TheSimpleEconomicsofOptimalReservationPolicies

DelhiSchoolofEconomicsGlennC.Loury

December14,2016

PartOne:TheDevelopmentvs.theAssignmentMarginPartTwo:Generalized‘Color-Blind’ReservationPolicies

ATribute:WhatIsMeantby“Schelling-esque”

• Broadinterests;playfulmind;masteryofstrategicanalysis;elegantwriting;imaginativelylinkingtheorywithpolicy.

• Taught“PublicPolicyinDividedSocieties”withTomin1980s.Encounteredwriterslike:AmartyaSen;AlbertHirschman;ErvingGoffman;LeoStrauss;KennethArrow;RobertMerton(Sr.);HowardRaiffa;MancurOlson;MichaelSpence;HaroldIsaacs;JonElster;ThomasPettigrew;MichaelWalzer;GunnarMyrdal;ThomasKuhn…(Igotaneducation!)

• Ourstudentsinvestigatedsuchtopicsas:theRomainEurope;theindigenousinCentralAmerica;untouchabililty inIndia;slavemarooncommunitiesintheCaribbean;skincolorcasteincitiesofNewOrleansandCharleston;signlanguagevs.lip-readingamongthedeaf;nameandaccentchangestodisguiseethnic/regionalorigins;collectivepunishment,pride,shameandreputation;racialprofiling;stigma;sexualdivisionsoflaborathomeandintheworkplace;endogamyandassortative mating…

• Weexploredconceptualpuzzlesinlecturesfromthatcourseabouttheworkingsof:rumors;seduction;riots;“passingforwhite”;anonymity;plausibledeniability;signaling;strategicimprecision;groupthink;codewordsanddog-whistlepolitics;discursivetaboosandnakedemperors;knowledgeofanother’sstateofknowledge;behaviorinpublic;differencebetweenpromises,threatsandbluffs.

• Inshort,IincurredanenormousintellectualdebttoTominthoseyears,onewhichIshallneverbeableadequatelytodischarge…Heforeveralteredmywayofthinkingabouttheintersectionbetweeneconomictheory,socialpolicyandrace– intheUnitedStatesandthroughouttheworld

TheProblemofOptimalReservationPolicy

(Anexerciseinoptimaltaxationtheory.See,e.g.,FryerandLoury,JPE2013)

PartOne

Reservations(AffirmativeAction)={concernabout‘groupness’}+{concernfor‘equality’}+{rationingaccesstoelitepositions}

AFFIRMATIVEACTIONPRESUPPOSESTHAT:

(1)thereisahierarchyofmore/lessdesiredpositions,(2)thereissignificantracial/ethnicgroupdiversityofidentities(3)thereissubstantialsocialdisparitybetweenthesegroups,(4)thereisapolitical/economicneedforgrouprepresentation

AGENERALDEFINITIONof“POSITIVEDISCRIMINATION”

(5)apolicymakerseekstoincreasethedisadvantagedgroup’srepresentationinhighstatuspositionsinanoptimalway.

I(withRolandFryer)build“EconomicModel”ofreservationpolicies.ThisIsaClassic(i.e.,oldfashioned!)AppliedTheoryExercise

Herearethekeyelementsofour“model”:(1)Twoidentitygroups,onerelatively“disadvantaged.”(Such

“backwardness”exogenous;yethasresourceallocationimplications.)

(2)Ascarcityofdesiredpositions;competitionforaccesstothem;AApresupposestherationingoftoppositions(assignmentmargin)

(3)Apossibilityforpeopletoraiseproductivitywithcostlyeffort;AAaltersincentivestomaketheseinvestments(developmentmargin)

(4)Reservationpoliciestoimprovepositionofdisadvantagedgroup

(5)Wecontrast“development”vs.“assignment-oriented”policies;aswellas“color-blind”(CB)vs.“color-sighted”(CS)policies.

TheoreticalQuestionsofInterest

1)Whatkindofpolicyaccomplishesreservationgoalatleastsocialcost?(Taking“cost”seriously– thatis,consideringbothopportunityandinvestmentcosts.)

2)Howdoestheoptimalpolicyalterincentivesforhumancapitalinvestmentineachgroup?

3)Whereinproductivelife-cycle– at“development”or“assignment”margin– isitbesttointervene?

AppliedTheoryisusefulwhenitsuppliesinsightintoproblemthatcanguideourthinking.Theintuitiveinsightsofthisexerciseareasfollows:

(Oneadefaultoptionpayingzero)

ElementsofTheBaselineModel- Acontinuumofagentsofunitmeasure;twogroups,AandB- Acontinuumofscarce‘slots’oflessthanunitmeasure- Twoproductionstages:

- (i) exante workersacquirehumancapital;HCiscostly;thedistributionofthiscostdifferbetweengroups

- (ii)expost workersbidinacompetitivemarketplaceforaccessto‘slots’

- Anagent+a‘slot’createsoutputvaluedatagent’sproductivity.- InvestmentinHC(stochastically)makesagentsmoreproductive.- ‘Slots’inelastically supplied(thiseasilyrelaxed).Representation

amongslot-holdersderivesfromagroup’sexpostdistributionofproductivity.Policyaimstohelp“disadvantaged”gainslots.

- AApolicyasubsidy/taxonHCinvestmentoronslotacquisition.

Hereareourthreemainresults:

(1)LFEquilibriumallocationisefficientandunequal

(2)OptimalCSPolicyEntirely“Assignment”-Orientedwhenagentsfullyandcorrectlyanticipatelate-stagerentswhichvarybyproductivityandgroupmembership

(3)OptimalCBPolicySubsidizesHCacquisitiononlyifthe“disadvantaged”arebetterrepresentedonthedevelopmentmarginthanontheassignmentmargin

Regulatorcommitsto a policy

Agentsreceiveendowments

( )ci,

Agents chooseeffort

{ }1,0Îe

Agentslearn theirproductivities

( )vi,

Slotsareallocated

Productionoccursand paymentreceived

Figure 1: Sequence of Actions

DimensionsofAffirmativeActionPolicyconsidered:(A)Developmentvs.AssignmentMargin(B)Blindvs.Sightedpreferentialpolicy.

“Policy”=Subsidiestoeffortand/orslotacquisitionDevelopmentmargin

Assignmentmargin

decreasing

(1)FirstweanalyzetheLFEquilibriumallocationofHCandslots:

Letπ bethefractionwhoacquiredHCandletpbethepriceofaslot.Thenthefractionofpopulationwillingtobuyaslotis:

Figure 2: Competitive Equilibrium under Laissez-faire

p

p1

( ) θπ,pF -=1

( ) ( )ò¥

- D=p

dvvFG p1

Mp

Mp( )q-- 110F ( )q-- 111F

Ifslotsgotomostproductive:

IfHCacquiredbybestendowed:

But,whatwouldefficiencyrequire?

PrivatereturnforthemarginalHCinvestor

SocialMBofHCinvestment

IntuitionforwhyLFEquilibriumAllocationisEfficient

Equatingmarginalsocialbenefitsandcostsrequires:

A’sgetmoreHCthanB’sunderLF

A’sbetterrepresentedinslotsthanB’sunderLF

ReservationpoliciesaimtoincreaserepresentationofB’samongstslotholdersabovethisLFequilibriumlevel

(2) ConsidernowtheoptimalCSreservationpolicy

μ0

Figure4:UniquenessofEquilibriumUnderaConvexLikelihoodFunction

ξ(μ)

μ

[a(μ)- ]dF(π,μ)

0

Figure4

+Φ(μ)=

Φ(μ)

- -+

OntheRelativeEfficiencyofGeneralizedColor-BlindPolicy

(AnempiricalexercisedrawnfromworkwithTolga Yuret andRolandFryer)

PartTwo

AffirmativeActionwithoutExplicitRacialDiscrimination

• Color-blind(non-raciallydiscriminatory)affirmativeactionexploitsstatisticalassociationsinthepopulationbetweenanapplicant’sracialidentityandhis/hernon-racialtraits

[Texas10%Planfamouslyillustratesthenon-transparency]

• Apolicymakeralterstheweightgiventonon-racialtraitsforallapplicantsinsuchawayastoincreasetheyieldinselectionprocessfromatargetedgroup.

• Oneconsequenceofthiskindofpolicyisthatselectionefficiencymustingeneralbereducedforallapplicants.Policycan’tbe‘conditionally’(withingroup)meritocratic.

AnIllustrativeExampleofColor-BlindAffirmativeAction

StudentsinareaAareexcluded,andinareaBareincluded,bythepolicy.TherearemoredisadvantagedgroupstudentstobefoundinareaBthaninareaA.

FindinganOptimalPolicy:ThePlanner’sProblem

AcademicPerformanceEquation:

RacialIdentityEquation[prob {applicantintargetedgroup}]:

UseDatatoEstimate(presumed)LinearRelationships

Laissez-FaireSolution:ThresholdRuleonPredictedPerformance

Color-SightedAffirmativeActionSolution:Race-SpecificThresholds

Color-BlindAffirmativeAction:Modifiedweightsinscoringequation