Endogenous Mnmum Partcaton n Internatonal Envronmental Agreements: An Exermental Analyss Davd M. McEvoy Deartment of Economcs, Aalachan State Unversty, Boone NC, USA Todd L. Cherry Deartment of Economcs, Aalachan State Unversty, Boone NC, USA CICERO Center for Internatonal Clmate and Envronmental Research-Oslo, Oslo NORWAY John K. Stranlund Deartment of Resource Economcs, Unversty of Massachusetts-Amherst, Amherst MA USA 1. Introducton Almost all nternatonal envronmental agreements (IEAs) requre a mnmum number of countres to ratfy the agreement before t enters nto force. If the mnmum membersh condton s met, as well as other accomanyng condtons, the treaty becomes actve and ratfyng countres are bound to ther commtments. If the condton s not met, the treaty never enters nto force and affected countres are not bound by ts rovsons. Mnmum membersh requrements are standard n treates that address global envronmental ssues, and Barrett (2003,. 165-194) rovdes a thorough examnaton of membersh requrements n nternatonal envronmental agreements. For examle, the Kyoto Protocol to the Unted Natons Framework Conventon on Clmate Change requred ratfcaton by at least 55 artes ror to ts entry nto force n February 2005. Smlarly, the Montreal Protocol on Substances that Delete the Ozone Layer requred at least 11 countres to ratfy t before t entered nto force n 1989. 1 Examles of mnmum membersh requrements extend to treates that address nternatonal rsk and securty, such as the Treaty on the Non-Prolferaton of Nuclear Weaons, whch requred the ratfcaton of the fve nuclear natons (at that tme) lus 40 addtonal natons. The Chemcal Weaons Conventon requred ratfcaton by at least 65 natons before t entered nto force n 1997. Whle many treates requre ratfcaton by a subset of affected artes to enter nto force, some requre all artes to jon. For examle, the Conventon for the Protecton of the Marne 1 Both the Kyoto and Montreal rotocols ncluded an extra rovson to ensure artcants reresented a mnmum level of global emssons. Members to the Kyoto Protocol had to reresent at least 55 ercent of the total 1990 greenhouse gas emssons. Smlarly, the Montreal Protocol requred reresentaton of at least two-thrds of the total 1986 consumton of ozone-deletng substances. 1
Envronment of the North-East Atlantc requred accesson of all contractng artes, and the Treaty of Lsbon requred ratfcaton by all Euroean Unon member states. Because of ther wde-sread use n nternatonal agreements, there s a small gametheoretc lterature on the role of mnmum membersh requrements. Black et al. (1992) fnd that an exogenously mosed mnmum membersh requrement can ncrease artcaton wth an nternatonal envronmental agreement. A smlar fndng s dscussed n Carraro and Snscalco (1992). Clearly, however, natonal soveregnty requres that all rovsons of nternatonal treates, ncludng membersh requrements, be determned endogenously by affected artes. Carraro et al. (2009) rovde an analyss of endogenous mnmum artcaton requrements n IEAs, and fnd that the mechansm ncreases the sze of cooeratve coaltons relatve to the non-cooeratve baselne. Partcularly relevant for our study, Carraro et al. also fnd that endogenous mnmum artcaton requrements can lead to effcent outcomes. 2 However, emrcal data on the effectveness of mnmum artcaton constrants n IEAs s absent because of the lack of counterfactuals and controls necessary for careful analyss. Consequently, we use laboratory exerments to evaluate the effectveness of endogenously determned mnmum requrements n motvatng coalton formaton to rovde ublc goods. Of course, laboratory exerments, lke the game-theoretc models they stem from, dramatcally smlfy the nternatonal negotaton rocess. However, the exermental aroach allows us to examne the erformance of artcular nsttutons n a controlled envronment. Snce nternatonal envronmental agreements are desgned to address collectve acton roblems between resource users, the same fundamental tensons that exst between countres can be smulated n a laboratory envronment, and the results of exerments can shed lght on how nsttutonal rules, n ths case mnmum artcaton rules, affect coalton formaton. 3 We begn by develong a theoretcal model of endogenous agreement formaton to rovde a ublc good, ncludng the endogenous determnaton of a mnmum membersh requrement. Our model s a smlfed verson of the one n Carraro et al., yeldng clearer redctons so that t s amenable to tests wth exermental data. The game we analyze conssts 2 A recent workng aer by Wekard et al. (2009) extends the theoretcal analyss by Carraro et al. (2009) to nclude heterogeneous agents under dfferent sharng rules. Harstad (2006) models coaltons of heterogeneous agents that contrbute to a ublc good and derves otmal artcaton rules as well as solvng for oltcal equlbra (.e., Condorcet wnners). 3 The use of laboratory exerments n the evaluaton of ublc olces s well establshed (Plott 1987; Shogren and Hurley 1999; Cason and Plott 1996; Stranlund et al. 2011), and exerments are artcularly well suted to evaluate the effectveness of dfferent voluntary nsttutons. 2
of two stages. The frst stage s unque n the exermental coalton formaton lterature n that ndvduals vote on a mnmum membersh requrement. In the second stage, each ndvdual decdes whether they wll jon a coalton to rovde the ublc good and a coalton forms f the membersh requrement s met. We demonstrate that exected-ayoff-maxmzng ndvduals wll choose to adot the mnmum membersh requrement that s equal to the effcent coalton sze, and that ths coalton wll form. Ths theoretcal result s robust to whether the effcent agreement s the grand coalton or a smaller coalton. We desgned our laboratory exerments to test these redctons. Results show that when effcency requres all layers to jon an agreement, subjects adoted the effcent mnmum membersh requrement about 75 ercent of the tme. Condtonal on subjects adotng the effcent mnmum membersh requrement, effcent agreements formed over 90 ercent of the tme. Consequently, n these cases we observe sgnfcantly hgher effcency than other coalton formaton exerments that do not nclude endogenous mnmum membersh requrements (e.g., Kosfeld et al. 2009; Dannenberg et al. 2010; McEvoy et al. 2011). The results were not as ostve when effcency requred only 50 ercent artcaton. Whle subjects stll adoted the effcent mnmum membersh requrement about 75 ercent of the tme, the effcent coalton formed just over half of the tme. Interestngly, the effcent coalton was blocked n about one-thrd of the cases n whch t was adoted as the membersh condton. Whle ths s nconsstent wth a theoretcal model of ndvduals wth standard references, we demonstrate that ths behavor s consstent wth a theory that allows for references concernng nequalty n the manner of Fehr and Schmdt (1999). 4 The lesson for nternatonal envronmental olcy makng s clear: endogenous mnmum artcaton requrements are effectve at achevng hgh levels of cooeraton, but they may be sgnfcantly less effectve when the artcaton requrements allow for freerders. Although no exermental research has nvestgated the effectveness of mnmum membersh requrements drectly, a sgnfcant lterature has done so ndrectly wth analyses of mnmum contrbutng sets n ublc good games (e.g., Raoort 1985; Erev and Raoort 1990; Cadsby and Maynes 1999; Cooer and Stockman 2002; McEvoy 2010). In these games, all ndvdual contrbutons to the ublc good are returned f there are too few contrbutors. In 4 Others have conjectured that references over nequalty mght lay mortant roles n nternatonal cooeraton because all treates must tackle ssues of equty (Rngus et al. 2002; Lange and Vogt 2003). 3
contrast wth our game, mnmum contrbutng sets are not determned by the layers themselves. A related lterature on endogenous nsttuton formaton n ublc goods games has receved much attenton recently. Most of ths lterature exlores the formaton of nsttutons that govern all layers (e.g., Walker et al. 2000; Gurerk et al. 2006; Tyran and Feld 2006; Kroll et al. 2007; Sutter et al. 2010). Tycally, however, nternatonal treates are formed to restrct the behavor of only artcatng natons. A handful of recent studes that are motvated by nternatonal treaty formaton examne coalton formaton n ublc goods games (e.g., Kosfeld et al. 2009; Dannenberg et al. 2010; McEvoy et al. 2011; Barrett and Dannenberg 2012), but none consder endogenous mnmum membersh requrements. 5 The remander of the aer roceeds as follows. In the next secton we develo our theoretcal model and derve ts redctons. In secton 3 we descrbe the exermental desgn we use to test these redctons. We resent the results of the exerments n secton 4 and conclude n secton 5. 2. Theory Consder a game n whch n layers decde whether to contrbute a sngle unt to a ublc good. Our model s a varant of the semnal model by Barrett (1994). Let the number of ndvduals who contrbute to the ublc good (and the total suly of the ublc good) be s. Let b > 0 denote the shared beneft layers receve from contrbutons to the ublc good u to s n and let c > 0 denote the ndvdual cost of contrbutng. The basc ayoff functon of a layer that contrbutes to the ublc good s = A+ bs- c, for s s, [1] where A s a ostve constant. Assume that c > b so that no layer would contrbute to the ublc good n a standard, non-cooeratve Nash equlbrum. However, suose that collectve welfare s maxmzed when s ndvduals contrbute ther unts to the ublc good. In the tycal coalton formaton game, collectve welfare s maxmzed when everyone contrbutes; that s, 5 The sequence of decsons n some of the coalton formaton exerments dffers sgnfcantly from the sequence of decsons n nternatonal treaty formaton. For examle, n the exerments of Kosfeld et al. (2009), layers frst decde whether to jon a coalton, and then the members vote on whether to contrbute to the ublc good. Hence, n ther analyss members of a coalton decde what the coalton should accomlsh after they make ther artcaton decson. In contrast, the layers n our study understand ex ante what they are requred to do n a coalton before they make ther decson to jon or not. Ths corresonds more closely to the actual rocess of treaty formaton, where countres tycally decde the commtments of the coalton members and what trggers entry nto force before they decde whether to ratfy (jon). 4
when s = n. However, we also allow for the ossblty that t s effcent that the ublc good be rovded by a coalton that s smaller than the grand coalton. We assume a smle case of ths n whch ndvdual contrbutons yeld a return of b u to an aggregate level and addtonal contrbutons yeld a return of zero. For examle, abatement actvtes that move emssons levels below the absortve caacty of the natural envronment wll not yeld addtonal envronmental benefts. Examles of ths also nclude any roject for whch contrbutons n excess of what s requred to rovde the good do not yeld ublc benefts. In ether case, f s s effcent, then n( A + bs )- cs > na, whch requres nb > c. Gven the motvaton for collectve acton to rovde the ublc good, suose that the layers are able to form a cooeratve coalton n a two-stage game. In the frst stage (the votng stage), all layers vote on the mnmum number of members requred for a coalton to form. Players cannot vote for a membersh requrement equal to zero and they cannot ot out of ths vote. We call the outcome of ths vote the mnmum membersh requrement. In our exerments we mlement a luralty votng rule so that the number that receves the most votes becomes the membersh requrement. 6 In stage two of the coalton formaton game (the coalton stage), the layers decde ndeendently and sequentally whether or not to jon the coalton. 7 The order n whch the layers make ther jon/not jon decsons s unknown n the votng stage of the game, and each otental order s equally lkely. Ths order s revealed to the layers n the coalton stage. Decsons to jon or not jon are observed by all other layers n the second stage. 8 If enough layers jon so that the membersh requrement s met, the coalton forms and ts members rovde ther unts of the ublc good. Throughout we call such a coalton an effectve coalton. Those that do not jon an effectve coalton do not rovde ther unts of the ublc good (because c > b), but stll beneft from ts rovson. If the mnmum membersh requrement s not met, an effectve coalton does not form and no layer contrbutes to the ublc good. 6 A luralty votng rule s often mlemented n local and natonal electons to determne a sngle wnner when there are more than two canddates. See Myerson and Weber (1993) for an analyss of votng equlbra under luralty votng rules. 7 Although our game s motvated by the model of Carraro et al. (2009), t s not a secal case of ther model. Ths s rmarly due to the facts that they requre unanmty n the vote for the membersh requrement and layers make ther decson to jon an agreement smultaneously. 8 In fact, havng the layers decde to jon or not n sequence and wth erfect nformaton about these decsons s a reasonable descrton of the actual rocess of treaty accessons. Dfferences n the lengths of natonal debates about the decson to ratfy a treaty and dfferng ostons of a treaty on natonal legslatve agendas mly that ratfcaton decsons must be sequental. Moreover, the decson to ratfy a treaty or not tends to be very ublc. 5
We look for a subgame erfect equlbrum for ths game, consstng of ndvdual votes for the mnmum membersh requrement n the frst stage of the game and decsons to jon or not jon a coalton n the second stage. An equlbrum s found by backward nducton, so we start by descrbng the coalton stage. At ths ont n the game a mnmum membersh requrement has been chosen. Denote the membersh requrement as s. Usng [1], those who decde to jon a coalton wth s members earn: ì A+ bs- c for s s f s³ s; m ï ( s) = ía+ bs - c for s> s f s³ s; ï î A f s< s. [2] Throughout the suerscrt m ndcates the layer s a member of a coalton. Nonmembers, dentfed by the suerscrt nm, earn: nm ì A+ bs for s s f s³ s; ï ( s) = ía+ bs for s> s f s³ s; ï î A f s< s. [3] From [2] and [3] t s clear that when an effectve coalton forms, nonmembers earn strctly hgher rofts than members, because they enjoy the benefts of ublc good contrbutons wthout ncurrng the cost of contrbutng. However, f the mnmum membersh requrement s not met, both members and nonmembers earn ther noncooeratve ayoff A. Players wll jon an effectve coalton only f t s roftable for them to do so n the sense that they earn at least as much n the coalton as they would f no coalton formed. Thus, a m coalton s roftable for ts members f and only f ( s s³ s ) = A+ bs- c³ A. Assume m throughout that a coalton wth s members s strctly roftable so that ( s s ³ s ) > A, or m rather, bs - c > 0. Note from [2] that ( s s³ s ) s ncreasng n s u to s and then s constant. Combned wth b < c, these relatons mly that there exst coalton szes that are strctly greater than one and weakly less than s that are roftable. The smallest of these roftable coaltons s: m { } { } smn = mn s ( s s³ s ) = A = mn s s³ c/ b, [4] 6
where smn Î (1, s]. For an effectve coalton to form n the second stage of the game both the membersh requrement and the roftablty requrement must be satsfed. The layers make ther decsons to jon or not jon sequentally. Defne a crtcal layer as one whose choce to not jon a coalton revents the coalton from formng. That s, a layer s crtcal f and only f n- s layers have already oted out of the coalton. Suose at frst that the membersh requrement s s ³ s. A crtcal layer n ths stuaton wll always mn choose to jon a coalton of s members. To see why, note frst that f a crtcal layer refuses to jon a coalton then no coalton wll form and the layer wll earn A. However, the layer earns a hgher ayoff f he s art of a roftable coalton. So, f a crtcal layer jons a coalton then he ether earns ths hgher ayoff f all the other crtcal layers also jon, or he earns the ayoff A f one of the other crtcal layers refuses to jon and a coalton does not form. Therefore, when s ³ s a crtcal layer wll always jon a coalton because he cannot be mn worse off by dong so and he may be strctly better off. Snce all crtcal layers wll jon a coalton, a noncrtcal layer would never jon, because t s always more roftable to stay out of a roftable coalton. Therefore, gven s ³ s, the outcome of the second stage coalton mn game s that an effectve coalton of s ndvduals wll form. Moreover, snce nonmembers earn strctly hgher ayoffs than members, the frst n- s layers n the sequence wll decde to not jon the coalton and the last s layers wll decde to jon. In the second stage of the game, all members of the coalton make ther contrbutons to the ublc good, whle the remanng layers contrbute nothng. Now suose that the membersh requrement s s < s. In ths case, a crtcal layer wll choose to not jon because he would be jonng an unroftable coalton. Snce no crtcal layer wll jon a coalton f s < s, the outcome of the second stage coalton game n ths mn case s that an effectve coalton wll not form and all layers contrbute nothng to the ublc good. To sum u, the equlbrum of the second stage coalton formaton game s a coalton sze and rovson of the ublc good s * such that mn s * = s f s ³ smn and s * = 0 f s < smn. In 7
the frst case the frst n- s * layers to decde whether or not to jon the coalton choose not to, whle the last s * layers jon the coalton. 9 Now let us examne the determnaton of the mnmum membersh requrement s n the votng (frst) stage of the game. Followng Carraro et al. (2009), we assume that layers vote sncerely n the sense that they vote for the membersh requrement that gves them the hghest exected ayoff from the ersectve of the frst stage of the game. 10 From our descrton of the coalton stage of the game, f the membersh requrement s not less than the mnmum roftable coalton, a layer s ayoff s determned by hs oston n the order n whch the layers make ther decsons whether to jon a coalton. Recall that ths sequence s unknown n the frst stage of the game. Hence, a layer that exects an effectve coalton of s layers to form n the second stage evaluates the robablty that he wll be a member of ths coalton as s/ n and the robablty that he wll not be a member as ( n- s)/ n. Hs exected ayoff from the ersectve of the frst stage of the game s then: m ( ) ( ) nm vs () = s/ n () s + ( n- s)/ n () s. [5] Remove the s constrant from [2] and [3], substtute the results nto [5], and dfferentate wth resect to s to obtan: ìb- c/ n> 0, for s s; v () s = í î - c/ n < 0, for s > s. Equaton [6] ndcates that the exected ayoff of every layer s maxmzed at the effcent coalton sze. Gven that all layers vote sncerely n the frst stage of the game, each of them votes to mlement the effcent coalton as the mnmum membersh requrement. That s, s = s. Movng ahead to the coalton formaton stage, snce the effcent coalton sze s [6] 9 Others have examned sequental decson makng n threshold ublc good games. Erev and Raoort (1990) and Cooer and Stockman (2002) derve smlar equlbra to ours n threshold ublc good games n whch layers are assgned the order n whch they must decde whether to contrbute to a ublc good. In ther studes a threshold s secfed exogenously, whch s referred to as the mnmum contrbutng set. We noted the smlarty between mnmum contrbutng sets and mnmum membersh requrements for nternatonal treates n the ntroducton. McEvoy (2010) exlores the endogenous order of sequental decsons n ublc good games and fnds that the tmng of artcaton decsons s senstve to the threshold n these games. In artcular, he fnds that subjects are more lkely to rush to ot out of voluntary coaltons when the free-rdng ayoff s larger. 10 Palfrey (1984) and Osborne and Slvnsk (1996) also analyze games gven sncere votng. 8
roftable, s = s ³ s. Therefore, the coalton s * = s wll form. Obvously, f s = n, then all mn layers wll jon the coalton. If s < n, then the frst n- s layers to make ther jon/not jon decson wll choose to not jon, whle the last s layers jon the coalton. 11 The man redcton of the theory s that the endogenous determnaton of a mnmum membersh requrement allows layers to form an effcent coalton to rovde a ublc good. In the next secton we resent our exermental desgn used to test ths redcton under two scenaros; one n whch effcency requres full artcaton (.e., the grand coalton) and one n whch effcency requres only artal artcaton. 3. Exerments Followng the theoretcal model, our exerments have two stages, a votng stage and a coalton formaton stage. The context of the exerment s farly generc; subjects decde whether to jon a coalton (called an agreement) wth ts members makng a dscrete choce to contrbute to the ublc good (called a ublc account). We mlement two exermental treatments that dffer accordng to the returns to ndvdual contrbutons to the ublc good. In one treatment the margnal return to contrbutons s constant so that the effcent coalton s the grand coalton. In the other treatment, the margnal return to ublc good contrbutons s constant u to an aggregate level and then zero so that the effcent coalton s smaller than the grand coalton. We chose arameter values of n = 6, A = 10, and c = 10 for each treatment. In one treatment the margnal return to all ndvdual contrbutons was set at b = 4.5. Snce nb - c > 0 for all contrbutons, the effcent coalton n ths case s sx ndvduals ( s = 6 ). In the other treatment, b = 4.5 for contrbutons u to three unts and then zero after three unts. The effcent coalton sze n ths case s three ndvduals ( s = 3 ). Pluggng our arameter values nto equaton [4] reveals a mnmum roftable coalton sze of three members. Therefore, n both treatments, coaltons of three or more are roftable for the members. 11 Carraro et al. (2009) rovde suffcent condtons for ther game to result n the formaton of the grand coalton. Our game satsfes those suffcent condtons. Carraro et al. do not examne the case n whch the effcent coalton s smaller than the grand coalton. 9
All sessons were run at the exermental economcs laboratory at [nsert unversty] usng software secfcally desgned for ths exerment. 12 Subjects were recruted from the undergraduate and graduate student oulatons. Two sessons were mlemented for each of the treatments. In each sesson, three grous of sx subjects were n the lab. These grous of sx were reshuffled each erod throughout the exerment, whch lasted 20 erods. 13 For each treatment we have 720 ndvdual-level observatons, whch nclude ther votes for the membersh requrement n the frst stage and ther decsons to jon a coalton n the second stage. We also have 120 grou-level observatons on coalton formaton, ublc good rovson and overall grou effcency. The sessons lasted for roughly 1 hour, subjects were ad ther cumulatve earnngs and earned $16.50 on average (20 exermental dollars = $1). In the frst stage of the exerments, subjects smultaneously voted on the mnmum membersh requrement for a coalton to form n the second stage. The membersh requrement that receved the most votes was mlemented n the second stage of the game. Tes were settled by a random draw. In the coalton formaton stage, each subject decded whether or not to jon the coalton. Followng the theoretcal model, these decsons were made sequentally under erfect nformaton. Each of the sx subjects n a grou was randomly assgned an order n whch to make decsons, and ths order changed each erod. 14 For examle, f a subject was assgned an order number of three, then she had to wat for the frst two layers to submt ther choces before she could make her decson. Once a subject made ther choce they could not change t. Durng ths stage, all subjects were nformed about whether the subjects before them joned the agreement or dd not jon the agreement. They were also constantly remnded of the membersh requrement for the agreement to form. Therefore, each layer knew wth certanty whether ther artcaton decson was crtcal for the coalton to form. If enough layers joned the coalton to satsfy the mnmum membersh requrement, then the coalton formed and those that joned contrbuted to the ublc good. Those who dd 12 The exerment nstructons can be found at: htt://davemcevoy.weebly.com/uloads/2/2/7/0/2270780/nstructons_ere2014.df 13 To mtgate reutaton effects, we follow the lterature wth subject anonymty and a stranger desgn. Though merfect, the stranger desgn ensured no grou was reeated, whch was known by subjects. Anonymty condtons dd not allow subjects to track other subjects or ther decsons. Wth smlar anonymty condtons, Fehr and Gächter (2000) fnd behavor s equvalent across merfect and erfect stranger desgns. 14 Subjects were not aware of ther decson order when votng on the mnmum membersh requrement n the frst stage. 10
not jon dd not contrbute. If too few subjects joned the coalton to satsfy the membersh requrement, then no coalton formed and no one contrbuted to the ublc good. 4. Results Our exermental data suggest the followng broad conclusons. The majorty of subjects n both treatments voted for effcent mnmum membersh requrements. These votes led to the adoton of the effcent membersh requrements n roughly three out of every four trals for both treatments. When effcency requred full artcaton (the s = 6 treatment), coaltons formed n 85 ercent of all trals. The effcent coalton almost always formed (91.3 ercent) when the effcent membersh requrement was adoted. Overall, effcency was very hgh n ths treatment, about 87.4 ercent as measured by the rato of realzed grou earnngs to maxmum grou earnngs. Hence, grou results n the s = 6 treatment closely matched our theoretcal redctons that grous wll use the membersh requrement to form effcent coaltons. However, erformance was sgnfcantly worse n the treatment for whch a 3-layer coalton was effcent (the s = 3 treatment). In ths treatment coaltons formed n only 61 ercent of all trals and the effcent coalton formed n only about half the trals. Consequently, average effcency was sgnfcantly lower n these treatments (about 80 ercent) than n the s = 6 treatments. Interestngly, the effcent coalton was blocked about a thrd of the tme when the effcent membersh requrement was adoted. Ths behavor s not consstent wth a theory of coalton formaton that ncludes only ndvduals wth standard ayoff-maxmzng references. However, we wll demonstrate that ths behavor s consstent wth a theory that allows for references over nequalty. We begn our detaled analyss of the results by examnng the data on votng for the membersh requrement n the frst stage of the exerments. Table 1 rovdes votes and referenda outcomes by membersh requrement and treatment. The frst row n each cell contans the number of votes and ercentage of total votes (out of 720 for each treatment) for that mnmum membersh requrement. The second row n each cell contans the number of tmes and ercentage of trals n the treatment (out of 120) that membersh requrement was mlemented. Under the s = 6 treatments, the 6-layer membersh requrement receved 55.6 ercent (400 of 720) of total votes, whch s consderably more than the 19.3 ercent receved by the 11
second most referred oton of a 5-layer membersh requrement. The remanng four otons receved even fewer votes. Ths votng behavor resulted n the selecton of the effcent membersh requrement n 76.7 ercent (92 of 120) of referenda. [Table 1] The ercentage of votes for effcent membersh requrements s very smlar across the two treatments. In the s = 3 treatment, the 3-layer membersh requrement receved 56.8 ercent of the votes. Membersh requrements of sze two receved the second most wth 21.2 ercent of votes. Mrrorng the results from the s = 6 treatment, votng led to the adoton of the effcent membersh requrement n 76.7 ercent (92 of 120) of referenda. Fgure 1 llustrates the ercentage of votes for effcent membersh requrements over erods for both treatments. To summarze, the majorty of subjects n both treatments voted for effcent membersh requrements, and these were adoted n roughly three out of every four trals. [Fgure 1] Fgure 1 suggests that the tme seres of the ercentages of votes for the effcent coalton are very smlar between the two treatments. We confrm ths wth results from a Probt model condtonng ndvdual votng decsons on treatment, erod fxed effects and subject-secfc random effects. These results are reorted n the frst column of Table 2. Note that the treatment effect ( s = 3 ) s nsgnfcant. In addton, the Probt model n the second column of Table 2 confrms that the lkelhood of grous adotng the effcent membersh requrement s statstcally equvalent n the two treatments. [Table 2] Recall that our theoretcal model yelds the redcton that exected-ayoff-maxmzng layers would vote for mnmum membersh requrements equal to effcent coalton szes. Our exermental results from the votng stage are broadly consstent wth ths redcton n that the majorty of subjects voted to adot the effcent membersh requrements. However, n contrast wth our theoretcal model we do observe sgnfcant, though mnorty, votng for smaller-than- 12
effcent membersh requrements. Our theoretcal model s not helful n exlanng why 45 ercent of votes were cast for neffcent agreement szes. It s nterestng to note that n each treatment the second most frequent vote was for one member less than the effcent agreement sze. These votes are consstent wth layers attemtng to ncrease ther chances to free rde on roftable agreements. For examle, a lone free rder on a coalton of fve layers n the full artcaton treatment would be the hghest ossble earner. Of course there are other ossble exlanatons for ths behavor. If layers are not confdent that other grou members wll jon the agreement when t s ratonal to do so (f for examle, they have a tremblng hand when makng ther artcaton decson), then a lower artcaton threshold may aear less rsky. 15 Whle the results from the votng stage are equvalent n the two treatments, the results from the coalton formaton stage dffer sgnfcantly. Table 3 contans results concernng coalton formaton by mnmum membersh requrement and treatment. For each membersh requrement/treatment combnaton we rovde the number of tmes a coalton formed under the membersh requrement, ths number as a ercentage of total trals, and coalton formatons as a ercentage of tmes the membersh requrement was adoted. The fnal column n Table 3 contans the number and ercentage of trals a coalton of any sze formed (.e., all effectve coaltons). [Table 3] Under the s = 6 treatment, coaltons of any sze formed n 102 of 120 trals (85 ercent). In 84 of 120 trals the effcent coalton formed (70 ercent). Moreover, when layers adoted the effcent membersh requrement of sx layers, coaltons almost always formed (84 of 92, 91.3 ercent). Thus, coaltons formed qute frequently n the s = 6 treatments and most coaltons were effcent. Other coalton szes formed much less frequently. Ths suggests that the man reason why coaltons dd not form n a subset of trals s because grous sometmes faled to mlement the 6-layer membersh requrement. In both treatments, f a coalton faled to form then no layer contrbuted to the ublc good and each earned 10 exermental dollars. 15 We thank an anonymous referee for suggestng ths ossble exlanaton. See McGnty (2011) for an examle of tremblng hand equlbra n a coalton formaton game. 13
In contrast, coaltons formed sgnfcantly less frequently under the s = 3 treatment. Overall, coaltons formed n 60.8 ercent of trals n ths treatment, whch s sgnfcantly lower than the 85 ercent coalton formaton rate under the s = 6 treatment. Ths s confrmed by the results of the thrd model n Table 2, whch s a Probt model of total coalton formaton. Note that the dummy for the s = 3 treatment s negatve and sgnfcant. Furthermore, the effcent coalton formed n 51.7 ercent of trals (62 of 120), comared wth 70 ercent of trals n the s = 6 treatment. The most strkng dfference between the two treatments s the ercentage of coaltons that formed condtonal on the adoton of an effcent membersh requrement. In both treatments, the referenda resulted n effcent membersh requrements n 92 of 120 trals. Wth the s = 6 treatment, coaltons formed n 84 of those 92 trals (91.3 ercent). However, under the s = 3 treatment, coaltons formed n 62 of those 92 trals (67.4 ercent). The fourth Probt model n Table 2 confrms that the lkelhood of a coalton formng when the effcent membersh requrement was adoted s sgnfcantly lower n the s = 3 treatment. Let us exlore ths henomenon more closely, snce t mles that some ndvduals wllfully blocked effcent coaltons n the sense that they were crtcal for the formaton of the coalton but refused to jon so the coalton faled to form. The 3-layer membersh requrement was mlemented n 92 out of 120 trals (76.7 ercent from Table 1) under the s = 3 treatment. The effcent coalton faled to form n 30 of these trals. These blocks are nconsstent wth a model that contans only ndvduals wth standard exected-ayoffmaxmzng references. Such ndvduals would never block a roftable coalton, and effcent coaltons are always roftable. However, these blocks are consstent wth the resence of subjects who are averse to dsadvantageous nequalty. When s = 3, the effcent outcome requres that the three non-members earn strctly hgher ayoffs than the three members. If layers dslke ayoff nequalty, t s ossble that coaltons that are roftable n terms of materal ayoffs are no longer roftable n terms of utlty. In fact, mnmum roftable coalton szes for nequalty-averse layers wll be weakly greater than those for layers wth standard references. Therefore, nequalty-averse layers may block effcent coaltons that are not ndvdually roftable gven ther nequalty references. That nequalty averse ndvduals requre hgher mnmum roftable coalton szes s demonstrated theoretcally n Kosfeld et al. (2009) for a game that s smlar to ours. We demonstrate ths result for our model n the aendx. 14
We comlete our data analyss wth results on average ublc good rovson and average effcency n Table 4. Effcency for each grou n each erod s calculated as the rato of aggregate ayoffs to maxmum attanable ayoffs. As exected, ublc good rovson and effcency were lower n the s = 3 treatment than n the s = 6 treatment. The sgnfcance of the dfference n effcency levels s confrmed n the lnear regresson results contaned n the fnal column of Table 2. [Table 4] To judge the erformance of the endogenous determnaton of mnmum membersh requrements, we can comare the effcency level of our s = 6 treatment (87.4 ercent) to recent exermental coalton formaton studes that do not nclude ths feature. The effcency level n ths treatment s qute hgh relatve to these other studes. 16 For examle, Kosfeld et al. (2009) conducted two coalton formaton treatments whch dffered n the mnmum number of members requred for coaltons to be roftable (ether 3 or 2 out of 4). As noted earler, subjects n ther exerments frst decded whether to jon a coalton, and then n a second stage the coalton members voted whether to contrbute all of ther endowment to the ublc good or not. Effcency levels n ther exerments were 51 ercent and 70 ercent for mnmum roftable coalton szes of 3 and 2, resectvely. Among a number of treatments n McEvoy et al. (2011) were two coalton formaton treatments that dffered n terms of the ndvdual costs of rovdng the good, roducng dfferent szes of mnmally roftable coaltons. These were then set as mnmum membersh requrements. One treatment requred 3 of 10 subjects to jon before a coalton formed whle the other had a membersh requrement of 6 of 10 subjects. The authors dd not allow contrbutons from nonmembers and dd not allow contrbutons f a coalton dd not form; hence ther effcency measures are farly conservatve. Effcency levels were 59.6 ercent for the 3-layer membersh requrement and 56.2 ercent for the 6-layer membersh requrement. Subjects erformed much worse n the exerments of Dannenberg et al. (2010). They conducted three coalton formaton treatments wth 10-layer grous. The authors reort an 16 We cannot use the lterature to judge the erformance of our s = 3 treatment, because all other coalton formaton exerments requre the formaton of the grand coalton for effcent rovson of a ublc good. 15
effcency level of 24 ercent for one treatment n whch coalton members contrbuton decsons were determned automatcally by maxmzng jont welfare. In another treatment coalton members only contrbuted half of what was requred to maxmze jont welfare and effcency fell to 12 ercent. The effcency level was 29 ercent n a thrd treatment n whch coalton members endogenously determned the requred mnmum contrbuton. Although there are sgnfcant dfferences n the rotocols between the exerments n Dannenberg et al. (2010) and our own (ncludng grou szes), the comarson suggests that endogenous thresholds serve as effectve coordnaton devces n coalton formaton games. 5. Concluson Many nternatonal envronmental agreements nclude a mnmum membersh requrement for entry nto force. Deste the wde-sread use of these requrements, lttle s known about ther effectveness. We have analyzed a coalton formaton game that ncludes the endogenous determnaton of a mnmum membersh requrement and then tested the theoretcal redctons of the game usng a seres of laboratory exerments. The man redcton of our theoretcal model s that agents wll vote to adot effcent coalton szes as membersh requrements and that these coaltons wll form. Our exermental results are largely consstent wth the theoretcal redctons when effcency requres the grand coalton to form. In ths treatment, coaltons formed 85 ercent of the tme and over 90 ercent of these were the effcent grand coalton. These results demonstrate the value of the endogenously determned membersh requrements. In fact, the level of effcency for ths treatment s sgnfcantly hgher than n other coalton formaton exerments that do not nclude the endogenous determnaton of membersh requrements. However, n our treatment for whch the effcent coalton requred only a subset of the grou, coaltons formed only 60 ercent of the tme and effcent coaltons were delberately blocked about a thrd of the tme. If these blocks had not occurred, erformance n ths treatment would have matched the erformance of the treatment that requred the grand coalton to form for effcent rovson of the ublc good. Although ndvduals wth standard references would never block effcent coaltons from formng, these actons are consstent wth nequalty-averse ndvduals. Equty concerns may hel exlan the choce of membersh requrements n many exstng voluntary nsttutons; n artcular, the fact that many nternatonal agreements requre very hgh levels of artcaton (Barrett 2003). In lght of our results t s ossble that equty 16
concerns can lmt the formaton of nternatonal agreements when membersh requrements would allow free rders. One mght exect that neffcently hgh membersh requrements would emerge to lmt freerdng, although we do not observe ths n our exerments. The role of equty references n the formaton of voluntary agreements s not well understood, so further research n ths area would be benefcal. Another caveat s that our analyss assumes homogenety n the costs and benefts of rovdng a ublc good. Future research should relax ths smlfyng assumton and exlore the role of endogenous mnmum artcaton requrements among heterogeneous layers. Our objectve was to emrcally test a feature of nternatonal governance endogenous mnmum artcaton - that s ncluded n almost all envronmental treates. Although our laboratory exerments necessarly abstract from the many ntrcaces nvolved wth nternatonal management of shared resources, the results shed lght on the effectveness of the nsttuton n a controlled envronment. The take away message for stakeholders n nternatonal dlomacy s that endogenous mnmum artcaton requrements can be effectve at fosterng cooeraton, but may be sgnfcantly less effectve when targeted artcaton allows for free rdng. Acknowledgements The authors wsh to thank Steffen Kallbekken, Mchael McKee, Shue Anderson and afflates of CICEP for helful comments on revous versons of ths aer. Ths research was art of RCNroject 209701. References Barrett, Scott. 1994. Self-enforcng Internatonal Envronmental Agreements. Oxford Economc Paers 46(5): 878-894. Barrett, Scott. 2003. Envronment and Statecraft: The Strategy of Envronmental Treaty Makng. Oxford, U.K.: Oxford Unversty Press. Barrett, Scott and Astrd Dannenberg. 2012. Clmate Negotatons under Scentfc Uncertanty. Proceedngs of the Natonal Academy of Scences 109(43): 17372-6. Black, Jane, Maurce D. Lev and Davd de Meza. 1993. Creatng a Good Atmoshere: Mnmum Partcaton for Tacklng the Greenhouse Effect. Economca 60(239): 281-93. 17
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Walker, J.M., Roy Gardner, Andrew Herr and Elnor Ostrom. 2000. Collectve Choce n the Commons: Exermental Results on Proosed Allocaton Rules and Votes. The Economc Journal, 110(460): 212-34. Wekard, Hans-Peter, Leo Wangler and Andreas Freytag. 2009. Mnmum Partcaton Rules wth Heterogeneous Countres. Jena Economc Research Paers 2009-077, ISSN 1864-7057. Aendx Here we ncororate nequalty averson nto our model to demonstrate that mnmum roftable coaltons are weakly larger for nequalty averse ndvduals than for ndvduals wth standard references. We follow Fehr and Schmdt (1999) n modelng references over nequalty. Suose at frst that s = n and s = 0. Gven the fnancal ayoffs [2] and [3] wth these restrctons, defne the utlty of a member of an effectve coalton wth s members as: b å ( ) å ( ), [7] m m a m m u () s = () s - max j - (),0 s - max () s - j,0 n-1 n-1 j¹ j¹ where a > 0 catures the layer s loss from dsadvantageous nequalty and 0 nm j 20 b > catures her loss from advantageous nequalty. Snce () s - () s = c and () s - () s = 0from [2] and [3], [7] can be wrtten as: m acn ( - s) u () s = A+ bs-c-. [8] n -1 Smlarly, the utlty of a nonmember of an effectve coalton wth s members s: m b å ( ) å ( ), [9] nm nm a nm nm u () s = () s - max j - (),0 s - max () s - j,0 n-1 n-1 whch can be wrtten as j¹ j¹ nm bsc u () s = A+ bs-. [10] n - 1 It s straghtforward to show that the free-rdng ncentve s reserved n ths model f ( n -1)( b - 1) < a ; that s, as long as the averson to advantageous nequalty s not too strong relatve to the averson to dsadvantageous nequalty. Incororatng the effcent coalton sze s n to determne ndvdual ayoffs yelds: m j m
u u m nm ì a ( n- s) c A + bs - c - for s s; ï n -1 () s = í ï a ( n- s) c A + bs - c - for s > s; ïî n -1 ì bsc A + bs - for s s; n 1 () s = ï í - ï bsc A + bs - for s > s. ïî n -1 Usng [11], an ndvdual s mnmum roftable coalton sze can be characterzed as: [11] [12] s = ŝ f ŝ s > ŝ f ŝ > s, where cn ( - 1) + acn sˆ =. bn ( - 1) + a c [13] To demonstrate s, we frst derve s ˆ as the soluton to: a( n- s) c A+ bs-c- = A. [14] n -1 m Snce u () s n [11] s ncreasng n s, f sˆ However, f sˆ > s, then s must be the soluton to s then s ˆ s s mnmum roftable coalton sze. a( n- s) c A + bs -c - = A. [15] n -1 Plug s ˆ nto [14] and s nto [15], set the resultng equatons equal to each other and collect terms to obtan b(ŝ s ) = α c(!s ŝ ) / (n 1), whch mles that s > ŝ f sˆ > s. Recall from [4] that the mnmum roftable coalton sze for an ndvdual wth standard references s smn = mn{ s s³ c/ b}. From [13],!s ŝ, sˆ s ncreasng nα, and sˆ = c/ b for a = 0. Together, these mly!s s mn for an ndvdual wth dsadvantageous nequalty averson (.e., a > 0). Therefore, such an ndvdual has a weakly hgher mnmum roftable coalton sze than an ndvdual wth standard references. By substtutng n our exermental arameters nto equaton [13] we can demonstrate how largeα must be to ncrease the mnmum roftable coalton sze beyond the effcent sze. In the treatment wth an effcent coalton of three members, f α exceeds 0.584, then the mnmum roftable coalton for an ndvdual wll exceed three members. As a frame of 21
reference, at least 40 ercent of layers n Fehr and Schmdt s analyss were estmated to have α > 0.50. 22
Fgure 1: Percentage of votes for effcent coaltons by treatment Table 1: Indvdual votes and referenda outcomes by mnmum membersh requrement and treatment Mnmum membersh requrement 1 2 3 4 5 6 Totals s = 6 35 (4.9%) 27 (3.8%) 53 (7.4%) 66 (9.2%) 139(19.3) 400 (55.6%) 720 2 (1.7%) 3 (2.5%) 6 (5.0%) 7 (5.8%) 10 (8.3%) 92 (76.7%) 120 s = 3 91 (12.6%) 153 (21.2%) 409 (56.8%) 32 (4.4%) 9 (1.3%) 26 (3.6%) 720 7 (5.8%) 19 (15.8%) 92 (76.7%) 1 (0.8%) 0 (0.0%) 1 (0.8%) 120 To of each cell: Number of votes for each mnmum membersh requrement (ercent of total votes by treatment). Note there are 720 ndvdual votes er treatment. Bottom of each cell: Number of tmes each mnmum membersh requrement was mlemented (ercent of total trals by treatment). Note there are 120 grou-level observatons er treatment. 23
Vote on effcent MMR s = 3 0.029 = 0.817 Model 131.69 = 0.000 erod effects (ch-square) 109.54 = 0.000 subject effects (ch-square) 665.64 = 0.000 Table 2: Regresson results comarng the two treatments Effcent referenda outcomes 0.006 = 0.922 Total coalton formaton -0.264 = 0.000 Effcent coalton formaton -0.268 = 0.003 Effcency -0.069 = 0.015 24.83 = 0.073 44.27 = 0.001 22.97 = 0.115 3.20 = 0.000 18.57 20.56 5.89 2.58 = 0.182 = 0.2468 = 0.970 = 0.001 --- --- --- --- n 1440 240 240 184 240 Notes: The frst four columns reort average margnal effects (and -values) for the s = 3 treatment (relatve to the s = 6 treatment) from Probt regressons. The frst model controls for erod fxed effects and subject random effects. The other three Probt regressons are at the grou-level and control for erod fxed effects. The last model s a lnear regresson wth a deendent varable defned as total grou earnngs/max grou earnngs and controls for erod fxed effects. Table 3: Coalton formaton by mnmum membersh requrement and treatment Mnmum membersh requrement 1 2 3 4 5 6 Total s = 6 1 1 5 4 7 84 102 0.8% 0.8% 4.2% 3.3% 5.8% 70.0% 85.0% 50.0% 33.3% 83.3% 57.1% 70.0% 91.3% s = 3 1 9 62 0 0 1 73 0.8% 7.5% 51.7% 0.0% 0.0% 0.8% 60.8% 16.7 47.7% 67.4% 0.0% 0.0% 100.0% To of each cell: Number of tmes coaltons formed. Mddle of each cell: Percentage coalton formaton by number of trals er treatment. Bottom of each cell: Percentage coalton formaton by adoted membersh requrement. 24
Table 4. Publc good rovson and effcency Average Publc Treatment Good Provson s = 6 4.75 (0.26) s = 3 1.78 (0.31) Effcency 87.4% (2.21) 79.6% (2.07) Standard errors are n arentheses. Each treatment conssts of 120 grou-level observatons. 25