Immigration, Human Capital Formation in addition to Endogenous Economic Growth © Isaac Ehrl
Henderson, Khali, Group Editor has reference to this Academic Journal, PHwiki organized this Journal Immigration, Human Capital Formation in addition to Endogenous Economic Growth © Isaac Ehrlich Jinyoung KimSUNY at Buffalo Korea UniversityMemorial Conference Honoring Gary Becker Chicago, October 16, 2015MotivationOver 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)
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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 educationEvidence from the USIn 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 in addition to about to exceed that of US natives. This trend has been sharpest as long as Asians immigrants, followed by Europeans in addition to others, all of whom overtook the US in college in addition to higher degrees.Whats the story behind these migration trends And how do they link with the observed pattern of economic growth in addition to skill composition in the economies of the major receiving in addition to sending countries over the last 4 decadesEducational Attainment of the Foreign-Born Population (in %) 25 Years in addition to Over vs. Total Native Population by year of Entry: 2012
Educational Attainment of the Foreign-Born Population (in %) 25 Years in addition to Over by World Region of Birth: 2012OutlineII. The approachIII. The modelThe benchmark model in addition to the migration decisionGrowth equilibrium, comp. dynamics, in addition to transitional pathsThe extended model in addition to diversity effectsAssessing the immigration surplus Testing propositions 2 in addition to 3 against intl data Concluding remarksII. The approachThats 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 as long as firms to adjust their capital assets or not long enough to allow as long as continuous accumulation of all relevant assets that can secure long-term growth.There is also a nascent literature that links migration in addition to growth using endogenous growth models based on either new-product innovation or human capital as long as mation 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 in addition to skill composition of migrants in addition to related trends in both sending in addition to receiving economies using what else but – a human-capital-based endogenous growth model.
II. The approachThe distinct property of our approach is that it treats migration flows (waves) in addition to their skill composition as endogenous variables that depend on indiv. choices & market as long as ces, 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) in addition to a source (S) country, in addition to two in addition to recognize two distinct groups of workers in addition to corresponding families within these countries skilled in addition to unskilled – where parents make fertility, HC investment, in addition to work decisions, which include the choice of staying in S or migrating to D, in addition to 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 in addition to a determinant of income distribution over the development process. An earlier attempt to implement such an extension is Idu (2012)III. The ModelSuch approach allows as long as a richer treatment of the migration problem in a GE context that accounts as long as 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 in addition to 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 as long as such interaction which is ascribed to diversity effects. The Benchmark Model SetupBasic 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 DMigrants are freely mobile internationally, in addition to skilled (unskilled) agents from S are perfect substitutes to skilled (unskilled) workers in DEach agent lives over two periods: childhood in addition to adulthood (when consumption, investment, work in addition to migration decisions are made)Each country has two sectors: high-tech (1) in addition to low-tech (2), each of which produces perfectly substitutable goods (thus avoiding any trade in goods) in addition to employs just one of the 2 skill types of workersHuman capital is the only reproducible asset – we abstract from a separate role of physical capital. But HC is producing both private in addition to external social benefits through knowledge spillover effects, which makes HC an engine of country-specific in addition to global growth as wellThe labor markets are competitive.
Human Capital FormationHuman capital production function is country- in addition to skill-specific: Hkit+1 = Aki hkit Hkit (ki ) ; k = d,s,m; i=1,2d= 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 offspringPF reflects endowed elements of diversity that are skill in addition to country-of-birth specific. It distinguishes skill from acquired knowledge (Ht+1). skill Aki = captures a bundle of personal abilities in addition to 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 as long as 3 types of knowledge spillover effects between generations, within countries, in addition to across countries:a. Intergenerational: transmission of knowledge from parents to childrenb. Within-country: unskilled learning from skilledc. Cross-country: skilled (unskilled) in S learn from skilled (unskilled) in D.Social Externalities in HC as long as mationThe HC production functions are given by (1a) Hd1t+1 = Ad1hd1t Hd1t as long as skilled natives in D (1b) Hm1t+1 = Ad1hm1t Hs1t as long as skilled migrants in D (1c) Hd2t+1 = Ad2hd2t Hd2t (dd2t)1 as long as unskilled natives in D (1d) Hm2t+1 = Ad2hm2t Hs2t (dd2t)1 as long as unskilled migrant in D (1e) Hs1t+1 = As1hs1t Hs1t (ds1t)2 as long as skilled natives in S (1f ) Hs2t+1 = As2hs2t Hs2t (ds2t)2(ss2t)1 as long as unskilled natives in S PFs are hierarchical: d1 =1; < 1; Adi > Asi in addition to Ak1 > Ak2 (k = d, s; i = 1, 2), but model allows as long as 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 effectsThe spillover factors dd2t (Nd1tHd1t+Ms1tHs1t)/(Nd2tHd2t+Ms2tHs2t) , ss2t (Ns1tHs1tMs1tHs1t)/(Ns2tHs2t Ms2tHs2t), ds1t (Nd1tHd1t+Ms1tHs1t)/(Ns1tHs1tMs1tHs1t), ds2t (Nd2tHd2t+Ms2tHs2t)/(Ns2tHs2tMs2tHs2t).(dd2t , ss2t): within-country spillovers; (ds1t, ds2t): cross-country spilloversThe 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 in addition to the larger is the relative size of the latter (the teacher/student ratio)
Consumption GoodsGoods 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 in addition to goods produced in the high-tech in addition to 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 = di (Ndit Ldit Hdit + Msit Lmit Hsit) di whereLdit, Lmit = total working hours of natives in addition to immigrants in skill group i di (Ndit + Msit)- [(NditHdit + MsitHsit)/(Ndit + Msit)]-Externality di is diminishing in quantity of labor as long as ce, Ndit+Msit, but increasing in quality of the average workers HCdi . A similar PF applies to country SThe wage rate per unit of HC is thus(5) dit = di(Ndit+Msit)-[(NditHdit+MsitHsit)/(Ndit+Msit)]-,(6) sit = si(NsitMsit)-[(NsitHsitMsitHsit)/(NsitMsit)]-. PreferencesThe Utility function of agents at period (generation) t in our OLG setting is(7) U(Ckit, Wkit) = [1/(1)][(Ckit)1-1] + [1/(1)][(Wkit)1-1]where (8) Ckit = Lkit kit Hkit = (1 vk nkit ki hkit nkit) kit Hkit = own consumption, in addition to (9) Wkit B (nkit) (kit+1 Hkit+1) ( =1, >1) = parental altruismFor immigrants in D,(10) U(Cmit, Wmit) = [1/(1)][(Cmit)1-1] + [1/(1)][(Wmit)1-1], (11) Cmit = Lmit dit Hsit = (1 vs nmit si hmit nmit i) dit Hsit, (12) Wmit B (nmit) (dit+1 Hmit+1), with =1 in addition to >1.Endogenous population evolves as follows: Ndit+1 = ndit Ndit + nmit Msit, in addition to Nsit+1 = nsit (Nsit Msit).Model SolutionsMembers of each of the six population groups decides on fertility in addition to human capital investment in children.Optimality conditions w.r.t fertility in addition to HC investment are:( as long as nkit ) 0 = (Ckit)- [ vk ki hkit] kit Hkit + (Wkit)- B (nkit)-1 kit+1 Hkit+1 ( as long as hkit) 0 = (Ckit)- [ ki nkit] kit Hkit + (Wkit)- B (nkit) kit+1 (Hkit+1/ hkit) ( as long as nmit) 0 = (Cmit)- [ vs si hmit] dit Hsit + (Wmit)- B (nmit)-1 dit+1 Hmit+1( as long as hmit) 0 = (Cmit)- [ si nmit] dit Hsit + (Wmit)- B (nmit) dit+1 (Hmit+1/ hmit).Explicit solutions as long as investment (15) hkit = vk/ [ki(1)], (i = 1, 2; k = d, s)(15a) hmit = vs/ [si(1)], (i = 1, 2)For fertility, we get an explicit solution only if the utility fn. has a log as long as m(16) nkit = (1)/ [vk (1+ )], (i = 1, 2; k = d, s)(16a) nmit = (1)[1 i] / [vs (1+ )].
Optimal MigrationAgents 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 in addition to S are equalized:(17) (Cmit)1- + (Wmit)1- = (Csit)1- + (Wsit)1- (i = 1, 2)In a log utility case, the arbitrage condition in eq (17) then becomes(18)si (Nsit Msit)-(Hsit)- = (1 i) di(Ndit + Msit)-[(NditHdit + MsitHsit)/(Ndit + Msit)]-or(18a) sit (1 i) dit = 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. PropositionsProposition 1. There is a positive in addition to unique solution as long as 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) < (1 i) (di/si) (Hdit /Hsit)-.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 as long as equilib. migration.Both propositions are tested in addition to found to be consistent with a comprehensive WB panel on migration involving 5 receiving countries from 190 sending countries Growth Equilibrium Steady StateExistence of a globally balanced & stable growth equilibrium requires:A threshold level of parental investments in offsprings HC: dHkit+1/dHkit = Ad1(hd1t) = vd (Ad1/d1)/(1) = (1+g) >1 , which implies :a. hd1 > (1//Ad1); in addition to b. (Ad1/d1)/(Ad2/d2) = (As1/s1)/(As2/s2); i.e.,ifRelative efficiency parameters in knowledge in addition to good production are the same in D in addition to S.equal relative (not absolute) endowed productivity levels in goods production in D in addition to S:d1 / d2 = s1 / s2 Higher shadow marginal costs of fertility in D relative to S; vd > vsSubject to these conditions we derive a stable steady state global equilibrium with the following properties:
Growth Equilibrium Steady StateProperties:Population in addition to human capital attainments rise by the same proportion within in addition to across countries.Fertility, in addition to population growth rates of both skill groups are constant in addition to equal across both natives in addition to immigrants in each country. Thus: Ms1t/Nd1t = Ms2t/Nd2t; in addition to Ms1t/Ms2t = Nd1t/Nd2t Human capital growth rates are equalized across skill groups in addition to countries, converging on the growth rate of the skilled group in the destination country.Thus relative human capital, wage rates in addition to hence full income per-capita equalize within in addition to across country in addition to as long as each skill group across countries: Hd1 /Hs1 = Hd2 /Hs2 ; wd1 /ws1 = wd2 /ws2But the steady state fertility rates remain higher in the source, relative to the destination country. A constant in addition to persisting fraction of each skill group in S migrates to D (see the simulation results in Table 1). Comparative DynamicsOur 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 followsAn equi-proportional rise in the knowledge production technology in D in addition to S, affecting only the skilled in D in addition to S (represents a skill-biased technological shock [SBTS]A similar, but neutral rise in knowledge production affecting all skill groupsA decline in the immigration tax as long as both skill groups An increase in he cost of fertility just in D or in both D in addition to SAnalysis can explain immigration waves of a push nature, such as the Syrian. Focusing on the impact of the SBTS. Fig. 1 shows that itRaises the global growth rate; Raises the skill composition of migration in addition to the pop. shares of migrants relative to natives in D But lowers the pop. share of the skill ratio in SRaises the ave. wage in addition to HC level (thus full income) of skilled migrants in D rel to SIt thus raises income disparity in addition to the Gini coefficient both within skill groups in D (not shown in Table 1) in addition to across countries. Comparative Dynamics Effects of key structural parameter shifts in the GEsteady state Parameters in the benchmark case: Ad1 =10, As1 =8, Ad2 =5, As2 = 4, 1 = 0.2, 2 = 0.2, vd = 0.06, vs = 0.04, d1 = 1, d2 = 1, s1 = 1, s21 = 1, = 0.9, = 0.7, = 1.3, 1 = 0.4, 2 =0.4, = 0.1, = 0.6, B = 1, d1 = 1, s1 = 1, d2 = 1, s2 = 1.Comparative dynamics in the steady state are simulated by increasing Ad1, As1, Ad2, As2, vd, vs , or decreasing 1, 2, 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 thatBy raising both Ad1 in addition to As1 simultaneously in addition to leaving Ad2 in addition to 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 in addition to Transitional Paths Isolating the contribution of the Shock-induced Migration to the total effect of the SBTS in DWe decompose the total effect of the SBTS into (1) the part that would be attributable to it alone in addition to 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:When the skill composition of migrant flows [Ms1/(Ms1+Ms2)] in addition to relative pop. share (Ms1/Nd1) are restricted to be frozen at their initial steady state equilibrium values. 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 higher growth rate, a higher average human capital, wage rates, in addition to full income per workerc. a higher rate of fertility (but lower population ratio)A. lower rise in income inequality
Impact of Induced Migration Extended Model with Diversity EffectsWe extend our model by allowing as long as interaction between natives in addition to immigrants in the production of knowledge.Rationale: Diversity in background in addition to experience may enhance complementarities, especially across workers of the same skill level who acquired their knowledge in addition to creativity in different countries of birth (the classical example: the Manhattan project).Diversity: Aki (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
Main Results & FindingsThe 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 as long as the receiving country can be offset by negative immigration surpluses to the sending countries. But there are 2 scenarios under which both D in addition to S can gain:when all skilled migration is disallowed both losewhen 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.
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