Forschungsinstitut zur Zukunft der ArbeitInstitute for the Study of Labor

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Self‐Selection of Emigrants:Theory and Evidence on Stochastic Dominance inObservable and Unobservable Characteristics

IZA DP No. 9434

October 2015

George J. BorjasIlpo KauppinenPanu Poutvaara

Self‐Selection of Emigrants: Theory and Evidence on Stochastic Dominance in

Observable and Unobservable Characteristics

George J. Borjas Harvard Kennedy School, NBER and IZA

Ilpo Kauppinen

VATT Institute for Economic Research

Panu Poutvaara University of Munich, Ifo Institute, CESifo, CReAM and IZA

Discussion Paper No. 9434 October 2015

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IZA Discussion Paper No. 9434 October 2015

ABSTRACT

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

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.

NON-TECHNICAL SUMMARY We examine the self-selection of emigrants from Denmark, one of the richest and most redistributive European welfare states. We find strong evidence of positive self-selection of emigrants in terms of pre-emigration earnings, education and unobservable abilities. Differences in age and education can explain less than half of earnings differences between migrants and non-migrants. Strong positive self-selection of emigrants is not driven by immigration policies in destination countries. Self-selection of emigrants to other Nordic countries, which are rather similar to Denmark in having a relatively egalitarian income distribution and a generous welfare state, is also positive, but not as strong as self-selection to other EU countries, or the rest of the world. JEL Classification: F22, J61 Keywords: international migration, Roy model, self-selection Corresponding author: Panu Poutvaara Ifo Institute Poschingerstr. 5 81679 Munich Germany E-mail: poutvaara@ifo.de

* 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.

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1.IntroductionAcentralfindingintheeconomicliteratureoninternationalmigrationisthatemigrantsarenotrandomlyselectedfromthepopulationofthesourcecountries.Thenatureofthenon‐randomselectionaffectsthelevelandthedistributionofwelfarethroughtwomajorchannels.First,theskilldistributionofmigrantsaffectsthewagestructureinbothsendingandreceivingcountries(Borjas2003).Asecondeffecttakesplacethroughthepublicsector.Immigrationcreatesafiscalsurplusinthereceivingcountryifandonlyifthenetpresentvalueofthetaxpaymentsofimmigrantsexceedsthenetpresentvalueofthecoststheyimpose.Boththeimmigrationofnetrecipientsandtheemigra‐tionofnetpayersposeachallengetothepublictreasury(Wildasin1991;Sinn1997).BeginningwithBorjas(1987),therehasbeenagreatdealofinterestinderivingandempiricallytestingmodelsthatpredicthowmigrantsdifferfromnon‐migrants.ManyofthesestudiesrelyonanapplicationoftheRoymodelofoccupationalself‐selection.Aslongasskillsaresufficientlytransferableacrosscountries,thesortingofpersonsacrosscountriesismainlydeterminedbyinternationaldifferencesintherateofreturntoskills.AcountryliketheUnitedStateswouldthenattracthigh‐skilledworkersfrommoreegalitariancountries(i.e.,countriesofferingrelativelylowratesofreturntoskills)andlow‐skilledworkersfromcountrieswithgreaterincomeinequality(i.e.,countriesoffer‐inghigherratesofreturntoskills).Theevidenceindeedsuggestsanegativecross‐sectioncorrelationbetweentheearningsofimmigrantsintheUnitedStatesandincomeinequalityinthesourcecountries.1AlthoughtheexistingliteratureonimmigrantselectionfocusesmainlyontheU.S.con‐textoronmigrationflowsfrompoortorichcountries,therearealsosizablemigrationflowsbetweenrichcountries.AccordingtotheUnitedNations(2013),21.9millionper‐sonsfromEU15countriesnowliveoutsidetheirbirthplace,with42percentofthesemigrantslivinginotherEU15countriesandanadditional13percentlivingintheUnit‐edStates.2Thispaperexaminestheself‐selectionofemigrantsfromDenmark,oneoftherichestandmostredistributiveEuropeanwelfarestates.In2013,overaquartermillionDaneslivedoutsideDenmark(correspondingtoabout5percentoftheDanish‐bornpopula‐tion),with50percentofthemigrantslivinginotherEU15countriesand13percentintheUnitedStates(UnitedNations,DepartmentofEconomicandSocialAffairs2013).BecausethereturnstoskillsinDenmarkarerelativelylow,thecanonicalRoymodelpredictsthattheemigrantsshouldbepositivelyselectedinthesensethattheexpectedearningsofthemigrantsexceedtheexpectedearningsofthestayers.3However,there1Relatedcross‐countrystudiesincludeCobb‐Clark(1993)andBratsberg(1995).GroggerandHanson(2011)examinetheselectionofmigrantsacrossabroadrangeofcountriesusinganalternativetheoreti‐calframeworkwhereindividualsmaximizelinearutilityandmigrationisdrivenbyabsoluteearningsdifferencesbetweenhighandlow‐skilledworkers.2TheEU15countriesrefertothememberstatesoftheEuropeanUnionpriortotheexpansiononMay1,2004.3ForcomparisonsofgrosswagepremiafromtertiaryeducationacrosscountriesseeBoariniandStraus(2010).ArecentpaperstudyingreturnstocognitiveskillsisHanusheketal.(2015).Thestudyfindssig‐nificantcross‐countrydifferences.Moreover,thereturnsarerelativelylowinDenmarkaswellasinother

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havebeenfewsystematicstudiesoftheself‐selectionofmigrantsfromarelativelyegal‐itariancountrytoseewhetherthisisindeedthecase.4Ourtheoreticalanalysisshowsthatthecanonicalframeworkdoesnotonlyhavepredic‐tionsaboutthedifferencebetweentheexpectedearningsofmigrantsandnon‐migrants,whichisthebasisforthestandarddefinitionofpositiveornegativeselectioninthelit‐erature,butalsoaboutthestochasticorderingofthetwoearningsdistributions.Weshowthatthesameconditionsthatpredictthatmigrantsarepositivelyself‐selectedinthesenseofadifferenceinexpectedincomesalsopredictthattheincomedistributionofthemigrantswillfirst‐orderstochasticallydominatetheincomedistributionofthenon‐migrants.Thetheoryalsodistinguishesbetweenselectioninobservableandselec‐tioninunobservablecharacteristics.OurempiricalanalysisusestheDanishfullpopulationadministrativedatatoanalyzehowmigrantsandnon‐migrantsdifferintheirpre‐emigrationearningsandotherob‐servablecharacteristics.Toshedlightontheroleofunobservablecharacteristicsintheselectionprocess,weinvestigatehowmigrantsandnon‐migrantsdifferintermsofun‐observableearningsability,asmeasuredbyresidualsfromMincerianearningsregres‐sions.Ourempiricalresultsareinlinewiththepredictionsofthemodel:Danishemi‐grantsareindeedpositivelyself‐selectedbothintermsofearningsandintermsofre‐sidualsfromthewageregressions.FollowingourreframingofthecanonicalRoyframeworkintermsoftheconceptofstochasticdominance,ourstudyspecificallytestsforwhethertheearningsdistributionoftheemigrantsstochasticallydominatesthatofthestayers(aswouldbepredictedbythemodel).Theevidenceconfirmsthisstrongtheoreticalpredictionovermostofthesupportoftheearningsdistribution.OurstudyisrelatedtotheflurryofrecentpapersthatexaminetheselectionofmigrantsfromMexicototheUnitedStates.ThepioneeringanalysisofChiquiarandHanson(2005)mergedinformationfromtheU.S.censusonthecharacteristicsoftheMexicanmigrantswithinformationfromtheMexicancensusonthecharacteristicsoftheMexi‐cannon‐migrants.Becausethemergeddatadidnotreporttheearningsofmigrantspri‐ortothemove,pre‐migrationearningswerepredictedbasedonobservablecharacteris‐ticsofthemigrants.This“counterfactual”empiricalexercisesuggestedthatMexicanemigrantswerelocatedinthemedium‐highrangeoftheMexicanwagedistribution.ThefindingofintermediateselectionintheMexicancontextdoesnotseemconsistentwiththebasicimplicationsoftheRoymodelbecausetherateofreturntoskillsisfarlargerinMexicothanintheUnitedStates.MorerecentstudiesbyFernández‐HuertasMoraga(2011)andKaestnerandMalamud(2014)usesurveydatathatreporttheactualpre‐migrationearningsandfindevidenceofnegativeselection.Theyalsoconcludethatpartofthenegativeselectioncanbetracedtotheunobservablecharacteristicsthatdeter‐mineamigrant’searnings.Nordiccountries,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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Theimportantroleplayedbyunobservablecharacteristicsimpliesthatconstructingacounterfactualearningsdistributionforthemigrantsbasedonobservablecharacteris‐ticscangreatlybiasthenatureoftheselectionrevealedbythedata.Ourfindingssug‐gestthattheuseofsuchacounterfactualdistributionwilltendtounderstatethetrueselectioninearnings,sothattheselectionimpliedbythecounterfactualdistributionisfarweakerthanthetrueselection—regardlessofwhetherthereispositiveornegativeselection.ThenumericalbiasthatresultsfromusingthecounterfactualestimationissizableintheDanishcontext:morethanhalfofthedifferencebetweentheexpectedearningsofmigrantsandnon‐migrantsarisesbecauseofdifferencesinunobservedcharacteristics.Thepaperisorganizedasfollows.Section2sketchestheeconomictheoryunderlyingtheanalysisandderivestheoreticalpredictionsconcerningtheself‐selectionofemi‐grants,usingthenotionofstochasticdominanceasaunifyingconcept.Section3intro‐ducesanddescribestheuniquepopulationdatathatweuseandreportssomesummarystatistics.Sections4and5presentthemainempiricalfindings.Insection4,weexaminetheselectionintermsofobservedpre‐migrationearnings.Wepresentastatisticalmethodfortestingthetheoreticalimplicationthattheearningsdistributionoftheemi‐grantsshouldstochasticallydominatethecorrespondingdistributionofthenon‐migrants.Section5extendstheempiricalworkbyexaminingtheselectionthatoccursintheunobservedcomponentofearnings.Section6evaluatesthebiasthatresultsfrompredictingthepre‐migrationearningsofemigrantsfromtheearningsdistributionofnon‐migrants.Section7examineswhethertheselectionofpersonsmovingtootherEU15countriesdiffersfromtheselectionofmigrantsmovingtocountrieswhereimmi‐grationrestrictionscomeintoplay.Wefindthatimmigrationrestrictionshavelittleef‐fectontheselectionofemigrants.Finally,Section8summarizesthestudyanddrawssomelessonsforfutureresearch.2.TheoreticalframeworkPreviousliteratureontheself‐selectionofmigrantshasfocusedontheconditionalex‐pectationsofearningsdistributionsamongmigrantsandstayers.Inthissection,wede‐riveanovelresult:theRoymodelimpliesthatundercertainconditions,theearningsdistributionofmigrantsfirst‐orderstochasticallydominates,orisstochasticallydomi‐natedby,theearningsdistributionofstayers.Inabivariatenormalframework,itturnsoutthattheconditionsrequiredforstochasticdominanceareidenticaltotheconditionsthatdeterminethenatureofself‐selectionintermsofexpectedearnings.Wealsodecomposeself‐selectionintotwocomponents,onethatisdeterminedbydif‐ferencesinreturnstoobservableskillsbetweensourceandhostcountry,andonethatisdeterminedbydifferencesinreturnstounobservableskills.Thedistinctionbetweenobservableandunobservableskills,ofcourse,dependsontheempiricalframeworkandonthedatathatisbeingused;observableskillsincludethevariablesexplainingearn‐ingsthatareincludedinthedata,whilethecomponentofearningsthatisleftunex‐plainedbythedataistheunobservableskillcomponent.Eventhoughthecontentofthetwocomponentsdiffersamongdatasets,itislikelythatamajorpartofmigrantself‐selectionisdeterminedbytheunobservablecomponentsimplybecause“observables”tendtoexplainarelativelysmallfractionofthevarianceinearnings.

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Wetakeasourstartingpointthemigrationdecisionfacedbypotentialmigrantsinatwo‐countryframework,inlinewithBorjas(1987)andsubsequentliterature.Residentsofthesourcecountry(country0)considermigratingtothedestinationcountry(coun‐try1),andthemigrationdecisionisassumedtobeirreversible.Tosimplifythepresen‐tation,wefocusonasingleobservedskillcharacteristicsandsuppressthesubscriptthatindexesaparticularindividual.Forconcreteness,thevariablescanbethoughtofasgivingtheworker’syearsofeducationalattainment,butitincludesallthecharacteris‐ticsaffectingindividual’sincomethatareobservedinagivensetofdata.Residentsofthesourcecountryfacetheearningsdistribution:(1) log wherew0givesthewageinthesourcecountry;r0givestherateofreturntoobservableskills;andtherandomvariable0measuresindividual‐specificproductivityshocksre‐sultingfromunobservedcharacteristicsandisnormallydistributedwithmeanzeroandvariance .Thedistributionofobservableskillsinthesourcecountry’spopulationisgivenbys=s+s,wheretherandomvariablesisalsoassumedtobenormallydis‐tributedwithmeanzeroandvariance . Iftheentirepopulationofthesourcecountryweretomigrate,thispopulationwouldfacetheearningsdistribution:(2) log wheretherandomvariable1isnormallydistributedwithmeanzeroandvariance12 .Foranalyticalconvenience,weassumethatCov(0,s)=Cov(1,s)=0,sothattheindi‐vidual‐specificunobservedproductivityshocks(i.e.,the“residuals”fromtheregressionline)areindependentfromobservablecharacteristics.5Thecorrelationcoefficientbe‐tween0and1equals01.Itisalsoworthnotingthattherandomvariablesisindivid‐ual‐specificandhasthesamevalueforthesameindividualinbothcountries,whereas0and1arebothindividual‐andcountry‐specific. Equations(1)and(2)completelydescribetheearningsopportunitiesavailabletoper‐sonsborninthesourcecountry.AssumethatthemigrationdecisionisdeterminedbyacomparisonofearningsopportunitiesacrosscountriesnetofmigrationcostsC.Definetheindexfunction:(3) log ∆ , 5Amorerealisticassumptionwouldbethatthecorrelationbetweenobservedandunobservedskillsispositive.However,allowingforpositivecorrelationdoesnotchangethequalitativepredictionsofthemodel.

02

s2

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

wise. Migrationcostsvaryamongpersons—butthesignofthecorrelationbetweencosts(whetherindollarsorintime‐equivalentterms)andskills(bothobservedandunob‐served)isambiguousanddifficulttodetermine.Theheterogeneityinmigrationcostscanbeincorporatedtothemodelbyassumingthatthedistributionoftherandomvari‐ableinthesourcecountry’spopulationisgivenby=+,whereisthemeanlevelofmigrationcostsinthepopulation,andisanormallydistributedrandomvari‐ablewithmeanzeroandvariance .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.7 Inadditiontoidentifyingthedeterminantsoftheoutmigrationrateinequation(4),theRoymodelletsusexaminewhichpersonsfinditmostworthwhiletoleavethesourcecountry.8Inthefollowing,weexaminetheself‐selectionofemigrantsalongtwodimen‐sions:selectionintermsofobservableskillssandselectionintermsofunobservableskills0,whichtogethercombineintoselectionintermsoftotalproductivityorearn‐ings,asmeasuredbylogw0.LetFM(z)andFN(z)representthe(cumulative)probabilitydistributionsofskillsorearningsformigrantsandnon‐migrantsinthesourcecountry,respectively,wherez6If werenegativelycorrelatedwithskills,thenegativecorrelationwouldtendtoinducethemoreskilledtomigrate,creatingapositivelyselectedmigrantflow.Thiswouldstrengthenpositiveself‐selection,andweakennegativeself‐selection.7Itisstraightforwardtostudyequation(4)toconfirmthatthemigrationraterises,whenmeanincomeinthesourcecountryfalls,meanincomeinthehostcountryrises,returnstoobservedskillsinthesourcecountryfall,returnstoobservedskillsinthehostcountryrise,time‐equivalentmigrationcostsfallandwhenmeanobservedskillsriseifr1>r0orfallifr1<r0.8Throughouttheanalysis,weassumethat*isconstant.Themigrationflowiseffectivelyassumedtobesufficientlysmallthattherearenofeedbackeffectsonthelabormarketsofeitherthesourceordesti‐nationcountries.

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denotesaparticularmeasureofskills(e.g.,observableorunobservablecharacteristicsorincome).Bydefinition,theprobabilitydistributionofmigrantsFM(z)first‐ordersto‐chasticallydominatesthatofstayersFN(z)if:(5) ∀ ,andthereisatleastonevalueof forwhichastrictinequalityholds.9Fromnowon,wheneverwerefertostochasticdominance,wemeanfirst‐orderstochasticdominance.Equation(5)impliesthatalargerfractionofthemigrantshaveskillsaboveanythresh‐oldz*.Putdifferently,foranylevelofskillsz*,thepopulationdescribedbytheprobabil‐itydistributionFMismoreskilledbecausealargerfractionofthegroupexceedsthatthreshold.Themigrants,inshort,arepositivelyselected.Negativeselection,ofcourse,wouldoccurifthereversewastrueand z,withastrictinequalityholdingforatleastonevalueof .Iftheskilldistributionofmigrantsstochasticallydominatesthatofnon‐migrants,thestochasticdominancethenalsoimpliesthetypicaldefinitionofpositiveselectionthatisbasedonconditionalexpectations:(6) | 0 | 0 ,sothatmigrants,onaverage,aremoreskilledthanstayers.Conversely,iftheprobabilitydistributionofstayersstochasticallydominatesthatofmigrants,andtherewasnegativeselection,itwouldalsofollowthat | 0 | 0 .Theconverse,however,isnottrueforageneraldistribution:Aclaimofpositiveselectioninexpectations,asde‐finedbyequation(6),doesnotimplythattheskilldistributionofmigrantsstochastical‐lydominatesthatofnon‐migrants.Toderivethestochasticorderingoftheskilldistributionsofmigrantsandnon‐migrants,letf(x,v)beabivariatenormaldensityfunction,withmeans(x,v),variances ( x2,v2 ) andcorrelationcoefficient.Further,lettherandomvariablevbetruncatedfrombelowatpointaandfromaboveatpointb.Arnoldetal.(1993,p.473)showthatthe(margin‐al)momentgeneratingfunctionofthestandardizedrandomvariable(x‐x)/x,giventhetruncationofv,isgivenby:(7) / ,where=(a–v)/v;and=(b–v)v. Intermsofthemigrationdecision,thetruncationintherandomvariablev=v1–v0inthesampleofmigrantsisfrombelowandimpliesthat=–*=k,and=,wherekis

9Analternativeandperhapsmoreintuitivedefinitionofstochasticdominanceisintermsofquantiles.Let and bethequantilefunctionsoforder oftheskilldistributionsofmigrantsandnon‐migrants.FM(z)stochasticallydominatesFN(z)ifandonlyif forall01andthereisatleastonevalueof forwhichastrictinequalityholds.

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thetruncationpoint.Inthesampleofstayers,thetruncationinvisfromabove,andthetruncationpointsare=–and=k.Bysubstitutingthesedefinitionsintoequation(7),itcanbeshownthatthemomentgeneratingfunctionsfortherandomvariablegiv‐ingtheconditionaldistributionsofskillcharacteristicxformigrantsandstayersreduceto:(8)

1 Φ1 Φ

and(9)

ΦΦ .

ConsideranytwodistributionfunctionsF(z)andG(z).Thistle(1993,p.307)showsthatFwillstochasticallydominateGifandonlyif:(10) , ∀ 0,wheremFisthemomentgeneratingfunctionassociatedwithdistributionF;mGisthemomentgeneratingfunctionassociatedwithG.Therankingofthemomentgeneratingfunctionsinequation(10)implieswecande‐terminethestochasticrankingofthetwodistributionsbysimplysolvingfortherele‐vantcorrelationcoefficient,andcomparingequations(8)and(9).Suchacomparisonimpliesthat:(11) , 0 , 0.Inotherwords,migrantsarepositivelyselectedif>0,andarenegativelyselectedoth‐erwise.Considerinitiallythestochasticrankinginobservablecharacteristics.Theran‐domvariablex=s,andtherelevantcorrelationcoefficientisdefinedby:(12) , 1 .Equation(12)showsthatthestochasticorderingofthedistributionsofobservableskillsofmigrantsandnon‐migrantsdependsonlyoninternationaldifferencesintherateofreturntoobservableskills.Theskilldistributionofmigrantswillstochasticallydominatethatofstayerswhentherateofreturntoskillsishigherabroad.Conversely,theskilldistributionfornon‐migrantswillstochasticallydominatethedistributionformigrantsiftherateofreturntoobservableskillsislargerathome.Considernextthestochasticorderingintheconditionaldistributionsofunobservableskills0.Therelevantcorrelationfordeterminingthistypeofselectionisgivenby:

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(13) , 1 .Itfollowsthatthedistributionofunobservableskillsformigrantsstochasticallydomi‐natesthatfornon‐migrantswhen 1.Notethatthenecessaryconditionforposi‐tiveselectionhastwocomponents.First,theunobservedcharacteristicsmustbe“trans‐ferable”acrosscountries,sothat01issufficientlyhigh.Second,theresidualvarianceinearningsislargerinthedestinationcountrythaninthesourcecountry.Theresidualvariances02 and12 ,ofcourse,measurethe“price”ofunobservedcharacteristics:thegreatertherewardstounobservedskills,thelargertheresidualinequalityinwages.10Aslongasunobservedcharacteristicsaresufficientlytransferableacrosscountries,em‐igrantsarepositivelyselectedwhentherateofreturntounobservableskillsishigherinthedestination.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),whichdeterminesthenatureoftheselec‐tioninpre‐migrationearnings,dependsonthesignofaweightedaverageoftheselec‐tionthatoccursinobservableandunobservablecharacteristics.Interestingly,theweightisthefractionofthevarianceinearningsthatcanbeattributedtodifferencesinobservableandunobservablecharacteristics,respectively.Ifthereispositive(negative)selectioninboth“primitive”typesofskills,therewillthenbepositive(negative)selectioninpre‐migrationearnings.If,however,therearediffer‐enttypesofselectioninthetwotypesofskills,theselectionineachtypeisweightedbyitsimportanceincreatingthevarianceoftheearningsdistribution.Itiswellknownthatobservablecharacteristics(suchaseducationalattainment)explainarelativelysmallfractionofthevarianceinearnings(perhapslessthanathird).Asaresult,equation(15)impliesthatitistheselectioninunobservablesthatismostlikelytodeterminethena‐tureoftheselectioninthepre‐migrationearningsofemigrants.ThisimplicationplaysanimportantroleinexplainingwhytheevidencereportedinFernández‐HuertasMora‐ga(2011)andKaestnerandMalamud(2014)conflictswiththatofChiquiarandHanson(2005).10Thisinterpretationofthevariancesfollowsfromthedefinitionofthelogwagedistributioninthehostcountryintermsofwhatthepopulationofthesourcecountrywouldearniftheentirepopulationmigrat‐edthere.Thisdefinitioneffectivelyholdsconstantthedistributionofskills.

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Asmentionedearlier,thestochasticdominanceresultsnecessarilyimplyselectionintermsofconditionalexpectations.Inthecaseofbivariatenormaldistributions,itfol‐lowsthattheexpectationoftheearningsdistributionofmigrantsE(logw0|v*>*)isgivenby:(16) | ∗ Δ ∗ 1 Δ ∗

1 Δ ∗ ,where*)=(*)/[1(*)]>0,andisthedensityofthestandardnor‐maldistribution.Ascanbeseenbyexaminingequation(16),theconditionsthatdeter‐minetheself‐selectionintermsofexpectationsarethesameastheconditionsthatde‐terminethestochasticorderingoftheskilldistributionsofmigrantsandnon‐migrants.InthenormaldistributionframeworkthatunderliesthecanonicalRoymodel,stochas‐ticdominanceimpliesselectioninexpectations,andviceversa.Inempiricalapplications,however,thepredictionofstochasticdominanceislikelytobemuchlessrobustthanthepredictionsconcerningexpectationsbecausetestingforsto‐chasticdominancewillrequireamorerigoroustestthansimplycomparingtheaverageincomesorskillsofmigrantsandnon‐migrants.Ifonejustcomparestheaveragestofindouthowmigrantsareself‐selected,thefindingscanbecompatiblewiththepredic‐tionsoftheRoy‐modelevenifalargenumberofindividualsinthedatabehaveagainstthestochasticdominancepredictionsofthemodel.Asaresult,establishinganempiricalpatternofstochasticdominanceprovidesverystrongevidencethatdifferencesinskillpricesareindeedimportantinmigrationdecisions.3.DataOuranalysisusesadministrativedatafortheentireDanishpopulationfrom1995to2010.ThedataismaintainedandprovidedbyStatisticsDenmarkanditderivesfromtheadministrativeregistersofgovernmentalagenciesthataremergedusingauniquesocialsecuritynumber.11Foreachyearbetween1995and2004,weidentifiedallDanishcitizensaged25‐54wholivedinDenmarkduringtheentirecalendaryear.12Werestricttheanalysistopersonswhoworkedfulltime.13Migrationdecisionsofpart‐timeworkersorofworkersoutside

11AllresidentsinDenmarkarelegallyrequiredtohaveasocialsecuritynumber.Thisnumberisneces‐sarytomanyactivitiesindailylife,includingopeningabankaccount,receivingwagesandsalariesorsocialassistance,obtaininghealthcare,andenrollinginschool.12Aperson’sageismeasuredasofJanuary1sttheyearafterthereferenceyear.13Theadministrativedataallowsthecalculationofavariablethatmeasurestheamountof“workexpe‐riencegained”duringthecalendaryear.Themaximumpossiblevalueforthisvariableis1,000.Were‐strictoursampletoworkerswhohaveavalueof900orabove,sothatoursampleroughlyconsistsofpersonswhoworkedfulltimeatleast90percentoftheyear.Inordertomeasuretheworkexperiencegainedduringagivenyear,wesubtractthevaluefromthepreviousyearfromthecurrentvalueofthe

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thelaborforcemaybedrivenbydifferentfactors,andtheobservedincomeoftheseworkersmaynotbeindicativeoftheirtrueearningspotential.Theincomevariableforeachyearisconstructedbyaddingtheworker’sannualgrosslaborincomeandpositivevaluesoffreelanceincome.14Wemergedthisinformationwithdatafromthemigrationregisterfortheyears1995through2010.Themigrationregisterreportsthedateofemigrationandthecountryofdestination.EventhoughitispossibleforDanishcitizenstoemigratewithoutregister‐ing,weexpectthatthenumbersofpersonswhodosoissmallasitisalegalrequire‐mentforDanishcitizenstoreportemigration.Danishtaxlawsprovidefurtherincen‐tivesformigrantstoregisterwhentheyemigrate.Afteridentifyingthepopulationofinterest,wedeterminedforeachpersonwhetherheorsheemigratedfromDenmarkduringthefollowingcalendaryear.Ifwefoundthataparticularpersonemigrated,wesearchedforthepersoninthemigrationregisterforsubsequentyearstodetermineifthemigrantreturnedtoDenmarkatsomepointinthefuture,andrecordedthedateofpossiblereturnmigration.Themigrationregisterin‐cludesnear‐completeinformationonreturnmigration,asregistrationinDenmarkisrequiredforthereturnmigranttobeeligibleforincometransfersandtobecoveredbynationalhealthinsurance.Tofocusonmigrationdecisionsthatarepermanentinnature,werestricttheanalysistomigrationspellsthatareatleastfiveyearslong.15Wedefineamigrantasanindividualwhoisfoundinoneofthe1995‐2004cross‐sections,whoemigratesfromDenmarkdur‐ingthefollowingyeartodestinationsoutsideGreenlandortheFaroeIslands,andwhostaysabroadforatleastfiveyears.16Individualswhoemigratedforlessthanfiveyearswereremovedfromthedata,andtherestofthepopulationisthenclassifiedasnon‐migrants.17Theanalysisofbothmigrantsandnon‐migrantsisfurtherrestrictedtoonlyincludeDanishcitizenswhodonothavean“immigrationbackground.”18variable.Personswhohadamissingvalueforworkexperienceineitherofthetwoyearsweredroppedfromthesample.Missingvaluesinthisvariabletypicallyindicatethatthepersonspenttimeabroad.14Theinformationonearningsistakenfromthetaxrecordsforeachcalendaryear.Thisvariableiscon‐sideredtobeofhighqualitybyStatisticsDenmark.Somepersonsalsoreportnegativevaluesforfree‐lanceincome.Thesenegativevaluesarelikelytobeduetolossesarisingfrominvestmentsanddonotreflecttheproductivecharacteristicsoftheindividual.15Havingstayedabroadforfiveyearspredictslongermigrationspells.Forexample72%ofmenand71%ofwomenwholeftDenmarkin1996andwerestillabroadafterfiveyearswerealsoabroadaftertenyears.16GreenlandandtheFaroeIslandsareautonomousregionsbutstillpartofDenmark.WehaveexcludedthesedestinationsasmanyofthesemigrantscouldhaveoriginatedinGreenlandortheFaroeIslands,andmanywouldactuallybereturninghomeratherthanemigratingfromDenmark.Theexactdurationre‐quirementswere1,825daysorlongerforlong‐termmigrants. 17Wealsoexaminedtheselectionofshort‐termmigrantsandthequalitativeresultsaresimilartothosereportedbelow,althoughtheintensityofselectionisweaker.18StatisticsDenmarkdefinesapersontohave“noimmigrantbackground”ifatleastoneoftheparentswasborninDenmarkandthepersonis/wasaDanishcitizen.Wesearchedthepopulationregistersfrom1980to2010fortheparentsofthepersonsinoursample,andifaparentwasfoundheorshewasre‐quiredtobeaDanewithnoimmigrantbackgroundaswell.

12

Table1reportssummarystatisticsfromtheDanishadministrativedata.Thepaneldatasetcontainsover6.4millionmaleand5.1millionfemalenon‐migrants.Theconstruc‐tionofthedataimpliesthatnon‐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.Simi-larly, the 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.

19Bothmigrantsandnon‐migrants,aswellasshorter‐termmigrants,areincludedinthesecalculations.20Ifwerelaxtheconstraintsonlabormarketstatusandagetoenterthesample,theUnitedKingdomemergesasthelargestdestinationbecauseofthelargenumberofDanishstudentswhopursuetheiredu‐cationthere.

13

Tosummarize,thedescriptivefindingssuggestastrongdegreeofpositiveselection—atleastasmeasuredbyeducationanddifferencesintheconditionalmeansofearnings. 4.Selectioninpre‐migrationearningsThissectionpresentsempiricalevidenceontheself‐selectionofemigrantsfromDen‐markintermsofstandardizedpre‐emigrationearnings.Themainempiricalfindingisthatlong‐termemigrantsfromDenmarkwere,ingeneral,muchmoreproductivepriortotheirmigrationthanindividualswhochosetostay.Ofcourse,thesummarystatisticsreportedinTable1alreadysuggestpositiveselectionamongemigrantsbecausetheirstandardizedearningsexceededthoseofnon‐migrants.However,differencesinconditionalaveragescouldbemaskingsubstantialdifferencesbetweentheunderlyingprobabilitydistributions.Ourtheoreticalframeworkpredictsthatthedistributionofearningsformigrantsshouldstochasticallydominatethatofnon‐migrants.Asaresult,ourempiricalanalysiswillmainlyconsistofcomparingcu‐mulativedistributionsofstandardizedearningsbetweenmigrantsandnon‐migrants.Anadvantageofsimplygraphingandexaminingthecumulativedistributionsisthattheanalysisdoesnotrequireanytypeofkerneldensityestimation,andthatwedonotneedtoimposeanystatisticalassumptionsorparametricstructureonthedata.Wewillalsopresentkerneldensityestimatesoftheearningsdensityfunctionsasanalternativewayofpresentingthekeyinsights.Finally,wewillderiveandreportstatisticalteststode‐termineifthedatasupportthetheoreticalpredictionofstochasticdominance.Figure3aillustratesthecumulativeearningsdistributionsformalemigrantstoNordiccountries,malemigrantstodestinationsoutsideNordiccountries,andformalenon‐migrants.Thevaluesofthestandardizedearningsaretruncatedat‐2and2tomakethegraphsmoretractable.21Thefigureconfirmsthatmigrantswerepositivelyselecteddur‐ingthestudyperiod.ThecumulativedistributionfunctionofstandardizedearningsofmigrantstodestinationsoutsidetheNordiccountriesisclearlylocatedtotherightofthecorrespondingcumulativedistributionfornon‐migrants,aswouldbethecaseifthecumulativedistributionofmigrantsstochasticallydominatesthatofnon‐migrants.ThefigurealsoshowsthatthedistributionfunctionformigrantstootherNordiccountriesislocatedtotherightofthatfornon‐migrants.However,theselectionofthemigrantstoNordiccountriesseemsweaker.ThisweakerselectionmayarisebecausetherateofreturntoskillsinNordiccountriesisrelativelylowwhencomparedtothatinotherpo‐tentialdestinations.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.

14

Figure4apresentsthecorrespondingkernelestimatesofthedensityfunctionsofthelogarithmofstandardizedearningsformen,whileFigure4bpresentstherespectivegraphsforwomen.24Thedensityfunctionsagainrevealthepositiveselectionofmi‐grantsmovingoutsidetheNordiccountries,bothformenandwomen.Asisevidentfromthefigures,Kolmogorov‐Smirnovtestscomparingtheearningsdis‐tributionsfordifferentgroupsrejectthehypothesisthattheunderlyingearningsdistri‐butionsarethesameatahighlysignificantlevel.Inadditiontoshowingthatthecumu‐lativedistributionsaredifferent,itisalsoimportanttodetermineiftheevidencestatis‐ticallysupportsthetheoreticalpredictionthatthecumulativedistributionfunctionofmigrantsstochasticallydominatesthatofnon‐migrants.Statisticaltestsforfirst‐orderstochasticdominancearehighlysensitivetosmallchangesintheunderlyingdistribu‐tions,makingitdifficulttorankdistributionsinmanyempiricalapplications.25AsnotedbyDavidsonandDuclos(2013),itmaybeimpossibletoinferstochasticdominanceoverthefullsupportofempiricaldistributionsifthedistributionsarecontinuousinthetails,simplybecausethereisnotenoughinformationinthetailsformeaningfultestingofanystatisticalhypothesis.Itwouldthenmakesensetofocusontestingstochasticdomi‐nanceoverarestrictedrangeofthedistribution.Weapplyanapproachthatcharacter‐izestherangeoverwhichthevalueofthecumulativedistributionfunctionfornon‐migrantsisstatisticallysignificantlylargerthanthatofnon‐migrants.Inparticular,wecalculatethedifferencebetweenthecumulativedistributionfunctionswithconfidenceintervals.TocalculatetheconfidenceintervalsweusetoolsthatwereintroducedinAraar(2006)andAraaretal.(2009).26Moreformally,wetestthefollow‐ingnullhypothesisforeach ∈ ,where isthejointsupportofthetwodistributions:(17) H0:F(w))=FN(w)–FM(w) 0,againstthealternativehypothesis(18) H1:F(w))=FN(w)–FM(w) 0andcharacterizeanyrelevantrangeof whereweareabletorejectthenull.

23Forwomen,0.06%ofnon‐migrantsliebelowthelowertruncationpointand0.00%ofnon‐migrantslieabovethehighertruncationpoint.Therearenomigrantslyingbelowthelowerorabovethehighertrun‐cationpoint.24FollowingLeibbrandtetal.(2005)andFernandes‐HuertasMoraga(2011),weuseSilverman’srefer‐encebandwidthmultipliedby0.75topreventover‐smoothing.Thesamebandwidthisusedalsoinallthekerneldensityestimatesreportedinsubsequentcalculations.25Thiscanleadtodifficultiesinempiricalwork,andlessrestrictiveconceptssuchasrestrictedfirstorderstochasticdominance(Atkinson,1987)andalmoststochasticdominance(LeshnoandKevy,2002)havebeenproposed.26ThecalculationsareimplementedusingtheDASPStatamodulepresentedinAraarandDuclos(2013).

15

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.Althoughitisnotclearlyvisiblefromfig‐ure3a,thecumulativedistributionfunctionscrossnearthelowertailsofthedistribu‐tions.Figure5adepicts∆ w andlowerandupperboundsfora95%confidencein‐terval.29Thelowerboundoftheconfidenceintervalispositiveonmostoftherangecoveringthesupportsofthedistributions.Only2.0percentofthemigrantsand3.4per‐centofthenon‐migrantsliebelowthelowerboundoftherangewherethelowerboundoftheconfidenceintervalispositive,whereasthesharesofmigrantsandnon‐migrantsabovetheupperboundoftherangeare0.1and0.0percent.Putdifferently,theearningsofalmost98percentofmalemigrantstodestinationsoutsideNordiccountriesareontherangewherethecumulativedistributionfunctionfornon‐migrantsisstatisticallysignificantlyabovethefunctionformigrants.Figure5bdepicts∆ w andtheboundsfora95%confidenceintervalfornon‐migrantwomenandwomenmigratingtodestinationsoutsideNordiccountries.Only2.8percentofthemigrantsand4.1percentofthenon‐migrantshaveearningsbelowtherangewherethelowerboundoftheconfidenceintervalispositive,andanevensmaller0.2percentofthemigrantsand0.0percentofthenon‐migrantshaveearningsabovethisrange.WeinterpretthesefindingsassupportforthestochasticdominancepredictionforbothmenandwomenmigratingoutsideNordiccountries.Figures6aand6bandthebottompanelofTable4presentacorrespondinganalysisbycomparingthecumulativedistributionsofpersonswhomigratetootherNordiccoun‐trieswiththatofnon‐migrants.Almost12percentofmalemigrantsand16percentofmalenon‐migrantshaveearningsthatliebelowtherangewhere ∆ ispositive,andanother1.5percentofthemigrantsand0.7percentofthenon‐migrantshaveearn‐ingsabovetherange.Putdifferently,about87percentofthemalemigrantstoNordiccountrieshaveincomesontherangewhere ∆ ispositive.Forwomen,itcanbeseeninTable4thatalmost95percentofthemigrantsgoingtoNordiccountrieshave27Theasymptoticvarianceof∆ isderivedinAraaretal.(2009).28Chow(1989)provedthetheoremforthecaseofindependentsamples.DavidsonandDuclos(2000)showthattheresultsalsoextendtothecaseofpairedincomesfromthesamepopulation.29Theupperboundsarecalculatedsimilarlytothelowerbounds.

16

earningsontherangewhere ∆ ispositive.Tosumup,thefindingsoffersupporttothestochasticdominancepredictionformaleandfemalemigrantsregardlessoftheirdestination,althoughtheevidenceisweakerformenwhomigratedtoNordiccountries.AdditionalsupportforourtheorycomesfromMexico.OurtheorypredictsthattheearningsdistributionofmigrantsfromMexicototheUnitedStatesshouldbestochasti‐callydominatedbytheearningsdistributionofnon‐migrants.Fernández‐HuertasMoraga(2011)presentsthesedistributionsformen.Althoughhedoesnotpresentcon‐fidenceintervalsaswedo,thefiguressuggestapatternthatmirrorswhatwefindforDenmark,reversingthecurvesformigrantsandnon‐migrants.InMexico,thewagedis‐tributionofnon‐migrantsstochasticallydominatesthatofmigrants,apartfromanover‐lapforafewpercentatthebottomandconvergingatthetop.5.SelectioninunobservedcharacteristicsIntheprevioussection,wedocumentedtheselectionthatcharacterizesthemigrantsusingthetotalpre‐migrationearnings(afteradjustingforageandyear).Wenowexam‐ineaspecificcomponentofearnings,namelythecomponentduetounobservedcharac‐teristics.Inparticular,wenowadjustfordifferencesineducationalattainmentbetweenmigrantsandnon‐migrants(aswellasotherobservablevariables)byrunningearningsregressions,anddeterminewhetherthedistributionoftheresidualsdiffersbetweenthetwogroups.30Byconstruction,theresidualsfromaMincerianwageregressionreflectthepartofearn‐ingsthatisuncorrelatedwiththeobservedmeasuresofskill.Obviously,thedecomposi‐tionissomewhatarbitrarybecauseitdependsonthecharacteristicsthatareobservedandcanbeincludedasregressorsinthewageequation.Nevertheless,thestudyofemi‐grantselectionintermsofwageresidualsisimportantforanumberofreasons.First,selectionintermsofunobservablecharacteristicsshedslightontheimportanceofthequalityofjobmatchesrelativetotheskillcomponentthatisinternationallytrans‐ferable.Thetheorypredictsthatthenatureoftheselectioninunobservablecharacteris‐ticsdependsonthemagnitudeofthecorrelationcoefficientmeasuringhowthesourceanddestinationcountriesvaluethesetypesofskills.Aslongasthiscorrelationisstronglypositive(sothatunobservedcharacteristicsareeasilytransferableacrosscountries),Danishemigrantswouldbepositivelyselectedinunobservables.Afterall,thepayofftothesetypesofskillsislikelytobegreaterinthedestinationcountries.However,itcouldbearguedthatthecorrelationbetweenthewageresidualsinDen‐markandabroadmaybe“small”.Forexample,theresidualsfromthewageregressionmaybelargelyreflectingthequalityoftheexistingjobmatchintheDanishlabormarket,ratherthanmeasuringtheworker’sinnateproductivity.Totheextentthatthequalityofthejobmatchplaysanimportantroleingeneratingtheresidual,thecorrelationinthisresidualacrosscountrieswouldbeexpectedtobeweak(infact,apurerandommatch‐ingmodelwouldsuggestthatitwouldbezero).Asaresult,therewouldbenegativese‐

30Intheearningsregressionsweusenon‐standardizedannualearningsasthedependentvariable.Weincludeageandyearfixedeffectsandruntheregressionsseparatelyformenandwomen.

17

lectioninunobservedcharacteristicssimplybecauseDanishworkerswithgoodjobmatches(andhencehighvaluesoftheresidual)wouldnotmove.Second,thetheoryalsosuggeststhatthenatureoftheselectioninpre‐migrationearn‐ingsdependsonaweightedaverageoftheselectionthatoccursinobservableandun‐observablecharacteristics,withtheweightsbeingthefractionofearningsvarianceat‐tributabletoeachtypeofskill.Becauseobservablecharacteristicsplayonlyalimitedroleinexplainingthevarianceofearningsinthepopulation,itiscrucialtopreciselydelineatethenatureofselectioninunobservablecharacteristics.Table5reportstheMincerianwageregressionsthatweusetocalculatetheresiduals.Thesampleincludesthewholepopulationofprimeagedfulltimeworkerspooledovertheentire1995‐2004period.Inadditiontovectorsoffixedeffectsgivingtheworker’sageandeducationalattainment,wealsoincludetheworker’smaritalstatusandnumberofchildren.Theregressionsareestimatedseparatelyformenandwomen.Figure7apresentsthecumulativedistributionsofwageresidualsformalemigrantstoNordiccountries,malemigrantstodestinationsoutsideNordiccountries,andmalenon‐migrants.Thevaluesoftheresidualsaretruncatedat‐2and2,arangethatcoversprac‐ticallyallofthepopulation.31Thecumulativedistributionfunctionofresidualsforemi‐grantswhomovedoutsidetheNordiccountriesislocatedtotherightofthecumulativedistributionformigrantstoNordiccountries,whichinturnislocatedtotherightofthecumulativedistributionofthenon‐migrants.Thevisualevidence,therefore,providesastrongindicationthatmigrantsarepositivelyselectedintermsofunobservedcharac‐teristics.Figure7bpresentstheanalogousevidenceforwomen.32Thefigureshowsthatfemalemigrantsarealsopositivelyselectedintermsofwageresiduals.Aswasthecasewhencomparingthemeasureofpre‐migrationearningsintheprevioussection,these‐lectioninunobservedcharacteristicsislesspronouncedforwomenthanformen.Oneexplanationforthiscouldbethatmenaretypicallyprimaryearnersincouples.WealsoperformedKolmogorov‐Smirnovtestsonthedistributionsofresidualsfornon‐migrantsandmigrantstootherNordiccountriesandformigrantstootherdestinations(separatelyformenandwomen).Allthetestsclearlyrejectedthenullhypothesis,con‐firmingthatthedistributionsofresidualsindeeddifferamongthegroups.33Theevidenceonthepositiveselectionofmigrantsinunobservedcharacteristicsobvi‐ouslyimpliesthattheselectioninpre‐migrationearningsdocumentedintheprevioussectioncannotbeattributedsolelytothefactthatmigrantsaremoreeducated.Instead,wefindthatthereispositiveselectionwithineducationgroups.Thisresultalsohasim‐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.Therearenomigrantslyingbelowthelowerorabovethehighertrun‐cationpoint.33Thep‐valueforthetestbetweenwomenmigratingtootherNordiccountriesandtootherdestinationswas0.015andalltheotherp‐valueswere0.000,sothatalltestsclearlyrejectthehypothesisthattheobservationsaredrawnfromthesamedistribution.

18

plicationsontheinterpretationofearningsregressionresidualsingeneral.Theresidu‐alsfromwageregressionsaresometimesinterpretedasreflectingthevalueofthejobmatchbetweentheworkerandtheemployer.Ifahighvaluefortheresidualonlyre‐flectsagoodmatch,wewouldthenexpecttofindthatworkerswithlargeresidualswouldbelesslikelytochangejobsandlesspronetomigrate.Ourfindingsclearlyrejectthisinterpretation.Comparingresultsontheself‐selectiontootherNordiccountriesandtherestoftheworldsuggeststhatsearchforabetterjobmatchtothosewhohaveabadjobmatchinDenmarkismorepronouncedamongmigrantstootherNordiccoun‐tries.34Asintheprevioussection,wealsocalculatedthedifferencebetweenthecumulativedistributionfunctionswithconfidenceintervalstodeterminewhetherempiricalevi‐dencesupportsthestochasticdominanceprediction.ThetestresultsaresummarizedinTable6.Figure8adepicts∆ w andthelowerandupperboundsfora95%confi‐denceintervalforthecomparisonbetweennon‐migrantmenandmenmigratingtodes‐tinationsoutsideNordiccountries.Thelowerboundofthe95%confidenceintervalispositiveontherangeofresidualscoveringmostofthesupportofthetwodistributions.9.9percentofthemigrantsand15.2percentofthenon‐migrantshavewageresidualsbelowthelowerboundofthisrange,whereasthesharesofmigrantsandnon‐migrantsabovetheupperboundoftherangeare0.1and0.0percent.35Figure9adepicts∆ w andtheboundsfora95%confidenceintervalfornon‐migrantmenandmenmigratingtootherNordiccountries.A13percentshareofmi‐grantsand15percentofnon‐migrantshavevaluesofthewageresidualthatarebelowthelowerboundoftherangewherethelowerboundofthe95%confidenceintervalispositive,andsharesof2percentand1percentofmigrantsandnon‐migrantshaveval‐uesoftheresidualthatwouldplacethemabovethisrange.Putdifferently,theresidualsofover84percentofmalemigrantstodestinationsoutsideNordiccountriesareontherangewherethecumulativedistributionfunctionfornon‐migrantsisstatisticallysignif‐icantlyabovethefunctionformigrants.36Interestingly,thereisasizableareainthelefttailofthedistributionofresidualswheretheupperboundoftheconfidenceintervalisnegative.37

34Forthisgroup,returnstounobservedproductivityarenotasimportantacriterionforself‐selectionasamongmigrantstotherestoftheworld,simplybecausedifferencesinreturnstoskillsbetweenDenmarkandotherNordiccountriesareminor.Asaresult,themechanismofsearchingforabettermatchqualityismorepronounced.35Forwomen,20percentofmigrantsand25percentofnon‐migrantshaveearningsresidualsbelowthelowerboundoftherangewherethelowerboundoftheconfidenceintervalispositive,andsharesofmi‐grantsandnon‐migrantsabovetherangearelessthanonepercent.36Forwomen,20percentofmigrantsand25percentofnon‐migrantshaveearningsresidualsbelowthelowerboundoftherangewherethelowerboundoftheconfidenceintervalispositive,andsharesofmi‐grantsandnon‐migrantsabovetherangeare3percentand2percent.37A2percentshareofmigrantsand2percentshareofnon‐migrantshaveresidualsinthisarea,andtheinterpretationwouldbethatmalemigrantstootherNordiccountriesarenegativelyselectedintermsofresidualsinthelefttailofthedistribution.

19

Weconcludebysummarizingtheevidenceasfollows:thereisstrongpositiveselectioninunobservablecharacteristicsinthesampleofmigrantsthatmovedoutsidetheNordiccountriesandweakerevidenceofpositiveselectioninthesampleofmigrantswhomovedtootherNordiccountries. 6.BiasincounterfactualpredictionsThefactthatemigrantsareself‐selectedintheirunobservedcharacteristicsimpliesthatusingtheobservablecharacteristicsofmigrantstopredicttheircounterfactualearningshadtheychosennottomigratewillleadtobiasedresults.Duetodataconstraints,thisispreciselytheempiricalexerciseconductedbyChiquiarandHanson(2005),whoadoptthemethodologyintroducedbyDiNardo,Fortin,andLemieux(1996)andbuildacoun‐terfactualwagedensityofwhattheMexicanimmigrantswouldhaveearnedinMexicohadtheystayed.TheactualwagedensityofMexican“stayers”isthencomparedtothecounterfactualdensityformigrants.Byconstruction,thisapproachignorestheroleofunobservablecharacteristicsintheestimationofthecounterfactualwagedistribution.AclearadvantageoftheDanishadministrativedataisthattheearningsofemigrantscanbeobservedbeforetheyemigrate,sothereisnoneedtobuildacounterfactualden‐sity.Onejustneedstocomparetheearningsdistributionofnon‐migrantstotheactualdistributionoffuturemigrants,aswehavedoneintheprecedinganalysis.Theadminis‐trativedata,however,allowsustopreciselymeasuretheextentofthebiasresultingfromcarryingoutthecounterfactualexerciseinChiquiarandHanson(2005).Inpar‐ticular,wecancontrastthepredictedcounterfactualwagedistributionofmigrantshadtheynotmovedtotheactualwagedistributionofmigrantspriortotheirmove.Wecar‐ryoutthisexercisebypreciselyreplicatingthevariousstepsintheChiquiar‐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‐migrantswerenot

20

available.Wewouldinsteadattempttoestimateitfromtheobservablecharacteristicsofthemigrants.Theimpliedcounterfactualdistributionis:(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:(27)

1|1 1| .

AsinChiquiarandHanson(2005),theindividualweightsearecalculatedbyestimat‐ingalogitmodelwherethedependentvariableindicatesifapersonemigrated.There‐gressorsincludeavectorofagefixedeffects,avectorofschoolingfixedeffects,variablesindicatingwhethertheworkerismarriedandthenumberofchildren(andaninterac‐tionbetweenthesetwovariables),andavectorofyearfixedeffects.38Table7reportsthelogitregressionsestimatedseparatelybygender.Thecoefficientsarethenusedtocomputetheweightsforeachnon‐migrantpersoninthesample.39Figures10aand10b38Wealsotriedspecificationswithage,agesquaredandinteractionsofexplanatoryvariables,butwedonotreporttheseanalysesastheresultingcounterfactualdistributionsdidnotpracticallydifferfromthedistributionsresultingfromthissimplerspecification.39Asearlier,weuseSilverman’sreferencebandwidthmultipliedby0.75.

21

presenttheresultingcounterfactualdensityfunctionsofthelogarithmofstandardizedearningsaswellastheactualdistributionsformigrantsandnon‐migrants.40Thedifferencebetweentheactualdensityfornon‐migrantsandthecounterfactualden‐sityformigrantsreflectsthepartofself‐selectionthatisduetoobservablecharacteris‐tics.Similarly,thedifferencebetweenthecounterfactualandactualdensitiesformi‐grantsreflectsthepartofselectionthatisduetounobservedcharacteristics(i.e.,allthosevariablesthatcouldnotbeincludedinthelogitmodel).Onesimplewayofquantifyingthesedistributionaldifferencesistocomputetheaver‐agesofthevariousdistributions.ThesecalculationsarereportedinTable8.Considerinitiallytheresultsinthemalesample.Thedifferencebetweenthemeanoftheactualdistributionsformigrantsandnon‐migrantsis0.245logpoints,butthedifferencebe‐tweenthecounterfactualdistributionandthedistributionfornon‐migrantsis0.073.Thisimpliesthatonlyabout30percentofthepositiveselectioninpre‐migrationearn‐ingscanbeattributedtotheobservablecharacteristicsincludedinthelogitmodel,whileabout70percentisattributabletounobservabledeterminantsofproductivity.Thecalculationsinthefemalesampleyieldadifferenceof0.157logpointsbetweenthemeansoftheactualdistributionsformigrantsandnon‐migrantsandadifferenceof0.074pointsbetweenthecounterfactualdistributionandthedistributionfornon‐migrants.Asaresult,observableandunobservablecharacteristicseachaccountforabouthalfofthepositiveself‐selectioninthepre‐migrationearningsofwomen.41Thekeylessonisclear:selectioninunobservablecharacteristicsplaysacrucialroleinde‐terminingtheskillcompositionofemigrants.Thedistinctroleofobservablesandunobservablesindeterminingtheselectioninthepre‐migrationearningsofmigrantsisevidentifwereturntotheRoymodelandequa‐tion(16),whichpresentstheconditionalexpectationE(logw0|v*>*).Equation(16)yieldsaninterestingandpotentiallyimportantinsight.Thenatureoftheselectioninpre‐migrationearnings,ofcourse,isgivenbythesumoftheselectioninobservablesandtheselectioninunobservables.Note,however,thateachoftheseselec‐tiontermshasaweightingcoefficientthatrepresentsthevarianceinearningsattribut‐abletoobservablecharacteristics( r02S2)ortounobservablecharacteristics(02 ).Asnotedearlier,observablecharacteristicsexplainarelativelysmallfractionofthevari‐anceinearnings.Putdifferently,equation(16)impliesthatitistheselectioninunob‐servablesthatismostlikelytodeterminethenatureoftheselectionthatcharacterizestheemigrantsample.40Toconductthecounterfactualanalysiswepoolthesampleofallmigrants(regardlessofwhethertheymovedtoNordiccountriesornot).41Thecomponentofself‐selectionthatisduetounobservablecharacteristicsplaysasomewhatsmallerroleforwomen.Onereasoncouldbethatwomenaremoreoftentiedmigrants,andthemigrationdeci‐sionmaybemainlybasedontheskillsofthespouse.Thevarianceinincomeisalsosmallerforwomen,whichalsomakestheselectionbothintermsofobservableandunobservablecharacteristicsweaker.

22

Totheextentthatbothtypesofselections(i.e.,inobservablesandunobservables)workinthesamedirection,thecounterfactualexercisedescribedinthissectionwillinevita‐blyunderestimatethetrueextentofpositiveselectioninpre‐migrationearnings.Con‐versely,thecounterfactualexercisewillalsoattenuatetheextentof“true”negativese‐lectionifthereisnegativeselectioninbothcomponentsofskills.Infact,Fernández‐HuertasMoraga(2011)presentsacorrespondinganalysisusingsurveydatafromMexi‐coandfindsthatcounterfactualestimatesgreatlyunderestimatetheextentofnegativeselectioninthepre‐migrationearningsofMexicanswhomovetotheUnitedStates.Putdifferently,thecounterfactualexercisemayleadtoqualitativelyrightconclusionsaboutthenatureoftheselection,butitmayalsogenerateasizablebias,greatlyunderestimat‐ingthetrueextentofeitherpositiveornegativeselection. 7.SelectionandimmigrationrestrictionsAsappliedintheimmigrationliterature,theRoymodelfocusessolelyontheeconomicfactorsthatmotivatelaborflowsacrossinternationalborders.Themodelingtypicallyignoresthefactthattheseflowsoccurwithinapolicyframeworkwheresomereceivingcountriesenactdetailedrestrictionsspecifyingwhichpotentialmigrantsareadmissibleandwhicharenot.WecanusetheadministrativedatafromDenmark,combinedwiththeuniquepoliticalcircumstancesthatguaranteefreemigrationwithinEurope,topartiallyaddressthequestionofwhetherimmigrationpolicyaffectsselectionallthatmuchintheend.Specif‐ically,wecansubdividethegroupofmigrantswhomovedoutsideNordiccountriesintotwogroups:thosewhomovedtoacountryintheEU15ortoSwitzerland,andthosewhomovedtoacountryoutsidetheEU15andSwitzerland.Movementoflaborwasun‐restrictedbetweenDenmarkandotherEU15countriesandSwitzerlandintheperiodunderstudy,butwasobviouslyrestrictedbyimmigrationregulationstodestinationsoutsidetheEU15,suchastheUnitedStates.ItturnsoutthatthesedifferentimmigrationpoliciespursuedbytheEU15andSwitzer‐landandtherestoftheworldbarelymatterindeterminingtheselectionofDanishemi‐grants.Figure11adepictsthecumulativedistributionfunctionsofthelogarithmofstandardizedannualincomeformenandfigure11bforwomen.Itisevidentthatthedistributionfunctionsofstandardizedearningsareverysimilarforthetwogroupsofmigrants.42Wealsoconductedtheanalysisusingthewageresiduals(notshown),andthedistributionsofresidualsarealsosimilarbetweenthetwogroups.Thereisanimportantsenseinwhichthesepolicyrestrictionscannotmattermuch.Suppose,forexample,thatareceivingcountryenactsapolicythatlimitsentryonlytohigh‐skillimmigrants.Ifthehigh‐skillimmigrantsfromasendingcountrydonotfinditoptimaltomove,thepolicycannotforcethosehigh‐skillworkerstomigrate.Allthepol‐icycandoisessentiallycutthemigrationflowfromthatparticularsendingcountrydowntozero.Thelow‐skillworkerswouldliketomovebutarenotadmitted,andthehighskillworkersareadmissiblebuttheydonotwanttomove.42Forwomen,aKolmogorov‐Smirnovtestisnotabletorejectthenull‐hypothesisthattheobservationsforthetwogroupsofmigrantscomefromthesameunderlyingdistribution.

23

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 migra-tion costs. Although it is plausible that migration costs are higher when moving to other con-tinents, 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‐migrants.Ourtheoreticalanalysisalsodistinguishesbetweenselec‐tioninobservableandselectioninunobservablecharacteristics.OurempiricalanalysisusestheDanishfullpopulationadministrativedatatoanalyzetheself‐selectionofemigrants,intermsofeducation,earningsandunobservableability,measuredbyresidualsfromMincerianearningsregressions.Theresultsareinlinewiththetheory;themigrantsarebettereducatedandbothpre‐emigrationearningsandwageregressionresidualsofmigrantsstochasticallydominatethoseofnon‐migrantsovermostofthesupportofthedistributions.Consider,forexample,thecaseoffull‐timeworkersaged25‐54.For98percentofmenand97percentofwomenwhomigrateout‐sideotherNordiccountriesthecumulativeearningsdistributionintheyearbeforeemi‐grationstochasticallydominatesthatofnon‐migrantswitha95%confidenceinterval.Thedifferencebetweenthecumulativedistributionsisnotstatisticallysignificantlydif‐ferentineitherdirectionfortheremaining2to3percent.Decomposingtheself‐selectionintotalearningsintoself‐selectioninobservablecharac‐teristicsandself‐selectioninunobservablecharacteristics(asmeasuredbyresidualsfromMincerianwageregressions),revealsthatunobservedabilitiesplaythedominantrole.Formen,about70percentofthepositiveself‐selectioninpre‐migrationearningsisattributabletounobservabledeterminantsofproductivity.Forwomen,thefractionisabout50percent.Thissuggeststhatrelyingoncounterfactualdistributions,basedonobservedcharacteristics,wouldstronglyunderestimatepositiveself‐selection.Thisre‐sultcomplementstheFernández‐HuertasMoraga(2011)findingthatcounterfactualestimatesalsogreatlyunderestimatetheextentofnegativeselectioninthepre‐migrationearningsofMexicanswhomovetotheUnitedStates.Inshort,theuseofcoun‐terfactualearningsdistributionsbasedonobservablecharacteristicsgreatlyunderstatethetrueextentofselectionintotalearnings.Strongpositiveself‐selectioninresidualsalsosuggeststhatunobservedabilitiesplayamuchbiggerroleinmigrationdecisionsthanmatchquality.

24

Ourfindingsalsohaveimplicationsforimmigrationpolicies.Receivingcountriescanonlybasetheiradmissionpoliciesonskillvariablesthatareobserved,whereasmuchoftheselectionofimmigrantsis“hidden”intheirunobservedcharacteristics.Itcanbeexpectedthatmigrantswillbeself‐selectedintermsofunobservedcharacteristicsevenwhenadmissionrestrictionsareapplied,andtheself‐selectionamongthosefulfillingadmissioncriteriacanbeexpectedtoreflectrelativeskillprices.Thisraisesaquestionabouttheeffectivenessofpointsystemsthatarenecessarilybasedonobservablechar‐acteristics.Theimportanceofrelativeskillpricesisalsosupportedbyourseparateanalysesofself‐selectionofDanesmigratingtothecountriesbelongingtocommonEu‐ropeanlabormarket(excludingotherNordiccountriesthathaveskillpricessimilartoDenmark)andnothavinganyimmigrationrestrictions,andtheself‐selectiontotherestoftheworld.Thereisvirtuallynodifferenceintheself‐selectiontothesedestinationareas.

25

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Figure1.Evolutionoftheemigrationrate

a.Men

b.Women

29

Figure2.Evolutionofthedifferencebetweenaveragelogstandardizedearningsofmigrantsandnon‐migrants

a.Men

b.Women

30

Figure3.Distributionfunctionsofstandardizedannualearningsformigrantsandnon‐migrants

a.Men

b.Women

31

Figure4.Densityfunctionsforstandardizedearningsformigrantsandnon‐migrants

a.Men

b.Women

32

Figure5.Differenceofthecumulativedistributionfunctionsforpre‐migrationearningsbetweenmigrantsmovingoutsideNordiccountriesandnon‐migrants

a.Men

b.Women

33

Figure6.Differenceofthecumulativedistributionfunctionsforpre‐migrationearningsofmigrantsgoingtootherNordiccountriesandnon‐migrants

a.Men

b.Women

34

Figure7.Distributionfunctionsofresidualsfromearningsregressionformi‐grantsandnon‐migrants

a.Men

b.Women

35

Figure8.Differenceofthecumulativedistributionfunctionsofresidualsformi‐grantsgoingoutsideotherNordiccountriesandnon‐migrants

a.Men

b.Women

36

Figure9.Differenceofthecumulativedistributionfunctionsofresidualsformi‐grantsgoingtootherNordiccountriesandnon‐migrants

a.Men

b.Women

37

Figure10.Counterfactualandactualdensitiesofstandardizedgrossearnings

a.Men

b.Women

38

Figure11.Distributionfunctionsofannualgrossearningsformigrantstothe

EU15andSwitzerlandandmigrantstootherdestinationsa.Men

b.Women

39

Table1.Summarystatistics

Non‐migrantmenMigrantmen

Non‐migrantwomen

Migrantwomen

Observations 6450665 7323 5163129 3436Age

Average 39.8 33.0 40.2 35Median 40.0 35.4 40.0 33.0

Annualearningsin2010euros

Average 52725 68151 40299 46412Median 46675 57350 37976 42393

Standardizedannualearnings

Average 1.0 1.3 1.0 1.2Median 0.9 1.2 0.95 1.1

Table2.Numbersofmigrants,bydestination

Men WomenSweden 1466 699TheUnitedStates 763 363TheUnitedKingdom 725 432Norway 576 273Germany 560 249Spain 255 147Switzerland 233 118France 222 156Other 2523 999

40

Table3.Educationlevelsofnon‐migrantsandmigrantsgoingtoNordiccountries

ortootherdestinations

Men Women

EducationNon‐mi‐

grantsNordiccoun‐tries

Otherdes‐tinations

Non‐mi‐

grantsNordiccoun‐tries

Otherdes‐tinations

Comprehensiveschool 21.4 19.8 8.3 21.5 15.7 8.9Highschool 3.2 7.8 8.6 3.1 6.9 8.9Vocationalschool 49.8 43.5 30.3 41.8 36.5 30.8Advancedvoca‐tional 5.6 5.7 6.6 4.9 5.1 7.8Bachelororequivalent 12.2 11.6 20.6 23.3 22.9 25.4Master’sorequivalent 7.3 10.6 23.9 5.1 12.3 17.6Doctoralorequivalent 0.5 1.0 1.7 0.2 0.7 0.7Notes:Thecategory“advancedvocational”includesallthetertiaryeducationprogramsbelowthelevelofaBachelor’sprogramorequivalent.Programsonthislevelmaybereferredtoforinstancewithsuchtermsascommunitycollegeeducation,advancedvocationaltrainingorassociatedegree.

41

Table4.Summaryoftestsofstochasticdominanceindistributionsofstandard‐izedpre‐migrationearnings

Distributionsbeingcompared:

Percentofsamplebelowlowerbound

Percentofsampleaboveupperbound

Migrants Non‐migrants

Migrants Non‐migrants

MigrantsoutsideNordiccountriesandnon‐migrants

Male 2.0 3.4 0.1 0.0Female 2.8 4.1 0.2 0.0

MigrantstoNordiccoun‐triesandnon‐migrants

Male 11.6 15.5 1.5 0.7Female 2.6 4.1 2.6 1.3

Notes:Lowerboundandupperboundrefertotherangeoverwhichthedifferenceofthecumulativedis‐tributionfunctionsissignificantata95percentconfidencelevel.

42

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)

Highschool 0.224*** (0.00) 0.190*** (0.00)Vocationalschool 0.092*** (0.00) 0.089*** (0.00)Advancedvoca‐

tional 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)

ConstantAgefixedeffects

12.131***Yes

(0.00)

11.931***Yes

(0.00)

NR‐squared

64707200.2597

51737060.3062

*p

43

Table6.SummaryoftestsofstochasticdominanceindistributionsofresidualsDistributionsbeingcom‐pared:

Percentofsamplebelowlowerbound

Percentofsampleaboveupperbound

Migrants Non‐migrants

Migrants Non‐migrants

MigrantsoutsideNordiccountriesandnon‐migrants

Male 9.9 15.2 0.1 0.0Female 19.6 24.7 0.4 0.0

MigrantstoNordiccoun‐triesandnon‐migrants

Male 13.4 15.2 2.0 0.9Female 19.5 24.7 3.4 1.8

Notes:Lowerboundandupperboundrefertotherangeoverwhichthedifferenceofthecumulativedis‐tributionfunctionsissignificantata95percentconfidencelevel.

44

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)Highschool 1.377*** (0.05) 1.158*** (0.08)

Vocationalschool 0.186*** (0.04) 0.159** (0.06)Advancedvocational 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