The market for lawyers and quality layers in legal services

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1 RAND Journal of Economcs Vol. 43, No. 4, Wnter 0 pp The market for layers and qualty layers n legal servces Elsabetta Iossa and Bruno Jullen We study the functonng of the market for layers, consderng the strategc nteracton among ltgants, layers, and judges. We nvestgate the value of legal representaton and of systems of qualty certfcaton, such as the Queen s Counsel system. In our settng, hgher qualty layers obtan better-qualty evdence and are better able to nterpret t. Judges receve nformaton from the layers and have reputatonal concerns. We sho that reputatonal concerns generate a decson bas n favor of certfed layers and that ths causes msallocaton of layers at the market equlbrum. As a result, hereas a hgher qualty of layers ncreases elfare, publc nformaton over qualty may be elfare reducng.. Introducton Dstnctve layers of qualty exst thn the legal professon, and t s typcally observed that hgher-qualty layers are assgned hgher-value cases and receve hgher fees. As descrbed, for example, by Rosen 99 and by Garcano and Hubbard 009a, n the Unted States one can dstngush beteen to categores of professonal layers. The frst category comprses layers ho graduated from elte nsttutons, serve busness clents, and charge hgh fees. The second category serves more ndvdual clents and comprses layers ho graduated from loer-ter schools, charge loer fees, and provde largely routne, noncontested legal servces. Dependng on ther category, layers are then employed n dfferent la companes, th the most reputable companes employng the most talented and ell-traned layers. DEF, Unversty of Rome Tor Vergata, CEPR, CMPO and EIEF; Toulouse School of Economcs IDEI and GREMAQ; For helpful comments e sh to thank Julan Greenhll, Paul Grout, Ian Jett, Wllam Kovacc, Glat Levy, Nel Rckman, Gancarlo Spagnolo, Kathryn Sper, and semnar partcpants at Brunel Unversty, Brkbeck College, Enaud Insttute for Economcs and Fnance, European Unversty Insttute, Pars School of Economcs, Unversty of Brstol, Unversty of Essex, Unversty of Rome Tor Vergata, Unversty of Warck, and the 007 CMPO Workshop on the Economcs of Legal Servces and Justce n Brstol. Specal thanks go to edtor Jennfer Renganum and to anonymous referees for ther very helpful comments. Studyng the Chcago bar, Spurr 987 provdes evdence that nformaton, such as academc performance and qualty of la school, matters, as the market tends to assgn larger clams to hgher-qualty layers. The nformaton avalable has mproved consderably as specalzed journals such as the Legal Tmes, Amercan Layer, and Natonal La Journal no provde detaled nformaton on the performance of la frms and ndvdual layers. Copyrght C 0, RAND. 677

2 678 / THE RAND JOURNAL OF ECONOMICS Also, n many countres, agents can choose to self-ltgate rather than be represented by a professonal layer, and the qualty of self-representaton s loer on average than that of professonal representaton because there are no entry requrements to ensure mnmum qualty standards. Self-ltgaton s cheaper and manly used for small clams. Dstnctve layers of qualty result also from the presence of systems of qualty certfcaton, such as the Queen s Counsels QCs system n England and Wales. QCs are layers ho are certfed to have marked themselves out n the professon; n court, they ear a dstnctve unform th a short g and ng collar and th bands and slk gon over a specal court coat. They are typcally hred for more valuable cases, and from the day of ther appontment they beneft from an ncreased fee per hour. Schemes equvalent to the QC system exst, for example, also n Scotland, Northern Ireland, Canada, Ne Zealand, and South Australa. In ths artcle, e study the functonng of the market for layers to analyze the value of legal representaton and the desrablty of qualty certfcaton systems markng dstngushable layers of qualty thn the legal professon. We derve the demand for layers and the market mechansm through hch hgher-qualty layers obtan hgher fees. We buld a stylzed model here ltgants choose hether to hre a hgh-qualty layer or a lo-qualty layer or, as alternatve nterpretaton, they choose beteen professonal ltgaton and self-ltgaton. We use the terms certfed and uncertfed to dstngush beteen hghqualty and lo-qualty layers. Certfed layers receve a more nformatve sgnal about the state of the orld and are better able to nterpret the meanng of ther sgnal than uncertfed layers. For nstance, recept of a more nformatve sgnal may reflect better skll at generatng evdence, hereas hgher ablty to nterpret hat the sgnal means for the case may reflect better skll at applyng the relevant la to the evdence. A dspute s resolved through an ntal stage here the layers provde nformaton to a loer-court judge ho makes an ntal decson and, f the losng ltgant appeals, an appeals stage here an appeals court makes a fnal decson. The loer-court judge can be of to types: competent or ncompetent. Competent judges are able to nterpret the nformaton provded by the layers, hereas ncompetent judges cannot. The appeals court only comprses competent judges. Loer-court judges have prvate nformaton about ther type; they have reputatonal concerns n the sense that they sh to appear competent to an outsde evaluator. In practce, judges care about ho others perceve ther qualty, ether because of a general concern for prestge or nfluence or because ther reputaton can drectly nfluence ther career and future ncome. Emprcal evdence ndeed shos that the perceved qualty of judges plays an mportant role n ther promoton to hgher courts see Mcel and Cosgel, 994; Blanes Vdal and Leaver, 008; Levy, 005; and references theren. In ths settng, e sho that the gan for a ltgant from hrng a hgh-qualty layer s tofold. Frst, t allos for a more nformed appeals strategy, hch leads to more effcent appeals. Second, and crtcal to our analyss, hrng a certfed layer generates a decsonbas effect: ncompetent judges bas ther decsons n favor of certfed layers, due to ther reputatonal concerns. Ths decson-bas effect s dfferent from the bas toard the expected shon n Ottavan and Sørensen 006, also present n our artcle. It occurs because the more nformed appeals strategy of certfed layers reveals better nformaton about the competency of the judge. Incompetent judges then bas ther decsons n favor of certfed layers n order to mnmze the rsk of appeals from certfed layers and thus the nference about ther ablty. An mportant mplcaton of ths decson bas s that, although hgher qualty of layers ncreases elfare, publc nformaton over qualty may be elfare reducng. The qualty of layers mproves the accuracy of the decson by to mechansms. Frst, hgh-qualty layers provde better-qualty evdence. Second, hgh-qualty layers lead to more effcent appeals. Both these Also, reputable judges often take prestgous and ell-pad postons upon retrement from the judcals. It s not unusual, for example, for retred judges to become arbtrators n commercal dsputes or nternatonal transactons. C RAND 0.

3 IOSSA AND JULLIEN / 679 effects ncrease elfare. Instead, nformaton over qualty generates a tradeoff. On the one hand, t mproves matchng: n equlbrum, lo-qualty layers are hred n lo-value cases and receve a basc age, hereas hgh-qualty layers are hred n hgh-value cases and receve a hgh age. Ths matchng effect s elfare ncreasng, as better legal outcomes are more valuable for hgh-value cases. On the other hand, publc nformaton over the qualty of legal representaton generates the decson bas, and ths causes msallocaton of layers at the market equlbrum: cases neffcently arse here only one ltgant hres a certfed layer. Under some condtons, the socal value of nformaton over the qualty of legal representaton can then be negatve. Furthermore, at the market equlbrum there s overdemand of qualty; the decson-bas effect exacerbates the prsoner s dlemma problem of any legal process and results n excessve fees for layers. 3 We also analyze the effect of qualty certfcaton on the ncentves of layers to tran and rase ther ablty. We sho that certfcaton helps to rase qualty n the market but that free certfcaton may lead to excessve nvestment by layers and excessve supply of certfed layers. Our results ratonalze the percepton descrbed by respondents to a consultaton paper ssued by the Department of Consttutonal Affars, 003 n the Unted Kngdom nvestgatng the desrablty of the QC system: There as a percepton that QCs ere no nstructed n crcumstances here ther partcular sklls ere not really needed: for example because t mght be thought that judges ould pay more attenton to a QC s argument, or because a smple equalty of arms as needed just because the other sde had already nstructed a QC. The ncentves to pay more attenton to a QC s argument can thus be seen as reflectng the ncentve of less competent judges to favor ltgants represented by a QC. 4 In the second part of the artcle, e extend the model to allo for the possblty that hghqualty layers are able to nfluence the tral outcome, by rasng the chance of fndng evdence favorable to ther case. In partcular, e assume that certfed layers generate false postves,.e., they may be able to obtan favorable evdence hen the state of the orld s unfavorable. We sho that the decson-bas effect stll arses and that the man qualtatve nsghts of the basc model contnue to hold at the market equlbrum. We also check the robustness of our results. The artcle s organzed as follos. In Secton, e reve the related lterature. Secton 3 presents the basc model; Sectons 4 and 5 dscuss the decson-makng behavor of the judge and the outcome of the decson process thout and th an appeals system. Secton 6 studes the propertes of the market for layers and thus the ncentves to hre a certfed layer, and the equlbrum fees. Secton 7 focuses on the elfare analyss, lookng at the prvate and socal value of qualty of legal servces and of certfcaton and the ncentves of layers to tran and rase ther qualty. Secton 8 dscusses the extensons on uncertan appeals and nfluence and Secton 9 concludes. All proofs mssng from the text are n the Appendx.. Related lterature The legal lterature has long debated the mpact of layers capabltes n adjudcaton e.g., Galanter, 974. Consensus and evdence have been gathered on ho legal representaton makes for a sgnfcant dfference both n the lkelhood of recovery and n the amount recovered e.g., Ross, 970. A number of emprcal artcles have then analyzed the dynamcs of the market for layers and quantfed the reards from tranng and specalzaton Sauer, 998; Rosen, 99; and Pashgan, 977; Garcano and Hubbard, 009b. The theoretcal lterature on the value and 3 The presence of a prsoner s dlemma n ltgaton as frst ponted out by Ashenfelter and Bloom The QC system as also heavly crtczed for the potental for dscrmnaton due to a nontransparent selecton process based on secret soundngs thn legal crcles. Even hen the appontment system as reveed, the QC system contnued to be crtczed. Although t ould be nterestng to take the selecton process nto account, t ould be too cumbersome to do t here and t ould also add lttle to the present analyss, hch proves the potental unsutablty of the system even hen selecton s not a problem. C RAND 0.

4 680 / THE RAND JOURNAL OF ECONOMICS qualty of legal representaton, hoever, remans slm see Cooter and Rubnfeld, 989; Sper, 007; Shavell, 006 for a general dscusson on the economcs of ltgaton. Layers can affect the probablty of nnng through ther tral effort Hrshlefer and Osborne, 00 or through ther nformaton gatherng Deatrpont and Trole, 999. They may then effcently nform the court Bundy and Elhauge, 99 or mslead t Kaplo and Shavell 989. Layers advce may also have no effect on adjudcaton n a broad set of crcumstances Che and Severnov, 006. Our contrbuton to ths lterature s tofold. Frst, e derve the value of legal representaton endogenously, from the nteracton beteen ltgants, layers, and judges, thn the market mechansm, focusng on the role played by the reputatonal concerns of judges. 5 Second, e analyze ho nformaton on the qualty of legal representaton affects the functonng of the market for layers, and thus derve polcy mplcatons on the desrablty of a system of qualty certfcaton. Our artcle s also related to the lterature on careerst decson makers, such as regulators, managers, and experts, ho try to prove ther ablty to make the correct decson. 6 Reputatonal concerns may nduce experts to conform to some expected behavor and dsregard valuable nformaton e.g., El and Välmäk, 003, or nduce arbtrators to bas ther decsons n favor of long-term players hen these have based prors Iossa, 007. Transparency over decsons may then be detrmental hen t rases an agent s ncentves to conform to some expected behavor e.g., Prat, 005, but t ll be optmal f the expert has knon bas n favor of a partcular decson Bourjade and Jullen, 0. Career concerns may also nduce experts to msreport ther nformaton Ottavan and Sørensen, 006 or to bas ther decsons to be more revealng or more concealng of ther expertse Holmström, 999. So, for example, n Levy 005, careerst judges contradct precedents too often n order to sgnal ther ablty, hereas n Leaver 009, less able bureaucrats use soft polces to keep nterest groups quet and mstakes out of the publc eye. Our artcle s the frst to derve the demand for decson-makng expertse and the mplcatons of the reputatonal concerns on the effcency of the equlbrum n the market for experts. We also derve the nformatveness of a decson endogenously from the behavor of the nformed or unnformed party.e., her appeal strategy The base model The general settng. We consder a settng here hgh-qualty layers hold a qualfcaton to certfy that ther qualty s above a certan threshold. There s a mass of dsputes. For smplcty, e treat the occurrence of a dspute as an exogenous event and e model a dspute as a dsagreement beteen to partes, P and P, over the realzaton of a state of the orld θ. There are to states, θ =,, and t s common knoledge that Prθ = = q. We shall refer to q as the qualty of the case and assume that P has a eakly better case: q q. A dspute s resolved through an ntal stage here layers hred by partes generate and send sgnals facts to a loer-court judge ho makes an ntal decson and, f the losng ltgant appeals, an appeals stage here the appeals court makes a fnal decson. Once generated, a sgnal needs to be nterpreted to obtan relevant nformaton. The general structure of the game, hch e explan n detal belo, s the follong. Dsputes arse and states of the orld θ are realzed. The ltgants sequentally choose hether to hre a certfed layer or an uncertfed layer P chooses frst. 5 There s, of course, an extensve lterature on the role of nformaton and certfcaton for consumpton goods and servces. References nclude, among others, Shapro 986, Bglaser 993, and Lzzer 999. These papers focus on ncentves and asymmetrc nformaton ssues. We abstract from these ssues and focus on the nteracton beteen the partes on a case and the behavor of the judge. 6 See Bar-Isaac and Tadels 008 for a reve of the lterature on the reputatonal model. 7 Shavell 004 and Iossa and Palumbo 007 dscuss n depth the role of appeals as montorng mechansms of adjudcators, although n ther models there are no reputatonal concerns. C RAND 0.

5 IOSSA AND JULLIEN / 68 Each layer generates a sgnal and sends t to the loer-court judge. The sgnals transmtted are observed by the to layers and by the judge. The judge makes a decson based on hs nterpretaton of the sgnals. v The losng party decdes hether to appeal the judge s decson based on hs layer s nterpretaton of the sgnals. v In the event of an appeal, the appeals court observes the state of the orld and makes the fnal decson. We denote by d the decson of the loer-court judge and by D the outcome of the appeals process. We assume that there are only to possble decsons, d {, }. A decson d = makes P n the case and t s the most approprate n state θ =. We denote by D = 0 the case here there are no appeals, hereas D {, } prevals n the case of appeals. The layers. There s a mass of layers ho may ork for ltgants on a dspute or on some alternatve actvtes leadng to an expected utlty normalzed to zero. The mass s large enough for all ltgants to obtan legal representaton. Layers may be of to types, certfed or uncertfed, th a mass S < of certfed layers. We endogenze S n Secton 7, here e consder the ncentves of layers to become certfed. We denote by h for hgh the type of the certfed layer and by l for lo the type of an uncertfed layer. Certfed layers are of better qualty than uncertfed layers. Frst, they receve a more nformatve sgnal about the state of the orld. In partcular, e assume that a layer of P generates a sgnal s {, 0}, here s = s a perfectly nformatve sgnal that θ =. Instead, s = 0 s bad nes about θ =. A certfed layer fnds a favorable sgnal s = th probablty f θ =. An uncertfed layer fnds a favorable sgnal s = th probablty ν f θ =, hereas th complementary probabltes he fnds s = 0. Both types of layer fnd s = 0 th probablty f the state s θ = j. In other ords, hen the state s favorable, a certfed layer dscovers t hereas an uncertfed layer generates a false negatve th probablty ν. When nstead the state s θ = j, the layer of P fnds no favorable evdence that θ = rrespectve of hs type. 8 In our model, generatng evdence dffers from nterpretng the avalable evdence n the lght of legal prncples. Faced th a sgnal s, an agent ho s able to nterpret t knos hether s = or s = 0. An agent ho s unable to nterpret the evdence only knos s {, 0}. For nstance, the evdence could be a past decson and the layer lacks the legal knoledge to assess hether t s relevant or not for the current case. Or the evdence could be an expert report and the layer could be unable to assess ts credblty. Certfed layers are also better able at nterpretng. To smplfy, although ths has no mpact on our results, e assume that a certfed layer can perfectly nterpret the meanng of ther sgnal hereas an uncertfed layer cannot nterpret t at all. 9 Notce that e assume that all sgnals are transmtted, even hen the layer cannot nterpret t. 0 Ths s the case f sendng the sgnal s, hch s favorable th some probablty, s better than sendng no sgnal, because a meanngless sgnal ould be nterpreted by the judge as bad nes. We dscuss ths pont n the benchmark secton and notce here that t s consstent th the ve that legal representaton mples communcaton th the judge. 8 In the orkng paper Iossa and Jullen 00, e alloed for more qualty levels by assumng that certfed layers observe the state of the orld th probablty r > 0. Hgher r captured hgher qualty. Results ere qualtatvely the same, becomng sharper th hgher values of r. Notce that there s no loss of generalty n restrctng attenton to only to types of layers, because the analyss of cases apples to any par of layers. The demand for layers ould be more complex, hoever. 9 The analyss ould be smlar f the certfed layers ere only mperfectly able to nterpret the sgnals, and/or f the uncertfed layers had some nterpretaton ablty. It can be shon that hat matters s that the former has better ablty than the latter. 0 Settngs here nterested partes may fnd and msreport unfavorable nformaton have been extensvely analyzed n the lterature. See, for example, Mlgrom and Roberts 986. In the present context, ths ssue ould add lttle to our results hereas t ould complcate the analyss sgnfcantly. C RAND 0.

6 68 / THE RAND JOURNAL OF ECONOMICS In Secton 8, e extend the analyss to allo for the possblty that certfed layers alter the sgnal process n favor of ther clents by fndng false postves.e., by beng able to present favorable evdence hen the state of the orld s unfavorable. We denote by 0 the salary of an uncertfed layer and by the salary of a certfed layer. 0 s exogenously gven by the productvty on some outsde opton. For smplcty, e set 0 = 0. The judge and the appeals court. Judges take ther decsons upon recevng nformaton sgnals by the partes and nterpretng t. They have no nformaton of ther on. There are to types of loer-court judges: the competent C and the ncompetent I. Type C perfectly nterprets the messages sent by the layers, hereas type I cannot nterpret them. Types are prvate nformaton, and e let denote the proporton of competent judges. The model can be generalzed to contnuous types. For concseness, e ll assume throughout that q <, q q hch ll avod corner equlbra here one decson s taken th probablty one by the ncompetent judge and smplfy the formulas. The judge has reputatonal concerns n the sense that he shes to appear competent to an evaluator E, hs payoff beng equal to the posteror belef PrC. held by E about hs competency. We assume that the appeals court comprses only hghly competent judges ho observe θ and take the correct decson D = θ the term correct decson ll hereafter be used to denote the decson that the appeals court ould take. 3 Ths allos us to focus our attenton on the reputatonal concerns of loer-court judges hereafter smply referred to as the judge and the nterplay beteen judges competency and nformaton on layer qualty. We extend the analyss to allo for mstakes n appeals n Secton 8. The ltgants. The ltgants n a dspute also referred to as partes, P and P, obtan a zero payoff hen losng the case and a payoff V hen nnng t. The value V vares across dsputes and has a cumulatve dstrbuton functon FV. 4 Upon observng the judge s decson d, the party ho loses the dspute can choose to appeal the decson. Ths party then ncurs costs Ā.V for the appeal. 5 We assume that > Ā > q, hch s suffcent to ensure that an uncertfed layer never appeals and a certfed layer appeals f and only f he knos that the decson s not correct. Ā s publc nformaton. We extend the analyss to the case of uncertan appeals n Secton 8. The ltgants sequentally choose hether to hre a certfed layer at salary or an uncertfed layer at salary 0. Sequentalty s nnocuous and avods mrror equlbra n our model. Further, n practce, the game s ndeed sequental, th the plantff ntatng the case. We assume for concseness that P chooses frst, and then P chooses. As explaned n Secton 6, In a prevous verson, Iossa and Jullen 00, e also consdered the case of corner solutons. Results ere qualtatvely smlar to the one presented here. Notce that e assume that the judge does not care about hs decson d beng correct. The analyss ould extend th some altrusm n the judge s preferences. 3 Our results hold, provded that the appeals court comprses judges ho are suffcently more competent than loer-court ones. In practce, hgher courts comprse more experenced judges or panels of judges to ensure better decson makng. The hgher cost of appeals courts explans hy loer courts exst. 4 In a prevous verson, Iossa and Jullen 00, e also consder the case here there s a prvate bonus attached to nnng n the correct state. Results are qualtatvely smlar to the ones presented n the present verson. 5 Our results ould contnue to hold f e assumed that appeals costs ere hgher for certfed layers or that they are borne by both partes. See footnotes 8 and. C RAND 0.

7 IOSSA AND JULLIEN / 683 the reverse tmng leads to the same aggregate demand and a smlar elfare analyss. In order to focus on the value of legal representaton, e assume aay agency problems beteen layers and ther clents: the hred layer acts n the best nterest of hs clent and ths s publc nformaton. We further assume that ltgants are ntally unnformed about θ, thus rulng out the possblty that they attempt to sgnal ther on nformaton to the judge through ther choce of layer. 6 The reputaton. The reputaton of the judge s captured by the posteror probablty that he s competent based on the observaton of the decsons d and D, hether the layers of the partes n the dspute are certfed or not and hether they appeal. The sgnals sent by layers are excluded from the nformaton set used to derve the reputaton. 7 The equlbrum concept. We use the concept of sequental equlbrum to solve the model. Belefs are derved from players equlbrum strateges and the strateges are ratonal gven those belefs. As a smplfyng assumpton, e shall restrct attenton to equlbra such that C chooses the correct decson d c = hen he sees a sgnal s = ; and the decson of the judge depends only on hs belefs about θ. The frst assumpton rules out trval equlbra here the judge alays chooses the same decson d = and the decson d ould be nterpreted as ncompetency. The second one reflects the fact that at decson stage, hs belefs about θ are the only payoff-relevant nformaton for a judge. Equlbra satsfyng the to condtons alays exst. 4. Benchmark: the judcal game thout appeals Consder the benchmark here there s no possblty of appeals. Here, t s never ascertaned hether the decson of the judge n the loer court as correct or not; the judge s type can only be nferred from hs decson. The dfference beteen C and I s that C may learn the state of the orld from the sgnals transmtted by the layers, hereas I, beng unable to nterpret the nformaton, alays remans unnformed. In partcular, f no layer s certfed case ll, C learns the state hen one sgnal s favorable, s =, hereas he learns nothng from the sgnals f s = s = 0. If, nstead, at least one layer s certfed cases hl, hh, the sgnal of ths layer s perfectly nformatve about the state of the orld for C, so C s alays nformed. Suppose that, hen nformed, C takes the correct decson, that s, he takes the decson d = hen he sees s =.When unnformed, C s n all respects lke I, and they behave n the same ay. To smplfy the exposton, from no onard e refer to C as the nformed competent judge and to I as both the ncompetent judge and the unnformed competent one. We let z be the probablty that the judge chooses d = hen he s unnformed and thus holds belefs q. Usng Bayes rule, the expected payoff of I hen he chooses d = s gven by q ν + νz PrC d = = for =,, n case ll q ν + νz + z 3 q PrC d = = for =,, n case hl or hh. q + z Because decsons are never verfed, the only nontrval equlbra are such that the judge s ndfferent beteen the to decsons. Indfference then requres that the reputaton s the same for both decsons, hch occurs hen I mmcs the behavor of C by randomzng n the same proporton. 6 For a model that analyzes hether partes mght strategcally spend resources so as to sgnal ther postve belef about the correctness of ther case, see Daughety and Renganum Ths reflects the ve that the reputatonal concerns of the judges are th respect to the legal communty, or the legal body n charge of the promoton process or even the meda, hch does not observe all detals of the cases. C RAND 0.

8 684 / THE RAND JOURNAL OF ECONOMICS Lemma. Wth no appeals, the nformed competent judge chooses d = θ; the ncompetent judge chooses d = th probablty z = q. Proof. Recall that e focus on d = θ for C. Suppose that z =. Then a decson d perfectly q reveals that the judge s competent and, because q <, I has an ncentve to devate. Thus, + the equlbrum s n mxed strategy, hch requres that PrC d = = PrC d =. Usng 3, e obtan z = q. Q.E.D. In the absence of an appeals system, the state s never revealed; hether the judge s decson s correct or not s therefore never ascertaned. The reputaton attached to a decson d = must therefore be the same as the reputaton attached to a decson d =. Ths n turn requres I to choose d = th the same frequency as C, that s, th a probablty of q. If I ere to choose d = th probablty hgher than q, the updatng of belefs ould assgn a loer reputaton to a decson d = than to a decson d. Ths ould generate an ncentve for I to devate to d. Reputatonal concerns nduce I to mmc the behavor of C. Remark. Sgnal transmsson We have assumed that all sgnals are transmtted. We note here that t s ndeed an equlbrum behavor under the follong scenaro. Suppose that the judge expects the transmsson of nformaton and chooses d = th probablty q f unnformed as above. Let us nterpret no transmsson as an empty sgnal s =. There are to possble games e can consder. A frst possblty s that s = cannot be dstngushed from s = 0. Then, C ould react to s = as to s = 0 hereas I ould not react. Clearly, transmttng s an optmal strategy n ths case, because transmttng s {0, } s eakly better than transmttng s = 0 all the tme. The second possblty s that s = s observable by the judge. Then, no transmsson ould trgger some out-of-equlbrum-path reacton by the judge. Thus, t s suffcent that ths reacton s unfavorable to the party not transmttng for the equlbrum th transmsson to exst. A smple equlbrum behavor s d = j f does not transmt. Another smple possblty s that C reacts to s = as f s = 0 and I s reacton s Prd = q. 5. The judcal game th an appeals court Let us suppose no that appeals are possble and derve the behavor of the judge, gven the choce of the partes as to hether to hre a certfed layer. Dsputes th no certfed layers. The above analyss stll apples f both partes hre an uncertfed layer. In ths case, hen P observes a decson d = j, he antcpates that the probablty of reversng the decson on appeal s gven by Prθ = j d = = q j PrC, s = s = 0 d = + q j PrI d =, hch s strctly loer than q j and thus than Ā. Therefore, there s no appeal and the equlbrum s the same as n Lemma. Because the state s never ascertaned, reputatonal concerns only depend on the decson taken. Ths nduces I to mmc the behavor of C and choose d = th the same frequency. Dsputes th one certfed layer. We consder frst a dspute here P hres a certfed layer and Pj hres a noncertfed layer. As ponted out above, as C can alays nfer the state θ from the evdence shon by the certfed layer or the lack of evdence, he s fully nformed. Consder the follong strateges for the judge: C chooses the correct decson d c = θ. I randomzes beteen d = and d =, choosng d = th probablty z. It can easly be proven that ths strategy consttutes the optmal strategy for C. For concseness, e focus here on I. C RAND 0.

9 IOSSA AND JULLIEN / 685 Because I s unnformed and he shes to appear competent, he ll arbtrage beteen the reputaton effect n the case of no appeal and the rsk that hs decson s reversed on appeal, takng nto account the ncentves of the ltgants to appeal. The appeals strateges of the to layers thus play an mportant role n determnng the ncentves of I. The certfed layer, nterpretng the sgnals, knos θ. He appeals d = j hen he has favorable evdence and only n ths case. The uncertfed layer, beng unnformed, has belef facng d =, gven by Prθ = j d = = q j PrI d = < Ā. Therefore, he does not appeal. Thus, the only case of appeal occurs hen the certfed layer observes that the judge took the decson j and s =. Follong an appeal, the expected posteror probablty that the judge s competent s π. In the case here z j > 0, accordng to Baye s rule, an appeal reveals to E that the judge s ncompetent because d c =, leadng to a zero reputaton π = 0. Otherse, π s arbtrary. On the other hand, choosng d = j and facng no appeal s good nes. In ths case, the decson s knon to be correct and the reputaton s PrC d = j, no appeal = The expected payoff of I hen he chooses d = j s gven by μd = j = q π + q j + z. 4 Choosng d =, on the other hand, ensures that there ll be no appeal and a payoff gven by q μd = = PrC d = =. 5 q + z. + z Under condton, the equlbrum nvolves a mxed strategy z j > 0 and π = 0, hch leads to the follong proposton. Proposton. When party P hres a certfed layer and Pj does not, n equlbrum the competent judge chooses d = th probablty q, hereas the ncompetent judge chooses d = th unque probablty z hl, here q < z hl <. Proof. An equlbrum th 0 < z hl < requres q j + q =. 6 z hl q + z hl q The LHS ncreases th z from q j to q j, hereas the RHS decreases from to. A q + mxed-strategy equlbrum then exsts f q q + < q j, hch holds for = and = under condton because q q. Then, z solves 6a and s gven by z hl = q q j > q. 7 q q + If condton s volated, the equlbrum has z =, hch requres that q j π + q j =. Ths defnes a unque π<. Q.E.D. Proposton hghlghts the presence of a decson bas that arses from the nteracton beteen the reputatonal concerns of judges, the appeals system, and the publc nature of the qualty mark. Whereas C alays takes the correct decson, I bases hs decson n favor of the party th the certfed layer. Intutvely, the appeals strategy of a certfed layer depends on the underlyng state θ, and thus reveals better nformaton about the correctness of the judge s decson than the appeals strategy or lack of appeals of the unnformed layer. Ths s mportant, because reputatonal concerns exhbt some knd of rsk averson, n the sense that C RAND 0. PrC d = > q PrC d =,θ = + q PrC d =,θ.

10 686 / THE RAND JOURNAL OF ECONOMICS That s, I, ceters parbus, prefers to play safer and choose a decson hose correctness s never ascertaned rather than a decson that yelds a reputatonal gan hen found correct but a loss hen found rong. Ths makes I prefer a decson n favor of the certfed layer. To reestablsh ndfference, the reputatonal gan from choosng n favor of the uncertfed layer must ncrease. Ths s only possble f I chooses ths decson th loer frequency than C, hch underles the asymmetrc behavor of the judge. The corollary belo hghlghts the mplcaton of an ncrease n the expected competency of the judge and n the qualty of the case. Corollary. When P hres a certfed layer and Pj does not, the relatve decson bas z hl q /q s strctly postve, ncreasng n the probablty that the judge s competent, and n the qualty q of the case. Proof. From equaton 7, hch gves the result. z hl q q = q, Q.E.D. The relatve bas ncreases up to the pont here I alays announces the decson favorable to the certfed layer z hl = f condton s volated. When I plays safe by rulng n favor of the party th the certfed layer, hs type ll not be revealed. When he rules aganst ths party, nstead, he may be revealed as ncompetent but, f he turns out to be correct, hs reard ll be hgher. The relatve bas then determnes the value of the safe choce as the reputaton assocated th d = decreases th z hl /q. When q ncreases, the bet on the party th the uncertfed layer becomes less attractve, hch has to be compensated by a reducton of the reputaton th the safe decson. Smlarly, hen ncreases, the safe decson d = becomes relatvely more attractve, as t s more lkely to be generated by C. Ths must be compensated by an ncrease n the relatve lkelhood of choosng ths acton for I so as to preserve ndfference. Dsputes th to certfed layers. Suppose no that both partes hre a certfed layer. Both sdes may appeal a rong decson, so that the type of the judge s more lkely to be revealed through the appeal. Wth to certfed layers, the state s alays revealed: the appeals process alays reveals hether the decson s correct or not. In our settng, ths creates a decson bas n favor of P henever q > q. Proposton. Wth to certfed layers, the competent judge chooses d c = θ and the ncompetent judge chooses d = th probablty z hh. When q > q, there s a tendency for the ncompetent judge to conform n favor of the party th the better case: q < z hh < z hl and 0 < z hh < q. When q = q, so that cases are equally good, there s also no decson bas: z hh = q. Proof. The layer of P knos the sgnals and ll therefore appeal an ncorrect decson; no appeal ll sgnal that the decson s correct, hereas an appeal reveals that the judge s ncompetent, leadng to a zero reputaton. An equlbrum th 0 < z hh < musthave q = q + z hh, + z hh here C RAND 0. PrC d =, no appeal = + z.

11 IOSSA AND JULLIEN / 687 The equlbrum condton then gves Observe that Because by assumpton z hl q = /. z hh = q q j. q z hh = q q < q q q = z hl. <, t follos that zhh > 0. The equalty z hh = q holds at q = Q.E.D. Wth to certfed layers, I tends to favor the decson most lkely to be found correct. Ths fndng s remnscent of the expert s model of Ottavan and Sørensen 006. In ther settng, the state s alays revealed and an expert uncertan about the state of the orld shos a tendency to bas toard the expected. In our settng, th to certfed layers the state s also fully revealed, va the appeals system. Wth a zero payoff attached to a decson beng found ncorrect on appeal, ths mples that the expected reputatonal gan attached to a correct decson must be the same for d =,. If ths ere not the case, I ould devate to the decson yeldng a greater expected payoff. Wth q > q, e then obtan that the reputaton attached to a correct decson d = must be loer than the reputaton gan attached to a correct decson d =. Ths requres I to choose d = th hgher frequency than C, that s, th probablty greater than q. The bas dsappears f q = q, as n ths case C chooses d = th the same probablty as d =. Furthermore, ths bas s smaller than the one arsng th only one certfed layer. In both cases, the correctness of a decson d = s alays ascertaned, ether because the certfed layer of P appeals and reverses ths decson or because by not appealng he reveals that the decson s correct. Instead, the correctness of a decson d = s never ascertaned hen the layer of P s uncertfed and alays ascertaned hen he s certfed. Ceters parbus, choosng d = s therefore less rsky and more reardng for the judge hen there s only one certfed layer. Under the condton that I s ndfferent beteen d = and d =, t follos that the reputatonal gan attached to a decson d = found correct must be hgher n the settng th one certfed layer. Ths requres I to choose d = resp. d = th loer resp. hgher frequency hen there s one certfed layer than hen there are to. It should be apparent at ths stage that the hypothess that the uncertfed layer never appeals s nnocuous. Our qualtatve results ould hold provded that appeals costs are suffcently hgh that the uncertfed layers does not alays appeal. We come back to ths pont n the extenson on uncertan appeals n Secton The market for layers We no derve the demand for certfed layers, consderng the utlty of a ltgant n each possble scenaro. Because V s a scale factor, e focus on the probablty of nnng the case net of expected normalzed appeals cost, and e denote t by u. When nether party hres a certfed layer, the probablty that P ns s q and the normalzed utlty of a ltgant s u ll = q. 8 Compared to case ll, hrng a certfed layer hen the other party does not affects the legal outcome hen the judge s ncompetent, hch occurs th probablty. Then the chance for the party th the certfed layer, P, of obtanng a favorable decson n the loer court 8 Note that f appeals costs ere hgher for certfed layers, our results ould contnue to hold provded that the ncentves of certfed layers to appeal an ncorrect decson ere stronger than the ncentves to appeal of the unnformed uncertfed layers. C RAND 0.

12 688 / THE RAND JOURNAL OF ECONOMICS changes from q to q + q j z hl, as no cases ll also be on henever favored by the bas n state j. Furthermore, hen the loer court s decson s unfavorable, the certfed layer may dscover that the decson s ncorrect and appeal. The utlty of the party th the certfed layer s therefore u hl = q + q j z hl z hl q Ā. By contrast, the utlty of the party P th an uncertfed layer facng a certfed layer s u lh = q z hl j q. Wth to certfed layers, Proposton mples that the probablty that I chooses d = s z hh and the utlty of P s u hh = q z hh j q Ā. 9 Hrng a certfed layer hen the other sde has a certfed layer ensures that the decson s alays correct. Hoever, the appeals cost must be borne henever I s decson s ncorrect, hch occurs hen the state s.e., th probablty q buti chooses d = j hch occurs th probablty z hh j. To derve the demand for certfed layers, e then defne l u hl u ll and h u hh u lh. Thus, h and l capture, respectvely, the gan for a party from hrng a certfed layer hen the other party has a certfed layer and hen she does not. The gan for a ltgant from hrng a certfed layer s tofold: t stems from the decson-bas effect and from more nformed appeals. By hrng a certfed layer hen the opponent does not, a party gans a decson bas n her favor; hen the other party also has a certfed layer, the party gans that no decson bas aganst her ll arse. Also, a certfed layer dscovers and appeals ncorrect decsons more often than an uncertfed layer. It s easy to sho that l = q j z hl z hl q Ā 0 h q z hl j q z hh j Ā 0 > 0. Takng nto account the equlbrum values of z hl, t can be shon 9 that l l and h h. Hrng a certfed layer s more valuable for the party th the better case, as the bas ncreases th the qualty of the case Corollary. The party th the better case then benefts from a stronger ncrease n the nnng probablty and loer expected appeals costs as she ll appeal less often. We also have l > h.0 Ths s because the costs of appeals are borne less often hen the rval s layer s uncertfed, that s, hen favored by the bas than hen on equal footng th the compettor. Ths makes t, ceters parbus, more valuable to hre a certfed layer hen the other party does not have one. For a gven age, a party P s llng to hre a certfed layer henever V k, here k refers to the behavor of the other party. No let us defne l = l >h = h. Thus, h V s the hghest age at hch both partes are llng to hre a certfed layer, and l V s the hghest age at hch at least one party s llng to hre a certfed layer. 9 We have l l = q q Ā q q Ā + q q and h h = q q Ā q q. 0 We have l h = q q j q j + q Ā, hch s larger than q q j q j because Ā > q. C RAND 0.

13 IOSSA AND JULLIEN / 689 Lemma. For a gven age, the demand for certfed layers s characterzed as follos. f V >, both sdes hre a certfed layer; h f > V, only P hres a certfed layer; h l f > V, no sde hres a certfed layer. l Proof. Suppose <V h. Then, P chooses h because V l > V h >.The frst mover chooses h because t prefers to pay to nduce h, h nstead of l, h. Suppose >V l ; then, the second mover alays chooses l. The frst mover then prefers l as Vu ll > Vu hl. Suppose no that V l >>V h. The second mover P chooses l f the frst mover chooses h. The frst mover P chooses h because he prefers a stuaton here he s the sole one th the certfed layer to any stuaton here he has an uncertfed layer: <V l = V u hl ull < V u hl. Q.E.D. ulh Publc nformaton over the qualty of legal servce generates a matchng effect. Ltgants to a dspute form dfferent pools based on the amounts at stake: ceters parbus, those th hgh-value cases hre hgh-qualty layers and pay a hgh salary, hereas those th lo-value cases hre lo-qualty layers and pay a lo salary. For ntermedate values of, only one party hres the certfed layer. Whch party depends on the context, but under the assumpton that P moves frst, he ll choose to hre the layer. The emergence of an asymmetrc allocaton of layers stems n our model from the decsonbas effect, hch makes the value of a certfed layer larger f the other sde has none, l > h. If z hl ere equal to q for =,, as hen there s no bas, then e ould have l = h. In the lght of Lemma, the aggregate demand for certfed layers s equal to D = F F h l. Proposton 3. There exsts a unque and postve equlbrum salary. It s decreasng th the cost of appeal Ā. For q not too large or Ā large enough, t s ncreasng th. At the market equlbrum, demand D equals supply S. The equlbrum age decreases th the cost of appeals, as t s borne only th a certfed layer. For a gven age, the mass of cases th at least one certfed layer ncreases hen the lkelhood of facng a competent judge ncreases. Notce that the benefts of hrng a certfed layer s to create or correct for a bas. Ths s because the party does not care about hen t ns but only about nnng, and the better qualty of the evdence provded by the layer affects the qualty of the decson but not ts probablty dstrbuton. The cost s the age plus the expected appeals cost. Increasng judges average competency reduces both the expected benefts from the bas and the expected appeals cost for the frst certfed layer on the case, but the latter effect domnates rasng the value of the frst layer. For the second layer, hoever, the effects are reversed and the comparson s ambguous. But at least for Ā > q /q, ncreasng rases the value of the certfed layers at all margns margnal cases th one certfed layer and margnal cases th to certfed layers. Remark. Reverse tmng When P chooses the layer frst and q < q, a slght dfference arses n the demand for layers. Consderng Lemma, cases and are unchanged. Also, only one party hres a certfed layer n case. But the dentty of the party hrng the certfed layer depends on the sgn of V / h remember that /l </ h /h. When / l < V </ h, the party hrng the certfed layer s P and not P. To see ths, notce that n ths range P ould hre a certfed layer only f P does not. Moreover u hl V ulh V >l V >0, mplyng that P prefers to be the one hrng a certfed To see ths, notce that f z hl = q for =,, then l = h. Should appeals costs B < Ā be borne by the party facng an appeal, results ould be renforced. One can easly check that l ould reman unchanged hereas h ould decrease, because z hh > z hl makes u hh decrease faster th B than u lh. Thus, l h ould reman postve. C RAND 0.

14 690 / THE RAND JOURNAL OF ECONOMICS layer. For V above / h, P hres a certfed layer n any case and, as long as V </h, P prefers not to do t. Intutvely, ths holds because hrng a certfed layer s more valuable for the party th the better case.e., P, as explaned above, and for the party movng frst because l > h. So hen P moves frst, n equlbrum t may happen that she ll have stronger ncentves to hre the certfed layer than P. Notce that the aggregate demand s unchanged and the equlbrum prce does not depend on the tmng. The elfare analyss that follos ould be smlar, adjustng the formulas for the dentty of the party hrng the certfed layer e ll pont to mnor dfferences here they arse. 7. Welfare analyss The value of qualty. In the prevous secton, e have derved the gan for a ltgant from hrng a certfed layer, gven the choce of the other ltgant. In the corollary belo e fnd, hoever, that, hen t s calculated at the equlbrum, the value of qualty for the partes s negatve. Corollary. For V / h, each party obtans u hh V <u ll V. For V / l,/ h, party P obtans u hlv >ull V and the other party obtans ulh V < ullv. Moreover, V > V u hl + ulh >V uhh + u hh. Proof. Immedate, except for the last pont that follos from u hl + ulh = z hl q Ā u hh + u hh = z hhq + z hhq Ā, hch mples u hh + u hh < u hl + ulh as zhh > z hl. Q.E.D. There s a prsoner s dlemma problem for hgh V : the ltgants ould be better off f they each hred an uncertfed layer. Intutvely, each party has an ncentve to pay a hgher salary to hre a certfed layer n order to obtan a decson bas n her favor or correct one n her dsfavor. In equlbrum, both partes hre a certfed layer and pay the addtonal cost but obtan no decson bas. The effects of hrng a certfed layer are then reduced to creatng an appeals cost. Notce that the result s due to the fact that ltgants attach no value to a correct decson, hch ould be the case f the correct decson ere creatng ex post effcency gans. Typcally, socety ll care about the correct decson beng taken. As ponted out by Shavell 997, there s a dvergence beteen prvate and socal motves to use the legal system. When a party makes a ltgaton decson, she does not take nto account the legal costs that she nduces the opponent to ncur a negatve externalty, nor does she recognze assocated effects on deterrence and other socal benefts a postve externalty. Consequently, the prvately determned level of ltgaton can ether be socally excessve or nadequate. We assume, as seems reasonable, that the socal beneft of a correct decson ncreases th the value of the dspute V: a dspute beteen to frms over a patent orth $ bllon ll, ceters parbus, be more relevant from a socal perspectve than a dspute beteen to neghbors over parkng spaces orth $0,000. Let λv be the socal value of a correct decson. 3 The benefts from reversng a decson d θ to D = θ through appeals s λ Ā, hch e assume to be postve λ>ā. Ths mples that appeals costs are alays orth ncurrng for socety f the appeal leads to the correct decson. Ths seems reasonable, as otherse t ould be optmal not to have an 3 λ can also capture the ex ante value for contractual partes of better enforcement of contractual terms see Anderln, Fell, and Postlelate, 007, for a dscusson of the role of court decsons n ex ante ncentves. C RAND 0.

15 IOSSA AND JULLIEN / 69 appeals system. Then, the normalzed socal value from the judcal procedure s ωv, th ω = [PrD = θ + Prd = θ, D = 0]λ EA, here EA s the expected cost borne by the partes for appeals. In ths functon, e gnore the utlty of the judge and more generally the socal value of the nformaton generated on the judge. 4 The socal elfare s then = ω ll l 0 VdFV + ω hl h l VdF V + ω hh VdFV, 3 h here ω ll denotes the value of ω for cases here no ltgants hre uncertfed layers, and so on. A frst result s that qualty s valuable for socety, as follos. Proposton 4. The socal elfare s hgher f there are certfed layers than f all layers are of lo qualty. Intutvely, the qualty of layers s relevant, because t mproves the accuracy of the decson by to mechansms. Frst, hgh-qualty layers provde better-qualty evdence. Second, hghqualty layers correct rong decsons of ncompetent judges by appealng. Wth λ>ā, both effects mprove socal elfare, and hence hgh-qualty layers have postve socal value. 5 The socal value of qualty certfcaton. Although the qualty of layers has a postve mpact on elfare, ths does not mean that certfcaton leads to an effcent allocaton. In ths secton e sho that, for a gven supply of hgh-qualty layers, nformaton over qualty may be elfare reducng. The frst queston s hether certfcaton nduces a frst-best allocaton of layers. Proposton 5. The equlbrum allocaton nvolves too many cases th only one certfed layer and too fe cases th to certfed layers f ν<q Ā q q Ā + λ q q λ. 4 Certfcaton does not nduce a frst-best allocaton of layers, because the decson bas makes l > h and rases the mass of dsputes th only one certfed layer Lemma. Consder to cases th value V > V each th one certfed layer. The elfare s ω hl V + ω hl V. Suppose e allocate the to certfed layers to the case V so as to obtan ω ll V + ω hh V. We prove n the Appendx that under condton 4, V ω hh ω hl > V ω hl ω ll > 0, hch mples that the elfare s hgher hen both layers are on the same case. 6 Welfare ould be maxmzed by allocatng layers on the hghest-value case, hch ould occur f there ere no decson bas and l ere equal to h from expresson 0. Condton 4 holds f the qualty of any layer s not too small ν small, provded that cases are not too favorable to one party q q small or that the socal value λ of a correct decson s large compared to the cost of appeals. Then, n contrast th hat e have seen for the prvate value of qualty to a ltgant Lemma, from a socal pont of ve the margnal value of havng a certfed layer s hgher hen the other party also has a certfed layer than hen she does not. Ths stems from the value of appeals beng negatve for prvate partes but postve for socety Ā < 0 <λ Ā and from the decson bas reducng the socal value of a 4 Notce that n our model the judge s preferences are lnear n posteror belefs on hs ablty, so that hs ex ante expected utlty s ndependent of the equlbrum and equal to. A value of the nformaton on the judge could be accounted for by ncorporatng a component κπconvexnπ. 5 If P chooses the layer frst, the result has to be qualfed, because hen only P hres a certfed layer, the lkelhood that I takes the rong decson s larger than th no certfed layer. But t holds f q q s small and/or ν and λ Ā are not too small. 6 When P chooses frst, the condton s ν<mn q Ā q q j + Ā. λ qq λ C RAND 0.

16 69 / THE RAND JOURNAL OF ECONOMICS unque certfed layer by loerng the lkelhood that the layer s nformaton ll be used n the appeals process. 7 To study the effect of matchng and bases on the socal value of certfcaton, consder the allocaton that s obtaned f judges have no bas and layers are randomly allocated across cases. By ths e mean that unnformed judges choose d = th probablty q and that each party has a probablty S/ to be represented by a hgh-qualty layer. 8 Thus, a fracton S of cases have no certfed layers, a fracton SS of cases have only 4 one certfed layer, and the remanng fracton of cases have to certfed layers. The elfare n the absence of a system of certfcaton s then gven by S = ω ll + S S S V 4 4 ωhh + ω hl VdF V, 5 0 here ω hh and ω hl denote the socal value for cases th, respectvely, to and one certfed layers on the case but no decson bas, that s, here z hh = z hl = q. By decomposng the elfare under certfcaton gven by n expresson 3, the matchng effect and the decson-bas effect can be measured, respectvely, by m and db, here m = ω ll l 0 VdFV + ω hl h l VdFV + ω hh db = ω hl ω hl h VdFV + ω hh ω hh l and = m + db. VdFV, h VdFV, h Proposton 6. Suppose that q s close to / and ν s small. Then, the matchng effect that arses under a system of qualty certfcaton ncreases socal elfare, that s, m >0, hereas the decson-bas effect reduces t, that s, db < 0. Thus, the matchng effect that arses under a system of qualty certfcaton ncreases socal elfare f uncertfed layers are of suffcent qualty, hereas the decson-bas effect reduces t for q not too large or for ν small enough. Informaton on the qualty of legal servces generates a tradeoff. On the one hand, t affects the allocaton of layers by nducng hgh-qualty layers to serve clents th hgh-value cases. Ceters parbus, ths matchng effect s elfare enhancng because hgh-value cases are those here a correct decson s most valuable. On the other hand, a system of certfcaton creates a decson-bas effect that generates msallocaton of layers, reducng the lkelhood that the certfed layer s nformaton ll be used. When ths second effect prevals, a system of certfcaton reduces socal elfare. Ths s the case n the follong example. Corollary 3. Suppose that ν = 0, q = /, V s unformly dstrbuted on [ V, V ] here V s close to l S, and S s smaller but close to ; then the socal elfare ould be hgher th l h no nformaton on layers than th a system of certfcaton. The matchng effect decreases n ν, because the nformaton avalable to the judge hen layers are uncertfed s more precse the smaller s ν. The decson-bas effect s, nstead, unaffected by ν: th one certfed layer on the case, the nformaton from the uncertfed layer becomes useless to the judge. The value of certfcaton s therefore loer hen ν s smaller. Furthermore, under the condtons n the corollary, certfcaton results n only cases th one certfed layer, hch exacerbates the negatve mpact of the decson-bas effect on the effcency of the allocaton. Moreover, ths also mnmzes the beneft of the matchng effect: 7 Notce that hen a case nvolves only one certfed layer, socal elfare ould be maxmzed by nducng the ncompetent judge to be based aganst hm so as to nduce effcent use of nformaton. 8 Ths ould be the case f layers qualty ere not observable and there ere no appeals. C RAND 0.

17 IOSSA AND JULLIEN / 693 as all the layers are assgned to P, certfed layers are reallocated from P to lo-value cases. 9,30 Incentves to tran and the supply of layers. Suppose there s a tranng stage here layers choose hether to tran n order to rase ther ndvdual qualty. There s a test certfyng that qualty s hgh. Untraned layers have lo qualty. Rasng qualty from lo to hgh s costly. The cost of tranng s heterogeneous among layers, and e denote by Sc the mass of layers th a cost of tranng smaller than c. We assume that Sc s contnuous and ncreasng from 0 to on the real lne. Layers maxmze ther expected salary net of tranng cost. In our setup, ths mples that a layer ll ether tran and be certfed or ll not tran at all, n hch case hs qualty ll be lo. In ths settng, a system of certfcaton rases qualty by generatng an nvestment effect: t nduces layers to tran to rase ther salary from 0 to. In partcular, a layer chooses to tran f τ c 0, here τ s the prce of a certfcaton test. Then, the market equlbrum age solves D = S τ and the total number of certfed layers n the market s S τ. As layers antcpate that qualty certfcaton brngs hgher ncome, they have ncentves to make nvestments that enhance ther legal abltes. Because nvestment or equvalently certfcaton s costly, only the most capable layers obtan certfcaton and enjoy hgher equlbrum salares. Proposton 7. There exsts ˆλ such that there s an excessve supply of certfed layers hen τ = 0 free certfcaton f and only f λ<ˆλ. Moreover, ˆλ >Ā f ν q /3. Thus, for a gven certfcaton standard, henever the socal beneft of a correct decson s small, the number of layers ho choose to nvest n tranng s excessve compared to the socal optmum. The partes have here excessve ncentves to n, and hence excessve ncentves to hre certfed layers. 8. Extensons Our model has uncovered to potental bases n a judge s decson. One s due to a tendency to bas toard the expected that leads ncompetent judges to favor the party most lkely to n an appeal rulng n her favor at a frequency hgher than a competent judge. The second s a tendency to favor certfed layer. Ths second decson bas s a source of neffcences not only n the judcal outcome but also n the allocaton of layer, th too many cases th a sngle certfed layer. In ths extenson secton, e sh to study the robustness of our results on the decson bas n favor of talented layer. For ths purpose, e neutralze the frst bas by assumng that both partes are equally lkely to be correct, q = q = /. We then study the effect of uncertanty on appeal, and extend the proof-takng dmenson of qualty. 9 We have mplctly assumed that the nformaton about layers qualty that ltgants hold s the same as the one that judges hold. Although dfferences n practce may of course exst, t ould be dffcult to dentfy a general case. We note here, hoever, that the matchng effect depends on the nformaton avalable to ltgants, hereas the decson-bas effect depends on the nformaton avalable to the judge. Thus, the more respectvely less a certfcaton system affects the former respectvely latter, the greater the matchng effect respectvely decson-bas effect and thus the potental gan respectvely loss from a system of certfcaton. 30 Before concludng ths secton, e note that n practce a layer s qualty mght be observable to the judge even hen the layer s not certfed. For nstance, a layer on a case may have appeared before the judge on a prevous occason. The layer may also have appeared before other judges ho may pass on ther mpressons, ether nformally as gossp or as part of the consultaton process for judge appontment. Hoever, even f judges can observe a sgnal of layer qualty ndependently, they ll stll hold more precse nformaton hen qualty certfcaton s present, hch suffces to lead to our qualtatve results. C RAND 0.

18 694 / THE RAND JOURNAL OF ECONOMICS Uncertan appeal. The base model has the property that, n equlbrum, an appeal reveals a judge s ncompetency. Ths may not be the case n practce, for to reasons. Frst, the outcome of appeals may be uncertan; second, even a correct decson may be appealed. To address these ssues, e amend the model n to drectons. Uncertanty n appeals s captured by allong for some mstakes leadng to PrD = θ = χ, here χ s small enough n partcular smaller than /. We assume that the mstakes are ndependent of the true underlyng state of the orld. Ths amounts to sayng that appeals do not brng ne evdence but smply help to reveal and nterpret the evdence that as accessble to the layers. In partcular, appealng an nformed competent judge has no socal value, because the judge has all the nformaton. Hoever, appealng hen there s no certfed layer helps uncover the nformaton, hereas appealng an ncompetent judge helps nterpret the nformaton. Also, the appeals cost s random. It takes value A V, here A {0,Ā} and e denote by η the probablty of A = 0. We mantan the assumpton that Ā s large enough and χ small enough that, hen the appeals cost s hgh, only the certfed layer knong that d θ appeals. By contrast, an appeal alays occurs hen the cost s zero. The appeals cost s prvate nformaton of a party and hs layer, so that the ex post reputaton ncorporates the uncertanty about the motve of the appeal. Consder the judge s problem hen both partes hre an uncertfed layer. In ths case, the prevous logc apples and t s farly easy to see that the judge s equlbrum strategy s to choose the correct decson hen competent and nformed, and to randomze th equal probablty beteen the to decsons hen unnformed recall that for q = /. There s no appeal hen the appeals cost s hgh, and n ths case the judge s reputaton s unchanged, at. An appeal occurs hen the appeals cost s zero, leadng to a reputaton that depends on hether the decson s upheld or reversed: ν χ + ν/ PrC D = d = = ν χ + ν/ + / > νχ + ν/ PrC D d = = νχ + ν/ + / <. Wth to certfed layers, all the nformaton s avalable to the judge and the layers. Thus, an appeal occurs f the decson s not correct or f the appeals cost s zero. I faces a probablty of appeal η + η/, hereas C faces only a probablty η of appeal. It s mmedate to see that for q = /, the equlbrum entals the ncompetent judge randomzng th equal proporton beteen the to decsons. Let us no turn to the case here P has a certfed layer hereas Pj has an uncertfed layer. As before, e restrct attenton to nteror equlbra here z <. The behavor of the competent judge s unchanged, because choosng the correct decson s optmal n the event here the appeals cost s zero and ensures that no appeal occurs f the appeals cost s hgh. I ll rule n favor of the certfed layer th probablty z. Choosng d = ensures that an appeal only occurs th probablty η, and n ths case there s equal chance that the decson s upheld or reversed. We sho n the Appendx that the expected payoff s then η μ = + η χ χ z χ + z χ + z Suppose no that the judge rules aganst P and chooses d = j. In ths case an appeal occurs f A = 0orfθ =, and thus th probablty η + η/. Appeals act as a sgnal that the decson may not be correct and thus that the judge s ncompetent. We obtan n ths case a payoff μ j = η + η χ χ η + z j χ + z + η η+ ηχ j χ + z. 7 ηχ j An nteror equlbrum s such that μ = μ j. C RAND 0.

19 IOSSA AND JULLIEN / 695 Despte the uncertanty, the man nsghts reman vald. Faced th dversely competent layers, I gans from avodng the decson beng challenged by the most nformed layer, as ths ould leak more nformaton about hs type. In partcular, e sho n the Appendx that Proposton s vald; I favors the certfed layer more often than C: / < z hl = z hl <. By symmetry, both partes attach the same value to the certfed layer, and e sho n the Appendx that the value l of a certfed layer hen the opposte party s layer s not certfed s strctly larger than the value h of a certfed layer hen the other party s layer s certfed. Hence, the market equlbrum s the same and there s a range of ntermedate cases th only one certfed layer. Proposton 8. Suppose χ 0 and η<. When only P hres a certfed layer, a decson bas n favor of P arses, that s, z hl > /. Moreover, l > h > 0 and the equlbrum s the same as n Lemma. Proposton 5 holds under the condton ν< z hl χ Ā λ. Thus, the analyss extends to ths more general case. Remark 3. The settng th uncertan appeals allos us to reemphasze that the decson bas n cases th only one certfed layer s due to the combnaton of reputatonal concerns of judges and the transmsson va the appeals system of the better nformaton held by the certfed layers. As n the benchmark case here there are no appeals, hen appeals are free and alays take place, no decson bas arses. Wth η =, the better nformaton of the certfed layers ould play no role. See the Appendx. False postves. In hat precedes, e have focused on a stuaton here a certfed layer can mprove the decson-makng process by provdng better-qualty nformaton. In legal systems, hoever, layers can also nfluence the decson by alterng the sgnal process n favor of ltgants.to capture ths possblty, e no suppose that f P hres a certfed layer, then the accuracy of the sgnal depends on the true state th Pr s = θ =, h = > Pr s = θ = j, h = ν h > 0. Hence, a certfed layer can generate a false postve. We stll assume that the lo-qualty layer can only produce false negatves: ν l = Pr s = 0 θ =, l ;Prs = θ = j, l = 0. Then, e have Pr θ = s s, h > /, so that a certfed layer alone ould gude the decson, but at the same tme Prs = = / + ν h / > /, so that the certfed layer s more lkely to generate a favorable decson than the reverse. Hence, hrng a certfed layer even thout appeals ould rase the chances of nnng the case f there ere no other layer. We mantan the assumpton that χ = η = 0 and q = /. We also preserve the equlbrum structure here C chooses the decson most lkely to be correct hereas I randomzes, by assumng that ν h s not too large. Consder no the behavor of judges hen ν h > 0. Notce that the stuaton th no certfed layers s the same as before. In the case of to certfed layers, a repetton of our earler analyss shos that C ll contnue to take the correct decson condtonal on the nformaton avalable. A dfference s that t may be the case that the nformaton s not conclusve, that s, s = and s =. In ths case, C randomzes th equal eght on both decsons, as does I. C RAND 0.

20 696 / THE RAND JOURNAL OF ECONOMICS Whenever P hres a certfed layer and Pj hres an uncertfed layer, the correct decson s stll to follo the sgnals hen they are consstent, Pr θ = s = 0 = 0 Prθ = s =, s j = 0 = > + ν h ν l, but hen the to sgnals conflct, C should follo the uncertfed layer. Indeed, Prθ = s =, s j = j = 0. As e can see, the ablty to generate favorable nformaton can backfre, n that the nformaton of a uncertfed layer domnates n the decson. 3 Thus, C chooses to rule n favor of the certfed layer only f s = and s j = 0. Ths occurs th probablty Q = Pr s =, s j = 0 = + ν hν l >. We mantan the assumpton that Ā s large enough so that the uncertfed layer never appeals and Ā < +ν h ν l, hch ensures that the certfed layer appeals d = j hen s = and s j = 0. The expected payoff of I from choosng d = s Q μ =. Q + z If, nstead, he chooses d = j, he ll be appealed by the certfed layer of P f and only f d = s the correct decson. In ths case appeal s uncertan, but the appeals decson reveals that the judge s ncompetent. Hence, the reputaton falls to zero follong the appeals, rrespectve of the outcome. 3 Therefore, hs payoff ll be Q μ j =. + z j As before, the dfference beteen μ and μ j s decreasng n z ; further, t s no ncreasng n Q, hch suggests that the equlbrum value of z ll be nondecreasng n Q. Gven that the nfluence effect s to rase the chance of obtanng a favorable decson, n equlbrum e stll have the follong. Proposton 9. Suppose ν h > 0 and ν l > 0. When only P hres a certfed layer, a decson bas, n favor of P arses, that s, z hl > Q, and s ncreasng th ν h and ν l. When certfed layers can alter the sgnal process n favor of ltgants, the decson-bas effect s renforced because t s more lkely that a decson aganst the certfed layer trggers an appeal. Gven the bas z, the lkelhood of nnng a case th a certfed layer faced th an uncertfed layer s Q + z hl Q h = Q + z hl + z hl = Q + > Q, + ν h ν l here e account for the fact that the sgnals s =, s j = 0 are not fully nformatve about θ, hence about the outcome of the appeal. The prvate value of the certfed layer s then gven by h = Q h 4 Ā l = Q h Q zhl Ā. 3 A smlar effect as hghlghted n Shn Ths s due to our assumpton that η = 0. C RAND 0.

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