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The brain drain and the world distribution of income

Andrew Mountford a,⁎, Hillel Rapoport b,c,d,1

a Dept. Economics, Royal Holloway College, University of London, Egham, Surrey TW20 OEX, UK b Department of Economics, Bar-Ilan University, Israelc EQUIPPE, University of Lille, Franced Center for International Development, Harvard University, United States

a b s t r a c ta r t i c l e i n f o

Article history:

Received 10 February 2009Received in revised form 27 October 2009

Accepted 9 November 2009

JEL classi cation:

O40

F11

F43

Keywords:

Migration

Growth

Brain drain

World distribution of income

Endogenous fertility

Skilled emigration (or brain drain) from developing to developed countries is becoming the dominantpattern of international migration today. Such migration is likely to affect the world distribution of incomeboth directly, through the mobility of people, and indirectly, as the prospect of migration affects the rate of

return to education in both the sending and receiving economies. This migration pattern will therefore affect

human capital accumulation and fertility decisions in both the sending and receiving economies. This paperanalyzes these effects in a dynamic two country model of the world economy where agents in both countriesmake optimal fertility and human capital decisions. The implications of the analysis for the world

distribution of income are derived in the light of recent empirical ndings of the brain drain literature. Theanalysis shows that the current trend towards predominantly skilled emigration from poor to rich countries

may in the long run increase inequality in the world distribution of income as relatively poor countries growlarge in terms of population. In the short run however, it is possible for world inequality to fall due to rises inGDP per capita in large developing economies with suf ciently low skilled emigration rates.

© 2009 Elsevier B.V. All rights reserved.

1. Introduction

Skilled emigration (or brain drain) from developing to developedcountries is becoming the dominant pattern of international migration

today. Such migration is likely to affect the world distribution of incomeboth directly, through the mobility of people, and indirectly, as theprospect of migration affects the rate of return to education in both thesending and receiving economies. This migration pattern will therefore

affect human capital accumulation and fertility decisions in both thesending and receiving economies. This paper analyzes these effects in adynamictwo countrymodel of the world economywhereagentsin bothcountries make optimal fertility and human capital decisions. The

implications of the analysis for the world distribution of income arederived in the light of recent empirical ndings of the brain drainliterature. The analysis shows that the current trend towards predom-inantly skilled emigration from poor to rich countries may in the long

run increase inequality in the world distribution of income as relativelypoor countries grow large in terms of population. In the short run

however, it is possible forworld inequalityto fall due to risesin GDPpercapita in large developing economies with suf ciently low skilledemigration rates.

It is important to analyze theeffects of brain drain migration patterns

on theworlddistributionof incomesince this typeof migration hasbeengrowing signicantly over the last 25 years. Throughout the 1990s thegrowth rate of internationalskilledmigrationhas beennearly triple thatof unskilled migration, and most of that increase was due to skilled

migration from developing to developed countries. Emigration rates in2000 were three times higher than average for the highly educated andskilled — and twelve times higher among emigrants from low-incomecountries (Docquier and Marfouk, 2006).2 This signicant development

in the world economy gives riseto important economic questions. Is thebrain drain from developing to developed countries likely to be atransitoryor a permanent featureof theworldeconomy? Will it increasethe rate of economic growth in the sending economies, in the receiving

economies, and in the world economy? Will the brain drain promoteconvergence or divergence in the world distribution of income?

The prospect of migration affects the rate of return to education in

both the sending and receiving economies and will therefore affecthuman capital accumulation and fertility decisions in both places.Migration will therefore affect the world distribution of income both

Journal of Development Economics 95 (2011) 4–17

⁎ Corresponding author. Tel.: +44 1784 443906; fax: +44 1784 439534.

E-mail addresses: [email protected] (A. Mountford),

[email protected] (H. Rapoport).1 Center for International Development, Kennedy School of Government, Harvard

University, 79 JFK Street, Cambridge, MA 02138, United States. Tel.: +1 617 496 0897;

fax: +1 617 495 8753. 2 See Section 2 below for a discussion of the empirical trends.

0304-3878/$ – see front matter © 2009 Elsevier B.V. All rights reserved.

doi:10.1016/j.jdeveco.2009.11.005

Contents lists available at ScienceDirect

Journal of Development Economics

j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / d ev e c

http://-/?-mailto:[email protected]:[email protected]://dx.doi.org/10.1016/j.jdeveco.2009.11.005http://www.sciencedirect.com/science/journal/03043878http://www.sciencedirect.com/science/journal/03043878http://dx.doi.org/10.1016/j.jdeveco.2009.11.005mailto:[email protected]:[email protected]://-/?-


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growth in theworld economy.This paper focuses on the implications of brain drain migration since, as detailed in Section 2.2 below, skill-biased

immigration policies are becoming dominant in OECD economies andskilledemigration rates areon therise indevelopingcountries.Howeverit should be stressed that the same method of analysis (i.e., its mirror-

image) can be used to analyze primarily low-skill migration move-ments. Our theoretical mechanisms rely on a positive differentialprobability of migration for skilled workers. Should this be reversed infavor of unskilled workers, increased fertility and decreased human

capital investment in the sending country would result. While specictemporary migration (e.g., of the guestworker type) do target unskilledworkers, the global picture — and, therefore, the relevant one foranalyzing the effect of international migration on the world distribution

of income — is that of a strong positive selection of internationalmigrants.

Empiricallythere is alsomuch evidence in favor of a quantity/qualitytrade off in fertility decisions. In a notable microeconometric study of

family's fertility decisions in rural India, Rosenzweig andWolpin(1980)found that the occurrence of multiple births (i.e., an exogenous increasein family size) brought abouta decline in child quality. Recentstudies indeveloped economies, however, where the enforcement of child labor

and public education laws implies a much lower differential cost inbringing up skilled children,nd no evidencefor a family size effect, see

e.g. Black et al. (2007) study using Norwegian data and Angrist et al.(2010) study on Israel. In cross countrymacroeconomic analysisfertility

rates are persistently shown to have a negative effect on growth,see forexample Barroand Sala-I-Martin(2004). Kremer andChen (1999,2002)using cross-country regressions found higher fertility was associated

with lower levels of education and that this effect is greater in moreunequal societies, which is consistent with the existence of a quality/quantity trade off, although as Kremer and Chen allow, such results arenot denitive due to endogeneities inherent in their regression model.

2.2. Recent trends in migration

Recent comparative data on international migration by skill levelreveal that over the last few decades the brain drain has increased notonly in magnitude (i.e., in terms of total number of highly skilledimmigrants) butalso, in mostcases, in intensity (i.e., relative to thestock

of highly educated people remaining in the source countries). Thismeans thatthe rate of growthof internationalskilled migrationhas beeneven more rapid thanthat of educational attainments in most regions of

the developing world.Fig. 1a shows this evolution using panel data fromDefoort (2008), where skilled emigration rates are expressed inpercentage of the total skilled population (i.e., migrants included).Fig. 1b gives brain drain rates for selected countries in 2000, with

adjustments for counting people whoimmigratedonly after a given age.It is readily seen from Fig. 1a and b that brain drain rates varyenormously across countries and regions.

The rise in brain drain migrationhas beencausedby a combination

of selective immigration policies on the demand side and an increasedtendency for workers to positively self-select into migration on thesupply side.6 Selective immigration policies such as the point-system

were

rst introduced in Australia and Canada in the early 1980s, andthen gradually spread to other OECD countries. Recent examplesinclude the adoption of the point-system by the United Kingdom in2005 and the “chosen immigration” policy adopted in France in 2006.

There is a clear decreasing relationship between emigration rates

and country size (see Fig. 2). Docquier and Marfouk (2006) show thatthese differences cannot be attributed to the educational structure of the home country population or to a higher ratio of skilled to totalemigrationrates in small countries. The latter are simplymore open to

migration (as they are to trade). Another important determinant of

Fig. 1. a) The rst panel shows the increase in brain drain migration over the last three decades. b) The second panel shows corrected and general brain drain rates for selected

countries in 2000.

Source: Authors' computations using Defoort (2008). Source: Computed from Beine et al. (2007).

6 There are very few exceptions to this empirical regularity that international

migrants positively self-select with respect to education, as conrmed by recent micro(Gould and Moav, 2008; Yashiv, 2008) and macro (Grogger and Hanson, 2011; Belot

and Hatton, 2008; Beine et al., 2009; Beine et al., 2011 ) studies. A notable exception is

the case of Mexico (see Chiquiar and Hanson, 2005; McKenzie and Rapoport, 2010).

Fig. 2. The inverse relationship between the skilled emigration rate and population size

(in 2000).

Source: Docquier and Marfouk (2006).

6 A. Mountford, H. Rapoport / Journal of Development Economics 95 (2011) 4–17

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skilled emigration is a country's income level, with the highest skilledemigration rates being observed in middle-income countries. The factthat skilled emigration rates tend to be lower in relatively af uentcountries is explained by the low wage differentials between these

countries and potential destinations. The reasons why they are alsolower in poor countries are less obvious and could be due to a varietyof causes, including the role of credit constraints on education and

migration decisions or the lower transferability of human capital,

which we do not attempt to model in this paper.The theoretical model below will show that the brain drain canhave a positive or negative effect on human capital accumulationin the

sending economy depending ceteris paribus on the rate of emigrationof skilled workers. As in previous models, the potential for brain drainmigration to be benecial to the sending economy is based on theassumption that the ability to migrate is uncertain and that migrationprospects affect agents' education and fertility decisions in the sending

economies.7 There is much empirical evidence supporting this

assumption at both the micro and macro level. Micro-level evidencecomes mainly from (small) countries case-studies (see, e.g., GibsonandMcKenzie, 2011, Chand andClemens, 2008). Macro-level evidenceis provided by Beine et al. (2008), who found a signicant positive

effect of skilled emigration on gross human capital formation(with anelasticity of about 5%) in a cross-section of developing countries. 8

Using their point estimate (an elasticity of 5%) to compute counter-

factual simulations, they nd that the countries that experience a net

positive brain drain generallycombine lowlevels of human capital andlow skilled emigration rates, and conversely for the countriesexperiencing a net loss. There appears to be more losers than winners

among sending countries, however the latter include the largestcountries in terms of population size. As we will show in Section 5,these forces areconsistent with thedecline in world incomeinequalityduring the 1980s and 1990s, and should act to reinforce the evolutionof the world distribution of income as described in Sala-I-Martin

(2006).

3. An autarkic economy

In this section we describe an economy when there is no migration. We consider an overlapping generations economy where in each period t output, Y

t , may be produced using two factors of production, skilled labor, H

t , and unskilled labor L

t , under perfect competition. The levels of H

t and L

t are determined endogenously by theoptimaldecisions of agents. Agents live for two periods and areendowed with one unit of labor in their secondperiod.Agentsare identical in all respects except for their level of ability, a, which we will assumeis distributeduniformlyoverthe unit interval,[0, 1]andindependentlyof the ability level of their parent. If the agent becomes skilled,then agent i can supply g t +ai ef ciency units of skilled labor, where

g t is the rate of growth of frontiertechnology. Otherwise the agent remains unskilled and supplies one ef ciency unit of unskilled labor. This impliesthat an increase in the rate of technological progress will increase the number of ef ciency units a skilled worker supplies and will ceteris paribusincrease the relative wage of skilled workers, as in Galor and Moav (2000)and Gould et al. (2001).9 The level of technology, At , ineach period is givenandtechnological progress from one period to the nextis related to thelevel of human capital accumulationin theeconomyand so is alsodetermined

endogenously.We rst set out the production function and factor prices before analyzing agents' fertility and education decisions and the economy's dynamics.

3.1. Production and factor prices

In each period output is produced using two factors according to a constant returns to scale production function

Y t = At H αt L

1−αt ð1Þ

where H t and Lt are the levels of skilled and unskilled labor in the economy.

Dening ht ≡H t /Lt , factor prices for each factor are given by their marginal products and hence

wH t = α At h

α−1t ; w

Lt = ð1−αÞ At h

α

t ð2Þ

Thus we can write

wLt wH t

= ð1−αÞ

α ht ð3Þ

3.2. Individuals' preferences and budget constraints

In theirrst periodof life individuals are dependent on their parent who decides whether or not they become skilled.As described above, skilledindividuals can supply g t +ai ef ciency units of skilled labor while those remaining unskilled can supply only one ef ciency unit of unskilled labor.

Individuals make optimal decisions over fertility, consumption and the training of their offspring (Becker (1981)). Following de la Croix and

Doepke (2003, 2004), Galor and Mountford (2006) and Moav (2005) the preferences of a member of generation t (i.e., an individual who is born in

7 See Docquier and Rapoport (2009) for a recent survey of this literature.8 See also Beine, Docquier and Rapoport (2009) for a sensitivity analysis.9 For simplicity this paper abstracts away from the ‘erosion’ effect of technological progress analyzed by Galor and Moav (2004). However an ‘erosion effect’, whereby a higher

rate of growth of technological progress has a disruptive effect on current workers' productivity while also having a positive effect on future productivity, could easily be included

without qualitatively affecting the results of the paper by adding a factor (1 −ε g t ) to the expressions for the ef ciency units of labor supplied by skilled and unskilled workers.


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period t −1) are dened over their consumption in period t , c t , and the total income of their offspring, dt + 1, and are represented by the utilityfunction:

ut = c θt d

1−θt + 1 ð4Þ

Individuals are assumed to be ‘small’ and so take the wage rate and growth rate in periods t and t +1 as given. Individuals optimally allocate theirtimebetweenlabor force participation andchild rearing. Denoting the timerequired to bring up skilledoffspring as,τ s, and the time requiredto bringup unskilled offspring as, τ u, where we assume that 0bτ ubτ sb1, the budget constraint of a member i of generation t , is

c t + wit ðτ

sn

H t + τ

un

Lt Þ≤w

it for i = s; u ð5Þ

where nt H and nt

L are the measures of skilled and unskilled offspring respectively.

3.3. Optimization

Agents choose a measure of time, n, to spend on fertility.10 For each offspring the parent must make an education decision.Since each family is aprice taker in the labor market this amounts to choosing a threshold ability level, at + 1

⋆ , such that all offspring with ability level above at + 1⋆ will be

educated to a skilled level, while those with an ability level of less than at + 1⋆ will remain unskilled.11

A member i of generation t 's optimization problem can thus be written as the following

fc t ; nt ; a⋆t + 1g = argmax c

θt ðnt ½w

H t + 1∫

1a⋆t + 1

ð g t + 1 + aiÞdi + wLt + 1a

⋆t + 1Þ

1−θð6Þ

such that, for i = s, u,

c t + nt ½τsð1−a⋆t + 1Þ + τ

ua⋆t + 1w

it = w

it ð7Þ

The optimization gives the following optimal decision rules for consumption and fertility.

c t = θwit ð8Þ

nt = 1−θ

τ sð1−a⋆t + 1Þ + τ ua⋆t + 1ð9Þ

3.3.1. The education decision

Optimization with respect to at + 1⋆ implies that

ðwH t + 1ð g t + 1 + a⋆t + 1Þ−wLt + 1Þ

wH t + 1∫1a⋆t + 1

ð g t + 1 + aiÞdi + wLt + 1a

⋆t + 1

= τ

s−τu

τsð1−a⋆t + 1Þ + τua⋆t + 1

ð10Þ

Eq.(10)providesan intuitivecondition forthe parentaleducational choice. If thecost of rearing skilled andunskilled offspringwerethe same, then itwould be optimal to educate offspringup to the point wherethe earnings of the marginalworker, with ability level at + 1

⋆ , would be thesame whethers/he became skilled or not. However the extra cost of rearing skilled offspring implies that parents will need to get a greater return from education(i.e., the opportunity cost of education is the possibility of increasing fertility by (τ s−τ u)/(τ s(1−at + 1⋆ ) +τ uat + 1⋆ )). Hence in equilibrium it must bethe case that wt + 1

H ( g t + 1 +at + 1⋆ ) is greater than wt + 1

L.

3.4. Technological progress

We assume, following Galor and Moav (2000), that the rate of technological progress, g t ≡( At − At −1)/ At −1 is an increasing function of theskill intensity of the economy.12 That is:

g t = ϕðht −1Þ; where ϕ′ðht −1Þ N 0 and ϕð0Þ N 0: ð11Þ

10 This is a sensible approach in the representative agent framework and is commonly used in the literature, see for example Barro and Becker (1989), Becker (1981), de la Croix

and Doepke (2003, 2004) and Doepke (2005).11 For simplicity this paper abstracts away from the inuence of parental human capital on individual's human capital accumulation, as in Moav (2005) and De la Croix and

Doepke (2003). However intuitively, if skilled migrants have a comparative advantage in producing skilled offspring then this will reinforce the tendency derived in Section 4 for

the receiving economy to have a higher equilibrium human capital intensity than the sending economy.12 The assumption of a positive relationship between growth and human capital accumulation is a common one in the literature, see for example Nelson and Phelps (1966),

Findlay (1978), Barro and Sala-I-Martin (2004) and also Galor and Moav (2004), who provide an excellent survey of empirical support for this relationship.




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3.5. Equilibrium

In this section we describe properties of the no-migration equilibrium using two propositions which show that there exists a unique

equilibrium level of at + 1⋆ which is decreasing in the rate of growth of technology.

Proposition 1. In each period there is a unique equilibrium level of at+1⋆ .

Proof. Using Fig. 3 and Eqs. (3) and (10). Eq. (10) can be rearranged and simplied to give

wLt + 1wH t + 1

=ð g t + 1 + a

⋆t + 1Þðτ

sð1−a⋆t + 1Þ + τua⋆t + 1Þ−ðτs−τuÞ∫1a⋆t + 1 ð g t + 1 + aiÞdi

τs ð12Þ

which is an increasing function of at + 1⋆ . This is the ratio of inverse factor supply functions and is labelled ‘supply’ in Fig. 3.

Eq. (3) can be written

wLt + 1wH t + 1

= ð1−αÞ

α

∫1a⋆t + 1

ð g t + 1 + aiÞdi

a⁎ ð13Þ

which is a decreasing function of at + 1⋆ . This is the inverse ratio of inverse factor demand functions and is labeled ‘demand’ in Fig. 3.

Fig. 3 plots both these conditions and illustrates the equilibrium level of at + 1⋆ . □

Proposition 2. The equilibrium level of ht is an increasing function of the level of g

t .

Proof. Equating Eqs. (11) and (12), and rearranging gives,

ð1−αÞα

∫1a⋆t + 1 ð g t + 1 + aiÞdia⁎t + 1

−ð g t + 1 + a

⋆t + 1Þðτ

sð1−a⋆t + 1Þ + τ

ua⋆t + 1Þ−ðτ

s−τuÞ∫1a⋆t + 1 ð g + a iÞdiτs

= 0

Totally differentiating and rearranging gives the following

da⋆t + 1dg t + 1

= ð1−αÞð1−a⋆t + 1Þ =αa

⋆t + 1−τu = τs

ð1−αÞ½a⋆t + 1ð g t + 1 + a⋆t + 1Þ + ∫1a⋆t + 1

ð g + aiÞdiÞ =αa⁎2t + 1 + ðτ

sð1−a⋆t + 1Þ + τua⋆t + 1Þ = τs

Hence da⋆t + 1dg t + 1

b0 iff (1−α )(1−at + 1⋆ )/α at + 1⋆ bτ u/τ s. Solving the integrals in Eqs. (12) and (11), and rearranging shows that this will always bethe case in equilibrium. Thus a higher level of g t +1 implies a lower equilibrium level of at +1

⋆ and a higher level of ht + 1. □

Corollary 1. The equilibrium level of nt is a decreasing function of the level of g t .

Proof. This follows from Eq. (9) and Proposition 2. □

3.6. Growth dynamics in an economy with no migration

Proposition 2 shows that ht is an increasing continuous function of g t and from Eq. (11) g t + 1 is an increasing function of ht . Together theseimply the following rst order difference equation for the growth rate of technology,

g t + 1 = ϕðht ð g t ÞÞ ð14Þ

where from above it follows that d g t + 1/d g t N0.

The dynamic system may have multiple steady state equilibria. Multiple steady state equilibria are common in models of fertility and growthand can occur in the models of Becker et al. (1990), Barro and Becker (1989), Kremer and Chen (2002) and Moav (2005). It is important to note

that in this model it is not the case that all families in economies in low steady state equilibria converge to a low level of education. Rather, as in

Fig. 3. A unique equilibrium level of at + 1⋆ under no migration.



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Moav (2005), there will exist both educated and uneducated workers in rich and poor economies, but in different proportions. As d g t + 1/d g t N0

∀ g t it follows that steady state levels of g t will be either stable or unstable as depicted in Fig. 4.

4. The effect of brain drain migration on sending and receiving countries

In this section we describe the effects of a permanent brain drain on both the sending and receiving economies. We show that a brain draincan increase the growth rate in both the sending and receiving economies. We do this for each economy separately. In Section 5 we put the two

economies together andanalyze in a general equilibrium model the joint evolution of income per capita andpopulation in the world economy. Toaccount for the imperfect international mobility of labor we assume for simplicity that migration is limited to a proportion, x%, of the receivingeconomy's working population.13

4.1. The receiving economy

The permanent immigration of skilled workers to an economy will have both static and dynamic effects on the receiving economy. The staticeffect reduces the proportion of indigenous agents who choose to become skilled workers and this ceteris paribus increases the fertility rate. Thedynamic effect is for the receiving economy to converge to a new higher steady state growth rate. This has a positive effect on the proportion of

agents who choose to become skilled workers and a negative effect on the fertility rate. Thus if the dynamic effect outweighs the static effect, thelong run effect of the permanent immigration of skilled workers will be a raised level of human capital accumulation, a lower fertility rate and anincrease in the growth rate in the receiving economy. We demonstrate these results in the following subsections.

4.1.1. Static effects

The immigration of skilled workers to an economy will, ceteris paribus, decrease the equilibrium wage of skilled workers. This will, ceteris

paribus, reduce the proportion of indigenous agents who become skilled workers and so increase the fertility rate. Nevertheless the proportion of skilled labor in the economy, h, will increase as a result of the skilled immigration. This is shown in the following lemma and corollary where we

denote the equilibrium ratio of skilled to unskilled labor after the immigration of M skilled workers as hBD(M ), where M is x% of the receivingeconomy's working population.

Lemma 1. The immigration of M skilled workers ceteris paribus increases the equilibrium ratio of skilled to unskilled labor, with hBD(M) an increasing

function of M.

Proof. Using Fig. 5 and Eqs. (12) and (13). Under an inow of M skilled workers the equilibrium factor price ratio becomes

wLt + 1wH t + 1

= ð1−αÞ

α

∫1a⋆t + 1

ð g t + 1 + aiÞdi + M ð g t + 1 + a–

M Þ

at + 14 ð15Þ

Fig. 4. Growth dynamics under multiple steady state equilibria.

13 This is a simplifying assumption but one which we conjecture would be the equilibrium policy in a simple median voter political economy model of the receiving economy

where agents also receive utility from an exogenous public good such as land.

Fig. 5. For a given growth rate, skilled immigration reduces the proportion of indigenous agents becoming skilled.


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where a–M is the average ability level of the immigrating workers. Thus the factor price relationship (13) shifts upwards (i.e., the increasedsupply of skilled labor will increase the equilibrium level of wt

L+ 1 /wt + 1

H for every given level of at + 1⋆ ).

The relationship between w t L/wt

H and the optimal threshold level of at + 1⋆ for indigenous workers is not affected by the inow of skilled

workers. Thus as Fig. 5 shows, in equilibrium the optimal level of at at + 1⋆ rises but so does wt

L/wt H . Since wt

L/wt H =((1−α )/α )ht this implies that ht

also rises in equilibrium. □

Corollary 2. The immigration of skilled workers ceteris paribus increases the fertility rate, nt of the receiving economy.

Proof. From Lemma 1 we know that an inow of skilled workers will increase the optimal level of at + 1

⋆ and hence from Eq. (9) the corollary

follows. □

4.1.2. Dynamic effects

Forevery givenlevel of g t , Lemma 1 shows that theinowof x% skilled workers will increase the equilibrium level of ht . This will increase g t + 1 andso may lead ultimately to a fall in fertility in the receiving economy as the following lemma and corollary demonstrate.

Lemma 2. The permanent immigration of x% skilled workers increases the equilibrium growth rate of the receiving economy.

Proof. The inow of x% skilled workers increases the equilibrium level of ht . This implies that the dynamic equation now becomes g t =ϕ(ht −1( g t − 1, x)) where ht − 1 is an increasing function of both arguments. Thus as depicted in Fig. 6, a permanent immigration of x%skilled workers each period shifts up the function ϕ(ht −1( g t −1, x)) relative to ϕ(ht −1( g t −1, 0)) and so increases the steady state rate of growth. □

This implies that if the growth effect is suf

ciently strong, permanent skilled immigration can increase human capital levels and reduce thefertility levels in the receiving economy. This is shown in the following corollary.

Corollary 3. If the positive dynamic effect from permanentskilled immigration outweighsthe negative staticeffect then permanentskilled immigration

can increase human capital levels and reduce the rate of population growth in the receiving economy.

Proof. By example. Consider the economy where α =1/3, τ s=0.95, τ u=τ s/2, θ= 1/3. Then if g = 0.01 then at + 1⋆ = 0.819 and n = 1.188. If there

is a 1%inow of skilled immigrants eachperiod and g remains at 0.01 then at + 1⋆ rises to 0.820 and n rises to 1.189. If however there is a 1% inow

of skilled immigrants each period and g rises to 0.5 then at + 1⋆ falls to 0.817 and n falls to 1.186. □

4.2. The sending economy

The emigration of skilled workers may increase or decrease the growth rate in the sending economy. The loss of emigrating skilled agents will

ceteris paribus reduce the level of ht but the possibility of emigration will also increase the incentive to accumulate human capital. In this section

we demonstrate that the latter effect dominates the former if emigration is limited and the wage gain from emigration is suf

ciently high. This casehas been analyzed in the literature before, see forexample Mountford (1997) and Kanbur and Rapoport (2005), and the same intuition applies here.We will assume that the sending economy takes the immigration policy of the receiving economy as given, so that each level of x% of the

working population of the receiving economy translates into a maximum number, M , of emigrants from the sending economy. We denote thereceiving economy as economy A, and the sending economy as economy B. We will also assume that the ability to emigrate is randomly allocatedin the event that there is an excessof qualied candidates and so the probability of successful emigration, p, is equal to M t /(1−at + 1⋆ )N t B where N t Bis the population of the sending economy in period t .14, 15

Fig. 6. Dynamic effects of Brain Drain Immigration.

14 We are assuming that the receiving economy can only observe the level of education of an agent not his/her level of ability, ai.This is a common assumption in the literature —

see Beine et al. (2001, 2008) for discussions on this point.15 We do not model endogenous migration choices here, and so all agents in the less advanced economy would want to migrate to the more advanced economy. However the

migration choice could be made endogenous in this environment by introducing unobservable individual characteristics, such as differential migration costs, into the model. This

could take the form of a discount factor on foreign earnings distributed independently of ability (as, e.g., in Katz and Rapoport, 2005) or of a draw of lexicographic preferences for

location and earnings. This would not qualitatively affect our results. An illustrative example using the latter modeling strategy is available upon request.


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The factor market equilibrium condition under emigration now becomes:

wL;Bt + 1

wH ;Bt + 1=

ð1−αÞα

∫1a⋆t + 1

ð g t + 1 + aiÞdi−M ð g + ð1 + a⋆t + 1Þ = 2Þ

a⁎

24

35 ð16Þ

where (1+ at + 1⋆ )/2=āM is the average ability level of an emigrant and w t + 1

H ,B and w t + 1L,B are the skilled and unskilled wages in the sending

economy B.

The individual agents' decision problem is also changed by the possibility of emigration. A member i of generation t now optimizes thefollowing, taking factor prices and p as given:

c θt ðnt ½ð pw

H ; At + 1∫

1a⋆t + 1

ð g At + 1 + aiÞdi + ð1− pÞw

H ;Bt + 1∫

1a⋆t + 1

ð g Bt + 1 + aiÞdiÞ + w

L;Bt + 1a

⋆t + 1Þ

1−θð17Þ

where wt + 1H , A is the skilled wage in the receiving economy, economy A . This expression is maximized subject to the same budget constraint,

Eq. (7), and gives rise to the following optimality condition for at + 1⋆ :

wL;Bt + 1

wH ;Bt + 1=

ð pðwH ; At + 1 = wH ;Bt + 1Þð g

At + 1 + a

⋆t + 1Þ + ð1− pÞð g Bt + 1 + a

⋆t + 1ÞÞðτ

sð1−a⋆t + 1Þ + τua⋆t + 1Þ

τs

−ðτ

s−τuÞð pðwH ; At + 1 = wH ;Bt + 1Þ∫

1a⋆t + 1

ð g At + 1 + a

⋆t + 1Þ + ð1− pÞ∫

1a⋆t + 1

ð g Bt + 1 + aiÞdiÞ

τs

ð18Þ

Note that since wt + 1H , A

Nwt + 1H ,B this relationship implies a higher level of wt + 1

L,B /wt + 1H ,B forevery level of at + 1

⋆ than that in Eq. (12) for when thereis no migration.

Lemma 3. The possibility for M skilled workers to emigrate from the less advanced economy, B, to the more advanced economy A, increases the

proportion of agents who choose to become skilled in economy B.

Proof. Using Eqs. (16) and (18) and Fig. 3. Noting that an increase in M shifts down the factor demand relationship for wt + 1L,B /wt + 1

H ,B in Eq. (16)andthat the factorsupply relationshipfor wt + 1

L,B /wt + 1H ,B inEq. (18) isalwaysabove thatfor whenthere is nomigration inEq. (12), thenusing Fig.3

it follows that the equilibrium level of a* will be lowered by Brain Drain emigration. □

Corollary 4. The ability of M skilled workers to emigrate from the less advanced economy, B, decreases the fertility rate of economy B.

Proof. From Lemma 3 we know that an outowof M skilled workers will decrease the optimal level of at + 1⋆ in economy B and hence from Eq. (9)

the corollary follows. □Whether the emigration of M skilled workers raises the equilibrium level of h in economy B depends on whether the positive (incentive)

effect of an increase in human skill accumulation is stronger than the negative (dilution) effect of emigration. In the following proposition weshow that if wt + 1

H , A is suf ciently high for a given level of M then the level of h in economy B will increase.

Lemma 4. The possibility for M skilled workers to emigrate from the less advanced economy B to the advanced economy A increases the equilibrium

level of ht in economy B if the skilled wage in the advanced economy, w t+1H,A , is suf ciently large.

Proof. The factor demand relationship for wt + 1L,B /wt + 1

H ,B in Eq.(16)does not depend on wt +1H , A and is downward slopingin the (wt + 1

L,B /wt + 1H ,B ,a⁎) space.

Whereas the factor supply relationship for wt + 1L,B /wt + 1

H ,B in Eq. (18) does depend on wt + 1H , A . Eq. (18) can be rearranged to give,

wL;Bt + 1

wH ;Bt + 1=

ð pðwH ; At + 1 = wH ;Bt + 1Þ½ð g

At + 1 + a

⋆t + 1Þðτ

sð1−a⋆t + 1Þ + τua⋆t + 1Þ−ðτ

s−τuÞ∫1a⋆t + 1 ð g At + 1 + a

⋆t + 1Þdi

τs

+ð1− pÞ½ð g Bt + 1 + a

⋆t + 1Þðτ

sð1−a⋆t + 1Þ + τua⋆t + 1Þ−ðτs−τuÞ∫1a⋆

t + 1ð g Bt + 1 + a

⋆t + 1ÞdiÞ

τs ð19Þ

which implies that an increase in wt + 1H , A increases this relationship and so increases the equilibrium ratio wt + 1

L,B /wt + 1H ,B for a given level

of M . □

5. The evolution of the world economy

In Section 4 we considered the sending and receiving economies

separately.In this section we putthese twoeffects together andconsiderthe generalequilibriumof the world economy and the joint evolution of the world distribution of income per capita and population. We analyzethe effects of brain drain migration on this evolution. We assume a

world economy made up of two economies A and B where the

technological level in economy A is higher than that in economy B, i.e.

At AN At

B.16 We begin in Section 5.1 by describing the dynamics of

16 We focus on the asymmetric case where there is a signicant difference in

technology between the two economies. If the two countries were identical in every

respect, including initial conditions, then it would be indeterminate whether agentswould migrate from economy A to economy B or vice versa. However as long as there

is a suf cient difference in the technology levels between the two economies it will be

the case that agents migrate from the less advanced to the more advanced economy.


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technological diffusion in the world economy. In Section 5.2 we thendescribe the evolution of the world economy when there is nomigration. We show that if economies A and B are identical and tendingto the same steady state growth rate, then the world distribution of

income will be stable. However if economies are tending towardsdifferent steady state equilibria, due to innate differences acrosscountries, multiple steady states, or the pattern of international

trade,17 then although the world distribution of income per capita

across economies will be stable, the world distribution of populationwill diverge as poorer economies grow large in terms of population.18

In Section 5.3 we analyze the effects of brain drain migration on

the world distribution of income. We do this by highlighting threedifferent cases that can arise within our model, ranging fromdivergence (or human capital dilution) to convergence (or catching-up), and a third case where the brain drain can potentially createdivergence in the world economy while increasing human capital

accumulation in both the sending and receiving economies. We arguethat the current evolution of the world income distribution asdescribed by Sala-I-Martin (2006) can be seen as a combination of these three cases. Some large economies with low skilled emigration

rates may well be on a catching up trajectory while other economiesmay be losers or only temporary gainers.

5.1. Technological diffusion in the world economy

We assume, in the spirit of Findlay (1978) and Nelson and Phelps(1966), that frontier technology diffuses from the most advancedeconomy, A, to the less advanced economy, B, with a lag.19 In keeping

with the discussion in Section 1 we assume that this diffusion of technology raises the level of technology and increases the produc-tivity of both skilled and unskilled labor in an unbiased manner. Thiscontrasts with the growth of frontier knowledge which followingGalor and Moav (2000) is assumed to be skill biased.20 We follow

Findlay (1978) and Nelson and Phelps (1966) in assuming that therate of diffusion is positively related to the size of the gap between thetechnological levels in the two economies, A A− AB, that is:21

ABt = A

Bt −1ð1 + g

Bt Þ + λð A

At −1− A

Bt −1Þ ð20Þ

where λ N ¯ g B. As economies A and B tend to their steady states, theirgrowth rates g t

A and g t B will tend to their constant steady state growth

rates, ¯ g A and ¯ g B:

5.2. Evolution of the world economy under no migration

In this section we show that if economies A and B are identical andtendingto a unique steady state growthrate thenthe world distribution

of income will be stable. This is shown in proposition 3. However if economies are tending towards different steady state equilibria, thenalthough the world distribution of income per capita across economies

will be stable, theworld distributionof populationwill divergeas poorer

economies grow large in terms of population.Proposition 3. If economies A and B are identical except for their initial

levels of population and technology and are converging to the same

steady state rate of growth, i.e. ¯ g At = ¯ g Bt , then the world will converge

to a stable equilibrium, with a stable income distribution and a constant

proportion of the world population in each economy.

Proof. By assumption both countries will have the same steady stateequilibrium growth rate of technology, i.e. ¯ g A = ¯ g B and so will havethe same equilibrium levels of human capital accumulation and

fertility. When both economies have attained their steady stategrowthrates, Eq. (20) can be iterated forwardto show that in the limit

At A= At

B and so there is no tendency for levels of technology in the twoeconomies to diverge. Thus the proposition follows. □

Proposition 4. If economies A and B are tending to different steadystaterates of growthwhere ¯ g At N ¯ g

Bt but are otherwise identical, then the long

run world distribution of income per capita across economies will be

stable butthe world distribution of population will be divergent as poorer

economies grow large in terms of population.

Proof. When both economies have attained their steady state growth

rates Eq. (20) can be iterated forward to show that in the long run thetechnological level of economy B tends to a constant fraction of that of economy A,

ABt =

λ

λ + ¯ g A− ¯ g B A

At ð21Þ

Thus the ratio of the technology levels in the two economies will bestable. Given that both economies will also tend to a steady state level of

g and h this implies that the ratio of per capita income in the twoeconomies will also be constant. The fertility rates in the twoeconomies,however, will be different since ¯ g At N ¯ g

Bt . From Proposition 2 and

Lemma 1 the rate of population growth in economy B will be higher

than that in economy A and so economy B will grow large in terms of population.

5.3. Evolution of the world economy under brain drain migration

In this section we focus on three cases to illustrate the potentialeffectsof thebrain drain on the world distribution of income. Werstshow howa brain drain can cause divergence in the world economy by causing two

economies that would otherwise converge to the same steady state levelof income and rate of population growth to diverge. We next show that if the brain drain increases the level of human capital in the sendingeconomy suf ciently, it is also possible for the brain drain to enable an

economy on a lower steady state growth path to catch up with aneconomy on a higher steady state growth path. Finally we alsodemonstrate the possibility for a brain drain to decrease the skill ratio inthe sending economy. While the early literature focused on the last of

these cases (i.e., a brain drain being detrimental to thesendingeconomy—see, e.g., Bhagwati and Hamada (1974)), the evidence presented above inSection 2 suggests that all three cases may be present in the worldeconomy.

We rst consider the case where brain drain migration causes adivergence with human capital gains in both economies. If there is

brain drain migration, Proposition 3 no longer holds and so two

17 Appendix A describes how the model can be adapted to incorporate international

trade effects.18 In the analysis in this section we mainly focus on the equilibrium where the world

population has a divergent long run equilibrium with the population growth in the

sending economy higher than that in the receiving economy. However it is also

possible for a steady state to exist where the difference in fertility rates between the

two economies is exactly offset by migration so that the population growth in both the

sending and receiving economies is the same.19 See Keller (2001) for evidence on the importance of technological diffusion for

technology growth in developing economies.20 As explained in our Introduction, we make the assumption that increases in

technology due to diffused technology are skill-neutral whereas increases in the

growth of frontier knowledge are skill biased. This assumption is consistent with the

argument of Galor and Moav (2000) who argue that the empirical evidence supports

the view that the dynamism associated with new technologies is skill biased so that

skilled workers earn relatively more in economies where new technologies are being

generated, while the level of technology is modeled as being skill-neutral (i.e., over

time technology becomes adapted so that all skill levels' productivity is increased).

Thus when considering the issue of international technological diffusion one has a

choice between regarding diffused technology as being adapted technology which isskill neutral or as being frontier technology and so skill biased. In this paper we think it

is more reasonable to think of diffused technology as older adapted technology and so

treat it as skill-neutral.21 See Basu and Weil (1998) for a discussion of the issue of different types of

advances in technology and on the importance of appropriate factor endowments for

technology diffusion.


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identical economies that would otherwise converge to the samesteady state equilibria can converge to different steady state equilibriaas a result of brain drain migration. In this case the brain drain will

have caused a divergence in the world economy and will have in-creased world inequality of income. It should be stressed howeverthat in this case the brain drain will also have increasedthe world rateof growth and so increased long run income levels in all economies of

the world. This is demonstrated in the following proposition andcorollaries:

Proposition 5. If economies A and B are identical except for their levels

of population and technology, where At AN At

B, the probability of emigra-

tionis suf ciently low andthe permanentskilled immigration reduces the

rate of population growth in the receiving economy as in Corollary 3,

then the equilibrium of the world economy will be stable and have the

following properties:

(i) a permanent brain drain migration of agents from economy B toeconomy A

(ii) the level of output per capita in economy B will be a constant fraction of that in economy A

(iii) a higher rate of population growth in economy B than in economy A.

Proof. As the probability of emigration is suf cientlysmall, fromEq. (17),economy B tends to its autarkic equilibrium. From Lemma 2 this impliesthat g AN g B. If the permanent skilled immigration reduces the rate of population growth in the receiving economy as in Corollary 3, then

economy A's rate of population growth will be below that of economy B.Thusthe equilibrium is stable: economy A will maintainits leadin frontiertechnology while economy B will maintain its lead in population size. □

Corollary 5. Long run income inequality between countries is increasing

in the rate of brain drain migration in the equilibrium described in

Proposition 5.

Proof. Economy B is close to its autarkic equilibrium and so ht B can be

treated as a constant and hence g B and λ are constants also. In the longrun ht

A and g A can also be treated as constants and hence Eq. (20)holds. It follows that the ratio of At

B/ At A declines when g A increases. □

Corollary 6. Worldgrowth is increasing in therateof brain drain migration

in the equilibrium described in Proposition 5.

Proof. Growth in economy A will increase from Lemma 2 and growth

in economy B will increase from the technology diffusion Eq. (20). □

Finally one should emphasize that Corollary 3 is a suf cient but not anecessary condition for such an equilibrium to be locally stable. If economies A and B differ for exogenous reasons, such as multiple steady

state equilibria, so that under no migration g AN g B, then it follows fromCorollary 1 thatthe rate of populationgrowthin economyB is greater thanthat in economy A. Brain drain migration will thus reinforce the pattern of relative technological growth rates. If Corollary 3 does not hold, the brain

drain will work against the pattern of relative population growth rates,however as long as the population growth rate in economy B remainsgreater than that in economy A then the equilibrium will still be stable.

We illustrate this case in Fig. 7 where we simulate the evolution of

the world income distribution for the case where the initialtechnological levels in the two economies are A A=10 and AB=3.33,the level of immigration into A is 0.1% of A's working population,

α =1 /3 , θ =1 /3 , τ s , A =0 .8 5 , τ u , A =0 .6 , τ s , B =0 .9 5 , τ u , B =0 .5 ,

N A= 10,000 and N B=10,000.

Finally the dynamic equations are set suchthat economy A isaboveadynamic growth threshold so that g t + 1

A =(ht A)0.5 while economy B is

below a growth threshold so that g t + 1B =(ht

B)0.5/1000 (i.e., frontier

growth in economy B is practically zero). The technological diffusionparameter is set to follow λ=0.3+ht −1

B . Brain drain migration beginsin period 6. The simulations show that the brain drain causes the skillintensityto rise in economy A whichquicklyconverges to a new steady

state. The skill intensity in economy B also risesas the incentive to investin human capital is high since the technological difference between Aand B is large while the actual numbers leaving economy B is small. This

situation is stable as the population growth rate of economy B is higherthan that of economy A. The incentive to invest in human capital ineconomy B falls as the probabilityof successfully emigratingfalls. In thelimit economy B returns to its autarkic skill intensity while economy A

remains at itsnew higher skill intensity. Although in the long runworldinequality will havebeen increased, as Fig. 7 shows,it could well be thatin the short run, the brain drain will have caused a temporary decreasein world inequality due to the increased skill accumulation in the

sending economy. Despite increasing world inequality, by increasingthe world rate of growth, the brain drain will also have increased thelong run income of all agents in the world via technological diffusion.22

However this case need not occur for all economies. It is also

possible for the brain drain to enable an economy on a lower steadystate growth path to catch up with an economy on a higher steadystate growthpath. Consider the case depicted in Fig. 8 where economyA and B are precisely the same except that Economy A is at a higher

Fig. 7. A brain drain with increased human capital accumulation in both the sending and receiving economies but with divergence in the world economy as the sending economy

grows large in population size. The dashed lines represent the evolving human capital intensity, ht , in each economy in response to Brain Drain Migration, and the horizontal lines

show the steady state level of ht before migration in the relevant economy. The vertical line in each graph shows the time period after which migration begins.

22 This contribution of brain drain migration to a global public good (knowledge,

technological progress) was emphasized by Grubel and Scott (1966).


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steady state equilibrium level of h which implies a higher steady state

level of growth. If the brain drain increases the level of h in economy Bso that it rises above the unstable steady state equilibrium level of hthen economy B will converge to a new higher steady state rate of growth. This is the case shown in Fig. 8.23

Finally for some countries the dilution effect of a brain drain willdominate the incentive effects and so a brain drain can also reduce theskill intensity in the sending economy. This case is depicted in Fig. 9.

As implied by Lemma4, if the technological gap between economies issmall, as is the case between developed economies, there is little extraincentive to accumulate human capital in the sending economy inorder to migrate. Nonetheless, skilled agents will still emigrate sincewages are higher in the more advanced economy, hence the sending

economy will experience a reduction in its equilibrium skill intensity.A counterfactual aspect of the model is that when the technologicalgap between sending and receiving countries is large, then humancapital depletion does not occur except at very high probabilities of

successful migration where the population of the sending economy

declines signicantly. Nevertheless, human capital depletion wouldstill occur in less advanced economies at lower rates of skilledemigration if the extra incentive to accumulate human capital in orderto migrate was counteracted by the inability of the sending economy

to easily expand its education provision.24 This could be due, forexample, to credit constraints on human capital and migrationinvestment, as we suggested in Section 2 to explain the lower skilled

emigration rates in the poorest countries.Thus the Brain Drain can have a positive or negative effect on

human capital accumulation in the sending economy depending onthe relative strengths of the incentive (or brain gain) and dilution (orbrain drain) effects. 25 This is consistent with the empirical analysis of

Beine et al. (2008) whose counterfactual simulations suggest the

Fig. 8. Catching up dynamics in the sending economy due to brain drain migration. The dashed l ines represent the evolving human capital intensity, ht , in each economy in response

to Brain Drain Migration, and the horizontal lines show the steady state level of ht before migration in the relevant economy. The vertical line in each graph shows the time period

after which migration begins.

23 In this simulation α =1/3, θ=1/3, τ s, A= τ s,B=0.85, τ u, A = τ u,B=0.6, and

N A=N B=10000. Finally the dynamic equations are set such that economy A is abovea dynamic growth threshold so that g t +1

A =0.75 while economy B is below a growth

threshold so that g t +1B =0.7 and the technological diffusion parameter is set to follow

λ=0.7.

Fig. 9. Human Capital Depletion in the sending economy due to brain drain migration. The dashed lines represent the evolving human capital intensity, ht , in each economy in

response to Brain Drain Migration, and the horizontal lines show the steady state level of ht before migration in the relevant economy. The vertical line in each graph shows the time

period after which migration begins.

24 In this simulation α =1/3,θ=1/3, τ s, A=0.85,τ u, A=0.6, τ s,B=0.798,τ u,B=0.539,

and N A=N B=10,000. Finally the dynamic equations are set such that economy A is

above a dynamic growth threshold so that g t +1 A =0.72 while economy B is below a

growth threshold so that g t + 1B =0.7 and the technological diffusion parameter is set to

follow λ=0.7.25 Scenarios 1, 2 and 3 above were generated by altering the difference in the

technology levels between the two economies. However the size of the incentive effect

relative to the dilution effect will also be affected by other variables in the system, such

as the level of x and the relative population sizes.




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brain drain is associated with a net increase in human capitalaccumulation in some countries and a net decrease in (a majority) of others. Interestingly, the winning countries in their sample includecountries such as China, India, Indonesia, or Brazil, which together

represent more than 80% of the sample population. Again, theimplication for the world distribution of income is that brain drainmigration will accelerate the rate of convergence of the main

globalizers, at least in the short run, and further marginalize small

countries with high skilled emigration rates, typically Sub-saharanandCentral American countries. If anything, theimplied impact on theworld distribution of income will strengthen the trends predicted by

Sala-I-Martin (2006): a decrease in global inequality in the next fewdecades as India, China and other Asian countries catch up, and then arenewed increase in global inequality as the presence of divergingcountries will become increasingly palpable.

6. Conclusion

This paper develops a model for the joint evolution of the worlddistribution of income per capita and the world distribution of

population. It shows that even if the distribution of income per capitaof economies in the world is stable in the long run, the worlddistribution of income may be divergent due to differences inpopulation growth rates. Brain drain migration may exacerbate thispotential for divergence in the world economy, although it should be

stressed that while brain drain migration patterns can increaseinequality in terms of income per capita between countries and skewthe world distribution of income towards the poorer economies with

higher rates of population growth, the brain drain is also likely toincrease the growth rate of income per capita in both the sending andreceiving economies.

The paper shows that the emergence of the brain drain as a

dominant pattern of international migration is likely to reinforce thecurrent evolution of the world income distribution as described bySala-I-Martin (2006) through a combination of the three casesdescribed in Section 5. In the short run it is possible for world

inequality to fall due to rises in GDP per capita in large developing

economies with low skilled emigration rates (e.g., India, China) but inthe long run, inequality in the world distribution of income mayincrease as the countries which lose from the brain drain will also

grow large in terms of population.

Acknowledgements

Hillel Rapoport acknowledges the support of the Agence Françaisede Développement and of the Adar Foundation at Bar-Ilan University.

We thank participants at the Development Workshop, UniversitéCatholique de Louvain, the Minerva DEGIT XI Conference in Jerusalem,

the Globalization and Brain Drain Conference at Bar-Ilan and HebrewUniversities, for their comments, with special thanks to Eran Yashivand Raouf Boucekkine. All remaining errors are our own.

Appendix A. The relationship to the effects of international trade

The analysis in this paper is complementary to the recent work on

the different implications of international trade for human capitalaccumulation and fertility in technologically advanced and lessadvanced economies. Notably Galor and Mountford (2006, 2008)have shown how international trade, by increasing the demand for

skilled-intensive goods in the technologically advanced economies,increases the demand for skilled labor and so increases human capitalaccumulation and reduces fertility in technologically advancedeconomies. Conversely in the less technologically advanced econo-

mies international trade increases the demand for unskilled-intensivegoods which increases the demand for unskilled labor and so reduces

human capital accumulation and increases fertility. In terms of the

analysis in this paper, for the less advanced economy international

trade can be thought of as shifting the demand for human capitalinwards so that there is a lower level of ht for any given level of g t and so a downward shift in the growth dynamics relationship g t + 1 =

ϕ(ht ( g t )) in Fig. 4.To see this consider a simple two sector model of the economy

described in Section 3 where there is a human capital intensive good,

Y t , produced with the same technology as in Section 3.1.

Y t = At H αt L

1−α y;t ð22Þ

and an unskilled good X t produced with a linear technology

X t = At L x;t ð23Þ

where L y,t + L x,t = Lt .If preferencesare also adapted to the two sector framework so that

ut = c x,t η c y.t

θ dt + 11− θ− η where c i,t is the consumption of good i at time

t , i = X , Y , then it is easily shown that in autarky the relative price of good X in terms of good Y , pt , is given by (1−α )h y,t α , where h y,t is nowH t /L y,t and that the proportion of unskilled labor working in sector X ,

L x,t /Lt is a constant which is increasing in η , the budget share of theunskilled labor intensive good. This implies that the labor marketdemand curve becomes wLt = w

H t =

ð1−αÞα

h y;t = ð1−αÞ

α ht :L = L y;t . Thus

the higher the budget share of the unskilled intensive goods, η , the

more the demand curve shifts out in Fig. 3, and so the higher theequilibrium level of a⁎ and the lower equilibrium skill intensity in theeconomy. This is intuitive. In terms of the growth dynamics a highervalue of η implies a lower human capital intensity for every given

level of g t and so a lower steady state level of growth, ceteris paribus.Consider now the case of a small open economy operating at a world

price ratio, p⁎, which is greater than autarkic price. In international tradeequilibrium this implies that h y,t will rise and that the equilibrium wage

ratio wt L/wt

H will also rise. The factor demand line for the small openeconomy will be a horizontal line at the increased level of wt

L/wt H which

will imply a higher equilibrium level of a* and a lower equilibrium skill

intensity in the economy. This also is intuitive. The increased demand for

unskilled labor caused by international trade affects the economy in thesame way as increased domestic demand for unskilled goods, it reducesequilibrium human capital intensity and, ceteris paribus, equilibrium

growth.Thus the analysis in this paper on the potentially uneven effects of

migration patterns on the world distribution of income are comple-mentary to the effects of international trade. Indeed a pattern of

international trade where a less technologically advanced economyspecializes in unskilled intensive goods gives an additionalreasonwhy atechnologically less advanced economy will have a higher fertility rateand lower rate of growth under no migration, which supports the

uneven evolution of the world economy described in Proposition 5.

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