An Experimental Test of the Lucas Asset Pricing Model

Transcription

1 An Expermental Test of the Lucas Asset Prcng Model Sean Crockett, John Duffy, and Yehuda Izhakan Aprl 26, 2018 Abstract We mplement a dynamc asset prcng experment n the sprt of Lucas (1978) wth storable assets and non-storable cash. In the frst treatment, we mpose dmnshng margnal returns to cash to ncentvze consumpton smoothng across perods. We fnd that subjects use the asset to smooth consumpton, although the asset trades at a dscount relatve to the rsk-neutral fundamental prce. Ths under-prcng s a departure from the asset prce bubbles observed n the large expermental asset prcng lterature orgnatng wth Smth et al. (1988) and can be ratonalzed by consderng subjects rsk averson wth respect to uncertan money earnngs. In a second treatment, wth no nduced motvaton for trade à la the Smth et al. desgn, we fnd that the asset trades at a premum relatve to ts expected value and that shareholdngs are hghly concentrated. Elmnaton of asset prce uncertanty n addtonal expermental treatments serves to renforce the same observatons, and suggests that speculatve behavor explans the departure of prces from fundamental value n the absence of a consumpton-smoothng motve for asset trades. Keywords: Asset Prcng, Lucas Tree Model, Expermental Economcs, General Equlbrum, Intertemporal Choce, Macrofnance, Consumpton Smoothng. JEL Classfcaton Numbers: C90, D51, D91, G12. Baruch College, Cty Unversty of New York; sean.crockett@baruch.cuny.edu Unversty of Calforna, Irvne; duffy@uc.edu Baruch College, Cty Unversty of New York; yud@stern.nyu.edu; For useful comments and suggestons, we thank the edtor, Dmtr Vayanos, and four anonymous referees, as well as Elena Asparouhova, Peter Bossaerts, Crag Brown, Gullaume Frechette, John Geanakoplos, Steven Gjerstad, Davd Porter, Stephen Spear and semnar partcpants at varous conferences and unverstes. We thank Jonathan Lafky for assstance wth programmng the experment. Fundng for ths project was provded by the Detrch School of Arts and Scences of the Unversty of Pttsburgh.

2 1 Introducton Consumpton-based general equlbrum asset prcng, poneered by Stgltz (1970), Lucas (1978), and Breeden (1979), remans a workhorse model n fnancal economcs and macrofnance. Ths approach relates asset prces to rsk and tme preferences, dvdend payments, and other fundamental determnants of asset values. 1 Whle ths class of theoretcal models has been extensvely tested usng archval feld data, the evdence to date has not been too supportve of the models predctons. Estmated or calbrated versons of the standard model generally under-predct the actual premum n the return to equtes relatve to bonds, the so-called equty premum puzzle (e.g., Hansen and Sngleton 1983, Mehra and Prescott 1985, and Kocherlakota 1996). Furthermore, the actual volatlty of asset prces s typcally much greater than the model s predcted volatlty based on changes n fundamentals alone, the so-called excess volatlty puzzle (Shller 1981, and LeRoy and Porter 1981). 2 A dffculty wth testng ths model usng feld data s that mportant parameters are unknown and must be calbrated, approxmated, or estmated n some fashon. An addtonal dffculty s that the avalable feld data (e.g., aggregate consumpton data) may be subject to measurement error (Wheatley 1988) or may not approxmate well the consumpton of asset market partcpants (Mankw and Zeldes 1991). A typcal approach s to specfy a dvdend process and calbrate ndvduals preferences to ths process usng mcro-level data. However, mcro-level data may not be drectly relevant to the doman or frequency of the data examned n macrofnance studes. We follow a dfferent path by analyzng data from a laboratory experment wth controlled ncome and dvdend processes, allowng for precse measurement of consumpton and asset holdngs. nduce the statonarty assocated wth the Lucas model s nfnte horzon and tme dscountng by mplementng an ndefnte horzon wth a constant contnuaton probablty. In addton, we nduce heterogenety n consumer types to create a clear motvaton for subjects to engage n trade. 3 degree of control afforded by the laboratory presents an opportunty to dagnose the causes of specfc devatons from theory, whch are not dentfable usng feld data alone. Most prevous dynamc asset prcng experments depart n sgnfcant ways from consumptonbased models. 4 In the early lterature (e.g., Forsythe et al. 1982, Plott and Sunder 1982, and Fredman et al. 1984), cyclc type-dependent dvdends are nduced to motvate trade, resultng n market prces 1 For surveys, see e.g., Campbell (2018), Cochrane (2005) and Lengwler (2009). 2 Nevertheless, Cochrane (Page 455, 2005) stresses that whle the consumpton-based model works poorly n practce (...) t s n some sense the only model we have. The central task of fnancal economcs s to fgure out what are the real rsks that drve asset prces and expected returns. Somethng lke the consumpton-based model nvestor s frst-order condtons for savngs and portfolo choce has to be the startng pont. 3 In ths respect, we devate from the theoretcal lterature, whch frequently presumes a representatve agent and derves equlbrum asset prces at whch the equlbrum volume of trade s zero. 4 Some studes test the statc captal-asset prcng model (CAPM) over multple repettons; e.g., Bossaerts and Plott (2002), Asparouhova et al. (2003), and Bossaerts et al. (2007). We The 1

3 that effectvely aggregate prvate dvdend nformaton and converge toward ratonal expectatons values. Whle ths result s n lne wth the effcent markets vew, the prmary motvaton for exchange s not ntertemporal consumpton-smoothng as n the Lucas model. In later, hghly nfluental work, Smth et al. (SSW, 1988) mplement a smple four-state..d. dvdend process common to all subjects. A fnte number of tradng perods ensures that the expected value of the asset declnes over tme at a constant rate. Unlke the earler type-dependent dvdend experments, there s no nduced motve for subjects to engage n any trade n the asset. Nevertheless, SSW observe substantal tradng, wth prces typcally startng below the fundamental value then rapdly soarng above for a sustaned duraton of tme before fnally collapsng near the known fnal perod of the experment. Ths bubble-crash pattern has been replcated n many studes under a varety of treatment condtons, and has become the prmary focus of a large expermental lterature on asset prce formaton. 5 Much attenton has been devoted to explorng the means by whch the frequency of bubbles can be reduced or even elmnated by usng some varants of the SSW desgn. 6,7 Experments n the SSW tradton share the followng features. Subjects are gven a large, one-tme endowment (or loan) of expermental cash, called francs. Thereafter, an ndvdual s franc balance vares wth her asset purchases, sales, and earned dvdends. Francs carry over from one perod to the next over the fnte horzon of the market. Followng the termnal perod, franc balances are converted nto money earnngs usng a lnear exchange rate. Ths desgn dffers from the sequence of consumpton/savngs choces faced by consumers n standard nfnte horzon ntertemporal models; n essence, t abstracts from the consumpton-smoothng ratonale for trade n assets. By contrast, subjects n our experment receve an exogenous endowment of francs at the start of each perod, whch we nterpret as ncome, n addton to franc-denomnated dvdend payments on assets held. Then, an asset market s opened, wth each transacton mpactng the subject s franc balances. Crtcally, after the asset market s closed, each subject s end-of-perod franc balance s converted to dollars and stored n a prvate payment account from whch the subject cannot wthdraw durng the experment, whle her asset poston carres forward to the next perod wth a fxed and known probablty. Thus, all francs dsappear from the system at the end of each perod. That s, n the language of Lucas (1978) francs are pershable frut that get consumed each perod, whle assets 5 Key papers nclude Porter and Smth (1995), Le et al. (2001), Dufwenberg, et al. (2005), Haruvy and Noussar (2006), Haruvy et al. (2007), Hussam et al. (2008), Le and Vesely (2009), Lugovskvy et al. (2011) and Krchler et al. (2012). For a revew of the lterature, see Plott and Smth (Chapters 29-30, 2008). 6 These varants nclude addng short sales or futures markets, computng expected values for subjects, mplementng a constant dvdend, nsertng nsders who have prevously experenced bubbles, usng professonal traders n place of students as subjects, framng the problem dfferently, or usng dfferent prce determnaton mechansms 7 Hommes et al. (2005, 2008) employ a dfferent ntertemporal framework that exploted a no arbtrage condton between rsky and rsk-free assets. In each perod, prce forecasts from subjects are elcted and leveraged to calculate optmal ndvdual demands for the rsky asset. Equatng aggregate demand wth a fxed supply yelds prces, aganst whch forecasts are evaluated and compensated. 2

4 are potentally long-lved trees. 8 We motvate trade n our baselne ( concave ) treatment by ntroducng a heterogeneous, cyclc ncome process and a concave franc-to-dollar exchange rate, so that the long-lved asset becomes a vehcle to ntertemporally smooth consumpton. Ths s a crtcal feature of most macrofnance models, whch are bult around the permanent ncome model of consumpton, but t s absent from the expermental asset prcng lterature. In our alternatve ( lnear ) treatment, the franc-to-dollar exchange rate s lnear as n SSW-type desgns; snce the dvdend process s common to all subjects, there s no nduced reason for subjects to trade the asset, a desgn that connects our macrofnance economy wth the laboratory asset market desgn of SSW. We show theoretcally that f subjects are ntrnscally rsk neutral wth regard to uncertan money earnngs, the (constant) equlbrum prce (henceforth the fundamental prce ) n both our lnear and concave exchange rate treatments s the same and s equal to the fundamental prce n the analogous nfnte horzon economy. Importantly, however, equlbrum consumpton s characterzed by perfect consumpton smoothng n the concave treatment, and s unrestrcted n the lnear treatment. If subjects are nstead ntrnscally rsk averse wth regard to uncertan money earnngs, we show theoretcally that the equlbrum prce n each perod wll be strctly less than the fundamental prce, that prces wll converge to a steady state equlbrum prce that s weakly less than the fundamental prce, and for a gven dstrbuton of rsk preferences ths steady state prce wll be the same n both the concave and lnear treatments. To explore the role of rsk averson n our experment, we measure subjects ntrnsc rsk atttudes usng the Holt-Laury (2002) pared lottery choce nstrument. Whle our expermental desgn manly serves as a brdge between the expermental asset prcng and macrofnance lteratures, t also has some relevance for laboratory research on ntertemporal consumpton-smoothng, whch typcally excludes tradeable assets. 9 A man fndng of ths lterature s that subjects have dffculty ntertemporally smoothng ther consumpton n the manner prescrbed by the soluton to a dynamc optmzaton problem. By contrast, n our expermental desgn, n whch ntertemporal consumpton-smoothng s mplemented by buyng and sellng assets at marketdetermned prces, we fnd strong evdence that subjects are able to smooth consumpton n a manner that s qualtatvely (f not quanttatvely) smlar to the dynamc equlbrum soluton. Ths fndng may also reflect the consderably smpler and non-stochastc ncome process that we use n our desgn. Our man expermental fndngs can be summarzed as follows. Frst, n our lnear exchange rate treatment (where there s no nduced motve for trade), prces are most frequently sustaned at 8 Notce that francs play a dual role as consumpton good and medum of exchange wthn a perod, whle assets are the only ntertemporal store of value. 9 See, e.g., Hey and Dardanon (1988), Noussar and Matheny (2000), Ballnger et al. (2003), Carbone and Hey (2004), Carbone and Duffy (2014), and Messner (2016). 3

5 levels above the fundamental prce (on average, 32% above). However, the frequency, magntude, and duraton of such prce bubbles s dramatcally reduced n our concave exchange rate treatment, where assets trade at an average dscount of 24% relatve to the fundamental prce. The hgher prces n the lnear economes are drven by a concentraton of shareholdngs among the most rsk-tolerant subjects n the market, dentfed by the Holt-Laury elctaton. By contrast, n the concave economes, most subjects actvely trade shares n each perod to smooth ther consumpton n the manner predcted by theory. Consequently, shareholdngs are much less concentrated. Thus, market thn-ness and hgh prces appear to be endogenous features of the lnear treatment. We conclude that the frequency, magntude, and duraton of asset prce bubbles can be reduced by the presence of an ncentve to ntertemporally smooth consumpton, a key feature of most dynamc asset prcng models that s completely absent from the SSW desgn used n the expermental asset prcng lterature. To better understand ndvdual consumpton and savngs decsons, we conduct an addtonal, ndvdual choce experment n whch subjects can buy or sell assets wth the expermenter at a known, constant prce. In ths experment, the only uncertanty each subject faces s the duraton of the plannng horzon; ther endowments and the exchange rates reman the same as n the market experment. We observe that the removal of prce uncertanty strengthens the man fndngs from our market experment. Namely, ndvduals facng a concave exchange rate use the asset to ntertemporally smooth ther consumpton, whle those facng a lnear exchange rate adopt far more heterogeneous postons. Further, subjects facng hgh prces n the lnear exchange rate condton are less lkely to hold large share quanttes, relatve to the market experment, suggestng that speculatve motves account for the bubbles observed n the lnear market experment. In related, concurrent research, Asparouhova et al. (2016) mplement a Lucas asset experment n whch there are short-lved francs and two long-lved assets: trees yeldng stochastc dvdends and rsk-free (consol) bonds. Rather than nduce consumpton smoothng through a concave exchange rate, subjects n ther experment are pad only for francs held n the termnal perod of the ndefnte horzon. Thus, Asparhouhova et al. rely on ntrnsc subject rsk averson to smooth consumpton;.e., a rsk-averse subject should avod holdng too few francs n any perod n case that perod s the termnal one. Asparouhova et al. use endogenous consumpton-smoothng to nvestgate mportant questons n fnance lke the equty premum puzzle and the co-varaton of fnancal returns wth aggregate wealth. By contrast, we focus on the comparatve statc mpact of consumpton-smoothng when such ncentves are exogenously weak or strong, brdgng the gap between the consumptonbased Lucas asset prcng model and the expermental lterature ntated by SSW. Lke Asparouhova et al., we fnd some qualfed support for the predctons of the Lucas asset prcng model, n that prce realzatons are consstent wth compettve equlbrum levels when there s an nduced motve 4

6 to ntertemporally smooth consumpton and takng nto account subject s ntrnsc rsk averson. 2 The Lucas asset prcng framework In ths secton, we frst descrbe a Lucas (1978) nfnte horzon economy. We then consder the ndefnte horzon analog that we use n our experment. Fnally, we ntroduce the specal case of constant dvdend payments, a fxed aggregate endowment, and determnstc ndvdual ncome, whch are features of our expermental desgn. For ths case, we prove convergence to a steady state equlbrum n whch the prce s weakly less than the fundamental prce of the asset, provded weakly rsk-averse ntrnsc preferences. 2.1 Infnte horzon model Consder a Lucas (1978) pure exchange economy, comprsed of a non-storable consumpton good (frut) and an nfntely-lved asset (tree). At each dscrete tme, t, there s a fxed, fnte and perfectly dvsble number of outstandng shares, K, of the asset. Each share yelds an dentcal but potentally tme-dependent dvdend, D t, n perod t. Dvdends are pad n unts of the consumpton good at the begnnng of each perod. Let P t denote the ex-dvdend prce of a share,.e., f the share s sold, the sale occurs after the exstng owner receves that perod s dvdend D t. Nether borrowng nor short sellng s permtted. Ownershp of shares s determned each perod n a compettve market. Denote by kt the number of shares of the asset that consumer owns at the begnnng of perod t, wth ntal endowment k0. In each perod the economy has a fnte populaton, L, of consumers. Each consumer s characterzed by a strctly monotonc, strctly concave, bounded, and twce contnuously dfferentable nstantaneous utlty functon U : R + R that vanshes at zero. 10 That s, U ( ) c t > 0, U ( ) c t < 0, and U (0) = 0, where c t s the consumpton of pershable goods by consumer at tme t. In addton to the dvdend payment, each consumer receves an exogenous endowment of the consumpton good, denoted yt, at the begnnng of each perod t. Ths endowment may vary from perod to perod and may be dfferent across consumers. Thus, the total resources avalable to each consumer n a gven perod are the exogenous endowment, plus the sum of dvdends, plus (mnus) the sale (purchase) value of assets shares. Formally, whch mples that y t + D t k t + P t k t }{{} Resources k t+1 = = c t + P t kt+1, }{{} (1) Usage ( 1 + D ) t kt + 1 ( y P t P t c t). (2) t 10 R + stands for the set of nonnegatve real numbers,.e., R + = {x x 0, x R}. 5

7 Equaton (1) also mples the market clearng condtons K = k t and C t = c t, (3) for every t. Snce endowment and dvdends cannot be stored and the utlty functon s strctly monotonc, these resources are completely consumed n each perod. That s, C t = Y t + D t K, (4) where Y t = y t s the aggregate endowment n the economy at tme t. Each consumer,, faces the followng objectve functon, v ( [ m 0) = max β t U ( c t) ] (5) lm τ E t s.t. k t+1 = {c t} t=0 E 0 t=0 ( 1 + D ) t kt + 1 ( y P t P t c ) t t m t+1 = (P t+1 + D t+1 ) k t+1 where, to rule out non-fundamental solutons, the transversalty condton [ β τ U ( ) ] c t+τ (Pt+τ + D t+τ ) kt+τ = 0 s assumed to hold. 11 The coeffcent β (0, 1) s the (common) perod dscount factor, and E t [ ] stands for the expectaton condtonal upon the nformaton set (belefs) avalable to consumer at tme t. The varable m t+1 denotes the value of resources consumer chooses to transfer to tme t + 1 va the shareholdngs that she adopts at tme t. By the strct monotoncty of U, the budget constrant of each consumer s bndng n equlbrum. That s, c t = y t + (P t + D t ) k t P t k t+1. (6) Snce nether borrowng nor short sellng are permtted, we must have that c t 0 and k t 0. Hence, when the soluton to the maxmzaton problem n Equaton (5) mples c t < 0 or k t < 0, a boundary soluton s obtaned snce utlty functons are strctly monotonc. The same holds when the soluton mples that k t > K. Henceforth, we focus on characterzng the unque nteror equlbrum soluton. The consumer s maxmzaton problem n Equaton (5) can be rewrtten n the form of Bellman s (recursve) equaton v ( m t) ( = max {c t} U c t [ v ( m t+τ ) [ + βe t v ( m )] t+1, (7) ) m t+τ ] wth the transversalty condton lm τ βτ E t = 0. Suppose the value functon, v, s dfferentable. The frst order condton (FOC) for an nteror soluton at each tme t = 1, 2, 3... s 0 = U ( c t ) βe t [ v ( m t+1 ) P t+1 + D t+1 P t ], (8) 11 When U s lnear, the transversalty condton need not hold; n that case, non-fundamental bubble solutons are possble. 6

8 for every consumer. By the Envelope Theorem (e.g., Mlgrom and Segal (2002)), Thus, the FOC n Equaton (8) becomes P t = βe t v ( m t+1 ) = U ( c t+1 ). (9) [ U ( c t+1 ) U ( c t ) (P t+1 + D t+1 ) ], (10) whch, by applyng the law of terated expectatons, can be rewrtten as [ ( ) ] P t = E t β τ U c t+τ U ( ) D t+τ. (11) c t The term β U (c t+τ) U (c t) τ=1 s referred to as the stochastc dscount factor, and the term U (c t+τ) to as the ntertemporal margnal rate of substtuton. U (c t) s referred Equaton (11) does not assume a partcular form for the utlty functon U, and must hold for any equlbrum prce functon. 12 Equaton (11) holds for such a representatve consumer. 13 When all consumers have the same utlty functon and belefs, Because the utlty functon s strctly monotonc, markets clear. Fnally, by Lucas (Proposton 1, 1978), the pars v (m t ) and P t, whch are the soluton to the maxmzaton problem n Equaton (5), defne a unque equlbrum. 2.2 Indefnte horzon model wth nduced preferences Snce we cannot study an nfnte number of perods n the laboratory, we move to a related ndefnte horzon settng, where the economy contnues to the next perod wth a known, constant probablty, π. The economy remans comprsed of pershable frut and a fxed number of asset shares n a potentally long-lved tree. Frut (endowment ncome, dvdends, and net ncome from the sale of shares) s denomnated n an expermental currency called francs. Consumpton nvolves the converson of these franc balances nto real money earnngs ( dollars ) usng the exchange functon u : R + R + at the end of each perod. Ths exchange functon s strctly monotonc, strctly concave, bounded, twce contnuously dfferentable, and vanshes at zero. 14 The exchange functon s appled to control a consumer s objectve functon and provde ncentves to consume. A concave u nduces a dmnshng margnal utlty of consumpton and motvates consumpton smoothng through trade n the asset market. Thus, henceforth, we refer to u as an nduced utlty functon and to the concavty of u as nduced rsk averson. By contrast, we wll 12 Recall that, n equlbrum, the prce of assets must be such that each consumer does not want to modfy her asset holdngs at any tme t. 13 À la Constantndes (1982), a representatve nvestor can be defned as an artfcal nvestor whose tastes and belefs are such that f all nvestors n the economy had tastes and belefs dentcal to hs, the equlbrum n the economy remans unchanged. When consumers have heterogeneous belefs or utlty functons, the exstence of a representatve nvestor requres ether the market be complete (Dybvg and Ingersoll, 1982), or consumers have homogeneous belefs and tme-addtve utlty functons (Constantndes, 1980). 14 That s, u ( ) > 0, u ( ) < 0 and u (0) = 0. 7

9 henceforth refer to U as the unobserved ntrnsc (or homegrown) utlty functon of consumer. Later, we show that the functon u effectvely plays a role smlar to U n Equaton (11) when consumers are ntrnscally rsk neutral, but we wll also consder cases where consumers are ntrnscally rsk averse. In each perod t, consumer chooses a quantty, s t, of francs to convert (save) nto dollars, c t = u ( t s t), whch s added to her accumulated consumpton quantty (expermental earnngs) ζ t = c τ. These consumpton earnngs are not avalable to use durng the experment (dollars accrue n a vrtual lock box); at the end of the experment a subject s cumulatve balance s pad n cash. At the end of each perod a lottery determnes whether the economy contnues to the next perod wth probablty π or ends wth probablty 1 π. If the economy ends, then all asset shares vansh and consumpton of the accumulated dollars takes place. 15 If the economy contnues, then shareholdngs carry over to the next perod. In ths ndefnte horzon economy, each consumer faces the maxmzaton problem v ( [ m 0) = max (1 π) π t β t U ( ζt) ] (12) s.t. k t+1 = {s t} t=0 E 0 t=0 ( 1 + D ) t kt + 1 ( y P t P t s ) t t m t+1 = (P t+1 + D t+1 ) kt+1 t ζt = τ=0 c τ c t = u ( yt + D t kt ( + P t k t kt+1)), [ where the transversalty condton lm τ E t (1 π) π τ β τ U ( ) ζ t+τ u ( ) ] s t+τ (Pt+τ + D t+τ ) kt+τ = 0 s assumed to hold. 16 The frst constrant can be rewrtten to defne the quantty of francs that consumer converts nto dollars (saves) at tme t, s t = y t + D t k t + P t ( k t k t+1). (13) Snce both u and U are strctly monotonc, ths budget constrant s always bndng. The maxmzaton problem n Equaton (12) can be rephrased n the form of the Bellman s (recursve) equaton v ( m t) = max {s t} (1 π) ( U ζt ) [ + πβe t v ( m t+1)] wth the transversalty condton lm τ (1 π) πτ β τ E t τ=0 (14) [ v ( m ) ] t+τ m t+τ = 0. The FOC of an nteror 15 In the experment, subjects partcpate n several such ndefnte horzon economes (whch we call sequences). Thus, they are only pad ther accumulated earnngs followng the last of these sequences. 16 In the case where both U and u are lnear a possblty we allow for n our experment the transversalty condton need not hold. However, even n that case, snce the total resources of our expermental economy are held fxed, the transversalty condton must nevertheless hold. 8

10 soluton of ths problem s then [ ] 0 = (1 π) U ( ) ζ t u ( ) s t πβe t v ( ) m P t+1 + D t+1 t+1. (15) P t By Lemma 1 (see Appendx), v ( m t+1 ) = (1 π) U ( ζ t+1 ) u ( s t+1 ). (16) Thus, for every tme t, the equlbrum prce satsfes [ U P t = πβe ( ) ( ) ] ζ t+1 t U ( ) u s t+1 ζ t u ( ) s (P t+1 + D t+1 ), (17) t for all, and, by the law of terated expectatons, can be rewrtten as [ ( ) ( ) ] P t = E t π τ β τ U ζ t+τ U ( ) u s t+τ ζ t u ( ) s D t+τ. (18) t τ=1 Notce that when all consumers are ntrnscally rsk neutral (.e., when U s lnear), and the length of a sequence s suffcently short so that there s no mpatence (.e., β = 1), then Equaton (18) smplfes to Equaton (11) provded that: () The contnuaton probablty, π, equals the (constant) dscount factor n the nfnte horzon model, and () The nduced utlty functon, u, n the ndefnte horzon model matches the ntrnsc perod utlty functon, U, n the nfnte horzon model of the last subsecton. Thus, we may treat our ndefnte horzon model as an nduced preference mplementaton of the nfnte horzon model of Subsecton 2.1 under the assumpton that consumers are ntrnscally rsk neutral wth respect to the uncertan amounts of money they earn n our experment The model mplemented n the laboratory To mplement the model descrbed n the prevous secton n the laboratory, we make four addtonal assumptons. Frst, the dvdend n every tme perod, t, s constant, D t = D. 18 Second, the endowment, y t, that each consumer receves s determnstc. Thrd, the aggregate endowment of ncome s constant over tme, and ths s common knowledge. Fourth, we assume that β = 1; snce consumers cannot spend cumulatve dollar earnngs untl the end of the experment and savngs do not earn any nterest, there s no reason to treat dollars earned n dfferent perods dfferently. The frst three assumptons, along wth the assumpton we mantan throughout that aggregate shares are constant over tme, mply that aggregate resources avalable for savng S t = so that S t = S for all t. Summarzng these assumptons, we have s t are held constant over tme, 17 Ths dstncton between nduced and ntrnsc rsk averson wll prove useful later on n explanng our expermental fndngs and that s why we ntroduce t here. 18 When the dvdend s stochastc and consumers are strctly rsk averse, t s straghtforward to show that a steady state equlbrum prce does not exst. Instead, the prce wll depend (at a mnmum) upon the current realzaton of the dvdend, whch affects current consumpton and accordngly the ntertemporal margnal rate of substtuton. Mehra and Prescott (1985) derve equlbrum prcng n a representatve agent verson of the nfnte horzon model wth a fnte-state Markov dvdend process. 9

11 Assumpton 1. Aggregate ncome and shares n the economy are constant, dvdends are constant, ndvdual endowment ncome s determnstc, and there s no tme dscountng. Under these desgn-motvated assumptons, any ratonal expectatons equlbrum sequence of prces and allocatons through perod t s determnstc, condtonal on reachng perod t. We can thus dscard the expectaton operator, E t [ ], n Equatons (17) and (18); the only uncertanty s horzon uncertanty,.e., whether perod t + τ wll be reached. When the ntrnsc utlty functon of all consumers s lnear (.e., consumers are ntrnscally rsk neutral), we next show the prce n each perod s equal to the fundamental prce. Proposton 1. Suppose that Assumpton 1 holds and the ntrnsc utlty, U, s lnear for each consumer. Then, the prce n each perod s constant and equal to the fundamental prce P t = πd 1 π P. (19) Further, f the nduced utlty, u, s strctly concave for each consumer, then equlbrum savngs satsfes s t = s t+1 s, (20) for every tme t and every consumer. If nstead u s lnear, equlbrum savngs are restrcted only by the budget constrant. The proof of Proposton 1 and all subsequent Propostons can be found n Appendx A. Proposton 1 demonstrates that when U s lnear for every consumer, the equlbrum prce s equal to the expected value of the dvdend stream and s ndependent of the nduced utlty functon, u. Our expermental desgn explots ths ndependence result. Under the assumpton that consumers are ntrnscally rsk neutral, we can vary the nduced utlty functon and not alter the equlbrum prce predcton. Indeed, as we dscuss later n Secton 3, our experment compares and contrasts the case where the nduced utlty functon s lnear, as n the SSW expermental approach, wth the case where the nduced utlty functon s strctly concave, ntroducng a consumpton-smoothng ncentve for exchange whch s the core feature of the Lucas model. Thus, our expermental desgn enables us to make a connecton between the SSW desgn and the Lucas asset prcng model. We next prove that f each consumer s ntrnscally rsk averse,.e., her ntrnsc utlty U s strctly concave, and f each consumer s nduced utlty functon u s weakly concave, the equlbrum prce n every perod s strctly less than the fundamental prce gven by Equaton (19). In ths case, the certanty equvalent of the dvdend stream flowng from the asset s less than ts expected value for ntrnscally rsk-averse consumers. Proposton 2. Suppose that Assumpton 1 holds, the ntrnsc utlty, U, s strctly concave, and 10

12 the nduced utlty, u, s weakly concave. Then, the equlbrum prce at tme t satsfes P t < P. (21) We next focus on a wde class of possble specfcatons for the ntrnsc utlty functon, U ; specfcally, constant absolute rsk averson(cara) and decreasng absolute rsk averson (DARA). For these specfcatons, we seek to dentfy comparatve statc mplcatons from whether the nduced utlty functon, u, s concave or lnear. Specfcally, we show that prces necessarly converge to a steady state equlbrum prce, n the lmt as t approaches nfnty, ndependent of the nduced utlty functon. Thus, the connecton between the SSW expermental asset prcng framework and the Lucas asset prcng model extends to ntrnscally rsk-averse consumers; we are able to vary an nduced ncentve to smooth consumpton whle keepng the underlyng steady state fundamentals unchanged. We begn wth the assumpton that the ntrnsc utlty functon, U, exhbts CARA, n whch case accumulated wealth does not affect the consumer s current portfolo choce. 19 The CARA utlty functon can be specfed as: U ( ζt ) 1 e γ ζt = γ. (22) Each consumer s ntrnsc rsk averson s summarzed by a parameter γ > 0, where rsk averson s ncreasng n γ. Proposton 3. Suppose that Assumpton 1 holds and each consumer s strctly rsk averse wth CARA ntrnsc utlty, U. When the nduced utlty functon, u, s weakly concave for every consumer, lm t P t = πd e γ c π P < P, (23) where c = lm t c t, for each consumer. Further, when u s lnear for every consumer, the constant prce and consumpton specfed n Equaton (23) characterze a unque equlbrum at every tme t > 1. Ths proposton mples that, when all ntrnsc utlty functons are strctly CARA, the economy converges to a unque steady state equlbrum n whch the prce, P, and consumpton, c (and thus savngs, s ), of every consumer are constant over tme. The steady state prce s strctly less than the fundamental prce and s mplemented n the second and all subsequent perods f the nduced utlty functon s lnear. Corollary 1. Suppose that Assumpton 1 holds, each consumer s strctly rsk averse wth CARA ntrnsc utlty, U, and the nduced utlty functon, u, s weakly concave for each. Then, n a steady state equlbrum, consumer s savngs, s, s strctly decreasng n the rsk averson parameter γ. Further, the steady state equlbrum prce s decreasng n γ. 19 Indeed, Sherstyuk et al. (2013) fnd no evdence of wealth effects for cumulatve payment procedures such as the one we mplement, whch suggests that CARA may be a reasonable approxmaton for U. 11

13 Suppose now that all consumers have ntrnsc DARA utlty. That s, the consumers rsk averson decreases as wealth ncreases. In ths case, the equlbrum prce sequence converges to the fundamental prce from below, as the followng proposton shows. Proposton 4. Suppose that Assumpton 1 holds, each consumer s strctly rsk averse wth DARA ntrnsc utlty, U, and the nduced utlty, u, s weakly concave for each. Then, as tme t tends to nfnty, the economy converges to the fundamental prce P. Further, when u s strctly concave, there exsts a unque lmtng savng allocaton s for every consumer, whle f nstead u s lnear, equlbrum savngs are restrcted only by the budget constrant. The recursve Equaton (17) s typcally under-determned. Yet, t s nstructve to consder an example wth an analytcal soluton. For that purpose, we assume that both the nduced utlty functon, u, and the ntrnsc utlty functon, U, exhbt homogeneous constant relatve rsk averson (CRRA). 20 The CRRA utlty functon s specfed by U ( (ζt) Ct ) 1 γ 1 γ, f γ 1; = ln ( ζt ) f γ = 1. Proposton 5. Suppose that Assumpton 1 holds, the ntrnsc utlty, U, for each consumer s CRRA wth rsk averson parameter γ > 0, and the nduced utlty, u, for each consumer s CRRA wth curvature parameter δ 0. In addton, suppose there are an equal number of two types of consumers, who dffer only n ther endowments. Then the equlbrum prce n perod t s ( ) τ γ P t = D π τ t+1 (24) τ + 1 τ=t Further, each consumer s consumpton s constant across all perods. Ths proposton mples that, when the ntrnsc utlty functon s homogeneous and CRRA, each consumer perfectly smoothes her consumpton over tme. Further, nether the equlbrum prce nor the savngs allocaton depends on the nduced utlty functon. The equlbrum prce sequence s monotoncally ncreasng over tme and converges to the fundamental prce from below (consstent wth Propostons 2 and 4) n the lmt as t approaches nfnty. In summary, when consumers are ntrnscally rsk neutral, the equlbrum prce n each perod s equal to the fundamental prce. When consumers are ntrnscally rsk averse, the equlbrum prce n each perod s strctly less than the fundamental prce, and converges to a unque steady state equlbrum prce and savngs allocaton. Concernng DARA ntrnsc utlty, the emergent prce s equal to the fundamental prce. Concernng CARA ntrnsc utlty, the emergent prce s strctly less than the fundamental prce. Concernng homogeneous CRRA utlty, the equlbrum prce can be characterzed 20 CRRA s a specal case of DARA, whch we use for our nduced utlty functon n the experment. 12

14 analytcally for each perod t, s strctly ncreasng over tme, converges to the fundamental prce (snce CRRA utlty s wthn the DARA class of utlty functons), and does not depend on nduced utlty u. 2.4 Hypotheses Based on the theory developed n Secton 2.3, we present the followng hypotheses, whch we test n our experment: Hypothess 1. Prces n both the lnear and concave nduced utlty treatments are weakly less than the fundamental prce, P. An alternatve hypothess, nconsstent wth the theoretcal results of Secton 2.3 but consstent wth the large lterature on asset prce bubbles begnnng wth SSW, s the followng: Hypothess 2. Prces n the lnear nduced utlty treatment exceed the fundamental prce P, whle prces n the concave nduced utlty treatment are weakly less than P. Ths alternatve hypothess can be motvated by belef heterogenety. Consumer s subjectve belefs, as reflected n the probabltes used to assess E t [ ], mpact the equlbrum prce and allocaton descrbed by Equaton (17). Schenkman and Xong (2003) and Hong et al. (2006) explore how heterogeneous belefs about realzed dvdends can generate equlbrum prces exceedng an asset s fundamental value. An overconfdent or optmstc buyer may consume less to buy more assets, to the pont of holdng the entre asset supply. Whle dvdends are fxed n our experment, optmsm or overconfdence wth respect to expected future prces may play a related role out of equlbrum. Alternatvely, t s possble for consumers to subjectvely and dfferently weght the contnuaton probablty, π, (e.g., Kahneman and Tversky, 1979), whch may also mpact prces. Fnally, there s the possblty that rsk-seekng behavor drves prces above fundamentals. We do not attempt to model these bubble mechansms. However, there are good reasons to thnk that heterogeneous belefs may dsproportonately mpact choces when the nduced utlty functon s lnear as opposed to when t s concave, whch are the two man treatments of our experment (as descrbed n the next secton). Suppose that a subject s nduced and ntrnsc utlty functons are both lnear, and the subject holds the (rgd) belef n perod t that P t+1 > P t > P. If ths subject buys at date t and sells at date t + 1, hs expected gan s π(p t+1 + D) P t per share. If ths expected gan s postve, the subject would want to buy as many shares as possble n perod t, and may choose to sell shares n the next perod at P t+1 to other subjects who beleve that prces wll contnue to apprecate beyond that perod. Of course, gven fxed franc resources, such bubbly expectatons cannot be sustaned ndefntely, but there can be a farly long sequence of postve expected value draws, one 13

15 of whch wll result n termnaton wth hgh probablty. 21 Alternatvely, a subject wth these same belefs pursung the same speculatve strategy would, under a concave nduced utlty functon, be heavly penalzed for the hgh varance n hs perod-by-perod consumpton levels that resulted from such speculaton. Thus, the logc for Hypothess 2 s that under a lnear nduced utlty functon we are more lkely to see bubbly prces arsng from heterogeneous belefs whle under a concave nduced utlty functon, the ndvdual s need to smooth consumpton should dampen the extent of msprcng of the asset, so that prces should be more n lne wth our theoretcal predctons. When the nduced utlty functon u s concave, consumers perfectly smooth ther consumpton provded that ther ntrnsc utlty functon s lnear (rsk neural) or n the DARA steady state equlbrum, whle consumpton s unrestrcted for nduced lnear utlty. However, n Proposton 5 we show that for ntrnscally rsk averse consumers there exst economes n whch consumers perfectly smooth ther consumpton regardless of whether u s concave or lnear. Consderaton of these results leads us to the followng hypothess. Hypothess 3. When the nduced utlty, u, s concave, subjects use the asset to ntertemporally smooth ther consumpton to the same or to a greater extent than when u s lnear. In addton, we consder two further hypotheses that follow from the prevous secton: Hypothess 4. For a gven nduced utlty functon u, prces are hgher n sessons wth a hgher dvdend payment D. Hypothess 5. For a gven nduced utlty functon u and dvdend, prces are lower n sessons wth hgher degrees of rsk averson as measured by Holt-Laury scores. 3 Expermental desgn We seek to determne the extent to whch the prce and shareholdng predctons of the Lucas asset prcng model are supported n a laboratory experment. Valung shares n our ndefnte horzon mplementaton s more complcated than n SSW, and n fact no partcpant possesses suffcent nformaton to calculate the equlbrum prce. Therefore, we assess the extent to whch observed prces can be ratonalzed by knowledge of fundamentals alone, namely the asset s dvdend, the contnuaton probablty, the subject s nduced utlty functon, and the subject s ncome process. Our experment was desgned wth the ntent of testng Hypotheses 1-5, as presented n the prevous secton. 21 Ths scenaro shares some features wth the centpede game, n whch backward nducton and fnte resources should nduce fundamental behavor, yet expermental evdence (e.g., McKelvey and Palfrey, 1992) confrms a lack of backward nducton reasonng relatve to the complete nformaton Nash equlbrum. It also shares some features of the wnner s curse, wheren the subject who beleves the bubble wll last the longest gets stuck holdng the asset durng the crash. 14

16 3.1 Income, dvdends, and nduced utlty We focus on two varatons n model parameters. Frst, we examne whether changes n the value of the fxed dvdend payment, D, affect the prce of the asset, as theory asserts that a larger dvdend payment a fundamental factor nduces a hgher steady state equlbrum prce. Changng the dvdend payment provdes a smple test of a comparatve statcs predcton of the theory, as stated n Hypothess Second, we examne whether the strength of the consumpton-smoothng objectve matters, by varyng the curvature of the subjects nduced utlty functons, u, over consumpton. Ths latter treatment varaton s novel to our desgn, and enables us to connect and dfferentate our Lucas asset prcng model fndngs wth results from SSW-nspred experments. Changes n u are used to address Hypotheses 1-3. We use a 2 2 desgn where the treatment varables are: 1) the nduced utlty functon u, whch s ether strctly concave as n the Lucas model (page 1431, 1978) or lnear as n SSW s approach; and 2) the dvdend, D, whch s ether hgh or low. We conduct twenty laboratory sessons (fve per treatment) of the ndefnte horzon economy ntroduced n Sectons 2.2 and 2.3. In each sesson, there are twelve subjects, sx of each nduced utlty type, for a total of 240 subjects. The endowments and nduced utlty functons of the two subject types n all treatments are gven n Table 1. # Subjects k 0 {y t } u (s t ) f t s odd 44 f t s even 24 f t s odd 90 f t s even δ 1 + α 1 s η1 t δ 2 + α 2 s η2 t Table 1: Induced Utlty and Endowment Parameters In each sesson, the franc endowment, y t, for each type {1, 2} follows the same determnstc two-cycle. Subjects are nformed that the aggregate endowment of ncome and shares wll reman constant throughout the sesson, but otherwse are only prvy to nformaton regardng ther own ncome, shareholdngs, and nduced utlty functon. In each sesson, dvdends take a constant value of ether D = 2 or D = 3, and the nduced utlty functon u s ether lnear or concave for both subject types. Thus, our four treatments are C2 (concave nduced utlty, D = 2), C3 (concave nduced utlty, D = 3), L2 (lnear nduced utlty, D = 2), and L3 (lnear nduced utlty, D = 3). We adopt a constant dvdend framework snce our prmary motvaton s to nduce an economc ncentve for trade n a standard macrofnance settng. Porter and Smth (1995) show that mplementng constant dvdends n the SSW desgn does not substantally reduce the ncdence or magntude of asset prce bubbles. 22 Alternatvely, we could have changed other fundamental factors, such as the contnuaton probablty, π. We chose to vary the dvdend, as changes n the dvdend process s a common treatment varaton n the expermental asset prcng lterature. 15

17 The nduced utlty parameters are chosen so that subjects earn $1 per perod at the (ntrnsc) rsk neutral compettve equlbrum n C2 and L2. By contrast, C2 subjects can earn, on average, $0.45 per perod n autarky (no trade). In L2, expected earnngs n autarky equal the compettve equlbrum earnngs due to the lnear exchange rate. A hgher dvdend results n modestly hgher benchmark payments. In L3 and C3, subjects earn on average $1.06 per perod n the rsk neutral compettve equlbrum, whle the autarkc payoff n C3 s on average $0.58 per perod. Ths doublng of payoffs between compettve equlbrum and autarky s chosen to make the dfferences salent to subjects, n lne wth pror research (Gneezy and Rustchn, 2000). The nduced utlty functon used n each treatment s presented to the subjects both as a table and a graph (see Appendx C). In our baselne treatments C2 and C3, we set η < 1 and α η > Gven our cyclc ncome process, Equaton (17) and the budget constrant can be used to show that rsk neutral or DARA steady-state shareholdngs follow a two-cycle between the ntal share endowment, k Even[t] = k 0, and kodd[t] = keven[t] + y Odd[t] y Even[t] 2P. (25) + D Notably, n the steady state, subjects smooth consumpton by buyng asset shares durng hgh ncome perods and sellng shares durng low ncome perods. When D = 2 by Equaton (19), the fundamental prce s P = 10. In turn, Equaton (25) mples that, at the fundamental prce equlbrum, a type 1 subject n our C2 treatment holds 1 share n odd perods and 4 shares n even perods, and a type 2 subject holds 4 shares n odd perods and 1 share n even perods. When D = 3, the fundamental prce s P = 15, and n equlbrum, a type 1 subject n our C3 treatment cycles between 1 and 3 shares, whle a type 2 subject cycles between 4 and 2 shares. Our prmary varaton on the baselne concave treatments s to set η = 1 for both agent types so that there s no longer an ncentve to smooth consumpton. 24 The lnear treatments am to examne an envronment that s closer to the SSW framework. In SSW s desgn, the dvdend process s common to all subjects and dollar payoffs are lnear n francs, so ntrnsc rsk-neutral subjects have no nduced motvaton to engage n trade. Under (alternatve) Hypothess 2, n L2 and L3 assets wll trade at prces greater than the fundamental prce, P, n lne wth SSW s bubble fndngs. Ths, however, contradcts our theoretcal predcton (Hypothess 1) that the curvature of nduced utlty has no mpact on the steady state equlbrum prce for subjects regardless of ther nduced utlty treatment. As s standard n asset market experments, nether borrowng nor short sellng s permtted;.e., s t 0 and k t 0. In partcular, we mpose the followng tradng constrants: y t + D t k t + P t ( k t k t+1) 0, and k t Specfcally, η 1 = 1.195, α 1 = , δ 1 = , and η 2 = , α 2 = , δ 2 = In these lnear nduced utlty treatments, α 1 = , α 2 = , and δ 1 = δ 2 = 0. 16

18 The experment s desgned n such a way that these restrctons only bnd out of equlbrum. 3.2 The contnuaton probablty π As noted earler, we seek to nduce the statonarty assocated wth an nfnte horzon and constant tme dscountng by mplementng an ndefnte horzon wth a stochastc number of tradng perods. 25 Thus, from a subject s perspectve, a share of the asset today s worth more than a share tomorrow not because she s mpatent, but because the asset may cease to have value n the next perod. In each perod, trade takes place for three mnutes n a centralzed marketplace. At the end of each perod, one subject n rotaton takes a turn rollng a sx-sded de n publc vew of the other partcpants. If the de roll n perod t s between 1 and 5 nclusve, the economy contnues for another perod. In ths case, each ndvdual s asset poston s carred over to the start of perod t + 1. If the de roll s 6, the economy termnates and all subjects asset postons are declared worthless. Thus, the probablty that assets contnue to have value n future tradng perods s π = 5/6. Subjects are recruted for a three-hour sesson, durng whch they partcpate n several sequences, each consstng of an ndefnte number of three-mnute tradng perods. Each sequence of tradng perods ends upon a de roll of 6. We choose to have subjects partcpate n several ndefnte sequences to better famlarze them wth the role played by the contnuaton probablty π. We nstruct subjects that after one hour of play (followng the readng of the nstructons) the current sequence beng played wll be the fnal one;.e., the next tme a 6 s rolled the sesson wll come to a close. Ths desgn ensures a reasonable number of tradng perods, whle at the same tme lmts the possblty that sessons last longer than the 3-hour recrutment wndow. Indeed, we never faled to complete the fnal sequence wthn the three hour tme wndow for each sesson. 26 The expected mean (medan) number of tradng perods per sequence n ths desgn s 6 (4), respectvely. The realzed mean (medan) s 5.2 (4) n our sessons. On average there are 3.4 sequences per sesson. Gven π and our adopted values of D, the fundamental prce of the asset n treatments C2 and L2 s 10, whle the fundamental prce of the asset n treatments C3 and L3 s 15. When subjects are ntrnscally rsk neutral, Proposton 1 mples that the prce across all treatments should equal the fundamental prce. When all subjects exhbt ntrnsc CARA utlty, Proposton 3 mples that prces should converge to a value less than 10 n C2 and L2, and to a value less than 15 n C3 and L3. When 25 We follow the dynamc asset prcng experment of Camerer and Wegelt (1993) n ths regard. Ths technque for mplementng nfnte horzon envronments n a laboratory settng s qute standard n game theory experments (e.g., Bó and Fréechette, 2011 and has a rch hstory, begnnng wth Roth and Murnghan (1978). 26 In the nstructons, subjects are nformed that f the fnal sequence s not completed wthn one hour, they would be nvted back to the lab as quckly as mutually possble to complete the fnal sequence. In ths event, subjects would be pad mmedately for the prevous (completed) sequences, but would be pad for the entrety of the fnal sequence at the concluson of the follow-up sesson. Ther fnancal stake n that fnal sequence s derved from at least 20 perods of play (tradng perods are three mnutes long), whch made the event an unlkely ( ( ) %) but compellng motvator to 6 get subjects back to the lab. As t turns out, we dd not have to brng subjects back for any contnuaton sesson. 17

19 all subjects exhbt ntrnsc DARA utlty, Proposton 4 mples that prces should converge to the fundamental prce n all treatments. To get some sense of the expected speed of convergence, consder homogeneous ntrnsc logarthmc utlty (the lmtng utlty as the CRRA preference parameter tends to 1) and homogeneous CRRA nduced utlty parameter 2.3 (approxmately the value used n the experment). 27 Then the prce equaton n Proposton 5 mples an equlbrum prce equal to 77% of the fundamental prce n the frst perod and 96% of the fundamental prce by perod 18 (the mean sesson length n our experment). So t s not mplausble to expect convergence to the fundamental prce by the end of the experment. 3.3 The tradng mechansm General equlbrum models do not specfy the actual mechansm by whch prces are determned and assets are exchanged. We adopt the double aucton mechansm for trade, snce t s well known to relably converge to compettve equlbrum n a wde range of expermental markets. To ths end, we use the double aucton module n Fschbacher s (2007) z-tree software. Pror to the start of each three-mnute tradng perod t, each subject s nformed of her current asset poston, k t, and the number of francs she has avalable for trade, y t + Dk t. After all subjects clck a button confrmng they understand ther asset and franc allocatons, tradng begns. Subjects can post buy or sell orders for one unt of the asset at a tme. They can sell as many assets as they have avalable, or buy as many assets as they wsh, provded they mantan a balance of at least 11 francs. 28 We nsttute a standard bd-ask mprovement rule: buy offers have to mprove on (exceed) exstng buy offers and sell offers have to mprove on (undercut) exstng sell offers to be posted n the (open) lmt order book. Subjects can agree to buy or sell at a currently posted prce (.e., submt a market order) by clckng on the Bd/Ask, mmedately after whch the transacton s executed and the prce publcly posted. After a trade, the order book s cleared, but subjects can (and do) mmedately begn repostng buy and sell orders. A hstory of transacton prces and tradng volume s always present on subjects screens. In addton to ths nformaton, each subject s franc and asset balances are adjusted n real tme n response to any transactons. 3.4 Subjects, payments and tmng Subjects are undergraduate students from the Unversty of Pttsburgh, 18 years of age or older. Subjects could partcpate n no more than one sesson of our experment. There are no other exclusons 27 For one subject endowment type we nduce a value of about 2.2 and for the other type we nduce a value of about A mnmum postve franc balance s mplemented because the nduced utlty of zero francs n the concave treatments s mnus nfnty. The payoff assocated wth 11 francs n the concave treatments s $9.67 ( $15.13) for type 1 (2) subjects. Only 2 out of 120 subjects reached ths boundary (once each) n the concave treatments, the boundary was reached 31 tmes (out of more than 2,000 subject-perods) n the lnear treatments. 18

20 on subject partcpaton. At the begnnng of each sesson, 12 subjects are randomly assgned a role as ether a type 1 or type 2 agent, wth 6 subjects of each type. Subjects reman n the same role for the duraton of the sesson. They are seated at vsually solated computer workstatons and are gven wrtten nstructons that are also read aloud pror to the start of play n an effort to make the nstructons publc knowledge. As part of the nstructons, each subject s requred to complete two quzzes to test comprehenson of the nduced utlty functon, the asset market tradng rules and other features of the envronment. The sesson does not proceed untl all subjects have answered these quz questons correctly. Instructons (ncludng quzzes, payoff tables, charts and endowment sheets) are reproduced n Appendx C. 29 Subjects are recruted for a three hour sesson, but a typcal market ends after a lttle more than two hours, ncludng nstructons (nstructons take about 35 mnutes). An addtonal 15 mnutes s devoted to the Holt-Laury elctaton task, whch s conducted at the end of each sesson and not announced n advance. Payoffs are earned from every perod of every sequence n the sesson. Mean (medan) payoffs are $22.65 ($22.41) per subject n the lnear sessons and $18.75 ($19.48) n the concave sessons, ncludng a $5 show-up payment but excludng the payment for the Holt-Laury ndvdual choce experment. 30 Mean payments are hgher n the lnear sessons because the sum of ndvdual subject payments are constant across perods. Whereas socal welfare s unquely optmzed at the fundamental prce equlbrum n the concave sessons. Followng the end of each tradng perod, t, subject s franc balance, s t, s determned for that perod. The dollar amount of ths franc-consumpton holdng, u (s t), accrues to subject s cumulatve cash earnngs from all pror tradng perods. Ths dollar amount s pad at the completon of the sesson. The tmng of events n our expermental desgn s summarzed below: t dvdends pad; 3-mnute tradng perod consumpton takes place: de roll: t + 1 francs=dkt + y t, usng a double aucton s t = Dk t + y t assets=kt. to trade assets and francs. + contnue ) P t,j (kt,j k t,j 1. to t + 1 j w.p. 5/6, else end. In ths tmelne, j ndexes the transacton completed by subject n perod t. P t,j s the prce governng the jth transacton for n t. k t,j s the number of shares held by after her jth transacton n perod t. In the autarkc case where a subject does not transact, s t = Dk t + y t. In equlbrum, prces faced by all subjects wthn a perod are dentcal. Under the double aucton mechansm, however, they can dffer wthn and across perods and subjects. 29 Copes of the nstructons and materals are avalable at duffy/assetprcng/. 30 Subjects earned an average of $7.22 for the subsequent Holt-Laury experment and ths amount was added to subjects total from the asset prcng experment. 19

21 3.5 Subject rsk preferences Followng completon of the last sequence of tradng perods, begnnng wth Sesson 7 we nvte subjects to partcpate n a further bref experment nvolvng a sngle play of the Holt-Laury (2002) pared-lottery choce nstrument. Ths task s commonly used to measure ndvdual rsk atttudes, and we collected ths data n order to test Hypothess 5. After the market experment, subjects are nformed that, f they are wllng, they can partcpate n a second experment that wll last an addtonal mnutes for whch they can earn an addtonal monetary payment from the set { $0.30, $4.80, $6.00, $11.55 }. 31 All subjects agreed to partcpate n ths second experment. Appendx C ncludes the nstructons for the Holt-Laury task Expermental Sessons We conduct 20 sessons of our market experment. 33 Each sesson nvolves 12 subjects wth no pror experence n ths desgn (240 subjects total). The treatments used are summarzed n Table 2. Sesson u (s ) D Holt-Laury test Sesson u (s ) D Holt-Laury test 1 Concave 2 No 11 Concave 3 Yes 2 Concave 3 No 12 Lnear 3 Yes 3 Lnear 2 No 13 Lnear 3 Yes 4 Lnear 3 No 14 Concave 3 Yes 5 Lnear 2 No 15 Concave 2 Yes 6 Concave 2 No 16 Lnear 2 Yes 7 Lnear 3 Yes 17 Concave 3 Yes 8 Concave 3 Yes 18 Lnear 3 Yes 9 Concave 2 Yes 19 Concave 2 Yes 10 Lnear 2 Yes 20 Lnear 2 Yes Table 2: Assgnment of Sessons to Treatment We began to admnster the Holt-Laury task followng completon of the asset prcng experment n sessons 7 through 20, after t became apparent to us that t mght help us to explan the substantal varaton n ndvdual behavor that we observed n the lnear treatments. Thus, n 14 of our 20 sessons, we have Holt-Laury measures of ndvdual subject s tolerance for rsk (168 of our 240 subjects, or 70%). 31 These payoff amounts are three tmes those offered by Holt and Laury (2002) n ther low-payoff treatment. We scale up the possble payoffs to make the amounts comparable to the steady state earnngs over an average sequence of tradng perods. 32 The Java scrpt used to carry out the Holt-Laury test may be found at duffy/assetprcng/. 33 We also conduct a follow-up ndvdual choce experment, as descrbed n Secton 5. 20

22 4 Expermental fndngs We begn by reportng a couple of fndngs regardng tradng volume and market effcency. Frst, tradng volume s smlar across treatments, wth mean volume per perod around 25 shares n C3 and 23 shares n the other three treatments (the Wlcoxon two-taled p-value s.529 for pooled lnear vs. concave treatments,.222 for C3 vs. C2, and.691 for C3 vs. L3). 34 Second, mean (medan) allocatve effcency earnngs as a fracton of the maxmum expected payoff at the fundamental prce s 0.73 (0.80) for the concave treatment economes wth no dfference by dvdend payment, whle the lnear treatment economes are fully effcent by constructon. In the next two subsectons we report fndngs related to economes wth concave or lnear nduced utlty 4.1 Fndngs for nduced concave utlty Consstent wth Hypothess 1, we have: Fndng 1. In the concave utlty treatment (η < 1), observed transacton prces at the end of the sesson are less than or equal to P n 9 of 10 sessons. To depct ths vsually, Fgure 1 dsplays medan transacton prces by perod for the concave sessons, D = 2 n Panel A and D = 3 n Panel B. Sold dots represent the frst perod of a new ndefnte tradng sequence. To facltate comparsons across sessons, prces are transformed nto percentage devatons from the fundamental prce P. For example, a prce of -40% n Panel A, where D = 2, reflects a prce of 6, whereas a prce of -40% n Panel B, where D = 3, reflects a prce of 9. Fgure 1: Equlbrum-normalzed Prces, Concave Sessons Medan Prce, % Devaton from Eq sesson 1 sesson 6 sesson 9 sesson 15 sesson 19 new sequence Medan Prce, % Devaton from Eq sesson 2 sesson 8 sesson 11 sesson 14 sesson 17 new sequence Perod (a) Concave D = Perod (b) Concave D = 3 Of the ten concave utlty sessons depcted n Panels A and B of Fgure 1, half end relatvely close to the asset s fundamental prce, wth a devaton from ths prce between -15% and 7%. The other 34 There s consderably more between-sesson varaton n tradng volume n the lnear sessons; the standard devaton of volume between lnear sessons s 8.0 shares, vs. 2.9 shares n the concave sessons. 21

23 half end well below t, wth a devaton between -30% and -60%. Several sessons do experence upward pressure on prces above the fundamental prce (most notably, sessons 8 and 9), but these bubbles are self-correctng by the end of the sesson. 35 Importantly, these correctons are wholly endogenous, rather than beng trggered by a known fnte horzon as n SSW. We emphasze that, whle prces n the concave treatment le at or below P, subjects are never nformed of ths fundamental tradng prce, as s done n some of the SSW-type asset market experments. A man mplcaton of consumpton-based asset prcng models, as conjectured n Hypothess 3, s addressed n the next fndng. Fndng 2. In the concave utlty treatments, there s strong evdence that subjects use the asset to ntertemporally smooth ther consumpton. Fgure 2: Per Capta Consumpton-Smoothng Sesson 1, dv = 2 Sesson 2, dv = 3 Per Capta Shares Per Capta Shares Perod Perod Sesson 6, dv = 2 Sesson 8, dv = 3 Per Capta Shares Per Capta Shares Perod Perod Sesson 9, dv = 2 Sesson 11, dv = 3 Per Capta Shares Per Capta Shares Perod Perod Sesson 14, dv = 3 Sesson 15, dv = 2 Per Capta Shares Per Capta Shares Perod Perod Sesson 17, dv = 3 Sesson 19, dv = 2 Per Capta Shares Per Capta Shares Perod Perod Fgure 2 depcts the per capta shareholdngs of type 1 subjects by perod (per capta shares of type 35 Formal evdence supportng ths statement s presented n the dscusson related to Fndng 3. 22

24 2 subjects s fve mnus ths number). Dashed vertcal lnes denote the fnal perod of a sequence, 36 and dashed horzontal lnes mark fundamental prce equlbrum shareholdngs (the bottom lne for odd perods of a sequence, and the top lne for even perods). Recall that equlbrum shareholdngs are cyclc, ncreasng n hgh ncome perods and decreasng n low ncome perods. As Fgure 2 ndcates, ths pattern s precsely what occurred n each and every perod on a per capta bass. 37 Poolng across all concave sessons, on average type 1 subjects (on net) buy 1.94 shares n odd perods (when they have a large endowment of francs) and sell 1.75 shares n even perods (when they have a small endowment). By contrast, n the lnear sessons subjects buy only 0.53 mean shares n odd perods and sell 0.25 shares n even perods. Thus, whle there s a modest degree of consumpton-smoothng n the lnear sessons, consumpton-smoothng s nearly four tmes as large n the concave sessons. Ths ndcates that consumpton-smoothng observed n Fgure 2 s attrbuted to the concavty of the nduced utlty functon u, and not to the cyclc ncome process alone. Fgure 3: Indvdual Consumpton-Smoothng Cumulatve Dstrbuton of Subjects Lnear Sessons Concave Sessons Proporton of Perods n whch Subject Actvely Smoothed Consumpton Consumpton-smoothng n the concave nduced utlty sessons s prevalent across ndvduals. Fgure 3 presents the cumulatve dstrbuton, across subjects, of the proporton of perods n whch a subject actvely smoothes consumpton, pooled by nduced utlty. Half of the subjects n the concave sessons strctly smooth consumpton n more than 80% of all tradng perods, whle less than 2% of subjects n the lnear sessons smooth consumpton so frequently. Well over 90% of the subjects n the concave sessons smooth consumpton n at least half of the perods, whereas only 35% of subjects n the lnear sessons smooth consumpton so frequently. The dfference between these dstrbutons s sgnfcant to many dgts usng a Wlcoxon rank-sum test. Note that the comparatve absence of 36 Thus, there are two allocatons assocated wth each vertcal lne (except the fnal lne): One for the fnal allocaton of the sequence, and the other for the re-ntalzed share endowment of the followng sequence (always one unt). 37 In ths fgure, the perod numbers shown are aggregated over all sequences played. From a subject s perspectve, each sequence starts wth perod 1. 23

25 consumpton-smoothng n the lnear sessons s not ndcatve of ant-consumpton smoothng behavor. Rather, t results from the fact that many subjects n the lnear treatment do not actvely trade any shares n many perods. Prevous expermental evdence on whether subjects can learn to smooth consumpton n an optmal manner wthout tradeable assets has not been encouragng. By contrast, n our smpler settng, where subjects must engage n trade n the asset n order to smooth consumpton, and can observe the transacton prces for that asset n real tme, we fnd strong evdence for consumpton-smoothng behavor. 4.2 Fndngs for nduced lnear utlty Fndng 3. Transacton prces n the lnear utlty sessons are sgnfcantly hgher than transacton prces n the concave utlty sessons. Fgure 4 dsplays medan transacton prces by perod for the lnear sessons, D = 2 n Panel A and D = 3 n Panel B. As n Fgure 1, sold dots represent the frst perod of a new ndefnte tradng sequence, and prces are transformed nto percentage devatons from the fundamental prce. Fgure 4: Equlbrum-normalzed Prces, Lnear Sessons Medan Prce, % Devaton from Eq sesson 3 sesson 5 sesson 10 sesson 16 sesson 20 new sequence Medan Prce, % Devaton from Eq sesson 4 sesson 7 sesson 12 sesson 13 sesson 18 new sequence Perod (a) Lnear D = Perod (b) Lnear D = 3 Table 3 dsplays medan transacton prces over several frequences by sesson, as well as an average of these medan prces by treatment (frst row, boldface type). Notce that for a gven dvdend value D = 2 or 3, nconsstent wth Hypothess 1 but consstent wth the alternatve Hypothess 2, the average treatment prce at each frequency s hgher n the nduced lnear utlty treatment than n the correspondng nduced concave utlty treatment. Further, Table 3 reveals the prce dfference between lnear and concave treatments nvolvng the same value of D generally dverges over tme: The mean treatment prce s monotoncally ncreasng n the lnear treatments and decreasng n the concave treatments. These trends at the sesson level can be dentfed usng the Mann-Kendall τ 24

26 Medan Frst Pd Fnal Half Fnal 5 Pds Fnal Pd τ p-value C2-Mean S S S S S < L2-Mean S S S S < S C3-Mean S S S < S S L3-Mean S S S S S < Table 3: Medan Transacton Prces By Sesson and Treatment statstc, a non-parametrc measure of monotonc trend. 38 The τ values and sgnfcance levels are reported n the last two columns of Table 3. Fve of ten lnear sessons have a sgnfcantly postve trends, whle only one has a sgnfcantly negatve trend (p <.05). Four of ten concave sessons have a sgnfcantly negatve trend, whle only one has a sgnfcantly postve trend (p <.05). Thus, of 11 sgnfcant trends, 9 are dvergng by treatment, ncreasng the prce dfference between concave and lnear sessons over tme. We reject the null hypothess that the sgn of sgnfcant trends s drawn from the same bnomal dstrbuton n the two nduced utlty treatments (ch-squared test p-value s.036). Ths evdence suggests that prce dfferences between the concave and lnear sessons would lkely have been greater f our expermental sessons had nvolved more perods of play. We thus look for treatment dfferences n medan prces durng the fnal perod of each sesson, as such prces best reflect learnng and the long-term trends n these markets, and further, provde the nearest observaton to steady state convergence n the event that ntrnsc (unobserved) utlty s DARA (Proposton 4). To begn our analyss of prce dfferences by treatment, we frst note that, usng a Wlcoxon sgn- 38 Here τ [ 1, 1], where τ = 1 ndcates a strctly monotonc negatve trend, τ = 1 a strctly monotonc postve trend, and τ = 0 mples no trend. 25

27 rank test, we cannot reject the null hypothess that fnal perod prces n treatments C2, C3, and L3 are less than or equal to the fundamental prce, P, whch was 10, 15 and 15, respectvely. However, we can reject the null hypothess that fnal perod prces n treatment L2 are less than or equal to the fundamental prce (p =.031). Next, comparng nduced utlty treatments for a fxed dvdend level, the dstrbuton of fnal perod prces between L2 and C2 s sgnfcantly dfferent (Wlcoxon two-taled p-value s 0.019) but the dstrbuton of fnal perod prces between L3 and C3 s not (p-value s 0.139). Nevertheless, mean dfferences are qute large n both cases: Poolng data accordng to the two nduced utlty treatments alone (for both dvdend values) we fnd that on average, the medan fnal-perod prce n the nduced lnear sessons s 32% above the fundamental prce, whle n the nduced concave sessons t s 24% below the fundamental prce. 39 The assocated pooled Wlcoxon p-value s 0.011, so we reject the null hypothess that equlbrum-normalzed fnal perod prces n the pooled lnear sessons are drawn from the same dstrbuton as the concave sessons. Thus, there s strong evdence that the dfference n nduced utltes caused a strong mpact on prces by the end of the sesson. Prces are consderably greater than the fundamental value n the lnear sessons, and consderably lower than the fundamental value n the concave sessons. Surprsngly, the treatment varaton n the dvdend value dd not nduce the predcted mpact on prces n the ntal perods of our experment, although t has some mpact by the fnal perod, as summarzed n Fndng 4 and the dscusson below. Fndng 4. For a gven nduced utlty functon u, by the fnal perod, mean prces are hgher n sessons wth hgher dvdend payments, D. Consstent wth Hypothess 4, Table 3 reveals that the mean of fnal perod prces across the fve sessons of C2 s 8.3, relatve to 10.4 n C3. The mean fnal prce n L2 s 15.6 relatve to a mean fnal prce of 16 n L3. Thus, by the end of the experment, prces ndeed tended to be greater when D = 3 than when D = 2 (though smaller when normalzed as a percentage change from the fundamental prce). However, ths result s not statstcally sgnfcant. We note that ths result s ntally reversed. As Table 3 reveals, the mean frst perod prce n C2 s 10.9 relatve to 8.4 n C3, and the mean frst perod prce n L2 s 13.0 relatve to 9.4 n L3. In fact, normalzng prces to be expressed as a fracton of the fundamental prce, every sesson n C2 (L2) ntalzes at a hgher normalzed prce than every sesson n C3 (L3), whch s statstcally sgnfcant. Ths dfference n ntal condtons may be a consequence of hgher (lower) franc balances relatve to the fundamental value of the asset n the low (hgh) dvdend treatments 40 or t could smply take 39 We justfy poolng by the two nduced utlty treatments because the dstrbutons of fnal perod prces n C2 vs. C3 and L2 vs. L3 are not sgnfcantly dfferent from each other at the 5% level (p-values of and 0.094, respectvely). 40 The total value of the fxed stock of 30 shares at the fundamental prce when D = 3 s = 450 francs per perod 26

28 Fgure 5: Dstrbuton (by Treatment) of Mean Shareholdngs Durng the Fnal Two Perods Cumulatve Dstrbuton of Subjects Lnear Sessons Concave Sessons Mean Shares Durng Fnal Two Perods some tme for subjects to develop an apprecaton for the relatonshp between the dvdend and asset values. Thus, dvdend has an unexpectedly negatve (though relatvely small) mpact on prces n the frst perod, when the nduced utlty functon u appears to have lttle mpact on prces. However, by the end of the sesson, mean (non-normalzed) prces are hgher for D = 3 than for D = 2, wthn each nduced utlty condton. Therefore, by the end of the experment, nduced utlty s the man determnant of prce dfferences, and on average, varaton n the dvdend level has the expected comparatve statc mpact. Fndng 5. In the lnear nduced utlty treatment, the asset s hoarded by just a few subjects. In the lnear utlty sessons, where there s no clear motvaton to engage n trade n the asset, markets are nevertheless actve. Nearly half of the subjects ultmately sell all of ther shares, and a small number of subjects accumulate most of the shares. Fgure 5 dsplays the cumulatve dstrbuton of mean ndvdual shareholdngs durng the fnal two perods of the fnal sequence of each sesson, pooled accordng to the nduced utlty functon. 41 We average across two perods to account for consumpton-smoothng. We focus on fnal shareholdngs because t can take several perods wthn a sequence for a subject to acheve a targeted poston due to the budget constrant. Forty-two percent of subjects n the lnear sessons hold an average of 0.5 shares or less durng the fnal two perods. By contrast, just 8% of subjects n the concave sessons hold so few shares. At the other extreme, 17% of (number of shares tmes the value of each share at the fundamental prce), whle the total value of the 30 shares when D = 2 s = 300 francs. The total quantty of francs avalable per perod when D = 3 s = 894 francs (ncome per subject par tmes 6 pars plus total shares tmes dvdend), whle the quantty when D = 2 s = 864. So the value of shares as a percentage of total resources per perod s about 50% when D = 3 but only 34% when D = 2. Cagnalp, Porter, and Smth (1998), among others, report that ncreasng francs relatve to a fxed total (fundamental) value ncreases asset prces n the SSW settng. Thus, t s possble than an analogous effect happens n our desgn, resultng n the ntal mss-prcng. 41 We use the fnal sequence wth a duraton of at least two perods. 27

29 subjects n the lnear sessons average at least 6 shares durng the fnal two perods, whle only 6% of subjects n the concave sessons hold so many. The nequalty n the dstrbuton of shareholdngs can be measured by the Gn coeffcent, whch s equal to zero when each subject holds an dentcal quantty of shares and s equal to one when a sngle subject owns all shares. Across all treatments, n autarky the Gn coeffcent s 0.3. Ths s also the value of the Gn coeffcent over the fnal two perods of the fundamental prce equlbrum n treatment C2. In C3, the Gn coeffcent s slghtly lower (0.25). The mean Gn coeffcent for mean shareholdngs n the fnal two perods of all concave sessons s 0.37, not so far from the equlbrum values. By contrast, the Gn coeffcent n the pooled lnear sessons s sgnfcantly larger, at 0.64 (statstcally sgnfcant to many sgnfcant dgts). Ths dfference reflects the hoardng of a large number of shares by just a few subjects n the lnear sessons, behavor that s absent n the concave sessons Fndngs for ntrnsc rsk preferences Our hypotheses mply that, when subjects are ntrnscally rsk neutral, the observed prce should be P n all treatments. Further, when subjects are characterzed by strct DARA ntrnsc utlty, observed prces should converge to P n all treatments. Fnally, when subjects are characterzed by CARA ntrnsc utlty, observed prces should be less than P. Begnnng wth our seventh expermental sesson, we ask subjects to partcpate n a second experment nvolvng the Holt and Laury (2002) pared lottery choce rsk elctaton task. Ths second experment takes place after the concluson of the asset market experment, and s not announced n advance to mnmze any potental nfluence on decsons n the asset market. In ths second experment, whch takes about 5 mnutes to complete, subjects face a seres of 10 choces between bnary lotteres A and B. The payments of lottery A are $6 and $4.80, and those of lottery B are $11.55 and $0.30. For each choce j { 1, 2,..10 }, the probablty of gettng the hgh payoff n ether lottery s 1 10j. One of the ten choces s selected at random, wth the chosen lottery played for payment. As detaled n Holt and Laury, a rsk-neutral expected utlty maxmzer should choose B the hgh-varance lottery 6 tmes. We defne a subject s HL score as the number of tmes the subject selects the rsker lottery B. HL scores lower (greater) than 6 ndcate rsk averse (rsk seekng) behavor. In our sessons, the mean HL score s 3.87 wth a standard devaton of 1.81, ndcatng moderate overall rsk averson; ndeed, 83.3 percent of subjects are classfed as rsk averse, 10.1 percent as rsk neutral and the remanng 6.6 percent as rsk-seekng, a farly typcal dstrbuton. 42 Interestngly, exactly two of twelve subjects n each of the ten lnear sessons hold an average of at least 6 shares of the asset durng the fnal two tradng perods. Recall that the aggregate endowment n all sessons s 30 shares. Thus, the subjects n the rght tal of the dstrbuton n Fgure 5 are dvded up evenly across the ten lnear sessons. 28

30 To compare behavor n lnear versus concave nduced utlty treatments, we regress (usng OLS) a subject s mean shareholdngs durng the fnal two perods on the subject s HL score, wth sesson fxed effects and robust standard errors clustered on sesson-level observatons. In the lnear case, the estmated coeffcent on the HL score s 0.65 wth p-value (Table B.1). Thus, a one standard devaton ncrease n the HL score (equal to 1.8 addtonal hgh-varance choces) mples a subject s expected to hold nearly 1.2 addtonal shares of the asset by the end of the sesson. Ths s a large mpact, as there are only 2.5 shares per capta n these economes. 43 We further note that the medan HL score of the largest shareholder per lnear sesson s 6, and the medan HL score of the two largest shareholders per sesson s 5. The mean HL score of these 14 subjects (7 sessons) s 5.125, relatve to a mean of across all subjects. On the other hand, n the concave case, the estmated coeffcent s wth (cluster-robust) p-value (Table B.3), a statstcally nsgnfcant and small mpact. Thus, the HL score s a far more useful predctor of fnal shareholdngs n the lnear sessons. Ths result for lnear nduced utlty s consstent wth Breaban and Noussar (2015), who report that subjects wth hgher HL scores tend to hold more assets n a SSW-related experment. Fndng 6. Rsk-tolerant subjects tend to hold sgnfcantly more shares of the asset n the lnear treatment sessons, but not n the concave treatment sessons. Fnally, we test Hypothess 5, that sessons wth hgher HL scores trade at hgher prces n both the concave and lnear treatments. We report the relaton between the mean HL score and medan fnal perod prce at the sesson level. What follows s robust to many other summary statstcs for the dstrbuton of HL scores, such as the medan, upper quartle, etc. Followng Taylor (1987), we use treatment as a blockng varable and calculate the weghted average Spearman s Rho a nonparametrc measure of correlaton across treatments, assumng that ρ and ρ j are ndependent for any par of treatments and j. Lettng n be the number of sessons n treatment, the weghted average ρ = ρ (n 1) (n 1) = The statstc ρ (n 1) = s a draw from a standard normal dstrbuton, wth assocated p-value of Thus, the null hypothess of a sgnfcant relaton between HL scores and prce s rejected. Smlarly, the test statstcs are also qute small for both the lnear and concave treatments alone. Fndng 7. We do not dentfy a sgnfcant statstcal relaton between mean HL score and fnal perod medan prce at the sesson level. 43 Snce the dstrbuton of HL scores wthn-sesson s endogenous, for addtonal robustness, we also regress each subject s share of the sum of HL scores wthn-sesson on her average fnal shareholdngs. The coeffcent s wth p-value (Table B.2). Playng aganst the observed frequency of HL scores (across all sessons) for the other eleven subjects n each sesson, a rsk-neutral subject wth an HL score of 6 s predcted to hold 0.74 shares more than a subject wth a score of 5, even larger than the predcton obtaned usng the raw score approach. 29

31 Ex-post, ths fndng s not so surprsng. Prces n the lnear treatment sessons are typcally greater than the equlbrum prce bounds dentfed n Secton 2.3, and Hypothess 5 s derved under the assumpton of equlbrum behavor. Further, concentrated asset holdngs n the lnear treatment (Fndng 5) weakens the lkelhood that a central measure of HL scores correlates wth prces. In the concave treatment sessons, the strength of the nduced preference parameters mples that the dfference between the optmal savngs path and perfect consumpton-smoothng (under whch the market mechancally clears when everyone smoothes) s relatvely small for a wde range of prces. Consder, for example, an ntrnscally rsk-neutral subject n treatment C3 who faces a constant prce of 6 (relatve to a fundamental prce of 15). By Equaton (17), she should ncrease her savngs by about 10% per perod. In ths treatment, an ntrnscally rsk-averse subject should ncrease ther savngs by less (or not at all). Thus, the salence of Hypothess 5 s modest, as excess demand off the equlbrum path s expected to be small. As noted above, we conduct the Holt-Laury test only after the market experment concludes, as the market s the man focus of our study. However, ths order of tasks may affect outcomes n the Holt-Laury rsk elctaton. To rule ths out, we regress ndvduals HL scores on treatment dummy varables ( lnear or D3 ), and on the ndvduals earnngs from the frst part of our experment (asset market). The OLS regresson fndngs, wth robust standard errors clustered on sesson-level observatons as reported n Table B.4, ndcate that nether treatment varables nor subjects earnngs are statstcally sgnfcant factors n explanng HL scores across sessons. Ths s reassurng evdence that the HL scores, elcted followng the asset prcng part of the experment, are not affected by asset market condtons or payoff outcomes. 4.4 Dscusson of hgh prces n the nduced lnear utlty sessons Market behavor for the nduced concave utlty treatment s consstent wth our hypotheses: Fnal prces are at or below P, there s wdespread consumpton-smoothng, and a hgher dvdend leads to hgher fnal prces. By contrast, n the nduced lnear utlty treatment, we observe fnal prces that are greater than P n 7 out of 10 sessons, contradctng Hypothess 1 but consstent wth the bubble prces reported by SSW (Hypothess 2) that motvated our experment. We brefly consder several ratonalzatons for these dfferences, before turnng to an explcatng experment. Rsk-seekng behavor. Snce more rsk-tolerant subjects tend to hold more shares n the nduced lnear utlty sessons (Fndng 6), a possble explanaton for the hgh prces n that treatment s that rsk-seekng subjects drve prces above P. In total, we conduct seven nduced lnear utlty sessons for whch we have HL scores. Three of these sessons have no rsk-seekng subjects present, yet each of these sessons end at a medan prce above P. One of the seven sessons has three rsk-seekng 30

32 subjects, yet the prce n ths sesson remans consderably lower than P n every perod of the sesson. Of the remanng three sessons, wth one rsk-seekng subject each, two conclude at a medan fnal perod prce above P, and one ends below. Of the two hgh-prce sessons, n one of them the rskseekng subject ends the sesson wth 3 shares, and averages holdng 1.4 shares per perod. In the other, the rsk-seekng subject ends the sesson holdng 15 shares, and averages holdng 7.8 shares per perod. Thus, we observe hgh prces beng drven by a subject dentfed as rsk-seekng n only 1 of 7 sessons. It would appear that rsk-seekng preferences alone, as dentfed by the HL score, s nsuffcent to explan the hgh prces we observe n the lnear nduced utlty sessons. Probablty weghtng. Kahneman and Tversky (1979) propose that, whle makng decsons, ndvduals tend to act as f they dstort probabltes through a probablty weghtng functon. Subsequent studes (e.g., Tversky and Kahneman (1992), Camerer and Ho (1994)) show that the medan ndvdual tends to underweght hgh probabltes and overweght low probabltes. In our experment, such dstortons would tend to lower prces rather than rase them, as the contnuaton (termnaton) probablty would tend to be perceved as less than (greater than) 5/6 (1/6). Other studes (e.g., Brnbaum and McIntosh (1996), Etchart (2009), and Kemel and Travers (2016)) have shown that ndvduals tend to overweght the probabltes of low outcomes (low future prces) and underweght the probabltes of hgh outcomes (hgh future prces). Agan, such dstortons (pessmsm) would tend to lower prces rather than rase them. However, as emphaszed by Gonzalez and Wu (1999), there s substantal heterogenety n these dstortons. For smplcty, consder a subject wth both lnear u and U, but a probablty weghtng functon w (π). Clearly, the subject should buy as many shares of the asset as possble for a constant prce less than Dw (π) 1 w (π), and sell for a constant prce greater than Dw (π). Thus, t only takes one 1 w (π) of twelve subjects wth w ( ) 5 6 > 5 6 (.e., subject overweghts π) to support prces greater than P. Whle we mght expect some relaton between subject s HL score and w ( 5 6), ths relaton need not be monotonc across subjects. Speculatve tradng. If a subject beleves prces wll ncrease over tme, a strategy of purchasng shares n the current perod and sellng them n a future perod may be ratonalzable even f the current prce s greater than P. As prevously mentoned n secton 2.4, Schenkman and Xong (2003) and Hong et al. (2006) develop models n whch optmstc or overconfdent nvestors can push equlbrum prces beyond fundamentals. As we dd not elct belefs, we do not brng evdence to bear on ths hypothess, but we do note Haruvy et al. (2007) provde evdence of overly optmstc belefs about prces n the standard SSW desgn. 31

33 5 Elmnatng tradng uncertanty Indvduals n our market experment face two sources of uncertanty: () about the horzon length and () about tradng opportuntes (.e., prces and lqudty). To focus on the former, we conduct an addtonal set of expermental sessons n whch we elmnate tradng uncertanty by allowng ndvdual subjects to buy and sell an unlmted number of shares of the asset at an exogenously fxed prce. 44 We refer to ths experment as the ndvdual choce experment, and to the prevous experment as the market choce experment. In ths new ndvdual choce experment, we adhere to our market choce framework as closely as possble. We agan set π = 5 6 and assgn all subjects the Type 1 endowments and 2-cycle ncome process. 45 We nduce the Type 1 utlty functons, concave or lnear u, from the market experment as one treatment varable. Each subject s decsons have no spllover effects onto other subjects, and are restrcted only by her own budget constrant. We fxed the dvdend on the asset to D = 2, so the rsk-neutral fundamental prce of the asset n all of these ndvdual choce sessons s P = 10. A second treatment varable s the fxed prce at whch subjects can buy or sell the asset, P {7, 10, 13}. Subjects wth nduced concave utlty ether face a prce of 7 or 10 for the entre experment, whch we refer to as treatments C2-7 and C2-10, respectvely. Subjects wth nduced lnear utlty ether face a prce of 10 or 13 for the entre experment, whch we refer to as treatments L2-10 and L Both rsk preferences and probablty weghtng may mpact on behavor n ths ndvdual choce experment. 47 However, there s no scope for speculaton to play a role n the ndvdual choce experment, as subjects face no uncertanty wth respect to prce or lqudty n these experments. In the ndvdual choce sessons, subjects are asked to enter a desred quantty of shares n a text box and choose whether to Buy or Sell that number of shares. Subjects who wsh to mantan ther share poston n the current perod are nstructed to enter 0 n the text entry box and clck ether Buy or Sell. Thus, the effort to hold a poston was equal to the effort to buy or sell shares. Table 4 summarzes the treatments of ths ndvdual choce experment, whch nvolves sx expermental sessons wth 12 subjects per sesson splt equally between two treatments. (72 subjects n total). 48 We have thus have 18 ndependent observatons for each of the four ndvdual choce 44 We thank an anonymous referee for suggestng ths treatment. 45 As prces are exogenous n our ndvdual choce experment, there s no longer any need to have two player types. 46 Recall that mean prces n the concave market choce sessons average 24% below P, whle mean prces n the lnear market choce experments average 32% above P. The two non-fundamental prce treatments, (prces of 7 n the concave treatment (C2-7) or 13 n the lnear treatment (L2-13) thus reflect the mean devatons we found n the market choce experment. 47 Regardng the mpact of probablty weghtng, consder a rsk-neutral subject for whom w (π = 5/6) = 7 8. Ths subject wll value one unt of the asset at 14 francs when D = 2 (as opposed to the unweghted prce of 10 francs). Thus, when facng a fxed prce of 13 francs, ths subject should optmally purchase as many shares as her budget constrant allows. 48 The subjects n these ndvdual choce sessons are Unversty of Pttsburgh undergraduates who dd not prevously 32

34 Sesson u (s) D Prces (# Subjects) 17 Concave 2 7 (6) 10 (6) 18 Concave 2 7 (6) 10 (6) 19 Concave 2 7 (6) 10 (6) Concave 2 7 (18) 10 (18) 20 Lnear 2 10 (6) 13 (6) 21 Lnear 2 10 (6) 13 (6) 22 Lnear 2 10 (6) 13 (6) Lnear 2 10 (18) 13 (18) Table 4: Indvdual choce sessons treatments C2-7, C2-10, L2-10 and L2-13. At the end of these sessons, subjects are agan asked to complete a Holt-Laury rsk preference elctaton Consumpton smoothng We frst consder the proporton of perods that a subject buys (sells) shares n hgh (low) ncome perods. The dstrbutons of these proportons across subjects are sgnfcantly dfferent (to many sgnfcant dgts) between the pooled lnear and concave ndvdual choce treatments. The dfference n consumpton-smoothng between the lnear ndvdual choce and lnear market treatments s nsgnfcant (p-value 0.88), whle the dfference between the concave ndvdual choce and concave market treatments s sgnfcant (p-value 0.001); subjects smooth consumpton even more frequently n the concave ndvdual choce treatments. In fact, nearly half of subjects smooth ther consumpton n every perod. The standard devaton of consumpton relatve to autarky across perods provdes addtonal evdence for strong consumpton smoothng n the concave ndvdual choce treatment. 50 Poolng subjects nto lnear and concave treatments, ths statstc s sgnfcantly dfferent from autarky n both cases, but n opposte drectons. In fact, only 3 of 36 subjects have a standard devaton of consumpton greater than autarky n the concave treatments, whle only 5 of 36 subjects have a standard devaton of consumpton less than autarky n the lnear treatments. Fndng 8. The extent of consumpton smoothng s sgnfcantly greater n the concave ndvdual choce settng than n the concave market choce settng, whch we attrbute to the prce certanty of the ndvdual choce settng. Elmnatng prce uncertanty has no effect on the extent of consumpton smoothng n the lnear utlty settng, where t contnues to be far less than n the concave treatment. partcpate n any of our market choce experments. 49 The nstructons we use n these sessons are reported n Appendx C. 50 The means of these ratos are 1.58 and 1.33 n L2-10 and L2-13, and 0.52 and 0.57 n C2-10 and C2-7, respectvely. 33

35 5.2 Tradng volume In the concave ndvdual choce treatment wth a fxed prce of 10, (C2-10), the mean decson s to sell 2 shares n even (low-ncome) perods and to buy 2.5 shares n odd (hgh-ncome) perods. In the concave treatment wth a fxed prce of 7, (C2-7), the mean decson n even perods s to sell 2.7 shares, and the mean decson n odd perods s to buy 3.4 shares. Perfect consumpton smoothng requres buyng (sellng) 3 shares n hgh (low) ncome perods of treatment C2-10 and 4 shares n treatment C2-7. Thus, mean tradng volume s wthn one share of perfect consumpton-smoothng n both treatments. Consstent wth Equaton (25), whle the overwhelmng tendency n both concave treatments s to smooth consumpton, the volume of trade s substantally larger when the prce s 7 rather than 10. In both odd and even perods, the dstrbuton of choces n C2-10 vs. C2-7 are sgnfcantly dfferent from each other, wth Wlcoxon p-values less than Fndng 9. Tradng volume s sgnfcantly larger wth a fxed prce of 7 as compared wth a fxed prce of 10 n the concave treatments, wth the mean extent of consumpton smoothng between treatments roughly constant. In the lnear sessons, u (s t+1 ) = 1. Gven a constant prce P, dvdend D, and our mantaned u (s t) assumpton that β = 1, Equaton (17) can be rearranged as U (ζ t+1 ) P =. For an ntrnscally U (ζ t) π(p+d) rsk-averse subject facng P P as n our treatments L2-10 and L2-13, ths expresson mples that U (ζ t+1 ) U (ζ t) 1, whch s nfeasble snce short sales are not permtted (recall that ζ t+1 = ζ t + c t+1 ). Therefore, such ntrnscally rsk-averse subjects should sell all of ther shares n the frst possble nstance so as to maxmze ther current consumpton. However, few of our subjects cash out as predcted; n fact, only 5 of 33 subjects (15%) are even close to the predcton that a subject who s strctly rsk averse n L2-10 or weakly rsk averse n L2-13 wll sell all of her shares n the frst perod and hold no shares throughout the experment. 51 However, mean tradng volume at the hgher prce s nearly cut n half, from 3.9 shares per perod when the prce s 10 to just 1.7 shares when the prce s Fndng 10. In the lnear treatments, mean tradng volume s more than double for a prce of 10 relatve to a prce of 13, comparatve statcs whch are consstent wth expected utlty theory reasonng. However, only a few subjects (15%) ndvdually behave n a manner even loosely consstent wth cashng out as predcted by ther HL score under expected utlty theory. 51 We conservatvely defne a near cash out crtera as: (1) Holdng fewer than one share on average n the fnal two perods, (2) Endng at least one-thrd of all perods wth zero shares, and (3) Holdng less than two shares per perod on average throughout the sesson. Only 2 of 33 subjects actually held zero shares throughout the experment as predcted. 52 Nearly one-thrd of all trades nvolve more than 5 shares of the asset n L2-10, whle just over 10% of trades nvolve more than 3 shares n L

36 5.3 Intrnsc rsk averson To examne the relaton between shareholdngs and Holt-Laury scores, we consder mean shareholdngs durng the fnal two perods as we dd n the market choce experment. Recall that n the pooled lnear market choce experments, 42% of subjects hold less than one share durng the fnal two perods, whle 16% hold at least 6 shares. By comparson n L2-13 (L2-10), 44% (17%) of subjects hold less than one share durng the fnal two perods, whle 11% (28%) hold sx or more. Thus, at the hgh prce, subjects n the lnear ndvdual choce experment are far more lkely to cash out and less lkely to hold a large number of shares. Consstent wth the market choce experment, the relaton between HL score and fnal shareholdngs n both concave ndvdual choce treatments s nsgnfcant accordng to an OLS regresson. Also consstent wth the market choce experment, n the lnear ndvdual choce treatment, the mpact of HL score on fnal shareholdngs n treatment L2-10 s postve and statstcally sgnfcant. 53 However, n the lnear ndvdual choce treatment L2-13, the relaton between HL score and fnal shareholdngs s statstcally nsgnfcant; n fact, the estmated coeffcent s negatve (see Table B.6). Ths unexpected fndng suggests a re-nvestgaton of the market choce experment data. We partton the lnear market choce sessons for whch we have HL scores nto those wth an average prce n the fnal two perods at least 30% greater than the fundamental value, and sessons wth a lower prce. 54 For the low-prce group, the relaton between HL score and fnal shares s postve but nsgnfcant (the estmated coeffcent s 0.39 wth p-value ), whle for the hgh-prce group the relaton s postve and sgnfcant (the estmated coeffcent s 0.81 wth p-value ). The results are reported n Tables B.7 and B Thus, HL scores are predctve of shareholdngs for hgh but not low prces n the lnear market choce sessons, and for low but not hgh prces n the lnear ndvdual choce sessons. To develop some nsght nto what drves ths dfference, we consder shareholdngs for three HL score clusters (rsk averse, approxmately rsk neutral, and rsk seekng), subdvded nto low- and hgh-prce sessons. Table 5 dsplays average fnal shares. Subjects generally purchase fewer shares under hgh prces except the rsk-neutral group n a market choce settng, who on average purchase far more shares. Whle there s no sgnfcant dfference between the dstrbuton of shareholdngs for the rsk-neutral group versus other subjects when prces are low (Wlcoxon p-value ), n the 53 The coeffcent on HL score s large, 0.93, wth assocated p-value of Full results are reported n Table B Ths partton has several useful propertes: (1) Thrty percent represents the hgh-prce desgnaton n the ndvdual choce experment; (2) Thrty percent separates the market choce treatment sessons nto two relatvely equal-szed groups; and (3) There s a dstnct break n prces between the two groups; the low-prce group concludes at prces of -33%, -13%, 13%, and 20%, whle the hgh-prce group fnshes at 80%, 100% and 115%. 55 Adjustng for HL score heterogenety between sessons by regressng a subject s share of the total HL score wthnsesson on fnal shareholdngs confrms ths result. The slope coeffcent s 21 wth a p-value of n the low-prce case, whle the coeffcent s 53 wth a p-value of n the hgh-prce case. 35

37 market choce sessons there s a sgnfcant dfference when prces are hgh (p-value ). Fnal Shareholdngs by HL Score Treatment Prce HL 1-4 HL 5-7 HL 8-10 Market Low Market Hgh Choce Low NaN Choce Hgh NaN Table 5: Mean Fnal Shares n Lnear Indvdual Choce Sessons Fndng 11. The dstrbuton of fnal shareholdngs n the ndvdual choce sessons appears to be relatvely consstent wth shareholdngs n the market choce sessons for both concave and lnear nduced utlty. However, whle subjects tend to hold fewer shares n the lnear ndvdual choce sessons when the prce s hgh, n the lnear market choce sessons, subjects who are approxmately rsk neutral accordng to the Holt-Laury elctaton substantally ncrease ther shareholdngs. In the lnear ndvdual choce experment, hgh prces cause subjects to purchase fewer shares. However, n the lnear market choce experment one group of subjects ncreases ts demand for shares at far greater prces: the group of subjects dentfed as approxmately rsk neutral by the Holt- Laury elctaton. Thus, speculaton about the lkelhood of future prce ncreases may play a more substantal role than rsk-seekng behavor or probablty weghtng n causng the large prce bubbles we observe n the lnear market choce experment. But why are the approxmately rskneutral subjects the ones who bd up assets prces? Here, we must ourselves become speculatve, and pont to the exstng lterature for some possble clues. De Martno et al. (2013) report an ncreased propensty to rde fnancal bubbles n a SSW settng for ndvduals whose economc value computatons are affected by socal sgnals. Ther nterpretaton s that ndvduals who ncorporate nferences about the ntentons of others when makng fnancal decsons are the most lkely to bd asset prces above fundamentals, fuelng a bubble. They stress that these results suggest that durng fnancal bubbles, partcpants choces are less drven by explct nformaton avalable n the market (.e., prces and fundamentals) and are more drven by other computatonal processes, perhaps magnng the path of future prces and lkely the behavor of other traders (p. 1223). That s, ndvduals wth a strong theory of mnd (ToM) suffer enhanced susceptblty to buyng assets at prces exceedng ther fundamental value (p. 1223). Ibanez et al. (2013) establsh a strong relaton between flud ntellgence and ToM, whle Benjamn et al. (2013) establsh a relaton between cogntve ablty and small-stakes rsk neutralty. Assumng that the assocated correlatons aggregate so that small-stakes rsk neutralty s assocated wth hgher ToM, approxmately rsk-neutral subjects may bd up asset prces n our lnear market choce exper- 36

38 ment, but demand fewer shares n our ndvdual choce experment at hgh prces, because n the ndvdual choce experment there are no ntentons of others to predct, and thus no speculatve rewards. 6 Concluson The consumpton-based asset prcng model s a workhorse framework that contnues to be used n macroeconomcs and fnance, despte weak emprcal support usng non-expermental feld data. In ths paper, we develop and test an mplementaton of the comparatve statc predctons of consumptonbased asset prcng models n the controlled condtons of the laboratory whch allows for more careful control over the envronment and data measurement than s possble usng feld data. Thus, one am of ths paper s to provde a test of consumpton-based asset prcng models under hghly favorable condtons, abstractng from nosy potental confounds. A second am of ths paper s to buld a brdge between the expermental asset prcng lterature, whch has typcally followed the SSW expermental desgn, and the consumpton-based asset prcng models used n the macro fnance lterature. We fnd that the consumpton-based asset prcng model performs well n some dmensons. In partcular, we fnd strong evdence n our concave nduced utlty treatment that subjects use the asset to ntertemporally smooth ther consumpton by buyng shares n hgh-ncome perods and sellng shares n low-ncome perods. Further, we fnd that prces respond to changes n economc fundamentals, e.g., to changes n the dvdend the asset pays. Fnally, we are able to ratonalze the prces we observe, mostly at or below the fundamental prce, by accountng for subjects ntrnsc rsk averson. Ths latter fndng s new to the lterature and would be hard to obtan outsde of the laboratory. For comparson purposes, we also mplement a lnear nduced utlty market treatment that s closer to the SSW desgn n the sense that subjects are not exogenously motvated to use the asset to smooth consumpton or to engage n any trade whatsoever. In ths treatment, we fnd that asset prces are consderably hgher than n the comparable concave nduced utlty treatment. Sx of our ten lnear utlty economes experence sustaned devatons above the fundamental prce, and n fve of those sessons the bubble exhbts no sgn of collapse. By contrast, when consumpton-smoothng s nduced n an otherwse dentcal economy, as n our concave treatment, such prce bubbles are less frequent, of lower magntude, and of shorter duraton. Thus, one man take-away from our experment for macroeconomc and fnance researchers s that concavty of the utlty functon s not only necessary for consumpton smoothng; t s also essental to prevent asset prce bubbles from arsng. Indeed, n a follow-up ndvdual choce experment, we nfer that speculaton rather than rskseekng behavor or probablty weghtng s the most lkely cause of bubbles n the lnear market 37

39 choce experment. Subjects dentfed as approxmately rsk neutral accordng to the Holt-Laury pared choce task are the prmary buyers of assets durng lnear market bubbles, but these same subjects buy comparatvely fewer shares at a constant prce above fundamentals n the ndvdual choce experment, where speculaton s not possble. Our research can be extended n at least three dstnct drectons. Frst, the expermental desgn can be moved a step closer to the envronments used n the macrofnance lterature by addng a Markov process for dvdends and/or a known, constant growth rate n endowment ncome. Such treatments would allow for the exploraton of the robustness of our present fndngs to stochastc or growng envronments. Further, the desgn could be extended to nduce consumpton-smoothng through overlappng generatons rather than cyclc ncome and concave nduced utlty. Second, t could be useful to combne varous elements of our desgn wth the much-studed expermental desgn of Smth et al. (1988) to further explore reasons for the observed dfferences n behavor under our desgn versus the desgn of SSW. For example, one could add a constant contnuaton probablty to the fnte horzon, lnear (nduced) utlty desgn of SSW. Would the nteracton of a fnte horzon wth random termnaton nhbt bubbles relatve to the SSW desgn? Or s an nduced economc ncentve to trade necessary to prevent a small group of speculators from effectvely settng prces across a broad range of economes? Fnally, our approach suggests that heterogenety n ndvdual characterstcs, namely preferences for rsk as dentfed by the pared choce lottery task, plays a role n the determnaton of asset prces, partcularly n the extent of the departures of asset prces from fundamentals. However, ths mpact appears not to be drven by a mechancal applcaton of expected utlty theory, but rather a correlaton between proxmty to rsk neutralty and the lkelhood to engage n speculatve actvty. Theoretcal work whch pars rsk atttudes wth belef dstrbutons that support speculatve behavor may prove useful to explan the mechancs of asset prce bubbles. We leave these extensons and addtonal expermental desgns to future research. 38

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42 Lucas Jr, R. E. (1978) Asset prces n an exchange economy, Econometrca: Journal of the Econometrc Socety, pp Lugovskyy, V., D. Puzzello, S. Tucker et al. (2011) An expermental study of bubble formaton n asset markets usng the tâtonnement tradng nsttuton: Department of Economcs and Fnance, College of Busness and Economcs, Unversty of Canterbury. Mankw, N. G. and S. P. Zeldes (1991) The consumpton of stockholders and nonstockholders, Journal of fnancal Economcs, Vol. 29, No. 1, pp McKelvey, R. D. and T. R. Palfrey (1992) An expermental study of the centpede game, Econometrca: Journal of the Econometrc Socety, pp Mehra, R. and E. C. Prescott (1985) The Equty Premum: A Puzzle, Journal of Monetary Economcs, Vol. 15, No. 2, pp Mlgrom, P. and I. Segal (2002) Envelope theorems for arbtrary choce sets, Econometrca, Vol. 70, No. 2, pp Noussar, C. and K. Matheny (2000) An expermental study of decsons n dynamc optmzaton problems, Economc Theory, Vol. 15, No. 2, pp Plott, C. R. and V. L. Smth (2008) Handbook of expermental economcs results, Vol. 1: Elsever. Plott, C. R. and S. Sunder (1982) Effcency of expermental securty markets wth nsder nformaton: An applcaton of ratonal-expectatons models, The Journal of Poltcal Economy, pp Porter, D. P. and V. L. Smth (1995) Futures contractng and dvdend uncertanty n expermental asset markets, Journal of Busness, pp Roth, A. E. and J. K. Murnghan (1978) Equlbrum behavor and repeated play of the prsoner s dlemma, Journal of Mathematcal psychology, Vol. 17, No. 2, pp Schenkman, J. A. and W. Xong (2003) Overconfdence and speculatve bubbles, Journal of Poltcal Economy, Vol. 111, No. 6, pp Sherstyuk, K., N. Taru, and T. Sajo (2013) Payment schemes n nfnte-horzon expermental games, Expermental Economcs, Vol. 16, No. 1, pp Shller, R. J. (1981) Do Stock Prces Move Too Much to be Justfed by Subsequent Changes n Dvdends? Amercan Economc Revew, Vol. 71, No. 3, pp Smth, V. L., G. L. Suchanek, and A. W. Wllams (1988) Bubbles, crashes, and endogenous expectatons n expermental spot asset markets, Econometrca: Journal of the Econometrc Socety, pp Stgltz, J. E. (1970) A consumpton-orented theory of the demand for fnancal assets and the term structure of nterest rates, The Revew of Economc Studes, Vol. 37, No. 3, pp Taylor, J. M. (1987) Kendall s and Spearman s correlaton coeffcents n the presence of a blockng varable, Bometrcs, pp Tversky, A. and D. Kahneman (1992) Advances n Prospect Theory: Cumulatve Representaton of Uncertanty, Journal of Rsk and Uncertanty, Vol. 5, No. 4, pp Wheatley, S. (1988) Some tests of the consumpton-based asset prcng model, Journal of Monetary Economcs, Vol. 22, No. 2, pp

43 Appendces A Proofs Lemma 1. The equlbrum soluton to the maxmzaton problem, defned n Equaton (12), satsfes v ( ) m t = (1 π) U ( ) ζ t u ( ) s t. (26) Proof. Drop the superscrpt and wrte s t as a functon s t (m t ) of m t, such that the soluton s t depends on m t. That s, s t (m t ) s a functon that solves the maxmzaton problem n Equaton (12) for any gven m t. Defne the functon f (m t, s t (m t )) = (1 π) U (ζ t ) + πβe t [v (m t+1 )]. (27) By the Envelope Theorem (e.g., Mlgrom and Segal (2002)), the total dervatve of f s Snce k t+1 can be wrtten k t+1 = 1 P t (m t + y t s t ), Thus, Dfferentatng f wth respect to s t gves df dm t = f m t + f s t ds t dm t. (28) m t+1 = P t+1 + D t+1 P t (m t + y t s t ). (29) [ f = πβe t v (m t+1 ) P ] t+1 + D t+1. (30) m t P t f s t = (1 π) U (ζ t ) u (s t ) πβe t [ v (m t+1 ) P ] t 1 + D t+1. (31) P t By the frst order condton n Equaton (15), ths expresson s equal to zero. Thus, snce df dm t = v (m t ), by Equatons (28) and (30), Now, by the FOC n Equaton (15), [ πβe t v (m t+1 ) P ] t+1 + D t+1 P t Therefore, [ v (m t ) = πβe t v (m t+1 ) P ] t+1 + D t+1. (32) P t v (m t ) = (1 π) U (ζ t ) u (s t ). = (1 π) U (ζ t ) u (s t ). (33) Proof of Proposton 1. Snce ntrnsc utlty U s lnear, by Equaton (17), n equlbrum u ( s ) ( ) u j s j t+1 u ( t+1 ) s = ( ), (34) t u j s j t 42

44 for every tme t and every par of consumers and j. When the nduced utlty, u, s lnear, u (s t+1) = 1 u (s t) for each consumer n every tme t, regardless of the savngs. When the nduced utlty u s strctly concave, suppose that there exsts an equlbrum allocaton such that s t < s t+1 for some. Snce aggregate resources are fxed, there must be some consumer j for whom s j t > s t+1. But, snce u s strctly concave, then u ( s ) t+1 u ( ) s < t ( ) u j s j ( t+1 ), (35) u j s j t whch volates Equaton (17). Thus, s t = s t+1 and u (s t+1) = 1 for every consumer. That s, n both u (s t) cases, when u s ether lnear or concave, u (s t+1) = 1. Therefore, Equaton (18) can be smplfed to P t = D t=1 u (s t) π t. Snce π < 1, ths geometrc sum smplfes to P t = πd 1 π for all t. Concernng the second part of the proposton, snce u s strctly concave, equlbrum savngs are constant over tme for every consumer, whch defnes a unque savngs level s t = s t+1 = s for each consumer. Proof of Proposton 2. By Equaton (17), n equlbrum, U ( ) ( ) ( ) ζ t+1 U ( ) u s U j ζ j t+1 ζ t u ( t+1 ) s = ( t U j ζ j t ) uj ( s j t+1 u j ( s j t ) ) (36) for all consumers, j and t > 0. Snce ζt+1 = ζ t + c t+1 > ζ t (.e., nterorty s assumed and no borrowng s allowed) and U s strctly concave by assumpton, then U (ζt+1) < 1 for every consumer U (ζ t). Suppose that U (ζt+1) u (s t+1) 1. Then u (s t+1) U (ζt) u (s t) u (s t) allocaton, however, s not feasble snce total resources are fxed. Thus, U (ζt+1) and t. The sum n Equaton (18) s then less than P, for whch U (ζ t+1) U (ζ t) > 1, and thus s t+1 < s t for all. Such an U (ζt) u (s t+1) u (s t) u (s t+1) u (s t) < 1 for all = 1 for every t. Proof of Proposton 3. In equlbrum, Equaton (17) must be satsfed for all consumers at every perod t. Thus, γ c t+1 + ln [ u ( ] s t+1) u ( ) s t ) ( = γ j c j t+1 + ln uj s j ( t+1 ) (37) u j s j t for all, j. Let s be consumer s savng n steady state. Frst, to show that there exsts a unque feasble allocaton such that s t = s t+1 = s for each and Equaton (37) s satsfed for every par of consumers and j, suppose to the contrary that there exsts an allocaton such that s t = s t+1 > s for some. Snce resources are fxed, then there [ exsts ] s j t = sj t+1 < sj for some consumer j. Snce c t+1 s ncreasng n s t+1 and by constructon ln = 0, then γ c t+1 > γ u ( s ) ) t+1 = γ j u (s j j t+1 > u (s t+1) u (s t) 43

45 γ j c j t+1, a volaton of Equaton [ (37). ] Therefore, s s unque for each consumer. When u u s lnear, ln (s t+1) = 0 for any s t and s t+1, whch completes the proof for ths case. u (s t) Assume now that u s strctly concave. Let Z t+1 be the equlbrum value of Equaton (37) at tme t. That s, Z t+1 γ u ( s ) [ u ( s )] + ln t+1 t+1 u ( ) s, (38) t for every consumer and j. In a steady state equlbrum, Z t+1 = γ u ( s t+1), denoted Z. Suppose at tme t a nonempty set of consumers I t = { : s t > s }. Then, by Equaton (37), there exsts a } nonempty set of consumers J t = {j : s j t < sj. Let H t = { h : s h t = s h }, whch may be empty. To prove convergence, t s suffcent to show that s l t+1 sl < s l t s l, where L = H I J l L l L s the set of all consumers. Frst, suppose that Z t+1 = Z. Snce u s strctly ncreasng and strctly concave, s t > s t+1 > s for any I t, and s j t < sj t+1 < sj for any j J t ; otherwse Equaton (37) does not hold. Further, s h t+1 = sh t = s h for h H t. Thus, s l t+1 sl < s l t s l. l L l L Next, suppose Z t+1 > Z. Equaton (37) then mples that s j t+1 < sj for all j J t, s h t+1 < sh for all h H t, and s t+1 < s t for all I t. Splt I t nto A t = { : I t, s t+1 s }, whch may be empty, and B t = { : I t, s < s t+1 < } s t. 56 Snce total resources are fxed, s t s = s j, t sj I t j J t and snce n addton s j t+1 < sj for all j A t H t J t, then s t+1 s = s j. t+1 sj B t j A t H t J t But, by the defnton of B t, s t+1 s < s t s. Thus, s l t+1 sl < s l t s l. B t I t l L l L Snce ths holds for any t, lm s l t s l = 0. Therefore, lm s l t = s l, for every consumer l. The t l L t proof for Z t+1 < Z s smlar. Proof of Proposton 4. When U s DARA, as t, U tends to a lnear form. Proposton 1, prce converges to P, and f u s strctly concave, savngs satsfy s t = s t+1 = s. Then, by Proof of Proposton 5. Let = {1, 2} denote the two types of consumers. By Equaton (17), ( ) c 1 γ ( ) 1 s 1 δ ( ) 1 c 2 γ ( ) = 1 s 2 δ 1. (39) c c1 2 s 1 2 c c2 2 s 2 2 By Walras Law, let s 1 t = Sx t and s 2 t = S (1 x t ), where x t (0, 1), and S s the total possble savngs. Then, substtuton ths usng c t = (s t) 1 δ 1 δ nto Equaton (39), provdes ( ) x 1 δ γ (x1 ) ( ) δ 1 (1 x 1 ) 1 δ γ (1 ) δ x1 x 1 δ 1 + x 1 δ = x 2 2 (1 x 1 ) 1 δ + (1 x 2 ) 1 δ. (40) 1 x 2 Snce the left hand sde of Equaton (39) decreases n x 2 and the rght hand sde ncreases n x 2, the 56 Note that j H t J t mples j J t+1, whle I t can be a member of I t+1, J t+1, or H t+1. 44

46 soluton x 1 = x 2 s unque. Thus, ( ) c 1 γ ( ) 1 s 1 δ 1 c c1 2 s 1 = 2 Smlarly, n the followng perod, ( c c 1 ) γ ( ) 2 s 1 δ 2 c c1 2 + c1 3 s 1 = 3 and so on, such that n perod t ( ζt 1 ) γ ( ) s 1 δ t ζt 1 + c1 t+1 s 1 = t+1 The result then follows by substtutng ths sequence nto Equaton (18). Proof of Corollary 1. Immedately obtaned by Equaton (23). ( ) 1 γ. (41) 2 ( ) 2 γ, (42) 3 ( ) t γ. (43) t

47 B Regresson Results Table B.1: OLS Regresson of Fnal Shares on HL Scores wth Sesson Fxed Effects, Lnear Treatments (Clustered Standard Errors) s = β 0 + β 1h + (sesson dummes) +ε s = average shares of subject durng the fnal 2 perods of the (lnear) sesson h = HL score of subject n the (lnear) sesson Coeffcent Standard Error z P > z [95% Confdence Interval] β [ , ] β 2 (S7) [ , ] β 3 (S10) [ , ] β 4 (S12) [ , ] β 5 (S16) [ , ] β 6 (S18) [ , ] β 7 (S20) [ , ] β 0 (S13) [ , ] R-squared: , Root MSE: Table B.2: OLS Regresson of Fnal Shares on HL Score Shares, Lnear s = β 0 + β 1h + ε s = average shares of subject durng the fnal 2 perods of the (lnear) sesson h = HL score of subject dvded by the sum of HL scores wthn the sesson Coeffcent Standard Error z P > z [95% Confdence Interval] β β Resdual standard error: on 82 degrees of freedom Multple R-squared: 0.168, Adjusted R-squared: F-statstc: on 1 and 82 DF, p-value:

48 Table B.3: Errors) OLS Regresson of Fnal Shares on HL Scores, Concave (Clustered Standard s = β 0 + β 1h + ε s = average shares of subject durng the fnal 2 perods of the (concave) sesson h = HL score of subject n the (concave) sesson Coeffcent Standard Error z P > z [95% Confdence Interval] β [ , ] β 2 (S8) [ , ] β 3 (S9) [ , ] β 4 (S14) [ , ] β 5 (S15) [ , ] β 6 (S17) [ , ] β 7 (S19) [ , ] β 0 (S11) [ , ] R-squared: , Root MSE: Table B.4: Lnear Regresson of HL Score on Treatment Dummes and Earnngs h = β 0 + β 1Lnear + β 2D3 + β 3P ay + ɛ h = subject s Holt Laury score Lnear: lnear treatment dummy D3: d = 3 treatment dummy P ay = subject s earnngs OLS Regresson Number of obs = 168 R 2 (overall): Wald χ 2 (3) = 2.91 corr(u, X) = 0 (assumed) Prob > χ 2 = h Coef. Std. Error t P > t [95% Confdence Interval] β [ , ] β [ , ] β [ , ] β [ , ] 47

49 Table B.5: OLS Regresson of Fnal Shares on HL Scores, L2-10 Choce s = β 0 + β 1h + ε s = average shares of subject durng the fnal 2 perods of the sesson h = HL score of subject n the sesson Coeffcent Standard Error z P > z β β Resdual standard error: on 16 degrees of freedom Multple R-squared: , Adjusted R-squared: F-statstc: on 1 and 16 DF, p-value: Table B.6: OLS Regresson of Fnal Shares on HL Scores, L2-13 Choce s = β 0 + β 1h + ε s = average shares of subject durng the fnal 2 perods of the sesson h = HL score of subject n the sesson Coeffcent Standard Error z P > z β β Resdual standard error: on 16 degrees of freedom Multple R-squared: , Adjusted R-squared: F-statstc: on 1 and 16 DF, p-value:

50 Table B.7: OLS Regresson of Fnal Shares on HL Scores, Lnear Market Low Prce s = β 0 + β 1h + ε s = average shares of subject durng the fnal 2 perods of the sesson h = HL score of subject n the sesson Coeffcent Standard Error z P > z β β Resdual standard error: on 46 degrees of freedom Multple R-squared: , Adjusted R-squared: F-statstc: 2.61 on 1 and 46 DF, p-value: Table B.8: OLS Regresson of Fnal Shares on HL Scores, Lnear Market Hgh Prce s = β 0 + β 1h + ε s = average shares of subject durng the fnal 2 perods of the sesson h = HL score of subject n the sesson Coeffcent Standard Error z P > z β β Resdual standard error: on 34 degrees of freedom Multple R-squared: , Adjusted R-squared: F-statstc: on 1 and 34 DF, p-value:

51 C Instructons The nstructons dstrbuted to subjects n the C2 treatment are reproduced on the followng pages. Subjects n the C3 treatment receve dentcal nstructons, except that dvdends were changed from 2 to 3 throughout. Subjects n the L2 and L3 treatments receve dentcal nstructons to ther counterparts n C2 and C3, respectvely, except for the fourth paragraph. The modfed fourth paragraph n the nstructons for the L2 and L3 treatments s reproduced at the end of the C2 treatment nstructons. Followng these nstructons we present a reproducton of the endowment sheets, payoff tables, and payoff charts for all subjects. After these supplements we present the nstructons dstrbuted to all subjects for the Holt-Laury pared-choce lottery. Fnally, we present nstructons for the ndvdual choce experment, specfcally for treatments C2-7 and C2-10; nstructons for treatments L2-10 and L2-13 are smlar. A complete set of all nstructons used n all treatments of ths experment can be found at texttthttp:// duffy/assetprcng/. 50

52 Expermental Instructons [Treatment C2] I. Overvew. Ths s an experment n the economcs of decson makng. If you follow the nstructons carefully and make good decsons you may earn a consderable amount of money that wll be pad to you n cash at the end of ths sesson. Please do not talk wth others for the duraton of the experment. If you have a queston please rase your hand and one of the expermenters wll answer your queston n prvate. Today you wll partcpate n one or more sequences, each consstng of a number of tradng perods. There are two objects of nterest n ths experment, francs and assets. At the start of each perod you wll receve the number of francs as ndcated on the page enttled Endowment Sheet. In addton, you wll earn 2 francs for each unt of the asset you hold at the start of a perod (please look at the endowment sheet now). Durng the perod you may buy assets from or sell assets to other partcpants usng francs. Detals about how ths s done are dscussed below n secton IV. At the end of each perod, your end-of-perod franc balance wll be converted nto dollar earnngs. These dollar earnngs wll accumulate across perods and sequences, and wll be pad to you n cash at the end of the experment. The number of assets you own carry over from one perod to the next, f there s a next perod (more on ths below), whereas your end-of-perod franc balance does not -you start each new perod wth the endowment of francs ndcated on your Endowment Sheet. Therefore, there are two reasons to hold assets: (1) they provde addtonal francs at the begnnng of each perod and (2) assets may be sold for francs n some future perod. Please open your folder and look at the Payoff Table showng how your end-of-perod franc balance converts nto dollars. The Payoff Chart provdes a graphcal llustraton of the payoff table. There are several thngs to notce. Frst, very low numbers of francs yeld negatve dollar payoffs. The lowest number n the payoff table s 11 francs. You are not permtted to hold less than 11 francs at any tme durng the experment. Second, the more francs you earn n a perod, the hgher wll be your dollar earnngs for that perod. Fnally, the dollar payoff from each addtonal franc that you earn n a perod s dmnshng; for example, the payoff dfference between 56 and 57 francs s larger than the dfference between 93 and 94 francs. NOTE: The total number of francs and assets held by all partcpants n ths market does not change over the course of a sequence. Further, the number of francs provded by each asset, 2, s the same for all partcpants. 51

53 II. Prelmnary Quz Usng your endowment sheet and payoff table, we now pause and ask you to answer the followng questons. We wll come around to verfy that your answers are correct. 1. Suppose t s the frst perod of a sequence (an odd-numbered perod). What s the number of assets you own? 2. What s the total number of francs you have avalable at the start of the frst perod, ncludng both your endowment of francs and the 2 francs you get for each unt of the asset you own at the start of the perod? 3. Suppose that at the end of the frst perod you have not bought or sold any assets, so your franc total s the same as at the start of the perod (your answer to queston 2). What s your payoff n dollars for ths frst perod? 4. Suppose that the sequence contnues wth perod 2 (an even-numbered perod), and that you dd not buy or sell any assets n the frst perod, so you own the same number of assets. What s the total number of francs you have avalable at the start of perod 2, ncludng both your endowment of francs and the 2 francs you get for each unt of the asset you own at the start of a perod? 5. Suppose agan that at the end of perod 2 you have not bought or sold any assets, so your franc total s the same as at the start of the perod (your answer to queston 4). What s your payoff n dollars for ths second perod? What would be your dollar earnngs n the sequence to ths pont? III: Sequences of Tradng Perods As mentoned, today s sesson conssts of one or more sequences, wth each sequence consstng of a number of perods. Each perod lasts 3 mnutes. At the end of each perod your end-of-perod franc balance, dollar payoff and the number of assets wll be shown to you on your computer screen. One of the partcpants wll then roll a de (wth sdes numbered from 1-6). If the number rolled s 1-5, the sequence wll contnue wth a new, 3-mnute perod. If a 6 s rolled, the sequence wll end and your cash balance for that sequence wll be fnal. Any assets you own wll become worthless. Thus, at the start of each perod, there s a 1 n 6 (or about 16.7 percent) chance that the perod wll be the last one played n the sequence and a 5 n 6 (or about 83.3 percent) chance that the sequence wll contnue wth another perod. If less than 60 mnutes have passed snce the start of the frst sequence, a new sequence 52

54 wll begn. You wll start the new sequence and every new sequence just as you started the frst sequence, wth the number of francs and assets as ndcated on your endowment sheet. The quantty of francs you receve n each perod wll alternate as before, between odd and even perods, and the total number of assets avalable for sale (across all partcpants) wll reman constant n every perod of the sequence. If more than 60 mnutes has elapsed snce the begnnng of the frst sequence then the current sequence wll be the last sequence played; that s, the next tme a 6 s rolled the sequence wll end and the experment wll be over. The total dollar amount you earned from all sequences wll be calculated and you wll be pad ths amount together wth your $5 show-up fee n cash and n prvate before extng the room. If, by chance, the fnal sequence has not ended by the three-hour perod for whch you have been recruted, we wll schedule a contnuaton of ths sequence for another tme n whch everyone here can attend. You would be mmedately pad your earnngs from all sequences that ended n today s sesson. You would start the contnuaton sequence wth the same number of assets you ended wth n today s sesson, and your franc balance would contnue to alternate between odd and even perods as before. You would be pad your earnngs for ths fnal sequence after t has been completed. IV. Asset Tradng Rules Durng each three mnute (180 second) tradng perod, you may choose to buy or sell assets. Trade happens on the tradng wndow screen, show below. The current perod s shown n the upper left and the tme remanng for tradng n ths perod (n seconds) s ndcated n the upper rght. The number of francs and assets you have avalable s shown on the left. Assets are bought and sold one unt at a tme, but you can buy or sell more than one unt n a tradng perod. To submt a bd or buyng prce for an asset, type n the amount of francs you are wllng to pay for a unt of the asset n the Buyng prce box on the rght. Then clck on the Post Buyng Prce button on the bottom rght. The computer wll tell you f you don t have enough francs to place a buy order; recall that you cannot go below a mnmum of 11 francs n your account. Once your buy prce has been submtted, t s checked aganst any other exstng buy prces. If your buy prce s hgher than any exstng buy prce, t wll appear under the Buyng Prce column n the mddle rght of the screen; otherwse, you wll be asked to revse your bd upward - you must mprove on exstng bds. Once your buy prce appears on the tradng screen, any player who has a unt of the asset avalable can choose to sell t to you at that prce 53

55 by usng the mouse to hghlght your buy prce and clckng on the button Sell at Hghest Prce (bottom center-rght of the screen). If that happens, the number of francs you bd s transferred to the seller and one unt of the asset s transferred from the seller to you. Another possblty s that another person wll choose to mprove on the buy prce you submtted by enterng a hgher buy prce. In that case, you must ncrease your buy prce even hgher to have a chance of buyng the asset. Tradng Wndow Screen To submt a sellng or ask prce for an asset, type n the amount of francs you would be wllng to accept to sell an asset n the Sellng offer box on the left and then clck the Post Sellng Prce button on the bottom left. Note: you cannot sell an asset f you do not presently have an asset avalable to sell n your account. Once your sell prce has been submtted, t s checked aganst any other exstng sell prces. If your sell prce s lower than any exstng sell prces, t wll appear on the tradng screen under the Sellng Prce column n the mddle left of the screen; otherwse, you wll be asked to revse your sell prce downward - you must mprove on exstng offers to sell. Any partcpant who has enough francs avalable can choose to buy the asset from you at your prce by usng the mouse to hghlght your sell prce and 54

56 clckng on the button labeled Buy at Lowest Prce (bottom center-left of the screen). If that happens, one unt of the asset s transferred from you to the buyer, and n exchange the number of francs you agreed to sell the asset for s transferred from the buyer to you. Another possblty s that another person wll choose to mprove on the sell prce you submtted, by enterng an even lower sell prce. In that case, you wll have to lower your sell prce even further to have a chance of sellng the asset. Whenever an agreement to buy/sell between any two players takes place, the transacton prce s shown n the mddle column of the tradng screen labeled Transacton Prce. If someone has chosen to buy at the lowest prce, all sellng prces are cleared from the tradng screen. If someone has chosen to sell at the hghest prce, all buyng prces are cleared from the tradng screen. As long as tradng remans open, you can post new buy and sell prces and agree to make transactons followng the same rules gven above. The entre hstory of transacton prces wll reman n the mddle column for the duraton of each tradng perod. At the end of each perod, you wll be told your end-of-perod franc balance and dollar payoff for the perod, along wth your cumulatve total dollar payoff over all perods played n the sequence thus far. At then end of each sequence (whenever a 6 s rolled), we wll ask you to wrte down, on your earnngs sheet, the sequence number, the number of tradng perods n that sequence and your total dollar payoff for that sequence. V. Fnal Quz Before contnung on to the experment, we ask that you consder the followng scenaros and provde answers to the questons asked n the spaces provded. The numbers used n ths quz are merely llustratve; the actual numbers n the experment may be qute dfferent. You wll need to consult your payoff table to answer some of these questons. Queston 1: Suppose that a sequence has reached perod 15. What s the chance that ths sequence wll contnue wth another perod - perod 16?. Would your answer be any dfferent f we replaced 15 wth 5 and 16 wth 6? Crcle one: yes / no. Queston 2: Suppose a sequence ends (a 6 s rolled) and you have n assets. What s the value of those n assets?. Suppose nstead, the sequence contnued nto another perod (a 1-5 s rolled)-how many assets would you hold n the next perod?. For questons 3-6 below: suppose at the start of ths perod you are gven 70 francs. In addton, you own 3 assets. 55

57 Queston 3: What s the maxmum number of assets you can sell at the start of the 3-mnute tradng perod?. Queston 4: What s the total number of francs you wll have avalable at the start of the tradng perod (ncludng francs from assets owned)?. If you do not buy or sell any assets durng the 3-mnute tradng perod, what would be your end-of-perod dollar payoff?. Queston 5: Now suppose that, durng the 3-mnute tradng perod, you sold 2 of your 3 assets: specfcally, you sold one asset for a prce of 4 francs and the other asset for a prce of 8 francs. What s your end-of-perod franc total n ths case?. What would be your dollar payoff for the perod?. What s the number of assets you would have at the start of the next perod (f there s one)?. Queston 6: Suppose that nstead of sellng assets durng the tradng perod (as n queston 5), you nstead bought one more asset at a prce of 18 francs. What would be your end-ofperod franc total n ths case?. What would be your dollar payoff for the perod?. What s the number of assets you wll have at the start of the next perod (f there s one)?. VI. Questons Now s the tme for questons. If you have a queston about any aspect of the nstructons, please rase your hand. What follows below s the fourth paragraph of the nstructons for subjects n the L2 and L3 treatments. Please open your folder and look at the Payoff Table showng how your end-of-perod franc balance converts nto dollars. The Payoff Chart provdes a graphcal llustraton of the payoff table. There are several thngs to notce. Frst, the lowest number n the payoff table s 11 francs. You are not permtted to hold less than 11 francs at any tme durng the experment. Second, the more francs you earn n a perod, the hgher wll be your dollar earnngs for that perod. Fnally, the dollar payoff from each addtonal franc that you earn n a perod s the 56

58 same; the formula for convertng between francs and dollars s fxed and s gven at the bottom of your table. 57

59 ENDOWMENT SHEET [Type 1 subject, d = 2] Ths nformaton s prvate. Please do not share wth others. Intal franc balance n all odd perods (frst, thrd, ffth, etc.): 110 Intal franc balance n all even perods (second, fourth, sxth, etc.): 44 Assets you own n the frst perod: 1 Francs pad per asset at start of each perod: 2 Therefore, you wll begn the frst perod wth *2 = 112 francs 58

60 ENDOWMENT SHEET [Type 2 subject, d = 2] Ths nformaton s prvate. Please do not share wth others. Intal franc balance n all odd perods (frst, thrd, ffth, etc.): 24 Intal franc balance n all even perods (second, fourth, sxth, etc.): 90 Assets you own n the frst perod: 4 Francs pad per asset at start of each perod: 2 Therefore, you wll begn the frst perod wth *2 = 32 francs 59

61 ENDOWMENT SHEET [Type 1 subject, d = 3] Ths nformaton s prvate. Please do not share wth others. Intal franc balance n all odd perods (frst, thrd, ffth, etc.): 110 Intal franc balance n all even perods (second, fourth, sxth, etc.): 44 Assets you own n the frst perod: 1 Francs pad per asset at start of each perod: 3 Therefore, you wll begn the frst perod wth *3 = 113 francs 60

62 ENDOWMENT SHEET [Type 2 subject, d = 3] Ths nformaton s prvate. Please do not share wth others. Intal franc balance n all odd perods (frst, thrd, ffth, etc.): 24 Intal franc balance n all even perods (second, fourth, sxth, etc.): 90 Assets you own n the frst perod: 4 Francs pad per asset at start of each perod: 3 Therefore, you wll begn the frst perod wth *3 = 36 francs 61

63 [Type 1 subject, concave treatments (C2 and C3)] 62

64 [Type 1 subject, concave treatments (C2 and C3)] 63

65 [Type 2 subject, concave treatments (C2 and C3)] 64

66 [Type 2 subject, concave treatments (C2 and C3)] 65

67 [Type 1 subject, lnear treatments (L2 and L3)] 66

68 [Type 1 subject, lnear treatments (L2 and L3)] 67

69 [Type 2 subject, lnear treatments (L2 and L3)] 68

70 [Type 2 subject, lnear treatments (L2 and L3)] 69

71 Instructons [Holt-Laury Pared Lottery Task] You wll face a sequence of 10 decsons. Each decson s a pared choce between two optons, labeled Opton A and Opton B. For each decson you must choose ether Opton A or Opton B. You do ths by clckng next to the rado button correspondng to your choce on the computer screen. After makng your choce, please also record t on the attached record sheet under the approprate headngs. The sequence of 10 decsons you wll face are as follows: Decson Opton A Opton B 1 Receve $ out of 100 draws OR Receve $ out of 100 draws OR Receve $ out of 100 draws Receve $ out of 100 draws 2 Receve $ out of 100 draws OR Receve $ out of 100 draws OR Receve $ out of 100 draws Receve $ out of 100 draws 3 Receve $ out of 100 draws OR Receve $ out of 100 draws OR Receve $ out of 100 draws Receve $ out of 100 draws 4 Receve $ out of 100 draws OR Receve $ out of 100 draws OR Receve $ out of 100 draws Receve $ out of 100 draws 5 Receve $ out of 100 draws OR Receve $ out of 100 draws OR Receve $ out of 100 draws Receve $ out of 100 draws 6 Receve $ out of 100 draws OR Receve $ out of 100 draws OR Receve $ out of 100 draws Receve $ out of 100 draws 7 Receve $ out of 100 draws OR Receve $ out of 100 draws OR Receve $ out of 100 draws Receve $ out of 100 draws 8 Receve $ out of 100 draws OR Receve $ out of 100 draws OR Receve $ out of 100 draws Receve $ out of 100 draws 9 Receve $ out of 100 draws OR Receve $ out of 100 draws OR Receve $ out of 100 draws Receve $ out of 100 draws 10 Receve $ out of 100 draws OR Receve $ out of 100 draws OR Receve $ out of 100 draws Receve $ out of 100 draws After you have made all 10 decsons, the computer program wll randomly select 1 of the 10 decsons and your choce for that decson wll be used to determne your payoff. All 10 decsons have the same chance of beng chosen. Notce that for each decson, the two optons descrbe two dfferent amounts of money you can receve, dependng on a random draw. The random draw wll be made by the computer and wll be a number (nteger) from 1 to 100 nclusve. Consder Decson 1. If you choose Opton A, then you receve $6.00 f the random number drawn s 10 or less, that s, n 10 out of 100 possble random draws made by the computer, or 10 percent of the tme, whle you receve $4.80 f the random number s between 11 and 100, that s n 90 out of 100 possble random draws made by the computer, or 90 percent of the tme. If you choose Opton B, then you receve $11.55 f the random number drawn s 10 or less, that s, n 10 out of 100 possble random draws made by the computer, whle you receve $

72 f the random number s between 11 and 100, that s n 90 out of 100 possble random draws made by the computer, or 90 percent of the tme. Other decsons are smlar, except that your chances of recevng the hgher payoff for each opton ncrease. Notce that all decsons except decson 10 nvolve random draws. For decson 10, you face a certan (100 percent) chance of $6.00 f you choose Opton A or a certan (100 percent) chance of $11.55 f you choose Opton B. Even though you make 10 decsons, only ONE of these decsons wll be used to determne your earnngs from ths experment. All 10 decsons have an equal chance of beng chosen to determne your earnngs. You do not know n advance whch of these decsons wll be selected. Consder agan decson 1. Ths wll appear to you on your computer screen as follows: The pe charts help you to vsualze your chances of recevng the two amounts presented by each opton. When you are ready to make a decson, smply clck on the button below the opton you wsh to choose. Please also crcle your choce for each of the 10 decsons on your record sheet. When you are satsfed wth your choce, clck the Next button to move on to the next decson. You may choose Opton A for some decsons and Opton B for others and you may change your decsons or make them n any order usng the Prevous and Next buttons. When you have completed all 10 choces, and you are satsfed wth those choces you wll need to clck the Confrm button that appears followng decson 10. The program wll check that you have made all 10 decsons; f not, you wll need to go back to any ncomplete decsons and complete those decsons whch you can do usng the Prevous button. You can also go back and change any of your decsons pror to clckng the confrm button by usng the Prevous button. Once you have made all 10 decsons and clcked the Confrm button, the results screen wll tell you the decson number 1, 2,... 10, that was randomly selected by the computer program. Your choce 71

73 of opton A or B for that decson (and that decson only) wll then be used to determne your dollar payoff. Specfcally, the computer wll draw a random number between 1 and 100 (all numbers have an equal chance) and report to you both the random number drawn and the payoff from your opton choce. Your payoff wll be added to the amount you have already earned n today s experment. Please crcle the decson that was chosen for payment on your record sheet and wrte down both the random number drawn by the computer program and the amount you earned from the opton you chose for that decson on your record sheet. On the computer montor, type n your subject ID number, whch s the same number used to dentfy you n the frst experment n today s sesson. Then clck the Save and Close button. Are there any questons before we begn? Please do not talk wth anyone whle these decsons are beng made. If you have a queston whle makng decsons, please rase your hand. 72

74 Record Sheet Player ID Number Crcle Opton Choce Decson 1 A B Crcle Opton Choce Decson 2 A B Crcle Opton Choce Decson 3 A B Crcle Opton Choce Decson 4 A B Crcle Opton Choce Decson 5 A B Crcle Opton Choce Decson 6 A B Crcle Opton Choce Decson 7 A B Crcle Opton Choce Decson 8 A B Crcle Opton Choce Decson 9 A B Crcle Opton Choce Decson 10 A B At the end of ths experment, crcle the Decson number selected by the computer program for payment. Wrte down the random number drawn for the selected decson (between 1 and 100): Wrte down your payment earned for ths part of the experment: $ 73

75 Expermental Instructons [Treatments C2-7 and C2-10] I. Overvew. Ths s an experment n the economcs of decson makng. If you follow the nstructons carefully and make good decsons you may earn a consderable amount of money that wll be pad to you n cash at the end of ths sesson. Please do not talk wth others for the duraton of the experment. If you have a queston please rase your hand and one of the expermenters wll answer your queston n prvate. Today you wll partcpate n one or more sequences, each consstng of a number of tradng perods. There are two objects of nterest n ths experment, francs and assets. At the start of each perod you wll receve the number of francs as ndcated on the page enttled Endowment Sheet. In addton, you wll earn a dvdend of 2 francs for each unt of the asset you hold at the start of a perod (please look at the endowment sheet now). Durng the perod you may buy or sell assets usng francs at the prce lsted on the endowment sheet. Detals about how ths s done are dscussed below n secton IV. At the end of each perod, your end-of-perod franc balance wll be converted nto dollar earnngs. These dollar earnngs wll accumulate across perods and sequences, and wll be pad to you n cash at the end of the experment. The number of assets you own carry over from one perod to the next, f there s a next perod (more on ths below), whereas your end-of-perod franc balance does not you start each new perod wth the endowment of francs ndcated on your Endowment Sheet. Therefore, there are two reasons to hold assets: (1) they provde addtonal francs at the begnnng of each perod and (2) assets may be sold for francs n some future perod. Please open your folder and look at the Payoff Table showng how your end-of-perod franc balance converts nto dollars. The Payoff Chart provdes a graphcal llustraton of the payoff table. There are several thngs to notce. Frst, very low numbers of francs yeld negatve dollar payoffs. The lowest number n the payoff table s 11 francs. You are not permtted to hold less than 11 francs at any tme durng the experment. Second, the more francs you earn n a perod, the hgher wll be your dollar earnngs for that perod. Fnally, the dollar payoff from each addtonal franc that you earn n a perod s dmnshng; for example, the payoff dfference between 56 and 57 francs s larger than the dfference between 93 and 94 francs. 74

76 II. Prelmnary Quz Usng your endowment sheet and payoff table, we now pause and ask you to answer the followng questons. We wll come around to verfy that your answers are correct. 1. Suppose t s the frst perod of a sequence (an odd-numbered perod). What s the number of assets you own? 2. What s the total number of francs you have avalable at the start of the frst perod, ncludng both your endowment of francs and the 2 francs you get for each unt of the asset you own at the start of the perod? 3. Suppose that at the end of the frst perod you have not bought or sold any assets, so your franc total s the same as at the start of the perod (your answer to queston 2). What s your payoff n dollars for ths frst perod? 4. Suppose that the sequence contnues wth perod 2 (an even-numbered perod), and that you dd not buy or sell any assets n the frst perod, so you own the same number of assets. What s the total number of francs you have avalable at the start of perod 2, ncludng both your endowment of francs and the 2 francs you get for each unt of the asset you own at the start of a perod? 5. Suppose agan that at the end of perod 2 you have not bought or sold any assets, so your franc total s the same as at the start of the perod (your answer to queston 4). What s your payoff n dollars for ths second perod? What would be your dollar earnngs n the sequence to ths pont? III: Sequences of Tradng Perods As mentoned, today s sesson conssts of one or more sequences, wth each sequence consstng of a number of perods. Each perod wll last approxmately 2 mnutes. At the end of each perod your end-of-perod franc balance, dollar payoff and the number of assets wll be shown to you on your computer screen. One of the partcpants wll then roll a de (wth sdes numbered from 1-6). If the number rolled s 1-5, the sequence wll contnue wth a new, 3-mnute perod. If a 6 s rolled, the sequence wll end and your cash balance for that sequence wll be fnal. Any assets you own wll become worthless. Thus, at the start of each perod, there s a 1 n 6 (or about 16.7 percent) chance that the perod wll be the last one played n 75

77 the sequence and a 5 n 6 (or about 83.3 percent) chance that the sequence wll contnue wth another perod. If fewer than 14 total perods have occurred n ths experment, a new sequence wll begn. You wll start the new sequence and every new sequence just as you started the frst sequence, wth the number of francs and assets as ndcated on your endowment sheet. The quantty of francs you receve n each perod wll alternate as before, between odd and even perods. If at least 14 perods have taken place snce the start of the experment, then the current sequence wll be the last sequence played; that s, the next tme a 6 s rolled the sequence wll end and the experment wll be over. The total dollar amount you earned from all sequences wll be calculated and you wll be pad ths amount together wth your $5 show-up fee n cash and n prvate before extng the room. If, by chance, the fnal sequence has not ended by the three-hour perod for whch you have been recruted, we wll schedule a contnuaton of ths sequence for another tme n whch everyone here can attend. You would be mmedately pad your earnngs from all sequences that ended n today s sesson. You would start the contnuaton sequence wth the same number of assets you ended wth n today s sesson, and your franc balance would contnue to alternate between odd and even perods as before. You would be pad your earnngs for ths fnal sequence after t has been completed. IV. Asset Tradng Rules You wll make your decson to buy or sell assets by enterng nformaton nto the Pre-Trade Wndow, an example of whch s presented below. The current sequence appears n the upperleft corner of the screen, the current perod number n the rght. The next four lnes wthn the wndow provde you wth nformaton regardng your franc and asset poston at the begnnng of the perod. For example, n the wndow below, you would begn the current perod wth an endowment of 110 francs and 1 unt of the asset. Snce each unt of the asset pays an addtonal 2 francs, your total avalable francs to start the perod would be 112. Below ths nformaton you are remnded of the prce of each unt of the asset (n ths example the prce s 10 francs, but the prce you wll actually use s presented on your Endowment Sheet), and you are asked to decde whether you d lke to buy or sell unts of the assets at ths prce. In the example below, the Buy button has been selected. After you have decded whether 76

78 you wll be a buyer or a seller, you wll enter how many unts of the asset you d lke to trade. Recall that you cannot sell a greater quantty of assets than you currently possess, and that you cannot buy so many unts of the asset that your current franc balance would drop below 11. If you would lke to trade nothng n ths perod, choose the Buy or Sell button (t doesn t matter whch one) and enter a quantty of 0. Once you have entered your desred quantty, clck the red OK button to complete the transacton. When you clck ths button, your decson s fnal. Pre-Trade Wndow After you have made your tradng decson, you wll be presented wth a new wndow, as depcted n the Post-Trade Wndow below. In ths example, you have made the decson to buy two unts of the asset. Snce you started the perod wth 112 francs, and snce assets cost 10 francs each, you would end the perod wth *2 = 92 francs and 3 unts of the asset (recall that you started the perod wth one unt). Your dollar payoff for the perod, based on your end-of-perod franc balance of 92 francs, would be $1.21 (you can confrm ths amount on your Payoff Table). Your cumulatve earnngs over all perods n the current sequence are also dsplayed. Post-Trade Wndow After all of the experment partcpants have clcked the OK button, the de 77

79 wll be rolled to determne f the sequence wll contnue. On a roll of 1-5, the sequence wll contnue. You would begn the next perod of the sequence wth your endowment ncome (n the example above, you would begn perod 2 wth endowment ncome of 44 francs, as stated on your Endowment Sheet), dvdend ncome (n ths example 6 francs, because you hold 3 unts of the asset, and each unt pays a dvdend of 2 francs), and your assets from the prevous perod (n ths example, 3 unts). On a roll of 6 the sequence s over, n whch case we wll ask you to wrte down, on your Earnngs Sheet, the sequence number, the number of tradng perods n that sequence and your total dollar payoff for that sequence. V. Fnal Quz Before contnung on to the experment, we ask that you consder the followng scenaros and provde answers to the questons asked n the spaces provded. The numbers used n ths quz are merely llustratve; the actual numbers n the experment may be qute dfferent. You wll need to consult your payoff table to answer some of these questons. Queston 1: Suppose that a sequence has reached perod 15. What s 78