EmployeeRecruitingandtheL akeW obegonE¤ect¤

JohnM oranD epartmentofEconomics

SyracuseU niversity

JohnM organW oodrowW ilsonSchoolPrincetonU niversity

June2001

A bstract

Employers, educationalinstitutions, andotherorganizations areoften facedwith theproblem ofselectingthemostquali…ed candi-dateto…llanavailableposition. Tothis end, manyemployers haveadoptedatournament-likeprocedureconsistingofaninitialphaseinwhichrecommendationssolicitedfromthird-party“referees” areusedtoeliminateunquali…ed candidates, followedbyan interviewphasein which the remainingcandidates are ordinally ranked. W e showthattheuniqueequilibriumarisingunderthismechanismentailsem-bellishmentbyboth candidates andreferees (aphenomenon knownas the “L ake W obegon e¤ect”), but, despite this, always results intheselectionofthemostquali…edcandidate. O thernotablefeaturesoftherecruitingprocess, suchas di¢cultyindistinguishingbetweencandidates, changingperceptionsofcandidatesovertime, andtheuseof“wishlists” byrecruitersarealsoaccountedfor.

JEL Classi…cationN os.: L 20, J7 1, D 82, J00Keywords: R ecruiting, Tournament, Embellishment

¤T he second author gratefully acknowledges …nancial support from the N ationalScience Foundation. A ddress all correspondence to: John M oran, Center for Pol-icy R esearch, Syracuse U niversity, 426Eggers H all, Syracuse, N Y 13244-1020. Email:jmoran@ maxwell.syr.edu.

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1 IntroductionM anyorganizationsarefacedwiththeproblemofidentifyingthemostquali-…edcandidateto…llanavailableposition. A crucialdi¢cultythatrecruitersfaceis thattheunderlyingskills andabilities ofthecandidates arenotdi-rectlyobservable;instead, employersmustattempttoinfertheabilities ofcandidatesbasedonevidenceprovidedbythecandidates themselves. Suchevidencemighttaketheformofresumes, scoresonstandardizedtests, orre-portsofpastachievements. M uchoftheevidencethatcandidatesprovideisalterable(atsomecost)inamannerthatisundetectablebytherecruiter. A saresult, candidateshaveanincentivetoengageinpracticesthat“accentuatethepositive” whenreportingtheirquali…cations, andrecruitersmustthendecidetowhomtoo¤erthepositiononthebasisofthispossiblyembellishedinformation.

Itisoftenarguedthatrecruiterscansolvethisproblembysolicitingrec-ommendations from third-party“referees.” H owever, thosewhoareinthebestpositiontoprovideinformationareoftenfriendsorcloseassociates ofthecandidates, thus raisingtheprospectthatreferees, likethecandidatesthemselves, mayhaveincentivestooverstatethequali…cationsofthosetheyrecommend.1 Fewjobapplicants, forexample, receiveatrulybadreference,whilemanyenjoyrecommendationswhicharehighlyfavorable. Embellish-mentisalsoendemicinacademicadmissionrecommendations - somuchsothatstandardizedrecommendationformsareincreasinglydesignedtoantici-pateclusteringintheupperpercentilesofachievement. (TwosuchformsareillustratedinFigure1;onefrom alargepublicuniversityandanotherfromaprivateuniversity). T histendencytowardoverstatementhasbeentermedthe“L akeW obegone¤ect,” afterthemythicaltownofthesamename - aplacewhere, “allthemenarestrong, allthewomengoodlooking, andallthechildrenareaboveaverage.”2

Inlightofthislackofveracity, recommendationsplayasurprisinglyim-1W hilefewwhoproviderecommendations admittoout-and-outlying, itseems clear

thatreferencesofteninvolvesomedegreeofembellishment. W henpressed, thosewhoini-tiallydenyembellishingtypicallyconcedetohaving“emphasizedthestrongpoints” ofthecandidate. T heyalsoacknowledgetheirreluctancetovolunteerunfavorableinformation,andadmitto“downplaying” knownweaknesses.

2 M axwellandL opus (19 9 4) usetheterm “L akeW obegone¤ect” inconjunctionwithexaggeratedclaimsofacademicachievmentonthepartofcollegestudents. T hetownofL akeW obegonwasintroducedbyG arrisonKeillorinhisradioprogram, “A PrairieH omeCompanion” (seeKeillor).

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portantroleinthechoiceamongcandidates. T his isparticularlytrueinthelabormarket, whereroughlyhalfofallworkers…ndjobsthroughreferencesprovidedbyfriendsorrelatives (M ontgomery, 19 9 1). Furthermore, workerswhoobtain jobs through personalreferralearn higherinitialsalaries andhavelowerturnoverthanworkerswho…nd jobs throughothermeans (Si-monandW arner, 19 9 2). T hese…ndings suggestthat, despitethepresenceoftheL akeW obegone¤ect, thirdpartyevaluationsdoresultinsigni…cantinformationtransmission. T hisapparentcontradiction, betweentheimpliedinformationalvalueofemployeerecruitingproceduresontheonehand, andthesystematicembellishmentembodiedintheL akeW obegone¤ectontheother, raisestwoquestionswhichfromthefocusofthispaper. First, doesthecandidaterecruitmentprocess, plaguedwithmisinformationandembellish-mentatalllevels, leadtotheselectionofthemostquali…edcandidates?A ndsecond, ifembellishmentiscostly, andtherecruitingproceduresucceeds inselectingthemostquali…edcandidate, whyistheL akeW obegone¤ectsuchapervasivephenomenon?

Toexaminethesequestionswestudyarecruitingprocedurecommonlyusedbyemployersandotherinstitutions. Speci…cally, weconsideramech-anism consistingofan initialsolicitation phase inwhichrecommendationsobtainedfromthird-partyrefereesareusedtoscreenoutallcandidateswhofallbelowaminimum abilitythreshold, followedbyan interviewphase inwhichtheremainingcandidatesareordinallyrankedandthehighestrankedcandidateis hired. W eshowthatthismechanism hasauniquesymmetricperfectBayesianequilibriumwhichentailsembellishmentbybothcandidatesandreferees, yetalwaysresults intheselectionofthemostquali…edcandi-date.

A key assumption ofourmodelis thatembellishmentis costly. T hisassumptionre‡ectsagrowingrecognitionintheliteraturethat, inmanyset-tings, agentsmayneedtoexpendresources tofalsifythepubliclyrevealedstateofnature(seeL ackerandW einberg(19 8 9 ), M aggiandR odriguez-Clare(19 9 5), andCrockerandM organ, (19 9 8)). Indeed, as L ackerandW einberghavenoted, “T herearemany instances inwhich ‘lying’aboutthestateofnaturerequiresmorethansimplysendingafalsesignal... O ften, costlyac-tionsmustbetakentolendcredencetothesignalsbeingsent.”3 T hisseemsespeciallytrueinarecruitingsetting, wheree¤ectivemisrepresentationofacandidate’sabilityislikelytorequiregreatere¤ortthanatruthfulaccount-

3L ackerandW einberg(19 8 9 ), p. 1347 .

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ing. Forexample, inordertoconvincinglyoverstateacandidate’sability, arefereemightneedtoexpendadditionale¤orttocraftastrategicallywordedrecommendation, orspendadditionaltimelobbyingonthecandidate’s be-half. T hus, whenrecommendingtwocandidatesofdi¤eringability, arefereewouldhavetoexpendgreatere¤ortonbehalfoftheless ablecandidateinorderforthecandidatestoappearequallyquali…ed.

Inthesamevein, thecandidatehimselfmayengage incostlyactivitiesinane¤orttoin‡atearecruiter’sperceptionofhim. Forthecandidate, thenatureoftheseactivitieswilldependontheparticularenvironmentconsid-ered. W henapplyingforajob, thesemightincludetimespentresearchingtheemployer, practicinginterviewingskills, brushingup on buzzwords inrelevantsubjects, orpolishingone’s pastemploymentoreducationalexpe-riences, whileinthecaseofacademicadmissions, testpreparationservices,suchasthosewhichpreparestudentsfortheSA T , M CA T , andL SA T , areagoodexampleofawayinwhichcandidatesexpendresourcestoappearmorequali…edthantheyactuallyare.4 T hedistinguishingfeatureofeachoftheseexamplesisthatacandidatewithlesserskill, ability, orknowledgewillneedtoengageinmorefalsi…cationinordertoappearasquali…edasamoreablerival.

T hemechanismswestudyare, ine¤ect, rank-ordertournaments inthatemployers areabletodistinguish, onarelativebasis, the“paper” quali…-cations ofcandidates, butcannotdirectlyobservetheirinherent“quality”orsuitabilityfortheposition. O urresults di¤eralongseveraldimensionsfromstandardtournamentmodels, suchasthoseofL azearandR osen(19 81)and R osen (19 86).5 M ostobviously, ourmodelis oneofadverseselectionratherthanmoralhazard. T husthequestionsweconsiderfocusonensuringthatthemostsuitablejobcandidateis selected, ratherthaninducingopti-male¤ortonthepartofacurrentemployee. Second, attributes speci…ctotherecruitingprocess leadtopoolingoutcomes in the…rststagethatareatypicaloftournamentmodelsgenerally. T heapplicationofamultiple-stagetournamenttoemployeeselectionisalso, toourknowledge, novel.

4Somecarein interpretation is requiredhere. Forourpurposes, itis importantthattheactivityinquestionnotenhancetheparticularskillsvaluedbytherecruiter. Instead,wehaveinmindsuchthingsaslastminutecrammingandothershort-termstrategiesthathavenolong-term e¤ectonthecandidate’s underlyingskilllevel, butwhichcreatetheappearancethatthecandidateismorequali…edthanheis. N eedlesstosay, this isnotanissuewhenrecommendationsareprovidedbyreferees.

5Foranexcellentsurveyoftheliteratureontournaments, seeM cL aughlin(19 88).

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T hepaperproceeds as follows. Inthenextsectionwepresentasimplemodelofawidelyobservedtwo-stagerecruitingmechanism. Insectionthreeweshowthattheuniquesymmetricequilibriumarisingunderthismechanismleads tooptimalcandidateselectiondespitethepresenceofembellishmentbybothcandidatesandreferees(theL akeW obegone¤ect). Inaddition, themodelalsoo¤ersapredictionaboutthepatternofembellishmentobservedinthescreeningstageofthegame, andisshowntobeconsistentwithanum-berofothernotablefeaturesoftherecruitingprocess, suchasdi¢cultyindistinguishingbetweencandidates, changingperceptionsofcandidatesovertime, andtheuseof“wishlists” byrecruiters. Sectionfourcontainsconclud-ingremarks. L ongerproofsofkeypropositionsareprovidedinA ppendixA .In A ppendixB , weexaminecandidateselectionunderfourvariationsoftherecruitinggame: aone-stageprocedurebasedonthird-partyrecommenda-tions alone;aone-stageprocedurebasedoncandidate interviews alone;atwo-stageprocedurewhichreverses theorderinwhichcandidates andref-erees arepolled;and atwo-stageprocedure inwhich onlythecandidatesthemselvesparticipate.

2 TheM odelW econsidertheproblem facedbyanuninformedrecruiter(employer, edu-cationalinstitution, etc.) whoseeksto…llapositionwiththemostquali…edcandidate.6 T hereareN potentialcandidates, i= 1;2 ;:::N fortheposition,eachofwhom brings tothemarketagiven skilllevelµ 2 [0 ;1] (hereafterlabeled“ability”), drawnfromaknownatomlessdistributionF(µ)withden-sityf(µ) > 0 . T hepayo¤ toarecruiterwhenhiringacandidateofabilityµis¼ (µ), where¼ (¢) is increasinginµ and¼ (0 ) = 0:A candidatewhoishiredreceivesawage, w ;thatissetpriortothestartoftherecruitingprocessandremains …xedthroughout.7 W ewritethepayo¤ functionoftherecruiteras

6W hileourmodeldeals explicitlywiththecaseinwhichthereis asinglevacancytobe…lled, ourresultsgeneralizetothecasewheretherearelidenticalvacanciesandeachcandidatecan…llatmostonevacancy.

7 T heassumptionofapredeterminedwageisconsistentwithobservedpracticeacrossavarietyof…rmsandindustries. Forinstance, in…elds suchasaccounting, bankingandconsulting, salaries are setin advance and remain largely beyond thecontrolofthosechargedwithmakinghiringdecisions. T hesameis true inacademiclabormarkets forjuniorfacultywhere, inmanyinstances, salariesaredeterminedseparatelyfromtheprocessbywhichcandidatesareselected.

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¼ (µ); which is netofw:In theeventthattheposition is leftvacant, thepayo¤ totherecruiterisnormalizedtozero. T hereisacostk> 0 to…llingtheposition sothenetbene…ttoarecruiterwhohires aµ-typecandidateis ¼ (µ)¡k. Ifµ wereknown, therecruiterwouldonly selectacandidateofabilityµ if¼ (µ)¡k¸ 0:L etµmin2 (0 ;1) denotetheminimum levelofability such thatunderfullinformation therecruiterwould be indi¤erentbetween…llingthepositionorleavingitvacant. W ewillrefertocandidateswithabilitylessthanµminas“unquali…ed.”

Inassessingthecandidates, therecruitermightrelyoninformationpro-videdbyarefereeassociatedwithcandidatei;aswellasfrom self-reportingbycandidateihimself. Eachcandidate’sabilityisrevealedtothecandidateandthecandidate’s referee, butnottotherecruiterortotheothercandi-datesorreferees. H owever, thedistributionofcandidateabilitiesiscommonlyknown. A tvariousstages inthehiringprocesscandidatesandrefereesmaybeaskedtomakereports (r) abouttheabilityofthecandidate. Indoingso, weassumethatbothpartiescan, atsomecosttothemselves, e¤ectivelymisrepresentthetrueabilityofthecandidate.8 T hecosttoeachpartyoffalsifyingthecandidate’s abilityis givenbythefunction g(r¡µ):O uras-sumptionsaboutthecostfunctionsofcandidatesandrefereesareanalogoustoL ackerandW einberg. Speci…cally,

A 1. g(r¡µ)(= 0 if r¡µ = 0> 0 if r¡µ 6= 0

A 2. g0(r¡µ)¸°forr¡µ¸0 where°> 0

A 3. g00(¢) > 0

(A 1) implies thatmisrepresentingthecandidate’s abilityis morecostlythanreportingtruthfully. (A 2) and(A 3) implythatfalsi…cationcosts areincreasinginthesizeofthemisrepresentation, andthatg is invertibleoverthedomainr¡µ¸0:Itisworthnotingthatwhiletheassumptiong0(0 ) > 0issharedwiththemodelofL ackerandW einberg(19 8 9 ), intheirmodelthiscondition is needed togenerateregions ofno-falsi…cation in thecontracts

8 Speci…cfalsi…cationactivitiesarediscussedintheintroduction.

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they consider. In ourmodel, this assumption is a technicalone used toensurethatequation(2 ) (shownbelow) iswell-behavedattheboundary. A sasubsequentexamplehighlights, the…rst-stagegameresultsarenota¤ectedbyweakeningthisassumptiontog0(0 )¸0:

Tohighlightthee¤ectsoffalsi…cationoninformationtransmissionwith-outconfoundinginsuranceorriskconsiderations, weassumethatallcandi-datesandrefereesareriskneutral.9 T hus, theutilityofcandidateioftypeµ whosubmitsareportr is

Ui(r;µ) =(w ¡g (r¡µ) ifhired¡g (r¡µ) ifnothired

wherew is thereward(wage) inunits ofanumerairegoodifiobtains thepositionandg is thefalsi…cationcostfunctiondenominatedinunitsofthenumerairegood. Similarlytheutilityofi’sassociatedrefereeis

Vi(r;µ) =(v¡g (r¡µ) ifiishired¡g (r¡µ) ifiisnothired

wherev istherewardinunitsofthenumerairegoodtoi’srefereeifiobtainsthe position and g is the falsi…cation costfunction denominated in unitsofthenumerairegood. Inspecifyingthereferee’s utilityfunction, wehaveassumedthattherefereereceives somebene…tfrom havingtheircandidateobtain theposition. T his bene…tmayeitherbetangible, aswouldbethecaseifthecandidatewereabletousetheirpositiontoprovideassistancetothereferee, orintangible, aswouldoccurifthereferee’spreferencesre‡ectadegreeofaltruism towardsthecandidate.

W eassumethattherecruitercommits tothemechanism usedtoselectcandidatesandstudytheequilibriumpropertiesofaclassofmechanismsfre-quentlyobservedinpractice. Speci…cally, therecruitingmechanismconsistsoftwostages: an initialstageinwhichunquali…edcandidates areremovedfrom consideration;andasecondstage inwhichtheremainingcandidates

9 Sincetherearetwodiscreteoutcomesthata¤ectacandidate’sutility(beinghiredvs.notbeinghired), ourmodelreadilyextendstocaseswherecandidateshavepreferencesoftheform:

U i(r;µ)=u(w)¡g(r¡µ)

whereu isastrictlyconcavefunction. Toseethis, noticethatwemaynormalizeu(0 )=0andu(w)=1 forpreferencesinthisclass. A nidenticalargumentholdsforthepreferencesofreferees. T his, ine¤ect, yieldsthepreferencesweconsider.

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areordinallyranked. T hehighestrankedcandidateinthesecondstageob-tainstheposition. Intheeventofatieinthesecondstage, oneofthetiedcandidates isselectedatrandom.

Fortheremainderofthepaper, wewillassumethatthe…rststageoftheprocess isbasedonthird-partyrecommendationswhilethesecondstageentailsdirectinterviewingofthecandidates. InA ppendixB , wedemonstratethatourresultsdonotdependontheorderinwhichcandidatesandrefereesarepolled, however, bothstagesoftheprocessarerequiredtoensureoptimalcandidateselection.

3 EquilibriumCharacterization3.1 InterviewsW ebeginwiththesecond-stage(interview)game. Supposethatintherec-ommendationstageoftheprocessallcandidateswhoseabilitieswerebelowsomethresholdµ0wereeliminatedfrom consideration. Eachoftheremain-ingcandidatescompetesforrewardw associatedwithobtainingtheposition.Candidatessimultaneouslymakereportsabouttheirabilityandthecosttoacandidateoftypeµ ofmakingareportr isg (r¡µ):T hepositionisawardedtothecandidatewhoreportsthehighestability, whichcanbeinterpretedashavingappearedmostquali…edduringtheinterview.

3.1.1 Equilibrium

Sincethegameissymmetric, werestrictattentiontosymmetricequilibriumreportingstrategies. W ebeginbyshowingthatallsymmetricequilibriumreportingstrategiesaremonotonic.

Proposition1 Suppose ½ (µ) is asymmetricequilibrium reportingstrategytothesecond-stagegame. Thenforallµ; ½ (µ) is non-decreasing.

Proof. SeeA ppendixA .

N ext, supposewithoutlossofgeneralitythatwhencandidates 2 ;3;:::;Nfollowthereportingstrategy½ (µ), candidate1 choosesareportr tomaxi-mize:

U (rjµ) = wF³½¡1 (r)

N ¡1¡g (r¡µ)

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whereF (½¡1 (r))N ¡1 istheprobabilityofbeinghiredgivenareportofr:D i¤erentiatingweobtain

w (N ¡1)f (½¡1 (r))F (½¡1 (r))N ¡2½0(½¡1 (r))

¡g0(r¡µ) = 0

U singsymmetry,

w (N ¡1)f(µ)F (µ)N ¡2½0(µ)

¡g0(½ (µ)¡µ) = 0

R earranging, weobtainthedi¤erentialequation:

½0(µ) =w h N ¡1 (µ)g0(½ (µ)¡µ)

(1)

whereh N ¡1 (µ) isthedensityofthehighestofN ¡1 independentdrawsfromF (µ):

Since equation (1) is a …rst-ordernonlineardi¤erentialequation, itisusefultode…ne© (r;µ)´ w h N ¡1(µ)

g0(r¡µ) :W emakethefollowingtechnicalassumptions, which donota¤ectthe

economicsoftheresults, butconsiderablysimplifythecharacterizationofanequilibrium.

A 4. © is L ipschitz.

A 5. T hereexists aµ 2 (0 ;1) suchthatforµ · µ; w h N ¡1 (µ)·°andforµ > µ;N °> w h N ¡1 (µ) > °:

T heequilibriumreportingstrategyischaracterizedinProposition2.

Proposition2 The unique symmetric Bayesian N ash equilibrium ofthesecond-stagegameconsistsofareportingstrategy, ½ (µ), where:

½ (µ) = µ forµ < µ

and½ (µ) solvesthedi¤ erentialequation

½0(µ) =w h N ¡1 (µ)g0(½ (µ)¡µ)

(2)

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andendpointcondition:10

½³¹µ´= µ if ¹µ¸µ0

½ (µ0) = µ0 if ¹µ < µ0forµ¸µ

Proof. SeeA ppendixA .

Proposition2 implies, amongotherthings, thatcandidatesofsu¢cientlylowabilitywillnot…nditintheirinteresttoembellishtheir(modest)qual-i…cations. Inparticular, when¹µ > µ0; candidateswithabilities from µ0to¹µwillchoosetoreporttruthfully.11

In Proposition3, weestablishthatembellishmentis an integralpartofany symmetricequilibrium. Indeed, when µ0 > ¹µ; almostallcandidateschoosetoembellish.

Proposition3 Embellishmentoccurs foralmostallcandidateswithabilityµ 2 (max

³µ;µ0 ;1]:

Proof. Forallµ > max³µ;µ0 ; if½ (µ) = µ; then ½0(µ) > 1:H ence, there

canbeonly…nitelymanypointswhereembellishmentdoesnotoccur.

Someproperties oftheequilibrium strategies areworth noting. First,sincereportingstrategiesaremonotonic, itfollowsthattheordinalrankingobtainedfrom thecandidates’embellishedquali…cationswillbeidenticalto

10R ecallthatcandidateswithµ < µ0wereremovedfrom considerationduringthe…rstround. T hus, ifµ0¸µ, thenitisautomaticthatµ¸µ.

11 A nalternativeinterpretationofthesecond-stagecompetition is as follows: Supposethatnbidderscompeteinasingle-object, …rst-priceall-payauctionwhereitis commonknowledgethattheobjectis worthwtoeachbidder. B idders di¤erin theirskill(µ)inpreparingbids in thefollowingfashion: A biddermay, atnocost, makeabidequaltohis type, butbids aboveone’s typeareincreasinglycostly. Sincesubmittingabidofagiven levelis moreexpensive forless skilled bidders, bid strategies thatare increasinginabidder’s typearise in equilibrium. T hus, e¢cientsorting(intheform ofallocatingthe objecttothe bidderwith the highesttype) is achieved by virtue ofthefactthat“signaling”- intheform ofbiddingtoacertainlevel- isdi¤erentiallycostlyacrosstypes.A t…rstglance, thismayappeartobedi¤erentfrommanyapplicationsincontracttheoryinwhichatype-dependenttransferpaymentisrequiredinordertoa¤ectseparation. H ere,thetransferisnottype-dependentperse, butitisprobabilisticallytype-dependentduetothefactthatthecandidate’slikelihoodofobtainingthepositionisanincreasingfunctionofµ:

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theordinalrankingofthecandidates’trueabilities. T heunderlyingeco-nomicsofthisfollowsfromthefactthatsincemarginalembellishmentcostsareincreasing, alevelofpubliclyobservablecredentialsthatispro…tableforalowerabilitytypewillbeevenmorepro…tableforahigherabilitycandidate.Toseethis, noticethattogeneratethesamelevelofpubliclyrevealedqual-i…cations, alowertypemustexpendgreaterresourcesthanahigherabilitycandidate, whiletheexpected bene…tofpresentingidenticalpublicquali-…cations areexactlythesame. T hus, competitionforthepositionensuresthatthepubliclyobservedcredentials oflowerabilitycandidateswillneveroutshinethosewithhigherability. Furthermore, theform thatthiscompe-titiontakes impliesthatapositivemeasureofcandidateswillalwayschooseto“accentuatethepositive” and reporthigherthan theirtrueability. Inotherwords, onaverage, candidates areaboveaverage, a…ndingwhich isconsistentwiththeL akeW obegone¤ect.

ToobtainsomeadditionalintuitionforwhyL akeW obegone¤ectsneces-sarilyariseinthis context, itis instructivetoexaminewhytruth-tellingisnotanequilibrium. Supposethatallofthecandidateswereinitiallyfollow-ingatruth-tellingstrategy. N ow, acandidatewith su¢cientlylowabilitywouldperceivethegainsfromasmallamountofembellishmenttobefairlylow(sinceitis likelythathisabilityis signi…cantlybelowthatofthehigh-estabilityapplicant). Sincethemarginalcosts ofevenasmallamountoffalsi…cationarepositive, theselowabilitycandidateswouldbecontentwithtruth-telling. A candidatewithhigher(butnotthehighest) abilitywouldbemoreoptimisticabouthisprospectsof“embellishinghiswaytothetop,”andhence, wouldbewillingtoincurthecostsofengaginginsomefalsi…ca-tion. O bviously, candidatesintheuppertailoftheabilitydistributionwouldperceivelittleupsideinfalsifying, andhence, wouldbecontenttoreporthon-estly. T hus, itis thecandidates ofmedium abilitywhohavethestrongestincentives toembellish. Inequilibrium, higherabilitycandidates recognizetheseincentivesandreactbyfalsifyingtheirowntypes, sincebytellingthetruth theywould beviewedas medium types in theeyes oftherecruiterandwouldthereforefacethesameincentivestofalsifyas themedium abil-itycandidates. T his e¤ect“reverberates” allthewaytothehighestabilitycandidateswhomustthenembellishsimplytodistinguishthemselves frommedium types. T heupshotis thattheresultingequilibrium preserves theordinalrankingofcandidateswhileatthesametimeleadingtosystematicembellishment(theL akeW obegone¤ect) onthepartofcandidates.

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Finally, observethatthereportingstrategiesarisingintheinterviewstagedonotrequirerecruitersto“invertback” orinanywaydecipherthereportsissuedbythecandidates. Instead, recruitersarefreetodelegateinterviewingduties tounsophisticated agents whowillsimply hire the candidatewhoappearsmostquali…edduringtheinterview.

To see allofthis more easily, considerthe following example. Sup-posethatthereare4 candidates competingforaposition whosevalue is1. T hecandidates’abilities arei.i.d. draws from theuniform distributionon [0 ;1]:Candidateshavebeenpre-screenedsothatonlycandidateswhosereported ability exceeds 1

2 are being interviewed. Finally, letg (r¡µ) =34

³(r¡µ)2 + (r¡µ)

´forr ¸µ:O nemayreadilyverifythat© is L ipschitz

andthataµ satisfying(A 5) occursatµ = 12 :T heequilibrium strategy½(µ)

is implicitlycharacterizedby:

½0£µ12(½¡µ)+

14

¶= µ2

½µ12

¶=

12

A numericalsolutiontothis system ofequations (illustrated in Figure 2)highlightsthediscrepancybetweentruth-telling, representedbythethinline,andthequali…cationlevelsclaimedinequilibrium, representedbythethickline. N otethatdespitetheexistenceofsystematicembellishment, therelativerankingofcandidates is preserved in equilibrium. Thus, therecruitercanobtain fullordinalrevelationandhirethehighestabilitycandidate inthesecond-stagegame, eveninthepresenceoftheL akeW obegone¤ect.

3.2 R ecommendationsN owconsiderthe…rst-stagegame. Therecruiter’sobjectiveistochoosetherecommendationthreshold r¤ foradvancingcandidates tothesecondstageinamannerwhichmaximizesexpectedpayo¤s.

3.2.1 Equilibrium

Toremoveunquali…edcandidatesfromfurtherconsideration(i.e. thosewithµ < µmin) , therecruiterseekstocreateashortlistofcandidateswithability

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above some threshold µ0¸ µmin.12 Toachieve this, the recommendationthreshold r¤mustbesetinamannerwhichleaves referees justindi¤erentbetween embellishingtomeetthe threshold forthemarginaltypes. T heindi¤erenceconditionforrefereesofthemarginaltypes isgivenby

vH N ¡1 (µ0)¡g (r¤¡µ0) = 0r¤ = g¡1 (vH N ¡1 (µ0))+ µ0

whereH N ¡1 (µ0) isthedistributionfunctionofthehighestofN ¡1 indepen-dentdraws from F(µ):O bservethatthechosenrecommendation thresholdr¤ isalwaysabovetheunderlyingabilitythresholdµ0usedtoadvancecandi-datestothesecondround. Thus, inthepresenceoftheL akeW obegone¤ect,recruiters…nditintheirinteresttospecifyaminimumreportedquali…cationlevelwhichexceeds theactualquali…cations (ability) neededtoadequatelyfunction inthejob. T his appears tobeacommonstrategyinpractice, asemployersfrequentlyenumerate“wishlists” ofjobquali…cations inexcessofwhatisultimatelydeemedacceptable.

Itis immediatethatthiscuto¤ ruleimpliesthatequilibrium recommen-dationstrategies inthe…rst-stagegameare:

Proposition4 Referees submitrecommendationsaccordingto:

r (µ) = µ if µ 2 [0 ; µ0)= r¤ if µ 2

hµ0; g¡1 (vH N ¡1 (µ0))+ µ0

i

= µ if µ 2 (g¡1 (vH N ¡1 (µ0))+ µ0; 1]

andbelievethatthesecond-stagegamewillberesolvedaccordingtoProposi-tion2.

Tosummarize, theuseofacuto¤ rulebytherecruiterresults inrecom-mendationsthatareincreasinginthetrueabilityofthecandidatebutwhichexhibitpoolingatsomecuto¤ levelr¤:L owerabilitycandidatesarehonestlyreported, asare“superstars” whosetrueabilityliesabovethethresholdr¤.T hemiddlerangeofcandidates, whoseabilitylies between µ0and r¤, arealluniformlyreportedas beingofability r¤:T hus, theaverageabilityre-portedbyreferees is greaterthanthetruestatisticalaverageabilityofthecandidates, leadingtoaL akeW obegone¤ectintherecommendationstage

12Fornow, weallowµ0toremainarbitary;later, wewillsetittoitsoptimallevel, µmin.

13

ofthegameaswell. M oreover, theexistenceofamasspointofcandidates,allofwhomreceiverecommendationr¤, meansthatasubsetofcandidatesofdi¤eringabilitieswillinitiallyappearindistinguishabletotherecruiter. T hisis inkeepingwiththeoften-expressedviewthatcandidatescanbedi¢culttodistinguishbasedontheirrecommendationsalone.

Foroptimalcandidateselection, therecruiterneedstospecifyathresholdthatscreensoutallcandidateswhoseabilitiesarebelowµmin= ¼¡1 (k):T hus,µ0= µmin, andtheoptimalthresholdis:

r¤= g¡1³vH N ¡1

³¼¡1 (k)

´+ ¼¡1 (k):

T his expressionleads totheobvious implications thatscreeningstandardswillbecomemorestringentwheneitherthecostof…llingtheposition in-creases, orthedistributionofabilityshiftsinamannerconsistentwith…rst-orderstochasticdominance.

A lthoughwehaveassumedthatfalsi…cationcostssatisfyA 1-A 3, poolingbyreferees willoccureven ifwerelaxtheseassumptions.13 T hefollowingexampleisillustrative. Supposethattherearefourcandidateseachofwhoseability is an i.i.d. drawfrom theuniform distribution on [0 ;1]:T heref-erees obtain utilityof 2 by successfullyplacingtheircandidates andhavefalsi…cationcosts g = (r¡µ)2 :

Q uali…ed candidates arethosewhoseabilityexceeds 12 :T his induces a

recommendationthresholdofr¤= 1

T hus, theaveragereportedabilityofcandidates is

E(r) =58

asopposedtoatrueaverageof12 . Finally, halfthecandidatesreceiverecom-mendationsindicatingthattheyhavethehighestconceivablelevelofability;thus, onpaper, candidateswillbealmost“toogoodtobetrue.”

N otice thatthe bunchingofcandidate types which occurs duringtherecommendation stagegets sortedoutintheinterviewstage. T hatis, thelowerabilitycandidatestendtoperform worseintheinterviewthanwould

13Speci…cally, theassumptionthatg0(0 )> 0 is madesolelytogeneratewellbehaveddi¤entialequationscharacterizingreportinginthesecond-stagegame. T hisexampleshowsthatforthe…rst-stagegame, thisassumptionmaybedropped.

14

havebeen envisioned basedon theirrecommendations. In …gure 2, thesecandidates arethosewhoseabilities liebetween .5 and .825. A tthesametime, the higherability candidates willgenerally exceed the expectationscreatedbytheirrecommendations. A saresult, themodelisconsistentwithaphenomenonwherebycandidates“comeacross” di¤erentlyintheinterviewandrecommendationphasesoftheprocess, leadingrecruiterstochangetheirrankings intheaftermathoftheinterviews.

4 ConclusionT heanalysis presentedheredemonstratesthatawidelyobservedtwo-stagerecruitingprocedurecanbeusedtoidentifythemostquali…edcandidateforaposition, evenwhenthecandidates’quali…cationsaresubjecttoembellish-mentbyboththecandidatesthemselvesandthirdpartieschosentoevaluatethem. O ptimalcandidateselectionarisesasaconsequenceofthedi¤erentialcosts ofembellishingthequali…cations ofcandidates withdi¤erentunder-lyingabilities. T his inducesasortingamongtheembellishedquali…cationsofcandidates thatis ordinallyrevealing. T hatis, iffalsi…cationcosts risewiththedegreeofembellishment, competitionamongcandidates leads toanordinalrankingofembellishedquali…cationlevelsthatis identicaltotheordinalrankingofthecandidates’truequali…cations. A nimplicationisthatrecruiterswhochoosethebestcandidate“onpaper” indeedobtainthemostquali…edindividual. G iventhisdecisionrulebyrecruiters, acandidatewhorefrainedfrom embellishmentwouldbeleapfroggedintheselectionprocessbyless quali…edcandidates;thus, the L akeW obegone¤ectcanbeseenasaconsequenceofthenegativeexternalities associatedwithcompetitionforrentsfromthedesiredemploymentopportunity.

Inthe…rststageofthehiringprocess, themodelpredicts aclusteringoftherecommendationsmadeonbehalfofcandidateswithaverageabilities.T hisseemsconsistentwiththeviewthatcandidatesofdi¤erentabilitiesareofteninitiallyhardtodistinguish. T hemodelalsoprovidesarationaleforthepracticeofspecifyinga“wish list” ofminimum jobquali…cations inexcessofthoseactuallyneededforadequateperformanceinthejob;thatis, sincetherecruiteranticipates receivingembellishedreports onbehalfofaveragecandidates, itisessentialtoraisethestatedquali…cationthresholdabovetheactualthresholdneededtoensureadequateperformance. Finally, becausethepartialpoolingofcandidatesthatoccurs inthe…rststageisresolvedin

15

thesecondstage, themodelo¤ersanexplanationforwhyrecruiters’rankingsofcandidatesarelikelytochangeastheprocessunfolds.

T hemodelpresentedhereis, ofcourse, ahighlystylizedversionofem-ployeerecruitment. T hus, itisusefultoconsidertherobustnessofourresultstoperturbations andextensions ofthemodel. T hroughout, wehavemadethesimplifyingassumptionthattheapplicationoffalsi…catione¤ortleadstoadeterministicoutcome in terms ofpublicly revealed ability. W e caneasilyrelaxthis assumptiontoallowforastochasticidiosyncraticcompo-nenttorevealedabilitythatis independentoffalsi…cationactivities. A partfrom endpointe¤ects, suchan extensionwillhavenoimpactonmarginalfalsi…cationincentivesandhence, subjecttothenoisecomponentofabilityrevelation, alloftheaboveresultswillcontinuetohold. N ote, however, thatsuchanoisetermwouldnotallowforbeliefsthatperfectly“invertback” inasignalingversionofthemodel, thushighlightingthedi¤erencebetweenourtournament-likeapproachandonebasedonsignaling.

A notherextensionmightbetohaverefereesandcandidatesreceiveimper-fectlycorrelatedsignalsofthecandidate’strueability. Inthiscase, recruiterswouldhavetoconsidernotonlythecostofutilizingthe“interview” tech-nology, butalsotherelativeprecisionofthesignalsheldbythetwoparties.N onetheless, boththeL akeW obegone¤ectandour…ndingthatcandidatesareaccuratelyrankedinthesecondstageoftheprocesswouldstillbepresentinasymmetricequilibrium.

Finally, whilethemechanism westudyalways leads totheselectionofthemostquali…edcandidate, italsoentails wastefulfalsi…cationactivitiesonthepartofbothcandidatesandreferees, andrequiresthattheshortlistofcandidates beevaluated twice (…rst, by third-party referees, and later,viadirectinterviewing). T hus, aninterestingquestioniswhatconstitutesanoptimalrecruitingmechanismwhenoneiscognizantofthecoststobothcan-didatesandrecruitersofadministeringtherecruitingprocedure?A nsweringthisquestionisbeyondthescopeofthepresentpaperandremainsforfutureresearch.

16

R eferences[1]Crocker, Keith and John M organ, 19 9 8. “Is H onesty the B est Pol-

icy?CurtailingInsuranceFraudthroughO ptimalIncentiveContracts,”JournalofPoliticalEconomy, 106, 355-37 5.

[2]H irsch, M orris and Stephen Smale, 19 7 4. D i¤ erentialEquations, D y-namicalSystems, andL inearA lgebra(A cademicPress, N ewYork).

[3]Keillor, G arrison.“PrairieH omeCompanion,” signatureline, M innesotaPublicRadio.

[4]L acker, Je¤rey and John W einberg, 19 89 .“O ptimalContracts underCostlyStateFalsi…cation,” JournalofPoliticalEconomy, 9 7 , 1345-1363.

[5]L azear, EdwardandSherwinR osen, 19 81. “R ank-O rderTournamentsas O ptimum L aborContracts,” JournalofPoliticalEconomy, 89 , 841-864.

[6]M aggi, G iovanni andA ndresR odriguez-Clare, 19 9 5.“CostlyD istortionofInformation in A gencyProblems,” RandJournalofEconomics, 26,67 5-689 .

[7 ]M axwell, N an and Jane L opus, 19 9 4. “T he L ake W obegon E¤ectinStudentSelf-R eportedD ata,” A mericanEconomicReview- PapersandProceedings, 84, 201-205.

[8]M cL aughlin, Kenneth, 19 88, “A spectsofTournaments M odels: A Sur-vey,” In: R onaldEhrenberg, (Eds.), ResearchinL aborEconomics, Vol-ume9 . JA I Press, G reenwich, ConnecticutandL ondon, 225-256.

[9 ]M ilgrom, Pauland R obertW eber, 19 82. “A T heoryofA uctions andCompetitiveB idding,” Econometrica, 50, 108 9 -1122.

[10]M ontgomery, James, 19 9 1. “SocialN etworks and L abor-M arketO ut-comes: Toward an Economic A nalysis,” A merican Economic Review,81, 1407 -1418.

[11]R ainville, EarlandPhillipB edient, 19 81, ElementaryD i¤ erentialEqua-tions, SixthEdition, (M acmillan, N ewYork).

17

[12]R osen, Sherwin, 19 86. “Prizes and Incentives in Elimination Tourna-ments,” A mericanEconomicReview, 7 6, 7 01-7 15.

[13]Simon, Curtis and John W arner, 19 9 2. “M atchmaker, M atchmaker:T heE¤ectofO ldBoyN etworksonJob M atchQ uality, Earnings, andTenure,” JournalofL aborEconomics, 10, 306-330.

[14]Spence, M ichael, 19 7 3. “Job M arketSignaling,” Q uarterlyJournalofEconomics, 8 7 , 355-37 4.

18

5 A ppendixA - Proofs5.1 ProofofProposition1Supposethatthecontrary is true. First, noticethatstrategies suchthat½ (µ) < µ arenotrationalizable. H ence, thereexists µ;bµ with associatedstrategies ½ (µ) and½

³bµ´suchthatµ < bµ; ½ (µ) > ½

³bµ´¸bµ and

¯µ¡bµ

¯¯< "

forsmall":B yconvexityoftheg function, wehavethat

g (½ (µ)¡µ)¡g³½³bµ

´¡µ

´> g

³½ (µ)¡bµ

´¡g

³½³bµ

´¡bµ

´:

Incentivecompatibilityrequiresthat

F (µ)N ¡1 v¡g (½ (µ)¡µ)¸F³µ

N ¡1v¡g

³½³bµ

´¡µ

´

andF

³µ

N ¡1v¡g

³½³µ´¡µ

´¸F (µ)N ¡1 v¡g

³½ (µ)¡µ

´

H ence,

g³½ (µ)¡bµ

´¡g

³½³bµ

´¡bµ

´¸g (½ (µ)¡µ)¡g

³½³bµ

´¡µ

´

butthisisacontradictionandplaying½ (µ)fortypebµ isapro…tabledeviation.

5.2 ProofofProposition2First, notethatsinceallcandidatetypes µ < µ0areeliminatedfrom consid-erationinthesecondstage, itis su¢cienttocharacterizebiddingfunctionsfortypes intheinterval[µ0;1]:W ebeginbyprovingseverallemmaswhichplacerestrictionsonthecharacteristicsofequilibriumreportingstrategies.

L emma5 N oequilibrium reportingstrategycancontainatoms.

Proof. Supposenot. T henthereexistssomeopenintervaloftypes, (µ1;µ2 );thatmake the same report, r; in equilibrium. Suppose thatthe highestabilitycandidatemakingreportr is µ2 andthelowestis µ1:Inthis caseacandidateofabilityµ 2 (µ1;µ2 )obtainsexpectedpayo¤sthatarestrictlylessthanvF (µ2 )N ¡1¡g (r¡µ):H owever, bysendingaslightlyhigherreportr0;

19

suchacandidatecanearnarbitrarilyclosetovF (µ2 )N ¡1¡g (r¡µ):T hisisapro…tabledeviation.

Sinceequilibrium reportingstrategiescontainnoatomsandareincreas-ing, wemaythendeducethatequilibrium reportingstrategies are strictlyincreasing.

L emma6Forallcandidatesofabilityµ 2 (µ0;1), anyequilibrium reportingstrategyis continuous.

Proof. Supposenot, thenthereexists atype µ1 suchthatlim µ"µ1 ½ (µ) <lim µ#µ1 ½ (µ):If½ (µ1) > lim µ"µ1 ½ (µ);thenacandidateofabilityµ1 canlowerhiscostsbya…niteamountbychoosingthereportr = lim µ"µ1 ½ (µ);with-outa¤ectinghis probabilityofwinning. If½ (µ1) < lim µ#µ1 ½ (µ); thencan-didates with abilities slightly above µ1 can, by reducingtheirreports tor = ½ (µ1); savea…niteamountin falsi…cationcosts whilereducingtheirchancesofwinningbyanarbitrarilysmallamount. Bothoftheseareprof-itabledeviations.

Since reporting strategies are strictly increasingand continuous, theymustbealmosteverywheredi¤erentiable.

L emma7 Equilibriumreportingstrategiesmusthavethepropertythat½ (µ0) =µ0:

Proof. Toseethis, supposethatanequilibrium strategyhadthepropertythat½ (µ0) > µ0:Inthatcase, sincetherearenoatoms, acandidatecanlowerhiscostsbyreporting½ (µ0) = µ0withouta¤ectinghisprobabilityofwinning.T his isapro…tabledeviation.

G ivenlemmas5, 6, and7 , wemaynowproceedtotheproofofProposition2. First, notethatsince© is L ipschitz, asolutionto(2)exists(R ainvilleandBedient(19 81), p. 29 8). M oreover, since½0(µ)¸0 forallµ; suchasolutionis increasing. ByT heorem 1 inChapter15 ofH irschandSmale, weknowthatthesolutiontothedi¤erentialequationis locallyunique. B ystandardtechniquesthelocalsolutionmaybeextended(seeH irschandSmale, chapter8, Section5).

N extweshowthatsuchasolution is aB N E. Supposethatcandidate1pretendsthathistypeis z whenhistrueabilityisµ andallothercandidatesareemployingthestrategy ½:Clearly, anystrategy ½ (z ) < µ is dominated

20

byreportingtruthfully;hencewerestrictattentiontocaseswhere½ (z )¸µ:Candidate1’smarginalutilityis

M U1 (z jµ) =w h N ¡1 (z )½0(z )

¡g0(½ (z )¡µ)

Evaluatingthe…rst-orderconditionatµ = z and substitutingin for½0(z )yields

M U1 (z jµ) = g0(½ (z )¡z )¡g0(½ (z )¡µ)

R ecallthat½ (z ) ¸ z ; hence, for z < µ; M U1 (z jµ) > 0 and for z > µ;M U1 (z jµ) < 0:T hus, ½ isaB N E.14

Sinceanysymmetricequilibriumreportingstrategyisalmosteverywheredi¤erentiableandhastheendpointcondition½ (µ0) = µ0;weknowthatequa-tion (2) is necessary. T hus, wemay apply standard di¤erentialequationuniqueness theorems (seeabove) toestablishthat½ (¢) is theuniquesym-metricincreasingequilibrium.

6 A ppendixB - A lternativeExtensiveForms1. Supposethatinthe…rststagecandidatesarepolled, followedbyashort-listofreferees. T hen, thepropertiesofthemechanism areidentical. Toseethis, noticethattheonlydi¤erencebetweentheutilities ofreferees versuscandidateswasintheirutilityfromobtainingtheposition(orfromsupport-ingacandidatewhoobtained theposition). In short, ifwechanged theextensiveformofthegametointerviewsfollowedbyrecommendations, andadoptedacuto¤ strategyintheinterviewphase, alloftheprecedingresultswouldcontinuetohold.

2. Supposethatonlythesecond-stageproceduretookplace. T hen, thehighestabilitycandidatewouldstillbeselectedsincePropositions 1 and2holdforthecasewherethecuto¤ inthe…rst-stagegamewasr¤= 0:H owever,theabilityofthis candidateneednotexceedµmin;hence, wedonotobtainoptimalcandidateselectionwiththisprocedure.

14R elaxingA 5 results inthepossibilityof: (1)multipleintersectionswiththe½(µ)=µboundary; or(2) truth-tellingeverywhere (ifw is smallrelative to ° ): Possibility (1)simplyintroducesadditionaltechnicalcomplexitywithoutalteringthequalitativeordinalrevelationresult, whilepossibility(2)representstheeconomicallyuninterestingcasewherefalsi…cationistooexpensivetoemploy.

21

3. Supposethatonlythe…rst-stageproceduretookplaceandacandidatewasselectedrandomlyfromamongthosewhoserecommendationsexceededr¤:Inthiscase, theindi¤erenceconditionforreferees is

v(n ¡1)(1¡F (µ0))

¡g (r¤¡µ0) = 0:

andµ0solves v(n ¡1) = g (r¤¡µ0)(1¡F (µ0)):

Forµ < r¤;g (r¤¡µ)(1¡F (µ))isdecreasing, andforµ = r¤;g (r¤¡µ)(1¡F (µ)) =0 . H ence, providedg (r¤) > v

(n¡1); thereexistsauniqueµ02 (0 ;r¤) solvingtheaboveequationandwecanwritetherecruiter’smaximizationsolelyasafunctionofµ0. T hus, therecruiterselects µ0tomaximize

(E(¼ (µ)jµ > µ0)¡k)P r(max(µ1;µ2 ;:::;µn) > µ0)

=Ã

11¡F (µ0)

Z1

µ0¼ (t)f (t)d t¡k

! ³1¡F (µ0)n

´:

D i¤erentiatingwithrespecttoµ0, anecessaryconditionis

³1¡F (µ0)n

´Ãf(µ0)

(1¡F (µ0))2Z1

µ0¼ (t)f (t)d t¡¼ (µ0)f (µ0)

1¡F (µ0)

!

¡nF (µ0)n¡1 f (µ0)Ã

11¡F (µ0)

Z1

µ0¼ (t)f (t)d t¡k

!

= 0:

andµ0solves³1¡F (µ0)n

´

³nF (µ0)n¡1

´(1¡F (µ0))

=E(¼ (µ)jµ > µ0)¡k

E(¼ (µ)jµ > µ0)¡¼ (µ0):

Itis immediatethatµ0> µmin;hence, foragivencostof…llingtheposition,thestringencyofstandards in the…rst-stageprocedure is higherthanun-derthetwostagemechanism. Itis alsoimmediatethatoptimalcandidateselectiondoesnotoccurwithsuchaprocedure.

4. Considerthecasewherethecandidatesthemselvesundergothetwo-stageprocedure. O nemaythinkofthis as candidates submittingresumesfortheposition inthe…rststage. Candidateswhoseresumes exceedsome

22

thresholdaretheninvitedforface-to-faceinterviews. Supposethatthe…rst-stageprocedurescreens allcandidateswithabilitybelowµ0 inequilibrium.Clearly, second-stagereportingstrategiesareidenticaltothoseinProposition2. T hus, theexpectedsurplusofacandidatewithabilityµ inthesecondstageis

S(µ) = wF (µ)N ¡1¡g (½ (µ)¡µ)

where½ (µ) is thereportingstrategygiven in Proposition 2. W hen µ · ¹µ;½ (µ) = µ soitfollowsthatS(µ) is increasinginµ:W henµ > ¹µ;equation(2 )holdsand, uponsubstitution, itfollowsthat

S0(µ) = g0(½ (µ)¡µ)> 0

T hus, theexpectedsurplus is increasinginability.Supposethatinthe…rststage, athresholdr¤ isemployed. Ifacandidate

oftypeµ0embellishesuptor¤ (orgreater) inthe…rststage, sheanticipatesreceivingsurplus ofS(µ0) in the second stage. T he costofembellishingup to r¤ in the …rststage is g (r¤¡µ0):T hus, foracandidateoftype µ0

tobe indi¤erentbetween embellishingup to r¤ in the …rststageandnotembellishingtothislevelrequiresthat

S(µ0)¡g (r¤¡µ0) = 0:

O bviouslythecostofembellishingup tor¤ is greaterforcandidates withabilitybelowµ0;and, asweshowedabove, surplusisincreasinginµ:T hus, nocandidatewithabilitybelowµ0willchoosetoembellishup tor¤:A similarargumentimplies thatallcandidates withabilities above µ0willchoosetoembellishtoatleastthatlevelinthe…rststage. A saresult, wehaveshownthatin atwo-stageprocedurewhere candidates themselves participateatbothstages, anoptimalsortingstillholds. Indeed, noticethatwhenv = w ;thethresholdtoinduceoptimalsortingis setatexactlythesamelevelaswhen therefereeand thecandidateare separateplayers. T his is becausethemarginaltypedoesnotfalsifyinthesecond-stageinterviews, soS(µ0) =wF (µ)N ¡1 = vH N ¡1 (µ0):Ingeneral, theoptimalthresholdwilldependonw:

23

Figure 1 – Clustering in recommendations 2. Evaluation: In comparison with other students in the same field who have the same amount of experience and training, I rate this person as follows: Top

5% Top 10% Top 20% Upper 50% Unable to

rate Knowledge in proposed subject of study

Ability to grasp new concepts

Originality, intellectual creativity

Mathematical and logical thought

Written expression Oral expression Laboratory skills (if applicable)

Perseverance towards goals

Potential as teacher (if applicable)

Figure 2 – Equilibrium Lake Wobegon Effects

0.5

0.7

0.9

1.1

1.3

1.5

0.5 0.6 0.7 0.8 0.9 1θ

ρ

Truth-telling

Equilibrium Embellishment