ISSN Environmental Economics Research Hub Research Reports. The Implications of Risk and Uncertainty Aversion in Public Goods Games

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1 ISSN Envronmental Economcs Research Hub Research Reports The Implcatons of Rsk and Uncertanty Averson n Publc Goods Games Veronka Nemes and Lata Gangadharan Research Report No. 107 June 2011 About the authors Veronka Nemes s a Research Student n the Centre for Energy and Envronmental Markets, The Unversty of New South Wales and Vctoran Government Department of Sustanablty and Envronment. Lata Gangadharan s from the Department of Economcs, Monash Unversty The authors are grateful to Charles R. Plott for hs valuable comments and to Jonathan Payne for hs help n runnng the experments. 1

2 Envronmental Economcs Research Hub Research Reports are publshed by the Crawford School of Economcs and Government, Australan Natonal Unversty, Canberra, 0200 Australa. These Reports present work n progress beng undertaken by project teams wthn the Envronmental Economcs Research Hub (EERH). The EERH s funded by the Department of Sustanablty, Envronment, Water, Populaton and Communtes under the Commonwealth Envronment Research Faclty. The authors would lke to thank the Namo Catchment Management Authorty and n partcular Anna Cronn for ther assstance n conductng ths study. The vews and nterpretatons expressed n these Reports are those of the author(s) and should not be attrbuted to any organsaton assocated wth the EERH. Because these reports present the results of work n progress, they should not be reproduced n part or n whole wthout the authorsaton of the EERH Drector, Professor Jeff Bennett (jeff.bennett@anu.edu.au) Crawford School of Economcs and Government THE AUSTRALIAN NATIONAL UNIVERSITY 2

3 Table of Contents Abstract 4 1. Introducton 5 2. Lterature Revew 7 3. Expermental Desgn Results Conclusons 27 References 30 Tables 32 Fgures 36 3

4 Abstract In ths paper we examne how ndvduals behave n stuatons of rsk and uncertanty n publc and prvate goods context. We fnd that subjects are wllng to pay a much hgher amount to fnd out nformaton relatng to the probabltes of provdng the prvate good than nformaton relatng to the publc good even f ths nformaton has greater consequences for the ndvdual n he publc goods context. We fnd strong support for the free-rder hypothess and extend t to cases when rsk and uncertanty are present. We fnd that subjects treat rsks and uncertantes assocated wth the provson of prvate good and publc good dfferently. JEL classfcaton: C91, Q00, H41 Keywords: Expermental Economcs, Publc Goods, Rsk Averson, Uncertanty Averson, Decson Makng 4

5 1. Introducton Due to ts mportance and mplcatons, decson makng has been studed by researchers from a wde range of felds ncludng economcs, psychology, poltcal, and envronmental scence. Partcular effort has also been devoted to studyng how people perceve, quantfy, process and evaluate the probabltes of certan events. In the expermental economc work on rsky decson makng, probabltes are typcally provded or assumed to be known wth precson. However, ths contrasts wth experence n the real world whch s more commonly characterzed by vagueness or ambguty concernng probabltes. Probabltes relatng to envronmental events such as clmate change, ranfall, temperature, changes n the ecosystem or the consequences of polluton are a prme example where probabltes are not known wth certanty. In the area of clmate change, for example, a great deal of uncertanty exsts regardng expected global mean temperature changes, sea level rse, meltng of glacers, ncrease of extreme weather events, costs of mtgaton and adaptaton, and avalablty of future technology. How to translate global clmate change to local mpacts s also uncertan. Polcy makers often use models wth varous scenaros whch may occur wth dfferent probabltes. Uncertanty regardng the probabltes of these events s sometmes used as a reason to delay polcy mplementaton. A key queston n the current research s how decson makers use nformaton when they face rsks (known probabltes) and uncertanty (unknown probabltes) and n what way does better knowledge about probabltes alter decsons. We nvestgate decson makers preference for known or unknown probabltes when they face prvate and publc goods scenaros. Research queston also nclude determnng relatonshps between rsk-atttudes, wllngness to pay for nformaton on probabltes assocated to returns n a prvate and publc good context, and decson makers contrbutons to the publc good. Dstngushng between known and unknown objectve probabltes dates back to Knght (1921), wth hs rsk versus uncertanty dchotomy. Knght suggested usng the term uncertanty when 5

6 objectve probabltes are unknown and the term rsk when the objectve probabltes are known. Though Knght s dstncton between rsk and uncertanty s plausble, several economsts have been skeptcal of whether the dstncton has any behavoral sgnfcance. Theorsts followng the path of subjectve expected utlty theory (SEU) bypass ths ssue by assumng that the payoffs for a game are already measured as utltes. In the SEU theory the dstncton between known and unknown objectve probablty s pontless because subjectve probabltes are known to decson makers and are nferable from choces. Therefore, whether the subject knows the true objectve probabltes s not relevant. Indvduals behave as f they were maxmzng the expected value of some utlty functon over outcomes, wth respect to some probabltes. Accordng to ths reasonng, ndvduals atttude towards rsk and uncertanty should be equvalent, provded the expected (subjectve) probabltes of outcomes under uncertanty concde wth the known probabltes of those same outcomes under rsk. Despte the appeal of the SEU theory, most of the emprcal evdence suggests that people do make dstncton between known and unknown probabltes. The questons to what extent do rsk averson and uncertanty averson exst, how they depend on dfferent factors, and how they nfluence decsons s ultmately an emprcal ssue. Laboratory experments can provde a control of probabltes and payoffs and, therefore, provde a natural ground for testng the dfference that known and unknown probabltes make n the decsons. Gven that the majorty of envronmental problem can be charactersed as ether a publc good or a common pool resource game, studyng how people make decsons when probabltes are known or unknown can contrbute to understandng decson-makng n the feld of envronment. Rsk and uncertanty, and hence the dstncton between known and unknown probabltes have not yet been extensvely studed n a publc goods expermental context. In ths paper we use experments desgned to capture the dfference n the behavour of subjects under rsk and uncertanty usng the standard publc goods game framework. The rsk behavour of the subjects s captured n two ways: frst, subjects partcpate ndvdually n a lottery game 6

7 where they face known probabltes. Second, they partcpate n a publc goods game where they face rsk or uncertanty. In the latter case subjects are gven the opportunty to learn the probablty. In ths sense the choce to learn the nformaton nherent n the probablty of provson of the prvate/publc good s endogenous to the partcpants. In Secton 2 we revew the relevant lterature, n Secton 3 we descrbe the expermental procedures and the detals of the treatment setup, n Secton 4 we provde detals of the results, and n Secton 5 we conclude and suggest some possble mplcaton of our research fndngs. 2. Lterature Revew Rsk has been a fundamental element of both theoretcal and emprcal research n decson makng. Research has shown that people tend to have dfferent rsk preferences 1 when facng gans or losses (Kahneman and Tversky, 1979; Allson and Messck, 1985; Andreon, 1995), when probabltes are hgh or low (Kahneman and Tversky, 1979; Cohen et al., 1987; Tversky and Kahneman, 1992) 2, when the stake s hgh or low (Kachelmeer and Shehata, 1992) when buyng or sellng (Kachelmeer and Shehata, 1992) and when probabltes are n the context of socal and nonsocal domans (Loewensten et al., 1989). Though rsk averson has proven to provde valuable nsghts nto decson makng n fnancal nvestment, nsurance and technologcal nvestment decsons, t has lmted applcablty to several real lfe scenaros, such as decsons regardng clmate change scenaros that are better characterzed by vagueness or ambguty concernng probabltes. Ellsberg (1961) put emprcal content to Knght s dea and found that, when confronted wth the choce to bet on urn I contanng 50 red and 50 black balls n known proportons (the rsky urn) or to bet on urn II wth 100 red and black balls n unknown proportons (the uncertan or ambguous 1 The most common descrpton for rsk preferences n the lterature s rsk neutral, rsk lovng and rsk averse dependng on the decson maker s preference over a lottery and ts expected value. 2 One of the man results of several laboratory experments (Kahneman and Tversky, 1979; Cohen et al., 1987; Tversky and Kahneman, 1992) s the nterestng pattern of rsk atttudes: rsk averson for gans and rsk lovng for losses at hgh probablty, and rsk averson for losses and rsk lovng for gans at low probablty. 7

8 urn), the majorty of subjects preferred to bet on the former, an atttude termed snce then uncertanty averson or ambguty averson. What s more nterestng s that many subjects contnued to prefer urn I when ts rato of red and black balls was reduced to 49:51. Ellsberg s work has generated a great deal of nterest n both the realms of the theoretcal and emprcal research. In the feld of theoretcal research, Ellsberg (1961) provded an nstructve counter example to SEU theory and argued that vagueness about probabltes could lead people to volate the Savage axoms of consstent behavor upon whch modern Bayesan decson theory and nference s based. Ellsberg (1961) contended that some of these volatons were conscous and delberate and not careless mstakes that would be retracted after careful reflecton. 3 Ellsberg (1961) concluded that Bayesan theory was applcable to decson-makng under rsk but not to decson-makng under uncertanty. Heath and Tversky (1991) convey that Ellsberg present a serous problem for expected utlty theory and other models of rsky choce, because ( ) most decsons n the real world depend on uncertan events whose probabltes cannot be precsely assessed. ( ) [T]he applcablty of the standard model of rsky choce s severely lmted. (p. 6.) Though Ellsberg dd not run formal experments, hs thought experments were frequently replcated and extended. Becker and Brownson (1964) dd the frst study n whch they presented the subjects wth choces of varyng ambguty. The subjects chose between urns contanng 100 red and black balls. Drawng a red ball pad $1. The authors operatonalzed ambguty as the range of probabltes; the dfference n ambguty s the dfference n the ranges whle the center 3 Ellsberg made a test on Savage hmself. Savage volated hs own axoms. Ellsberg, therefore, concluded, that a reacton consstent wth Savage axom s by no means a unversal reacton; on the contrary, t would be exceptonal. ( ) Responses do vary. There are those who do not volate the axoms, or say they won t, even n these stuatons ( ); such subjects tend to apply the axoms rather than ther own ntuton, and when n doubt, to apply some form of the Prncple of Insuffcent Reason. Some volate the axoms cheerfully, even wth gusto ( ); others sadly but persstently, havng looked nto ther hearts, found conflcts wth the axoms and decded ( ) to satsfy ther preferences and let the axoms satsfy themselves. Stll others ( ) tend, ntutvely, to volate the axoms but feel gulty about t and go back nto further analyss. ( ) The mportant fndng s that, after rethnkng all ther offendng decsons n the lght of the axoms, a number of people who are not only sophstcated but reasonable decde that they wsh to persst n ther choces. (Ellsberg, 1961 p ) 8

9 of probabltes was kept constant. For example, one urn had exactly 50 red balls; another had between 15 and 85 red balls, the thrd had between 25 and 75 red balls and the last urn had between 40 and 60 red balls. There was also an urn wth unknown contents (red ball between 0 and 100). Subjects chose between pars of urns, dfferng n the range of red balls, and sad how much they would pay to draw from ther preferred urn. The authors found that subjects always pcked the less ambguous urn and pad hgh amounts to avod ambguty. Subjects, therefore, were wllng to pay to avod the ambguous course of acton even f that acton had an expected value equal to the alternatve unambguous course of acton. For example, they pad an average of $.36 to choose from an urn wth 50 red balls nstead of an ambguous urn unknown number of red balls even f the expected value of a draw n both cases were $.50. The authors also concluded that as the dfference n the ambguty between two urns decreased, the amount of money subjects were wllng to pay to choose the course of acton wth less ambguty decreased but the amounts subjects specfed were not always proportonal to the dfferences n ranges assocated wth each par of urns. Subsequently, several research (e.g., Slovc and Tversky, 1974; MacCrmmon and Larsson, 1979; Curley and Yates, 1985; Kahn and Sarn, 1988; Curley and Yates, 1989; and Bernascon and Loomes, 1992) found consstent and strong support for ambguty averson n varants of the Ellsberg problems. Hogarth and Kunreuther (1989) demonstrated that even sophstcated subjects who recognzed that, from an expected utlty theory pont of vew, ambguty should not matter ndcated a strong averson to ambguty. Rsk atttudes are generally consdered to be dstngushed from atttudes towards uncertanty (Camerer and Weber, 1992; Cohen et al., 1987; Curley et al. 1986; Hogarth and Enhorn, 1990; Fox and Tversky, 1995). Frsch and Baron (1988) conclude that when nformaton regardng the probabltes s mssng, people may overwegh the worse possbltes and adjust ther choce on the sde of cauton. Chow and Sarn (2002) examned, n an expermental settng, the role of mssng nformaton and ts mpact on the attractveness of a bet. The authors dstngushed 9

10 between known, unknown and unknowable uncertantes. The unknown certanty was a case where the subject dd not know the probablty but beleved that some other person mght know t, whle unknowable uncertanty was where the subject beleved that the probabltes were unknown to everyone. The results suggest that the case when the probabltes are known s preferred to the cases when the probablty s unknown and unknowable. However, the unknowable case s preferred over the unknown case,.e. vagueness n probablty s more tolerated when others also lack the nformaton about probablty and are therefore perceved to be n the same boat. Sandler et al. (1987) use a probablstc model n a publc goods context. In ther model the total quantty of publc goods s probablstc, and ndvduals bd to ncrease the amount of the good. They showed that the bd of an ndvdual depends on rsk averson, and that an ncrease n rsk wll lead to a decrease n expendture on the publc goods for a rsk-averse ndvdual. Studes, therefore, suggest that the attractveness of a bet s nfluenced by several factors over and beyond probabltes and payoffs. Rather than smply extendng the exstng lterature on decson makng n the presence of rsk and uncertanly, we are nterested n fndng out how decsons are made n the context of publc goods n the presence of rsk and uncertanty. There are several examples of ths scenaro. Decson makng n the feld of envronment for example s abundant wth problems that can be charactersed as publc good games wth unknown probabltes. Clmate change, bodversty loss, ecosystem degradaton are only some of the global envronmental problems that fall nto ths category. Rather than confnng our research to the smple choce problem, we take the research on uncertanty averson and rsk averson and apply t n the context of publc goods games. It s common wsdom that people behave dfferently when makng decsons about prvate and publc goods. The ssue we explore here s whether rsk and uncertanty atttudes dffer n the two cases as well. Though the publc goods game s more complex than a smple lottery choce setup and thus adds some nose to our data such as strategc uncertanty, we keep varables affectng the 10

11 strategc uncertanty constant (e.g., group sze, communcaton) throughout the varous treatments. The study helps us understand how ndvduals behave n real lfe stuatons where they face rsk or uncertanty and decde on allocatng resources to prvate or publc goods. 3. Expermental Desgn 3.1. Expermental Procedure Ten sessons were run, each sesson ncluded 3 treatments, one lottery game, and a questonnare. Fve subjects partcpated n each of the ten sessons. All subjects partcpated n all treatments, namely Baselne, Uncertanty n Prvate Goods and Uncertanty n Publc Goods treatments. 4 Each treatment conssted of a sequence of ffteen decson makng perods. A group of fve partcpants faced the same nvestment dlemma and made smultaneous decsons. The experment was programmed and conducted wth the software z-tree (Fschbacher, 1999). It was emphaszed to the partcpants that ther own decsons were prvate nformaton appearng on ther own screens only and were not to be dscussed wth other partcpants. To allow for the consderaton of results of the prevous perods, partcpants were asked to record ther ndvdual ncome n every perod and any addtonal nformaton they found relevant to ther decsons. At the end of the Uncertanty n Prvate Goods and Uncertanty n Publc Goods treatments subjects were asked to specfy ther wllngness-to-pay to learn the nformaton on probablty when t was attached to the prvate or the group account, respectvely. A questonnare was also completed by the partcpants at the end of the sesson. 4 There were some addtonal treatments run n each sesson. The results of these treatments are reported n Gangadharan and Nemes (2009). For the purpose of explorng further the dfference between rsk averson and uncertanty averson, we have selected three of the treatments n the current paper. We have controlled for order effects and concluded, that the results n the treatments were ndependent of each other. Selectng only three of the seven treatments, therefore, had no mpact on the accuracy of the results. 11

12 3.2. Treatment Descrpton Baselne Treatment The baselne treatment s a standard publc goods game. At the start of each perod, each subject was gven the same number of tokens or expermental dollars (E$),. Subjects had to dvde these tokens between contrbutng to a prvate account ( x ) and a group account ( g ). Investment nto the prvate account earned expermental dollars to the ndvdual only. Contrbutons to the publc account earned G n 1 G expermental dollars to each partcpant, where n g. The parameters and mght be thought of as the effcency factors on the prvate and the publc accounts, respectvely. Contrbutons to the publc account, therefore, yelded the same return to all partcpants, dependng on the sum of all contrbutons but rrespectve of the ndvdual s contrbuton. Therefore, the publc account exhbted the publc goods non-excludble and non-rval characterstcs. At the end of each perod, subjects learnt the aggregate level of contrbuton to the publc good and ther return from the prvate as well as the publc account. In the Baselne treatment, ndvdual s payoff s gven by: (1) u G x n The subjects must maxmze ths utlty functon, subject to a budget constrant ( x g ), a publc goods dentty ( G n g 1 ), and a non-negatvty constrant ( g 0 ). Let s defne M as the margnal per capta return (MPCR) the amount that s generated for each member of the group when one ndvdual contrbutes a token to the publc good. It can also be 12

13 seen as the margnal rate of substtuton of the prvate good for the publc good or as a measure of ncentves to contrbute to the publc good. 5 (2) M u / G u / g n The socal dlemma arses f M 1. In ths case, a unt nvestment nto the prvate account provdes a subject wth more payoff than a unt nvestment nto the publc account. On the other hand, takng from every partcpant a unt of prvate nvestment and contrbutng t to the group account makes each partcpant better off. Thus, the unque domnant strategy s to free rde (.e., g 0 for ) whle the socally optmal Pareto effcent soluton requres every partcpant to contrbute all ther tokens to the group account (.e., g for ). Uncertanty n Prvate Goods Treatment In the Uncertanty n Prvate Goods treatment subjects face uncertanty regardng the probablty of return from the prvate account. Subjects know that the probablty of return from the prvate account s determned by drawng a random number from a unform dstrbuton but the exact probablty s not dsplayed to the partcpants. Whether the actual payment wll be made once the partcpants made ther nvestment decsons, s determned by a random number generaton process. Therefore, there s uncertanty (.e., unknown probablty) regardng the return from the nvestment nto the prvate account. To learn the exact probablty of return, partcpants must pay a fee of f 20 from ther endowments. When partcpants choose to do so, the nformaton regardng the probablty of return from the prvate ( p x ) account s dsplayed on the computer screen. Ths nformaton remans the prvate nformaton for those partcpants who pad the fee for the nformaton. Partcpants who pad 20 expermental dollars for the nformaton reman wth f 80 tokens to nvest n that perod. 5 The MPCR was ntroduced by Isaac et al (1984). 13

14 Ths treatment allows us to dvde the partcpants nto two dstnct groups: those who are wllng to pay and, therefore, know the exact value of the probablty (facng rsk) and those who do not (facng uncertanty). In order to mantan the payoff equvalence wth the Baselne treatment, the parameters have been modfed and set 2, For subjects who act under uncertanty (.e., do not wsh to know the probablty) the expected value of margnal per capta rato remans equvalent to that n the Baselne treatment,.e. EM For subjects who choose to obtan the probablty assocated wth the prvate account, the expected margnal per capta rato changes. At the end of the Uncertanty n Prvate Goods treatment a questonnare was flled out by the partcpants to assess ther wllngness-to-pay for the nformaton regardng the probablty of return from the prvate account. The Uncertanty n Prvate Goods treatment s employed to learn about the uncertanty atttude of partcpants n a publc goods - prvate goods contexts when the uncertantes are related to the prvate good. Uncertanty n Publc Goods Treatment The Uncertanty n Publc Goods treatment mrrors the Uncertanty n Prvate Goods treatment. In the Uncertanty n Publc Goods treatment subjects face an uncertanty regardng the probablty of provson of publc good. Subjects know that ths probablty s determned by drawng a random number from a unform dstrbuton but the exact value of the probablty s not dsplayed to the partcpants. Therefore, there s uncertanty (.e., unknown probablty) regardng the return from the nvestment nto the publc account. To learn the exact probablty of return, partcpants must pay a fee of f 20 from ther endowments. When partcpants choose to do so, the nformaton regardng the probablty of return from the publc ( p g ) account s dsplayed on the computer screen. Ths nformaton remans the prvate nformaton for those partcpants who pad the fee for the nformaton. Partcpants who pad 20 expermental dollars for the nformaton reman wth f 80 tokens to nvest n that perod. 14

15 Agan, at the end of the Uncertanty n Publc Goods treatment a questonnare was flled out by the partcpants to assess ther wllngness-to-pay for the nformaton regardng the probablty of return from the publc account. The Uncertanty n Publc Goods treatment s employed to learn about the uncertanty atttude of partcpants n a publc goods - prvate goods contexts when the uncertantes are related to the publc good. Lottery Game In order to control for rsk averson pror to the computerzed experment, we asked the subjects to partcpate n a hand run lottery game smlar to the procedures descrbed n Holt and Laury (2002). Partcpants had to ndcate ther preferences between two lotteres n ten games. In the frst case, Opton A represents the sure payoff of $7 and Opton B represents a lottery where dependng on the number drawn from a bngo cage, the payment s n the extremes of $2 (wth probablty.9) or $12 (wth probablty.1). Under these condtons, most people wll choose Opton A. As the probablty of the hgh payoff outcome ncreases, people tend to cross over to Opton B. For example, a rsk neutral person would choose Opton A n the frst four tasks before swtchng to Opton B. The more rsk-averse the person, the later he wll swtch over to Opton B. Subjects ndcated a preference, Opton A or Opton B, for each of the ten pared lottery choces wth an understandng that one of these choces would be selected at random at the end of the sesson and played to determne the earnngs for the opton selected. Conductng the lottery game was mportant to reveal the rsk preferences of the partcpants. Ths s mportant for us n the analyss n order to separate the effects of atttude of rsk averson from other possble systematc effects on decsons under rsk and uncertanty. Conductng the lottery game gves us an addtonal measure of the rsk preference of the subjects whch we can then compare wth ther behavor n the publc goods experments where they face rsk and uncertanty and can also help compare our results wth other smlar studes. Demographc Questonnare 15

16 Qualtatve and quanttatve nformaton were also collected from each partcpant at the end of the sesson n the form of a questonnares. 4. Results In ths secton we frst examne the results from the lottery game and then we analyze the relatonshp between subjects rsk atttudes and ther subsequent decsons to avod uncertanty. Research queston nclude determnng whether rsk-seekng or rsk-averse ndvduals are more lkely to pay for nformaton on probabltes assocated wth prvate and group accounts. We also examne the relatonshp between rsk atttudes, wllngness to pay to reveal the probablty and ndvdual contrbutons to the publc good Rsk Atttudes The partcpants pattern of choces n the lottery game sheet provded an ordnal measure of ther rsk atttude. Rsk averson s represented by the convexty or concavty of an ndvdual s utlty functon when faced wth the choce between an uncertan payoff and a safe bet. One way to assess the convexty or concavty of ths functon s to fnd the bet at whch the partcpant s ndfferent between the safe and rsky opton. In the present context ths pont s represented by the choce game at whch the partcpant swtches from choosng Opton A to Opton B. Thus, each subject was gven a score from 1 to 10 based upon the game at whch they swtched from choosng the rskless choce (Opton A) to the rsky choce (Opton B). The subjects scores therefore ranged from 1 (rsk averse) to 10 (rsk seekng) wth a score of 5 for a rsk neutral subject. The majorty of subjects were slghtly rsk averse. Fgure 1 shows that 74 percent of the subjects swtched from the rskless choce (Opton A) to the rsky choce (Opton B) at the sxth choce game or afterwards and thus are categorzed as rsk averse. Ten percent of the subjects swtched 16

17 at the ffth choce game, they are marked as rsk neutral, whle 16% swtched before or at the fourth game, hence they are rsk lovers. 6 As explaned n the desgn secton, we also collected demographc data from the 50 subjects and we are nterested n examnng whether these demographc characterstcs can explan behavor towards rsk n ths lottery game. Table 1 presents estmates of rsk atttudes from an ordered probt and a bnary probt model. In the ordered probt model, rsk atttudes are thought to be of three knds: rsk lovng, rsk neutral and rsk averse. The dependent varable hence takes three values 0, 1 and 2. The bnary probt rsk model separates subjects nto two categores: rsk lovers (those who swtched at or before the ffth choce game) and rsk averse (those who swtched at or after the sxth choce game). In both the ordered and the bnary probt model the ndependent varables are the demographc varables, lke sex of the subject (sex), age (age), how long they have lved n Australa (auslved), whether they have taken courses n economcs (econ) etc. The equatons estmated for the rsk atttudes are the followng: rskorder takes three values and s estmated as an ordered probt and probt: r _ lover takes two values and s estmated as a bnary (3) rskorder 1 sex 2age 3school 4econ 5auslved 6councl (4) r _ lover 1sex 2age 3school 4econ 5auslved 6councl As shown n Table 1, t s only whether subjects have taken courses n economcs that s sgnfcant at 10% sgnfcance level; subjects who have taken courses n economcs are more lkely to be rsk lovers. 6 Subjects often seemed to hestate around task 5 where there was an expected payoff equvalence between Opton A and Opton B; choces near the swtch pont were often crossed out and changed. Two subjects out of the ffty swtched between Opton A and Opton B more than once. 17

18 4.2. Uncertanty Averson Table 2 and Fgure 2 summarze the number of tmes subjects pad to fnd out the nformaton about the probabltes they face, n each perod. In both treatments subjects start wth the same rate (34%). However, n the Uncertanty n Publc Goods treatment, ths number drops dramatcally. In the Uncertanty n Prvate Goods treatment, there s no partcular tme trend (the number of tmes subjects want to know the probablty ncreases slghtly and then stays at around 44%). The average number of tmes the subjects pad to reveal the probablty n the Uncertanty n Prvate Goods treatment s 43 percent whle the average number of tmes the subjects pad to reveal the probablty n the Uncertanty n Publc Goods treatment s 12 percent across all tme perods. The t-statstc for the dfference s hghly sgnfcant wth a p-value of After each of these treatments we asked the subjects an open ended queston about how much they would be wllng to pay out of ther ntal endowment to reveal the probablty regardng the provson of the (prvate or the publc) good. We fnd that subjects were wllng to pay 17 expermental dollars n the Uncertanty n Prvate Goods treatment and 9 expermental dollars n the Uncertanty n the Publc Goods treatment. The dfference s also sgnfcant (p value= 0.003). Ths result corroborates prevous studes that show that subjects pay substantal premums to avod ambguty from around 10 to 20 % of expected value of probablty (MacCrmmon and Larsson, 1979; Curley and Yates, 1989 and Bernascon and Loomes, 1992) and up to 72 % (Becker and Brownson, 1964), but extends the results by dstngushng between the probablty nformaton relatng to the prvate good and the publc good. In the former case the wllngness to pay to resolve the uncertanty s hgher. Ths result may be vewed as an extenson of the common result of the general publc goods games, where typcally subjects are wllng to pay less to the publc account than to the prvate account. One explanaton of ths result may be related to the strategc uncertanty that s present n publc good games, It may be the case that subjects are not wllng to pay to obtan nformaton about probabltes relatng to the publc account knowng that there stll remans a strategc uncertanty wth whch they can do nothng to reduce or 18

19 elmnate. It seems that t s the presence of the strategc uncertanty that results n the reduced wllngness to pay for the probablty nformaton. Table 3 presents the average contrbutons proportonal to the endowment n the Uncertanty n Prvate Goods and Uncertanty n Publc Goods treatments and compares them to the Baselne treatment. In the Baselne treatment the only uncertanty that subjects face s strategc uncertanty. In the other two treatments, we keep the strategc uncertanty constant and add an addtonal uncertanty factor regardng the provson of the prvate or the publc good. We fnd that n the Uncertanty n Prvate Goods treatment, the contrbutons are sgnfcantly hgher than n the baselne treatment (usng both t-test and the wlcoxon test). When facng uncertanty on the prvate good, subjects contrbute more towards the publc good. Ths could be due to two reasons. Frst, subjects havng pad for the nformaton regardng probabltes on prvate account may have dscovered that the probabltes are low. Hence, ther ncentves to contrbute to the publc account relatve to the prvate account (EM) have ncreased. Second, subjects may dvert away from the uncertan outcome and thus contrbute more to the publc good. We attempt to separate out these factors n Fgures 3 and 4. As seen n Fgure 3 Panel A and Panel B, the contrbuton levels of the subjects who know the probabltes seem to follow a pattern (marked by damond shaped symbols) whle the contrbuton levels of the subjects who do not know the probabltes, seems to be random n both treatments (marked by squares). In the Uncertanty n Prvate Goods treatment (Fgure 3 Panel A), the ncrease n the probablty of provson of the prvate good decreases the contrbuton levels to the publc good. In the Uncertanty n Publc Goods treatment (Fgure 3 Panel B) the ncrease n the probablty of provson of the publc good ncreases the contrbuton levels to the publc good. Thus, n both treatments subjects react to the change n probabltes and the consequent change n EM. Fgure 4 Panel A and Panel B show, however, that the response to the change n the probabltes assocated wth the prvate and the publc account are not at all smlar. In the Uncertanty n 19

20 Prvate Goods treatment the probabltes seem to be lnearly related to the contrbuton levels. Subjects seem to take these probabltes as a drect gude of how to splt ther money between the prvate and the publc account. They follow ths pattern of gradually ncreasng ther contrbuton levels despte the fact that the Nash equlbrum (zero contrbuton) and the Pareto optmum (full contrbuton) reman unchanged. Note, that t s only when the probablty of provson of the prvate good s very hgh ( p.8) that the Pareto optmal outcome concdes wth the Nash x equlbrum of zero contrbuton. Subjects seem to realze ths and the contrbuton levels collapse to zero. In the Uncertanty n Publc Goods treatment the response to the probabltes seem to be less drect; t s only when the probablty of provson of the publc good s very hgh ( p.8) that the contrbuton levels start to converge to the Pareto Optmal outcome. Note, that n the Uncertanty n Publc Goods treatment for any probablty hgher than p. 4 the Pareto Optmal contrbuton level s 100%, whle the Nash Equlbrum remans at zero contrbuton level. Fgure 5 reveals mportant nformaton: t shows the average proportonal contrbutons of the subjects separated out by the known and unknown probabltes for both treatments. As expected and descrbed prevously, the contrbuton levels of the subjects who know the probabltes adjusts to the nformaton nherent n the probablty value and the consequent change n EM. Hence the hgh volatlty of contrbuton levels across perods. However, from what was thought to be random contrbuton levels prevously n Fgure 3 Panel A and Panel B, there seems to emerge a pattern over tme. In the Uncertanty n Prvate Goods treatment, when the probabltes are not know (uncertanty) the contrbuton levels exhbt a downward slopng trend over tme. Despte the downward slopng trend, the contrbuton levels reman sgnfcantly hgher than the contrbuton levels wth unknown probabltes n the Uncertanty n Publc Goods treatment. In the Uncertanty n Publc Goods treatment the contrbuton levels of those who do not know the probablty (uncertanty) remans very low (below 10%) throughout the ffteen perods. There are g g 20

21 several examples for both patterns n the lterature. For example, Isaac et al. (1984; 1985 ) and Andreon (1986) have all replcated, under a varety of condtons, contrbutons whch begn at ntermedate levels but then decay n multple trals. Reasons for the decay nclude learnng and punshng others for not contrbutng. Learnng n our case may mean that subjects learn freerdng behavor from others or that they learn to become less uncertanty averse. Subjects seem to be less uncertanty averse over tme when uncertanty s related to the prvate good and thus prefer the external uncertanty relatve to the strategc uncertanty over tme. In both Fgure 3 Panel A and Panel B we fnd that some subjects are wllng to pay for the nformaton regardng the probabltes of provson of the prvate and the publc good, however do not seem to take ths nformaton nto consderaton when decdng on contrbutons. For example, despte the probablty of return from the prvate account beng very low (Panel A), some subjects contrbute all ther endowment towards the prvate account. In Panel B, even when the probablty of provson of the publc good s very hgh, subjects do not contrbute to the publc good. The nterestng thng s not the nvestment decson, per se, but the fact that these subjects were wllng to pay for the nformaton about the probabltes despte the fact ths nformaton dd not seem to play a role n ther decsons. One explanaton we fnd for ther behavor s that these subjects do not lke makng decsons n the face of uncertanty. Even f they have decded ex ante about ther contrbuton, they are wllng to pay a fee to reveal the nformaton just to avod makng decsons n the face of uncertanty. Next, we examne the relatonshp between rsk atttudes of subjects and ther wantng to know the probablty assocated wth provson of the good. Table 4 presents the estmates from an ordered probt equaton n whch the dependent varable ( want _ to _ know) takes the value of 1 when subjects want to know the probablty they face and are wllng to pay a fee for t. Ths want to know varable s a functon of tme (nvperod), sex of the subject (sex), age of the subject (age), lag of total contrbutons to the publc account ( lsumcontr b), rsk atttudes (two 21

22 dummes: rsk _ lover, rsk _ neutral ), lag of the outcome of the good (lout), a bnary varable whether the good was provded or not n the prevous perod 7, and the subject s wllngness to pay to reveal the probablty related to the prvate good ( wtp _ prv) and to the publc good ( wtp _ pub). (5) want _ to _ know nvperod sex age lsumcontrb kt t 1 rsk wtp _ pub 5 _ lover 6rsk _ neutral 7loutt 1 8wtp _ prvk 9 k t Where = ndvdual (50 ndvduals) k = treatment (2 treatments) t = perod number (1-15) However, the rsk varables could be correlated wth the unobserved determnants of the want to know varable resultng n a standard endogenety problem. We control for ths by estmatng an equaton for rsk and then usng the predcted values from t. We present estmates from both exogenous and endogenous rsk specfcatons. We use the predcted value from the ordered probt (Eq. 3) model (Psuedo R-squared of the ordered probt model: 0.12). The above equaton was estmated separately for both the Uncertanty n Prvate Goods and Uncertanty n Publc Goods treatment. The results show (see Table 4) that n the Uncertanty n the Publc Goods treatment subjects have a hgher probablty of wantng to know the probablty of provson, but ths tapers off by the end of the treatment. Hgher total contrbutons to the publc account n the prevous perod ( lsumcontr b) decrease the probablty of subjects wantng to know the probablty of provson of the prvate good n ths perod, for the Uncertanty n Prvate Goods treatment, whle hgher total contrbutons ncrease the probablty of subjects 7 The bnary varable lout s 1 ( yes return ) f the random number generated s less or equal to the probablty or return from the correspondng account. Consequently, lout s 0 ( no return ) f the random number generated s greater than the probablty of return from the correspondng account. 22

23 wantng to know the probablty of provson of the publc good n the Uncertanty n Publc Goods treatment. Subjects are usng the total contrbutons of all the members n the prevous perod as nformaton to resolve the uncertanty. In the Uncertanty n Prvate Goods treatment, when subjects see that the total contrbutons were hgh then they perhaps feel that the publc good would gve them a hgher return and these subjects are, therefore, less wllng to spend money on fndng out the probablty relatng to the prvate good. In the Uncertanty n Publc Goods treatment, when subjects see that contrbutons are hgh n the prevous perod, then they perhaps feel that knowng the probablty relatng to the publc good would be a good use of ther money (otherwse they would be loosng out) and, therefore, want to nvest n fndng out the probablty they face. In case the subjects make assumptons about the number of partcpants who know the probabltes by observng the contrbuton levels, then our results corroborate those n Chow and Sarn (2002) who suggest that the case when the probabltes are unknowable s preferred over the unknown case (unknown to subject but known to someone else),.e. vagueness n probablty s more tolerated when others also lack the nformaton about probablty and are therefore perceved to be n the same boat. We should, however, note that for the Uncertanty n Publc Goods treatment the number of subjects who want to know the probablty s very low (partcularly over tme, See Table 2) and, therefore, for ths treatment, we should be careful n nterpretng the results. Subjects who are wllng to pay a hgher amount to reveal the uncertanty (a hypothetcal queston) are also more lkely to pay the fee n the experment to know the uncertanty n both the Uncertanty n Prvate Goods and Uncertanty n Publc Goods treatments. Rsk lovng subjects (n the Uncertanty n Prvate Goods treatment) and rsk neutral subjects (n both treatments) exhbt a hgher probablty of wantng to know the probablty relatng to the provson of the good as compared to the baselne dummy of rsk averse subjects. The lottery game that determnes the rsk atttudes of the subjects captures external rsk (known probabltes) but nether atttudes towards uncertanty (unknown probabltes) nor atttudes toward strategc 23

24 uncertanty. Rsk lovers n the lottery game would be wllng to take a gamble wth know probabltes. How would they behave wth unknown probabltes, whch s what they face n the two treatments n ths study? It seems that when facng unknown probabltes, subjects who are classfed as rsk neutral and rsk lovers n the lottery game are more nterested and wllng to pay a fee to know the probablty they face. The probablty revealng mechansm may be thought of as a gamble tself. The nformaton subjects gan when payng a fee may help them n ther decsons, especally f the probabltes are ether very hgh (>.8) or very low (<.2). However, n case the probablty s n the md-range (around.5-.6) then the nformaton gves lttle gudance to the subjects about how to behave. So when they have to decde to pay a fee for a gamble, the rsk lover and the rsk neutral subject wll more lkely do so. Rsk averse subjects seem to avod spendng money on ths gamble. Another lne of reasonng s that requestng unlaterally the probablty nformaton may be seen as a rsky strategy (others may not request t and, therefore, the subject ends up payng for t). Therefore, subjects who pad for the probablty run the rsk of ncurrng even greater losses should others not adhere to ths strategy. Further, we are nterested n nvestgatng whether subjects wth dfferent rsk profles behave dfferently n terms of contrbutons to prvate and publc goods. In addton, do subjects who are wllng to pay to resolve the uncertanty use ths nformaton and contrbute towards the publc good? To examne the relatonshp between wllngness to pay and contrbutons of ndvdual subjects, we conduct multvarate analyss n whch we use a random effects generalzed least squares (GLS) model. Agan the estmaton s conducted separately for the two treatments. The dependent varable s the proportonal contrbutons ( contrbut on) made by ndvduals to the publc good. (6.) contrbuton nvperod lout EM ldevaton t 1 2 t t 1 want 5 _ to _ know 6rsk _ loverhat 7 rsk _ neutralhat t 24

25 The ndependent varable that we use are the followng: tme perod (nvperod), lag of outcome of the good (lout), the expected margnal per capta rato ( EM ), the dfference between the ndvdual and group contrbuton n the prevous perod (ldevaton ). Furthermore, we use the predcted value of want to know ( want _ to _ know) from the equaton above (Eq. 5.) to test whether ths varable has a dfferent mpact dependng on whether t s endogenous or exogenous. We also use the predcted values from the ordered probt rsk equaton (Eq. 3.) as ndependent varables ( rsk _ loverhat) and ( rsk _ neutralhat) to explan contrbuton levels. 8 We fnd (see Table 5) that subjects who pay to change the probablty from uncertanty to rsk have a sgnfcantly hgher probablty of contrbutng to the publc good n the Uncertanty n Publc Goods treatment (as seen n Fgure 5 as well). In the Uncertanty n the Prvate Goods treatment, the mpact s sgnfcant only at the margnal level (10% level of sgnfcance). Also ths mpact changes sgn dependng on whether the specfcaton has an endogenous want to know or not. 9 The negatve sgn makes ntutve sense as subjects who are wllng to pay for more nformaton about the prvate account, would then be contrbutng ether accordng to the nformaton they receve or accordng to some nherent preferences. Table 5 also shows that lout, the varable whch measures whether the good was provded n the prevous perod s postve and sgnfcant (Uncertanty n Prvate Goods ) and negatve and sgnfcant (Uncertanty n Publc Goods) n the treatment ndcatng that a provson of the good n the prevous perod ncreases and decreases the contrbuton to the global good n the current perod. Also, ldevaton, the dfference between the ndvdual and group contrbuton n the prevous perod and EM, the expected margnal per capta rato are very substantal n explanng contrbutons. 8 Ideally t would be good to estmate a system of equatons (rsk atttudes, want to know and contrbutons), however we found t dffcult to obtan dentfyng varables to make ths estmaton meanngful. 9 The predcted value of want to know has rsk accounted for n ts specfcaton and therefore n that specfcaton, t leads to a lowerng of contrbutons towards the publc good. 25

26 The expected margnal per capta rato ( EM ) s postve and hghly sgnfcant n explanng contrbutons. Ths result corroborates prevous fndngs and suggests that even when the domnant strategy of Nash equlbrum of zero contrbuton s mantaned, hgher margnal ncentves, per se, sgnfcantly ncreased contrbuton levels. The ndvdual level, tme specfc data that we analyzed above helps us examne the relatonshp over tme between these varables. Next we examne the relatonshp between average contrbutons and the average wllngness to pay to reveal the probablty across the 15 tme perods for all 50 subjects. Aggregatng across perods mght reduce the dramatc mpact of the change n the EM varable. Snce hgh and low probabltes (selected randomly from a unform dstrbuton) even out across all ffteen perods (expected value of.5) the EM may be regarded as constant across all the perods n the two treatments. We use the predcted value from the want to know equaton (Eq. 5), also presented n Table 4. (Adjusted r-squared s 0.18 and 0.37 for the Uncertanty n Prvate Goods and Uncertanty n Publc Goods treatments, respectvely). (7.) avg _ want _ to _ know 1sex 2age rsk 3 _ loverhat 4rsk _ neutralhat 5wtp _ prvk 6 wtp _ pub k (8.) avg _ contrbuton 1 avg _ want _ to _ know _ hatk 2sex rsk 3 _ 4 loverhat rsk _ neutralhat The results show (see Table 6 and 7) that consstent wth the results relatng to the ndvdual level, tme specfc data, the subjects who want to know the probablty also contrbute sgnfcantly more to the publc good n the Uncertanty n Publc Goods treatment. In the Uncertanty n Prvate Goods the varable s not sgnfcant. 26

27 5. Conclusons In the followng we summarze the results and draw some mplcatons of the research results. We use clmate change negotatons, as well as research on mtgaton and adaptaton actons as an example to demonstrate how the above results may be applcable. It s well establshed n the expermental lterature that people behave dfferently when they make decsons about prvate and publc goods. We extend the exstng lterature by explorng whether these behavoural dfferences perssts or amplfed when rsk and uncertanty s ntroduced n a prvate and publc goods context and how rsk and uncertanty atttudes may relate to the observed behavour. Our results show that subjects are wllng to pay a much hgher amount to fnd out nformaton relatng to the probabltes of provdng the prvate good than nformaton relatng to the publc good. In both the prvate and the publc good context subjects start wth wantng to know the probablty at the same rate (34% of the tmes) but n the publc goods context ths number drops dramatcally very soon whle n the prvate good context ths number ncreases slghtly. The average number of tmes the subjects pad to reveal the probablty n the prvate goods context s much hgher (43%) than n the publc goods context (12%). Ths pattern may also be observed n clmate change negotatons: after the ntal promnence of research on clmate change mpacts and mtgaton (dscoverng probabltes relatng to a publc good) there can currently a shft be observed towards more research relatng to adaptaton (probabltes relatng to prvate good) by countres. These results are nterestng gven that the nformaton on probablty may have greater consequences on the return n the publc good context than t does n a prvate good context. One explanaton may be that even when objectve probabltes are known n the publc goods context, uncertanty regardng the behavour of others (e. strategc uncertanty) exsts n the publc goods context. The mplcatons of these fndngs for clmate change, for example, may be that wthout 27

28 an nternatonal collaboratve effort (.e. wth strategc uncertanty regardng the actons of other states), ndvdual states contrbuton towards scentfc effort to gan nformaton regardng the lkely mpact of clmate change may be much less than when nternatonal agreements are acheved (.e. wth reduced strategc uncertanty). Reducng the strategc uncertanty thus may ncrease ndvdual states wllngness to contrbute not only towards reducng clmate change per se but also towards reducng external (envronmental) uncertanty by ganng more accurate nformaton on the lkely mpact. Ths may have been observed also when early negotatons lead to the Montreal Protocol (reduced strategc uncertanty) and to ncreased scentfc understandng about the lkely mpact of ozone layer depleton by the collaboratng states. The contrbuton levels n the publc goods context s so low that our fndngs provde strong support for the free-rder hypothess and extend these well establshed fndngs for cases when rsk and uncertanty are present. Decson-makers thus may learn uncertanty averson from others when nformaton s costly the same way as they learn to free-rde from others. Subjects seem to be less uncertanty averse over tme when uncertanty s related to the prvate good and thus prefer the external uncertanty relatve to the strategc uncertanty over tme. Subjects tend to take nto consderaton outcome of the past perod and also use contrbuton of others as a gude n ther behavour (e.g. devaton from the group contrbuton and sum of contrbutons n prevous perod are hghly sgnfcant n determnng contrbuton levels). The mplcatons of these fndngs for clmate change negotatons, for example, s that n the presence of rsk and uncertanty decson makers ncreasngly use the behavour of other partcpants and the outcomes of prevous perods as gudance n ther decsons. Ths ndcates that transparency of nternatonal negotatons could serve as an mportant factor n the success of the negotatons. Intal successful collaboraton may result n contnued success whle ntal low levels of contrbutons may also persst. The negotatons leadng to ban on 28