Immigration, Human Capital Formation
and Endogenous Economic Growth ©
Isaac Ehrlich
Jinyoung Kim
SUNY at Buffalo
Korea University
Memorial Conference Honoring Gary Becker
Chicago, October 16, 2015
Motivation
• Over the last 4 decades, the US & 4 major receiving countries have
experienced a surge in immig. rel’ to 7 earlier decades. (Fig. A)
• Surprise: The surge has been characterized by a continuous rise in
the skill composition of immigrants with 13+ yrs of education (In Fig. B:
blue = world bank & purple = IAB institute data on migrant populations in 4 receiving
countries; Green = Barro-Lee data on total populations in the same countries.)
• While natives in destination countries have also exhibited a similar
increase, the immigrants’ rel’ to natives’ skill ratio has also been rising.
• In most of these countries, the skill composition of immig. has been
higher than that of natives. (World Bank 75-2000; IAB 80-2010 data)
Fig. A: US Immigration, 1850-2010
(Singer & Hall, 2015 Brookings)
Weighted averages of the skill composition of the migrant population
vs. total domestic population in major destination countries
Population age 25+ with 13+ years of education
Evidence from the US
• In the US, these trends have been less pronounced because of the
bimodal distribution of immigrants by education.
• But even average years of schooling have been on rise since 1940
(J. Smith 2014). Moreover, US Census data over last few decades
show the skill level of migrants to be catching up and about to
exceed that of US natives. This trend has been sharpest for Asians
immigrants, followed by Europeans and “others”, all of whom
overtook the US in college and higher degrees.
• What’s the story behind these migration trends? And how do they
link with the observed pattern of economic growth and skill
composition in the economies of the major receiving and sending
countries over the last 4 decades?
Educational Attainment of the Foreign-Born Population (in %) 25 Years and Over
vs. Total Native Population by year of Entry: 2012
Educational Attainment of the Foreign-Born Population (in %) 25 Years
and Over by World Region of Birth: 2012
Outline
II. The approach
III. The model
a.
b.
c.
d.
The benchmark model and the migration decision
Growth equilibrium, comp. dynamics, and transitional paths
The extended model and diversity effects
Assessing the “immigration surplus”
IV.Testing propositions 2 and 3 against int’l data
IV.Concluding remarks
II. The approach
• That’s a tough question.
•
The bulk of the large migration literature to date has explored the relation between migration & the labor market,
over time periods too short for firms to adjust their capital assets or not long enough to allow for continuous
accumulation of all relevant assets that can secure long-term growth.
•
There is also a nascent literature that links migration and growth using endogenous growth models based on
either new-product innovation or human capital formation as engines of growth. But all models, take migration to
be an exogenous variable.
• In the Becker-Lucas tradition, we set out to explore the relation
between the observed trends in the volume of and skill composition
of migrants and related trends in both sending and receiving
economies using – what else but - a human-capital-based
endogenous growth model.
II. The approach
• The distinct property of our approach is that it treats migration flows
(waves) and their skill composition as endogenous variables that
depend on indiv. choices & market forces, not strictly on exogenous
shocks like gov. quotas or building big walls.
• So this has prompted us to develop a two-country GE model
involving both a destination (D) and a source (S) country, and two
and recognize two distinct groups of workers and corresponding
families within these countries – skilled and unskilled - where
parents make fertility, HC investment, and work decisions, which
include the choice of staying in S or migrating to D, and different skill
groups are linked through knowledge spillover effects.
•
The model is an extension of an earlier paper by us EK (JHC 2007) in which we modeled
the role of HC as both an engine of growth and a determinant of income distribution over
the development process. An earlier attempt to implement such an extension is Idu (2012)
III. The Model
• Such approach allows for a richer treatment of the migration
problem in a GE context that accounts for the interactions between
both countries.
• But it also creates a complicated model in which the global GE
involves 6 groups of interacting agents from 2 distinct skill groups in
2 countries comprised of both natives and immigrants. Needless to
say, to solve this system we need to make a # of rigid assumption.
• We develop two version of our model: “a benchmark model” which
ignores any interactions between natives & immigrants in knowledge
production. In the other, we allow for such interaction which is
ascribed to “diversity effects”.
The Benchmark Model Setup*
•
Basic assumptions: We use a 2-country, 2-skill-group which includes:
–
–
–
–
–
–
Six types of agents: skilled (i=1) or unskilled (i=2) who are natives to
destination (D) or source (S) countries, or are migrants from S to D
Migrants are freely mobile internationally, and skilled (unskilled) agents
from S are perfect substitutes to skilled (unskilled) workers in D
Each agent lives over two periods: childhood and adulthood (when
consumption, investment, work and migration decisions are made)
Each country has two sectors: “high-tech” (1) and “low-tech” (2), each
of which produces perfectly substitutable goods (thus avoiding any
trade in goods) and employs just one of the 2 skill types of workers
Human capital is the only reproducible asset - we abstract from a
separate role of physical capital. But HC is producing both private and
external social benefits through knowledge spillover effects, which
makes HC an engine of country-specific and global growth as well
The labor markets are competitive.
Human Capital Formation
Human capital production function is country- and skill-specific:
Hkit+1 = Aki hkit Hkit (Δki )γ ;
k = d,s,m; i=1,2
d= destination; s= source; m= migrants in D; 1= skilled; 2= unskilled; t= time period (=generation)
Parents determine the fraction of production capacity hki to be invested in their offspring
 PF reflects endowed elements of diversity that are skill and country-of-birth specific. It
distinguishes skill from acquired knowledge (Ht+1). “skill” Aki = captures a bundle of
personal abilities and creativity, but is also country-specific (k), capturing the technol.
of knowledge transmission & freedom of thought necessary to create it in k = d,s
 The specification allows for 3 types of knowledge spillover effects between
generations, within countries, and across countries:
a. Intergenerational: transmission of knowledge from parents to children
b. Within-country: unskilled learning from skilled
c. Cross-country: skilled (unskilled) in S learn from skilled (unskilled) in D.
Social Externalities in HC formation
•
The HC production functions are given by
(1a) Hd1t+1 = Ad1hd1t Hd1t
(1b) Hm1t+1 = Ad1hm1t Hs1t
(1c) Hd2t+1 = Ad2hd2t Hd2t (Δdd2t)γ1
(1d) Hm2t+1 = Ad2hm2t Hs2t (Δdd2t)γ1
(1e) Hs1t+1 = As1hs1t Hs1t (Δds1t)γ2
(1f ) Hs2t+1 = As2hs2t Hs2t (Δds2t)γ2(Δss2t)γ1
for skilled natives in D
for skilled migrants in D
for unskilled natives in D
for unskilled migrant in D
for skilled natives in S
for unskilled natives in S
 PFs are hierarchical: Δd1 =1; γ < 1; Adi > Asi and Ak1 > Ak2 (k = d, s; i = 1, 2), but
model allows for assimilation of same-skill groups once they arrive in D (sharing the
same Adi). Migrants’ kids fully assimilate w/ native kids & realize the same HC, Hd.
(NAS report)
Spillover effects
The spillover factors
Δdd2t ≡ (Nd1tHd1t+Ms1tHs1t)/(Nd2tHd2t+Ms2tHs2t) ,
Δss2t ≡ (Ns1tHs1t−Ms1tHs1t)/(Ns2tHs2t −Ms2tHs2t),
Δds1t ≡ (Nd1tHd1t+Ms1tHs1t)/(Ns1tHs1t−Ms1tHs1t),
Δds2t ≡ (Nd2tHd2t+Ms2tHs2t)/(Ns2tHs2t−Ms2tHs2t).
(Δdd2t , Δss2t): within-country spillovers; (Δds1t, Δds2t): cross-country spillovers
 The logic of these specifications is that the learning benefits to the groups
with lesser knowledge are higher the higher is disparity in knowledge
attainments relative to the transmitting group and the larger is the relative
size of the latter (the teacher/student ratio)
Consumption Goods
•
Goods Production : exhibits CRTS w.r.t. to effective labor, but is also s.t.
external effects. We assume that the labor market is competitive w/ full
employment and goods produced in the “high-tech” and “low-tech” sectors
are perfect substitutes in consumption, which avoids dealing with trade.
• For skill group i in country D, the PF is:
(3) Qdit = Γdi (Ndit Ldit Hdit + Msit Lmit Hsit) Ψdi where
–

–
Ldit, Lmit = total working hours of natives and immigrants in skill group i
Ψdi ≡ (Ndit + Msit)-φ [(NditHdit + MsitHsit)/(Ndit + Msit)]μ-φ
Externality Ψdi is diminishing in quantity of labor force, Ndit+Msit, but
increasing in quality of the average worker’s HCdi .
• A similar PF applies to country S
• The wage rate per unit of HC is thus
(5) ωdit = Γdi(Ndit+Msit)-φ[(NditHdit+MsitHsit)/(Ndit+Msit)]μ-φ,
(6) ωsit = Γsi(Nsit−Msit)-φ[(NsitHsit−MsitHsit)/(Nsit−Msit)]μ-φ.
Preferences
The Utility function of agents at period (generation) t in our OLG setting is
(7) U(Ckit, Wkit) = [1/(1−σ)][(Ckit)1-σ−1] + δ [1/(1−σ)][(Wkit)1-σ−1]
where
(8) Ckit = Lkit ωkit Hkit = (1 − vk nkit − θki hkit nkit) ωkit Hkit = own consumption,
and
(9) Wkit ≡ B (nkit)β (̃ωkit+1 Hkit+1)α (α =1, β >1) = parental altruism
•For immigrants in D,
(10) U(Cmit, Wmit) = [1/(1−σ)][(Cmit)1-σ−1] + δ [1/(1−σ)][(Wmit)1-σ−1],
(11) Cmit = Lmit ωdit Hsit = (1 − vs nmit − θsi hmit nmit − τi) ωdit Hsit,
(12) Wmit ≡ B (nmit)β (ωdit+1 Hmit+1)α, with α =1 and β >1.
•Endogenous population evolves as follows:
Ndit+1 = ndit Ndit + nmit Msit, and Nsit+1 = nsit (Nsit − Msit).
Model Solutions
•
Members of each of the six population groups decides on fertility and
human capital investment in children.
• Optimality conditions w.r.t fertility and HC investment are:
(for nkit ) 0 = (Ckit)-σ [− vk − θki hkit] ωkit Hkit + δ(Wkit)-σ B β (nkit)β-1 ωkit+1 Hkit+1
(for hkit) 0 = (Ckit)-σ [− θki nkit] ωkit Hkit + δ (Wkit)-σ B (nkit)β ωkit+1 (Hkit+1/ hkit)
(for nmit) 0 = (Cmit)-σ [− vs − θsi hmit] ωdit Hsit + δ (Wmit)-σ B β (nmit)β-1 ωdit+1 Hmit+1
(for hmit) 0 = (Cmit)-σ [− θsi nmit] ωdit Hsit + δ (Wmit)-σ B (nmit)β ωdit+1 (Hmit+1/ hmit).
• Explicit solutions for investment
(15) hkit = vk/ [θki(β−1)], (i = 1, 2; k = d, s)
(15a) hmit = vs/ [θsi(β−1)], (i = 1, 2)
• For fertility, we get an explicit solution only if the utility fn. has a log form
(16) nkit = δ (β−1)/ [vk (1+ δβ)], (i = 1, 2; k = d, s)
(16a) nmit = δ (β−1)[1 − τi] / [vs (1+ δβ)].
Optimal Migration
•
•
Agents with skill level i emigrate from country S to country D as long as the
lifetime utility of residing in D is higher than that in S.
The flow of migrants (Msit) is determined at the point where the utility level of
the marginal migrant in country D and S are equalized:
(17) (Cmit)1-σ + δ(Wmit)1-σ = (Csit)1-σ + δ(Wsit)1-σ
•
(i = 1, 2)
In a log utility case, the “arbitrage condition” in eq (17) then becomes
(18)Γsi (Nsit − Msit)-φ(Hsit)μ-φ = (1− τi) Γdi(Ndit + Msit)-φ[(NditHdit + MsitHsit)/(Ndit + Msit)]μ-φ
or
(18a) ωsit − (1− τi) ωdit = 0,
–
The equilibrium levels of migration flows of both skill levels are reached when
the wage in the source country equals the corresponding wage rate in
destination net of the migration entry “tax” rate.
Propositions
 Proposition 1. There is a positive and unique solution for the flows
of all skill-specific workers choosing to migrate from their source
country to the destination country at any given time period provided
the following condition is met:
(Ndit /Nsit)φ < (1− τi) (Γdi/Γsi) (Hdit /Hsit)μ-φ.
–
The condition implies that the stock of HC capital & gains in production in
D rel’ to S should be sufficiently high, or the rel’ pop. level in D sufficiently
low, to attract the same-skill migrants, given the opp/costs to the migrant.
 Proposition 2. A rise in the human capital stocks of specific skill
groups in the destination country (Hdit) will increase the flow of
migrants from the source country (Msi).
• The proof follows directly from the arbitrage condition for equilib. migration.
 Both propositions are tested and found to be consistent with a
comprehensive WB panel on migration involving 5 receiving countries from
190 sending countries
Growth Equilibrium Steady State
Existence of a globally balanced & stable growth equilibrium requires:
➢A threshold level of parental investments in offspring’s HC:
dHkit+1/dHkit = Ad1(hd1t)* = vd (Ad1/θd1)/(β−1) = (1+g*) >1 , which implies :
– a. hd1 > (1//Ad1); and b. (Ad1/θd1)/(Ad2/θd2) = (As1/θs1)/(As2/θs2); i.e.,if
– Relative efficiency parameters in knowledge and good production are
the same in D and S.
➢equal relative (not absolute) endowed productivity levels in goods
production in D and S:
– Γd1 / Γd2 = Γs1 / Γs2
➢Higher shadow marginal costs of fertility in D relative to S;
− vd > vs
➢Subject to these conditions we derive a stable steady state global equilibrium
with the following properties:
Growth Equilibrium Steady State
Properties:
• Population and human capital attainments rise by the same proportion within
and across countries.
o Fertility, and population growth rates of both skill groups are constant and equal across
both natives and immigrants in each country. Thus:
Ms1t/Nd1t = Ms2t/Nd2t; and Ms1t/Ms2t = Nd1t/Nd2t
o Human capital growth rates are equalized across skill groups and countries, converging on
the growth rate of the skilled group in the destination country.
o Thus relative human capital, wage rates and hence full income per-capita equalize within
and across country and for each skill group across countries:
Hd1 /Hs1 = Hd2 /Hs2 ; wd1 /ws1 = wd2 /ws2
• But the steady state fertility rates remain higher in the source, relative to the
destination country.
•
A constant and persisting fraction of each skill group in S migrates to D (see
the simulation results in Table 1).
Comparative Dynamics
▪
Our recursive dynamic system is too complex to be solved analytically. We thus
resort to numerical simulations. Table 1 provides a solution to the benchmark
model. We proceed w/ comp. dynamics raising all “pull” factors 20% as follows
▪
▪
▪
▪
▪
▪
An equi-proportional rise in the knowledge production technology in D and S, affecting
only the skilled in D and S (represents a skill-biased technological shock [SBTS]
A similar, but “neutral” rise in knowledge production affecting all skill groups
A decline in the immigration “tax” for both skill groups
An increase in he cost of fertility just in D or in both D and S
Analysis can explain immigration waves of a “push” nature, such as the Syrian.
Focusing on the impact of the SBTS. Fig. 1 shows that it
▪
▪
▪
▪
▪
Raises the global growth rate;
Raises the skill composition of migration and the pop. shares of migrants relative to
natives in D
But lowers the pop. share of the skill ratio in S
Raises the ave. wage and HC level (thus full income) of skilled migrants in D rel’ to S
It thus raises income disparity and the Gini coefficient both within skill groups in D (not
shown in Table 1) and across countries .
Comparative Dynamics
Effects of key structural parameter shifts in the GE
steady state
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
nd1
= nd2
ns1
= ns2
nm1
= nm2
hd1
hd2
hs1
= hm1
hs2
=hm2
Gth
rate
(i) Benchmark
2.0906
3.2207
2.5157
0.2
0.2
0.1333
0.1333
(ii) Ad1 =12, As1 =9.6
2.1198
3.2642
2.5508
0.2
0.2
0.1333
Ad2 =6, As2 =4.8
2.1198
3.2642
2.5508
0.2
0.2
(iv) τ1 = τ2 = 0.16
2.0907
3.2208
2.6436
0.2
(v) vd =.072
1.7462
3.2659
2.5287
(vi) vd=.072, vs=.048
1.7470
2.6912
2.1023
(9)
(10)
(11)
(12)
(13)
(14)
Ms1/
Ms1/
Nd1
Ns1
= Ms2/ = Ms2/
Nd2
Ns2
Δdd2
= Δss2
Δds1
= Δds2
Hd1/
Hs1
= Hd2/
Hs2
ωd1/
ωs1
= ωd2/
ωs2
2
0.1803
0.2101
5.6569
4.8140
3.0820
1.5728
0.1333
2.4
0.1807
0.2094
8.9234
4.8140
3.1025
1.5785
0.1333
0.1333
2.4
0.1807
0.2094
5.6569
4.8140
3.1025
1.5785
0.2
0.1333
0.1333
2
0.1664
0.2143
5.6569
4.8140
2.7713
1.4874
0.24
0.24
0.1333
0.1333
2.4
0.2282
0.2886
5.6569
7.5938
4.0429
1.7247
0.24
0.24
0.16
0.16
2.4
0.1804
0.2100
5.6569
4.8140
3.0861
1.5739
(iii) Ad1=12, As1 =9.6
▪Parameters in the benchmark case: Ad1 =10, As1 =8, Ad2 =5, As2 = 4, τ1 = 0.2, τ2 = 0.2, vd = 0.06, vs = 0.04, θd1 = 1, θd2 = 1, θs1 = 1, θs21 = 1,
σ=
0.9, δ = 0.7, β = 1.3, γ1 = 0.4, γ2 =0.4, φ = 0.1, μ = 0.6, B = 1, Γd1 = 1, Γs1 = 1, Γd2 = 1, Γs2 = 1.
▪Comparative dynamics in the steady state are simulated by increasing Ad1, As1, Ad2, As2, vd, vs , or decreasing τ1, τ2, by 20 percent, holding other
parameters constant at the benchmark values.
Skill-biased Technological Shock (SBTS)
• We also focus on SBTS also because of the its implications about
the shape of the transitional dynamic path linking the initial with the
new steady state of balanced growth. We can predict that
• By raising both Ad1 and As1 simultaneously and leaving Ad2 and As2
intact the reulting dynamic paths assume the following shapres:
• Proposition 3. A SBTS will gradually increase the skill composition
of migrants along a transitional dynamic path leading to the
balanced growth steady state as well as the steady state ratio of
skilled migrants to skilled natives in destination.
• Proposition 4: A synchronized SBTS will gradually increase the
human capital level of skilled relative to unskilled groups in each
country over the transitional dynamic path leading to the balanced
growth steady state as well as the in the steady state itself.
Skill-biased Shock and Transitional Paths
Isolating the contribution of the Shock-induced
Migration to the total effect of the SBTS in D
❑ We decompose the total effect of the SBTS into (1) the part that
would be attributable to it alone and the part contributed by the rise
in the skill composition of migrants the SBTS has induced.
❑ To do so, we simulate the dynamic paths under two scenarios:
a. When the skill composition of migrant flows [Ms1/(Ms1+Ms2)] and relative
pop. share (Ms1/Nd1) are restricted to be frozen at their initial steady state
equilibrium values.
b. When immigration is unrestricted, which is our benchmark model.
❑ As the charts show: the unrestricted skill composition of migration
contributes the following changes in destination:
a.
b.
c.
d.
A higher growth rate,
a higher average human capital, wage rates, and full income per worker
a higher rate of fertility (but lower population ratio)
A. lower rise in income inequality
Impact of Induced Migration
Extended Model with Diversity Effects
• We extend our model by allowing for interaction between natives
and immigrants in the production of knowledge.
• Rationale: Diversity in background and experience may enhance
complementarities, especially across workers of the same skill level
who acquired their knowledge and creativity in different countries of
birth* (the classical example: the Manhattan project).
• Diversity: A*ki (di) = Aki (1 + di) (k = d, s; i = 1, 2)
where di = Msi/(Ndi+Msi).**
* Supported by new evidence in Alesina et al. (2015)
** Our simulations estimate d = 13.3%; Latest CIS data estimate d=13.1%
Extended Model with Diversity Effects
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
nd1
= nd2
ns1
= ns2
nm1
= nm2
hd1
hd2
hs1
= hm1
hs2
=hm2
Growt
h
rate
Ms1/
Nd1
= Ms2/
Nd2
Ms1/
Ns1
= Ms2/
Ns2
Δdd2
= Δss2
Δds1
= Δds2
Hd1/
Hs1
= Hd2/
Hs2
ωd1/
ωs1
= ωd2/
ωs2
2.1109
3.2510
2.5401
0.2
0.2
0.1333
0.1333
2.2664
0.1537
0.2306
5.6569
6.5806
3.2198
1.5768
2.1401
3.2945
2.5752
0.2
0.2
0.1333
0.1333
2.7203
0.1540
0.2300
8.9234
6.5846
3.2413
1.5825
Ad2 =6, As2 =4.8
2.1401
3.2945
2.5752
0.2
0.2
0.1333
0.1333
2.7203
0.1540
0.2300
5.6569
6.5846
3.2413
1.5825
(iv) τ1 = τ2 = 0.16
2.1098
3.2493
2.6677
0.2
0.2
0.1333
0.1333
2.2501
0.1429
0.2334
5.6569
6.4631
2.8921
1.4909
(v) vd =.072
1.7663
3.3017
2.5575
0.24
0.24
0.1333
0.1333
2.7811
0.1887
0.3188
5.6569
10.976
4.2373
1.7319
(vi) vd =.072, vs =.048
1.7640
2.7164
2.1226
0.24
0.24
0.16
0.16
2.7198
0.1537
0.2305
5.6569
6.5814
3.2241
1.5779
(i)
Benchmark
w/ diversity
(ii) Ad1 =12, As1 =9.6
(iii) Ad1 =12, As1 =9.6,
Immigration Surplus
• The immigration surplus (IS): measures the net costs and benefits to
natives resulting from increased migration to D (and S).
• Distinct contribution of our model relative to conventional estimates:
– Replacing short term/static estimate, by long-tern dynamic estimates
– Treating immigration change as endogenous, resulting from a change in
basic structural parameters, rather than treating it as an exogenous
variable
– Estimating the effect of the change jointly at D and at S, giving an idea
about its impact on the global economy
• The following table presents simulation estimates of reductions in
measures of welfare of natives in D and S following imposed
immigration restrictions relative to their values when immigration is
unrestricted, as estimated by our benchmark and extended models.
Immigration Surplus: % change in welfare measures’ level
when migration is restricted (positive values = loss from restriction= IS gain)
Destination
Welfare measure
A. Skill comp. held constant
Human capital
Full income
Consumption
Utility
B. Skilled mig. disallowed
Human capital
Full income
Consumption
Utility
C. Unskilled mig. disallowed
Human capital
Full income
Consumption
Utility
D. Diversity: Skill comp.
held constant
Human capital
Full income
Consumption
Utility
E. Diversity: All migration
disallowed
Human capital
Full income
Consumption
Utility
Source
5th generation
after a SBTS
10th generation
after a SBTS
15th generation
after a SBTS
15th generation
after a SBTS
0.63
0.67
0.67
0.18
1.10
1.15
1.15
0.32
1.53
1.48
1.47
0.43
-26.4
-23.7
-23.8
-7.36
33.1
28.9
42.2
10.0
62.6
59.9
67.5
23.1
81.4
79.8
83.6
35.2
98.7
99.9
99.9
49.8
-12.8
-14.6
-13.4
-3.65
-21.2
-24.1
-22.6
-5.68
-28.7
-33.0
-31.2
-7.30
98.4
98.5
98.5
60.9
0.86
1.07
1.07
0.19
1.43
1.77
1.77
0.36
2.05
2.40
2.38
0.49
-14.5
-2.44
-2.75
-5.35
52.9
61.7
61.3
9.08
74.8
83.7
83.5
16.5
86.6
93.0
92.9
23.3
99.9
99.9
99.9
69.8
Immigration Surplus: % change in welfare measures’ growth rates
when migration is restricted
Destination
Source
Avg. ann. growth rate
within 5 generations
Immigration restricted
[unrestricted]
Avg. ann. growth rate
within 10 generations
Immigration restricted
[unrestricted]
Avg. ann. growth rate
within 15 gen.
Immigration restricted
[unrestricted]
Avg. ann. growth rate
within 15 gen.
Immigration restricted
[unrestricted]
Human capital of natives
2.943 [2.947]
2.950 [2.954]
2.953 [2.956]
3.008 [2.955]
Full income of natives
4.132 [4.137]
4.137 [4.141]
4.139 [4.142]
4.189 [4.140]
Human capital
2.694 [2.947]
2.628 [2.954]
2.580 [2.956]
1.967 [2.955]
Full income
3.878 [4.137]
3.813 [4.141]
3.766 [4.142]
2.543 [4.140]
Human capital
3.013 [2.947]
3.011 [2.954]
3.008 [2.956]
2.057 [2.955]
Full income
4.207 [4.137]
4.204 [4.141]
4.200 [4.142]
3.222 [4.140]
D. Diversity: Skill
composition held
constant
Human capital
3.374 [3.378]
3.381 [3.385]
3.383 [3.387]
3.417 [3.386]
Full income
4.792 [4.798]
4.796 [4.801]
4.798 [4.803]
4.807 [4.801]
Human capital
2.947 [3.378]
2.954 [3.385]
2.956 [3.387]
1.713 [3.386]
Full income
4.204 [4.798]
4.208 [4.801]
4.210 [4.803]
2.192 [4.801]
A. Skill composition
held constant
B. Skilled migration
disallowed
C. Unskilled migration
disallowed
E. Diversity: all
migration disallowed
IV. Empirical Analysis: Data Description
We are testing propositions 2 and 3 empirically using data on:
▪International migration. The World Bank has published Panel data
on International Migration, 1975-2000, containing migration stocks by
educational attainment in 6 key OECD destination countries: Australia,
Canada, France, Germany (not used here because of E-W division),
the UK and the US. The Panel is estimated to cover approximately 77
percent of the world’s migration population.
▪Other regressors:
▪Per capita GDP data (GDPc) from the Penn World Table (2012) is
used as proxies for the average human capital (education) levels of
skilled natives and migrants in destination and source countries.
▪Distance between countries, common language, contiguity, and
colonial experience are obtained from the GEODist data at the CEPII
(French Research Center in International Economics).
Table 5: Summary Statistics
Variable
SM
TOM
GDPcd
Description
Total number of skilled immigrants from source counties
residing in destination country
Total number of immigrants from source countries residing in destination country
Real per-capita GDP in destination
Mean [Std. Dev.]
11281
[43570]
32821
[156277]
25906
[5573]
GDPcs
Real per-capita GDP in source
8652
[10965]
COMLANG
COLONY
DIST
CONTIG
Dummy variable accounting for whether source country
and destination country share a common language
Dummy variable accounting for whether source country
and destination country have ever had a colonial link
Distance between the capital city of source country and
destination country (in kms)
Dummy variable accounting for whether source country
and destination country are contiguous
0.3527
[0.4779]
0.1279
[0.3340]
8580
[4406]
0.0128
[0.1125]
Empirical Model Specification-new
Testing proposition 2: (Ms1 will be rising with Hd1 holding constant Hs1 and
other correlates)
Since our data include stock measures of the migrant populations, rather than
flow measures, we first need to convert the stock measures into a flowequivalent form. The regression model thus involves two steps:
First Step:
Following Ehrlich and Kim (2007), we specify migration stock values as a
function of past migration flows using a growth regression format: the stock
of the immigrant population (SMsdt) in D in year t is expressed as a function
of its initial value in year 0 and the average growth rate of the net migration
flows accumulated over the period 0-t, g(t), as follows:
(22) SMsdt = (SMsd0) exp[g(t)⋅t] exp(εsdt),
where subscripts s, d, and t denote source country, destination country, and
year, respectively, and εsdt stands for a random error.
Empirical Model Specification-new
Second Step:
The function gM(t) is specified to take the following form:
(23) g(t) = β1 + β2lnGDPcdt + β3lnGDPcst + β4Xsdt
where GDPckt (k=d,s) is a proxy for human capital level of skilled agents in D or S,
and Xsdt includes the other measurable determinants of migration stocks which
approximate our theoretical “migration cost” variable.
-
Empirically we define skilled migrants in the WB panel as those with at least college
education.
Taking a log transformation of equation (22) and combining it with equation (23),
(24) lnSMsdt = β0 + β1 t + β2 t⋅lnGDPcdt + β3 t⋅lnGDPcst + β4 t⋅Xsdt + β5 lnTOMsdt +ust +νdt +εsdt
Proposition 2 can be tested by its consistency with the qualitative values of the
estimated regression coefficients of equation (24).
Empirical Model Specification-new
Testing proposition 3: (a SBTS will raise Msi /(Ms1+Ms2) over trans. to SS)
In this analysis we convert the stock of skilled migrants (SM) a concurrent flow
term by taking the first difference of SM over two consecutive periods:
(25) ΔSMsdt ≡ SMsdt+1 −SMsdt.
For the resulting flow variable ΔSM serving as a dependent variable, we use a
standard linear model with country-specific fixed effects:
(26) lnΔSMsdt = γ0 + γ1lnTOMsdt + γ2T + γ3GDPcdt + γ4GDPcdt2 + γ5GDPcdt3
+ γ6lnGDPcst + γ7Xsdt + ust + νdt + εsdt.
To convert the dependent variable measuring the flow of skilled migration into
its share in concurrent total flow of migrants, as defined in proposition 3, we
enter as an additional variable the total number of immigrants in log form
(TOM). We also add the variables comprising the X vector in equation (26),
including language similarity, past colonial status, distance, and contiguity.
Table 6: Linking the equilibrium stocks of skilled migrants with the
equilibrium levels of their associated determinants by proposition 2
Dependent Variable: lnSM
lnTOM
.75392577***
T
.07275002***
T*lnGDPcd
.00772416***
T*lnGDPcs
-.0035206***
T*COMLANG
-.00672696***
T*COLONY
.01199498***
T*lnDIST
-.01022738***
T*CONTIG
-.00459365***
Adj. R2
N
Note: * p<0.1; ** p<0.05; *** p<0.01.
0.9777
4684
Table 7: Testing the predicted dynamic path of skilled migration flows
following a SBTS over the period 1975-2000
Dependent Variable: ΔSM (= SMt+1
−SMt)
lnTOM
T
Model 1
Model 2
.65347373***
.64110331***
0.014404
-0.01034
GDPcd
.00056973***
GDPcd2
-1.809e-08**
GDPcd3
1.893e-13**
1.7264526***
lnGDPcd
lnGDPcs
-0.05114
-0.00274
COMLANG
0.056032
COLONY
-0.01778
lnDIST
-.27162541***
CONTIG
-.34716462***
Adj. R2
N
0.8491
3427
Note: * p<0.1; ** p<0.05; *** p<0.01.
0.8506
3427
Figure 3: Fitted Regression Lines Linking Skilled Immigrants and Per Capita Income
Note:
1. This figure is based on the regression results of Model 1 in Table 7.
2. The GDPcd values on the x-axes of all panels cover 95% of the observations on GDPc d used in our regressions.
Main Results & Findings
• Despite the harsh rigidities of the model, it offers testable propositions
about the impact of “pull” factors, such as a SBTS on trends in
migration flows (rising), their skill composition (rising), their impact on
human capital formation, wage rates, and FIPC (upward)
• The first two propositions are found to be consistent with a regression
analysis of migration flows into 5 major destination countries including
most recently the US.
• We use the model to isolate the net contribution of immigration to the
SBTS effects. The induced rise in the skilled composition of migration
contributes positively to LR human capital formation, the average
wage level of esp. unskilled migrants, and despite a reduction in
skilled natives’ wages, ultimately even skilled wages due to the
induced effect of migration.
• These implications indicate that unlike SR and static estimates of the
IS, predicting that ‘the IS is positive only if wages fall’ – this is not the
case concerning the LR effects of migration.
Main Results & Findings
• The analysis also provides new insights concerning LR estimates of
the immigration surplus. While conventional estimates put them at
less than 1% of GDP, considering the total measure our estimates
indicate that they can contribute quite larger increases not just in the
levels of full income per-capita after 5 generations but in the growth
rate of per-capita income after 15 generations (approximating a SS.)
• The gains for the receiving country can be offset by negative
immigration surpluses to the sending countries. But there are 2
scenarios under which both D and S can gain:
– when all skilled migration is disallowed – both lose
– when all migration is disallowed – at least when immigration is assumed to
confer diversity gains.
• It thus looks that immigration can be a win-win proposition in the LR.
And even the brain drain may not be so bad as the term sounds.