Scale, Selection, and Sorting in International Migration: Lectures 1 and 2 Gordon H. Hanson UC San Diego and NBER
Feb 08, 2016
Scale, Selection, and Sorting in International
Migration:Lectures 1 and 2
Gordon H. HansonUC San Diego and NBER
2
Questions confronting current migration research What explains the scale of international migration?
Flows are small (despite large wage differences)
Which individuals select themselves into migration? In most source countries, migrants are positively selected by skill
How do migrants sort themselves across destinations? There is positive sorting of migrants across destinations
3
Scale of international migration
Fraction of World population comprised of international migrants
2.0%
2.2%
2.4%
2.6%
2.8%
3.0%
1980 1985 1990 1995 2000 2005
UN Migration Report, 2005
4
Gains to international migration
Table 2: Estimates of the wage ratios of observably equivalent workers (male, urban, 35 years old) comparing late arrivers working in the US vs. their country of birth
Column I II III IV V VI
Specification Category Category Category Mincer
Schooling 9-12 5-8 13-16
Geom. Avg. 9-
12
Raw wage ratios, no controls
Annual dollar gain in column I
Average 4.36 4.86 4.15 4.06 7.27 $14,999
Median 3.93 3.87 3.05 3.44 6.2 $15,339
Clemens, Montenego and Pritchett (2008)
6
Positive selection of emigrants is nearly universal
Afghanistan
AlbaniaAlgeria
Angola
ArgentinaArmenia
Australia
Austria
AzerbaijanBahamas, TheBahrain
Bangladesh
Barbados
Belarus
Belgium
Benin
Bhutan
Bolivia
Bosnia and Herzegovina
Botswana
Brazil
Brunei
Bulgaria
Burkina Faso
Burundi
Cambodia
Cameroon
Canada
Cape Verde
Central African Republic
Chad ChileChina
Colombia
Comoros
Congo, Dem. Rep.Congo, Rep.
Costa Rica
Cote d'Ivoire
Croatia
Cuba CyprusCzech Republic
DenmarkDjibouti
Dominican RepublicEast TimorEcuador
Egypt
El Salvador
Equatorial Guinea
Eritrea Estonia
Ethiopia
Fiji
Finland
France
Gabon
Gambia, The
Georgia
GermanyGhana
GreeceGuatemala
Guinea
Guinea-Bissau
Guyana
Haiti
Honduras
Hong Kong
HungaryIceland
India
Indonesia
Iran
Iraq
Ireland
Israel
Italy
Jamaica
Japan
Jordan
KazakhstanKenya
Korea
Kuwait
Kyrgyzstan
Lao PDR
Latvia
Lebanon
Lesotho
LiberiaLibya
Lithuania Luxembourg
Macao, China
Macedonia
MadagascarMalawi
Malaysia
Mali
MaltaMauritania
Mauritius
Mexico
Moldova
Mongolia
Morocco
Mozambique
Myanmar
NamibiaNepal
NetherlandsNew Zealand
Nicaragua
Niger
Nigeria
Norway
Oman
Pakistan
PanamaPapua New Guinea
Paraguay Peru
Philippines
Poland
Portugal
Qatar
Romania
RussiaRwanda
Saudi Arabia
SenegalSerbia
Sierra Leone
Singapore
Slovakia
Slovenia
Solomon Islands
Somalia
South Africa
Spain
Sri Lanka
Sudan
Suriname
Swaziland
SwedenSwitzerlandSyrian Arab Republic
Taiwan
TajikistanTanzania
ThailandTogo
Trinidad and Tobago
Tunisia
Turkey
Turkmenistan
UK
US
Uganda
Ukraine
United Arab Emirates
Uruguay
UzbekistanVenezuela, RB
Vietnam
West Bank and Gaza
Zambia
Zimbabwe
0.2
.4.6
.8S
hare
of m
ore
educ
ated
am
ong
mig
rant
s
0 .2 .4 .6 .8Share of more educated among population
Selection of migrants, 2000
7
Positive sorting of emigrants across OECD destinations
Share of OECD immigrants by destination region and education, 2000
Education level Destination All Primary Secondary TertiaryNorth America 0.514 0.352 0.540 0.655
Europe 0.384 0.560 0.349 0.236
All OECD 0.355 0.292 0.353
8
Literature
Migrant scale & selection Borjas; Chiquiar & Hanson; McKenzie & Rapoport; Mayda
Rosenzweig; Grogger & Hanson; Belot & Hatton; Brücker & Defoort
Brain drain Adams; Ozden & Schiff; Beine, Docquier & Rapoport
Docquier, Lohest & Marfouk; Desai, McHale & Kapur
Sorting of migrants Borjas, Bronars & Trejo; Dahl; Grogger & Hanson
10
Model
Wage is fn. of education (primary (j=1), secondary (j=2), tertiary (j=3)), for person i from source s in destination h
Migration costs (fixed and skill-specific components)
Utility (with α > 0 and an iid extreme value RV)
j jhish hW exp( )
j jshish shC f g
jish
jish
jih
jish )CW(U
jish
11
Scale equation
Log odds of migrating from source s to destination h
Scale of migration should rise as rises (the level difference in destination-source wages)
jshsh
js
jhj
s
jsh gf)WW(
EEln
is the population share of education group j in s that migrates to h
is the population share of education group j in s that remains in s
jshE
jsE
js
jh WW
13
Selection equation
Difference scale equation between high skill (j=3) and low skill (j=1) groups to obtain selection equation:
On left-hand side Difference in log odds of emigrating between high-skill and low-skill
groups (positive value indicates positive selection)
On right-hand side: (1) difference in skill-related wage differences between destin. and
source countries, (2) difference in migration costs for high and low-skilled migrants, (3) common migration costs (fsh) disappear
3 13 3 1 1 3 1sh shh s h s sh sh3 1
s s
E Eln ln [(W W ) (W W )] (g g )
E E
14
Estimating equations
Scale equation (assume fsh and gjsh are function of xsh)
Selection equation (assume gjsh is function of xsh)
Coefficient on wages in scale and selection equations is the same
jj jj 3sh
s sh shh shjs
Eln (W W ) x I( j 3) x
E
'x)]WW()WW[(EEln
EEln j
shsh1s
3s
1h
3h1
s
3s
1sh
3sh
15
Data on migrant stocks
Emigration: Beine, Docquier, and Rapoport (2006) Counts of emigrants in 15 OECD destination countries from 192
source countries by education level for 2000
Population: Age 25 and older
Immigrants: those born outside country of current residence
Education groups: Primary (0-8 years of schooling), Secondary (9-12 years of schooling), Tertiary (13+ years of schooling)
16
Earnings data
Measuring skill related wage differences in 1990s Sources
Luxembourg Income Survey, WDI combined with WIDER
Measure difference in wages between high-skilled and low-skilled as difference in earnings at 80th and 20th percentiles
For WDI/WIDER, assume lny ~ N(μ,σ), such that E(y)=exp(μ+σ2/2) Given gini, G, variance in log income is:
and α quantile of y is (for Zα, the α quantile of N(0,1)):
1 G 122
2y exp( Z / 2)
17
Controls for migration costs
Language Anglophone destination, common language in source and destin.
Geography Log distance, contiguity, longitude difference
History Colonial relationships
Immigration policy Share of asylees and refugees in destination country immigration Visa waivers, Schengen signatories by source-destination
18
Legal status of US immigrants, 2005
Legal Permanent Resident Aliens
10.5 million (28%)
Unauthorized Migrants 11.1 million (30%)
Temporary Legal Residents 1.3 million (3%)
Refugee Arrivals 2.6 million (7%)
Naturalized Citizens 11.5 million (31%)
19
US legal immigrants by entry status
P E R S O N S O B T A IN IN G G R E E N C A R D S : 2002-2006
Im m ediate relatives of U.S . c itiz ens
44%
E m ploym ent-bas ed preferenc es
16%
R efugees and As ylees12%
D ivers ity5%
O ther4%
F am ily-s pons ored preferenc es
19%
22
Estimating equations
Scale equation (assume fsh and gjsh are function of xsh)
Selection equation (assume gjsh is function of xsh)
Coefficient on wages in scale and selection equations is the same
jj jj 3sh
s sh shh shjs
Eln (W W ) x I( j 3) x
E
'x)]WW()WW[(EEln
EEln j
shsh1s
3s
1h
3h1
s
3s
1sh
3sh
23
Results for scale and selection regressions (clustered standard errors in
parentheses, other regressors not shown)
js
jh WW
)WW()WW( 1s
3s
1h
3h
Scale Selection
0.018
(0.029)
0.072
(0.013)
Observations 2786 1393
R2 0.44 0.47
Clusters 15 15
In the selection regression, fixed migration costs are differenced away, while in the scale regression they are not
In theory, coefficient estimates should be identical
24
What happens if migration costs are proportional to wages, as in Borjas (1987)?
Let wages, costs be as before but assume log utility
Further, assume migration costs are proportional to wages, such that
)exp()CW(U jish
jish
jih
jish
j jshish hC W
25
Log utility and proportional migration costs Scale and selection equations are
jj jsh
s shhjs
Eln (ln W ln W )
E
3 33 3sh sh s1 1
sh s
E Eln ln ( )
E E
Scale
Selection
where λ>0 and δ3h = ln W3
h / W1h (Mincerian return to tertiary education)
27
Linear utility versus log utility (clustered standard errors in parentheses, other regressors not shown)
js
jh WW
)WW()WW( 1s
3s
1h
3h
js
jh WlnWln
)( 1s
3h
Linear utility Log utility
Wages Scale Selection Wages Scale Selection
0.018 -0.435
(0.029) (0.087)
0.072 -1.307
(0.013) (0.186)
Observations 2786 1393 Observations 2786 1393
R-squared 0.44 0.47 R-squared 0.29 0.17
Clusters 15 15 Clusters 15 15
In theory, all wage coefficients should be positive
28
Log utility model predicts negative selection
ARM
AUS
AUT
AZE
BEL
BFA
BGD
BGR
BHS
BLR
BOL BRA
BWA
CAF
CANCHE
CHL
CHN
CMRCOL
CRI
CZEDEU
DNK
DOM
ECUEGY
ESPEST
ETH
FINFRAGBR
GEO
GHA
GINGMB
GRC
GTMGUY
HKG
HND
HRV
HUN
IDN
IRLISR
ITA
JAM
JOR
JPN
KAZ
KGZ
KOR
LSO
LTU
LUXLVA
MDA
MDG
MEX
MKD
MLI
MUS
MYS
NGA NIC
NLDNOR
NPL
NZLPAK
PAN
PERPHL
POL
PRT
PRY
ROM
RUS
SEN
SGP
SLV
SVKSVNSWE
SWZ
THA
TJK
TKM
TTO
TUR
UGA
UKR USA
UZB
VEN
VNM
ZAF
ZMB
ZWE
.51
1.5
22.
53
log
inco
me
80th
- 2
0th
pctil
es
-4 -2 0 2 4log income 20th pctile
neg. selection of mig. to US
neg. selection of mig. to Ger.
29
While linear utility model predicts negative selection
ARM
AUS
AUT
AZE
BEL
BFABGD
BGR
BHS
BLRBOL
BRABWA
CAF
CAN
CHE
CHL
CHNCMR
COLCRI
CZE
DEU
DNK
DOMECUEGY
ESP
EST
ETH
FIN
FRAGBR
GEOGHAGINGMB
GRC
GTMGUY
HKG
HND
HRVHUN
IDN
IRLISR
ITA
JAMJOR
JPN
KAZ
KGZ
KOR
LSO
LTU
LUX
LVA
MDAMDG
MEX
MKD
MLI
MUSMYS
NGA
NIC
NLD
NOR
NPL
NZL
PAK
PANPERPHL
POL
PRT
PRYROM
RUS
SEN
SGP
SLVSVK
SVN
SWE
SWZTHA
TJK
TKM
TTOTUR
UGA
UKR
USA
UZB
VEN
VNM
ZAF
ZMB
ZWE
05
1015
2025
inco
me
80th
- 20
th p
ctile
s, 0
00s
US
D
0 5 10 15 20income 20th pctile, 000s USD
pos. selection of mig. to US
pos. selection of mig. to Ger.
30
Data strongly support positive selection of emigrants
Afghanistan
AlbaniaAlgeria
Angola
Argentina
Armenia
Australia
Austria
Azerbaijan
Bahamas, The
BahrainBangladesh
Barbados
BelarusBelgium
Benin
Bhutan
Bolivia
Bosnia and Herzegovina
BotswanaBrazil
Brunei
Bulgaria
Burkina Faso
Burundi
CambodiaCameroon
Canada
Cape Verde
Central African Republic
Chad
ChileChina
Colombia
ComorosCongo, Dem. Rep.
Congo, Rep.
Costa RicaCote d'Ivoire
CroatiaCuba Cyprus
Czech RepublicDenmark
Djibouti
Dominican RepublicEast Timor
Ecuador
Egypt
El Salvador
Equatorial Guinea
Eritrea
EstoniaEthiopia
Fiji
Finland
France
Gabon
Gambia, The
Georgia
Germany
Ghana
Greece
Guatemala
Guinea
Guinea-Bissau
GuyanaHaiti
HondurasHong Kong
HungaryIceland
India
Indonesia
IranIraq
Ireland
IsraelItaly
Jamaica
Japan
Jordan
Kazakhstan
Kenya
KoreaKuwait
Kyrgyzstan
Lao PDR
Latvia
Lebanon
Lesotho
Liberia
Libya
LithuaniaLuxembourg
Macao, China
Macedonia
Madagascar
Malawi
MalaysiaMali
Malta
Mauritania
Mauritius
Mexico
Moldova
Mongolia
Morocco
Mozambique
MyanmarNamibiaNepal
Netherlands
New ZealandNicaragua
Niger
NigeriaNorway
Oman
PakistanPanama
Papua New Guinea
ParaguayPeru
PhilippinesPolandPortugal
Qatar
Romania
Russia
Rwanda
Saudi Arabia
SenegalSerbia
Sierra Leone
Singapore SlovakiaSlovenia
Solomon Islands
Somalia
South Africa
Spain
Sri Lanka
Sudan
Suriname
Swaziland
Sweden
SwitzerlandSyrian Arab Republic
Taiwan
Tajikistan
Tanzania
Thailand
Togo
Trinidad and Tobago
Tunisia
Turkey
Turkmenistan
UK
US
Uganda
Ukraine
United Arab Emirates
Uruguay
Uzbekistan
Venezuela, RB
Vietnam
West Bank and Gaza
ZambiaZimbabwe
-8-6
-4-2
02
Log
odds
of e
mig
ratio
n fo
r ter
tiary
edu
cate
d
-8 -6 -4 -2 0 2Log odds of emigration for primary educated
31
Why negative selection fails: productivity differences International wage differences
Suppose in Nigeria Tertiary educated earn $5,000 a year, while primary educated earn
$1,000 (meaning return to extra year of education is 20%)
while in the US Tertiary educated earn $40,000 a year, while primary educated earn
$20,000 (meaning return to extra year of education is 8%)
Predicted pattern of migrant selection Proportional-cost model predicts negative selection: δN – δUS > 0
Fixed-cost model predicts positive selection: WTUS- WT
N > WPUS- WP
N
Because of large differences in US-Nigerian raw labor productivity, gain to migration is higher for tertiary educated
32
Positive selection versus negative selection Condition for migrants to be positively selected by skill
Ignoring migration costs, condition becomes
13 31sh sh
1 3 1 3s s s h
gW 1W (W W )
31sh
1 3s h
WW
Ratio of return to skill in source relative to destination (>1)
Ratio of labor productivity in destination relative to source (>1)
33
Estimating fixed migration costs
Scale equation with source-destination fixed effects is an alternative way to write the selection equation
Estimate equation with a full set of source-destination dummies
Divide dummy coefficients by –α to estimate fixed costs fsh
To capture skill specific migration costs, include controls for costs (xsh) interacted with dummy for skill group
jj jjsh
s sh j shh shjs
Eln (W W ) f x
E
34
Estimated fixed migration costs, selected countries (000s of 2000 USD, relative to US-Mexico migration costs)
Destination
Source Australia Canada France Germany UK US
China 80.3 56.8 90.8 88.6 87.7 55.6Guatemala 105.8 45.0 83.8 80.1 96.9 8.9Jamaica 76.8 -1.7 67.2 51.0 -9.3 -3.0Mexico 117.0 59.6 90.5 82.5 90.6 0.0Poland 45.6 26.4 27.9 5.2 42.9 29.8
Turkey 63.2 68.0 40.1 7.9 53.3 60.4
Vietnam 39.6 31.0 38.5 45.5 61.8 21.0
36
Sorting equation
Collect terms with source country subscripts in selection equation (ie, add source fixed effects), which yields:
Only requires data on wages in destination
Common coefficient on wages in scale, selection, sorting eqs.
s1sh
3sh
1h
3h1
sh
3sh )gg()WW(
EEln
)WW()E/Eln( 1s
3s
1s
3ss
37
Estimating equations
Scale equation (assume fsh and gjsh are function of xsh)
Selection equation (assume gjsh is function of xsh)
Sorting equation (assume gjsh is function of xsh)
jj jj 3sh
s sh shh shjs
Eln (W W ) x I( j 3) x
E
'x)]WW()WW[(EEln
EEln j
shsh1s
3s
1h
3h1
s
3s
1sh
3sh
shssh1h
3h1
sh
3sh x)WW(
EEln
38
Earnings and Taxes
Earnings data from household surveys in rich countries Luxembourg Income Survey
Adjusting for tax treatment across OECD destinations
Low-wage tax rate (67% of average production worker wage)
High-wage tax rate (167% of average production worker wage)
Tax rate includes income taxes net of benefits (as tallied by OECD) plus both sides of the payroll tax
Rates are averaged over 1996-2000
39
LIS data on wage levels and differences (000s USD)Tax treatment Pre Pre Pre Post Post Post
Percentile 20th 80th Diff. 20th 80th Diff.
Australia 17.31 34.96 17.66 14.04 23.73 9.69
Austria 16.62 30.89 14.27 10.15 16.11 5.96
Canada 16.48 39.78 23.30 11.93 25.63 13.69
Denmark 27.68 54.49 26.81 16.26 26.06 9.80
France 13.62 30.36 16.74 7.86 14.50 6.64
Germany 24.84 48.08 23.24 13.29 21.32 8.03
Ireland 16.23 31.36 15.13 12.23 17.49 5.26
Netherlands 27.99 47.38 19.38 16.88 26.44 9.56
Norway 23.08 49.99 26.92 15.16 27.84 12.68
Spain 12.14 26.05 13.91 8.05 15.37 7.33
Sweden 18.81 37.75 18.93 9.75 16.92 7.17
US 24.30 64.67 40.37 17.22 40.98 23.76
UK 22.44 48.60 26.16 16.50 31.97 15.47
40
Regression results (other regressors suppressed)Table 4: Regression results from linear-utility model Equation: Scale Selection Sorting Sorting Sorting Sorting Wage data source: WDI/
WIDER WDI/
WIDER WDI/
WIDER WDI/
WIDER LIS LIS
Variable (1) (2) (3) (4) (5) (6) j
sj
h WW 0.018
(0.029) )WW()WW( 1
s3s
1h
3h 0.072
(0.013) )WW( 1
h3h , pre-tax 0.060 0.026
(0.026) (0.013) )WW( 1
h3h , post-tax 0.103 0.048
(0.045) (0.022) Observations 2786 1393 1393 1393 1214 1214 R-squared 0.44 0.47 0.61 0.61 0.63 0.63 Clusters 15 15 15 15 13 13
similarity of coefficients pre vs. post tax
41
Additional regressorsEquation: Selection Sorting Sorting Wage data source: WDI WDI LIS Variable (2) (4) (6) Anglophone dest. 0.567 0.636 0.678 (0.183) (0.256) (0.241) Common language 1.268 0.352 0.332 (0.248) (0.139) (0.124) Contiguous -0.384 -1.007 -1.097 (0.373) (0.237) (0.240) Longitude diff. -0.009 0.004 0.005 (0.003) (0.002) (0.003) Log distance 0.676 -0.259 -0.279 (0.131) (0.097) (0.111) LT colonial rel. -0.711 -0.445 -0.550 (0.193) (0.161) (0.137) ST colonial rel. -0.395 -0.187 -0.224 (0.431) (0.257) (0.276) Visa waiver -0.299 0.364 0.471 (0.135) (0.172) (0.203) Schengen sig. 0.402 0.403 0.507 (0.166) (0.252) (0.304) Asylee share -2.512 -3.635 -4.007 (0.818) (0.709) (0.810) Observations 1393 1393 1214 R-squared 0.47 0.61 0.63
42
Decomposing the immigrant skill gap
Why do some destinations get more skilled migrants?
Redefine key variables to write sorting regression as:
By properties of OLS, we have
Differencing between US, destination h yields immigrant skill gap decomposition
sh 0 1 sh 2 h s shy x W
h 0 1 h 2 h hˆ ˆ ˆ ˆy x W
US h 1 US h 2 US h US hˆ ˆ ˆ ˆy y x x W W
43
Skill gaps among destination countriesMean Skill Levels among Immigrants, by Destination Country
DestinationMean log skill share
Mean share
tertiary educated
Mean share
primary educated
Immigrant skills gap
USA 2.01 0.58 0.11 0.00Ireland 1.39 0.53 0.14 0.62Canada 1.30 0.68 0.22 0.71Australia 1.29 0.56 0.18 0.72Norway 1.15 0.37 0.13 0.86New Zealand 0.71 0.48 0.25 1.30United Kingdom 0.40 0.41 0.28 1.61Sweden 0.28 0.36 0.27 1.73Spain -0.03 0.25 0.25 2.04France -0.10 0.40 0.44 2.11Germany -0.31 0.37 0.49 2.32Denmark -0.51 0.27 0.42 2.52Austria -0.54 0.25 0.39 2.55Netherland -0.54 0.26 0.44 2.55Finland -0.75 0.26 0.51 2.76
44
Explaining the immigrant skill gap
Destination Wage diff. Share asylee Share explained ResidualAustralia 0.84 -0.07 0.78 0.22Austria 0.36 0.39 0.98 0.02Canada 0.99 -0.13 0.76 0.24Denmark 0.28 0.36 0.87 0.13Finland 0.38 0.09 0.68 0.32France 0.44 0.22 0.96 0.04Germany 0.44 0.05 0.76 0.24Ireland 1.52 0.83 1.95 -0.95Netherland 0.32 0.55 1.10 -0.10New Zealand 0.64 -0.26 0.32 0.68Norway 0.53 0.40 1.64 -0.64Spain 0.50 -0.06 0.74 0.26Sweden 0.55 0.36 1.27 -0.27UK 0.35 0.22 0.58 0.42
Mean 0.58 0.21 0.96 0.04
Share of immigrant skill gap explained by variables in sorting regression (other regressors not shown)
45
Concluding remarks Dominant features of international migration are small scale,
positive selection and positive sorting A simple model of income maximization can go a long way in
accounting for these outcomes
Wage differences contribute to positive selection and why educated migrants choose Anglophone countries over continental Europe
Methodological issues Bilateral migration costs (broadly defined) appear to be large
Not controlling for unobserved bilateral migration costs yields inconsistent estimates of how wages affect migration
Models with log utility and proportional costs fail to explain scale or skill composition of emigration
Seemingly crude measures of absolute skill-based wage differences perform surprisingly well
47
Results for proportional migration costs (Borjas)Table 5: Regression results from log-utility model Equation: Scale Selection Sorting Sorting Sorting Sorting Wage data source: WDI/
WIDER WDI/
WIDER WDI/
WIDER WDI/
WIDER LIS LIS
Variable (1) (2) (3) (4) (5) (6) j
sjh WlnWln -0.435
(0.087) )( 1
s3h -1.307
(0.186) 3h , pre-tax 3.929 5.338
(0.767) (0.886) 3h , post-tax 3.342 4.146
(0.761) (1.297) Observations 2786 1393 1393 1393 1214 1214 R-squared 0.29 0.17 0.40 0.38 0.43 0.38 Clusters 15 15 15 15 13 13