immigration economics a review - david card...2016/04/06 · april, 2016 abstract we review...
TRANSCRIPT
Immigration Economics: A Review
David Card Giovanni Peri UC Berkeley UC Davis and NBER and NBER
April, 2016
Abstract
We review Immigration Economics (IE) by George J. Borjas, published in 2014 by Harvard
University Press. The book is written as a graduate level textbook, and summarizes and updates
many of Borjas' important contributions to the field over the past 30 years. A key message of
the book is that immigration poses significant costs to many members of the host‐country labor
market. Though the theoretical and econometric approaches presented in the book will be very
useful for students and specialists in the field, we argue that book presents a one‐sided view of
immigration, with little or no attention to the growing body of work that offers a more nuanced
picture of how immigrants fit into the host country market and affect native workers.
*We are extremely grateful to Gaetano Basso and Ingrid Hägele for their assistance.
1
Immigration Economics: A Review
GeorgeBorjasistheleadingeconomicscholarofimmigration.Overthepastthree
decadeshehasauthoredorco‐authoreddozensofpapersthathaveopenedupnewlinesof
investigationandhelpframethewaythateconomiststhinkaboutimmigration.Hehasalso
writtentwopreviousbooksonthetopic–Friends or Strangers? The Impact of Immigrants
on the U.S. Economyin1990,andHeaven’s Door: Immigration Policy and the American
Economyin1999–andcontributedimportantreviewstotheJournal of Economic
LiteratureandtheHandbook of Labor Economics.
Borjas’newbook,ImmigrationEconomics(IE),summarizesmuchofhispastwork,
updatingtheempiricalworkinsomeofhisseminalpapersandaddressingconcernsthat
havebeenraisedbyotherresearchers(includingus).IEiswrittenasagraduate‐level
textbook,carefullylayingoutaseriesofneoclassicalmodelsanddescribingempirical
methodsindetail.Ittakesatechnical/pedagogicalapproach,withcomprehensive
footnotesandappendicesandextendeddiscussionsofproblemslikeimputationerrorand
attenuationbias.Itveryrarelytalksaboutpolicyimplicationsandnevertakesapolitical
stand.Thisisabookforscholarsandadvancedstudentsofeconomics,ratherthanpolicy‐
makersorthegeneralpublic.Becauseofthisfocus,IEhasthepotentialtoserveasa
referenceforthoseinterestedinunderstandingthestateoftheartinthemodelingand
statisticalanalysisofmanyimmigration‐relatedissues.
Thecontentsofthebook'sninechapters,andtheirrelationshiptoBorjas'previous
work,aresummarizedinTable1.ApartfromChapter3,whichisentirelytheoretical,each
chapterisfocusedaroundoneortwokeysubstantivequestions,typicallystartingwitha
simplemodel,thenpresentingsomebasicdescriptiveevidence,andultimatelydiscussing
2
detailedtablesofeconometricestimates.1AsisclearfromTable1,IEfocusesalmost
exclusivelyonthelabormarket,specificallyonunderstandingthedeterminantsof
immigrants'earnings(Chapters1and2),oftheirchildren'searnings(Chapter9)andthe
impactsofimmigrantarrivalsonnativeearnings(Chapters3‐8).Eachchapterisbasedon
oneortwoofBorjas'earlierpapers.Readerswhoarefamiliarwiththeearlierpaperswill
findthatthestoryhasnotchanged,thoughthemodelpresentationinIEisstreamlined
(andsometimesgeneralized),theempiricalanalysisisoftenupdated,andthereissome
discussionoftheinterveningliterature.
ThemainachievementofIEisitscomprehensiveperspectiveonthelabormarket
aspectsofimmigration.Intheintroductionofthebook,Borjasdescribeshiscentraltheme
asthis:
"... immigration has consequences, and these consequences generally imply that some
people lose while others benefit...” (page4)
AsaglanceatthethirdcolumnofTable1suggests,thisthemeisparticularlyclearinthe
corechaptersonlabormarketimpacts,whereBorjas'theoreticalmodel(Chapter3),
descriptiveevidence(Chapter4),baselinesimulations(Chapter5),andcasestudiesofhigh
skilledimmigration(Chapter8)allunderscorethecostsofimmigrationforcompeting
nativeworkers.
GiventhecentralimportancethatBorjasattachestotheissueoflabormarket
impacts,inthisreviewweconcentrateonthesecorechapters.Themodelingand
interpretationoflabormarketimpactsisanareawhereeconomicsismostinneedof
1 The models in IE are not "structural" in the modern sense of providing a complete specification of the data generating process for the data under consideration. Rather, Borjas specifies a simple model -- e.g., an aggregate production function -- and then estimates equations that can be interpreted as stochastic approximations of the relations implied by the model.
3
consensus,wheresimplecorrelationscanhelpusunderstandthedata,andwherethe
lessonsfromtheanalysisofimmigrationhavethestrongestspilloverstootherfields
includingurbaneconomicsandproductivityanalysis.Thisisalsothemainareawhereour
ownresearchonimmigrationhasbeenfocused.
I. Descriptive Correlations
AsignificantpartofIEistakenupwithbasicdescriptivecorrelationsbetweenthe
presenceofimmigrantsandthelabormarketoutcomesofnatives.Chapter4isentirely
devotedtodocumentingthesecorrelations;theyalsofillasubstantialshareofChapter6.
ThesecorrelationsshapeBorjas'structuralmodelingchoicesandframehisdiscussionof
theliterature.Thereforeitisimportanttounderstandthespecificcorrelationsthathe
choosestofocuson.
a. What Are the Descriptive Correlations of Interest?
Althoughonemighthopethatanalystscouldagreeonthebasiccorrelationsthat
needtobeexplainedbyasuccessfulmodelofimmigrantimpacts,thisisnotthecase.
Rather,differencesinopinionoverthedescriptivecorrelationsofinteresthavebeen
centraltotheongoingdebateintheliteratureaboutthewageeffectsofimmigrationand
theimpactofimmigrantsonnativemobility.2Sincethisistheareawherewehavethe
mostreservationsaboutthematerialpresentedinIE,webeginbydescribinginsomedetail
ourdifferencesofopinionwithBorjas.
2 See Peri and Sparber (2011) for a discussion in the context of mobility responses to immigration. See also Card and DiNardo (2000).
4
Mostmodernempiricalstudiesofimmigrantimpactsbeginbyassumingthat
immigrantsandnativescanbeclassifiedintoarelativelysmallnumberofskillgroups,and
proceedtomodelimmigrationasashiftinthesupplyofdifferenttypesoflabor.Thisis
preciselythestartingpointofthetheoreticalanalysisinChapter3ofIE,whereBorjas
(equation3.8)definestherelativeshiftinthesupplyoflaborofskillgroupidueto
immigrationas:
i
ii L
dLm , (1)
whereLi representsthesizeoftheinitiallaborforceoftypei workersanddLiisthechange
inthistypeofworkersduetoimmigration.AsBorjasshowsinthisthoroughbutconcise
chapter,withconstantreturns‐to‐scaleintheaggregateproductionfunction,theimpactsof
immigrantinflowsareentirelyafunctionoftheserelativesupplyshifts.
Inlightofthistheoreticalframework,itseemsmostnatural(tous)todevelop
descriptiveevidencerelatingnativelabormarketoutcomestotheempiricalanaloguesof
thesesupplyshifts.3Specifically,ifweletMitrepresentthenumberofimmigrantworkers
inskillgroupi inagivenlabormarketinyeart,andletNitrepresentthecorresponding
numberofnativeworkers,theempiricalequivalentof(1),measuredindiscretetime‐
changesbetweencensusyearst‐10andt,is:
101010
10
it
it
itit
ititit L
M
MN
MMm (2)
3 Consistent with this reasoning, in Chapter 4 Borjas defines the "relevant wage elasticity" from his descriptive models as the derivative of the log wage of a given skill group with respect to the "immigration-induced percent increase in the labor supply of (the) group" (p. 85).
5
Astraightforwarddescriptiveanalysisbasedon(2)canbeconductedbyrelatingthe
changesinthemeasuredoutcomesofnativesofagivenskillgroupinagivenlabormarket
totheircorrespondingsupplyshocksduetoimmigration:
ititm
ititit mgroupskilltimeeffectsfixedyyy ),(10 (3)
where"fixed effects(time, skill group)"referstoaseriesofcontrolsforthetimeperiodand
skillgroupunderconsideration.
Incontrasttothisapproach,throughoutthedifferentchaptersofIEBorjasrelates
theoutcomesofnativeworkerstothefraction of immigrantsintheirskillgroupand
labormarketinyeart:
itit
itit MN
Mp
(4)
ThischoicewasusedinBorjas(2003)andseveralsubsequentpapers(Borjas2006,2009;
AydemirandBorjas,2007),andbyothereconomistswhoseworkiscitedinChapter4ofIE,
includingBonin(2011),Bratsbergetal.,(2012)andSteinhardt(2011).Ratherthan
relatingthechangesinlabormarketoutcomesofnativestothecorrespondingimmigrant‐
inducedsupplychanges,Borjasfitsdescriptivemodelsoftheform:
ititp
it pgroupskilltimemarketeffectsfixedy ),,( (5)
wherethesetoffixedeffectsisexpandedtoincludecontrolsforthelabormarketunder
consideration.
Withmarket‐specificfixedeffects,estimatesbasedonequation(5)are
approximatelyequivalenttoestimatingfirstdifferencedmodelsinwhichthekey
6
dependentvariableisthechangeinthefractionofimmigrantsinagivenskillgroupand
labormarket:4
ititp
it pgroupskilltimeeffectsfixedy ),( (6)
Superficially,thislooksalotlikeequation(3),andonemightbetemptedtothinkthatthe
twospecificationsareroughlyequivalent.Unfortunately,thatisnotthecase,andthe
differenceleadstodramaticallydifferentconclusionsaboutthedescriptivecorrelations
betweenimmigrantinflowsandnativelabormarketoutcomes,aswedocumentbelow.
Tounderstandthereasonsforthedifference,considerthefirst‐order
approximationtothechangeintheratiopit:
10
1010
10 )1(
it
itit
it
ititit L
Np
L
Mpp (7)
Tofirstorder,thechangeintheimmigrantshareisaweightedaverageoftheimmigrant‐
drivensupplyshock(10
it
it
L
M) andthechangeinthenumberofnative workersinskillgroup
i, dividedbythelaggedsizeofthegroup(10
it
it
L
N).5Sincenativelabormarketoutcomesare
ontheleft‐handsideofequation(6)itisextremelyimportantnottoconfoundthesenative
supplychangeswiththeimmigrantsupplyshocksthatarethefundamentalexogenous
variablesofinterest.
4 With only 2 periods, including market-specific fixed effects or first differencing within markets are exactly equivalent. With more periods, the first differences specification is somewhat more flexible, but would be expected to yield similar estimates of the key coefficient βp. 5 Equation (7) is only a first order approximation. Hence it is more accurate for small changes. For many US labor markets over 10 year intervals, like those analyzed in IE, large changes occurred, in which case a second order term (incorporating interactions of the changes in native and immigrant workers) is needed. Omission of this second order term will lead to additional biases.
7
Aparticularlytroublesomesourceofcorrelationcanariseifchangesinthenumber
ofnativeworkersinagivenskillgrouparepositivelycorrelatedwithchangesintheir
wages.Suchapositivecorrelationwillarisenaturallyiftherearerelativedemandshocks
inagivenmarketthatraisewagesanddrawinnewnativeworkers.Itispreciselybecause
ofconcernsoverthesetypesofshocks,whichcanleadtoapositive biasinthepartial
correlationbetweennativewagesandimmigrantinflows,thatresearchershaveattempted
todeviseinstrumentalvariablesfortherelativeinflowrateofimmigrantstodifferentlabor
markets(e.g.,AltonjiandCard,1991;Card,2001).Ironically,byusingpit asthemeasureof
immigrantmarketpressure,thispositivebiasleadstoanegative biasinthedescriptive
partialcorrelationspresentedinChapter4ofIE.Thisbiaswillbelarger,thelargerthe
initialshareofimmigrantsinthelabormarket, 10itp .
Evenmorealarmingisthespuriouscorrelationinducedbythisspecificationforthe
nativemobilitymodelspresentedinChapter6ofIE.Inthesemodels(reportedinTable
6.1)thedependent variableisthechangeinthenumberofnativesinagivenskillgroup,
orthecomponentofthechangeattributabletoout‐migrationorin‐migration.Essentially,
thesemodelsareequivalenttospecificationslike:
ititp
it
it peffectsfixedL
N
10
(8)
Inlightofequation(7),however,thedependentvariableismechanicallynegatively
correlatedwiththeindependentvariable.Asweshowinthenextsection,theresulting
estimatesbearlittlerelationshiptoestimatesfromthemoreappropriatespecificationwith
theimmigrant‐drivensupplyshockmitastheexplanatoryvariable.
8
ThesameissuespillsovertosomeofBorjas'structuralestimates.Specifically,in
Chapter6ofIE,hepresentsabehavioralmodeloflocationdecisionsbynativeworkers.
Thedependentvariableofthemainestimatingequation(equation6.5)isthechangeinthe
numberofnativeworkersinagivenskillgroup,standardizedbytheinitialsupplyoflabor
inthisskillgroup.Thekeyindependentvariableisthecumulatedchangeinthenumberof
immigrantsinthesameskillgroup,standardizedbytheinitialsupplyoflaborintheskill
group‐‐i.e.,mit.Ratherthanestimatingthisspecification,however,Borjasestimatesa
versionofequation(8).Inotherwords,despitethefactthathistheoreticalmodel
specificallyrelatesnativeinflowsandoutflowstomit,heactuallyusesΔpit .
b. Estimated Descriptive Correlations
Withthisbackground,weturntoasimplecomparisonofthedescriptive
correlationsthatariseusingeithertheimmigrantinflowmeasuremitortheimmigrantskill
sharepit.ThisexerciseisfacilitatedbythefactthatBorjashashelpfullypostedonline
manyofthedatasetsusedinthecorechaptersofIE,aswellastheprogramsthatareused
tocreatemanyofthetablesinIE6.
Table2showshowtheswitchindefiningthecorrelationofinterestaffectsthesign
andmagnitudeofthedescriptivecorrelationbetweenimmigrantinflowsandnativewages.
Row1ofthetablereproducesthespecificationsformaleworkersreportedinTables4.2
and4.5ofIEcorrespondingtoestimatesofequation(5)above.AsemphasizedbyBorjas,
therearetwosalientfeaturesofthesepartialcorrelations.First,theyareallnegativeand
statisticallysignificant,suggestingthatregardlessofthelevelofaggregationusedtodefine
6 We are also making available the codes and data (modified from IE) used to obtain our results. They can be accessed at the website of the Journal of Economic Literature.
9
labormarkets,agreaterimmigrantpresenceisassociatedwithlowernativewages.
Second,thecorrelationsaremorenegativeathigherlevelsofaggregation,leadingBorjasto
arguethat"...otherfactorsareperhapsdiffusingtheimpactofimmigrationacrosslocal
labormarketsorthattheremaybemeasurementerrorintheobservedimmigrantshare
forsmallergeographicunits."(p.86)
Row2ofTable2showswhathappenswhenthedependentandthekey
independentvariablesareexpressedinfirstdifferences,asinequation(6)above.The
magnitudeofthepartialcorrelationsisreducedbutthegeneralconclusionremainsthat
nativewagesarenegativelyrelatedtoimmigrantshares,withalargernegativecorrelation
athigherlevelsofaggregation.
Row3ofTable2,then,presentsthepartialcorrelationsfromourpreferred
specificationbasedonequation(3)above,whichrelateschangesinnativewagesto
immigrantinflows,expressedasafractionofthesizeoftheskillgroupspecificlaborforce
inthepreviousCensus.Insharpcontrasttotheestimatesofβp inrows1and2,the
estimatesofβm areallrelativelysmallinmagnitudeandexceptatthenationallevel,
positive.Moreover,theestimatesofβm areverysimilarasthelevelofaggregationchanges
frommetropolitanareatostatetoCensusdivision.Thepointestimateofβm atthenational
levelisnegative,butgiventherelativelylargesamplingerrorforthenationalestimateone
couldeasilyconcludethatthepartialcorrelationbetweenimmigrantinflowsandnative
wagesisclosetozeroandinvarianttothelevelofaggregation.
Partoftheexplanationforthedifferencebetweentheestimatesofthetwopartial
correlationsisrevealedinrow4,wherewerelatethechangeinnativewagestothe
componentofthechangeinΔpit thatisattributabletoinflowsoroutflowsofnativeworkers
10
(i.e.,totheterm–pit-10 ×ΔNit/Lit-10).Atthearealevel,changesinnativewagesarenegatively
correlatedwiththiscomponent,presumablybecausenativeworkerstendtomovetoareas
oftheUSwheretheirwagesaregrowing.Atthenationallevel,incontrast,thecorrelation
isimpreciselyestimatedbutinsignificantlydifferentfrom0.
ThecomparisonsacrosstherowsofTable2maybehelpfulfornon‐specialistswho
areawareofthedebatesintheimmigrationliteratureregardingtheimpactofimmigration
onnativewages,andpuzzledbythefactthatsomeanalysts‐‐includingBorjas‐‐believe
thereisastrongprimafaciecaseofanegativeimpact,whileothers‐‐includingus‐‐believe
thereisnot.Asshowninthetable,thestrengthandeventhesignofthebasicdescriptive
correlationsdependentirelyonwhatcorrelationsaredeemedtobeofinterest.Although
westronglybelievethattheelasticitiesofinterestaredefineddirectlybyequation(1)‐‐
leadingustofocusonthepartialcorrelationsinrow3ofTable2‐‐wehavelittlereasonto
expectanyconvergenceofopiniononthisissue.
c. Interpreting the "Descriptive Correlations"
WhiletheestimatesinChapter4ofIEarepresentedas"descriptivecorrelations",it
isimportanttokeepinmindthatthesearepartialregressioncoefficientsobtainedfrom
modelswitharichsetofcontrols.Consider,forexample,theestimatedcorrelationsinthe
fourthcolumnofTable2,whicharebasedonnationaldataformalewagesandimmigrant
inflows(orshares)in40differenteducation/experiencecells.Howshouldoneinterpret
theestimatedpartialcorrelationinrow3,whichis‐0.124?
11
AccordingtothemodellaidoutinChapter3,thechangeinwagesmeasuredat
periodtforworkersinagiveneducation(e)andexperience(x)cellisdeterminedbya
structuralequationoftheform:
extx
etex
text mmw
111log
(9)
whereδtisaperiodeffectthatincorporatestheadjustmentoftheaggregatecapital‐labor
ratioovertherelevantperiod,metistheproportionalincreaseinthenumberofworkersin
educationgroupe,mextistherelativeincreaseinthesupplyofworkersinthespecific
education/experiencegroupexovertherelevantperiod,andσe andσx arethepartial
elasticitiesofsubstitutionbetweeneducationgroupsandexperiencegroups,respectively.
Giventhatthemodelsincolumn4includeeducation‐group‐by‐timefixedeffects,which
willfullyabsorbmet,the‐0.124estimatecanthereforebeinterpretedasanestimateofthe
inverseelasticityofsubstitutionbetweenexperiencegroups.7Indeed,Borjas'structural
estimateofthisinverseelasticity,reportedinrow1ofTable5.1,is‐0.153.Similar
estimatesofthesameparameterarereportedinCardandLemieux(2001),Borjas(2003),
andOttavianoandPeri(2012).Thus,the"descriptivecorrelations"inTable2,andin
Chapter4ofIE,aremuchclosertomodel‐basedparameterestimatesthansimple
correlations.
Inanextendeddiscussiononpages127‐130ofIE,Borjasarguesthatthedescriptive
correlationspresentedinChapter4(andsummarizedinthetoprowofTable2)capturean
averageoftheown‐groupandcross‐groupelasticitiesofwageswithrespecttotheinflows
7 This is really a reduced form estimate from a system in which the first stage relates the overall number of workers in the education/experience group in year t to the associated immigrant inflow. In fact the first stage coefficient is not far from 1.
12
ofimmigrantsinvariousskillcategories.However,thisinterpretationisonlycorrectifthe
partialcorrelationisestimatedinaspecificationwithouteducation‐group‐by‐yeareffects.
Whentheseeffectsareincluded,astheyareinthemodelsusedinChapter4(andinallthe
specificationsreportedinTable2),theyabsorballormostoftherelevantcross‐
complementarityeffectsexertedbychangesinthenumberofworkersinothereducation
groups.Indeed,ifthenestedCESmodelunderlyingequation(9)iscorrect,thesefixed
effectsfullycontrolforallrelevantcross‐complementarities.
Nevertheless,itisinterestingtofollowBorjas’intuitionandaskwhathappenstothe
partialcorrelationbetweenwagesofworkersinspecificskillgroupsandthe
correspondingimmigration‐inducedrelativesupplyshockswhenthemodelisfitwithout
controllingforeducation‐timeeffects.Carryingoutthisexerciseusingallskillgroupsat
thenationallevelyieldsanestimatedpartialcorrelationof0.409(standarderror=0.092).
Theargumentpresentedonpages127‐130suggeststhatthiscanbeinterpretedasan
estimateoftheneteffectofimmigrant‐drivensupplyshocksoccurringthroughouttheskill
distributiononaveragewagesintheeconomy.Iftrue,then,theneteffectofimmigration
hasbeenpositive.Withouteducation‐group‐specifictimeeffectsintheestimatingmodel,
however,thepartialcorrelationbetweenwagesandimmigrantinflowsislikelytopickup
skill‐biasedtechnologicalchangesandotherfactorsthathappentobecorrelatedwith
immigrantsupplyshocks,sowearereluctanttoendorsethisinterpretation.
Tosummarize:the"descriptivecorrelations"estimatedfromanational‐levelmodel
witheducation‐group‐andexperience‐group‐specifictimeeffectsareactuallyinterpretable
asestimatesoftheinversepartialelasticityofsubstitutionbetweennarrowlydefinedskill
cells,andhavelittlebearingonthetotalwageeffectofimmigration.Ifoneconfines
13
attentiontonationalleveldata,asBorjasarguesisappropriate,thenamodelisneededto
simulatetheeffectsofimmigration.Analternativeapproachistofocusoncorrelationsata
lowerlevelofaggregation,likethecityorstate,andusethetrendsinothercitiesorstates
asadata‐drivencounterfactual.Assumingthatcorrelationsfocusonchangesinthenet
suppliesofdifferenttypesoflaborassociatedwithimmigrantinflows,webelievethat
thereisusefulinformationinthearea‐basedcorrelations.Specifically,assumingthatthere
isalocalproductionfunctiongeneratingthelocaldemandforlabor,thetheoretical
frameworkdevelopedinChapter3ofIEcanbeusedtounderstandhowimmigrant‐
inducedsupplyshocksaffectrelativewagesofnativesatthelocallevel.
d. Descriptive Correlations With Native Migration Flows
Asecondsetof"descriptivecorrelations"arepresentedinChapter6ofIE,relating
theinter‐areamigrationflowsofnativesinspecificskillgroupstothecorresponding
immigrantskillshares.Asnotedaboveinthediscussionofequation(8),webelievethese
correlationsareparticularlysusceptibletobiasesarisingfromthefactthatthemeasureof
immigrantpresenceusedbyBorjasismechanicallynegativelycorrelatedwithnetnative
migration.
Table3presentsaseriesofestimatesthatillustratetheissues,followingthesame
formatasTable2.Row1reproducesthespecificationsreportedinTable6.1ofIE.Using
theimmigrantsharepit asameasureofimmigrationpressure,itappearsthatnative
locationdecisionsareextremelysensitivetothepresenceofimmigrants:the‐0.664
estimatefornetnativemigrationacrossmetroareasincolumn1,forexample,suggests
thattheadditionof100newimmigrantsinagivenskillgroupinacityleadstoanet
14
reductionof66inthenumberofnativesinthatskillgroup,arisingfromacombinationof
reducednativein‐migration(alossof39natives)andincreasednativeout‐migration(a
lossof28natives).Theseestimatesimplythatnativemigrationflowsundofullytwo
thirdsofthesupplyeffectcausedbyimmigrantinflowstospecificcities.Theeffecton
statesissmaller,butstilleconomicallylargeandhighlysignificant.
Inrow2ofTable3wepresentspecificationsinwhichthekeyindependentvariable
isexpressedinfirstdifferences.AsinTable2,themagnitudeofthepartialcorrelationsis
reduced,buttheestimatesstillshowlargenegativeeffectsofimmigrantinflowsonnet
nativemigration.
Row3ofTable3presentsestimatesfromourpreferredspecificationwhichdirectly
relatesnativemigrationflowstoimmigrantinflows.Atthemetropolitanarealevelthe
estimatedresponsesarereducedinmagnitudeby85%,andsuggestthatthemigration
responsesofnativesonlyundoabout10%oftheeffectofimmigrantinflows.Atthestate
levelthenetnativemigrationeffectisevensmaller,andstatisticallyinsignificant.
Inrow4werelatethenativemobilityflowstothecomponentofthechangeinΔpit
thatisattributabletoinflowsoroutflowsofnativeworkers(i.e.,totheterm–pit-10 ×ΔNit/Lit-
10).Asexpected,wefindanegativecorrelationwithnativein‐migrationandapositive
correlationwithnativeoutmigration,bothparticularlystrongatthemetropolitanarea
level,thatexplainasignificantshareofthemeasuredmigrationresponsesinthe
specificationsinrows1and2.
Overall,weconcludethatBorjas'useofimmigrantskillsharesasthemeasureof
immigrantimpactleadstoaseriousexaggerationoftheresponsivenessofnatives'location
decisionstothepresenceofimmigrants.Atthecitylevel,ourapproach–whichisdirectly
15
consistentwiththestructuralmodeloutlinedbyBorjasinChapter6–suggeststhatnative
migrationflowsoffsetonlyabout10%oftheeffectofimmigrantinflows.Atthestatelevel,
ourapproachsuggestsanevensmalleroffset.
Again,acomparisonacrossthedifferentrowsofTable3maybeusefultonon‐
specialists,whoareawareofthesharpdifferenceofopinionbetweensomeanalysts–like
Borjas–whobelievethatimmigrationinflowsleadtolargeoffsettingmovementsof
natives,andotheranalysts–likeus–whobelievetheseoffsettingmobilityflowsare
small.The"evidence"dependsentirelyonhowonechoosestomodelimmigrationinflows.
Inourview,thetheoreticallyappropriateandempiricallydefensibleapproachsuggests
thattheoffsettingmobilityflowsofnativesaresmall.Basedonpastexperience,however,
wedonotexpectanyconvergenceofopiniononthenatureoftheappropriateevidence.8
II. Model-Based (Structural) Analysis of the Impacts of Immigration
NowweturntoadiscussionofwhatisarguablythecentralchapterinIE.InChapter
5,Borjaspresentsasetofsimulationresultsthatquantifytheeffectsofimmigrantarrivals
overtheperiodfrom1990to2010onthewagesofvariousnativegroups.Thesetup
followsthetemplateofBorjas'influential2003paperintheQuarterly Journal of Economics.
Aggregateoutputisproducedbya3‐levelnestedfunctionwithconstantreturnstoscale:
);,( tttt LKfQ (10a)
);,...,( 21 tJtttt LLLgL (10b)
);,...,( 21 teKtteteet LLLhL (10c)
8 The argument that native mobility rates should be related to immigrant arrival flows (rather than the contemporaneous fraction of immigrants) is made in Wright, Ellis and Reibel (1997), Card and DiNardo (2000), Card (2001), and Peri and Sparber (2011), but is not acknowledged by Borjas.
16
whereKtrepresentscapitalinyeart,Ltrepresentsaggregatelaborinput; L1t, L2t, ... LJt,are
theaggregateamountsoflaborineachofJeducationclasses;Lext istheamountoflaborin
education/experienceclassex inyeart(fore=1,..Jandx=1...K),λtrepresentsa2‐
dimensionalvectoroftechnologyparameters;θt isaJ‐dimensionalvectorofeducation‐
groupspecifictechnologyparameters,andαt isaJK‐dimensionalvectorofexperience‐
groupspecificparameters.ForhisbaselinesimulationsBorjasassumesfisCobb‐Douglas
(withlabor'sshareequaltos),gisaCESfunctionwithelasticityofsubstitutionparameter
σe,andhisaCESfunctionwithelasticityofsubstitutionparameterσx.
Inthismodelanincreaseinlaborsupply(regardlessofskillmix)hasnolongrun
effectonaveragewagesintheeconomyifthecostofcapitalisheldconstant,whileinthe
shortrunwithfixedcapital,theelasticityofaveragewageswithrespecttoaggregatelabor
supplyis–(1–s),whichBorjassetsto‐0.3.Theskill‐groupspecificimpactsofdifferent
laborinflowsdependonthetwoparametersσeandσx.Givenvaluesofthesetwo
elasticitiesandinformationontheskillsharedistributionsofimmigrantarrivalsitis
possibletosimulatetheeffectsonskill‐groupspecificaveragewages.
Table4summarizesthesimulationresults.ThetoprowshowsBorjas'baselinelong
runsimulatedimpactsofimmigrantinflowsoverthe1990‐2010periodforeachof5
educationgroupsandallnatives.(Thecorrespondingsimulatedimpactsassumingno
adjustmentofcapital–whichwebelievetobeunrealisticfora20yearperiod–areall
shifteddownby3.2%,reflectingthe11%increaseinoveralllaborsupplyBorjasattributes
toimmigrationovertheperiod).Thebaselinesimulationassumesthatσe=5andσx=6.7.
Thesimulatedgainsandlossesfordifferenteducationgroupsaresmallinmagnitude,with
17
thelargestnegativeeffect(‐3.1%)forhighschooldropouts,reflectingtherelativelylarge
inflowofpoorlyeducatedimmigrantsoverthepastseveraldecades.
Oneconcernaboutthesebaselinesimulationsisthatthepresumedstructureof
substitutionbetweendifferenteducationgroupsisincorrect.AsnotedinCard(2005,
2009)andOttavianoandPeri(2012),anddiscussedinsomedetailinChapter5ofIE,akey
issueisthedegreeofsubstitutabilitybetweendropoutsandhighschoolgraduates.Ifthese
twogroupsareperfectsubstitutes‐‐aswehavearguedinourearlierwork‐‐thenthe
impactofthelargeinflowsofimmigrantswithlessthanahighschooleducationisdiffused
acrossamuchlargersegmentofthenativeworkforce.Asshowninrow2ofTable4,with
thisassumptionthesimulatedimpactsofimmigrationforthebottomtwoeducationgroups
arenowverysmall,whiletheeffectsfortheothereducationgroupsareunchanged.Borjas
presentsavarietyofnewevidenceontheissueandultimatelyconcludesthat
"... the available evidence on the elasticity of substitution between high school dropouts
and high school graduates is not robust to assumptions made about the time path of
unobserved shocks to relative demand.... The sensitivity of the results suggests that the
nested CES framework does not provide a particularly useful approach for analyzing the
substitutability of labor between these two skill groups" (page124).
Asimilarissueariseswithregardtothedegreeofsubstitutabilitybetween
immigrantsandnativeswiththesameeducationandexperience.Manyanalystshave
notedthatimmigrantsandnativeswiththesameobservedcharacteristicsaretreated
differentlybythelabormarket.9Lewis(2013b)arguesthatanimportantsourceof
9 See e.g., Dustmann, Frattini and Preston (2015). In fact, the difference in age profiles of earnings for immigrants and natives has been a major concern in the immigration literature, and is taken up in Chapter 2 of IE. Friedberg (2000) showed that immigrants typically receive no return to their pre-migration experience.
18
imperfectsubstitutabilityislanguageability.10PeriandSparber(2009)documentthat
immigrantstendtospecializeinoccupationswithlowerintensityoflanguageand
communicationskills.Amongyoungerandlesseducatedimmigrantsanotherfactorislegal
status:manyoftheseimmigrantsareundocumented,andarepushedintocertaintypesof
jobswhereimmigrationlawscanbeeasilyevaded.
OttavianoandPeri(2012)andManacorda,ManningandWadsworth(2012)
introducedtheideaofusinga4‐levelnestedproductionfunctiontoincorporateimperfect
substitutionbetweenimmigrantsandnatives,andshowedthatevenasmalldegreeof
imperfectsubstitutioncanaltertheconclusionsaboutthewageimpactsofimmigration.As
showninrow3ofTable4,assumingthattheelasticityofsubstitutionbetweenimmigrants
andnatives(σNM)is20raisestheaveragewageimpactonnativestoasmallpositive
number,andreducesthesizeofthesimulatedlossesfornativedropouts.Assumingboth
perfectsubstitutionbetweendropoutsandhighschoolgraduates,andimperfect
substitutionbetweenimmigrantsandnativesyieldsthesimulationresultsinrow4of
Table4.Inthissimulationallnativegroupsexceptthosewithadvanceddegreesarefound
tobenefitfromrecentimmigrantinflows.
Aswiththeelasticityofsubstitutionbetweendropoutsandhighschoolgraduates,
Borjaspresentsavarietyofevidenceandultimatelyconcludesthatthelikelymagnitudeof
1/σNMissosmallasto...”notbeanimportantfactorinanassessmentofthelabormarket
impactofimmigrationintheUnitedStates.”(p.118).
Wearelessconvincedbyhisanalysis,asitincludesalargesetofnon‐modelbased
fixedeffectsthatdrasticallyreducetheidentifyingvariation.Infact,estimatesofallthe 10 Ferrar, Green and Riddell (2006) show that immigrants in Canada have lower literacy skills than otherwise similar natives, and argue that this accounts for some of the immigrant wage penalty.
19
criticalparametersintheaggregateproductionfunction(notjust1/σNM)arehighly
sensitivetoassumptionsaboutunobservedrelativeproductivitytrends.AsBorjas
documentsinTable5.1,estimatesof1/σevarysubstantially,dependingonhowonemodels
thetrendsintherelativefactorproductivityterms(λt)intheupperlevelnest.Estimatesof
1/σxaresimilarlysensitive.Forexample,addingexperience‐group‐by‐yeartrendsto
equation5.5(thebasicestimatingmodelfor1/σx)alongthelinesoftherobustnesschecks
proposedabovefor1/σNM,causestheestimateof1/σxtofallfromthebaselinevalueof
0.15(withastandarderrorof0.06)to0.07(withastandarderrorof0.05).Overallwe
believethatthebulkoftheevidencepointstowardasmall,butnon‐negligibledegreeof
imperfectcompetitionbetweennativeandimmigrantworkers.
IntheendBorjasconcludesthat...“thenestedCESstructuralapproachseemsfar
toosensitivetotheimpositionofunverifiable(butnecessary)assumptionstobeofmuch
useingivingarobustandconvincinganswer”abouttheimpactsofimmigrantinflows(p.
127).WhileweagreethattheprecisenumberscomingfromtheCESapproachare
somewhatvariable,wetakeadifferentlessonfromtheresultsinTable4.Tous,itseems
clearthatthesimulatedeffectsofimmigrantarrivalsonnativewagesarequitesmall,
underavarietyofspecificassumptionsusedinthesimulation.
III. Welfare and Productivity Effects of Immigration
Chapter7ofIEmovesfromtheanalysisofnativewageoutcomestotheoverall
economicbenefitsofimmigration.Themodel,however,isdecidedly"oldschool"(Barry
andSolingo,1966),andsimplycalculatesthesurplustrianglesassociatedwithanoutward
shiftinsupplyofvariousskillgroups,assumingverticalsupplycurves.Underthe
20
assumptionsofconstantreturnstoscale,fixedtechnology,andelasticcapitalsupplies,the
calculatedsurplusisnecessarilysmall,particularlyifimmigrantsarenottoodifferentfrom
natives.AsBorjasconcludes..."itismathematicallyimpossibletomanipulatethecanonical
modelofthecompetitivelabormarketsoastoyieldalargenetgainfromimmigrationto
theUnitedStates"(p.151).
Thisiscertainlytrue.Therealquestioniswhetheronewantstotakeseriouslyany
oftheideasinmoderngrowththeory,whichallowforeffectsofhumancapitalexternalities
(e.g.,Romer,1990;Moretti,2004a,2004b),skillvariety(Alesinaetal.,2013),task
specialization(GrossmanandRossi‐Hansberg,2011),marketintegration(Rivera‐Batizand
Romer,1992),andpotentialgainsfromrisingnumbersofscientistsandengineers(Jones,
2002).Thesemodelsallowforpotentialincreasingreturnstoscaleand/orendogenous
technologicalchange‐‐factorsthatarguablydominatethesecondordersurplus
calculationspresentedinChapter7,andhavebeenlinkedinrecentworktoimmigration
flows(e.g.,KerrandLincoln2010,Lewis2012a,Peri2012,Perietal.(2014),Ottavianoet
al.2013).
AttheendofChapter7Borjasdiscussesthewelfarecostsofimmigrationwhen
therearedecreasingreturnstoscale,buildingonamodelbyHamiltonandWhalley
(1984).Obviously,anymodelwithdecreasingreturnstoscalewillleadtonegative
spilloversfrompopulationgrowth,asMalthusfamouslynoted.Inlightoflastfewdecades
ofresearchoneconomicgrowth,however,itseemstousthattheMalthusianintuitionis
wrong,andthattheonlyreasononewouldentertainsuchamodelisforpurelyrhetorical
purposes.
21
FinallyChapter8ofIEreviewssomeinterestingcasestudiesofhighskilled
immigration,focusingonimpactsonproductivityininnovation(measuredbypatents)and
academia(measuredbythenumbersofpaperspublishedbymathematicians).Inthecase
ofpatents,foreignskilledworkersseemtobehighlyproductive(HuntandGauthier
Loiselle2010),withnoevidenceofanegativespilloverontheoutputofnatives(Kerrand
Lincoln2010;summarizedinTable8.2ofIE).Inthecaseofacademicmathematicians,
evidencefromBorjasandDoran(2012),summarizedonpages183‐190ofIE,suggests
immigrantarrivalsharmtheproductivityofnatives.Theyfindthatinflowsof
mathematiciansfollowingthecollapseoftheSovietUnionledtoareductioninthe
publicationsofUSmathematicianswhohadspecializedinareasinwhichtheRussian
mathematicianswereparticularlystrong,andadisplacementofUSacademicstolower‐
qualityacademicjobsandnon‐academicpositions.Overall,itappearsthattheproduction
ofscholarlypapersinmathematicsismuchclosertoa"zerosum"gamethanthe
productionofpatents,andthatmathematicianshavearelativelyhardtimeadjustingthe
focusoftheirresearchinmidcareer.Itishardtoarguewitheitherconclusion.
Whethertheimpactsofimmigrationonacademicmathematicsareusefulfor
thinkingaboutthegeneraleconomiceffectsofhighskilledimmigrationislessclear.The
numberofpositionsintopacademicinstitutionsandthenumberofpapersintopacademic
journalsarerelativelyrigid,sothesearenaturalplacestolookforstrongdisplacement
effects.Wedon'tthinka"fixedslots"paradigmislikelytobeasapplicableforthebroader
labormarket.Indeed,Peri,ShihandSparber(2014)findastrongpositivecorrelation
betweeninflowsofforeignSTEM(science,technology,engineeringandmath)workersand
thewagesofcollege‐educatednativesacrossUScities.
22
IV. Conclusions
GeorgeBoras'newbook,Immigration Economics,providesaconciseoverviewof
manyoftheimportantissuessurroundingimmigrationandlabormarkets.Thebookis
writtenasagraduateleveltextbook,andsummarizesandupdatesmanyofBorjas'
importantcontributionstothefieldoverthepast30years.Aparticularstrengthofthe
bookisthecloseattentiontointegratingsimpletheoreticalmodelswithsophisticated
econometricanalysis.Thechaptersonmodelinglabordemandandusingthemodelsto
evaluatetheeffectsofimmigrationonnativeoutcomesareclearandcomprehensive,and
willsurelyfindtheirwaytograduatereadinglists.
IncontrasttoBorjas'mostrecent(1999)bookHeaven’s Door: Immigration Policy
and the American Economy,Immigration Economicsismorenarrowlyfocusedoneconomic
analysis,withalmostnomentionofpolicyissues.Nevertheless,inalmosteverychapter
thebookmaintainsauniformlydismalviewaboutimmigration.Thisisparticularlytruein
thecorechaptersonimmigrantlabormarketimpacts,whichfocusondescriptive
correlations(Chapters4and6),simulations(Chapter5),andcasestudies(Chapter8)that
emphasizethecostsofimmigrationtonativeworkers.Aswehaveemphasized,Borjas'
choiceofwhichdescriptivecorrelationtopresent,whichparametervaluestouseinthe
simulations,andwhichcasestudiestoemphasizeallendupreinforcingthisdismalview.
Thus,althoughthebookisnon‐political,ithasaclearmessage:immigrationiscostlyto
manymembersofthehostcountry.
AfterreadingImmigration Economics,onebeginstowonderwhycountriesever
decidetohaveanyimmigrants,andwhymanycountriescontinuetoallowrelativelylarge
23
inflowsofimmigrants.Areimmigrationpoliciesmanipulatedbyanelitewhobenefitfrom
thesepoliciesattheexpenseofothers?Oristhebalanceofbenefitsversuscosts‐‐evenfor
nativeworkerswhoaremostdirectlyincompetitionwithimmigrants‐‐morepositivethan
onemightbeledtobelievefromreadingBorjas'latestbook?We,andmanyother
economists,comedownonthelatterside.Immigration Economics presentshalfthestory
abouttheeconomicsofimmigration.Theotherhalfofthestory,althoughaprominent
featureofmuchoftheworkdonebyothereconomistsduringthepastthreedecades,has
noplaceinthisbook.
24
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Table 1: Summary of Chapter Content: Immigration Economics.
Chapter and Related Articles Main Questions Answers
b. How large are implicit costs of migration? b. Very large.
a. At arrival to the U.S. how much less do immigrant men earn than natives? Is the gap bigger for recent cohorts?
a. New immigrants earn less than natives. Gap is bigger for recent cohorts, mainly because of rising returns to education.
b. In their first 10 years in the U.S. how much do average earnings of immigrant men rise? Is the rate of increase smaller for recent cohorts?
b. Immigrant earnings rise relatively slowly. The rate of increase is particularly low for more recent arrival cohorts.
a. What is the partial correlation between wages and the share of immigrants in a group?
a. Uniformly negative, but varying in magnitude.
b. How does this correlation vary with the level of aggregation: cities / states /divisions or national level?
b. More negative at higher levels of aggregation.
a. What are the simulated effects of immigrant arrivals from 1990 to 2010 on the wages of different education groups from a baseline model?
a. Largest effect on high school dropouts –6% assuming no capital accumulation, –3% assuming fixed return to capital.
b. Should the baseline model account for imperfect substitutability between immigrants and natives with similar skills?
b. Possibly
c. Should the baseline model allow for perfect substitutability between high school graduates and dropouts?
c. Possibly
a. Do men who immigrate to the U.S. have above- or below- average potential earnings in the U.S. relative to others from the same source country?
a. US immigrants are typically negatively selected -- more likely to come from the bottom than the top of the distribution.
Chapter 1: The Selection of Immigrants Borjas (1987, 2008)
Chapter 2: Economic Assimilation Borjas (1985, 1995a)
Chapter 5: The Wage Effects of Immigration: Structural Estimates Borjas (2003)
Note: table continues.
Chapter 3: Immigration and the Wage Structure: Theory Borjas (2003)
How does immigration affect wages in the short run (with fixed capital) and in the long run (with a fixed return to capital)?
In the short run, immigration lowers wages. In the long run, it may or may not affect average wages, but it lowers the relative wage of groups with higher inflow rates.
Chapter 4: The Wage Effects of Immigration: Descriptive Evidence Borjas (2003)
Table 1: Summary of Chapter Content: Immigration Economic, continued
Chapter and Related Articles Main Questions Answers
a. Do natives in a given age/education group move away when there is a higher share if immigrants in their group in the local market?
a. Yes. Native mobility rates across cities and states are relatively sensitive to immigrant shares.
b. Do firm investments vary with the local immigration rate of low skilled workers?
b. Yes. Firm investment choices are relatively sensitive to the shares of low-skilled immigrants in their local market.
Chapter 7: The Economic Benefits of Immigration Borjas (1995b)
What are the net effects of immigration on US income? Small positive gain (assuming fixed return to capital).
Chapter 8: High Skilled Immigration Borjas (2009); Borjas and Dorn (2012)
Are there positive spillover effects from high skilled immigration that offset the basic negative impacts?
High skilled immigrants lower wages and opportunities for high skilled natives. No evidence of positive spillovers.
Chapter 8: The Second Generation Borjas (1992, 1993)
a. Do US-born male children of immigrants earn more than 3rd and higher generation natives? Is the gap smaller for recent cohorts?
a. US born children of immigrants earn more than other natives, but the gap is smaller today than in the past.
b. How strong is the intergenerational correlation between immigrant fathers and their US-born sons?
b. The intergenerational correlation is high (at least 0.5). This is due in part to ethnic capital, which limits intergenerational progress for many subgroups.
Chapter 6: Labor Market Adjustments to Immigration Borjas, Freeman, Katz (1996); Borjas (2006)
Source: authors' summary of Immigration Economics.
Metropolitan Area State Census Division National
1. Borjas' specification: immigrant -0.058 -0.186 -0.237 -0.529 share in levels (p it ) (0.018) (0.029) (0.048) (0.102) (Table 4.2, row 1 and Table 4.5, col. 1)
2. Change in immigrant share (∆ p it ) -0.029 -0.058 -0.106 -0.237(0.011) (0.024) (0.043) (0.118)
3. Immigrant inflow (m it ) 0.036 0.049 0.022 -0.124(0.010) (0.019) (0.032) (0.132)
4. Contribution of native inflows to -0.102 -0.123 -0.135 0.078 change in immigrant share (0.024) (0.033) (0.047) (0.114) (–p it-10 ∆N it /L it-10 )
Coefficients in Row 1 are obtained by regressing the logarithm of native wages on the immigrant share of labor in the skill group controlling for skill-time, area-time and area-skill fixed effects. Coefficients in row 2 are obtained by regressing the change in the logarithm of native wages on the change of the immigrant share in the skill group and including skill-time and area-time fixed effects. Coefficients in row 3 are obtained by regressing the change in the logarithm of native wages on the inflow of immigrants in the skill group over the past decade (m it ) including skill-time and area-time fixed effects. Coefficients in row 4 are obtained regressing the change in the logarithm of native wages on the contribution of native inflows to the change in immigrants share and including skill-time and area-time fixed effects.
Table 2: Longitudinal Spatial Correlations Between Immigration and Native Male Wages: Reproduction and Extension of Tables 4.2 and 4.5 in Immigration Economics
Definition of Regional Labor Market
Specification and Explanatory Variable
Note: See notes to IE, Tables 4.2 and 4.5. Standard errors, clustered by skill group/region level (columns 1-3) and by skill group (column 4), in parentheses. Metro area models use data on male workers in 5 education groups and 8 experience groups from 1980, 1990, 2000 Census and 2009-2011 American Community Survey (42,770 observations). State, division, and national models add data from 1960 and 1970 Census (12,215 observations at the state level, 2,160 at the division level, 240 at the national level).
Net Native Migration
Native In-migration
Native Outmigration
Net Native Migration
Native In-migration
Native Outmigration
1. Borjas' specification: immigrant -0.664 -0.385 0.278 -0.323 -0.159 0.164 share in levels (p it ) (0.223) (0.198) (0.070) (0.099) (0.082) (0.049) (Table 6.1)2. Change in immigrant share (∆ p it ) -0.442 -0.248 0.193 -0.179 -0.019 0.160
(0.073) (0.065) (0.025) (0.062) (0.057) (0.039)
3. Immigrant inflow (m it ) -0.100 -0.048 0.051 -0.071 0.012 0.084(0.035) (0.030) (0.012) (0.043) (0.037) (0.021)
4. Contribution of native inflows to -0.210 -0.084 0.125 -0.071 -0.027 0.044 change in immigrant share (0.060) (0.047) (0.026) (0.090) (0.089) (0.043) (–p it-10 ∆N it /L it-10 )
Note: See notes to IE, Table 6.1. Standard errors, clustered by skill group/region level, in parentheses. Metro area models use data on male workers in 5 education groups and 8 experience groups from 1990 and 2000 Censuses and 2009-2011 American Community Survey and have 21,239 observations. State models add data from 1970 and 1980 Censuses and have 8,157 observations. Coefficients in row 1 are obtained by regressing the dependent variable listed at the top of the column on the immigrant share of labor in the skill group controlling for skill-time, area-time and area-skill fixed effects. Coefficients in row 2 are obtained by regressing the dependent variable listed at the top of the column on the change in the immigrant share in the skill group and including skill-time and area-time fixed effects. Coefficients in row 3 are obtained by regressing the dependent variable listed at the top of the column on the inflow of immigrants in the skill group over the past decade (mit), including skill-time and area-time fixed effects. Coefficients in row 4 are obtained by regressing the dependent variable listed at the top of the column on the contribution of native inflows to the change in immigrant share, including skill-time and area-time fixed effects.
Table 3: Longitudinal Spatial Correlations Between Immigration and Native Migration Flows (Based on IE, Table 6.1)
Native Flows Between Metropolitan Areas Native Flows Between States
Specification and Explanatory Variable
Table 4: Simulated Wage Impacts of U.S. Immigration 1990-2010 on Native Subgroups, Allowing Capital Adjustment
High School High School Some Four Years Post AllDropouts Graduates College College Graduate Natives
1. Baseline -3.1 0.4 0.9 -0.1 -0.9 0.0 Table 5.4, row 4
2. Assume Perfect Substitition between Dropouts -0.2 -0.2 0.9 -0.1 -0.9 0.0 and HS Graduates (σHS=0) Table 5.6, row 8
3. Assume Imperfect Substitition between -1.7 0.9 1.2 0.5 -0.1 0.6 Immigrants and Natives (σNM=20) Table 5.4, row 1
4. Assume Perfect Substitition between Dropouts 1.1 0.2 1.2 0.5 -0.1 0.5 and HS Graduates and Imperfect Substitution between Natives and Immigrants (σHS=0, σNM=20) Table 5.6, row 4
Notes: all estimated impacts taken from estimates reported in IE, chapter 5.
Education Subgroup: