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Essays in Labor Economics and Contract Theory
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Rao, Neel. 2012. Essays in Labor Economics and Contract Theory. Doctoral dissertation, Harvard
University.
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Thesisadvisor Author
ProfessorLawrenceKatz NeelDattatrayRao
Essays in Labor Economics and Contract Theory
Abstract
Thisdissertationconsistsofthreeessaysinlaboreconomicsandcontracttheory.
Thefirstessayexamineswhetherone’swageisbasedoninformationabouttheperformanceof
one’spersonalcontacts. Istudywagedeterminationundertwoassumptionsaboutbeliefformation:
individual learning, under which employers observe only one’s own characteristics, and social
learning, under which employers also observe those of one’s personal contacts. Using data on
siblings in the NLSY79, I test whether a sibling’s characteristics are priced into one’s wage. If
learning is social, then an older sibling’s test score should typically have a larger adjusted impact
on a younger sibling’s log wage than vice versa. The empirical findings support this prediction.
Furthermore, I perform several exercises to rule out other potential factors, such as asymmetric
skillformation,humancapitaltransfers,androlemodeleffects.
The second essay analyzes the influence of macroeconomic conditions during childhood on
the labor market performance of adults. Based on Census data, I document the relationship of
unemployment rates in childhood to schooling, employment, and income as an adult. In addition,
a sample from the PSID is used to study how the background attributes of parents raising children
vary over the business cycle. Finally, information from the NLSY79-CH is examined in order
to characterize the impact of economic fluctuations on parental caregiving. Overall, the evidence
is consistent with a negative effect of the average unemployment rate in childhood on parental
investmentsinchildrenandthestockofhumancapitalinadulthood.
Thethirdessaystudiesthebilateraltradeofdivisiblegoodsinthepresenceofstochastictrans-
action costs. The first-best solution requires each agent to transfer all of her good to the other
agent when the transaction cost reaches a certain threshold value. However, in the absence of
court-enforceable contracts, such a policy is not incentive compatible. We solve for the unique
maximal symmetric subgame-perfect equilibrium, in which agents can realize some gains from
trade by transferring their goods sequentially. Several comparative statics are derived. In some
cases,thefirst-bestoutcomecanbeapproximatedastheagentsbecomeinfinitelypatient.
iii
Contents
TitlePage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
1 SocialLearningintheLaborMarket: AnAnalysisofSiblings 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 SiblingModelswithEmployerLearning . . . . . . . . . . . . . . . . . . . . . . . 6
1.2.1 LaborMarketCharacteristicsofSiblings . . . . . . . . . . . . . . . . . . 6
1.2.2 InformationalContentofTestScoresandSchooling . . . . . . . . . . . . 8
1.2.3 IndividualLearning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.2.4 SocialLearning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.3 ExtensionsofEmployerLearningModels . . . . . . . . . . . . . . . . . . . . . . 18
1.4 EmpiricalImplementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.5 DatasetConstructionandDescription . . . . . . . . . . . . . . . . . . . . . . . . 25
1.6 EmpiricalResults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
1.6.1 JobSearchEstimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
1.6.2 SiblingAFQTImpacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
1.6.3 RobustnessChecks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
1.6.4 AdditionalPredictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
1.6.5 FalsificationExercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
1.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2 TheImpactofMacroeconomicConditionsinChildhoodonAdultLaborMarketOut-
comes 61
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
2.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
2.2.1 UnemploymentRateSeries . . . . . . . . . . . . . . . . . . . . . . . . . . 64
2.2.2 CensusSample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
2.2.3 PSIDSample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
2.2.4 NLSY79-CHSample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
2.3.1 CensusResults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
iv
Contents v
2.3.2 PSIDResults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
2.3.3 NLSY79-CHResults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
3 SequentialExchangewithStochasticTransactionCosts 100
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
3.2 RelatedLiterature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
3.3 ModelofStochasticTransactionCosts . . . . . . . . . . . . . . . . . . . . . . . . 106
3.4 AnalysisofModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
3.5 ComparativeStatics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
3.6 WelfareProperties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
3.7 VariationsoftheBasicModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
3.7.1 ModelwithStochasticSuppliesofGoods . . . . . . . . . . . . . . . . . . 126
3.7.2 ModelwithCostProportionaltoAmountTransferred . . . . . . . . . . . . 127
3.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
A AppendicestoChapter1 129
A.1 ProofsofMainTheoreticalResults . . . . . . . . . . . . . . . . . . . . . . . . . . 129
A.1.1 ProofofProposition1.2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . 129
A.1.2 ProofofProposition1.2.2 . . . . . . . . . . . . . . . . . . . . . . . . . . 130
A.1.3 ProofofProposition1.2.4 . . . . . . . . . . . . . . . . . . . . . . . . . . 133
A.2 SiblingsatSameAgeLevel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
A.3 EndogeneityofTestScore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
A.4 SibshipsofArbitrarySize . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
A.5 DataonMultipleSiblings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
A.6 SchoolingCoefficientsinLogWageRegression . . . . . . . . . . . . . . . . . . . 170
A.7 VarianceofChangeinLogWageResidual . . . . . . . . . . . . . . . . . . . . . . 172
A.8 EmpiricalImplementationofGeneralizedModel . . . . . . . . . . . . . . . . . . 180
A.9 MeasurementErrorinSchooling . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
A.10 AsymmetriesinVarianceofTestingError . . . . . . . . . . . . . . . . . . . . . . 202
A.11 Instrumental-VariablesRegressionswithCorrelatedMeasurementError . . . . . . 204
A.12 ComparativeStaticsforLearningModels . . . . . . . . . . . . . . . . . . . . . . 208
A.13 SimpleModelofEmployeeReferrals . . . . . . . . . . . . . . . . . . . . . . . . 210
A.14 Within-FamilyEstimatesofAFQTImpacts . . . . . . . . . . . . . . . . . . . . . 218
A.15 FurtherJobSearchEstimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
A.16 AFQTImpactsforYoungestandOldestSiblings . . . . . . . . . . . . . . . . . . 221
A.17 AFQTImpactsbyNumberofSiblings . . . . . . . . . . . . . . . . . . . . . . . . 226
A.18 AFQTImpactsforSiblingsatSameAgeLevel . . . . . . . . . . . . . . . . . . . 228
A.19 AFQTImpactsControllingforSchoolingatTimeofTest . . . . . . . . . . . . . . 237
A.20 SiblingHeightImpacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
A.21 AFQTImpactsonJointWork-WageOutcomes . . . . . . . . . . . . . . . . . . . 245
A.22 Instrumental-VariablesEstimatesofSchoolingCoefficients . . . . . . . . . . . . . 248
Contents vi
B AppendicestoChapter3 253
B.1 ProofofProposition3.4.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
B.2 ProofofTheorem3.4.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254
B.3 ProofofProposition3.4.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
B.4 ProofofCorollariestoTheorem3.4.4 . . . . . . . . . . . . . . . . . . . . . . . . 256
B.4.1 ProofofCorollary3.5.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
B.4.2 ProofofCorollary3.5.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . 257
B.5 ProofsofTheorem3.6.1andCorollary3.6.2 . . . . . . . . . . . . . . . . . . . . . 257
B.5.1 ProofofTheorem3.6.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257
B.5.2 ProofofCorollary3.6.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
B.6 ProofofTheorem3.7.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260
B.7 ProofofProposition3.7.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
References 264
Acknowledgments
IamthankfultoLawrenceKatz,RajChetty,andOliverHartfortheirwillingnesstoadvisethis
dissertationandfortheirguidanceduringthewritingprocess.
The chapters in this dissertation also benefitted from the comments of several individuals.
Roland Fryer, Edward Glaeser, and seminar participants at Harvard University provided useful
feedback on Chapter 1. A discussion with Rajeev Dehejia as well as comments by seminar par-
ticipants at Harvard University helped improve Chapter 2. Drew Fudenberg, Michihiro Kandori,
TakuoSugaya,andYasutoraWatanabemadevaluablesuggestionsonChapter3.
I am especially grateful to Yuichiro Kamada with whom I coauthored the third chapter of this
dissertation.
vii
Chapter 1
Social Learning in the Labor Market: An
Analysis of Siblings
1.1 Introduction
An important question in labor economics concerns the mechanisms through which personal
contactsinfluencejobsearchbehaviorandwagesettingdecisions. AsGranovetter’s(1974)classic
survey of workers in the Boston area illustrates, approximately half of all jobs are obtained with
thehelpofasocialcontact. Theextensiveuseoffriends,relatives,andacquaintancesinjobsearch
makesitpossibleforpersonalcontactstoplayaroleinshapingemployers’beliefsaboutaworker’s
skills. AsRees(1966)noteswhenstudyingworkersinaChicagoneighborhood,“Presentemploy-
ees tend to refer people like themselves, and they may feel that their own reputation is affected by
thequalityofthereferrals.” Likewise,Montgomery(1991)presentsamodelofjobsearchthrough
personal contacts in which workers belonging to the same reference group are endowed with sim-
ilar abilities and firms make wage offers to referred workers based on the performance of current
employees. Giventheimportanceofinformalsocialtiesinfindingajob,ananalysisoftheeffects
of social networks on the wage structure appears to be essential for a complete understanding of
thefunctioningoflabormarkets.
This paper develops and implements an empirical test for whether a worker’s wage incorpo-
ratesinformationontheperformanceofherpersonalcontacts. Combiningasiblingmodelsimilar
toGriliches(1979)withalearningmodelrelatedtoAltonjiandPierret(2001),Iconstructaframe-
1
Chapter1:SocialLearningintheLaborMarket: AnAnalysisofSiblings 2
work in which workers are organized into disjoint social groups composed of a small number of
agents with correlated abilities and differing ages, and I examine wage determination under two
competing assumptions about the market’s formation of beliefs: individual learning and social
learning. Under individual learning, a worker’s wage is set equal to the conditional expectation
of her productivity given only her own schooling and performance, whereas under social learn-
ing, a worker’s wage is set equal to the conditional expectation of her own productivity given the
schoolingandperformanceofallthemembersofhersocialgroup,includingherself.
Using sibling data from the NLSY79, I apply this framework to test for a form of statistical
nepotism in which a worker’s wage can be decomposed into a component based on a sibling’s
performance as well as a component based on one’s own performance. The basic logic behind
this test is as follows. If one sibling is older than another sibling, then employers should have
morepreciseinformationabouttheoldersibling,becausetheoldersibling’sperformanceislikely
to have been observed for a longer length of time. Consequently, when market participants form
Bayesian beliefs about the abilities of the two siblings, the older sibling’s average performance
would have a greater impact on employers’ mean beliefs about the younger sibling’s ability than
viceversa. Assumingthatthelabormarketiscompetitive,thisasymmetryshouldbereflectedinthe
wages of the two siblings. Hence, the component of the younger sibling’s wage attributable to the
older sibling’s ability would be larger than the component of the older sibling’s wage attributable
totheyoungersibling’sability.
Empirically, given data on the test scores and schooling of siblings, this weighting can be de-
tectedbyregressinganindividual’slogwageonherownandasibling’stestscoresandschooling.
As in much of the literature on employer learning, the test scores in the data are treated as being
known to the econometrician but not directly observable to employers. If employer learning is
nepotistic in nature, then the ratio of the coefficient on a sibling’s test score to the coefficient on
one’s own test score should typically be higher in a younger sibling’s log wage than in an older
sibling’s log wage. However, if employer learning is entirely individual, then the ratio of the co-
efficient on a sibling’s test score to the coefficient on one’s own test score should be the same
for both a younger and an older sibling. In addition to performing this simple test, I document
several pieces of evidence indicating that the main patterns observed in the data are unlikely to be
explainedbyfactorsunrelatedtothelearningprocessesstudiedinthispaper.
The empirical strategy here integrates elements from five largely distinct literatures in labor
Chapter1:SocialLearningintheLaborMarket: AnAnalysisofSiblings 3
economics. First, this paper is part of a sizeable literature on the identification of social effects.1
The most closely related paper in this literature is Case and Katz (1991), which attempts to detect
neighborhood influences by regressing an individual’s outcome variable on the background vari-
ables of her peers. The current paper tests for social learning by regressing a worker’s log wage
on a sibling’s test score as well as other control variables. In addition, I seek to address the con-
cerns of Manski (1993) regarding the difficulties in distinguishing between social and nonsocial
effects by focusing on the relative values of the coefficients on an older and a younger sibling’s
testscoresinsteadoftheabsolutevalueofthecoefficientonasibling’stestscoreinitself. Further-
more,becausesiblingsformaclearlydefinedsocialunit,theuseofsiblingdatamitigatessomeof
the econometric problems associated with the misspecification of peer groups. By contrast, when
usinginformationonfriends,suchissuesmaybemoresevere.
Second, this paper belongs to a long line of research that exploits the special structure of sib-
lingdatatoaddressavarietyofquestionsinlaboreconomics. Asnotedabove,themodelofsocial
groupsusedinthispaperisbasedonthesiblingmodelinGriliches(1979). Moreover,siblingdata
appearstoberelativelywellsuitedforthepurposeofanalyzingsocialeffectsinemployerlearning,
because non-twin siblings tend to have a moderately high correlation in ability. By contrast, if in-
dividualswereassignedtosocialgroupsmostlyatrandomasinsomequasi-experimentaldesigns,
then an individual’s performance might provide little information from which employers could
infertheabilityofherpeers,andifindividualsinthesamesocialgrouphadverysimilarcharacter-
istics as could be the case with identical twins, then it might be difficult to distinguish empirically
betweenthecomponentsofaperson’swagebasedonherownandherpeer’sperformance.
Third, this paper contributes to a growing literature on employer learning. In order to examine
socialinteractionsintheemployerlearningprocess,Iextendthebasicmethodologydevelopedby
Farber and Gibbons (1996) and Altonji and Pierret (2001). Given the assumption that the AFQT
scoresintheNLSY79arenotdirectlyobservabletoemployers,AltonjiandPierret(2001)develop
a test for statistical discrimination, in which employers use a worker’s easily observable charac-
teristicstoinferherproductiveability. Thoseauthorsfindthatemployersstatisticallydiscriminate
on the basis of education but not race. The current paper devises a test for statistical nepotism, in
whichemployersinferanindividual’sproductivitybasedpartlyoninformationaboutherrelatives.
1SeeIoannidesandLoury(2004)forareviewofexistingresearchonsocialeffectsinlabormarkets.