George J. BorjasIlpo KauppinenPanu Poutvaara

Self-Selection of Emigrants: Theory and Evidence on Stochastic Dominance in Observable and Unobservable Characteristics

VATT INSTITUTE FOR ECONOMIC RESEARCH

VATT Working Papers 67

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 self-selection 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

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1.IntroductionAcentralfindingintheeconomicliteratureoninternationalmigrationisthatemigrantsarenotrandomlyselectedfromthepopulationofthesourcecountries.Thenatureofthenon‐randomselectionaffectsthelevelandthedistributionofwelfarethroughtwomajorchannels.First,theskilldistributionofmigrantsaffectsthewagestructureinbothsendingandreceivingcountries(Borjas2003).Asecondeffecttakesplacethroughthepublicsector.Immigrationcreatesafiscalsurplusinthereceivingcountryifandonlyifthenetpresentvalueofthetaxpaymentsofimmigrantsexceedsthenetpresentvalueofthecoststheyimpose.Boththeimmigrationofnetrecipientsandtheemigrationofnetpayersposeachallengetothepublictreasury(Wildasin1991;Sinn1997).BeginningwithBorjas(1987),therehasbeenagreatdealofinterestinderivingandempiricallytestingmodelsthatpredicthowmigrantsdifferfromnon‐migrants.ManyofthesestudiesrelyonanapplicationoftheRoymodelofoccupationalself‐selection.Aslongasskillsaresufficientlytransferableacrosscountries,thesortingofpersonsacrosscountriesismainlydeterminedbyinternationaldifferencesintherateofreturntoskills.AcountryliketheUnitedStateswouldthenattracthigh‐skilledworkersfrommoreegalitariancountries(i.e.,countriesofferingrelativelylowratesofreturntoskills)andlow‐skilledworkersfromcountrieswithgreaterincomeinequality(i.e.,countriesofferinghigherratesofreturntoskills).Theevidenceindeedsuggestsanegativecross‐sectioncorrelationbetweentheearningsofimmigrantsintheUnitedStatesandincomeinequalityinthesourcecountries.1AlthoughtheexistingliteratureonimmigrantselectionfocusesmainlyontheU.S.contextoronmigrationflowsfrompoortorichcountries,therearealsosizablemigrationflowsbetweenrichcountries.AccordingtotheUnitedNations(2013),21.9millionpersonsfrom

1Relatedcross‐countrystudiesincludeCobb‐Clark(1993)andBratsberg(1995).GroggerandHanson(2011)examinetheselectionofmigrantsacrossabroadrangeofcountriesusinganalternativetheoreticalframeworkwhereindividualsmaximizelinearutilityandmigrationisdrivenbyabsoluteearningsdifferencesbetweenhighandlow‐skilledworkers.

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EU15countriesnowliveoutsidetheirbirthplace,with42percentofthesemigrantslivinginotherEU15countriesandanadditional13percentlivingintheUnitedStates.2Thispaperexaminestheself‐selectionofemigrantsfromDenmark,oneoftherichestandmostredistributiveEuropeanwelfarestates.In2013,overaquartermillionDaneslivedoutsideDenmark(correspondingtoabout5percentoftheDanish‐bornpopulation),with50percentofthemigrantslivinginotherEU15countriesand13percentintheUnitedStates(UnitedNations,DepartmentofEconomicandSocialAffairs2013).BecausethereturnstoskillsinDenmarkarerelativelylow,thecanonicalRoymodelpredictsthattheemigrantsshouldbepositivelyselectedinthesensethattheexpectedearningsofthemigrantsexceedtheexpectedearningsofthestayers.3However,therehavebeenfewsystematicstudiesoftheself‐selectionofmigrantsfromarelativelyegalitariancountrytoseewhetherthisisindeedthecase.4Ourtheoreticalanalysisshowsthatthecanonicalframeworkdoesnotonlyhavepredictionsaboutthedifferencebetweentheexpectedearningsofmigrantsandnon‐migrants,whichisthebasisforthestandarddefinitionofpositiveornegativeselectionintheliterature,butalsoaboutthestochasticorderingofthetwoearningsdistributions.Weshowthatthesameconditionsthatpredictthatmigrantsarepositivelyself‐selectedinthesenseofadifferenceinexpectedincomesalsopredictthattheincomedistributionofthemigrantswillfirst‐orderstochasticallydominatetheincomedistributionofthenon‐migrants.Thetheoryalsodistinguishesbetweenselectioninobservableandselectioninunobservablecharacteristics.2TheEU15countriesrefertothememberstatesoftheEuropeanUnionpriortotheexpansiononMay1,2004.3ForcomparisonsofgrosswagepremiafromtertiaryeducationacrosscountriesseeBoariniandStraus(2010).ArecentpaperstudyingreturnstocognitiveskillsisHanusheketal.(2015).Thestudyfindssignificantcross‐countrydifferences.Moreover,thereturnsarerelativelylowinDenmarkaswellasinotherNordiccountries,andhighintheUnitedStates,GermanyandtheUnitedKingdom,whichalsoareamongthemostpopulardestinationsofDanishmigrants.4StudiesoftheselectionofmigrantsacrossdevelopedcountriesincludeLundborg(1991),Pirttilä(2004),Klevenetal.(2014),andJungeetal.(2014).Manystudiesalsoexamineselectionissuesinahistoricalcontext;seeWegge(1999,2002),AbramitzkyandBraggion(2006),Abramitzky,Boustan,andEriksson(2012),Ferrie(1996),andMargo(1990).

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OurempiricalanalysisusestheDanishfullpopulationadministrativedatatoanalyzehowmigrantsandnon‐migrantsdifferintheirpre‐emigrationearningsandotherobservablecharacteristics.Toshedlightontheroleofunobservablecharacteristicsintheselectionprocess,weinvestigatehowmigrantsandnon‐migrantsdifferintermsofunobservableearningsability,asmeasuredbyresidualsfromMincerianearningsregressions.Ourempiricalresultsareinlinewiththepredictionsofthemodel:Danishemigrantsareindeedpositivelyself‐selectedbothintermsofearningsandintermsofresidualsfromthewageregressions.FollowingourreframingofthecanonicalRoyframeworkintermsoftheconceptofstochasticdominance,ourstudyspecificallytestsforwhethertheearningsdistributionoftheemigrantsstochasticallydominatesthatofthestayers(aswouldbepredictedbythemodel).Theevidenceconfirmsthisstrongtheoreticalpredictionovermostofthesupportoftheearningsdistribution.OurstudyisrelatedtotheflurryofrecentpapersthatexaminetheselectionofmigrantsfromMexicototheUnitedStates.ThepioneeringanalysisofChiquiarandHanson(2005)mergedinformationfromtheU.S.censusonthecharacteristicsoftheMexicanmigrantswithinformationfromtheMexicancensusonthecharacteristicsoftheMexicannon‐migrants.Becausethemergeddatadidnotreporttheearningsofmigrantspriortothemove,pre‐migrationearningswerepredictedbasedonobservablecharacteristicsofthemigrants.This“counterfactual”empiricalexercisesuggestedthatMexicanemigrantswerelocatedinthemedium‐highrangeoftheMexicanwagedistribution.ThefindingofintermediateselectionintheMexicancontextdoesnotseemconsistentwiththebasicimplicationsoftheRoymodelbecausetherateofreturntoskillsisfarlargerinMexicothanintheUnitedStates.MorerecentstudiesbyFernández‐HuertasMoraga(2011)andKaestnerandMalamud(2014)usesurveydatathatreporttheactualpre‐migrationearningsandfindevidenceofnegativeselection.Theyalsoconcludethatpartofthenegativeselectioncanbetracedtotheunobservablecharacteristicsthatdetermineamigrant’searnings.Theimportantroleplayedbyunobservablecharacteristicsimpliesthatconstructingacounterfactualearningsdistributionforthemigrantsbasedonobservablecharacteristics

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cangreatlybiasthenatureoftheselectionrevealedbythedata.Ourfindingssuggestthattheuseofsuchacounterfactualdistributionwilltendtounderstatethetrueselectioninearnings,sothattheselectionimpliedbythecounterfactualdistributionisfarweakerthanthetrueselection—regardlessofwhetherthereispositiveornegativeselection.ThenumericalbiasthatresultsfromusingthecounterfactualestimationissizableintheDanishcontext:morethanhalfofthedifferencebetweentheexpectedearningsofmigrantsandnon‐migrantsarisesbecauseofdifferencesinunobservedcharacteristics.Thepaperisorganizedasfollows.Section2sketchestheeconomictheoryunderlyingtheanalysisandderivestheoreticalpredictionsconcerningtheself‐selectionofemigrants,usingthenotionofstochasticdominanceasaunifyingconcept.Section3introducesanddescribestheuniquepopulationdatathatweuseandreportssomesummarystatistics.Sections4and5presentthemainempiricalfindings.Insection4,weexaminetheselectionintermsofobservedpre‐migrationearnings.Wepresentastatisticalmethodfortestingthetheoreticalimplicationthattheearningsdistributionoftheemigrantsshouldstochasticallydominatethecorrespondingdistributionofthenon‐migrants.Section5extendstheempiricalworkbyexaminingtheselectionthatoccursintheunobservedcomponentofearnings.Section6evaluatesthebiasthatresultsfrompredictingthepre‐migrationearningsofemigrantsfromtheearningsdistributionofnon‐migrants.Section7examineswhethertheselectionofpersonsmovingtootherEU15countriesdiffersfromtheselectionofmigrantsmovingtocountrieswhereimmigrationrestrictionscomeintoplay.Wefindthatimmigrationrestrictionshavelittleeffectontheselectionofemigrants.Finally,Section8summarizesthestudyanddrawssomelessonsforfutureresearch.2.Theoreticalframework

Previousliteratureontheself‐selectionofmigrantshasfocusedontheconditionalexpectationsofearningsdistributionsamongmigrantsandstayers.Inthissection,wederiveanovelresult:theRoymodelimpliesthatundercertainconditions,theearningsdistributionofmigrantsfirst‐orderstochasticallydominates,orisstochasticallydominatedby,theearningsdistributionofstayers.Inabivariatenormalframework,itturnsoutthat

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theconditionsrequiredforstochasticdominanceareidenticaltotheconditionsthatdeterminethenatureofself‐selectionintermsofexpectedearnings.Wealsodecomposeself‐selectionintotwocomponents,onethatisdeterminedbydifferencesinreturnstoobservableskillsbetweensourceandhostcountry,andonethatisdeterminedbydifferencesinreturnstounobservableskills.Thedistinctionbetweenobservableandunobservableskills,ofcourse,dependsontheempiricalframeworkandonthedatathatisbeingused;observableskillsincludethevariablesexplainingearningsthatareincludedinthedata,whilethecomponentofearningsthatisleftunexplainedbythedataistheunobservableskillcomponent.Eventhoughthecontentofthetwocomponentsdiffersamongdatasets,itislikelythatamajorpartofmigrantself‐selectionisdeterminedbytheunobservablecomponentsimplybecause“observables”tendtoexplainarelativelysmallfractionofthevarianceinearnings.Wetakeasourstartingpointthemigrationdecisionfacedbypotentialmigrantsinatwo‐countryframework,inlinewithBorjas(1987)andsubsequentliterature.Residentsofthesourcecountry(country0)considermigratingtothedestinationcountry(country1),andthemigrationdecisionisassumedtobeirreversible.Tosimplifythepresentation,wefocusonasingleobservedskillcharacteristicsandsuppressthesubscriptthatindexesaparticularindividual.Forconcreteness,thevariablescanbethoughtofasgivingtheworker’syearsofeducationalattainment,butitincludesallthecharacteristicsaffectingindividual’sincomethatareobservedinagivensetofdata.Residentsofthesourcecountryfacetheearningsdistribution:(1) log

wherew0givesthewageinthesourcecountry;r0givestherateofreturntoobservableskills;andtherandomvariable0measuresindividual‐specificproductivityshocksresultingfromunobservedcharacteristicsandisnormallydistributedwithmeanzeroandvariance .Thedistributionofobservableskillsinthesourcecountry’spopulationis 02

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givenbys=s+s,wheretherandomvariablesisalsoassumedtobenormallydistributedwithmeanzeroandvariance . Iftheentirepopulationofthesourcecountryweretomigrate,thispopulationwouldfacetheearningsdistribution:(2) log

wheretherandomvariable1isnormallydistributedwithmeanzeroandvariance12 .Foranalyticalconvenience,weassumethatCov(0,s)=Cov(1,s)=0,sothattheindividual‐specificunobservedproductivityshocks(i.e.,the“residuals”fromtheregressionline)areindependentfromobservablecharacteristics.5Thecorrelationcoefficientbetween0and1equals01.Itisalsoworthnotingthattherandomvariablesisindividual‐specificandhasthesamevalueforthesameindividualinbothcountries,whereas0and1arebothindividual‐andcountry‐specific. Equations(1)and(2)completelydescribetheearningsopportunitiesavailabletopersonsborninthesourcecountry.AssumethatthemigrationdecisionisdeterminedbyacomparisonofearningsopportunitiesacrosscountriesnetofmigrationcostsC.Definetheindexfunction:(3) log ∆ ,

5Amorerealisticassumptionwouldbethatthecorrelationbetweenobservedandunobservedskillsispositive.However,allowingforpositivecorrelationdoesnotchangethequalitativepredictionsofthemodel.

s2

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wheregivesa“time‐equivalent”measureofmigrationcosts(=C/w0).Thecross‐countrydifferenceinearningsnetofthetime‐equivalentmigrationcostforanindividualwithaverageobservedandunobservedcharacteristicsisgivenby=[(1–0)+(r1–r0)s–].Thedifferenceinearningsattributabletoindividualdeviationfromaveragecharacteristicsisgivenby ,wherevi=(ris+i)for∈ 0,1 .ApersonemigratesiftheindexI>0,andremainsintheorigincountryotherwise.

Migrationcostsvaryamongpersons—butthesignofthecorrelationbetweencosts(whetherindollarsorintime‐equivalentterms)andskills(bothobservedandunobserved)isambiguousanddifficulttodetermine.Theheterogeneityinmigrationcostscanbeincorporatedtothemodelbyassumingthatthedistributionoftherandomvariableinthesourcecountry’spopulationisgivenby=+,whereisthemeanlevelofmigrationcostsinthepopulation,andisanormallydistributedrandomvariablewithmeanzeroandvariance .However,Borjas(1987)andChiquiarandHanson(2005)showthattime‐equivalentmigrationcostsdonotplayaroleinthealgorithmthatdeterminestheselectionofemigrantsifeitherthosecostsareconstant(sothat2 =0),orifthecostsareuncorrelatedwithskills.Foranalyticalconvenience,weassumethattime‐equivalentmigrationcostsareconstant,sothat=.6Theoutmigrationratefromthesourcecountryisthengivenby:(4) 0 ∗ ∆ ∗ 1 ∆ ∗ ,

wherev*=(v1v0)/visastandardnormalrandomvariable;*=/v;v2 =Var(v1–v0);andisthestandardnormaldistributionfunction.76If werenegativelycorrelatedwithskills,thenegativecorrelationwouldtendtoinducethemoreskilledtomigrate,creatingapositivelyselectedmigrantflow.Thiswouldstrengthenpositiveself‐selection,andweakennegativeself‐selection.7Itisstraightforwardtostudyequation(4)toconfirmthatthemigrationraterises,whenmeanincomeinthesourcecountryfalls,meanincomeinthehostcountryrises,returnstoobservedskillsinthesourcecountryfall,returnstoobservedskillsinthehostcountryrise,time‐equivalentmigrationcostsfallandwhenmeanobservedskillsriseifr1>r0orfallifr1<r0.

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Inadditiontoidentifyingthedeterminantsoftheoutmigrationrateinequation(4),theRoymodelletsusexaminewhichpersonsfinditmostworthwhiletoleavethesourcecountry.8Inthefollowing,weexaminetheself‐selectionofemigrantsalongtwodimensions:selectionintermsofobservableskillssandselectionintermsofunobservableskills0,whichtogethercombineintoselectionintermsoftotalproductivityorearnings,asmeasuredbylogw0.LetFM(z)andFN(z)representthe(cumulative)probabilitydistributionsofskillsorearningsformigrantsandnon‐migrantsinthesourcecountry,respectively,wherezdenotesaparticularmeasureofskills(e.g.,observableorunobservablecharacteristicsorincome).Bydefinition,theprobabilitydistributionofmigrantsFM(z)first‐orderstochasticallydominatesthatofstayersFN(z)if:(5) ∀ ,andthereisatleastonevalueof forwhichastrictinequalityholds.9Fromnowon,wheneverwerefertostochasticdominance,wemeanfirst‐orderstochasticdominance.Equation(5)impliesthatalargerfractionofthemigrantshaveskillsaboveanythresholdz*.Putdifferently,foranylevelofskillsz*,thepopulationdescribedbytheprobabilitydistributionFMismoreskilledbecausealargerfractionofthegroupexceedsthatthreshold.Themigrants,inshort,arepositivelyselected.Negativeselection,ofcourse,wouldoccurifthereversewastrueand z,withastrictinequalityholdingforatleastonevalueof .8Throughouttheanalysis,weassumethat*isconstant.Themigrationflowiseffectivelyassumedtobesufficientlysmallthattherearenofeedbackeffectsonthelabormarketsofeitherthesourceordestinationcountries.

9Analternativeandperhapsmoreintuitivedefinitionofstochasticdominanceisintermsofquantiles.Let and bethequantilefunctionsoforder oftheskilldistributionsofmigrantsandnon‐migrants.FM(z)stochasticallydominatesFN(z)ifandonlyif forall0 1andthereisatleastonevalueof forwhichastrictinequalityholds.

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Iftheskilldistributionofmigrantsstochasticallydominatesthatofnon‐migrants,thestochasticdominancethenalsoimpliesthetypicaldefinitionofpositiveselectionthatisbasedonconditionalexpectations:(6) | 0 | 0 ,sothatmigrants,onaverage,aremoreskilledthanstayers.Conversely,iftheprobabilitydistributionofstayersstochasticallydominatesthatofmigrants,andtherewasnegativeselection,itwouldalsofollowthat | 0 | 0 .Theconverse,however,isnottrueforageneraldistribution:Aclaimofpositiveselectioninexpectations,asdefinedbyequation(6),doesnotimplythattheskilldistributionofmigrantsstochasticallydominatesthatofnon‐migrants.Toderivethestochasticorderingoftheskilldistributionsofmigrantsandnon‐migrants,letf(x,v)beabivariatenormaldensityfunction,withmeans(x,v),variances ( x2 ,v2 ) andcorrelationcoefficient.Further,lettherandomvariablevbetruncatedfrombelowatpointaandfromaboveatpointb.Arnoldetal.(1993,p.473)showthatthe(marginal)momentgeneratingfunctionofthestandardizedrandomvariable(x‐x)/x,giventhetruncationofv,isgivenby:(7) / ,where=(a–v)/v;and=(b–v)v. Intermsofthemigrationdecision,thetruncationintherandomvariablev=v1–v0inthesampleofmigrantsisfrombelowandimpliesthat=–*=k,and=,wherekisthetruncationpoint.Inthesampleofstayers,thetruncationinvisfromabove,andthetruncationpointsare=–and=k.Bysubstitutingthesedefinitionsintoequation(7),it

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canbeshownthatthemomentgeneratingfunctionsfortherandomvariablegivingtheconditionaldistributionsofskillcharacteristicxformigrantsandstayersreduceto:(8)

1 Φ1 Φ

and(9)

ΦΦ .

ConsideranytwodistributionfunctionsF(z)andG(z).Thistle(1993,p.307)showsthatFwillstochasticallydominateGifandonlyif:(10) , ∀ 0,wheremFisthemomentgeneratingfunctionassociatedwithdistributionF;mGisthemomentgeneratingfunctionassociatedwithG.Therankingofthemomentgeneratingfunctionsinequation(10)implieswecandeterminethestochasticrankingofthetwodistributionsbysimplysolvingfortherelevantcorrelationcoefficient,andcomparingequations(8)and(9).Suchacomparisonimpliesthat:(11) , 0 , 0.

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Inotherwords,migrantsarepositivelyselectedif>0,andarenegativelyselectedotherwise.Considerinitiallythestochasticrankinginobservablecharacteristics.Therandomvariablex=s,andtherelevantcorrelationcoefficientisdefinedby:(12) , 1 .Equation(12)showsthatthestochasticorderingofthedistributionsofobservableskillsofmigrantsandnon‐migrantsdependsonlyoninternationaldifferencesintherateofreturntoobservableskills.Theskilldistributionofmigrantswillstochasticallydominatethatofstayerswhentherateofreturntoskillsishigherabroad.Conversely,theskilldistributionfornon‐migrantswillstochasticallydominatethedistributionformigrantsiftherateofreturntoobservableskillsislargerathome.Considernextthestochasticorderingintheconditionaldistributionsofunobservableskills0.Therelevantcorrelationfordeterminingthistypeofselectionisgivenby:(13) , 1 .Itfollowsthatthedistributionofunobservableskillsformigrantsstochasticallydominatesthatfornon‐migrantswhen 1.Notethatthenecessaryconditionforpositiveselectionhastwocomponents.First,theunobservedcharacteristicsmustbe“transferable”acrosscountries,sothat01issufficientlyhigh.Second,theresidualvarianceinearningsislargerinthedestinationcountrythaninthesourcecountry.Theresidualvariances02 and1

2 ,ofcourse,measurethe“price”ofunobservedcharacteristics:thegreatertherewardstounobservedskills,thelargertheresidualinequalityinwages.10Aslongasunobserved

10Thisinterpretationofthevariancesfollowsfromthedefinitionofthelogwagedistributioninthehostcountryintermsofwhatthepopulationofthesourcecountrywouldearniftheentirepopulationmigratedthere.Thisdefinitioneffectivelyholdsconstantthedistributionofskills.

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characteristicsaresufficientlytransferableacrosscountries,emigrantsarepositivelyselectedwhentherateofreturntounobservableskillsishigherinthedestination.Finally,considerthestochasticrankingin“total”productivity.Theearningsdistributioninthesourcecountrygivenbyequation(1)canberewrittenas:(14) log 0 α0 0μs 0ε ε0 α0 0μ 0,wherethenormallydistributedrandomvariablev0hasmeanzeroandvariancev02 .Therelevantcorrelationfordeterminingthestochasticrankingoftheearningsdistributionsofmigrantsandnon‐migrantsis:(15) , 1 1 1 ,where ⁄ and1 ⁄ .Thesignofthecorrelationinequation(15),whichdeterminesthenatureoftheselectioninpre‐migrationearnings,dependsonthesignofaweightedaverageoftheselectionthatoccursinobservableandunobservablecharacteristics.Interestingly,theweightisthefractionofthevarianceinearningsthatcanbeattributedtodifferencesinobservableandunobservablecharacteristics,respectively.Ifthereispositive(negative)selectioninboth“primitive”typesofskills,therewillthenbepositive(negative)selectioninpre‐migrationearnings.If,however,therearedifferenttypesofselectioninthetwotypesofskills,theselectionineachtypeisweightedbyitsimportanceincreatingthevarianceoftheearningsdistribution.Itiswellknownthatobservablecharacteristics(suchaseducationalattainment)explainarelativelysmallfractionofthevarianceinearnings(perhapslessthanathird).Asaresult,equation(15)impliesthatitistheselectioninunobservablesthatismostlikelytodeterminethenatureoftheselectioninthepre‐migrationearningsofemigrants.Thisimplicationplaysan

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importantroleinexplainingwhytheevidencereportedinFernández‐HuertasMoraga(2011)andKaestnerandMalamud(2014)conflictswiththatofChiquiarandHanson(2005).Asmentionedearlier,thestochasticdominanceresultsnecessarilyimplyselectionintermsofconditionalexpectations.Inthecaseofbivariatenormaldistributions,itfollowsthattheexpectationoftheearningsdistributionofmigrantsE(logw0|v*>*)isgivenby:(16) | ∗ Δ ∗ 1 Δ ∗ 1 Δ ∗ ,where*)=(*)/[1(*)]>0,andisthedensityofthestandardnormaldistribution.Ascanbeseenbyexaminingequation(16),theconditionsthatdeterminetheself‐selectionintermsofexpectationsarethesameastheconditionsthatdeterminethestochasticorderingoftheskilldistributionsofmigrantsandnon‐migrants.InthenormaldistributionframeworkthatunderliesthecanonicalRoymodel,stochasticdominanceimpliesselectioninexpectations,andviceversa.Inempiricalapplications,however,thepredictionofstochasticdominanceislikelytobemuchlessrobustthanthepredictionsconcerningexpectationsbecausetestingforstochasticdominancewillrequireamorerigoroustestthansimplycomparingtheaverageincomesorskillsofmigrantsandnon‐migrants.Ifonejustcomparestheaveragestofindouthowmigrantsareself‐selected,thefindingscanbecompatiblewiththepredictionsoftheRoy‐modelevenifalargenumberofindividualsinthedatabehaveagainstthestochasticdominancepredictionsofthemodel.Asaresult,establishinganempiricalpatternofstochasticdominanceprovidesverystrongevidencethatdifferencesinskillpricesareindeedimportantinmigrationdecisions.

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3.Data

OuranalysisusesadministrativedatafortheentireDanishpopulationfrom1995to2010.ThedataismaintainedandprovidedbyStatisticsDenmarkanditderivesfromtheadministrativeregistersofgovernmentalagenciesthataremergedusingauniquesocialsecuritynumber.11Foreachyearbetween1995and2004,weidentifiedallDanishcitizensaged25‐54wholivedinDenmarkduringtheentirecalendaryear.12Werestricttheanalysistopersonswhoworkedfulltime.13Migrationdecisionsofpart‐timeworkersorofworkersoutsidethelaborforcemaybedrivenbydifferentfactors,andtheobservedincomeoftheseworkersmaynotbeindicativeoftheirtrueearningspotential.Theincomevariableforeachyearisconstructedbyaddingtheworker’sannualgrosslaborincomeandpositivevaluesoffreelanceincome.14Wemergedthisinformationwithdatafromthemigrationregisterfortheyears1995through2010.Themigrationregisterreportsthedateofemigrationandthecountryofdestination.EventhoughitispossibleforDanishcitizenstoemigratewithoutregistering,weexpectthatthenumbersofpersonswhodosoissmallasitisalegalrequirementfor

11AllresidentsinDenmarkarelegallyrequiredtohaveasocialsecuritynumber.Thisnumberisnecessarytomanyactivitiesindailylife,includingopeningabankaccount,receivingwagesandsalariesorsocialassistance,obtaininghealthcare,andenrollinginschool.12Aperson’sageismeasuredasofJanuary1sttheyearafterthereferenceyear.13Theadministrativedataallowsthecalculationofavariablethatmeasurestheamountof“workexperiencegained”duringthecalendaryear.Themaximumpossiblevalueforthisvariableis1,000.Werestrictoursampletoworkerswhohaveavalueof900orabove,sothatoursampleroughlyconsistsofpersonswhoworkedfulltimeatleast90percentoftheyear.Inordertomeasuretheworkexperiencegainedduringagivenyear,wesubtractthevaluefromthepreviousyearfromthecurrentvalueofthevariable.Personswhohadamissingvalueforworkexperienceineitherofthetwoyearsweredroppedfromthesample.Missingvaluesinthisvariabletypicallyindicatethatthepersonspenttimeabroad.14Theinformationonearningsistakenfromthetaxrecordsforeachcalendaryear.ThisvariableisconsideredtobeofhighqualitybyStatisticsDenmark.Somepersonsalsoreportnegativevaluesforfreelanceincome.Thesenegativevaluesarelikelytobeduetolossesarisingfrominvestmentsanddonotreflecttheproductivecharacteristicsoftheindividual.

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Danishcitizenstoreportemigration.Danishtaxlawsprovidefurtherincentivesformigrantstoregisterwhentheyemigrate.Afteridentifyingthepopulationofinterest,wedeterminedforeachpersonwhetherheorsheemigratedfromDenmarkduringthefollowingcalendaryear.Ifwefoundthataparticularpersonemigrated,wesearchedforthepersoninthemigrationregisterforsubsequentyearstodetermineifthemigrantreturnedtoDenmarkatsomepointinthefuture,andrecordedthedateofpossiblereturnmigration.Themigrationregisterincludesnear‐completeinformationonreturnmigration,asregistrationinDenmarkisrequiredforthereturnmigranttobeeligibleforincometransfersandtobecoveredbynationalhealthinsurance.Tofocusonmigrationdecisionsthatarepermanentinnature,werestricttheanalysistomigrationspellsthatareatleastfiveyearslong.15Wedefineamigrantasanindividualwhoisfoundinoneofthe1995‐2004cross‐sections,whoemigratesfromDenmarkduringthefollowingyeartodestinationsoutsideGreenlandortheFaroeIslands,andwhostaysabroadforatleastfiveyears.16Individualswhoemigratedforlessthanfiveyearswereremovedfromthedata,andtherestofthepopulationisthenclassifiedasnon‐migrants.17Theanalysisofbothmigrantsandnon‐migrantsisfurtherrestrictedtoonlyincludeDanishcitizenswhodonothavean“immigrationbackground.”18

15Havingstayedabroadforfiveyearspredictslongermigrationspells.Forexample72%ofmenand71%ofwomenwholeftDenmarkin1996andwerestillabroadafterfiveyearswerealsoabroadaftertenyears.16GreenlandandtheFaroeIslandsareautonomousregionsbutstillpartofDenmark.WehaveexcludedthesedestinationsasmanyofthesemigrantscouldhaveoriginatedinGreenlandortheFaroeIslands,andmanywouldactuallybereturninghomeratherthanemigratingfromDenmark.Theexactdurationrequirementswere1,825daysorlongerforlong‐termmigrants. 17Wealsoexaminedtheselectionofshort‐termmigrantsandthequalitativeresultsaresimilartothosereportedbelow,althoughtheintensityofselectionisweaker.18StatisticsDenmarkdefinesapersontohave“noimmigrantbackground”ifatleastoneoftheparentswasborninDenmarkandthepersonis/wasaDanishcitizen.Wesearchedthepopulationregistersfrom1980to2010fortheparentsofthepersonsinoursample,andifaparentwasfoundheorshewasrequiredtobeaDanewithnoimmigrantbackgroundaswell.

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Table1reportssummarystatisticsfromtheDanishadministrativedata.Thepaneldatasetcontainsover6.4millionmaleand5.1millionfemalenon‐migrants.Theconstructionofthedataimpliesthatnon‐migrantsappearinthedatamultipletimes(potentiallyonceineachcross‐sectionbetween1995and2004).Wewereabletoidentify7323maleand3436femalemigrants.Byconstruction,thesemigrantsarepersonswhowefirstobserveresidinginDenmarkandwholeftthecountryatsomepointbetween1996and2005.AsTable1shows,theDanishemigrantsareyoungerthanthenon‐migrants,regardlessofgender.Despitetheagedifference,theemigrantsearnedhigherannualincomesintheyearpriortothemigrationthanthenon‐migrants.Weconstructasimplemeasureof“standardizedearnings”thatadjustsfordifferencesinage,gender,andyeareffects.Standardizedearningsaredefinedbytheratioofaworker’sannualgrossearningstothemeangrossearningsofworkersofthesameageandgenderduringthecalendaryear.19Table1showsthatemigrantsearnmorethannon‐migrantsintermsofstandardizedearnings.Inparticular,maleemigrantsearnabout30percentmorethannon‐migrants,andfemaleemigrantsearnabout20percentmore.Table2reportsthenumberofemigrantsmovingtodifferentdestinations.ThelargestdestinationsforbothmenandwomenaretwootherNordiccountries,SwedenandNorway,aswellastheUnitedStates,theUnitedKingdomandGermany.20Thesefivecountriesaccountfor57percentofallemigration.Finally,itisalsointerestingtosummarizethelinkbetweeneducationandemigration.Table3reportstheeducationdistributionsfornon‐migrantsandmigrants.Itisevidentthatthemigrantstendtobemoreeducatedthanthenon‐migrants,amongbothmenandwomen.Forexample,50percentofDanishmalenon‐migrantshaveavocationaleducation,ascomparedtoonly30percentofmigrantstonon‐Nordicdestinations.Similarly, the 19Bothmigrantsandnon‐migrants,aswellasshorter‐termmigrants,areincludedinthesecalculations.20Ifwerelaxtheconstraintsonlabormarketstatusandagetoenterthesample,theUnitedKingdomemergesasthelargestdestinationbecauseofthelargenumberofDanishstudentswhopursuetheireducationthere.

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—atleastasmeasuredbyeducationanddifferencesintheconditionalmeansofearnings.

4.Selectioninpre‐migrationearnings

Thissectionpresentsempiricalevidenceontheself‐selectionofemigrantsfromDenmarkintermsofstandardizedpre‐emigrationearnings.Themainempiricalfindingisthatlong‐termemigrantsfromDenmarkwere,ingeneral,muchmoreproductivepriortotheirmigrationthanindividualswhochosetostay.Ofcourse,thesummarystatisticsreportedinTable1alreadysuggestpositiveselectionamongemigrantsbecausetheirstandardizedearningsexceededthoseofnon‐migrants.However,differencesinconditionalaveragescouldbemaskingsubstantialdifferencesbetweentheunderlyingprobabilitydistributions.Ourtheoreticalframeworkpredictsthatthedistributionofearningsformigrantsshouldstochasticallydominatethatofnon‐migrants.Asaresult,ourempiricalanalysiswillmainlyconsistofcomparingcumulative

18

distributionsofstandardizedearningsbetweenmigrantsandnon‐migrants.Anadvantageofsimplygraphingandexaminingthecumulativedistributionsisthattheanalysisdoesnotrequireanytypeofkerneldensityestimation,andthatwedonotneedtoimposeanystatisticalassumptionsorparametricstructureonthedata.Wewillalsopresentkerneldensityestimatesoftheearningsdensityfunctionsasanalternativewayofpresentingthekeyinsights.Finally,wewillderiveandreportstatisticalteststodetermineifthedatasupportthetheoreticalpredictionofstochasticdominance.Figure3aillustratesthecumulativeearningsdistributionsformalemigrantstoNordiccountries,malemigrantstodestinationsoutsideNordiccountries,andformalenon‐migrants.Thevaluesofthestandardizedearningsaretruncatedat‐2and2tomakethegraphsmoretractable.21Thefigureconfirmsthatmigrantswerepositivelyselectedduringthestudyperiod.ThecumulativedistributionfunctionofstandardizedearningsofmigrantstodestinationsoutsidetheNordiccountriesisclearlylocatedtotherightofthecorrespondingcumulativedistributionfornon‐migrants,aswouldbethecaseifthecumulativedistributionofmigrantsstochasticallydominatesthatofnon‐migrants.ThefigurealsoshowsthatthedistributionfunctionformigrantstootherNordiccountriesislocatedtotherightofthatfornon‐migrants.However,theselectionofthemigrantstoNordiccountriesseemsweaker.ThisweakerselectionmayarisebecausetherateofreturntoskillsinNordiccountriesisrelativelylowwhencomparedtothatinotherpotentialdestinations.22Figure3bpresentscorrespondingevidenceforwomen.23Themainfindingsarequalitativelysimilar,butthepositiveselectionseemsweaker.

21Thetruncationdoesnotaltertheresultsconsiderablyasthesharesofobservationsbelowthelowerandabovetheuppertruncationpointsaresmall.Further,thefollowinganalysisofdifferencesbetweencumulativedistributionfunctionsdoesnotusetruncation.0.07%ofnon‐migrants,0.19%migrantstootherNordiccountriesand0.11%ofmigrantstootherdestinationsliebelowthelowertruncationpoint.Correspondingly,0.03%ofnon‐migrantsand0.21%ofmigrantstodestinationsoutsideNordiccountrieslieabovetheuppertruncationpoint.TherearenomigrantstootherNordiccountriesabovetheuppertruncationpoint.22Moreover,someDanesmayliveinsouthernSwedenbutworkinDenmark.AsthistypeofmigrationisnotrelatedtoreturnstoskillsinthedestinationcountrythisshoulddecreasetheestimatedselectiontoNordiccountries.

19

Figure4apresentsthecorrespondingkernelestimatesofthedensityfunctionsofthelogarithmofstandardizedearningsformen,whileFigure4bpresentstherespectivegraphsforwomen.24ThedensityfunctionsagainrevealthepositiveselectionofmigrantsmovingoutsidetheNordiccountries,bothformenandwomen.Asisevidentfromthefigures,Kolmogorov‐Smirnovtestscomparingtheearningsdistributionsfordifferentgroupsrejectthehypothesisthattheunderlyingearningsdistributionsarethesameatahighlysignificantlevel.Inadditiontoshowingthatthecumulativedistributionsaredifferent,itisalsoimportanttodetermineiftheevidencestatisticallysupportsthetheoreticalpredictionthatthecumulativedistributionfunctionofmigrantsstochasticallydominatesthatofnon‐migrants.Statisticaltestsforfirst‐orderstochasticdominancearehighlysensitivetosmallchangesintheunderlyingdistributions,makingitdifficulttorankdistributionsinmanyempiricalapplications.25AsnotedbyDavidsonandDuclos(2013),itmaybeimpossibletoinferstochasticdominanceoverthefullsupportofempiricaldistributionsifthedistributionsarecontinuousinthetails,simplybecausethereisnotenoughinformationinthetailsformeaningfultestingofanystatisticalhypothesis.Itwouldthenmakesensetofocusontestingstochasticdominanceoverarestrictedrangeofthedistribution.Weapplyanapproachthatcharacterizestherangeoverwhichthevalueofthecumulativedistributionfunctionfornon‐migrantsisstatisticallysignificantlylargerthanthatofnon‐migrants.Inparticular,wecalculatethedifferencebetweenthecumulativedistributionfunctionswithconfidenceintervals.Tocalculatetheconfidenceintervalsweusetoolsthatwere

23Forwomen,0.06%ofnon‐migrantsliebelowthelowertruncationpointand0.00%ofnon‐migrantslieabovethehighertruncationpoint.Therearenomigrantslyingbelowthelowerorabovethehighertruncationpoint.24FollowingLeibbrandtetal.(2005)andFernandes‐HuertasMoraga(2011),weuseSilverman’sreferencebandwidthmultipliedby0.75topreventover‐smoothing.Thesamebandwidthisusedalsoinallthekerneldensityestimatesreportedinsubsequentcalculations.25Thiscanleadtodifficultiesinempiricalwork,andlessrestrictiveconceptssuchasrestrictedfirstorderstochasticdominance(Atkinson,1987)andalmoststochasticdominance(LeshnoandKevy,2002)havebeenproposed.

20

introducedinAraar(2006)andAraaretal.(2009).26Moreformally,wetestthefollowingnullhypothesisforeach ∈ ,where isthejointsupportofthetwodistributions:(17) H0:F(w))=FN(w)–FM(w) 0,againstthealternativehypothesis(18) H1:F(w))=FN(w)–FM(w) 0

andcharacterizeanyrelevantrangeof whereweareabletorejectthenull.Let bethestandarddeviationoftheestimator∆ w ,andletz()bethe(1–)thquantileofthestandardnormaldistribution.27DavidsonandDuclos(2000)showthattheestimator∆ w isconsistentandasymptoticallynormallydistributed.Wecanthendefinethelowerboundforaone‐sidedconfidenceintervalfor∆ as:28(19) ∆ ∆ w .WeestimatethestandarderrorsusingaTaylorlinearizationandallowforclusteringattheindividuallevel.Wethenimplementtheprocedurebycalculatingthelowerboundsoftheconfidenceintervalsfortheestimate∆ w definedinequation(19).Table4reportsthesharesofmigrantsandnon‐migrantswhoseearningsareoutsidetherangeoverwhichthemigrantdistributionstochasticallydominatesata95percentconfidencelevel.Considerfirstthedistributionsofnon‐migrantmenandmenmigratingtodestinationsoutsidetheNordiccountries.Althoughitisnotclearlyvisiblefromfigure3a,26ThecalculationsareimplementedusingtheDASPStatamodulepresentedinAraarandDuclos(2013).27Theasymptoticvarianceof∆ isderivedinAraaretal.(2009).28Chow(1989)provedthetheoremforthecaseofindependentsamples.DavidsonandDuclos(2000)showthattheresultsalsoextendtothecaseofpairedincomesfromthesamepopulation.

21

thecumulativedistributionfunctionscrossnearthelowertailsofthedistributions.Figure5adepicts∆ w andlowerandupperboundsfora95%confidenceinterval.29Thelowerboundoftheconfidenceintervalispositiveonmostoftherangecoveringthesupportsofthedistributions.Only2.0percentofthemigrantsand3.4percentofthenon‐migrantsliebelowthelowerboundoftherangewherethelowerboundoftheconfidenceintervalispositive,whereasthesharesofmigrantsandnon‐migrantsabovetheupperboundoftherangeare0.1and0.0percent.Putdifferently,theearningsofalmost98percentofmalemigrantstodestinationsoutsideNordiccountriesareontherangewherethecumulativedistributionfunctionfornon‐migrantsisstatisticallysignificantlyabovethefunctionformigrants.

Figure5bdepicts∆ w andtheboundsfora95%confidenceintervalfornon‐migrantwomenandwomenmigratingtodestinationsoutsideNordiccountries.Only2.8percentofthemigrantsand4.1percentofthenon‐migrantshaveearningsbelowtherangewherethelowerboundoftheconfidenceintervalispositive,andanevensmaller0.2percentofthemigrantsand0.0percentofthenon‐migrantshaveearningsabovethisrange.WeinterpretthesefindingsassupportforthestochasticdominancepredictionforbothmenandwomenmigratingoutsideNordiccountries.Figures6aand6bandthebottompanelofTable4presentacorrespondinganalysisbycomparingthecumulativedistributionsofpersonswhomigratetootherNordiccountrieswiththatofnon‐migrants.Almost12percentofmalemigrantsand16percentofmalenon‐migrantshaveearningsthatliebelowtherangewhere ∆ ispositive,andanother1.5percentofthemigrantsand0.7percentofthenon‐migrantshaveearningsabovetherange.Putdifferently,about87percentofthemalemigrantstoNordiccountrieshaveincomesontherangewhere ∆ ispositive.Forwomen,itcanbeseeninTable4thatalmost95percentofthemigrantsgoingtoNordiccountrieshaveearningsontherangewhere

∆ ispositive.Tosumup,thefindingsoffersupporttothestochasticdominance

29Theupperboundsarecalculatedsimilarlytothelowerbounds.

22

predictionformaleandfemalemigrantsregardlessoftheirdestination,althoughtheevidenceisweakerformenwhomigratedtoNordiccountries.AdditionalsupportforourtheorycomesfromMexico.OurtheorypredictsthattheearningsdistributionofmigrantsfromMexicototheUnitedStatesshouldbestochasticallydominatedbytheearningsdistributionofnon‐migrants.Fernández‐HuertasMoraga(2011)presentsthesedistributionsformen.Althoughhedoesnotpresentconfidenceintervalsaswedo,thefiguressuggestapatternthatmirrorswhatwefindforDenmark,reversingthecurvesformigrantsandnon‐migrants.InMexico,thewagedistributionofnon‐migrantsstochasticallydominatesthatofmigrants,apartfromanoverlapforafewpercentatthebottomandconvergingatthetop.5.Selectioninunobservedcharacteristics

Intheprevioussection,wedocumentedtheselectionthatcharacterizesthemigrantsusingthetotalpre‐migrationearnings(afteradjustingforageandyear).Wenowexamineaspecificcomponentofearnings,namelythecomponentduetounobservedcharacteristics.Inparticular,wenowadjustfordifferencesineducationalattainmentbetweenmigrantsandnon‐migrants(aswellasotherobservablevariables)byrunningearningsregressions,anddeterminewhetherthedistributionoftheresidualsdiffersbetweenthetwogroups.30Byconstruction,theresidualsfromaMincerianwageregressionreflectthepartofearningsthatisuncorrelatedwiththeobservedmeasuresofskill.Obviously,thedecompositionissomewhatarbitrarybecauseitdependsonthecharacteristicsthatareobservedandcanbeincludedasregressorsinthewageequation.Nevertheless,thestudyofemigrantselectionintermsofwageresidualsisimportantforanumberofreasons.

30Intheearningsregressionsweusenon‐standardizedannualearningsasthedependentvariable.Weincludeageandyearfixedeffectsandruntheregressionsseparatelyformenandwomen.

23

First,selectionintermsofunobservablecharacteristicsshedslightontheimportanceofthequalityofjobmatchesrelativetotheskillcomponentthatisinternationallytransferable.Thetheorypredictsthatthenatureoftheselectioninunobservablecharacteristicsdependsonthemagnitudeofthecorrelationcoefficientmeasuringhowthesourceanddestinationcountriesvaluethesetypesofskills.Aslongasthiscorrelationisstronglypositive(sothatunobservedcharacteristicsareeasilytransferableacrosscountries),Danishemigrantswouldbepositivelyselectedinunobservables.Afterall,thepayofftothesetypesofskillsislikelytobegreaterinthedestinationcountries.However,itcouldbearguedthatthecorrelationbetweenthewageresidualsinDenmarkandabroadmaybe“small”.Forexample,theresidualsfromthewageregressionmaybelargelyreflectingthequalityoftheexistingjobmatchintheDanishlabormarket,ratherthanmeasuringtheworker’sinnateproductivity.Totheextentthatthequalityofthejobmatchplaysanimportantroleingeneratingtheresidual,thecorrelationinthisresidualacrosscountrieswouldbeexpectedtobeweak(infact,apurerandommatchingmodelwouldsuggestthatitwouldbezero).Asaresult,therewouldbenegativeselectioninunobservedcharacteristicssimplybecauseDanishworkerswithgoodjobmatches(andhencehighvaluesoftheresidual)wouldnotmove.Second,thetheoryalsosuggeststhatthenatureoftheselectioninpre‐migrationearningsdependsonaweightedaverageoftheselectionthatoccursinobservableandunobservablecharacteristics,withtheweightsbeingthefractionofearningsvarianceattributabletoeachtypeofskill.Becauseobservablecharacteristicsplayonlyalimitedroleinexplainingthevarianceofearningsinthepopulation,itiscrucialtopreciselydelineatethenatureofselectioninunobservablecharacteristics.Table5reportstheMincerianwageregressionsthatweusetocalculatetheresiduals.Thesampleincludesthewholepopulationofprimeagedfulltimeworkerspooledovertheentire1995‐2004period.Inadditiontovectorsoffixedeffectsgivingtheworker’sageandeducationalattainment,wealsoincludetheworker’smaritalstatusandnumberofchildren.Theregressionsareestimatedseparatelyformenandwomen.

24

Figure7apresentsthecumulativedistributionsofwageresidualsformalemigrantstoNordiccountries,malemigrantstodestinationsoutsideNordiccountries,andmalenon‐migrants.Thevaluesoftheresidualsaretruncatedat‐2and2,arangethatcoverspracticallyallofthepopulation.31ThecumulativedistributionfunctionofresidualsforemigrantswhomovedoutsidetheNordiccountriesislocatedtotherightofthecumulativedistributionformigrantstoNordiccountries,whichinturnislocatedtotherightofthecumulativedistributionofthenon‐migrants.Thevisualevidence,therefore,providesastrongindicationthatmigrantsarepositivelyselectedintermsofunobservedcharacteristics.Figure7bpresentstheanalogousevidenceforwomen.32Thefigureshowsthatfemalemigrantsarealsopositivelyselectedintermsofwageresiduals.Aswasthecasewhencomparingthemeasureofpre‐migrationearningsintheprevioussection,theselectioninunobservedcharacteristicsislesspronouncedforwomenthanformen.Oneexplanationforthiscouldbethatmenaretypicallyprimaryearnersincouples.WealsoperformedKolmogorov‐Smirnovtestsonthedistributionsofresidualsfornon‐migrantsandmigrantstootherNordiccountriesandformigrantstootherdestinations(separatelyformenandwomen).Allthetestsclearlyrejectedthenullhypothesis,confirmingthatthedistributionsofresidualsindeeddifferamongthegroups.33Theevidenceonthepositiveselectionofmigrantsinunobservedcharacteristicsobviouslyimpliesthattheselectioninpre‐migrationearningsdocumentedintheprevioussectioncannotbeattributedsolelytothefactthatmigrantsaremoreeducated.Instead,wefindthatthereispositiveselectionwithineducationgroups.Thisresultalsohasimplicationson

31Formen,0.05%ofnon‐migrants,0.19%ofmigrantstootherNordiccountriesand0.11%ofmigrantstootherdestinationsliebelowthelowertruncationpoint.Correspondingly,0.03%ofnon‐migrantsand0.23%ofmigrantstodestinationsoutsideNordiccountrieslieabovetheuppertruncationpoint.TherearenomigrantstootherNordiccountriesabovetheuppertruncationpoint.32Forwomen,0.05%ofnon‐migrantsliebelowthelowertruncationpointand0.00%ofnon‐migrantslieabovethehighertruncationpoint.Therearenomigrantslyingbelowthelowerorabovethehighertruncationpoint.33Thep‐valueforthetestbetweenwomenmigratingtootherNordiccountriesandtootherdestinationswas0.015andalltheotherp‐valueswere0.000,sothatalltestsclearlyrejectthehypothesisthattheobservationsaredrawnfromthesamedistribution.

25

theinterpretationofearningsregressionresidualsingeneral.Theresidualsfromwageregressionsaresometimesinterpretedasreflectingthevalueofthejobmatchbetweentheworkerandtheemployer.Ifahighvaluefortheresidualonlyreflectsagoodmatch,wewouldthenexpecttofindthatworkerswithlargeresidualswouldbelesslikelytochangejobsandlesspronetomigrate.Ourfindingsclearlyrejectthisinterpretation.Comparingresultsontheself‐selectiontootherNordiccountriesandtherestoftheworldsuggeststhatsearchforabetterjobmatchtothosewhohaveabadjobmatchinDenmarkismorepronouncedamongmigrantstootherNordiccountries.34Asintheprevioussection,wealsocalculatedthedifferencebetweenthecumulativedistributionfunctionswithconfidenceintervalstodeterminewhetherempiricalevidencesupportsthestochasticdominanceprediction.ThetestresultsaresummarizedinTable6.Figure8adepicts∆ w andthelowerandupperboundsfora95%confidenceintervalforthecomparisonbetweennon‐migrantmenandmenmigratingtodestinationsoutsideNordiccountries.Thelowerboundofthe95%confidenceintervalispositiveontherangeofresidualscoveringmostofthesupportofthetwodistributions.9.9percentofthemigrantsand15.2percentofthenon‐migrantshavewageresidualsbelowthelowerboundofthisrange,whereasthesharesofmigrantsandnon‐migrantsabovetheupperboundoftherangeare0.1and0.0percent.35Figure9adepicts∆ w andtheboundsfora95%confidenceintervalfornon‐migrantmenandmenmigratingtootherNordiccountries.A13percentshareofmigrantsand15percentofnon‐migrantshavevaluesofthewageresidualthatarebelowthelowerboundoftherangewherethelowerboundofthe95%confidenceintervalispositive,andsharesof2percentand1percentofmigrantsandnon‐migrantshavevaluesoftheresidualthat34Forthisgroup,returnstounobservedproductivityarenotasimportantacriterionforself‐selectionasamongmigrantstotherestoftheworld,simplybecausedifferencesinreturnstoskillsbetweenDenmarkandotherNordiccountriesareminor.Asaresult,themechanismofsearchingforabettermatchqualityismorepronounced.35Forwomen,20percentofmigrantsand25percentofnon‐migrantshaveearningsresidualsbelowthelowerboundoftherangewherethelowerboundoftheconfidenceintervalispositive,andsharesofmigrantsandnon‐migrantsabovetherangearelessthanonepercent.

26

wouldplacethemabovethisrange.Putdifferently,theresidualsofover84percentofmalemigrantstodestinationsoutsideNordiccountriesareontherangewherethecumulativedistributionfunctionfornon‐migrantsisstatisticallysignificantlyabovethefunctionformigrants.36Interestingly,thereisasizableareainthelefttailofthedistributionofresidualswheretheupperboundoftheconfidenceintervalisnegative.37Weconcludebysummarizingtheevidenceasfollows:thereisstrongpositiveselectioninunobservablecharacteristicsinthesampleofmigrantsthatmovedoutsidetheNordiccountriesandweakerevidenceofpositiveselectioninthesampleofmigrantswhomovedtootherNordiccountries.6.Biasincounterfactualpredictions

Thefactthatemigrantsareself‐selectedintheirunobservedcharacteristicsimpliesthatusingtheobservablecharacteristicsofmigrantstopredicttheircounterfactualearningshadtheychosennottomigratewillleadtobiasedresults.Duetodataconstraints,thisispreciselytheempiricalexerciseconductedbyChiquiarandHanson(2005),whoadoptthemethodologyintroducedbyDiNardo,Fortin,andLemieux(1996)andbuildacounterfactualwagedensityofwhattheMexicanimmigrantswouldhaveearnedinMexicohadtheystayed.TheactualwagedensityofMexican“stayers”isthencomparedtothecounterfactualdensityformigrants.Byconstruction,thisapproachignorestheroleofunobservablecharacteristicsintheestimationofthecounterfactualwagedistribution.AclearadvantageoftheDanishadministrativedataisthattheearningsofemigrantscanbeobservedbeforetheyemigrate,sothereisnoneedtobuildacounterfactualdensity.Onejustneedstocomparetheearningsdistributionofnon‐migrantstotheactualdistribution36Forwomen,20percentofmigrantsand25percentofnon‐migrantshaveearningsresidualsbelowthelowerboundoftherangewherethelowerboundoftheconfidenceintervalispositive,andsharesofmigrantsandnon‐migrantsabovetherangeare3percentand2percent.37A2percentshareofmigrantsand2percentshareofnon‐migrantshaveresidualsinthisarea,andtheinterpretationwouldbethatmalemigrantstootherNordiccountriesarenegativelyselectedintermsofresidualsinthelefttailofthedistribution.

27

offuturemigrants,aswehavedoneintheprecedinganalysis.Theadministrativedata,however,allowsustopreciselymeasuretheextentofthebiasresultingfromcarryingoutthecounterfactualexerciseinChiquiarandHanson(2005).Inparticular,wecancontrastthepredictedcounterfactualwagedistributionofmigrantshadtheynotmovedtotheactualwagedistributionofmigrantspriortotheirmove.WecarryoutthisexercisebypreciselyreplicatingthevariousstepsintheChiquiar‐Hansoncalculations.Itisworthemphasizingthatthistypeofbiaswillarisenotonlyinstudiesthatexaminetheselectionofmigrants,butinanystudythatreliesonobservablestopredictacounterfactualwagedistribution.Let representthelogarithmofstandardizedannualearningsasdefinedearlier(i.e.earningsadjustedforage,gender,andyeareffects).Let | bethedensityfunctionofwagesinDenmark,conditionalonasetofobservablecharacteristics .Also,let beanindicatorvariableequaltooneiftheindividualmigratesthefollowingyearandequaltozerootherwise.Definefurther | 0 astheconditionaldensityofobservedcharacteristicsamongworkersinDenmarkwhochoosenottomigrate,and | 1 bethecorrespondingconditionaldensityamongmigrants.Theobservedwagedensityforthenon‐migrantsis(20) | 0 | , 0 | 0 .Similarly,theobserveddensityforthemigrantsis(21) | 1 | , 1 | 1 .

Uptothispoint,theanalysisreportedinthispaperconsistsofdirectlyestimatingandcomparingthedistributionfunctionsassociatedwiththedensitiesinequations(20)and(21).Supposethatthepre‐migrationearningsdensityfornon‐migrantswerenotavailable.Wewouldinsteadattempttoestimateitfromtheobservablecharacteristicsofthemigrants.Theimpliedcounterfactualdistributionis:

28

(23) | 1 | , 0 | 1 .Equation(23)correspondstothedensityofincomefornon‐migrants,butitisinsteadintegratedoverthedensityofobservablecharacteristicsformigrants.Notethatthecounterfactualdensityin(23)canberewrittenas:(24)

| 1 | , 0 | 0 | 1| 0

| , 0 | 0 , where || .Tocompute ,weuseBayes’lawtowrite:(25) | | and

| | ,

where istheunconditionaldensityofobservedcharacteristics.Wecanthencombinethesetwoequationstosolvefor:(26)

1|1 1|

01 .

TheproportionPr(I=0)/Pr(I=1)isaconstantrelatedtotheproportionofmigrantsinthedata.Itcanbesettooneinkerneldensityestimationwithoutlossofgenerality.Theweightweuseintheestimationisthengivenby:

29

(27) 1|

1 1| .AsinChiquiarandHanson(2005),theindividualweightsearecalculatedbyestimatingalogitmodelwherethedependentvariableindicatesifapersonemigrated.Theregressorsincludeavectorofagefixedeffects,avectorofschoolingfixedeffects,variablesindicatingwhethertheworkerismarriedandthenumberofchildren(andaninteractionbetweenthesetwovariables),andavectorofyearfixedeffects.38Table7reportsthelogitregressionsestimatedseparatelybygender.Thecoefficientsarethenusedtocomputetheweightsforeachnon‐migrantpersoninthesample.39Figures10aand10bpresenttheresultingcounterfactualdensityfunctionsofthelogarithmofstandardizedearningsaswellastheactualdistributionsformigrantsandnon‐migrants.40Thedifferencebetweentheactualdensityfornon‐migrantsandthecounterfactualdensityformigrantsreflectsthepartofself‐selectionthatisduetoobservablecharacteristics.Similarly,thedifferencebetweenthecounterfactualandactualdensitiesformigrantsreflectsthepartofselectionthatisduetounobservedcharacteristics(i.e.,allthosevariablesthatcouldnotbeincludedinthelogitmodel).Onesimplewayofquantifyingthesedistributionaldifferencesistocomputetheaveragesofthevariousdistributions.ThesecalculationsarereportedinTable8.Considerinitiallytheresultsinthemalesample.Thedifferencebetweenthemeanoftheactualdistributionsformigrantsandnon‐migrantsis0.245logpoints,butthedifferencebetweenthecounterfactualdistributionandthedistributionfornon‐migrantsis0.073.Thisimpliesthatonlyabout30percentofthepositiveselectioninpre‐migrationearningscanbeattributed38Wealsotriedspecificationswithage,agesquaredandinteractionsofexplanatoryvariables,butwedonotreporttheseanalysesastheresultingcounterfactualdistributionsdidnotpracticallydifferfromthedistributionsresultingfromthissimplerspecification.39Asearlier,weuseSilverman’sreferencebandwidthmultipliedby0.75.40Toconductthecounterfactualanalysiswepoolthesampleofallmigrants(regardlessofwhethertheymovedtoNordiccountriesornot).

30

totheobservablecharacteristicsincludedinthelogitmodel,whileabout70percentisattributabletounobservabledeterminantsofproductivity.Thecalculationsinthefemalesampleyieldadifferenceof0.157logpointsbetweenthemeansoftheactualdistributionsformigrantsandnon‐migrantsandadifferenceof0.074pointsbetweenthecounterfactualdistributionandthedistributionfornon‐migrants.Asaresult,observableandunobservablecharacteristicseachaccountforabouthalfofthepositiveself‐selectioninthepre‐migrationearningsofwomen.41Thekeylessonisclear:selectioninunobservablecharacteristicsplaysacrucialroleindeterminingtheskillcompositionofemigrants.Thedistinctroleofobservablesandunobservablesindeterminingtheselectioninthepre‐migrationearningsofmigrantsisevidentifwereturntotheRoymodelandequation(16),whichpresentstheconditionalexpectationE(logw0|v*>*).Equation(16)yieldsaninterestingandpotentiallyimportantinsight.Thenatureoftheselectioninpre‐migrationearnings,ofcourse,isgivenbythesumoftheselectioninobservablesandtheselectioninunobservables.Note,however,thateachoftheseselectiontermshasaweightingcoefficientthatrepresentsthevarianceinearningsattributabletoobservablecharacteristics( r02S2)ortounobservablecharacteristics(02 ).Asnotedearlier,observablecharacteristicsexplainarelativelysmallfractionofthevarianceinearnings.Putdifferently,equation(16)impliesthatitistheselectioninunobservablesthatismostlikelytodeterminethenatureoftheselectionthatcharacterizestheemigrantsample.Totheextentthatbothtypesofselections(i.e.,inobservablesandunobservables)workinthesamedirection,thecounterfactualexercisedescribedinthissectionwillinevitablyunderestimatethetrueextentofpositiveselectioninpre‐migrationearnings.Conversely,41Thecomponentofself‐selectionthatisduetounobservablecharacteristicsplaysasomewhatsmallerroleforwomen.Onereasoncouldbethatwomenaremoreoftentiedmigrants,andthemigrationdecisionmaybemainlybasedontheskillsofthespouse.Thevarianceinincomeisalsosmallerforwomen,whichalsomakestheselectionbothintermsofobservableandunobservablecharacteristicsweaker.

31

thecounterfactualexercisewillalsoattenuatetheextentof“true”negativeselectionifthereisnegativeselectioninbothcomponentsofskills.Infact,Fernández‐HuertasMoraga(2011)presentsacorrespondinganalysisusingsurveydatafromMexicoandfindsthatcounterfactualestimatesgreatlyunderestimatetheextentofnegativeselectioninthepre‐migrationearningsofMexicanswhomovetotheUnitedStates.Putdifferently,thecounterfactualexercisemayleadtoqualitativelyrightconclusionsaboutthenatureoftheselection,butitmayalsogenerateasizablebias,greatlyunderestimatingthetrueextentofeitherpositiveornegativeselection.7.Selectionandimmigrationrestrictions

Asappliedintheimmigrationliterature,theRoymodelfocusessolelyontheeconomicfactorsthatmotivatelaborflowsacrossinternationalborders.Themodelingtypicallyignoresthefactthattheseflowsoccurwithinapolicyframeworkwheresomereceivingcountriesenactdetailedrestrictionsspecifyingwhichpotentialmigrantsareadmissibleandwhicharenot.WecanusetheadministrativedatafromDenmark,combinedwiththeuniquepoliticalcircumstancesthatguaranteefreemigrationwithinEurope,topartiallyaddressthequestionofwhetherimmigrationpolicyaffectsselectionallthatmuchintheend.Specifically,wecansubdividethegroupofmigrantswhomovedoutsideNordiccountriesintotwogroups:thosewhomovedtoacountryintheEU15ortoSwitzerland,andthosewhomovedtoacountryoutsidetheEU15andSwitzerland.MovementoflaborwasunrestrictedbetweenDenmarkandotherEU15countriesandSwitzerlandintheperiodunderstudy,butwasobviouslyrestrictedbyimmigrationregulationstodestinationsoutsidetheEU15,suchastheUnitedStates.ItturnsoutthatthesedifferentimmigrationpoliciespursuedbytheEU15andSwitzerlandandtherestoftheworldbarelymatterindeterminingtheselectionofDanishemigrants.Figure11adepictsthecumulativedistributionfunctionsofthelogarithmofstandardizedannualincomeformenandfigure11bforwomen.Itisevidentthatthedistribution

32

functionsofstandardizedearningsareverysimilarforthetwogroupsofmigrants.42Wealsoconductedtheanalysisusingthewageresiduals(notshown),andthedistributionsofresidualsarealsosimilarbetweenthetwogroups.Thereisanimportantsenseinwhichthesepolicyrestrictionscannotmattermuch.Suppose,forexample,thatareceivingcountryenactsapolicythatlimitsentryonlytohigh‐skillimmigrants.Ifthehigh‐skillimmigrantsfromasendingcountrydonotfinditoptimaltomove,thepolicycannotforcethosehigh‐skillworkerstomigrate.Allthepolicycandoisessentiallycutthemigrationflowfromthatparticularsendingcountrydowntozero.Thelow‐skillworkerswouldliketomovebutarenotadmitted,andthehighskillworkersareadmissiblebuttheydonotwanttomove.Insum,thepositiveself‐selectionthatissoevidentintheDanishemigrantdatacannotbeexplainedbyimmigrationrestrictions.EventhoughlaborflowstotheEU15andSwitzerlandwereunrestricted,thereisnoevidenceofweakerpositiveselectiontothesecountriesthantotherestoftheworld.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‐selectionofemigrantsthanpreviouslyexamined.Thesameconditionsthathavebeenshowntoresultinemigrantsbeingpositively(negatively)self‐selectedintermsoftheiraverageearningsactuallyimplythattheearningsdistributionofemigrantsfirst‐orderstochasticallydominates(orisfirst‐orderstochasticallydominatedby)theearningsdistributionofnon‐

42Forwomen,aKolmogorov‐Smirnovtestisnotabletorejectthenull‐hypothesisthattheobservationsforthetwogroupsofmigrantscomefromthesameunderlyingdistribution.

33

migrants.Ourtheoreticalanalysisalsodistinguishesbetweenselectioninobservableandselectioninunobservablecharacteristics.OurempiricalanalysisusestheDanishfullpopulationadministrativedatatoanalyzetheself‐selectionofemigrants,intermsofeducation,earningsandunobservableability,measuredbyresidualsfromMincerianearningsregressions.Theresultsareinlinewiththetheory;themigrantsarebettereducatedandbothpre‐emigrationearningsandwageregressionresidualsofmigrantsstochasticallydominatethoseofnon‐migrantsovermostofthesupportofthedistributions.Consider,forexample,thecaseoffull‐timeworkersaged25‐54.For98percentofmenand97percentofwomenwhomigrateoutsideotherNordiccountriesthecumulativeearningsdistributionintheyearbeforeemigrationstochasticallydominatesthatofnon‐migrantswitha95%confidenceinterval.Thedifferencebetweenthecumulativedistributionsisnotstatisticallysignificantlydifferentineitherdirectionfortheremaining2to3percent.Decomposingtheself‐selectionintotalearningsintoself‐selectioninobservablecharacteristicsandself‐selectioninunobservablecharacteristics(asmeasuredbyresidualsfromMincerianwageregressions),revealsthatunobservedabilitiesplaythedominantrole.Formen,about70percentofthepositiveself‐selectioninpre‐migrationearningsisattributabletounobservabledeterminantsofproductivity.Forwomen,thefractionisabout50percent.Thissuggeststhatrelyingoncounterfactualdistributions,basedonobservedcharacteristics,wouldstronglyunderestimatepositiveself‐selection.ThisresultcomplementstheFernández‐HuertasMoraga(2011)findingthatcounterfactualestimatesalsogreatlyunderestimatetheextentofnegativeselectioninthepre‐migrationearningsofMexicanswhomovetotheUnitedStates.Inshort,theuseofcounterfactualearningsdistributionsbasedonobservablecharacteristicsgreatlyunderstatethetrueextentofselectionintotalearnings.Strongpositiveself‐selectioninresidualsalsosuggeststhatunobservedabilitiesplayamuchbiggerroleinmigrationdecisionsthanmatchquality.Ourfindingsalsohaveimplicationsforimmigrationpolicies.Receivingcountriescanonlybasetheiradmissionpoliciesonskillvariablesthatareobserved,whereasmuchofthe

34

selectionofimmigrantsis“hidden”intheirunobservedcharacteristics.Itcanbeexpectedthatmigrantswillbeself‐selectedintermsofunobservedcharacteristicsevenwhenadmissionrestrictionsareapplied,andtheself‐selectionamongthosefulfillingadmissioncriteriacanbeexpectedtoreflectrelativeskillprices.Thisraisesaquestionabouttheeffectivenessofpointsystemsthatarenecessarilybasedonobservablecharacteristics.Theimportanceofrelativeskillpricesisalsosupportedbyourseparateanalysesofself‐selectionofDanesmigratingtothecountriesbelongingtocommonEuropeanlabormarket(excludingotherNordiccountriesthathaveskillpricessimilartoDenmark)andnothavinganyimmigrationrestrictions,andtheself‐selectiontotherestoftheworld.Thereisvirtuallynodifferenceintheself‐selectiontothesedestinationareas.

35

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a.Men

b.Wom

men

Figurre1.Evolu

38

utionoftheeemigratioonrate

Figur

a.Men

b.Wom

e2.Evolut

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differencemigrant

39

ebetweentsandnon

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ogstandar

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re3.Distri

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40

standardiznon‐migran

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formigranntsand

Figurea.Men

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41

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42

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43

ativedistriotherNor

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rationts

Figure

a.Men

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44

residualsfrdnon‐migr

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45

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46

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47

tualdensittiesofstanndardized

grossearnnings

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48

annualgrdmigrants

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grantstothns

heEU15

49

Table1.Summarystatistics

Non-migrant men Migrant

men Non-migrant

women Migrant women

Observations 6450665 7323 5163129 3436 Age

Average 39.8 33.0 40.2 35 Median 40.0 35.4 40.0 33.0

Annual earnings in 2010 euros

Average 52725 68151 40299 46412 Median 46675 57350 37976 42393

Standardized annual earnings

Average 1.0 1.3 1.0 1.2 Median 0.9 1.2 0.95 1.1

50

Table2.Numbersofmigrants,bydestination

Men Women Sweden 1466 699The United States 763 363 The United Kingdom 725 432 Norway 576 273 Germany 560 249 Spain 255 147 Switzerland 233 118 France 222 156 Other 2523 999

51

Table3.Educationlevelsofnon‐migrantsandmigrantsgoingtoNordiccountriesor

tootherdestinations

Men Women

Education Non-migrants Nordic

countries Other

destinations Non-

migrants 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

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.Summaryoftestsofstochasticdominanceindistributionsofstandardizedpre‐migrationearnings

Distributions being compared:

Percent of sample below lower bound

Percent of sample above upper bound

Migrants Non-migrants Migrants Non-migrantsMigrants outside Nordic countries and non-migrants

Male 2.0 3.4 0.1 0.0 Female 2.8 4.1 0.2 0.0

Migrants to Nordic countries and non-migrants

Male 11.6 15.5 1.5 0.7 Female 2.6 4.1 2.6 1.3

Notes:Lowerboundandupperboundrefertotherangeoverwhichthedifferenceofthecumulativedistributionfunctionsissignificantata95percentconfidencelevel.

53

Table5.Mincerianearningsregressions,bygender

(1) men (2) women B Se B se

Married 0.068*** (0.00) -0.016*** (0.00) Children 0.025*** (0.00) -0.048*** (0.00)

High school 0.224*** (0.00) 0.190*** (0.00) Vocational school 0.092*** (0.00) 0.089*** (0.00)

Advanced vocational 0.186*** (0.00) 0.198*** (0.00) Bachelor 0.298*** (0.00) 0.225*** (0.00) Master’s 0.498*** (0.00) 0.536*** (0.00)

PhD 0.490*** (0.00) 0.622*** (0.00) 1996 0.020*** (0.00) 0.017*** (0.00) 1997 0.043*** (0.00) 0.041*** (0.00) 1998 0.078*** (0.00) 0.083*** (0.00) 1999 0.103*** (0.00) 0.112*** (0.00) 2000 0.141*** (0.00) 0.143*** (0.00) 2001 0.175*** (0.00) 0.175*** (0.00) 2002 0.207*** (0.00) 0.210*** (0.00) 2003 0.236*** (0.00) 0.235*** (0.00) 2004 0.252*** (0.00) 0.258*** (0.00)

Constant Age fixed effects

12.131*** Yes

(0.00)

11.931*** Yes

(0.00)

N R-squared

6470720 0.2597

5173706 0.3062

*p

54

Table6.SummaryoftestsofstochasticdominanceindistributionsofresidualsDistributions being compared:

Percent of sample below lower bound

Percent of sample above upper bound

Migrants Non-migrants

Migrants Non-migrants

Migrants outside Nordic countries and non-migrants

Male 9.9 15.2 0.1 0.0 Female 19.6 24.7 0.4 0.0

Migrants to Nordic countries and non-migrants

Male 13.4 15.2 2.0 0.9 Female 19.5 24.7 3.4 1.8

Notes:Lowerboundandupperboundrefertotherangeoverwhichthedifferenceofthecumulativedistributionfunctionsissignificantata95percentconfidencelevel.

55

Table7.Logitestimatesoftheprobabilityofemigration,bygender

(1) men (2) women B Se B se

Married -0.110** (0.04) -0.191*** (0.05) Children -1.137*** (0.05) -1.232*** (0.07)

Married*Children 0.460*** (0.07) 0.374*** (0.09) High school 1.377*** (0.05) 1.158*** (0.08)

Vocational school 0.186*** (0.04) 0.159** (0.06) Advanced vocational 0.648*** (0.06) 0.714*** (0.08)

Bachelor 1.097*** (0.04) 0.581*** (0.06) Master’s 1.652*** (0.04) 1.444*** (0.07)

PhD 1.723*** (0.10) 1.655*** (0.21) y1996 -0.032 (0.06) -0.001 (0.08) y1997 0.002 (0.06) -0.016 (0.08) y1998 -0.024 (0.06) -0.001 (0.08) y1999 0.230*** (0.05) 0.131 (0.08) y2000 0.260*** (0.06) 0.238** (0.09) y2001 0.161** (0.05) 0.146 (0.08) y2002 0.208*** (0.05) 0.046 (0.08) y2003 0.198*** (0.05) 0.112 (0.08) y2004 0.246*** (0.05) 0.178* (0.08)

Constant -6.700*** (0.08) -6.951*** (0.12) N 6470720 5173706

Pseudo 0.0540 0.0557 *p

56

Table8.Actualandcounterfactualdifferencesbetweentheaveragelogstandardizedearningsofmigrantsandnon‐migrants

Men Women Non-migrant average -0.065 -0.040Estimated average for migrants 0.008 0.034 True average for migrants 0.180 0.117 True difference 0.245 0.157 Counterfactual difference 0.073 0.074 Share of the actual difference explained by observable characteristics, %

29.6

47.0