Immigration, Human Capital Formation and Endogenous Economic Growth © Isaac EhrlichJinyoung Kim SUNY at Buffalo Korea University Memorial Conference Honoring.

Immigration, Human Capital Formation and Endogenous Economic Growth ©

Isaac Ehrlich Jinyoung KimSUNY 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 modela. The benchmark model and the migration decisionb. Growth equilibrium, comp. dynamics, and transitional pathsc. The extended model and diversity effectsd. Assessing the “immigration surplus”

IV.Testing propositions 2 and 3 against int’l data

V.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 hki

t 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 = Ad1hd1

t Hd1t for skilled natives in D

(1b) Hm1t+1 = Ad1hm1

t Hs1t for skilled migrants in D

(1c) Hd2t+1 = Ad2hd2

t Hd2t (Δdd2

t)γ1 for unskilled natives in D

(1d) Hm2t+1 = Ad2hm2

t Hs2t (Δdd2

t)γ1 for unskilled migrant in D

(1e) Hs1t+1 = As1hs1

t Hs1t (Δds1

t)γ2 for skilled natives in S

(1f ) Hs2t+1 = As2hs2

t Hs2t (Δds2

t)γ2(Δss2t)γ1 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 ≡ (Nd1

tHd1t+Ms1

tHs1t)/(Nd2

tHd2t+Ms2

tHs2t) ,

Δss2t ≡ (Ns1

tHs1t−Ms1

tHs1t)/(Ns2

tHs2t −Ms2

tHs2t),

Δds1t ≡ (Nd1

tHd1t+Ms1

tHs1t)/(Ns1

tHs1t−Ms1

tHs1t),

Δds2t ≡ (Nd2

tHd2t+Ms2

tHs2t)/(Ns2

tHs2t−Ms2

tHs2t).

(Δdd2t , Δss2

t): within-country spillovers; (Δds1t, Δds2

t): 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 (Ndi

t Ldit Hdi

t + Msit Lmi

t Hsit) Ψdi where

– Ldit, Lmi

t = total working hours of natives and immigrants in skill group i

Ψdi ≡ (Ndit + Msi

t)-φ [(NditHdi

t + MsitHsi

t)/(Ndit + Msi

t)]μ-φ

– Externality Ψdi is diminishing in quantity of labor force, Ndit+Msi

t, 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(Ndi

t+Msit)-φ[(Ndi

tHdit+Msi

tHsit)/(Ndi

t+Msit)]μ-φ,

(6) ωsit = Γsi(Nsi

t−Msit)-φ[(Nsi

tHsit−Msi

tHsit)/(Nsi

t−Msit)]μ-φ.

Preferences

The Utility function of agents at period (generation) t in our OLG setting is

(7) U(Ckit, Wki

t) = [1/(1−σ)][(Ckit)1-σ−1] + δ [1/(1−σ)][(Wki

t)1-σ−1]

where

(8) Ckit = Lki

t ωkit Hki

t = (1 − vk nkit − θki hki

t nkit) ωki

t Hkit = own consumption,

and

(9) Wkit ≡ B (nki

t)β (cωkit+1 Hki

t+1)α (α =1, β >1) = parental altruism

•For immigrants in D,

(10) U(Cmit, Wmi

t) = [1/(1−σ)][(Cmit)1-σ−1] + δ [1/(1−σ)][(Wmi

t)1-σ−1],

(11) Cmit = Lmi

t ωdit Hsi

t = (1 − vs nmit − θsi hmi

t nmit − τi) ωdi

t Hsit,

(12) Wmit ≡ B (nmi

t)β (ωdit+1 Hmi

t+1)α, with α =1 and β >1.

•Endogenous population evolves as follows:

Ndit+1 = ndi

t Ndit + nmi

t Msit, and Nsi

t+1 = nsit (Nsi

t − 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 = (Cki

t)-σ [− vk − θki hkit] ωki

t Hkit + δ(Wki

t)-σ B β (nkit)β-1 ωki

t+1 Hkit+1

(for hkit) 0 = (Cki

t)-σ [− θki nkit] ωki

t Hkit + δ (Wki

t)-σ B (nkit)β ωki

t+1 (Hkit+1/ hki

t)

(for nmit) 0 = (Cmi

t)-σ [− vs − θsi hmit] ωdi

t Hsit + δ (Wmi

t)-σ B β (nmit)β-1 ωdi

t+1 Hmit+1

(for hmit) 0 = (Cmi

t)-σ [− θsi nmit] ωdi

t Hsit + δ (Wmi

t)-σ B (nmit)β ωdi

t+1 (Hmit+1/ hmi

t).

• 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) nki

t = 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(Wmi

t)1-σ = (Csit)1-σ + δ(Wsi

t)1-σ (i = 1, 2)

• In a log utility case, the “arbitrage condition” in eq (17) then becomes

(18)Γsi (Nsit − Msi

t)-φ(Hsit)μ-φ = (1− τi) Γdi(Ndi

t + Msit)-φ[(Ndi

tHdit + Msi

tHsit)/(Ndi

t + Msit)]μ-φ

or

(18a) ωsit − (1− τi) ωdi

t = 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 /Nsi

t)φ < (1− τi) (Γdi/Γsi) (Hdit /Hsi

t)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 (Hdi

t) 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: dHki

t+1/dHkit = Ad1(hd1

t)* = 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/Nd1

t = Ms2t/Nd2

t; and Ms1t/Ms2

t = Nd1t/Nd2

t

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

▪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.

  (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

Gthrate

Ms1/Nd1

= Ms2/Nd2

Ms1/Ns1

= Ms2/Ns2

Δdd2

= Δss2

Δds1

= Δds2

Hd1/Hs1

= Hd2/Hs2

ωd1/ωs1

= ωd2/ωs2

(i) Benchmark 2.0906 3.2207 2.5157 0.2 0.2 0.1333 0.1333 2 0.1803 0.2101 5.6569 4.8140 3.0820 1.5728

(ii) Ad1 =12, As1 =9.6 2.1198 3.2642 2.5508 0.2 0.2 0.1333 0.1333 2.4 0.1807 0.2094 8.9234 4.8140 3.1025 1.5785

(iii) Ad1=12, As1 =9.6

Ad2 =6, As2 =4.8 2.1198 3.2642 2.5508 0.2 0.2 0.1333 0.1333 2.4 0.1807 0.2094 5.6569 4.8140 3.1025 1.5785

(iv) τ1 = τ2 = 0.16 2.0907 3.2208 2.6436 0.2 0.2 0.1333 0.1333 2 0.1664 0.2143 5.6569 4.8140 2.7713 1.4874

(v) vd =.072 1.7462 3.2659 2.5287 0.24 0.24 0.1333 0.1333 2.4 0.2282 0.2886 5.6569 7.5938 4.0429 1.7247

(vi) vd=.072, vs=.048 1.7470 2.6912 2.1023 0.24 0.24 0.16 0.16 2.4 0.1804 0.2100 5.6569 4.8140 3.0861 1.5739

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. A higher growth rate,

b. a higher average human capital, wage rates, and full income per worker

c. a higher rate of fertility (but lower population ratio)

d. 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

Growth

rate

Ms1/Nd1

= Ms2/Nd2

Ms1/Ns1

= Ms2/Ns2

Δdd2

= Δss2

Δds1

= Δds2

Hd1/Hs1

= Hd2/Hs2

ωd1/ωs1

= ωd2/ωs2

(i) Benchmark

w/ diversity 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

(ii) Ad1 =12, As1 =9.6 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

(iii) Ad1 =12, As1 =9.6,

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

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   Source

 Welfare measure 5th generationafter a SBTS

10th generationafter a SBTS

15th generationafter a SBTS

15th generationafter a SBTS

A. Skill comp. held constant        Human capital 0.63 1.10 1.53 -26.4Full income 0.67 1.15 1.48 -23.7Consumption 0.67 1.15 1.47 -23.8Utility 0.18 0.32 0.43 -7.36B. Skilled mig. disallowed        

Human capital 33.1 62.6 81.4 98.7Full income 28.9 59.9 79.8 99.9Consumption 42.2 67.5 83.6 99.9Utility 10.0 23.1 35.2 49.8C. Unskilled mig. disallowed        Human capital -12.8 -21.2 -28.7 98.4Full income -14.6 -24.1 -33.0 98.5Consumption -13.4 -22.6 -31.2 98.5Utility -3.65 -5.68 -7.30 60.9D. Diversity: Skill comp. held constant

Human capital 0.86 1.43 2.05 -14.5Full income 1.07 1.77 2.40 -2.44Consumption 1.07 1.77 2.38 -2.75Utility 0.19 0.36 0.49 -5.35E. Diversity: All migration disallowed

Human capital 52.9 74.8 86.6 99.9Full income 61.7 83.7 93.0 99.9Consumption 61.3 83.5 92.9 99.9Utility 9.08 16.5 23.3 69.8

Immigration Surplus: % change in welfare measures’ growth rateswhen migration is restricted

    Destination   Source

  Avg. ann. growth rate within 5 generations

Immigration restricted[unrestricted]

Avg. ann. growth rate within 10 generationsImmigration restricted

[unrestricted]

Avg. ann. growth rate within 15 gen.

Immigration restricted[unrestricted]

Avg. ann. growth rate within 15 gen.

Immigration restricted[unrestricted]

A. Skill composition held constant

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]

B. Skilled migration disallowed

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]

C. Unskilled migration disallowed

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]

E. Diversity: all migration disallowed

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]

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 Description Mean [Std. Dev.]     

SM Total number of skilled immigrants from source counties residing in destination country

11281

[43570]

TOM Total number of immigrants from source countries resid-ing in destination country

32821

[156277]

GDPcd Real per-capita GDP in destination 25906

[5573]

GDPcs Real per-capita GDP in source 8652

[10965]

COMLANG Dummy variable accounting for whether source country and destination country share a common language

0.3527

[0.4779]

COLONY Dummy variable accounting for whether source country and destination country have ever had a colonial link

0.1279

[0.3340]

DIST Distance between the capital city of source country and destination country (in kms)

8580

[4406]

CONTIG Dummy variable accounting for whether source country and destination country are contiguous

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 flow-equivalent 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(ε⋅ sdt),

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 lnGDPc⋅ dt + β3 t lnGDPc⋅ st + β4 t X⋅ sdt + 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 + γ5GDPcdt

3

+ 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.

lnTOM .75392577***

T .07275002***

T*lnGDPcd.00772416***

T*lnGDPcs-.0035206***

T*COMLANG -.00672696***

T*COLONY .01199498***

T*lnDIST -.01022738***

T*CONTIG -.00459365***

Adj. R2 0.9777

N 4684

Table 6: Linking the equilibrium stocks of skilled migrants with the equilibrium levels of their associated determinants by proposition 2

Note: * p<0.1; ** p<0.05; *** p<0.01.

Dependent Variable: lnSM

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)

  Model 1 Model 2

lnTOM .65347373*** .64110331***

T 0.014404 -0.01034

GDPcd.00056973***  

GDPcd2 -1.809e-08**  

GDPcd3 1.893e-13**  

lnGDPcd  1.7264526***

lnGDPcs-0.05114 -0.00274

COMLANG   0.056032

COLONY   -0.01778

lnDIST   -.27162541***

CONTIG   -.34716462***

     Adj. R2 0.8491 0.8506N 3427 3427

Note: * p<0.1; ** p<0.05; *** p<0.01.

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 GDPcd 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.