Millers, Commission Agents and Collusion in Grain Auction Markets: Evidence From Basmati Auctions in North India

Transcription

1 CDE Sepebe, 004 Milles, Coissio Ages ad Collusio i ai Aucio Makes: Evidece o Basai Aucios i Noh Idia A. BANERJI Eail: a.baeji@ecodse.og J. V. MEENAKSHI Eail: eea@ecodse.og Delhi School of Ecooics Wokig Pape No. 9 Cee fo Develope Ecooics Depae of Ecooics, Delhi School of Ecooics

2 Wokig Pape No.9 Milles, Coissio Ages ad Collusio i ai Aucio Makes: Evidece fo Basai Aucios i Noh Idia A. BANERJI & J. V. MEENAKSHI Absac This pape udeakes sucual esiaio of asyeic aucio odels i a ake fo basai, ad deecs he pesece of a cael cosisig of a lage i ake shae local ille ad coissio ages puchasig fo lage disa illes. The coacs beee he disa illes ad hei coissio ages help o explai he specific fo ha collusio akes. Siulaios idicae ha i he cael gais cosideably by colludig, ove he copeiive oucoe; ii hoeve, selles faes do o lose sigificaly ude collusio he he coissio ages bid; iii a koledgeable aucioee ould choose uch highe saig pices fo aucios he coissio ages bid, copaed ih he obseved saig pices. The pape also shos ha efficie collusio, he fo of collusio cooly assued i he lieaue, does o explai he daa ell. Keyods: Aucios, Caels, Agiculual Makes. JEL Classificaio: L, L4, Q. Ackoledgees We ae gaeful o he Reseve Bak of Idia fo fudig he field ok fo his pojec, Moolchad & Radheyshya oel fo ecouagee & logisical suppo, Ai Kua & especially Usav Kua fo excelle eseach assisace, ad T. C. A. Aa fo helpful coes.

3 . Ioducio Collusio aogs biddes i aucios has aaced he aeio of aius cells he old ove, ad, iceasigly, spued acadeic eseach. I a ipoa ealy pape, Hedicks ad Poe 989 sess he eed o ecogize ha he possibiliy of collusio, ad he fo ha i akes, is likely o deped o specific chaaceisics of he ake i quesio. I he pese pape, e udeake he deecio of collusio aogs buyes of basai paddy i a holesale ake i Paipa, usig a daase fo a piay suvey ha e coduced. I his ake, sales ake place hough ope ascedig aucios. We fid evidece of a siple ye ovel fo of collusio, hich is elaed o he fac ha soe of he biddes have osadad payoffs, specific o he coex of his ake. I paicula, payoffs fo a subse of biddes, codiioal o iig, ae iceasig i he i pice. We also ague ha he chaaceisics of his ake ok agais he possibiliy of 'efficie collusio', he pedoia fo of collusio discussed i he lieaue, ad sho ha he daa do o suppo i. The pape hus illusaes he geeal poi abou ake chaaceisics ad fos of collusio ade by Hedicks ad Poe. I also coibues o he elaively sall lieaue aalyzig he sucue of gai akes i developig couies. May such akes i Idia ad elsehee use aucios o asac gai, bu supisigly, vey fe sudies use aucio heoy o chaaceize hese akes ad sudy hei feaues. The buyes of basai paddy i Paipa ake ae ill oes ho pocess basai paddy io vaious gades of basai ice. Thei ills ad size of opeaios displays gea vaiaio. A oe ed, hee ae sall illes ho sell he pocessed ice i he doesic ake ude geeic aes; a he ohe, hee ae lage illes ih ecogized bad aes ad a sigifica pesece i ieaioal akes. Apa fo buye asyey, a oe ipoa disicio i his ake is beee local ad disa ills. May illes have ills locaed elaively close o he Paipa ake; ypically, such illes heselves paicipae i he biddig. O he ohe had, a fe lage illes ae locaed a cosideably lage disaces fo he Paipa is a disic i he Nohe Idia sae of Hayaa. I efficie collusio, if a biddig ig is he aucio, he good goes o ha ebe of he ig ho has he highes valuaio fo i.

4 ake, ad eploy he sevices of coissio ages called pakka ahias i local palace o bid a aucios ad buy gai o hei behalf. As paye fo his sevice, a coissio age ges % of he sale pice of ay lo of gai i.e., he i pice ha he puchases. Odiaily, biddes' payoffs i aucios decease i he i pice, ad oe iceive o collude, odiaily, is ha collusio eds o depess i pices. While a fulle descipio of he coissio ages ad hei elaioship o he illes hey buy fo is i Secio., e oe hee ha hei payoff fo iig a gai lo iceases i he i pice. Despie his, e fid ha hey ae pa of a cael. As saed ealie, he fo of collusio ha appeas o be i opeaio is o 'efficie collusio'. I such collusio, he cael ebes have a echais by hich hei values fo he objec o be aucioed ae evealed; he ebe ih he highes value is desigaed o bid fo he objec. The ope ad sigely ie boud aue of ascedig aucios i Paipa as descibed lae iliaes agais he kid of evelaio of values ha is ecessay fo efficie collusio. Moe ipoaly, codiioal upo iig, a coissio age pefes o i a a highe pice. So, i is o obvious ha excludig all bu oe cael ebes fo biddig, as i efficie collusio, is desiable fo his kid of playe. We fid ha he collusive odel hich bes descibes he daa Secio 4 akes place ihi a fou playe cael, hee of hose ebes ae coissio ages biddig o behalf of disa illes, he eaiig ebe beig a lage local ille ho is pese a he aucios. The cael divides up he los o be aucioed, ad, fo a give lo, i is eihe he local ille ho is desigaed o bid, o he goup copisig he coissio ages. I such collusio, each coissio age's pobabiliy of iig iceases by excludig he lage local ille fo biddig, heeas he i pice does o dop sigificaly, sice all coissio age cael ebes bid; he e effec of collusio is favoable fo all he cael playes Secio 5.. The aucio odels ha e use ae idepede codiioal o obseved chaaceisics of a lo such as qualiy pivae values IPV odels ha icopoae buye asyey. The ehodology is o esiae sucual paaeic odels. I paicula, he esiaio hee is suppoed by a ece ideificaio esul Ahey ad Haile 00, Meilijso 98 hich deosaes ha fo pivae values odels of

5 ascedig aucios, oe ca ive he joi disibuio of i pice ad ie ideiy o ucove he lae disibuios of all biddes. Sucual esiaio of aucio odels, hich bega ih Paasch 99, has expaded fas io a lage lieaue. The papes by Laffo, Ossad ad Vuog 995, Doald ad Paasch 996, uee, Peige ad Vuog 000, Capo 00, Hedicks, Pikse ad Poe 00, ad Hog ad Shu 00, fo a sall ad icoplee lis. Saee 00 is a ece suvey. Bajai ad Hoacsu 00 display soe expeieal evidece i suppo of his kid of sucual esiaio, by ay of aseig ciicis abou he sic aioaliy posulaes ha gove he behavio of playes i hese odels. The epiical lieaue o collusio ad is deecio is also goig fas. Besides Hedicks ad Poe 989 eioed above, Baldi, Mashall ad Richad 997, Poe ad Zoa 999, Bajai ad Ye 004 ae bu a fe ieesig exaples. The es of he pape is aaged as follos. Secio coais a descipio of Paipa ake, he aucio pocess, he playes, ad ou daase. Secio descibes he odels o be esiaed. Secio 4 discusses he esiaio esuls, hich sugges ha he odel icopoaig he collusive schee biefly discussed above descibes he daa bes. Secio 5 discusses esuls fo seveal siulaios ha use he paaee esiaes of he collusive odel. is, i is sho ha he payoffs o cael playes fo he above collusive schee ae uch highe ha fo copeiio, give ou paaee esiaes Secio 5.. Sice he collusio is o efficie, his esul is o obvious, ad us be deosaed o hold, fo give paaee esiaes. Nex, e copae i pices ude collusio ad ocoopeaio Secio 5.. We sho ha he ucoveioal collusio i his ake has, o aveage, a uch salle doad ipac o i pices ha i ould be oheise. ially, i Secio 5., hough e esche copuig opial eseve pices, e sho ha a aucioee ho is aae of he collusive schee ould use saig pices ha diffe vasly beee los o hich he lage local ille is desigaed o bid, ad hose o hich he goup of coissio ages bid. Secio 6 cocludes.

6 . The Basai Paddy Make i Paipa Basai is a aoaic, log-gai ice vaiey, go oly i Nohe Idia ad Pakisa. A lage popoio of Idia basai is expoed. Peiu basai o he Idia doesic ake eails a pices e ies geae ha hose fo cheap ice vaieies. The supply chai begis ih faes, ho haves basai paddy fo he iddle of Ocobe o lae Decebe, ad big he gai o egulaed akes o be aucioed 4. The paddy is bough by pivae illes, ho pocess i io ice. Pocessig icludes de-huskig, cleaig, polishig, ad sepaaig he ice io diffee qualiy gades. The ice he fids i ay io eail doesic ad ieaioal akes i vaious ays -- as geeic basai ice, ude he ille's bad ae, o ude he bad aes of diffee eailes o adig houses. Paipa is a sall i es of volue of asacios egulaed ake siuaed i he sae of Hayaa. Ou daa se coespods o he 999 haves seaso he basai aivals oaled appoxiaely 7,000 quials... The Aucio Pocess I ode o sell hei paddy, faes us coac ih ake ages ko as kacha ahias, hose job i is o eigh he gai, display he gai i los i he ake yad, ad povide oveigh soage, i eu fo pece of he pice a hich he gai sells. The los ae sold oe by oe hough a ascedig aucio. The aucioig of a lo begis ih he aucioee daig ou a hadful of gai fo i ad visually ispecig i fo qualiy. olloig his, he aouces a pe quial saig pice. Ieesed buyes also pick up hadfuls of gai ad visually assess is qualiy. The aucioee he aises he pice iceeally ad apidly, hile poeial buyes ay dop ou by hoig do he gai hey had picked up. The i pice is he pice a hich he las bu oe buye dops ou. The aucioee eceives 0.8 pece of he i pice. Regulaed akes fo foodgais ee se up ude he Make Regulaio Ac. Such a ake is u by a ake coiee hose fucios iclude aiaiig he physical ifasucue of he ake place, supevise eighe, sele dispues, appoi aucioees, aiai ake ecods o gai aivals ad sales, ad esue ha o uauhoized coss ae passed o o he fae. 4 I soe lage akes, sales see o ake place piaily hough bilaeal deals beee buyes ad selles, appaely because he ube of aucioees is oo sall o hadle he lage volue of gai aivals. 4

7 .. The Daa The daa se as cosuced usig a piay suvey ha e coduced i Ocobe- Novebe 999. This ifoaio as suppleeed usig ake coiee ecods, ad pesoal ievies ih illes ad faes. The ake coiee ecods povide us daa o each lo ha as aucioed fo he iddle of Ocobe hough Decebe. These daa, fo each lo, iclude he ideiies of he fae hose lo as aucioed ad he buye, he aou of paddy sold i quials, ad he i pice Rs. pe quial. These ecods cao be used as a basis fo aalyzig he aucios as hey do o ecod he qualiy of he lo sold. Basai paddy is heeogeeous i seveal qualiy chaaceisics, vaiaios i hich affec he sale pice. Secod, he ake coiee daa do o coai ifoaio o he aucioee's saig pice. Thid, hee is o ecod of eihe he ube of poeial biddes fo a lo, o he ube of biddes ha ae acive pos he aoucee of he saig pice. ially, hee is o ecod of he pices, duig a aucio, a hich vaious playes dopped ou, ad he ideiies of hese playes. I ode o edess hese shocoigs, e acked a ado saple of 495 basai aucios spead ove fou eeks i he peak akeig seaso. This fos ou coe daa se. o each lo i his daa se, e ee able o ecod diffee qualiy chaaceisics of he paddy, he aucioee's saig pice, he ube of acive biddes he ube obseved afe he saig pice as aouced, he i pice, ad he ideiy of he ie. Due o he apidiy ih hich aucios ake place, ad he lage ube of faes pese, hoeve, i as o possible o obseve ad ecod he ideiies of all acive biddes ad he pices a hich hey dopped ou of he biddig. Thus e have o ecod of paicipaio aes of playes, alhough i soe isaces oe ca ake easoable guesses. I ode o ecod qualiy chaaceisics, e alked o agiculual scieiss, ake coiee officials, agiculual expes okig ih he govee, ad biddes a he aucios o fid ou ha chaaceisics affeced paddy pices. o hese covesaios, seve qualiy chaaceisics eeged as beig poeially ipoa. These ae: oisue coe, uifoiy of gai size, gai luse, he peceages of chaff, gee ad iaue gai ad boke gais, ad a caegoy of 5

8 'ohe' vaiables ecapsulaig evidece of disease o pes ifesaio. If he oisue coe is oo lo, he gai is bile ad poe o beakig hile illig; bu beyod a poi, oe oisue siply eas hee is less ice pe kiloga of paddy. The ideal pe-illig oisue coe is aoud 4 pece. If he gai is dull, boke, o iaue, his aslaes afe illig io lo gade ice. The buyes a he aucio pefo siple visual ad ohe ess o evaluae qualiy such as beakig he gai ad lookig a he coss secio fo visual evidece of bileess. o each lo i ou saple, e pefoed siila ess hile he aucio as o, ad evaluaed each chaaceisic o a scale of eihe o os o bes o o poo ad good 5. Table displays suay saisics fo ou saple. Table : Suay Saisics of he Daa Mea Sadad Miiu Maxiu Deviaio Wi pice Rs./quial Saig pice Rs./quial Nube of acive biddes Moisue coe =ideal Uifoiy i gai size Absece of chaff. 0.6 Absece of bokes ai luse ee ad iaue. 0.4 gai Ohe Lab esig a saple fo each lo fo qualiy as o pacicable. 6

9 Noe he ahe ide age i he sa ad i pices, i iself oe idicaio of he subsaial heeogeeiy i he qualiy of basai los sold. The odal ube of acive biddes hose e obseved paicipaig i he biddig afe he aoucee of he sa pice aged beee ad 4. Apa fo he above vaiables, e cosuced a vaiable capuig he ube of poeial biddes o a give day, fo he ake coiee ecods. Afe cosulig ake coiee officials ad aucioees, e deeied ha his ube ould coespod o he ube of playes ho o oe ha oe lo o aucio o a give day 6. The ube of poeial biddes is hus a day-specific vaiable ad vaies beee 5 ad 0... The Buyes ad Biddes a he Basai Aucios As eioed above, basai paddy is bough by pivae illes, fo pocessig ad sale i doesic ad ieaioal akes. A fis feaue abou he buyes a Paipa ake is asyey. Aecdoal evidece suggess ha he size of ills diffes gealy acoss playes, ad ha illes ih lage, oe ode ills have he beefi of ecooies of scale. Soe of hese 'lage' illes also cae o ieaioal akes ha ae pehaps o accessible o sall playes bu ae lucaive. Diffeeial size of ills ay aslae, i he aucio, o diffeeial valuaios fo gai, ad heefoe, diffee aes of iig he aucios 7. Thee ee 4 lage buyes by ake shae i Paipa. Thei ake shaes i ou saple ae Playe : 8%; Playe A: %; Playe B: %; Playe D: %. 8 Ohe buyes had ake shaes ell belo 5%; e efe o hese as 'sall' buyes. Ohe ha buye asyey, he ipoa disicio o be ade, i he coex of he aucios a Paipa, is beee local illes, hose ills ae ihi a adius of abou e kiloees fo he ake, ad disa illes. Mos of he illes ae local icludig all he sall buyes, bu hee ae ipoa disa illes ih ills hich 6 Cases of poeial buyes ho ed up o iig ayhig o a give day appea o be fe, ad ae copesaed fo by cases of buyes ho i a fe los ad dop ou of he ake. By ad lage, os buyes say he couse ad bid fo los fo a eie day of aucios. 7 Sice e do o obseve paicipaio aes, his is a cojecue bu a easoable oe. 8 The aes of buyes ae ihheld o poec hei ideiies. 7

10 ae fa off fo he ake. Mills ae faily oed. Local ills ae epeseed a he biddig os ofe by a faily ebe ad soeies by a close associae of he faily oig he ill. As opposed o his, 'coissio ages' called pakka ahias bid fo, ad puchase gai o behalf of, he disa illes. Thei coacs o puchase gai sech ove he eie seaso. Each disa ille has oe such coissio age ho is licesed o opeae i egulaed akes such as Paipa o puchase gai o his behalf. Duig he biddig fo a lo, he coissio age is i coac ih his eploye by obile phoe. This coac eables he age o couicae he qualiy of he gai o he ille, ad he ille o ifo he age of his valuaio o illigess o pay fo he lo. If his age is he aucio, he ges % of he i pice. This fo of coac ih a 'coissio' equal o a peceage of he sale pice has a log hisoy. The coissio age is esposible fo deliveig he gai o he ille, ho laboaoyess a saple befoe accepig i. Because of his, ad because he ake coiee ecods he sale pice of each lo of gai, i is had fo a coissio age o iscouicae he qualiy of gai duig he biddig, o o isepo he i pice. Neveheless, he fo of he coac iplies ha a coissio age's payoff, ad iceives, ae o sadad. As a eceive of a peceage of he i pice, i is i his iees o i he lo a a highe, ahe ha a loe pice 9. I he Paipa ake, Playe is a lage local ille. Playes A, B ad D ae coissio ages epeseig disa ills. The disa illes have lage opeaios ha Playe. Playe sells seveal gades of ice boh i he doesic ake ad he Middle Eas. Soe of he ice ha Playe sells doesically, ad all he ice ha he sells ouside Idia, sells ude he bad aes of adig houses ad eailes. I coas, he disa illes sell doesically, ad o a lesse exe ieaioally, ude hei o, ell-ecogized bad aes. The esiaio i Secio 4 oks ih odels of codiioally idepede pivae values. The lage ake shaes of 4 playes ad he sall shaes of he ohes suggess ha he lage playes' values ae da fo sochasically doia 9 Ideed, if he ille is illig o pay up o v, he age ould pefe he pice o go all he ay up o v. Of couse, iig a his pice i a ascedig aucio ough o a he ille abou his age's pobiy. 8

11 disibuios. I ode o pobe he fo ha collusio aog he fou lage playes igh ake, e fis suaize ou saple daa usig odiay leas squaes. The depede vaiable is log i pice, ad he explaaoy vaiables ae: i he seve qualiy vaiables fo paddy; ii duies fo each of he eeks of ou suvey; iii a duy fo Playe ha akes he value if he o he paicula lo, ad 0 if he did o. iv A siila duy fo he goup of pakka ahias copisig Playes A, B ad D. Table peses he esuls. Table : OLS Regessio of log i pice o qualiy chaaceisics Depede Vaiable: Log Wi Pice Esiae -aio Moisue coe Uifoiy i gai size Absece of chaff Absece of boke gai ai luse ee & iaue gai Ohe facos Week duy Week duy Playe duy Pakka ahia duy Nube of acive biddes Cosa R-squaed = 0.6 I a IPV odel of a ascedig aucio, he i pice of a give lo of gai is he secod highes valuaio if his is geae ha he saig pice aogs he se of values ha he biddes have fo he lo. The posiive sigs o he qualiy vaiables heefoe idicae ha playes valuaios ae posiively elaed o qualiy chaaceisics. The duy vaiables associaed ih he lage playes sho ha Playe, he lage local ille, had i pices coespodig o he ake aveage coollig fo he igh 9

12 had vaiables, heeas he i pices fo he coissio ages ee highe. If he value disibuios of he lage playes doiae hose of sall playes, his is cosise ih he kid of collusive odel descibed i Secio.: a cael copisig Playes, A, B ad D collude, assigig biddig ighs o a lo o eihe Playe ih soe pobabiliy π o o he goup icludig playes A, B ad D ih pobabiliy - π. Theefoe, he Playe bids ad is, hee ae fee copeig poeial biddes, ad all of he ae sall playes. The i pice is a value da fo a sall playe s disibuio. Whe a coissio age, say Playe A is, hee ae oe copeig poeial biddes, icludig playes B ad D; he i pice is heefoe likely o be highe o aveage.. The Models We esiae siple asyeic idepede codiioal o obseved qualiy paaees pivae values aucio odels. The ai assupios coo o hese odels ae i Each poeial bidde i has a valuaio o illigess o pay v i fo a give lo, hich is pivaely ko o he bidde. ii v i is a ealizaio of a ado vaiable Vi hose disibuio i is coo koledge. iii The ado vaiables V,...,V ae idepede. The disibuios i, i =,...,, ae lo specific ad deped, fo isace, o he obseved qualiy chaaceisics of he lo. The assued idepedece is codiioal o hese lo specific chaaceisics e suppess he codiioig vaiables fo coveiece. We believe ha he asyeic IPV assupio is a easoable appoxiaio fo his ake. o he illes ho paicipae i he biddig, he valuaio fo a lo of gai is iepeed as he diffeece beee he eveue fo sellig he pocessed ice ad he coss of pocessig, aspo ad soage. The coissio ages ho bid o behalf of illes ae i cosa obile phoe coac ih he illes duig he biddig. Theefoe, i is easoable o assue ha hese ages have valuaios couicaed o he by he illes. Pocessig coss ae ko o vay acoss ills, 0

13 bu ae pivaely ko o illes 0. Ohe fi chaaceisics ha ay be pivaely ko ad coibue o diffeeces i valuaios ae he akes doesic o foeig ha a fi sells i, ad he qualiy gades of ice ha i deals i. The assupio of asyey ha he valuaios of diffee illes spig fo diffee lae disibuios is bee ha a a pioi esicio of syey, paiculaly because ake shaes of buyes Secio ae skeed. Alhough he daa do o ecod paicipaio aes of biddes, hee is good easo o believe ha he lage playes lised i Secio have syseaically highe valuaios ha he salle playes. This esuls i hei iig aucios oe fequely, hich is efleced i hei ake shaes. This is despie he fac ha collusio hich e esablish lae aogs he esics each of he o bid o fee los ha ould have bee he case i he absece of collusio. o he obseved ake shaes as ecoded by he ake coiee ad obaiig descipios of he ills, i es of hei size ad uove, ove he couse of ou ievies ih vaious ake playes, e assue ha hee ae fou lae value disibuios: i, i =,, = Playe, = Playe A, = Playes B ad D ad disibuio fo he sall playes. The diffee odels iply diffee joi disibuios fo he i pice ad he obseved ie. The use of his joi disibuio fo esiaio aises ou of a ece ideificaio esul Ahey ad Haile 00 Theoes a, i ad Meilijso 98. The esul iplies ha ude he codiioal IPV assupio, he joi disibuio of he secod highes ode saisic of he ado saple v,...,v of valuaios ad he ideiy of he ie uiquely ideifies he lae disibuios fo hich he valuaios ae da. 0 Oe key deeia of pocessig cos is he covesio faco o aio of uboke ice pe kilo of paddy. This depeds o ill-specific achiey i a pocessig ui, alog ih qualiy chaaceisics of he paddy such as oisue coe, ad hehe he pocessed oupu is paboiled o a ice. Covesio facos codiioal o paddy qualiy vay sigificaly acoss ills, ad ae pivaely ko. Ou daa liss he i pice fo each lo, bu ifoaio o ohe bids is abse. Thus siple ess of he IPV specificaio, such as a egessio of he highes bid o he secod highes bid ad qualiy vaiables, cao be pefoed o check fo pesece of coelaio. The absece of esale educes he appopiaeess of a aleaive, coo values faeok. o he ake coiee ecods, e fid ha Playe exied he ake o Novebe 9, 999, ih oe ha a oh lef i he peak akeig seaso. Ou saple eds soo afe. Theefoe, 's ake shae i ou saple is highe ha i is i he populaio deeied by he ake coiee ecods. This specificaio of disibuios us ou o be obus o chages.

14 .. The Nocoopeaive Model I is ell ko ha i his sadad odel, i is a doia saegy fo a playe ih valuaio v o say ih he biddig uil he pice asceds o equal his valuaio, ad o dop ou heeafe. Theefoe, he ie is he bidde ih he highes valuaio, ad he i pice is he secod highes valuaio, aogs he values v,...,v, povided ha boh valuaios exceed he aucioee's saig pice. The i pice is heefoe a ealizaio of he secod highes ode saisic. O he ohe had, he i pice is if exacly oe valuaio exceeds he saig pice, ad he lo is usold if all valuaios ae less ha he saig pice. I ou saple 7 pece of he los sold a he saig pice, ad e did o obseve ay usold los. Ou daa icludes, fo each aucioed lo, a ube p of poeial biddes, of hich ae sall playes, he aucioee's saig pice, a ube of acive biddes hose values exceed, he i pice, ad he ideiy of he ie. Ude he ocoopeaive odel, hee ae heefoe 4 poeial biddes i.e. 4 lage playes. So fo exaple, if Playe hose values ae da fo he disibuio is a a pice geae ha, he joi disibuio of he secod highes ode saisic, he ie beig equal o Playe, ad ou of 4 poeial biddes daig values highe ha is give by Equaio belo.

15 . 4,,..,..,...,, = d C d C d C d C d C d C H The fis of he six es i Eq coespods o eves i hich Playes A, B ad D have values less ha he saig pice, so ha he acive biddes cosis of Playe he ie ad - sall playes. As hee ae sall poeial biddes, hee ae C, - such eves. Noe ha he pobabiliy ha - sall playes have values exceedig is o sho, as i ges cacelled ih he sae e ha cops up i he deoiao i he loe ucaed es appeaig i he squae backes. I he squae backes, he iegal coves eves i hich all biddes values ae less ha o equal o he i pice, ad he folloig e elaes o he eve ha he ie Playe s value sicly exceeds he i pice, hile he ohe values ae less ha o equal o he i pice. I siila fashio o he eie fis e, he secod o sixh es capue eves i hich oe o oe of Playes A, B ad D have values exceedig. ially, oe ha Eq is valid if he ube of acive biddes is a leas 4. If =, he las e dops ou; if =, he las hee es dop ou. The desiy h coespodig o Eq is obaied by diffeeiaig i ih espec o see Appedix A. The axiu likelihood esiaio i Secio 4 uses his desiy fo daa

16 pois i hich he ie is Playe ad he i pice is geae ha he saig pice. Siila expessios H i, i = A, B, D, s, hold he he ies ae, especively, Playe A,B,D o a specific sall buye; he coespodig desiies h i ae used i he axiu likelihood esiaio of he odel. O he ohe had, Playe is a lo a he saig pice if oly his value fo he lo exceeds. I his case, he joi desiy of he i pice hich equals ad he ie beig Playe is give by equaio. P ipice =, ie = = [ ] Siila expessios ae used he ohe playes i a he saig pice fo a lo... Bid Roaio beee Playe ad he oup of Coissio Ages I his aleaive odel, he fou lage playes fo a cael. They collude by allocaig biddig ighs o each lo o eihe Playe, o he goup copisig Playes A, B ad D. This osadad fo of bid oaio is dive by he fac ha he coissio ages buy o behalf of illes, ad hei iceives ae o he sae as hose of he illes hey epese. Playe is a local ille. His chaces of iig a give lo i he absece of biddig by he ohe lage playes is highe ha i he ocoopeaive odel. Moeove, he i pices ae also likely o be loe, as hee ae o fee poeial biddes, ad i paicula biddes likely o have elaively high values ae abse. Theefoe, if Playe is assiged o bid o a sufficiely high ube of los, his expeced payoff is geae ha ude ocoopeaio. O he ohe had, a lage coissio age's payoff fo iig is a facio of he i pice. This payoff is highe he highe is he i pice. Theefoe, a bid oaio schee i hich all coissio ages bid fo a lo has o opposig effecs o he expeced payoff of a coissio age, elaive o ocoopeaio. Excludig Playe ipoves a coissio age's chaces of iig, bu also educes he expeced i pice. If he e effec o his expeced payoff is posiive, such a collusive schee ay ok, fo isace, by a hea o eve o ocoopeaio i fuue aucios if a playe deviaes 4

17 fo colludig. 4 Ude he hypohesis ha collusio akes his fo, he joi disibuio of he i pice, a specific playe beig he ie, ad ou of p biddes beig acive is soeha diffee. o exaple, fo a lo hich is o by Playe a a pice geae ha he saig pice, e ko ha he cael has assiged biddig ighs fo his lo o Playe. Theefoe, he joi disibuio is give by Eq belo. C H = C, d The ajo diffeece beee his ad he coespodig ocoopeaive expessio Eq is ha he lage coissio ages ae abse, as Playe is biddig. The desiy h C is he deivaive of Eq ih espec o see Appedix A. o los o by oe of he lage coissio ages, e ife ha he cael has assiged he goup copisig Playes A, B ad D bu o Playe o bid fo he lo. Joi desiies hi C, i = A, B, D fo he lage coissio ages ae heefoe deived by excludig Playe fo he se of poeial biddes. o los o by Playe a he saig pice, he joi desiy aalogous o Eq is give by Eq4 belo. h C = [ ] 4 Specifyig a joi disibuio ad desiy he a specific sall playe is a lo is oe coplicaed, sice e do o obseve hehe Playe, o he goup of coissio ages, as biddig fo his lo. Suppose he i pice is highe ha, a specific sall playe is, ad biddes ae acive hei values exceed. We fis ok ou he joi desiy ha ould obai if Playe ee he lage playe biddig, hs C, ad he joi desiy ha ould obai if he lage coissio ages ee hs C, CA C C s, s, CA biddig. o such los, e he use he joi desiy ah a h. The ube a ay be iepeed as he pobabiliy, codiioal o a specific sall playe iig 4 Of couse, such a hea, ad he suggesed odeig of collusive payoffs beig highe, is o ecessay o susai collusio. Moe sophisicaed saegies usig iax heas ad 'ecociliaio saes' also ok. Rece ok Skzypacz ad Hopehay 004 aalyzes ho efficie collusio ca be susaied i a epeaed Eglish aucio seig ih idepede pivae values. 5

18 he lo, ha Playe is a bidde. Siilaly, fo los sellig o specific sall playes a C C s, s, CA saig pices, e use he desiy ah a h... Ohe Models I addiio o he above, e have esiaed seveal ohe odels. To of hese ae oh epoig, as hey ca povide aleaive bechaks. We epo esiaes of hese odels i Appedix B. The fis of hese is he efficie collusio odel. I such collusio, he cael of colludig playes ay se up a pe-aucio 'kockou' i hich playes eveal hei values, he playe ih he highes evealed value ges o bid o he objec, ad asfe payes ae oked ou acoss playes. I such a echais, playes have a iceive o eveal hei ue values see aha ad Mashall 987 fo a ealy discussio. I he ake ha e sudy, efficie collusio aogs he fou cael ebes is o a poisig pospec fo o easos. Oe, aucios ae coduced i he ope, ad ake place apidly; boh hese facos pobably peclude oppouiies fo evealig valuaios ad hece efficie collusio. To, he iceives of he coissio ages ae osadad, so ha i is o obvious ha excludig all bu oe cael ebe fo biddig is bes fo such a age as his ay lead o oo lo a i pice. Neveheless, e esiae a efficie collusio odel ad es i agais he bid oaio descibed i Secio., as i is oe of he oe cooly discussed odels of collusio i he epiical aucios lieaue. The joi desiy of he i pice ad a specific cael ebe beig he ie, ad biddes beig acive, o ivolves a iegal. o exaple, suppose a cael playe, say Playe, is he ie, ad he i pice exceeds he saig pice. This iplies ha he ohe cael ebes have values less ha Playe 's value, ad Playe 's value exceeds he i pice. These ebes do' bid. Thus he i pice us be he value of oe of he sall playes, ad he es of he sall playes us have values less ha he i pice. Noe hoeve ha cael ebes ho do o bid ca also have values exceedig he i pice hece he iegal. The joi desiy is heefoe give by Eq5 belo. 6

19 h E = C, f. d The expessio akes io accou ha ay of he - sall playes ih values exceedig he saig pice could have he value hich equals he i pice; so his ca happe i - ays. The iegal descibes he eve ha Playe 's value exceeds, ad is he highes value aogs he cael ebes. O he ohe had, if Playe is a he saig pice, oe of he sall playes' values exceed he saig pice. Hece he joi desiy is E = d h 6 Joi desiies he he ie is soe ohe cael ebe ae siila. If he ie of a give lo is a specific sall playe ouside he cael, he joi desiy e ok ih uses he ifoaio ha all ohe playes have values less ha o equal o he i pice, hile he sall playe ho is has a highe value. Theefoe, he expessios ae close i fo o hose used fo he ohe odels. ially, e epo esuls fo a sadad bid oaio odel. I his odel, he collusive schee is ha fo ay give lo of gai, exacly oe of he fou cael playes ges he igh o bid. Who ges o bid fo a lo depeds o he oucoe of a adoizaio; evelaio of values is o ivolved. o a lage coissio age, he fac ha ohe lage playes ae abse, hile iceasig he pobabiliy of iig, deceases he expeced i pice. Agai, sice such a age's payoff iceases i he i pice, i is o clea ha such exclusio of ohe lage playes is ecessaily beeficial. We oe hee ha he egessio i Secio povides soe evidece agais sadad bid oaio, ad i favo of he collusive schee descibed i Secio.. Ude sadad bid oaio, e ould o expec ha he lage coissio ages ould have sigificaly highe i pices copaed o Playe 's i pices; bu his is a disic possibiliy ude bid oaio beee Playe ad he goup of lage coissio ages as a hole. 5 7

20 4. Esiaio ad Resuls I ode o esiae he o-coopeaive ad he vaious odels of collusio, e specify ha he lae disibuios of valuaios ad i, i =,, fo a give lo ae logoal ih eas x ad x β, i =,, β µ i, especively. Hee, x is a veco of chaaceisics fo lo, icludig he seve qualiy chaaceisics, duies fo o eeks, ad a cosa e; β is he coespodig veco of paaees. The µ ae i ea shifes fo he disibuios of he lage playes. We ake he siplifyig assupio ha he hee disibuios i have he sae vaiace. We esiae all odels usig he ehod of axiu likelihood, ih desiies specified as idicaed i he pevious secio. We fid ha he collusive schee descibed i Secio., viz. bid oaio beee Playe, he lage local ille ad he goup of lage coissio ages Playes A, B ad D bes descibes he daa. Paaee esiaes of his odel ae se ou belo i Table. Esiaes fo he o-coopeaive odel, alog ih he efficie collusio ad he sadad bid oaio odels, ae give i Appedix B. 8

21 Table : Paaee Esiaes fo Model ih Bid Roaio Beee Playe ad goup of Coissio Ages Esiae -aio Moisue coe Uifoiy i gai size Absece of chaff Absece of bokes ai luse ee & iaue gai Ohe facos Week duy Week duy Diffeece i ea fo Playe µ Diffeece i ea fo Playe A µ Diffeece i ea, Playes B ad D µ Vaiace Vaiace i Cosa Log Likelihood value The log likelihood value fo his odel is uch highe ha ha fo he ohe odels Appedix B. We also es beee he above odel ad he bechak ocoopeaive odel usig Vuog s 989 es. The es saisic evaluaes o.0 ad favous his fo of he collusive odel ove he ocoopeaive odel. The sigs o he qualiy vaiables ae posiive, idicaig ha playes values ae posiively affeced by highe qualiy. uhe, he lage local ille, Playe, ad he hee coissio ages A, B ad D da values fo disibuios codiioal o qualiy hich have highe eas ha he ea of he sall playes disibuio. This fis ell ih he fac ha he fou cael playes have lage ake shaes hile he 9

22 ohes do o. Noice also ha he ea fo Playe s disibuio is sigificaly loe ha fo he goup of coissio ages. Oe expecs, heefoe, ha Playe beefis gealy if he goup of coissio ages does o bid he he does. 5. Siulaios 5.. A Copaiso of Payoffs of he Lage Playes i he Pesece ad Absece of Collusio I ode o ge a sese of ho pofiable i is fo he cael o collude pe he odel i Secio., e coduc siulaios o evaluae he expeced payoffs ude collusio ad ocoopeaio. We fix he disibuios of he vaious playes, usig he paaee esiaes β ˆ, ˆ µ i, i =,,, of he collusive odel epoed i Table. The veco x is evaluaed a he aveage qualiy of he los ha sold i he hid eek of ou saple. We he siulae 0,000 aucios ih he playes daig values fo hei especive disibuios. To siulae he ocoopeaive odel, e have all playes da valuaios ad bid a evey aucio; hus hee is oe value da adoly fo he disibuio, oe fo, o fo, ad seveal vayig fo 5 o 0 fo. To siulae collusio, e evaluae oe sceaio hee Playe is he oly lage playe, ad aohe sceaio i hich Playes A, B ad D bu o Playe ae he lage playes ho paicipae. I eihe case, Playe s payoff, he he is, is he diffeece beee his valuaio ad he i pice. His aveage payoff pe lo is he su of hese diffeeces fo los ha he is, divided by 0,000. o a coissio age Playe A o B o D, he aveage payoff pe lo is pece of he su of i pices fo los o by he age, divided by 0, We use a saig pice of Rs. 89 pe quial, he aveage fo ha eek. Table 4 peses hese payoffs fo he lage playes, ude collusive ad ocoopeaive behavio 6. We vay he ube of sall poeial biddes beee 5 ad 0. Colus ad give Playe 's payoffs pe quial ude collusio ad 5 I os of ou siulaios copaig collusive vesus ocoopeaive payoffs, vey fe los ae usold i.e., a leas oe valuaio exceeds he saig pice. This is cosise ih ha e obseved i ou saple; e ecoded o lo ha eaied usold oce a saig pice had bee aouced. 6 Siulaios ih ohe qualiy vecos idicae siila esuls. 0

23 ocoopeaio. Colus 4 ad 5 give aveage i pices pe quial fo Playe B o D i pices fo Playe A ae vey siila as ell, ad hece o epoed, ude collusio ad ocoopeaio. Playe B's payoff fo a lo is % of his ies he ube of quials i he lo. Table 4: Expeced Payoffs Rs./quial of Lage Playes ude Collusio ad Nocoopeaio # sall o ude o ude o B/D o B/D ude poeial collusio ocoopeaio ude ocoopeaio biddes collusio = = = = = = As idicaed above, fo each of he lage playes, he expeced payoffs ude collusio exceed ha of ocoopeaive play. Sice he aveage lo of gai is abou 50 quials, he diffeece i expeced payoffs pe lo is fify ies he diffeece beee colus ad fo Playe ad % of 50 ies he diffeece beee colus ad 4 fo Playes B ad D. ive he lage expeced payoffs ude collusio, he cael ca be susaied, i a epeaed aucios seig, by deeig deviaios usig a hea o eve o ocoopeaio 7. This eieaes he key poi ha give ou paaee esiaes, he osadad collusive schee descibed i Secio. ca ok, oig o he diffee iceives of coissio ages, ad seves as a fuhe validaio of he collusive odel. 5.. The Effec of Collusio o Wi Pice 7 We do o odel his foally. Such foalizaio ould equie aeio o soe key deails, such as he capaciy cosais o he ills oed by cael playes, ad hei cue iveoies of paddy. Daa o hese ae uavailable.

24 We also use siulaios o copue aveage i pices ude collusive ad ocoopeaive behavio, fixig he disibuios i he ae descibed above. As befoe, ude bid oaio beee Playe ad he goup copisig Playes A, B ad D, e coside o sceaios: oe i hich Playe is he oly lage bidde, ad he ohe hee he coissio ages ae he lage biddes. The siulaio of ocoopeaio assues all fou lage biddes paicipae i he biddig. ive ha his is a osadad fo of collusio, i is ieesig o assess he exe o hich ake pices ae hus depessed. o copaisos, e also siulae i pices ude sadad bid oaio aogs he 4 lage playes Secio. alhough his fo of collusio does o chaaceize his ake. Hoeve, he sadad bid oaio odel igh chaaceize a aleaive ake sucue, oe hee he 4 lage playes ae all local illes. I ha case, close associaes ould dicae hei biddig, ad hei payoffs ulike hose of he coissio ages ould be sadad. If efficie collusio is had o cay ou due o he ope ad apid aue of he aucios, sadad bid oaio ay be a viable opio. Table 5 povides he esuls.

25 Table 5: Aveage i pices ude o fos of collusio ad ude ocoopeaio Rs./quial Nube of Collusio beee & Nocoopeaio Sadad bid sall goup of pakka ahias oaio playes daig bids Pakka ahias bids A bids valuaios fo bid Noe fis ha collusio beee Playe ad he coissio ages esuls i sigificaly loe i pices Rs pe quial, copaed o he ocoopeaive case, he Playe is he lage playe assiged o bid fo a lo. Hoeve, he he coissio ages bid, he diffeece declies shaply, o beee Rs. - pe quial. This is because o hese los, hee is oly oe less lage bidde; he Playe bids, hee ae fee lage biddes. Thus faes lose subsaially oly o los hee bids. Noe ha he highe aveage pices he he coissio ages bid is siila o he OLS egessio esul Table ha shoed ha hey pay highe pices ha Playe he hey i.

26 Had his ake bee chaaceized by sadad bid oaio isead, he pices eceived by faes ould have bee subsaially loe; by abou Rs pe quial o los ha Playe bids fo, o appoxiaely Rs loe o los ha Playe A bid o. So, e ay ife ha he fo of collusio hich descibes he daa bes, aely, bid oaio beee Playe ad he goup of coissio ages, loes pices uch less ha ohe fos of collusio. 5.. The Effec of Aleaive Saig Pices o Wi Pices ad Sales Peceage I is aual o ask hehe, give he esiaed lae disibuios, he saig pices fo los axiize he expeced eveue of he selles faes. Hoeve, i he gai ake seig of his pape, he aucioee is a ieediay ad o he oe of he gai. This leads o ieesig possibiliies ad quesios abou he opialiy of he eseve pices, fo exaple ha ae oheise abse. These quesios ae he subjec of ogoig eseach ad beyod he scope of his pape. Neveheless, i is useful o exploe i a siulaio, give he fo of collusio ha e deec, he expeced eveue ha aleaive saig pices esul i, fo a lo of gai of give qualiy. I Table 6, e pese a exac of he kid of esuls ha e ge as a ase o his quesio 8. I his exac, e agai ake he case of a lo of aveage qualiy i eek of he saple ad siulae 0,000 aucios each ih Playe, ad he goup of coissio ages, as he lage biddes. 8 If biddes ae syeic, he opial eseve pice does o deped o he ube of biddes. Sice ou seig has asyey, he siulaio epos esuls vayig he ube of biddes. 4

27 Table 6: The Effec of Aleaive Saig Pices o Wi Pice ad Sale Peceage Playe bids Pakka ahias bid Saig Pice % los sold Aveage i % los sold Aveage i : # sall poeial biddes pice of los sold Rs./quial pices of los sold Rs./quial = = =

28 If e assue ha a usold lo yields a payoff of 0, he uliplyig he aveage i pice ih he peceage of los sold gives a easue of expeced eveue. o Playe, e obseve ha highe saig pices educe he peceage of los sold ad icease he aveage i pice, ad ha he e effec is o educe expeced eveue. Of he saig pices epoed, he loes oe, Rs.800, coespods o he highes expeced eveue, iespecive of he ube of biddes. As opposed o his, he he goup of coissio ages bid, he highes saig pice epoed, Rs.000, coespods o he highes expeced eveue. So, if he aucioee ca deec he pae of biddig coespodig o ou collusive schee, oe isue available o hi is o ailo he saig pice quie diffeely, ad subsaially highe, he he coissio ages bid. I ou daa se, he aveage saig pice he he coissio ages A, B o D i is highe ha he is, by abou Rs.50. Ou siulaios idicae ha he diffeece ough o be uch lage, i ode o axiize expeced eveue. Coclusios This pape exaies basai paddy aucios i a gai ake i Noh Idia, usig e daa fo a piay suvey, hough he sucual esiaio of seveal siple aucio odels. I ioduces a key feaue ha chaaceizes his ake -- ha soe disa illes buy gai hough coissio ages, hose coacs ake hei payoffs osadad. I paicula, hei payoffs codiioal o iig icease i he i pice. This feaue ay help o explai he fo of collusio ha bes explais he daa: bid oaio beee a lage local ille ad he goup of coissio ages puchasig o behalf of lage disa illes. The pape also shos ha efficie collusio ihi his cael does o explai he daa ell. Siulaios he idicae he folloig pois. i The payoffs o cael ebes ude collusio of he fo descibed ae highe ha ude ocoopeaio. ii This fo of collusio has lile doad ipac o i pices o los o hich he goup of coissio ages bid. iii A aucioee coceed abou expeced eveue, ad aae of he fo of collusio, ould choose uch highe saig pices fo los o hich he coissio ages bid, vesus hose o hich he local lage ille bids. 6

29 Like alos all epiical ok o sucual esiaio of aucios, his pape eas each aucio i he daa se as a sepaae sigle ui aucio. Bu gai aucios acoss he haves ad akeig ohs ca aleaively be vieed as a uliui, sequeial aucio. This vie has he poeial o cosideably eich he ok i his pape, especially as he kid of collusio ha sees o be akig place is bee jusified i a faeok of epeaed aucios. Thee is soe ece, ieesig epiical ok i dyaic faeoks Jofe-Boe ad Pesedofe 00; Doald, Paasch ad Robe 00, ad a aep ca be ade o adap such ehods. Hoeve, daa o a leas o addiioal fos ae eeded befoe oe ca explicily odel a dyaic aucio ad esiae i. The fis is a full se of bids o pices a hich biddes dop ou 9 ; he secod is daa o ills' iveoies of paddy acoss he seaso. 9 This daa ill cosideably eich esiaio ad esig of he saic heoy as ell, by elagig he vaiey of odels ha ca be used cosideably beyod he codiioally idepede pivae values odel. 7

30 Refeeces Ahey, S., ad P. Haile 00. "Ideificaio of Sadad Aucio Models." Ecooeica, 70, Bajai, P. ad A. Hoacsu 00. "Ae Sucual Esiaes fo Aucio Models Reasoable? Evidece fo Expeieal Daa." N.B.E.R. Wokig Pape # Bajai, P. ad L. Ye 004. "Decidig beee Copeiio ad Collusio." Revie of Ecooics ad Saisics, 85, Baldi, L., R. Mashall ad J-. Richad 997. "Bidde Collusio a oes Sevice Tibe Sales." Joual of Poliical Ecooy, 05, Capo, S. 00. "Asyey ad Risk Avesio ihi he Idepede Pivae Paadig: The Case of he Cosucio Pocuees." Wokig Pape, Uivesiy of Noh Caolia. Doald, S. ad H. Paasch 996. "Ideificaio, Esiaio ad Tesig i Paaeic Epiical Models of Aucios ihi he Idepede Pivae Values Paadig." Ecooeic Theoy,, Doald, S., H. Paasch ad J. Robe 00. "Ideificaio, Esiaio ad Tesig i Epiical Models of Sequeial, Ascedig-Pice Aucios ih Muli-Ui Dead: A Applicaio o Sibeia Tibe Expo Peis." Wokig Pape. aha, D. ad R. Mashall 987. Collusive Bidde Behavio a Sigle-Objec Secod-Pice ad Eglish Aucio. Joual of Poliical Ecooy, 95, 7-9. uee, E., I. Peige ad Q. Vuog 000. "Opial Nopaaeic Esiaio of is Pice Aucios." Ecooeica, 68, Hedicks, K., J. Pikse ad R. Poe 00. "Epiical Iplicaios of Equilibiu Biddig i is-pice, Syeic, Coo Value Aucios." Revie of Ecooic Sudies, 70, Hedicks, K. ad R. Poe 989. "Collusio i Aucios." Aales d'ecooie e de Saisique, 5/6, 7-0. Hog, H. ad M. Shu 00. "Ecooeic Models of Asyeic Ascedig Aucios." Joual of Ecooeics,, Jofe-Boe, M. ad M. Pesedofe 00. "Esiaio of a Dyaic Aucio ae." Ecooeica, 7,

31 Laffo, J., H. Ossad ad Q. Vuog 995. "Ecooeics of is-pice Aucios." Ecooeica, 6, Meilijso, I. 98. "Esiaio of he Life-Tie Disibuio of he Pas fo he Auopsy Saisics of he Machie." Joual of Applied Pobabiliy, 8, Paasch, H. 99. "Decidig Beee he Coo ad Pivae Value Paadigs i Epiical Models of Aucios." Joual of Ecooeics, 5, 9-5. Poe, R., ad J.D. Zoa 999. "Ohio School Milk Makes: A Aalysis of Biddig." Rad Joual of Ecooics, 0, Saee, S. 00. "A Suvey of Rece Wok o Ideificaio, Esiaio ad Tesig of Sucual Aucio Models." I A. Ullah, A. Wa ad A. Chauvedi, eds. Hadbook of Applied Ecooeics ad Saisical Ifeece. Ne Yok: Macel Dekke. Skzypacz, A. ad H. Hopehay 004. Taci Collecio i Repeaed Aucio. Joual of Ecooic Theoy, 4, Vuog, Q "Likelihood Raio Tess fo Model Selecio ad No-esed Hypoheses." Ecooeica, 57,

32 0 Appedix A.. The Desiy Coespodig o H Eq. [ ] [ ] [ ] [ ] 4 } 4,,,,,, } { { } { A f g g C f g g C f g C f g C f g C f C h =. The Desiy Coespodig o H C Eq., A f C h C =

33 Appedix B.. Maxiu Likelihood Esiaes of he Nocoopeaive Model Esiaed -aio Coefficie Moisue coe =ideal Uifoiy i gai size =bes Pesece of chaff =bes Pesece of bokes =leas boke ai luse =bes ee & iaue gai =bes Ohe facos =bes Week duy Week duy Diffeece i ea fo Playe Diffeece i ea fo Playe A Diffeece i ea fo Playes B ad D Cosa Log Likelihood value Maxiu Likelihood Esiaes of he Efficie Collusio Model Esiaed -aio Coefficie Moisue coe =ideal Uifoiy i gai size =bes Pesece of chaff =bes Pesece of bokes =leas boke ai luse =bes ee & iaue gai =bes Ohe facos =bes

34 Week duy Week duy Diffeece i ea fo Playe Diffeece i ea fo Playe A Diffeece i ea fo Playes B ad D Cosa Log Likelihood value Maxiu Likelihood Esiaes of he Idividual Bid Roaio Model Esiaed -aio Coefficie Moisue coe =ideal Uifoiy i gai size =bes Pesece of chaff =bes Pesece of bokes =leas boke ai luse =bes ee & iaue gai =bes Ohe facos =bes Week duy Week duy Diffeece i ea fo Playe 0.80 Neg Diffeece i ea fo Playe A Diffeece i ea fo Playes B ad D 0.80 Neg Cosa Log Likelihood value * Coplee lis of okig papes is available a he CDE ebsie: hp://.cdedse.og/oklis.pdf