 5%, Wilcoxon s). Afr priod 7, coordinaion is vry high in boh ramns. No ha, ousid of quilibrium, i pays off for paricipans in h ngaiv fdback ramn o disagr wih h majoriy: if h avrag prdicion is high, h ralizd pric will b low. This drivs h hrogniy in prdicions in h arly priods and h fas convrgnc o h quilibrium pric. In h posiiv fdback ramn, on h ohr hand, agring wih h majoriy pays off sinc h mark pric will b clos o h avrag

9 9 pric prdicion. This quick coordinaion of pric prdicions in h posiiv fdback ramn is surprising, sinc paricipans wr no abl o obsrv ach ohrs prdicions during h xprimn, making h coordinaion islf "blind". Individual pric prdicions and aggrga mark prics can concisly b summarizd as xhibiing "slow coordinaion and fas convrgnc" in h ngaiv fdback ramn, and "fas coordinaion and slow convrgnc" in h posiiv fdback ramn. Linar prdicion ruls of h form 3 3, si ph, i +, i= 1 i= 1 (5) h = c + oi p i + p ν wr simad for ach individual paricipan. Prdicions of 71 ou of 78 paricipans could b dscribd succssfully his way (s Appndix B), which suggss ha paricipans us simpl linar forcasing ruls basd on rcn informaion o form prdicions. In fac, for 40 of h 78 paricipans prdicions can b dscribd by an vn simplr firs ordr hurisic (6) p α p + α p + ( α α ) 60 + β ( p p ) + ν. h, = h, For hs paricipans prdicions ar formd as a wighd avrag bwn h quilibrium pric of 60, h las obsrvd pric, h paricipans las own pric prdicion and a rnd rm ( p p ) β, masuring how paricipans rspond o h las pric chang. Figur rprsns hs 40 prdicion ruls in a prism of firs-ordr hurisics. In h posiiv fdback nvironmn (21 prdicion ruls, black dos) paricipans nd o bas hir prdicion on a wighd avrag of h las pric and prdicion and xrapola rnds in pas prics from hr ( α 1, α 2 > 0, α 1 + α 2 clos o 1 and β > 0 ) wihou aking h quilibrium pric ino accoun. On h ohr hand, mos of h simad prdicion ruls from h ngaiv fdback ramn (19 prdicion ruls, yllow dos) li along h α1 -axis ( α 2 and β clos o 0) implying ha ypically prdicions in ha ramn ar a wighd avrag bwn h las obsrvd pric and h quilibrium pric lvl.

10 10 III. Discussion No-classical conomic hory assums ha popl form xpcaions raionally (John F. Muh 1961, Robr E. Lucas and Edward Prsco, 1972). This implis ha on avrag mark paricipans mak corrc pric forcass and ha prics quickly convrg o hir mark claring quilibrium valus, hrby lading o an fficin allocaion of rsourcs (Eugn F. Fama, 1970, 1991). Howvr, larg flucuaions of prics on financial marks hav fuld h dba whhr his is indd a good dscripion of conomic bhavior (Robr J. Shillr, 1981, Wrnr F. DBond and Richard H. Thalr, 1985 and Pr M. Garbr, 1990). Our findings show ha whhr raional xpcaions givs a good dscripion of aggrga mark bhavior dpnds upon h undrlying xpcaions fdback srucur. In fac, commonly obsrvd diffrncs bwn xprimnal commodiy and financial marks (Vrnon L. Smih, 1962, Vrnon L. Smih al. 1988, Dhananjay K. God and Shyam Sundr, 1993 and Cars H. Homms al. 2005) can b aribud o a larg xn by his fdback srucur. Prics in a producion mark will b much mor sabl and closr o h quilibrium valu whn h produc (and producion chnology) has bn around for a whil and prics can flucua wildly only for rlaivly nw producs (.g. compur chips, Th Economis, 1996a,b, 2001). Th fac ha som sablishd commodiy marks rgularly xhibi flucuaions is consisn wih our conclusions sinc hs flucuaions may b aribud o h prsnc of dmand-drivn spculaors (Paul Cashin al. 2002, and W. Bruc Canols al. 1998). In conras, du o h posiiv fdback srucur, financial marks can asily divrg from h quilibrium pric and b rlaivly unsabl and xcssivly volail.

11 11 Rfrncs Bja, Avraham and Goldman, M. Barry. On h Dynamic Bhavior of Prics in Disquilibrium. Journal of Financ, 1980, 35 (2), pp Brock, William A. and Homms, Cars H. Hrognous Blifs and Rous o Chaos in a Simpl Ass Pricing Modl. Journal of Economics Dynamics and Conrol, 1998, 22 (8-9), pp Campbll, John Y., Lo, Andrw W. and MacKinlay, A. Craig. Th Economrics of Financial Marks, Princon, NJ: Princon Univrsiy Prss, Canols, W. Bruc, Thompson, Sarahln R., Irwin, Sco H. and Franc, Virginia G. An Analysis of h Profils and Moivaions of Habiual Commodiy Spculaors. Journal of Fuurs Marks, 1998, 18 (7), pp Cashin, Paul, McDrmo, John C. and Sco, Alasdair. Booms and Slumps in Commodiy Prics. Journal of Dvlopmn Economics, 2002, 69 (1), pp Cuhbrson, Kih. Quaniaiv Financial Economics: Socks, Bonds and Forign Exchang. Chichsr, UK: Wily, D Bond, Wrnr F.M. and Thalr, Richard. Dos h Sock Mark Ovrrac? Journal of Financ, 1985, 40 (3), pp Economis. Tha asonishing microchip. Scion Ladrs, 1996a, March 23, 338 (7958). Economis. Whn h chips ar down. Scion Smiconducors, 1996b, March 23, 338 (7958). Economis. Th gra chip glu. Scion Businss, 2001, Augus 11, 360 (8234). Ezkil, Mordcai. Th Cobwb Thorm. Quarrly Journal of Economics, 1938, 52 (2), pp

12 12 Fama, Eugn F. Efficin Capial Marks: A Rviw of Thory and Empirical Work. Journal of Financ, 1970, 25 (2), pp Fama, Eugn F. Efficin Capial Marks II. Journal of Financ, 1991, 46 (5), pp Fhr, Erns and Tyran, Jan-Robr. Individual Irraionaliy and Aggrga Oucoms. Journal of Economic Prspcivs, 2005, 19 (4), pp Fhr, Erns and Tyran, Jan-Robr. Limid Raionaliy and Sragic Inracion - Th Impac of h Sragic Environmn on Nominal Inria Univrsiy of S. Galln Dparmn of Economics working papr sris 2002 Frman, Richard B. Lgal Cobwbs : A Rcursiv Modl of h Mark for Nw Lawyrs. Rviw of Economics and Saisics, 1975, 57 (2), pp Frman, Richard B. A Cobwb Modl of h Supply and Saring Salary of Nw Enginrs. Indusrial and Labor Rlaions Rviw, 1976, 29 (2), pp Garbr, Pr M. Famous Firs Bubbls. Journal of Economic Prspcivs, 1990, 4 (2), pp God, Dhananjay K. and Sundr, Shyam. Allocaiv Efficincy of Marks wih Zro- Inllignc Tradrs: Mark as a Parial Subsiu for Individual Raionaliy. Journal of Poliical Economy, 1993, 101 (1), pp Haliwangr, John and Waldman, Michal. Raional Expcaions and h Limis of Raionaliy: An Analysis of Hrogniy Amrican Economic Rviw, 1985, 75 (3), pp Homms, Cars H., Sonnmans, Jop H., Tuinsra, Jan and van d Vldn, Hnk. Coordinaion of Expcaions in Ass Pricing Exprimns. Rviw of Financial Sudis, 2005, 18 (3), pp Krugman, Paul R. Th Oil-Hog Cycl. Th Nw York Tims, 2001, Novmbr 18, pp. 14.

13 13 Lucas, Robr E. and Prsco, Edward C. Invsmn undr Uncrainy. Economrica, 1972, 39 (5), pp Muh, John. F. Raional Expcaions and h Thory of Pric Movmns. Economrica, 1961, 29 (6), pp Nrlov, Marc. Adapiv Expcaions and Cobwb Phnomna. Quarrly Journal of Economics, 1958, 73 (2), pp Pors, Jan and Suns, Sigrid Sragic inracion, xrnaliis and coopraion in social dilmmas: xprimnal vidnc Working papr 2005 Shillr, Robr J. Do Sock Prics Mov Too Much o b Jusifid by Subsqun Changs in Dividnds. Amrican Economic Rviw, 1981, 71 (3), pp Smih, Vrnon L. An Exprimnal Sudy of Compiiv Mark Bhavior. Journal of Poliical Economy, 1962, 70 (3), pp Smih, Vrnon L., Suchank, Grry L. and Williams, Arlingon W. Bubbls, Crashs and Endognous Expcaions in Exprimnal Spo Ass Marks. Economrica, 1988, 56 (5), pp Zarkin, Gary A. Occupaional Choic: An Applicaion o h Mark for Public School Tachrs. Quarrly Journal of Economics, 1985, 100 (2), pp Acknowldgmns. W hank h Duch Scinc Foundaion (NWO) for financial suppor.

14 14 Figur 1: Prics and prdicions in h ngaiv fdback ramn. Each panl conains, for on xprimnal mark, im sris for h ralizd pric (in rd) and h im sris of individual prdicion of h six paricipans. Figur 2: Prics and prdicions in h posiiv fdback ramn. Each panl conains, for on xprimnal mark, im sris for h ralizd pric (in rd) and h im sris of individual prdicion of h six paricipans. Figur 3: Uppr panl givs h mdian, ovr h diffrn groups, of h absolu diffrnc bwn h mark pric and h quilibrium pric; h lowr panl givs h mdian, ovr h diffrn groups, of h sandard dviaions of individual prdicions. Solid lins corrspond o h ngaiv fdback ramn, brokn lins corrspond o h posiiv fdback ramn. Figur 4: Prism of Firs-Ordr Hurisics conaining h paramr vcors of h prdicion ruls of h form ph, = α 1p 1 + α 2 ph, 1 + ( α1 α 2 ) 60 + β ( p 1 p 2 ) + ν 1. Th smallr graph on h righ is a op-down viw of h prism. Yllow dos dpic prdicion ruls from paricipans in h ngaiv fdback ramn and black dos dpic ruls from paricipans in h posiiv fdback ramn. Posiiv (ngaiv) valus of β corrspond o a rnd following (rnd rvrsing) prdicion rul. Th spcial cass naivy, fundamnalism and obsinacy corrspond o p p 1, p, = 60 and h, = h ph, ph, 1 =, rspcivly. Finally, adapaion rfrs o a prdicion rul of h form ( ) h = p 1 + α ph, α, wih 0 < α < 1. p, 1 1

15 15 Figur 1: Prics and prdicions in h ngaiv fdback ramn. Each panl conains, for on xprimnal mark, im sris for h ralizd pric (in rd) and h im sris of individual prdicion of h six paricipans.

16 16 Figur 2: Prics and prdicions in h posiiv fdback ramn. Each panl conains, for on xprimnal mark, im sris for h ralizd pric (in rd) and h im sris of individual prdicion of h six paricipans.

17 17 Figur 3: Uppr panl givs h mdian, ovr h diffrn groups, of h absolu diffrnc bwn h mark pric and h quilibrium pric; h lowr panl givs h mdian, ovr h diffrn groups, of h sandard dviaions of individual prdicions. Solid lins corrspond o h ngaiv fdback ramn, brokn lins corrspond o h posiiv fdback ramn.

18 18 Figur 4: Prism of Firs-Ordr Hurisics conaining h paramr vcors of h prdicion ruls of h form ph, α 1p 1 + α 2 ph, 1 + ( α1 α 2 ) 60 + β ( p 1 p ) + ν = 2 1. Th smallr graph on h righ is a op-down viw of h prism. Yllow dos dpic prdicion ruls from paricipans in h ngaiv fdback ramn and black dos dpic ruls from paricipans in h posiiv fdback ramn. Posiiv (ngaiv) valus of β corrspond o a rnd following (rnd rvrsing) prdicion rul. Th spcial cass naivy, fundamnalism and obsinacy corrspond o p p 1, p, = 60 and h, = h ph, ph, 1 =, rspcivly. Finally, adapaion rfrs o a prdicion rul of h form ( ) h = p 1 + α ph, α, wih 0 < α < 1. p, 1 1

19 19 Appndix A: Th Main Exprimnal Compur Scrn Th main xprimnal compur scrn is givn in Figur A.1. Th figur shows h acual dvlopmn of on of h xprimnal marks, in his cas an Ass Pricing mark, from h prspciv of on of h paricipans. Th paricipan obsrvs boh a graphical and a numrical rprsnaion of h ralizd mark prics and his prvious pric prdicions, in h uppr lf and righ panl rspcivly. In h middl lf panl informaion is displayd rgarding h oal arnings so far of h paricipan, his arnings in h las priod and h prsn im priod of h xprimn. Th paricipan submis his pric prdicion for h nx priod in h lowr middl panl. Figur A.1: Th main xprimnal compur scrn. Th Duch labls ransla as follows: prijs = pric; voorsplling = prdicion; wrklijk prijs = mark pric; rond = round; oal vrdinsn = oal arnings; vrdinsn dz priod = arnings his priod; Wa is uw voorsplling voor d volgnd priod? = Wha is your prdicion for h nx priod?; En niuw rond is bgonnn = A nw round has sard.

20 20 Appndix B: Cofficin Esimas for Equaions (5) and (6) Par.no. c p -1 p -2 p -3 p -1 p -2 p -3 R 2 AC No No No * No * No No No * No Ys No No No * No No No No No No No No No Ys No No No No No No No * No * No No No No No No Tabl B.1: Prdicion ruls for h 36 paricipans of h ngaiv fdback ramn (las squars simaion of quaion (5)). Th firs column shows paricipans' numbrs, clusrd according o group; h scond hrough ighh column show cofficin simas; h las wo columns show h R-squard saisic and rpor on auocorrlaion in h rsiduals up o h 20 h ordr (Ljung-Box Q-saisics, 5% lvl). Insignifican variabls wr liminad on by on, largs p valu firs, unil all p valus wr blow 5%. An asrisk in h scond column indicas ha h consan is insignifican.

21 21 Par.no. c p -1 p -2 p -3 p -1 p -2 p -3 R 2 AC * No * No * No No * No * No * Ys * No * No * No * No * No * No * No * No * No * No No No * No No No No * No Ys * No Ys No Ys No * No * No * No * No Ys * No * No No No * No * No * No Tabl B.2: Prdicion ruls for h 42 paricipans of h posiiv fdback ramn (las squars simaion of quaion (5) in h papr). S h capion for Tabl B.1 for mor informaion.

22 22 PFOH Par.no. α 1 α 2 β Orig. par.no. Orig. gr.no. Labl N1 Naiv Fundamnalis N1 Non N1 Naiv & Fundamnalis N1 Fundamnalis N2 Non N2 Naiv Fundamnalis N3 Non N3 Naiv & Fundamnalis N3 Naiv Fundamnalis N4 Naiv Fundamnalis N4 Fundamnalis N4 Fundamnalis N5 Fundamnalis N5 Naiv & Fundamnalis N5 Naiv & Fundamnalis N5 Naïv N6 Fundamnalis N6 Non N6 Non P1 Naiv Trnd Followr P1 Naiv Trnd Followr P1 Adapiv Trnd Followr P1 Non P2 Adapiv Trnd Followr P2 Adapiv Trnd Followr P3 Naiv Trnd Followr P3 Adapiv Trnd Followr P3 Naiv Trnd Followr P4 Naiv Trnd Followr P4 Non P4 Non P4 Naiv & Adapiv Tr.Foll P5 Naiv & Adapiv Tr.Foll P6 Adapiv Trnd Followr P6 Naiv Trnd Followr P6 Naiv Trnd Followr P7 Non P7 Non P7 Naiv Trnd Followr P7 Adapiv Trnd Followr Tabl B.3: Prdicion ruls for boh ramns (las squars simaion of quaion (6)) for h Prism of Firs-Ordr Hurisics. Th firs column is h numbr of rlvan paricipans, clusrd according o ramn; h scond, hird and fourh columns show cofficin simas, simad by liminaing h las significan variabl unil all p valus wr blow 5%. This procdur was applid only o h linar prdicion ruls saisically quivaln o a rul in h Prism (Wald rsricion s, 5% lvl). Th fifh and sixh columns show h paricipan's original numbr and group (cf. Tabls B.1 and B.2); h svnh chcks for saisical quivalnc wih canonical ruls (Wald rsricion s, 5%).

23 23 Appndix C: Exprimnal Insrucions During ach of h four xprimnal sssions, a shor wlcoming mssag was rad aloud from papr, afr which h paricipans wr randomly assignd o a cubicl in h compur lab. In ach cubicl hr was a compur, som xprimnal insrucions on papr and som blank papr wih a pn. Th wo ramns had similar insrucions ha diffrd only in hir dscripion of h mark nvironmn. Whn all h paricipans wr sad, hy wr askd o rad h insrucions on hir dsks. Afr a fw minus, hy wr givn h opporuniy o ask qusions rgarding h insrucions, afr which h xprimn sard. Whn h 50 im priods wr compld, h paricipans wr askd o rmain sad and fill in h qusionnair, which was subsqunly handd ou o hm. Afr a rasonabl amoun of im, h paricipans wr calld o h an-room on by on o hand in h qusionnair and rciv hir arnings, in cash. Th paricipans lf h compur lab afr rciving hir arnings. Th xprimnal insrucions h paricipans rad in hir cubicls consisd of hr pars, oalling fiv pags. Th firs par conaind gnral informaion abou h mark h xprimn was abou o simula, which was of cours ramn-spcific. Th scond par conaind an xplanaion of h compur program usd during h xprimn. Th hird par displayd a abl rlaing h absolu prdicion rror mad in any singl priod o h amoun of crdis arnd in ha priod. Th convrsion ra bwn crdis and uros, bing 2600 crdis o 1 uro, was mad public by announcmn, sinc i was no lisd wih h abl. Th qusionnair afr h xprimn conaind 19 qusions, h firs 10 of which could b answrd only by h ingrs 1 hrough 5. Th xprimnal insrucions will b ranslad blow.

24 24 Translaion of xprimnal insrucions for ngaiv fdback ramn Exprimnal insrucions Th shap of h arificial mark usd by h xprimn, and h rol you will hav in i, will b xplaind in h x blow. Rad hs insrucions carfully. Thy coninu on h backsid of his sh of papr. Gnral informaion You ar an advisor of an imporr who is aciv on a mark for a crain produc. In ach im priod h imporr nds a good prdicion of h pric of h produc. Furhrmor, h pric should b prdicd on priod ahad, sinc imporing h good aks som im. As h advisor of h imporr you will prdic h pric P() of h produc during 50 succssiv im priods. Your arnings during h xprimn will dpnd on h accuracy of your prdicions. Th smallr your prdicion rrors, h grar your arnings. Abou h mark Th pric of h produc will b drmind by h law of supply and dmand. Th siz of dmand is dpndn on h pric. If h pric gos up, dmand will go down. Th supply on h mark is drmind by h imporrs of h produc. Highr pric prdicions mak an imporr impor a highr quaniy, incrasing supply. Thr ar svral larg imporrs aciv on his mark and ach of hm is advisd by a paricipan of his xprimn. Toal supply is largly drmind by h sum of h individual supplis of hs imporrs. Bsids h larg imporrs, a numbr of small imporrs is aciv on h mark, craing small flucuaions in oal supply. Abou h pric Th pric is drmind as follows. If oal dmand is largr han oal supply, h pric will ris. Convrsly, if oal supply is largr han oal dmand, h pric will fall.

25 25 Abou prdicing h pric Th only ask of h advisors in his xprimn is o prdic h mark pric P() in ach im priod as accuraly as possibl. Th pric (and your prdicion) can nvr bcom ngaiv and always lis bwn 0 and 100 uros in h firs priod. Th pric and h prdicion in priod 2 hrough 50 is only rquird o b posiiv. Th pric will b prdicd on priod ahad. A h bginning of h xprimn you ar askd o giv a prdicion for priod 1, V(1). Whn all paricipans hav submid hir prdicions for h firs priod, h mark pric P(1) for his priod will b mad public. Basd on h prdicion rror in priod 1, P(1) - V(1), your arnings in h firs priod will b calculad. Subsqunly, you ar askd o nr your prdicion for priod 2, V(2). Whn all paricipans hav submid hir prdicion for h scond priod, h mark pric for ha priod, P(2), will b mad public and your arnings will b calculad, and so on, for 50 conscuiv priods. Th informaion you hav o form a prdicion a priod consiss of: All mark prics up o im priod -1: {P(-1), P(-2),..., P(1)}; All your prdicions up unil im priod -1: {V(-1), V(-2),..., V(1)}; Your oal arnings a im priod -1. Abou h arnings Your arnings dpnd only on h accuracy of your prdicions. Th br you prdic h pric in ach priod, h highr will b your oal arnings. Th aachd abl liss all possibl arnings. Whn you ar don rading h xprimnal insrucions, you may coninu rading h compur insrucions, which hav bn placd on your dsk as wll.

26 26 Translaion of xprimnal insrucions for posiiv fdback ramn Exprimnal insrucions Th shap of h arificial mark usd by h xprimn, and h rol you will hav in i, will b xplaind in h x blow. Rad hs insrucions carfully. Thy coninu on h backsid of his sh of papr. Gnral informaion You ar an advisor of a radr who is aciv on a mark for a crain produc. In ach im priod h radr nds o dcid how many unis of h produc h will buy, innding o sll hm again h nx priod. To ak an opimal dcision, h radr rquirs a good prdicion of h mark pric in h nx im priod. As h advisor of h radr you will prdic h pric P() of h produc during 50 succssiv im priods. Your arnings during h xprimn will dpnd on h accuracy of your prdicions. Th smallr your prdicion rrors, h grar your arnings. Abou h mark Th pric of h produc will b drmind by h law of supply and dmand. Supply and dmand on h mark ar drmind by h radrs of h produc. Highr pric prdicions mak a radr dmand a highr quaniy. A high pric prdicion maks h radr willing o buy h produc, a low pric prdicion maks him willing o sll i. Thr ar svral larg radrs aciv on his mark and ach of hm is advisd by a paricipan of his xprimn. Toal supply is largly drmind by h sum of h individual supplis and dmands of hs radrs. Bsids h larg radrs, a numbr of small radrs is aciv on h mark, craing small flucuaions in oal supply and dmand. Abou h pric Th pric is drmind as follows. If oal dmand is largr han oal supply, h pric will ris. Convrsly, if oal supply is largr han oal dmand, h pric will fall.

27 27 Abou prdicing h pric Th only ask of h advisors in his xprimn is o prdic h mark pric P() in ach im priod as accuraly as possibl. Th pric (and your prdicion) can nvr bcom ngaiv and lis always bwn 0 and 100 uros in h firs priod. Th pric and h prdicion in priod 2 hrough 50 is only rquird o b posiiv. Th pric will b prdicd on priod ahad. A h bginning of h xprimn you ar askd o giv a prdicion for priod 1, V(1). Whn all paricipans hav submid hir prdicions for h firs priod, h mark pric P(1) for his priod will b mad public. Basd on h prdicion rror in priod 1, P(1) - V(1), your arnings in h firs priod will b calculad. Subsqunly, you ar askd o nr your prdicion for priod 2, V(2). Whn all paricipans hav submid hir prdicion for h scond priod, h mark pric for ha priod, P(2), will b mad public and your arnings will b calculad, and so on, for 50 conscuiv priods. Th informaion you hav o form a prdicion a priod consiss of: All mark prics up o im priod -1: {P(-1), P(-2),..., P(1)}; All your prdicions up unil im priod -1: {V(-1), V(-2),..., V(1)}; Your oal arnings a im priod -1. Abou h arnings Your arnings dpnd only on h accuracy of your prdicions. Th br you prdic h pric in ach priod, h highr will b your oal arnings. Th aachd abl liss all possibl arnings. Whn you ar don rading h xprimnal insrucions, you may coninu rading h compur insrucions, which hav bn placd on your dsk as wll.

28 28 Translaion of compur insrucions Compur insrucions Th way h compur program works ha will b usd in h xprimn, is xplaind in h x blow. Rad hs insrucions carfully. Thy coninu on h backsid of his sh of papr. Th mous dos no work in his program. Your arnings in h xprimn dpnd on h accuracy of your prdicions. A smallr prdicion rror in ach priod will rsul in highr arnings. To nr your prdicion you can us h numbrs, h dcimal poin and, if ncssary, h backspac ky on h kyboard. Your prdicion can hav wo dcimal numbrs, for xampl Pay anion no o nr a comma insad of a poin. Nvr us h comma. Prss nr if you hav mad your choic. Th br your prdicion, h mor crdis you will arn. On your dsk is a abl lising your arnings for all possibl prdicion rrors. For xampl, your prdicion was Th ru mark pric urnd ou o b This mans ha h prdicion rror is: Th abl hn says your arnings ar 1255 crdis (as lisd in h hird column [his is a yping rror, i should b scond column]). Th availabl informaion for prdicing h pric of h produc in priod consiss of: All produc prics from h pas up o priod -1; Your prdicions up o priod -1; Your arnings unil hn. [Th capion of h figur.] Th compur scrn. Th insrucions blow rfr o his figur. In h uppr lf cornr a graph will b displayd consising of your prdicions and of h ru

29 29 prics in ach priod. This graph will b updad a h nd of ach priod. In h rcangl in h middl lf you will s informaion abou h numbr of crdis you hav arnd in h las priod and h numbr you hav arnd in oal. Th im priod is also displayd hr, possibly along wih ohr rlvan informaion. On h righ hand sid of h scrn h xprimnal rsuls will b displayd, ha is, your prdicions and h ru prics for a mos h las 20 priods. A h momn of submiing your pric prdicion, h rcangl in h lowr lf sid of h figur will appar. Whn all paricipans hav subsqunly submid hir prdicions, h rsuls for h nx priod will b calculad. Whn vryon is rady rading h insrucions, w will bgin h xprimn. If you hav qusions now or during h xprimn, rais your hand. Somon will com o you for assisanc.