VATT Working Papers 67
Self-Selection of Emigrants:
Theory and Evidence on
Stochastic Dominance in
Observable and Unobservable
Characteristics
George J. Borjas
Ilpo Kauppinen
Panu Poutvaara
VATT INSTITUTE FOR ECONOMIC RESEARCH
VATT WORKING PAPERS
67
Self-Selection of Emigrants:
Theory and Evidence on Stochastic Dominance
in Observable and Unobservable
Characteristics
George J. Borjas
Ilpo Kauppinen
Panu Poutvaara
George J. Borjas, Harvard Kennedy School, NBER and IZA.
Ilpo Kauppinen, VATT Institute for Economic Research.
Panu Poutvaara, University of Munich and Ifo Institute, CESifo, CReAM and
IZA.
We thank participants at Norface Migration Network Conference, Journées
Louis-André Gérard-Varet, EEA and CEMIR Junior Economist Workshop in
2013, the Alpine Population Conference, UCFS Workshop, CESifo ESP area
conference and VfS annual conference in 2015 and seminars at UC Irvine, ETH
Zurich, Labour Institute for Economic Research, VATT, University of Linz, and
University of Salzburg for valuable comments. Financial support from Leibniz
Association (SAW-2012-ifo-3) is gratefully acknowledged.
ISBN 978-952-274-163-9 (PDF)
ISSN 1798-0291 (PDF)
Valtion taloudellinen tutkimuskeskus
VATT Institute for Economic Research
Arkadiankatu 7, 00100 Helsinki, Finland
Helsinki, April 2016
Self-Selection of Emigrants: Theory and Evidence on
Stochastic Dominance in Observable and Unobservable
Characteristics
VATT Institute for Economic Research
VATT Working Papers 67/2016
George J. Borjas – Ilpo Kauppinen – Panu Poutvaara
Abstract
We show that the Roy model has more precise predictions about the selfselection of migrants than previously realized. The same conditions that have
been shown to result in positive or negative selection in terms of expected
earnings also imply a stochastic dominance relationship between the earnings
distributions of migrants and non-migrants. We use the Danish full population
administrative data to test the predictions. We find strong evidence of positive
self-selection of emigrants in terms of pre-emigration earnings: the income
distribution for the migrants almost stochastically dominates the distribution for
the non-migrants. This result is not driven by immigration policies in destination
countries. Decomposing the self-selection in total earnings into self-selection in
observable characteristics and self-selection in unobservable characteristics
reveals that unobserved abilities play the dominant role.
Key words: international migration, Roy model, self-selection
JEL classes: F22, J61
1
1.Introduction
Acentralfindingintheeconomicliteratureoninternationalmigrationisthatemigrantsare
notrandomlyselectedfromthepopulationofthesourcecountries.Thenatureofthenon‐
randomselectionaffectsthelevelandthedistributionofwelfarethroughtwomajor
channels.First,theskilldistributionofmigrantsaffectsthewagestructureinbothsending
andreceivingcountries(Borjas2003).Asecondeffecttakesplacethroughthepublicsector.
Immigrationcreatesafiscalsurplusinthereceivingcountryifandonlyifthenetpresent
valueofthetaxpaymentsofimmigrantsexceedsthenetpresentvalueofthecoststhey
impose.Boththeimmigrationofnetrecipientsandtheemigrationofnetpayersposea
challengetothepublictreasury(Wildasin1991;Sinn1997).
BeginningwithBorjas(1987),therehasbeenagreatdealofinterestinderivingand
empiricallytestingmodelsthatpredicthowmigrantsdifferfromnon‐migrants.Manyof
thesestudiesrelyonanapplicationoftheRoymodelofoccupationalself‐selection.Aslong
asskillsaresufficientlytransferableacrosscountries,thesortingofpersonsacross
countriesismainlydeterminedbyinternationaldifferencesintherateofreturntoskills.A
countryliketheUnitedStateswouldthenattracthigh‐skilledworkersfrommore
egalitariancountries(i.e.,countriesofferingrelativelylowratesofreturntoskills)andlow‐
skilledworkersfromcountrieswithgreaterincomeinequality(i.e.,countriesoffering
higherratesofreturntoskills).Theevidenceindeedsuggestsanegativecross‐section
correlationbetweentheearningsofimmigrantsintheUnitedStatesandincomeinequality
inthesourcecountries.1
AlthoughtheexistingliteratureonimmigrantselectionfocusesmainlyontheU.S.context
oronmigrationflowsfrompoortorichcountries,therearealsosizablemigrationflows
betweenrichcountries.AccordingtotheUnitedNations(2013),21.9millionpersonsfrom
1Relatedcross‐countrystudiesincludeCobb‐Clark(1993)andBratsberg(1995).GroggerandHanson(2011)
examinetheselectionofmigrantsacrossabroadrangeofcountriesusinganalternativetheoretical
frameworkwhereindividualsmaximizelinearutilityandmigrationisdrivenbyabsoluteearningsdifferences
betweenhighandlow‐skilledworkers.
2
EU15countriesnowliveoutsidetheirbirthplace,with42percentofthesemigrantsliving
inotherEU15countriesandanadditional13percentlivingintheUnitedStates.2
Thispaperexaminestheself‐selectionofemigrantsfromDenmark,oneoftherichestand
mostredistributiveEuropeanwelfarestates.In2013,overaquartermillionDaneslived
outsideDenmark(correspondingtoabout5percentoftheDanish‐bornpopulation),with
50percentofthemigrantslivinginotherEU15countriesand13percentintheUnited
States(UnitedNations,DepartmentofEconomicandSocialAffairs2013).Becausethe
returnstoskillsinDenmarkarerelativelylow,thecanonicalRoymodelpredictsthatthe
emigrantsshouldbepositivelyselectedinthesensethattheexpectedearningsofthe
migrantsexceedtheexpectedearningsofthestayers.3However,therehavebeenfew
systematicstudiesoftheself‐selectionofmigrantsfromarelativelyegalitariancountryto
seewhetherthisisindeedthecase.4
Ourtheoreticalanalysisshowsthatthecanonicalframeworkdoesnotonlyhave
predictionsaboutthedifferencebetweentheexpectedearningsofmigrantsandnon‐
migrants,whichisthebasisforthestandarddefinitionofpositiveornegativeselectionin
theliterature,butalsoaboutthestochasticorderingofthetwoearningsdistributions.We
showthatthesameconditionsthatpredictthatmigrantsarepositivelyself‐selectedinthe
senseofadifferenceinexpectedincomesalsopredictthattheincomedistributionofthe
migrantswillfirst‐orderstochasticallydominatetheincomedistributionofthenon‐
migrants.Thetheoryalsodistinguishesbetweenselectioninobservableandselectionin
unobservablecharacteristics.
2TheEU15countriesrefertothememberstatesoftheEuropeanUnionpriortotheexpansiononMay1,
2004.
3ForcomparisonsofgrosswagepremiafromtertiaryeducationacrosscountriesseeBoariniandStraus
(2010).ArecentpaperstudyingreturnstocognitiveskillsisHanusheketal.(2015).Thestudyfinds
significantcross‐countrydifferences.Moreover,thereturnsarerelativelylowinDenmarkaswellasinother
Nordiccountries,andhighintheUnitedStates,GermanyandtheUnitedKingdom,whichalsoareamongthe
mostpopulardestinationsofDanishmigrants.
4StudiesoftheselectionofmigrantsacrossdevelopedcountriesincludeLundborg(1991),Pirttilä(2004),
Klevenetal.(2014),andJungeetal.(2014).Manystudiesalsoexamineselectionissuesinahistorical
context;seeWegge(1999,2002),AbramitzkyandBraggion(2006),Abramitzky,Boustan,andEriksson
(2012),Ferrie(1996),andMargo(1990).
3
OurempiricalanalysisusestheDanishfullpopulationadministrativedatatoanalyzehow
migrantsandnon‐migrantsdifferintheirpre‐emigrationearningsandotherobservable
characteristics.Toshedlightontheroleofunobservablecharacteristicsintheselection
process,weinvestigatehowmigrantsandnon‐migrantsdifferintermsofunobservable
earningsability,asmeasuredbyresidualsfromMincerianearningsregressions.Our
empiricalresultsareinlinewiththepredictionsofthemodel:Danishemigrantsareindeed
positivelyself‐selectedbothintermsofearningsandintermsofresidualsfromthewage
regressions.FollowingourreframingofthecanonicalRoyframeworkintermsofthe
conceptofstochasticdominance,ourstudyspecificallytestsforwhethertheearnings
distributionoftheemigrantsstochasticallydominatesthatofthestayers(aswouldbe
predictedbythemodel).Theevidenceconfirmsthisstrongtheoreticalpredictionover
mostofthesupportoftheearningsdistribution.
Ourstudyisrelatedtotheflurryofrecentpapersthatexaminetheselectionofmigrants
fromMexicototheUnitedStates.ThepioneeringanalysisofChiquiarandHanson(2005)
mergedinformationfromtheU.S.censusonthecharacteristicsoftheMexicanmigrants
withinformationfromtheMexicancensusonthecharacteristicsoftheMexicannon‐
migrants.Becausethemergeddatadidnotreporttheearningsofmigrantspriortothe
move,pre‐migrationearningswerepredictedbasedonobservablecharacteristicsofthe
migrants.This“counterfactual”empiricalexercisesuggestedthatMexicanemigrantswere
locatedinthemedium‐highrangeoftheMexicanwagedistribution.Thefindingof
intermediateselectionintheMexicancontextdoesnotseemconsistentwiththebasic
implicationsoftheRoymodelbecausetherateofreturntoskillsisfarlargerinMexico
thanintheUnitedStates.MorerecentstudiesbyFernández‐HuertasMoraga(2011)and
KaestnerandMalamud(2014)usesurveydatathatreporttheactualpre‐migration
earningsandfindevidenceofnegativeselection.Theyalsoconcludethatpartofthe
negativeselectioncanbetracedtotheunobservablecharacteristicsthatdeterminea
migrant’searnings.
Theimportantroleplayedbyunobservablecharacteristicsimpliesthatconstructinga
counterfactualearningsdistributionforthemigrantsbasedonobservablecharacteristics
4
cangreatlybiasthenatureoftheselectionrevealedbythedata.Ourfindingssuggestthat
theuseofsuchacounterfactualdistributionwilltendtounderstatethetrueselectionin
earnings,sothattheselectionimpliedbythecounterfactualdistributionisfarweakerthan
thetrueselection—regardlessofwhetherthereispositiveornegativeselection.The
numericalbiasthatresultsfromusingthecounterfactualestimationissizableintheDanish
context:morethanhalfofthedifferencebetweentheexpectedearningsofmigrantsand
non‐migrantsarisesbecauseofdifferencesinunobservedcharacteristics.
Thepaperisorganizedasfollows.Section2sketchestheeconomictheoryunderlyingthe
analysisandderivestheoreticalpredictionsconcerningtheself‐selectionofemigrants,
usingthenotionofstochasticdominanceasaunifyingconcept.Section3introducesand
describestheuniquepopulationdatathatweuseandreportssomesummarystatistics.
Sections4and5presentthemainempiricalfindings.Insection4,weexaminetheselection
intermsofobservedpre‐migrationearnings.Wepresentastatisticalmethodfortesting
thetheoreticalimplicationthattheearningsdistributionoftheemigrantsshould
stochasticallydominatethecorrespondingdistributionofthenon‐migrants.Section5
extendstheempiricalworkbyexaminingtheselectionthatoccursintheunobserved
componentofearnings.Section6evaluatesthebiasthatresultsfrompredictingthepre‐
migrationearningsofemigrantsfromtheearningsdistributionofnon‐migrants.Section7
examineswhethertheselectionofpersonsmovingtootherEU15countriesdiffersfromthe
selectionofmigrantsmovingtocountrieswhereimmigrationrestrictionscomeintoplay.
Wefindthatimmigrationrestrictionshavelittleeffectontheselectionofemigrants.Finally,
Section8summarizesthestudyanddrawssomelessonsforfutureresearch.
2.Theoreticalframework
Previousliteratureontheself‐selectionofmigrantshasfocusedontheconditional
expectationsofearningsdistributionsamongmigrantsandstayers.Inthissection,we
deriveanovelresult:theRoymodelimpliesthatundercertainconditions,theearnings
distributionofmigrantsfirst‐orderstochasticallydominates,orisstochasticallydominated
by,theearningsdistributionofstayers.Inabivariatenormalframework,itturnsoutthat
5
theconditionsrequiredforstochasticdominanceareidenticaltotheconditionsthat
determinethenatureofself‐selectionintermsofexpectedearnings.
Wealsodecomposeself‐selectionintotwocomponents,onethatisdeterminedby
differencesinreturnstoobservableskillsbetweensourceandhostcountry,andonethatis
determinedbydifferencesinreturnstounobservableskills.Thedistinctionbetween
observableandunobservableskills,ofcourse,dependsontheempiricalframeworkandon
thedatathatisbeingused;observableskillsincludethevariablesexplainingearningsthat
areincludedinthedata,whilethecomponentofearningsthatisleftunexplainedbythe
dataistheunobservableskillcomponent.Eventhoughthecontentofthetwocomponents
differsamongdatasets,itislikelythatamajorpartofmigrantself‐selectionisdetermined
bytheunobservablecomponentsimplybecause“observables”tendtoexplainarelatively
smallfractionofthevarianceinearnings.
Wetakeasourstartingpointthemigrationdecisionfacedbypotentialmigrantsinatwo‐
countryframework,inlinewithBorjas(1987)andsubsequentliterature.Residentsofthe
sourcecountry(country0)considermigratingtothedestinationcountry(country1),and
themigrationdecisionisassumedtobeirreversible.Tosimplifythepresentation,wefocus
onasingleobservedskillcharacteristicsandsuppressthesubscriptthatindexesa
particularindividual.Forconcreteness,thevariablescanbethoughtofasgivingthe
worker’syearsofeducationalattainment,butitincludesallthecharacteristicsaffecting
individual’sincomethatareobservedinagivensetofdata.Residentsofthesourcecountry
facetheearningsdistribution:
(1)
log
wherew0givesthewageinthesourcecountry;r0givestherateofreturntoobservable
skills;andtherandomvariable0measuresindividual‐specificproductivityshocks
resultingfromunobservedcharacteristicsandisnormallydistributedwithmeanzeroand
variance  02 .Thedistributionofobservableskillsinthesourcecountry’spopulationis
6
givenbys=s+s,wheretherandomvariablesisalsoassumedtobenormally
distributedwithmeanzeroandvariance  s2 .
Iftheentirepopulationofthesourcecountryweretomigrate,thispopulationwouldface
theearningsdistribution:
(2)
log
wheretherandomvariable1isnormallydistributedwithmeanzeroandvariance  12 .
Foranalyticalconvenience,weassumethatCov(0,s)=Cov(1,s)=0,sothatthe
individual‐specificunobservedproductivityshocks(i.e.,the“residuals”fromtheregression
line)areindependentfromobservablecharacteristics.5Thecorrelationcoefficientbetween
0and1equals01.Itisalsoworthnotingthattherandomvariablesisindividual‐specific
andhasthesamevalueforthesameindividualinbothcountries,whereas0and1are
bothindividual‐andcountry‐specific.
Equations(1)and(2)completelydescribetheearningsopportunitiesavailabletopersons
borninthesourcecountry.Assumethatthemigrationdecisionisdeterminedbya
comparisonofearningsopportunitiesacrosscountriesnetofmigrationcostsC.Definethe
indexfunction:
(3)
log
∆
,
5Amorerealisticassumptionwouldbethatthecorrelationbetweenobservedandunobservedskillsis
positive.However,allowingforpositivecorrelationdoesnotchangethequalitativepredictionsofthemodel.
7
wheregivesa“time‐equivalent”measureofmigrationcosts(=C/w0).Thecross‐country
differenceinearningsnetofthetime‐equivalentmigrationcostforanindividualwith
averageobservedandunobservedcharacteristicsisgivenby
=[(1–0)+(r1–r0)s–].Thedifferenceinearningsattributabletoindividual
,wherevi=(ris+i)for
deviationfromaveragecharacteristicsisgivenby
∈ 0,1 .ApersonemigratesiftheindexI>0,andremainsintheorigincountryotherwise.
Migrationcostsvaryamongpersons—butthesignofthecorrelationbetweencosts
(whetherindollarsorintime‐equivalentterms)andskills(bothobservedand
unobserved)isambiguousanddifficulttodetermine.Theheterogeneityinmigrationcosts
canbeincorporatedtothemodelbyassumingthatthedistributionoftherandomvariable
inthesourcecountry’spopulationisgivenby=+,whereisthemeanlevelof
migrationcostsinthepopulation,andisanormallydistributedrandomvariablewith
meanzeroandvariance  2 .However,Borjas(1987)andChiquiarandHanson(2005)show
thattime‐equivalentmigrationcostsdonotplayaroleinthealgorithmthatdeterminesthe
selectionofemigrantsifeitherthosecostsareconstant(sothat  2 =0),orifthecostsare
uncorrelatedwithskills.Foranalyticalconvenience,weassumethattime‐equivalent
migrationcostsareconstant,sothat=.6Theoutmigrationratefromthesourcecountry
isthengivenby:
(4)
0
∗
∆
∗
1
∆
∗
,
wherev*=(v1v0)/visastandardnormalrandomvariable;*=/v;  2v =Var(v1–
v0);andisthestandardnormaldistributionfunction.7
6If werenegativelycorrelatedwithskills,thenegativecorrelationwouldtendtoinducethemoreskilledto
migrate,creatingapositivelyselectedmigrantflow.Thiswouldstrengthenpositiveself‐selection,and
weakennegativeself‐selection.
7Itisstraightforwardtostudyequation(4)toconfirmthatthemigrationraterises,whenmeanincomeinthe
sourcecountryfalls,meanincomeinthehostcountryrises,returnstoobservedskillsinthesourcecountry
fall,returnstoobservedskillsinthehostcountryrise,time‐equivalentmigrationcostsfallandwhenmean
observedskillsriseifr1>r0orfallifr1<r0.
8
Inadditiontoidentifyingthedeterminantsoftheoutmigrationrateinequation(4),theRoy
modelletsusexaminewhichpersonsfinditmostworthwhiletoleavethesourcecountry.8
Inthefollowing,weexaminetheself‐selectionofemigrantsalongtwodimensions:
selectionintermsofobservableskillssandselectionintermsofunobservableskills0,
whichtogethercombineintoselectionintermsoftotalproductivityorearnings,as
measuredbylogw0.
LetFM(z)andFN(z)representthe(cumulative)probabilitydistributionsofskillsor
earningsformigrantsandnon‐migrantsinthesourcecountry,respectively,wherez
denotesaparticularmeasureofskills(e.g.,observableorunobservablecharacteristicsor
income).Bydefinition,theprobabilitydistributionofmigrantsFM(z)first‐order
stochasticallydominatesthatofstayersFN(z)if:
(5)
∀ ,
andthereisatleastonevalueof forwhichastrictinequalityholds.9Fromnowon,
wheneverwerefertostochasticdominance,wemeanfirst‐orderstochasticdominance.
Equation(5)impliesthatalargerfractionofthemigrantshaveskillsaboveanythreshold
z*.Putdifferently,foranylevelofskillsz*,thepopulationdescribedbytheprobability
distributionFMismoreskilledbecausealargerfractionofthegroupexceedsthatthreshold.
Themigrants,inshort,arepositivelyselected.Negativeselection,ofcourse,wouldoccurif
thereversewastrueand
z,withastrictinequalityholdingforatleastone
valueof .
8Throughouttheanalysis,weassumethat*isconstant.Themigrationflowiseffectivelyassumedtobe
sufficientlysmallthattherearenofeedbackeffectsonthelabormarketsofeitherthesourceordestination
countries.
9Analternativeandperhapsmoreintuitivedefinitionofstochasticdominanceisintermsof
quantiles.Let
and
bethequantilefunctionsoforder oftheskilldistributionsofmigrantsand
forall0
1andthere
non‐migrants.FM(z)stochasticallydominatesFN(z)ifandonlyif
isatleastonevalueof forwhichastrictinequalityholds.
9
Iftheskilldistributionofmigrantsstochasticallydominatesthatofnon‐migrants,the
stochasticdominancethenalsoimpliesthetypicaldefinitionofpositiveselectionthatis
basedonconditionalexpectations:
(6)
|
0
|
0 ,
sothatmigrants,onaverage,aremoreskilledthanstayers.Conversely,iftheprobability
distributionofstayersstochasticallydominatesthatofmigrants,andtherewasnegative
selection,itwouldalsofollowthat
|
0
|
0 .Theconverse,however,isnot
trueforageneraldistribution:Aclaimofpositiveselectioninexpectations,asdefinedby
equation(6),doesnotimplythattheskilldistributionofmigrantsstochasticallydominates
thatofnon‐migrants.
Toderivethestochasticorderingoftheskilldistributionsofmigrantsandnon‐migrants,let
f(x,v)beabivariatenormaldensityfunction,withmeans(x,v),variances ( 2x , 2v ) and
correlationcoefficient.Further,lettherandomvariablevbetruncatedfrombelowat
pointaandfromaboveatpointb.Arnoldetal.(1993,p.473)showthatthe(marginal)
momentgeneratingfunctionofthestandardizedrandomvariable(x‐x)/x,giventhe
truncationofv,isgivenby:
(7)
/
,
where=(a–v)/v;and=(b–v)v.
Intermsofthemigrationdecision,thetruncationintherandomvariablev=v1–v0inthe
sampleofmigrantsisfrombelowandimpliesthat=–*=k,and=,wherekisthe
truncationpoint.Inthesampleofstayers,thetruncationinvisfromabove,andthe
truncationpointsare=–and=k.Bysubstitutingthesedefinitionsintoequation(7),it
10
canbeshownthatthemomentgeneratingfunctionsfortherandomvariablegivingthe
conditionaldistributionsofskillcharacteristicxformigrantsandstayersreduceto:
(8)
1
Φ
1
Φ
and
(9)
Φ
Φ
.
ConsideranytwodistributionfunctionsF(z)andG(z).Thistle(1993,p.307)showsthatF
willstochasticallydominateGifandonlyif:
(10) , ∀
0,
wheremFisthemomentgeneratingfunctionassociatedwithdistributionF;mGisthe
momentgeneratingfunctionassociatedwithG.
Therankingofthemomentgeneratingfunctionsinequation(10)implieswecandetermine
thestochasticrankingofthetwodistributionsbysimplysolvingfortherelevant
correlationcoefficient,andcomparingequations(8)and(9).Suchacomparisonimplies
that:
(11) , 0
, 0.
11
Inotherwords,migrantsarepositivelyselectedif>0,andarenegativelyselected
otherwise.Considerinitiallythestochasticrankinginobservablecharacteristics.The
randomvariablex=s,andtherelevantcorrelationcoefficientisdefinedby:
,
(12) 1 .
Equation(12)showsthatthestochasticorderingofthedistributionsofobservableskillsof
migrantsandnon‐migrantsdependsonlyoninternationaldifferencesintherateofreturn
toobservableskills.Theskilldistributionofmigrantswillstochasticallydominatethatof
stayerswhentherateofreturntoskillsishigherabroad.Conversely,theskilldistribution
fornon‐migrantswillstochasticallydominatethedistributionformigrantsiftherateof
returntoobservableskillsislargerathome.
Considernextthestochasticorderingintheconditionaldistributionsofunobservableskills
0.Therelevantcorrelationfordeterminingthistypeofselectionisgivenby:
(13) ,
1 .
Itfollowsthatthedistributionofunobservableskillsformigrantsstochasticallydominates
thatfornon‐migrantswhen
1.Notethatthenecessaryconditionforpositive
selectionhastwocomponents.First,theunobservedcharacteristicsmustbe“transferable”
acrosscountries,sothat01issufficientlyhigh.Second,theresidualvarianceinearningsis
largerinthedestinationcountrythaninthesourcecountry.Theresidualvariances  20 and
 12 ,ofcourse,measurethe“price”ofunobservedcharacteristics:thegreatertherewards
tounobservedskills,thelargertheresidualinequalityinwages.10Aslongasunobserved
10Thisinterpretationofthevariancesfollowsfromthedefinitionofthelogwagedistributioninthehost
countryintermsofwhatthepopulationofthesourcecountrywouldearniftheentirepopulationmigrated
there.Thisdefinitioneffectivelyholdsconstantthedistributionofskills.
12
characteristicsaresufficientlytransferableacrosscountries,emigrantsarepositively
selectedwhentherateofreturntounobservableskillsishigherinthedestination.
Finally,considerthestochasticrankingin“total”productivity.Theearningsdistributionin
thesourcecountrygivenbyequation(1)canberewrittenas:
(14) log
0
α0
0μs 0ε
ε0 α 0
0μ 0,
wherethenormallydistributedrandomvariablev0hasmeanzeroandvariance  2v0 .The
relevantcorrelationfordeterminingthestochasticrankingoftheearningsdistributionsof
migrantsandnon‐migrantsis:
,
(15) 1
1
1 ,
where
⁄
and1
⁄
.
Thesignofthecorrelationinequation(15),whichdeterminesthenatureoftheselectionin
pre‐migrationearnings,dependsonthesignofaweightedaverageoftheselectionthat
occursinobservableandunobservablecharacteristics.Interestingly,theweightisthe
fractionofthevarianceinearningsthatcanbeattributedtodifferencesinobservableand
unobservablecharacteristics,respectively.
Ifthereispositive(negative)selectioninboth“primitive”typesofskills,therewillthenbe
positive(negative)selectioninpre‐migrationearnings.If,however,therearedifferent
typesofselectioninthetwotypesofskills,theselectionineachtypeisweightedbyits
importanceincreatingthevarianceoftheearningsdistribution.Itiswellknownthat
observablecharacteristics(suchaseducationalattainment)explainarelativelysmall
fractionofthevarianceinearnings(perhapslessthanathird).Asaresult,equation(15)
impliesthatitistheselectioninunobservablesthatismostlikelytodeterminethenatureof
theselectioninthepre‐migrationearningsofemigrants.Thisimplicationplaysan
13
importantroleinexplainingwhytheevidencereportedinFernández‐HuertasMoraga
(2011)andKaestnerandMalamud(2014)conflictswiththatofChiquiarandHanson
(2005).
Asmentionedearlier,thestochasticdominanceresultsnecessarilyimplyselectioninterms
ofconditionalexpectations.Inthecaseofbivariatenormaldistributions,itfollowsthatthe
expectationoftheearningsdistributionofmigrantsE(logw0|v*>*)isgivenby:
(16)
|
∗
Δ
∗
1
Δ
∗
1
Δ
∗
,
where*)=(*)/[1(*)]>0,andisthedensityofthestandardnormal
distribution.Ascanbeseenbyexaminingequation(16),theconditionsthatdeterminethe
self‐selectionintermsofexpectationsarethesameastheconditionsthatdeterminethe
stochasticorderingoftheskilldistributionsofmigrantsandnon‐migrants.Inthenormal
distributionframeworkthatunderliesthecanonicalRoymodel,stochasticdominance
impliesselectioninexpectations,andviceversa.
Inempiricalapplications,however,thepredictionofstochasticdominanceislikelytobe
muchlessrobustthanthepredictionsconcerningexpectationsbecausetestingfor
stochasticdominancewillrequireamorerigoroustestthansimplycomparingtheaverage
incomesorskillsofmigrantsandnon‐migrants.Ifonejustcomparestheaveragestofind
outhowmigrantsareself‐selected,thefindingscanbecompatiblewiththepredictionsof
theRoy‐modelevenifalargenumberofindividualsinthedatabehaveagainstthe
stochasticdominancepredictionsofthemodel.Asaresult,establishinganempirical
patternofstochasticdominanceprovidesverystrongevidencethatdifferencesinskill
pricesareindeedimportantinmigrationdecisions.
14
3.Data
OuranalysisusesadministrativedatafortheentireDanishpopulationfrom1995to2010.
ThedataismaintainedandprovidedbyStatisticsDenmarkanditderivesfromthe
administrativeregistersofgovernmentalagenciesthataremergedusingauniquesocial
securitynumber.11
Foreachyearbetween1995and2004,weidentifiedallDanishcitizensaged25‐54who
livedinDenmarkduringtheentirecalendaryear.12Werestricttheanalysistopersonswho
workedfulltime.13Migrationdecisionsofpart‐timeworkersorofworkersoutsidethe
laborforcemaybedrivenbydifferentfactors,andtheobservedincomeoftheseworkers
maynotbeindicativeoftheirtrueearningspotential.Theincomevariableforeachyearis
constructedbyaddingtheworker’sannualgrosslaborincomeandpositivevaluesof
freelanceincome.14
Wemergedthisinformationwithdatafromthemigrationregisterfortheyears1995
through2010.Themigrationregisterreportsthedateofemigrationandthecountryof
destination.EventhoughitispossibleforDanishcitizenstoemigratewithoutregistering,
weexpectthatthenumbersofpersonswhodosoissmallasitisalegalrequirementfor
11AllresidentsinDenmarkarelegallyrequiredtohaveasocialsecuritynumber.Thisnumberisnecessaryto
manyactivitiesindailylife,includingopeningabankaccount,receivingwagesandsalariesorsocial
assistance,obtaininghealthcare,andenrollinginschool.
12Aperson’sageismeasuredasofJanuary1sttheyearafterthereferenceyear.
13Theadministrativedataallowsthecalculationofavariablethatmeasurestheamountof“workexperience
gained”duringthecalendaryear.Themaximumpossiblevalueforthisvariableis1,000.Werestrictour
sampletoworkerswhohaveavalueof900orabove,sothatoursampleroughlyconsistsofpersonswho
workedfulltimeatleast90percentoftheyear.Inordertomeasuretheworkexperiencegainedduringa
givenyear,wesubtractthevaluefromthepreviousyearfromthecurrentvalueofthevariable.Personswho
hadamissingvalueforworkexperienceineitherofthetwoyearsweredroppedfromthesample.Missing
valuesinthisvariabletypicallyindicatethatthepersonspenttimeabroad.
14Theinformationonearningsistakenfromthetaxrecordsforeachcalendaryear.Thisvariableis
consideredtobeofhighqualitybyStatisticsDenmark.Somepersonsalsoreportnegativevaluesforfreelance
income.Thesenegativevaluesarelikelytobeduetolossesarisingfrominvestmentsanddonotreflectthe
productivecharacteristicsoftheindividual.
15
Danishcitizenstoreportemigration.Danishtaxlawsprovidefurtherincentivesfor
migrantstoregisterwhentheyemigrate.
Afteridentifyingthepopulationofinterest,wedeterminedforeachpersonwhetherheor
sheemigratedfromDenmarkduringthefollowingcalendaryear.Ifwefoundthata
particularpersonemigrated,wesearchedforthepersoninthemigrationregisterfor
subsequentyearstodetermineifthemigrantreturnedtoDenmarkatsomepointinthe
future,andrecordedthedateofpossiblereturnmigration.Themigrationregisterincludes
near‐completeinformationonreturnmigration,asregistrationinDenmarkisrequiredfor
thereturnmigranttobeeligibleforincometransfersandtobecoveredbynationalhealth
insurance.
Tofocusonmigrationdecisionsthatarepermanentinnature,werestricttheanalysisto
migrationspellsthatareatleastfiveyearslong.15Wedefineamigrantasanindividualwho
isfoundinoneofthe1995‐2004cross‐sections,whoemigratesfromDenmarkduringthe
followingyeartodestinationsoutsideGreenlandortheFaroeIslands,andwhostays
abroadforatleastfiveyears.16Individualswhoemigratedforlessthanfiveyearswere
removedfromthedata,andtherestofthepopulationisthenclassifiedasnon‐migrants.17
Theanalysisofbothmigrantsandnon‐migrantsisfurtherrestrictedtoonlyincludeDanish
citizenswhodonothavean“immigrationbackground.”18
15Havingstayedabroadforfiveyearspredictslongermigrationspells.Forexample72%ofmenand71%of
womenwholeftDenmarkin1996andwerestillabroadafterfiveyearswerealsoabroadaftertenyears.
16GreenlandandtheFaroeIslandsareautonomousregionsbutstillpartofDenmark.Wehaveexcluded
thesedestinationsasmanyofthesemigrantscouldhaveoriginatedinGreenlandortheFaroeIslands,and
manywouldactuallybereturninghomeratherthanemigratingfromDenmark.Theexactduration
requirementswere1,825daysorlongerforlong‐termmigrants.
17Wealsoexaminedtheselectionofshort‐termmigrantsandthequalitativeresultsaresimilartothose
reportedbelow,althoughtheintensityofselectionisweaker.
18StatisticsDenmarkdefinesapersontohave“noimmigrantbackground”ifatleastoneoftheparentswas
borninDenmarkandthepersonis/wasaDanishcitizen.Wesearchedthepopulationregistersfrom1980to
2010fortheparentsofthepersonsinoursample,andifaparentwasfoundheorshewasrequiredtobea
Danewithnoimmigrantbackgroundaswell.
16
Table1reportssummarystatisticsfromtheDanishadministrativedata.Thepaneldataset
containsover6.4millionmaleand5.1millionfemalenon‐migrants.Theconstructionofthe
dataimpliesthatnon‐migrantsappearinthedatamultipletimes(potentiallyonceineach
cross‐sectionbetween1995and2004).Wewereabletoidentify7323maleand3436
femalemigrants.Byconstruction,thesemigrantsarepersonswhowefirstobserveresiding
inDenmarkandwholeftthecountryatsomepointbetween1996and2005.AsTable1
shows,theDanishemigrantsareyoungerthanthenon‐migrants,regardlessofgender.
Despitetheagedifference,theemigrantsearnedhigherannualincomesintheyearpriorto
themigrationthanthenon‐migrants.
Weconstructasimplemeasureof“standardizedearnings”thatadjustsfordifferencesin
age,gender,andyeareffects.Standardizedearningsaredefinedbytheratioofaworker’s
annualgrossearningstothemeangrossearningsofworkersofthesameageandgender
duringthecalendaryear.19Table1showsthatemigrantsearnmorethannon‐migrantsin
termsofstandardizedearnings.Inparticular,maleemigrantsearnabout30percentmore
thannon‐migrants,andfemaleemigrantsearnabout20percentmore.
Table2reportsthenumberofemigrantsmovingtodifferentdestinations.Thelargest
destinationsforbothmenandwomenaretwootherNordiccountries,SwedenandNorway,
aswellastheUnitedStates,theUnitedKingdomandGermany.20Thesefivecountries
accountfor57percentofallemigration.
Finally,itisalsointerestingtosummarizethelinkbetweeneducationandemigration.
Table3reportstheeducationdistributionsfornon‐migrantsandmigrants.Itisevident
thatthemigrantstendtobemoreeducatedthanthenon‐migrants,amongbothmenand
women.Forexample,50percentofDanishmalenon‐migrantshaveavocationaleducation,
ascomparedtoonly30percentofmigrantstonon‐Nordicdestinations.Similarly, the
19Bothmigrantsandnon‐migrants,aswellasshorter‐termmigrants,areincludedinthesecalculations.
20Ifwerelaxtheconstraintsonlabormarketstatusandagetoenterthesample,theUnitedKingdom
emergesasthelargestdestinationbecauseofthelargenumberofDanishstudentswhopursuetheir
educationthere. 17
fraction of male migrants to non-Nordic destinations with a Master’s degree is 24 percent,
whereas only 7 percent of male non-migrants have a Master’s degree.
In order to add time dimension, the evolution of the emigration rate is presented in figure 1a for
men and in figure 1b for women separately for the whole population and for those with higher
education and without higher education. As we are looking at long-term migration, the
emigration rates are small, but there is an upward trend. The rate is higher for men and for those
with higher education. We also computed the difference between the average of the log
standardized earnings, or a degree of selection, for migrants and non-migrants for each year from
1995 to 2004 for men and women separately. The results are reported in figures 2a and 2b. There
is a downward trend in the difference for both men and women. The finding makes sense: when
the migrants are positively self-selected and the emigration rate gets bigger the average
standardized earnings of migrants should get smaller. However, the variation across years is
small, so that pooling the data is justified.
Tosummarize,thedescriptivefindingssuggestastrongdegreeofpositiveselection—at
leastasmeasuredbyeducationanddifferencesintheconditionalmeansofearnings.
4.Selectioninpre‐migrationearnings
Thissectionpresentsempiricalevidenceontheself‐selectionofemigrantsfromDenmark
intermsofstandardizedpre‐emigrationearnings.Themainempiricalfindingisthatlong‐
termemigrantsfromDenmarkwere,ingeneral,muchmoreproductivepriortotheir
migrationthanindividualswhochosetostay.
Ofcourse,thesummarystatisticsreportedinTable1alreadysuggestpositiveselection
amongemigrantsbecausetheirstandardizedearningsexceededthoseofnon‐migrants.
However,differencesinconditionalaveragescouldbemaskingsubstantialdifferences
betweentheunderlyingprobabilitydistributions.Ourtheoreticalframeworkpredictsthat
thedistributionofearningsformigrantsshouldstochasticallydominatethatofnon‐
migrants.Asaresult,ourempiricalanalysiswillmainlyconsistofcomparingcumulative
18
distributionsofstandardizedearningsbetweenmigrantsandnon‐migrants.Anadvantage
ofsimplygraphingandexaminingthecumulativedistributionsisthattheanalysisdoesnot
requireanytypeofkerneldensityestimation,andthatwedonotneedtoimposeany
statisticalassumptionsorparametricstructureonthedata.Wewillalsopresentkernel
densityestimatesoftheearningsdensityfunctionsasanalternativewayofpresentingthe
keyinsights.Finally,wewillderiveandreportstatisticalteststodetermineifthedata
supportthetheoreticalpredictionofstochasticdominance.
Figure3aillustratesthecumulativeearningsdistributionsformalemigrantstoNordic
countries,malemigrantstodestinationsoutsideNordiccountries,andformalenon‐
migrants.Thevaluesofthestandardizedearningsaretruncatedat‐2and2tomakethe
graphsmoretractable.21Thefigureconfirmsthatmigrantswerepositivelyselectedduring
thestudyperiod.Thecumulativedistributionfunctionofstandardizedearningsof
migrantstodestinationsoutsidetheNordiccountriesisclearlylocatedtotherightofthe
correspondingcumulativedistributionfornon‐migrants,aswouldbethecaseifthe
cumulativedistributionofmigrantsstochasticallydominatesthatofnon‐migrants.The
figurealsoshowsthatthedistributionfunctionformigrantstootherNordiccountriesis
locatedtotherightofthatfornon‐migrants.However,theselectionofthemigrantsto
Nordiccountriesseemsweaker.Thisweakerselectionmayarisebecausetherateofreturn
toskillsinNordiccountriesisrelativelylowwhencomparedtothatinotherpotential
destinations.22Figure3bpresentscorrespondingevidenceforwomen.23Themainfindings
arequalitativelysimilar,butthepositiveselectionseemsweaker.
21Thetruncationdoesnotaltertheresultsconsiderablyasthesharesofobservationsbelowthelowerand
abovetheuppertruncationpointsaresmall.Further,thefollowinganalysisofdifferencesbetween
cumulativedistributionfunctionsdoesnotusetruncation.0.07%ofnon‐migrants,0.19%migrantstoother
Nordiccountriesand0.11%ofmigrantstootherdestinationsliebelowthelowertruncationpoint.
Correspondingly,0.03%ofnon‐migrantsand0.21%ofmigrantstodestinationsoutsideNordiccountrieslie
abovetheuppertruncationpoint.TherearenomigrantstootherNordiccountriesabovetheupper
truncationpoint.
22Moreover,someDanesmayliveinsouthernSwedenbutworkinDenmark.Asthistypeofmigrationisnot
relatedtoreturnstoskillsinthedestinationcountrythisshoulddecreasetheestimatedselectiontoNordic
countries.
19
Figure4apresentsthecorrespondingkernelestimatesofthedensityfunctionsofthe
logarithmofstandardizedearningsformen,whileFigure4bpresentstherespectivegraphs
forwomen.24Thedensityfunctionsagainrevealthepositiveselectionofmigrantsmoving
outsidetheNordiccountries,bothformenandwomen.
Asisevidentfromthefigures,Kolmogorov‐Smirnovtestscomparingtheearnings
distributionsfordifferentgroupsrejectthehypothesisthattheunderlyingearnings
distributionsarethesameatahighlysignificantlevel.Inadditiontoshowingthatthe
cumulativedistributionsaredifferent,itisalsoimportanttodetermineiftheevidence
statisticallysupportsthetheoreticalpredictionthatthecumulativedistributionfunctionof
migrantsstochasticallydominatesthatofnon‐migrants.Statisticaltestsforfirst‐order
stochasticdominancearehighlysensitivetosmallchangesintheunderlyingdistributions,
makingitdifficulttorankdistributionsinmanyempiricalapplications.25Asnotedby
DavidsonandDuclos(2013),itmaybeimpossibletoinferstochasticdominanceoverthe
fullsupportofempiricaldistributionsifthedistributionsarecontinuousinthetails,simply
becausethereisnotenoughinformationinthetailsformeaningfultestingofanystatistical
hypothesis.Itwouldthenmakesensetofocusontestingstochasticdominanceovera
restrictedrangeofthedistribution.Weapplyanapproachthatcharacterizestherange
overwhichthevalueofthecumulativedistributionfunctionfornon‐migrantsis
statisticallysignificantlylargerthanthatofnon‐migrants.
Inparticular,wecalculatethedifferencebetweenthecumulativedistributionfunctions
withconfidenceintervals.Tocalculatetheconfidenceintervalsweusetoolsthatwere
23Forwomen,0.06%ofnon‐migrantsliebelowthelowertruncationpointand0.00%ofnon‐migrantslie
abovethehighertruncationpoint.Therearenomigrantslyingbelowthelowerorabovethehigher
truncationpoint.
24FollowingLeibbrandtetal.(2005)andFernandes‐HuertasMoraga(2011),weuseSilverman’sreference
bandwidthmultipliedby0.75topreventover‐smoothing.Thesamebandwidthisusedalsoinallthekernel
densityestimatesreportedinsubsequentcalculations.
25Thiscanleadtodifficultiesinempiricalwork,andlessrestrictiveconceptssuchasrestrictedfirstorder
stochasticdominance(Atkinson,1987)andalmoststochasticdominance(LeshnoandKevy,2002)havebeen
proposed.
20
introducedinAraar(2006)andAraaretal.(2009).26Moreformally,wetestthefollowing
nullhypothesisforeach
∈ ,where isthejointsupportofthetwodistributions:
H0:F(w))=FN(w)–FM(w) 0,
(17) againstthealternativehypothesis
H1:F(w))=FN(w)–FM(w) 0
(18) andcharacterizeanyrelevantrangeof whereweareabletorejectthenull.
Let
bethestandarddeviationoftheestimator∆
w ,andletz()bethe(1–)th
quantileofthestandardnormaldistribution.27DavidsonandDuclos(2000)showthatthe
estimator∆
w isconsistentandasymptoticallynormallydistributed.Wecanthen
definethelowerboundforaone‐sidedconfidenceintervalfor∆
as:28
(19) ∆
∆
w
.
WeestimatethestandarderrorsusingaTaylorlinearizationandallowforclusteringatthe
individuallevel.Wethenimplementtheprocedurebycalculatingthelowerboundsofthe
confidenceintervalsfortheestimate∆
w definedinequation(19).
Table4reportsthesharesofmigrantsandnon‐migrantswhoseearningsareoutsidethe
rangeoverwhichthemigrantdistributionstochasticallydominatesata95percent
confidencelevel.Considerfirstthedistributionsofnon‐migrantmenandmenmigratingto
destinationsoutsidetheNordiccountries.Althoughitisnotclearlyvisiblefromfigure3a,
26ThecalculationsareimplementedusingtheDASPStatamodulepresentedinAraarandDuclos(2013).
27Theasymptoticvarianceof∆
isderivedinAraaretal.(2009).
28Chow(1989)provedthetheoremforthecaseofindependentsamples.DavidsonandDuclos(2000)show
thattheresultsalsoextendtothecaseofpairedincomesfromthesamepopulation.
21
thecumulativedistributionfunctionscrossnearthelowertailsofthedistributions.Figure
5adepicts∆
w andlowerandupperboundsfora95%confidenceinterval.29The
lowerboundoftheconfidenceintervalispositiveonmostoftherangecoveringthe
supportsofthedistributions.Only2.0percentofthemigrantsand3.4percentofthenon‐
migrantsliebelowthelowerboundoftherangewherethelowerboundoftheconfidence
intervalispositive,whereasthesharesofmigrantsandnon‐migrantsabovetheupper
boundoftherangeare0.1and0.0percent.Putdifferently,theearningsofalmost98
percentofmalemigrantstodestinationsoutsideNordiccountriesareontherangewhere
thecumulativedistributionfunctionfornon‐migrantsisstatisticallysignificantlyabovethe
functionformigrants.
w andtheboundsfora95%confidenceintervalfornon‐migrant
Figure5bdepicts∆
womenandwomenmigratingtodestinationsoutsideNordiccountries.Only2.8percentof
themigrantsand4.1percentofthenon‐migrantshaveearningsbelowtherangewherethe
lowerboundoftheconfidenceintervalispositive,andanevensmaller0.2percentofthe
migrantsand0.0percentofthenon‐migrantshaveearningsabovethisrange.Weinterpret
thesefindingsassupportforthestochasticdominancepredictionforbothmenandwomen
migratingoutsideNordiccountries.
Figures6aand6bandthebottompanelofTable4presentacorrespondinganalysisby
comparingthecumulativedistributionsofpersonswhomigratetootherNordiccountries
withthatofnon‐migrants.Almost12percentofmalemigrantsand16percentofmalenon‐
migrantshaveearningsthatliebelowtherangewhere
∆
ispositive,andanother1.5
percentofthemigrantsand0.7percentofthenon‐migrantshaveearningsabovetherange.
Putdifferently,about87percentofthemalemigrantstoNordiccountrieshaveincomeson
therangewhere
∆
ispositive.Forwomen,itcanbeseeninTable4thatalmost95
percentofthemigrantsgoingtoNordiccountrieshaveearningsontherangewhere
∆
ispositive.Tosumup,thefindingsoffersupporttothestochasticdominance
29Theupperboundsarecalculatedsimilarlytothelowerbounds.
22
predictionformaleandfemalemigrantsregardlessoftheirdestination,althoughthe
evidenceisweakerformenwhomigratedtoNordiccountries.
AdditionalsupportforourtheorycomesfromMexico.Ourtheorypredictsthatthe
earningsdistributionofmigrantsfromMexicototheUnitedStatesshouldbestochastically
dominatedbytheearningsdistributionofnon‐migrants.Fernández‐HuertasMoraga
(2011)presentsthesedistributionsformen.Althoughhedoesnotpresentconfidence
intervalsaswedo,thefiguressuggestapatternthatmirrorswhatwefindforDenmark,
reversingthecurvesformigrantsandnon‐migrants.InMexico,thewagedistributionof
non‐migrantsstochasticallydominatesthatofmigrants,apartfromanoverlapforafew
percentatthebottomandconvergingatthetop.
5.Selectioninunobservedcharacteristics
Intheprevioussection,wedocumentedtheselectionthatcharacterizesthemigrantsusing
thetotalpre‐migrationearnings(afteradjustingforageandyear).Wenowexaminea
specificcomponentofearnings,namelythecomponentduetounobservedcharacteristics.
Inparticular,wenowadjustfordifferencesineducationalattainmentbetweenmigrants
andnon‐migrants(aswellasotherobservablevariables)byrunningearningsregressions,
anddeterminewhetherthedistributionoftheresidualsdiffersbetweenthetwogroups.30
Byconstruction,theresidualsfromaMincerianwageregressionreflectthepartofearnings
thatisuncorrelatedwiththeobservedmeasuresofskill.Obviously,thedecompositionis
somewhatarbitrarybecauseitdependsonthecharacteristicsthatareobservedandcanbe
includedasregressorsinthewageequation.Nevertheless,thestudyofemigrantselection
intermsofwageresidualsisimportantforanumberofreasons.
30Intheearningsregressionsweusenon‐standardizedannualearningsasthedependentvariable.We
includeageandyearfixedeffectsandruntheregressionsseparatelyformenandwomen.
23
First,selectionintermsofunobservablecharacteristicsshedslightontheimportanceof
thequalityofjobmatchesrelativetotheskillcomponentthatisinternationally
transferable.Thetheorypredictsthatthenatureoftheselectioninunobservable
characteristicsdependsonthemagnitudeofthecorrelationcoefficientmeasuringhowthe
sourceanddestinationcountriesvaluethesetypesofskills.Aslongasthiscorrelationis
stronglypositive(sothatunobservedcharacteristicsareeasilytransferableacross
countries),Danishemigrantswouldbepositivelyselectedinunobservables.Afterall,the
payofftothesetypesofskillsislikelytobegreaterinthedestinationcountries.However,it
couldbearguedthatthecorrelationbetweenthewageresidualsinDenmarkandabroad
maybe“small”.Forexample,theresidualsfromthewageregressionmaybelargely
reflectingthequalityoftheexistingjobmatchintheDanishlabormarket,ratherthan
measuringtheworker’sinnateproductivity.Totheextentthatthequalityofthejobmatch
playsanimportantroleingeneratingtheresidual,thecorrelationinthisresidualacross
countrieswouldbeexpectedtobeweak(infact,apurerandommatchingmodelwould
suggestthatitwouldbezero).Asaresult,therewouldbenegativeselectioninunobserved
characteristicssimplybecauseDanishworkerswithgoodjobmatches(andhencehigh
valuesoftheresidual)wouldnotmove.
Second,thetheoryalsosuggeststhatthenatureoftheselectioninpre‐migrationearnings
dependsonaweightedaverageoftheselectionthatoccursinobservableandunobservable
characteristics,withtheweightsbeingthefractionofearningsvarianceattributableto
eachtypeofskill.Becauseobservablecharacteristicsplayonlyalimitedroleinexplaining
thevarianceofearningsinthepopulation,itiscrucialtopreciselydelineatethenatureof
selectioninunobservablecharacteristics.
Table5reportstheMincerianwageregressionsthatweusetocalculatetheresiduals.The
sampleincludesthewholepopulationofprimeagedfulltimeworkerspooledoverthe
entire1995‐2004period.Inadditiontovectorsoffixedeffectsgivingtheworker’sageand
educationalattainment,wealsoincludetheworker’smaritalstatusandnumberofchildren.
Theregressionsareestimatedseparatelyformenandwomen.
24
Figure7apresentsthecumulativedistributionsofwageresidualsformalemigrantsto
Nordiccountries,malemigrantstodestinationsoutsideNordiccountries,andmalenon‐
migrants.Thevaluesoftheresidualsaretruncatedat‐2and2,arangethatcovers
practicallyallofthepopulation.31Thecumulativedistributionfunctionofresidualsfor
emigrantswhomovedoutsidetheNordiccountriesislocatedtotherightofthecumulative
distributionformigrantstoNordiccountries,whichinturnislocatedtotherightofthe
cumulativedistributionofthenon‐migrants.Thevisualevidence,therefore,providesa
strongindicationthatmigrantsarepositivelyselectedintermsofunobserved
characteristics.Figure7bpresentstheanalogousevidenceforwomen.32Thefigureshows
thatfemalemigrantsarealsopositivelyselectedintermsofwageresiduals.Aswasthe
casewhencomparingthemeasureofpre‐migrationearningsintheprevioussection,the
selectioninunobservedcharacteristicsislesspronouncedforwomenthanformen.One
explanationforthiscouldbethatmenaretypicallyprimaryearnersincouples.
WealsoperformedKolmogorov‐Smirnovtestsonthedistributionsofresidualsfornon‐
migrantsandmigrantstootherNordiccountriesandformigrantstootherdestinations
(separatelyformenandwomen).Allthetestsclearlyrejectedthenullhypothesis,
confirmingthatthedistributionsofresidualsindeeddifferamongthegroups.33
Theevidenceonthepositiveselectionofmigrantsinunobservedcharacteristicsobviously
impliesthattheselectioninpre‐migrationearningsdocumentedintheprevioussection
cannotbeattributedsolelytothefactthatmigrantsaremoreeducated.Instead,wefind
thatthereispositiveselectionwithineducationgroups.Thisresultalsohasimplicationson
31Formen,0.05%ofnon‐migrants,0.19%ofmigrantstootherNordiccountriesand0.11%ofmigrantsto
otherdestinationsliebelowthelowertruncationpoint.Correspondingly,0.03%ofnon‐migrantsand0.23%
ofmigrantstodestinationsoutsideNordiccountrieslieabovetheuppertruncationpoint.Thereareno
migrantstootherNordiccountriesabovetheuppertruncationpoint.
32Forwomen,0.05%ofnon‐migrantsliebelowthelowertruncationpointand0.00%ofnon‐migrantslie
abovethehighertruncationpoint.Therearenomigrantslyingbelowthelowerorabovethehigher
truncationpoint.
33Thep‐valueforthetestbetweenwomenmigratingtootherNordiccountriesandtootherdestinationswas
0.015andalltheotherp‐valueswere0.000,sothatalltestsclearlyrejectthehypothesisthatthe
observationsaredrawnfromthesamedistribution.
25
theinterpretationofearningsregressionresidualsingeneral.Theresidualsfromwage
regressionsaresometimesinterpretedasreflectingthevalueofthejobmatchbetweenthe
workerandtheemployer.Ifahighvaluefortheresidualonlyreflectsagoodmatch,we
wouldthenexpecttofindthatworkerswithlargeresidualswouldbelesslikelytochange
jobsandlesspronetomigrate.Ourfindingsclearlyrejectthisinterpretation.Comparing
resultsontheself‐selectiontootherNordiccountriesandtherestoftheworldsuggests
thatsearchforabetterjobmatchtothosewhohaveabadjobmatchinDenmarkismore
pronouncedamongmigrantstootherNordiccountries.34
Asintheprevioussection,wealsocalculatedthedifferencebetweenthecumulative
distributionfunctionswithconfidenceintervalstodeterminewhetherempiricalevidence
supportsthestochasticdominanceprediction.ThetestresultsaresummarizedinTable6.
Figure8adepicts∆
w andthelowerandupperboundsfora95%confidenceinterval
forthecomparisonbetweennon‐migrantmenandmenmigratingtodestinationsoutside
Nordiccountries.Thelowerboundofthe95%confidenceintervalispositiveontherange
ofresidualscoveringmostofthesupportofthetwodistributions.9.9percentofthe
migrantsand15.2percentofthenon‐migrantshavewageresidualsbelowthelowerbound
ofthisrange,whereasthesharesofmigrantsandnon‐migrantsabovetheupperboundof
therangeare0.1and0.0percent.35
Figure9adepicts∆
w andtheboundsfora95%confidenceintervalfornon‐migrant
menandmenmigratingtootherNordiccountries.A13percentshareofmigrantsand15
percentofnon‐migrantshavevaluesofthewageresidualthatarebelowthelowerbound
oftherangewherethelowerboundofthe95%confidenceintervalispositive,andshares
of2percentand1percentofmigrantsandnon‐migrantshavevaluesoftheresidualthat
34Forthisgroup,returnstounobservedproductivityarenotasimportantacriterionforself‐selectionas
amongmigrantstotherestoftheworld,simplybecausedifferencesinreturnstoskillsbetweenDenmarkand
otherNordiccountriesareminor.Asaresult,themechanismofsearchingforabettermatchqualityismore
pronounced.
35Forwomen,20percentofmigrantsand25percentofnon‐migrantshaveearningsresidualsbelowthe
lowerboundoftherangewherethelowerboundoftheconfidenceintervalispositive,andsharesofmigrants
andnon‐migrantsabovetherangearelessthanonepercent.
26
wouldplacethemabovethisrange.Putdifferently,theresidualsofover84percentofmale
migrantstodestinationsoutsideNordiccountriesareontherangewherethecumulative
distributionfunctionfornon‐migrantsisstatisticallysignificantlyabovethefunctionfor
migrants.36Interestingly,thereisasizableareainthelefttailofthedistributionof
residualswheretheupperboundoftheconfidenceintervalisnegative.37
Weconcludebysummarizingtheevidenceasfollows:thereisstrongpositiveselectionin
unobservablecharacteristicsinthesampleofmigrantsthatmovedoutsidetheNordic
countriesandweakerevidenceofpositiveselectioninthesampleofmigrantswhomoved
tootherNordiccountries.
6.Biasincounterfactualpredictions
Thefactthatemigrantsareself‐selectedintheirunobservedcharacteristicsimpliesthat
usingtheobservablecharacteristicsofmigrantstopredicttheircounterfactualearnings
hadtheychosennottomigratewillleadtobiasedresults.Duetodataconstraints,thisis
preciselytheempiricalexerciseconductedbyChiquiarandHanson(2005),whoadoptthe
methodologyintroducedbyDiNardo,Fortin,andLemieux(1996)andbuilda
counterfactualwagedensityofwhattheMexicanimmigrantswouldhaveearnedinMexico
hadtheystayed.TheactualwagedensityofMexican“stayers”isthencomparedtothe
counterfactualdensityformigrants.Byconstruction,thisapproachignorestheroleof
unobservablecharacteristicsintheestimationofthecounterfactualwagedistribution.
AclearadvantageoftheDanishadministrativedataisthattheearningsofemigrantscanbe
observedbeforetheyemigrate,sothereisnoneedtobuildacounterfactualdensity.One
justneedstocomparetheearningsdistributionofnon‐migrantstotheactualdistribution
36Forwomen,20percentofmigrantsand25percentofnon‐migrantshaveearningsresidualsbelowthe
lowerboundoftherangewherethelowerboundoftheconfidenceintervalispositive,andsharesofmigrants
andnon‐migrantsabovetherangeare3percentand2percent.
37A2percentshareofmigrantsand2percentshareofnon‐migrantshaveresidualsinthisarea,andthe
interpretationwouldbethatmalemigrantstootherNordiccountriesarenegativelyselectedintermsof
residualsinthelefttailofthedistribution.
27
offuturemigrants,aswehavedoneintheprecedinganalysis.Theadministrativedata,
however,allowsustopreciselymeasuretheextentofthebiasresultingfromcarryingout
thecounterfactualexerciseinChiquiarandHanson(2005).Inparticular,wecancontrast
thepredictedcounterfactualwagedistributionofmigrantshadtheynotmovedtothe
actualwagedistributionofmigrantspriortotheirmove.Wecarryoutthisexerciseby
preciselyreplicatingthevariousstepsintheChiquiar‐Hansoncalculations.Itisworth
emphasizingthatthistypeofbiaswillarisenotonlyinstudiesthatexaminetheselectionof
migrants,butinanystudythatreliesonobservablestopredictacounterfactualwage
distribution.
Let representthelogarithmofstandardizedannualearningsasdefinedearlier(i.e.
| bethedensityfunctionof
earningsadjustedforage,gender,andyeareffects).Let
wagesinDenmark,conditionalonasetofobservablecharacteristics .Also,let bean
indicatorvariableequaltooneiftheindividualmigratesthefollowingyearandequalto
zerootherwise.Definefurther
|
0 astheconditionaldensityofobserved
characteristicsamongworkersinDenmarkwhochoosenottomigrate,and
|
1 be
thecorrespondingconditionaldensityamongmigrants.Theobservedwagedensityforthe
non‐migrantsis
(20) |
0
| ,
0
|
0
.
1
.
Similarly,theobserveddensityforthemigrantsis
(21) |
1
| ,
1
|
Uptothispoint,theanalysisreportedinthispaperconsistsofdirectlyestimatingand
comparingthedistributionfunctionsassociatedwiththedensitiesinequations(20)and
(21).Supposethatthepre‐migrationearningsdensityfornon‐migrantswerenotavailable.
Wewouldinsteadattempttoestimateitfromtheobservablecharacteristicsofthe
migrants.Theimpliedcounterfactualdistributionis:
28
|
(23) | ,
1
|
0
1
.
Equation(23)correspondstothedensityofincomefornon‐migrants,butitisinstead
integratedoverthedensityofobservablecharacteristicsformigrants.Notethatthe
counterfactualdensityin(23)canberewrittenas:
(24) |
| ,
1
|
0
|
|
0
1
0
| ,
0
|
0
,
where
|
|
.Tocompute ,weuseBayes’lawtowrite:
|
(25) |
|
and
|
,
where
istheunconditionaldensityofobservedcharacteristics.
Wecanthencombinethesetwoequationstosolvefor:
(26) 1|
1
1|
0
.
1
TheproportionPr(I=0)/Pr(I=1)isaconstantrelatedtotheproportionofmigrantsinthe
data.Itcanbesettooneinkerneldensityestimationwithoutlossofgenerality.Theweight
weuseintheestimationisthengivenby:
29
(27) 1|
1
1|
.
AsinChiquiarandHanson(2005),theindividualweightsearecalculatedbyestimatinga
logitmodelwherethedependentvariableindicatesifapersonemigrated.Theregressors
includeavectorofagefixedeffects,avectorofschoolingfixedeffects,variablesindicating
whethertheworkerismarriedandthenumberofchildren(andaninteractionbetween
thesetwovariables),andavectorofyearfixedeffects.38Table7reportsthelogit
regressionsestimatedseparatelybygender.Thecoefficientsarethenusedtocomputethe
weightsforeachnon‐migrantpersoninthesample.39Figures10aand10bpresentthe
resultingcounterfactualdensityfunctionsofthelogarithmofstandardizedearningsaswell
astheactualdistributionsformigrantsandnon‐migrants.40
Thedifferencebetweentheactualdensityfornon‐migrantsandthecounterfactualdensity
formigrantsreflectsthepartofself‐selectionthatisduetoobservablecharacteristics.
Similarly,thedifferencebetweenthecounterfactualandactualdensitiesformigrants
reflectsthepartofselectionthatisduetounobservedcharacteristics(i.e.,allthose
variablesthatcouldnotbeincludedinthelogitmodel).
Onesimplewayofquantifyingthesedistributionaldifferencesistocomputetheaverages
ofthevariousdistributions.ThesecalculationsarereportedinTable8.Considerinitially
theresultsinthemalesample.Thedifferencebetweenthemeanoftheactualdistributions
formigrantsandnon‐migrantsis0.245logpoints,butthedifferencebetweenthe
counterfactualdistributionandthedistributionfornon‐migrantsis0.073.Thisimpliesthat
onlyabout30percentofthepositiveselectioninpre‐migrationearningscanbeattributed
38Wealsotriedspecificationswithage,agesquaredandinteractionsofexplanatoryvariables,butwedonot
reporttheseanalysesastheresultingcounterfactualdistributionsdidnotpracticallydifferfromthe
distributionsresultingfromthissimplerspecification.
39Asearlier,weuseSilverman’sreferencebandwidthmultipliedby0.75.
40Toconductthecounterfactualanalysiswepoolthesampleofallmigrants(regardlessofwhetherthey
movedtoNordiccountriesornot).
30
totheobservablecharacteristicsincludedinthelogitmodel,whileabout70percentis
attributabletounobservabledeterminantsofproductivity.
Thecalculationsinthefemalesampleyieldadifferenceof0.157logpointsbetweenthe
meansoftheactualdistributionsformigrantsandnon‐migrantsandadifferenceof0.074
pointsbetweenthecounterfactualdistributionandthedistributionfornon‐migrants.Asa
result,observableandunobservablecharacteristicseachaccountforabouthalfofthe
positiveself‐selectioninthepre‐migrationearningsofwomen.41Thekeylessonisclear:
selectioninunobservablecharacteristicsplaysacrucialroleindeterminingtheskill
compositionofemigrants.
Thedistinctroleofobservablesandunobservablesindeterminingtheselectioninthepre‐
migrationearningsofmigrantsisevidentifwereturntotheRoymodelandequation(16),
whichpresentstheconditionalexpectationE(logw0|v*>*).
Equation(16)yieldsaninterestingandpotentiallyimportantinsight.Thenatureofthe
selectioninpre‐migrationearnings,ofcourse,isgivenbythesumoftheselectionin
observablesandtheselectioninunobservables.Note,however,thateachoftheseselection
termshasaweightingcoefficientthatrepresentsthevarianceinearningsattributableto
observablecharacteristics( r02  2S)ortounobservablecharacteristics(  20 ).Asnotedearlier,
observablecharacteristicsexplainarelativelysmallfractionofthevarianceinearnings.Put
differently,equation(16)impliesthatitistheselectioninunobservablesthatismostlikely
todeterminethenatureoftheselectionthatcharacterizestheemigrantsample.
Totheextentthatbothtypesofselections(i.e.,inobservablesandunobservables)workin
thesamedirection,thecounterfactualexercisedescribedinthissectionwillinevitably
underestimatethetrueextentofpositiveselectioninpre‐migrationearnings.Conversely,
41Thecomponentofself‐selectionthatisduetounobservablecharacteristicsplaysasomewhatsmallerrole
forwomen.Onereasoncouldbethatwomenaremoreoftentiedmigrants,andthemigrationdecisionmaybe
mainlybasedontheskillsofthespouse.Thevarianceinincomeisalsosmallerforwomen,whichalsomakes
theselectionbothintermsofobservableandunobservablecharacteristicsweaker.
31
thecounterfactualexercisewillalsoattenuatetheextentof“true”negativeselectionif
thereisnegativeselectioninbothcomponentsofskills.Infact,Fernández‐HuertasMoraga
(2011)presentsacorrespondinganalysisusingsurveydatafromMexicoandfindsthat
counterfactualestimatesgreatlyunderestimatetheextentofnegativeselectioninthepre‐
migrationearningsofMexicanswhomovetotheUnitedStates.Putdifferently,the
counterfactualexercisemayleadtoqualitativelyrightconclusionsaboutthenatureofthe
selection,butitmayalsogenerateasizablebias,greatlyunderestimatingthetrueextentof
eitherpositiveornegativeselection.
7.Selectionandimmigrationrestrictions
Asappliedintheimmigrationliterature,theRoymodelfocusessolelyontheeconomic
factorsthatmotivatelaborflowsacrossinternationalborders.Themodelingtypically
ignoresthefactthattheseflowsoccurwithinapolicyframeworkwheresomereceiving
countriesenactdetailedrestrictionsspecifyingwhichpotentialmigrantsareadmissible
andwhicharenot.
WecanusetheadministrativedatafromDenmark,combinedwiththeuniquepolitical
circumstancesthatguaranteefreemigrationwithinEurope,topartiallyaddressthe
questionofwhetherimmigrationpolicyaffectsselectionallthatmuchintheend.
Specifically,wecansubdividethegroupofmigrantswhomovedoutsideNordiccountries
intotwogroups:thosewhomovedtoacountryintheEU15ortoSwitzerland,andthose
whomovedtoacountryoutsidetheEU15andSwitzerland.Movementoflaborwas
unrestrictedbetweenDenmarkandotherEU15countriesandSwitzerlandintheperiod
understudy,butwasobviouslyrestrictedbyimmigrationregulationstodestinations
outsidetheEU15,suchastheUnitedStates.
ItturnsoutthatthesedifferentimmigrationpoliciespursuedbytheEU15andSwitzerland
andtherestoftheworldbarelymatterindeterminingtheselectionofDanishemigrants.
Figure11adepictsthecumulativedistributionfunctionsofthelogarithmofstandardized
annualincomeformenandfigure11bforwomen.Itisevidentthatthedistribution
32
functionsofstandardizedearningsareverysimilarforthetwogroupsofmigrants.42We
alsoconductedtheanalysisusingthewageresiduals(notshown),andthedistributionsof
residualsarealsosimilarbetweenthetwogroups.
Thereisanimportantsenseinwhichthesepolicyrestrictionscannotmattermuch.
Suppose,forexample,thatareceivingcountryenactsapolicythatlimitsentryonlytohigh‐
skillimmigrants.Ifthehigh‐skillimmigrantsfromasendingcountrydonotfinditoptimal
tomove,thepolicycannotforcethosehigh‐skillworkerstomigrate.Allthepolicycandois
essentiallycutthemigrationflowfromthatparticularsendingcountrydowntozero.The
low‐skillworkerswouldliketomovebutarenotadmitted,andthehighskillworkersare
admissiblebuttheydonotwanttomove.
Insum,thepositiveself‐selectionthatissoevidentintheDanishemigrantdatacannotbe
explainedbyimmigrationrestrictions.EventhoughlaborflowstotheEU15and
Switzerlandwereunrestricted,thereisnoevidenceofweakerpositiveselectiontothese
countriesthantotherestoftheworld.Our results also have tentative implications for the
question of whether migration patterns reflect differences in rate of returns or migration costs.
Although it is plausible that migration costs are higher when moving to other continents, our
results suggest that such differences do not play a significant role in the sorting of emigrants
between Europe and other continents, most notably North America.
8.Conclusion
ThispapershowsthattheRoymodelhasmoredramaticpredictionsontheself‐selectionof
emigrantsthanpreviouslyexamined.Thesameconditionsthathavebeenshowntoresult
inemigrantsbeingpositively(negatively)self‐selectedintermsoftheiraverageearnings
actuallyimplythattheearningsdistributionofemigrantsfirst‐orderstochastically
dominates(orisfirst‐orderstochasticallydominatedby)theearningsdistributionofnon‐
42Forwomen,aKolmogorov‐Smirnovtestisnotabletorejectthenull‐hypothesisthattheobservationsfor
thetwogroupsofmigrantscomefromthesameunderlyingdistribution.
33
migrants.Ourtheoreticalanalysisalsodistinguishesbetweenselectioninobservableand
selectioninunobservablecharacteristics.
OurempiricalanalysisusestheDanishfullpopulationadministrativedatatoanalyzethe
self‐selectionofemigrants,intermsofeducation,earningsandunobservableability,
measuredbyresidualsfromMincerianearningsregressions.Theresultsareinlinewith
thetheory;themigrantsarebettereducatedandbothpre‐emigrationearningsandwage
regressionresidualsofmigrantsstochasticallydominatethoseofnon‐migrantsovermost
ofthesupportofthedistributions.Consider,forexample,thecaseoffull‐timeworkers
aged25‐54.For98percentofmenand97percentofwomenwhomigrateoutsideother
Nordiccountriesthecumulativeearningsdistributionintheyearbeforeemigration
stochasticallydominatesthatofnon‐migrantswitha95%confidenceinterval.The
differencebetweenthecumulativedistributionsisnotstatisticallysignificantlydifferentin
eitherdirectionfortheremaining2to3percent.
Decomposingtheself‐selectionintotalearningsintoself‐selectioninobservable
characteristicsandself‐selectioninunobservablecharacteristics(asmeasuredbyresiduals
fromMincerianwageregressions),revealsthatunobservedabilitiesplaythedominantrole.
Formen,about70percentofthepositiveself‐selectioninpre‐migrationearningsis
attributabletounobservabledeterminantsofproductivity.Forwomen,thefractionis
about50percent.Thissuggeststhatrelyingoncounterfactualdistributions,basedon
observedcharacteristics,wouldstronglyunderestimatepositiveself‐selection.Thisresult
complementstheFernández‐HuertasMoraga(2011)findingthatcounterfactualestimates
alsogreatlyunderestimatetheextentofnegativeselectioninthepre‐migrationearningsof
MexicanswhomovetotheUnitedStates.Inshort,theuseofcounterfactualearnings
distributionsbasedonobservablecharacteristicsgreatlyunderstatethetrueextentof
selectionintotalearnings.Strongpositiveself‐selectioninresidualsalsosuggeststhat
unobservedabilitiesplayamuchbiggerroleinmigrationdecisionsthanmatchquality.
Ourfindingsalsohaveimplicationsforimmigrationpolicies.Receivingcountriescanonly
basetheiradmissionpoliciesonskillvariablesthatareobserved,whereasmuchofthe
34
selectionofimmigrantsis“hidden”intheirunobservedcharacteristics.Itcanbeexpected
thatmigrantswillbeself‐selectedintermsofunobservedcharacteristicsevenwhen
admissionrestrictionsareapplied,andtheself‐selectionamongthosefulfillingadmission
criteriacanbeexpectedtoreflectrelativeskillprices.Thisraisesaquestionaboutthe
effectivenessofpointsystemsthatarenecessarilybasedonobservablecharacteristics.The
importanceofrelativeskillpricesisalsosupportedbyourseparateanalysesofself‐
selectionofDanesmigratingtothecountriesbelongingtocommonEuropeanlabormarket
(excludingotherNordiccountriesthathaveskillpricessimilartoDenmark)andnothaving
anyimmigrationrestrictions,andtheself‐selectiontotherestoftheworld.Thereis
virtuallynodifferenceintheself‐selectiontothesedestinationareas.
35
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38
Figurre1.Evolu
utionofthe
eemigratio
onrate
a.Men
b.Wom
men
39
ebetweenaveragelo
ogstandarrdizedearn
ningsof
Figure2.Evoluttionofthedifference
migranttsandnon‐migrants
a.Men
b.Wom
men
40
nctionsofsstandardizzedannuallearningsformigran
ntsand
Figurre3.Distributionfun
n
non‐migran
nts
a.Men
men
b.Wom
41
yfunctionssforstandardizedea
arningsforrmigrantssandnon‐m
migrants
Figure4.Density
a.Men
b.Wom
men
42
ure5.Diffe
erenceoftthecumula
ativedistriibutionfun
nctionsforrpre‐migrration
Figu
earn
ningsbetw
weenmigra
antsmovin
ngoutsideNordiccountriesan
ndnon‐mig
grants
a.Men
men
b.Wom
43
ure6.Diffe
erenceoftthecumula
ativedistriibutionfun
nctionsforrpre‐migrration
Figu
earningso
ofmigranttsgoingtootherNorrdiccountrriesandno
on‐migrantts
a.Men
men
b.Wom
44
Figure
e7.Distrib
butionfun
nctionsofrresidualsfrromearnin
ngsregresssionform
migrants
and
dnon‐migrrants
a.Men
b.Wom
men
45
gure8.Diffferenceoffthecumu
ulativedisttributionfu
unctionso
ofresidualssfor
Fig
migran
ntsgoingo
outsideoth
herNordiccountriesandnon‐m
migrants
a.Men
men
b.Wom
46
gure9.Diffferenceoffthecumu
ulativedisttributionfu
unctionso
ofresidualssfor
Fig
mig
grantsgoin
ngtootherNordiccountriesan
ndnon‐mig
grants
a.Men
men
b.Wom
47
gure10.Co
ounterfactu
ualandacttualdensittiesofstan
ndardizedgrossearn
nings
Fig
a.Men
men
b.Wom
48
Figure
e11.Distrributionfun
nctionsofannualgrossearnin
ngsformig
grantstoth
heEU15
andSwitze
erlandand
dmigrantsstootherd
destination
ns
a.Men
men
b.Wom
49
Table1.Summarystatistics
Non-migrant
men
Migrant
men
Non-migrant
women
Migrant
women
6450665
7323
5163129
3436
39.8
40.0
33.0
35.4
40.2
40.0
35
33.0
Annual earnings in
2010 euros
Average
Median
52725
46675
68151
57350
40299
37976
46412
42393
Standardized annual
earnings
Average
Median
1.0
0.9
1.3
1.2
1.0
0.95
1.2
1.1
Observations
Age
Average
Median
50
Table2.Numbersofmigrants,bydestination
Sweden
The United States
The United Kingdom
Norway
Germany
Spain
Switzerland
France
Other
Men
Women
1466
763
725
576
560
255
233
222
2523
699
363
432
273
249
147
118
156
999
51
Table3.Educationlevelsofnon‐migrantsandmigrantsgoingtoNordiccountriesor
tootherdestinations
Men
Women
Nonmigrants
Nordic
countries
Other
destinations
Nonmigrants
Nordic
countries
Other
destinations
Comprehensive
school
21.4
19.8
8.3
21.5
15.7
8.9
High school
3.2
7.8
8.6
3.1
6.9
8.9
Vocational
school
49.8
43.5
30.3
41.8
36.5
30.8
Advanced
vocational
5.6
5.7
6.6
4.9
5.1
7.8
Bachelor or
equivalent
12.2
11.6
20.6
23.3
22.9
25.4
Master’s or
equivalent
7.3
10.6
23.9
5.1
12.3
17.6
Doctoral or
equivalent
0.5
1.0
1.7
0.2
0.7
0.7
Education
Notes: The unit is percentage. The category “advanced vocational” includes all the tertiary education programs
below the level of a Bachelor’s program or equivalent. Programs on this level may be referred to for instance with
such terms as community college education, advanced vocational training or associate degree.
52
Table4.Summaryoftestsofstochasticdominanceindistributionsofstandardized
pre‐migrationearnings
Distributions being
compared:
Percent of sample below
lower bound
Percent of sample above upper
bound
Migrants
Non-migrants
Migrants
Non-migrants
2.0 2.8 3.4 4.1 0.1 0.2 0.0 0.0 11.6 2.6 15.5 4.1 1.5 2.6 0.7 1.3 Migrants outside Nordic
countries and nonmigrants
Male
Female
Migrants to Nordic
countries and nonmigrants
Male
Female
Notes:Lowerboundandupperboundrefertotherangeoverwhichthedifferenceofthecumulative
distributionfunctionsissignificantata95percentconfidencelevel.
53
Table5.Mincerianearningsregressions,bygender
Married
Children
High school
Vocational school
Advanced vocational
Bachelor
Master’s
PhD
1996
1997
1998
1999
2000
2001
2002
2003
2004
Constant
Age fixed effects
N
R-squared
(1) men
(2) women
B
Se
B
0.068***
(0.00)
-0.016***
0.025***
(0.00)
-0.048***
0.224***
(0.00)
0.190***
0.092***
(0.00)
0.089***
0.186***
(0.00)
0.198***
0.298***
(0.00)
0.225***
0.498***
(0.00)
0.536***
0.490***
(0.00)
0.622***
0.020***
(0.00)
0.017***
0.043***
(0.00)
0.041***
0.078***
(0.00)
0.083***
0.103***
(0.00)
0.112***
0.141***
(0.00)
0.143***
0.175***
(0.00)
0.175***
0.207***
(0.00)
0.210***
0.236***
(0.00)
0.235***
0.252***
(0.00)
0.258***
12.131***
(0.00)
11.931***
Yes
Yes
6470720
5173706
0.2597
0.3062
*p<0.05, ** p<0.01, *** p<0.001
se
(0.00)
(0.00)
(0.00)
(0.00)
(0.00)
(0.00)
(0.00)
(0.00)
(0.00)
(0.00)
(0.00)
(0.00)
(0.00)
(0.00)
(0.00)
(0.00)
(0.00)
(0.00)
The table reports OLS results for the log annual earnings. Individually clustered standard errors are in parentheses.
Coefficients for the age dummies are not shown.
54
Table6.Summaryoftestsofstochasticdominanceindistributionsofresiduals
Distributions being
compared:
Percent of sample
below lower bound
Percent of sample above upper bound
Migrants
Nonmigrants
Migrants
Non-migrants
Migrants outside Nordic
countries and non-migrants
Male
Female
9.9
19.6
15.2
24.7
0.1
0.4
0.0
0.0
Migrants to Nordic countries
and non-migrants
Male
Female
13.4
19.5
15.2
24.7
2.0
3.4
0.9
1.8
Notes:Lowerboundandupperboundrefertotherangeoverwhichthedifferenceofthecumulative
distributionfunctionsissignificantata95percentconfidencelevel.
55
Table7.Logitestimatesoftheprobabilityofemigration,bygender
Married
Children
Married*Children
High school
Vocational school
Advanced vocational
Bachelor
Master’s
PhD
y1996
y1997
y1998
y1999
y2000
y2001
y2002
y2003
y2004
Constant
N
Pseudo
(1) men
B
Se
-0.110**
(0.04)
-1.137***
(0.05)
0.460***
(0.07)
1.377***
(0.05)
0.186***
(0.04)
0.648***
(0.06)
1.097***
(0.04)
1.652***
(0.04)
1.723***
(0.10)
-0.032
(0.06)
0.002
(0.06)
-0.024
(0.06)
0.230***
(0.05)
0.260***
(0.06)
0.161**
(0.05)
0.208***
(0.05)
0.198***
(0.05)
0.246***
(0.05)
-6.700***
(0.08)
6470720
0.0540
*p<0.05, ** p<0.01, *** p<0.001
(2) women
B
-0.191***
-1.232***
0.374***
1.158***
0.159**
0.714***
0.581***
1.444***
1.655***
-0.001
-0.016
-0.001
0.131
0.238**
0.146
0.046
0.112
0.178*
-6.951***
5173706
0.0557
se
(0.05)
(0.07)
(0.09)
(0.08)
(0.06)
(0.08)
(0.06)
(0.07)
(0.21)
(0.08)
(0.08)
(0.08)
(0.08)
(0.09)
(0.08)
(0.08)
(0.08)
(0.08)
(0.12)
Notes: The table reports logit results for the long-term emigration. Individually clustered standard errors are in
parentheses. Coefficients for the age fixed effects are not shown.
56
Table8.Actualandcounterfactualdifferencesbetweentheaveragelogstandardized
earningsofmigrantsandnon‐migrants
Men
Women
Non-migrant average
Estimated average for migrants
True average for migrants
True difference
-0.065
0.008
0.180
0.245
-0.040
0.034
0.117
0.157
Counterfactual difference
0.073
0.074
Share of the actual difference explained
by observable characteristics, %
29.6
47.0