Skilled migration, human capital inequality and
convergence
Michel Beinea , Cecily Defoortb and Frédéric Docquierc
a
b
University of Luxemburg and Université Libre de Bruxelles
CADRE, University of Lille 2 and IRES, Catholic University of Louvain
c
FNRS and IRES, Catholic University of Louvain
November 2005
Abstract
In this paper, we analyze the evolution of human capital inequality across nations, and the
impact of the mobility of talented workers on the international distribution of human capital.
We derive testable predictions from an stylized theoretical model and then test them using
an original panel data set on international migration by educational attainment. We obtain
conditional convergence of schooling indicators over the period 1975-2000, with a relatively
high speed of convergence. Hence, the current distribution of human capital is not far from
the steady state distribution. Our findings also reveal that skilled migration fosters education
in intermediate income countries. The brain drain thus increases human capital disparities
between poorest and richest countries. However, skilled migration induces long-run beneficial
effects in 23 intermediate income countries.
JEL Classification: O15-O40-F22-F43
Keywords: Human capital, Convergence, Brain drain
1
Introduction
An undeniably stylized fact of the last 50 years is that, with a few exceptions, the poorest countries
of the world did not catch up with the industrialized nations in any meaningful way. Polarization
in incomes and growth rates suggest that the world growth process departs from the predictions
of the one-sector, convex model with complete markets (see Azariadis and Stachurski, 2005).
Although a considerable amount of research has been devoted to the understanding of growth and
development, economists have not yet discover how making poor countries richer. In this quest
for growth, human capital has usually been considered as the right answer.
Although the literature of the 1990’s has fuelled a growing skepticism about the role of schooling1 , recent empirical investigations of the contribution of human capital accumulation to long-run
growth are quite optimistic. De la Fuente and Domenech (2002) provided evidence that these counterintuitive results can be attributed to deficiencies in the data. After correcting for substantial
measurement errors, they estimate that human capital accounts for about 50 percent of the productivity differentials between OECD countries. Using direct measures of human capital based on
literacy scores (which outperform measures based on years of schooling), Coulombe and Tremblay
(2005) find a positive and highly significant effect of human capital on both transitory growth
transition path and long-run levels of productivity and GDP per capita. In a sample including
developed and developing countries, Cohen and Soto (2001) show that using ”good data” gives
”good results”.Improving human capital indicators, they obtain a macroeconomic return to schooling which is compatible with the microeconomic return derived from traditional survey data (i.e.
9 percent per year of schooling).
Benhabib and Spiegel (2002) and Aghion and Howitt (2005) provide another story. In a
Schumpeterian model of innovation and technology adoption, they show that the world long-run
growth rate is essentially determined in the leading economies. In these leading countries, human
capital determines the pace of technological progress. In the rest of the world, human capital
favors the country ability to innovate and to implement technological discoveries from the leaders.
However, since the long-run growth rate is exclusively determined by the leaders, there is no longrun relationship between the followers’ level of human capital and long-run growth. Anyway, the
country-specific level of schooling determines the distance to the technological frontier.
Our analysis builds on the fact that education is an imprortant determinants of inequality
across nations. We have two major objectives. First, we want to characterize the evolution
of human capital disparities over the last decades. Second, we want to examine whether skilled
migration has made the distribution of human capital more unequal. We address the latter issue in
the framework of the new literature on the brain drain.This literature puts forward that high-skill
migration entails beneficial feedback effects for the source countries. In particular, several authors
such as Stark et al. (1998), Vidal 1998), Mountford (1999), Beine et al. (2001, 2003), Stark and
Wang (2002) argued that migration prospects may foster education investments in developing
countries, thus making it possible for a brain drain to be beneficial to the source country (i.e., the
country may end up with a higher level of human capital after emigration is netted out). Their is
a great deal of anecdotal evidence that migration prospects indeed impact on people’s decisions
to invest in higher education. For example, in their survey on medical doctors working in the UK,
1 Human capital frequently turn out to be insignificant or to have the ”wrong” size. As a result, authors such as
Pritchett (1999) were tempted to reconsider the role of education on productivity growth.
2
Kangasniemi et al. (2004) report that about 30% of Indian doctors surveyed acknowledge that the
prospect of emigration affected their effort to put into studies; Commander et al. (2004) provide
clear indications that the software industry’s booming has been met with a powerful educational
response, partly related to migration prospects. Lucas (2004) argues that the choice of major
field of study (medicine, nursing, maritime training) among Filipino students respond to shift in
international demand.
Basically, we start from a stylized theoretical that which predicts persisting human capital disparities across countries. We distinguish the predictions on natives’ and residents’ human capital.
In intermediate income countries, skilled migration has a positive impact on natives’ education
choices (incentive effect) and an ambiguous impact on residents’ level of human capital. In very
poor and high-income country, we demonstrate that the incentive effect is likely to small. We also
show that our model is compatible with the fact that, despite considerable progress in educational
attainment, the poorest countries of the world did not catch up with high-income nations in terms
of GDP per capita.
Then, we the use data on education attainment over the period 1975-2000 to test these predictions. To account for the potential ”incentive effect” of migration prospects on human capital
formation in the source countries, human capital is measured as the proportion of skilled among
natives, rather than among residents. In a second step, the stock of human capital among residents
can be predicted by dropping out emigrants from natives. Based on a cross-section β-convergence
model, our results provide some support in favor of a convergence process. Nevertheless, the rate
of convergence is quite low, slightly above 1 percent per year, meaning that almost a century is
necessary for the human capital levels to converge to the same long run levels. As cross-section
results are subject to important mispecification bias (see Islam, 1995), we then use panel models
and control for unobserved heterogeneity. Our panel results reveal strong persistant disparities
in the long-run level of human capital, and a convergence speed which reaches 14 percent a year
suggesting that countries need on average 7 years to reach their long run human capital level.
Does the brain drain make the distribution more unequal? Empirically, cross-section empirical
studies by Beine et al. (2001, 2003) confirm that migration prospects have a positive and significant
impact on human capital formation between 1990 and 2000. Depending on the magnitude of the
migration rate and initial human capital stock, the ex-post response (after migration is netted
out) can be positive or negative. Mariani (2005) shows that the GDP growth rate is positively
affected by the skilled migration rate in countries where the middle class is sufficiently large. The
limit of these studies is that, due to data availability, they rely on cross-country regressions. They
fail at capturing the strong heterogeneity between countries; the exact causality between human
capital formation and skilled migration is not easy to detect. Here we extend these studies by
using original panel data on skilled migration over the period 1975 to 2000. Focusing on six
major destination countries (USA, Canada, Australia, Germany, UK and France), we compute
skilled emigration stocks and rates from all the world countries (one observation every 5 years)2 .
Both cross-section and panel tests show that skilled migration affects the long-run levels of human
capital among natives in intermediate income countries. As predicted by our theorectical model,
the effect is not significant in poor and rich countries. Relying on counterfactual experiments, it
2 Our methodology builds on Docquier and Marfouk (2005) who focus on the 30 OECD receiving countries but
provide 2 observations (1990 and 2000).
3
comes out that skilled migration has a positive global impact on human capital in a large number
of countries. Among the 33 medium income countries, the brain drain stimulates residents’ human
capital in 23 cases.
The structure of the paper is organized as follows.Section 2 describes a theoretical model characterizing human capital disparities across nations and explaining the effect of skilled migration.
In section 3, we present the data and empirical results. In Section 4, we use counterfactual experiment to simulate the impact of skilled migration on the average years of schooling among
residents. Finally, section 5 concludes.
2
Theory
In this section, we analyze the determinants of human capital in a model with heterogeneous agents.
We consider a developing economy populated by two-period lived heterogeneous individuals. The
proportion of individual opting for education is endgenous and determines the wage rate through
an externality. Labor if the only factor of production and the production function is linear. We
first characterize the closed economy equilibrium and then examine the effect of skilled emigration.
At each period t, a composite good is produced according linear production function. GDP per
capita is given by
yt = wt ht
(1)
where ht is the total labor force in efficiency unit, and the wage rate per efficiency unit of labor,
wt ≥ 1, is non decreasing function of the average level of human capital among adults, ht . This
spillover effect summarizes all the intergenerational externalities associated to human capital.
Young individuals offer one unit of human capital and earn a wage wt . However, they have the
possibility to spend a part of their income into education. There is a single education program and
individuals are heterogenous in their ability to learn. They are characterized by different education
costs, with high-ability individuals incurring a lower cost. The cost of education is expressed as
a proportion of the wage rate of teachers (considered as skilled workers). For a type-c agent is
denoted by
αcwt ηt
(2)
with α is the non subsidized proportion of education expenditure, ηt is the skill premium at period
t. Normalizing the number of efficiency units offered by an unskilled adult to one, an educated
adult offers ηt such units. The variable c distributed on [0, 1] according to a uniform density.
When adult, individuals offer all their time on the labor market with heterogeneous abilities
to produce. The economy-wide average level of human capital of the adults, ht , is a function of
the proportion of skilled workers in that generation, πt . We have ht = 1 + πt (ηt − 1).
To model the effect of human capital on productivity, we assume a threshold externality:
wt =
© ξt
if ht < h∗
w(ht ) if ht ≥ h∗
(3)
where h∗ < ηt is the threshold level of human capital above which the economy exit out the poverty
trap; ξt is a random iid process of unitary mean, constant variance and cumulative distribution
F (ξ)3 . The random component ξt has a double effect in our model. It first depicts the stonger
3 Typically,
we can consider a lognormal process: ln ξt+1 Ã N (0, σ)
4
volatility of output in poor countries. Second, it captures productivity shocks that can lead to
growth miracles despite bad historical conditions.
Above the threshold h∗ , the wage rate is an increasing and concave function of ht such that
e
e
w(h∗ ) ≥ 1.The expected future wage amounts to wt+1
= E(ξt+1 ) = 1 if ht+1 < h∗ and wt+1
=
h∗ −1
∗
∗
∗
w(ht+1 ) if ht+1 ≥ h . Note that the condition ht ≥ h can be rewritten as πt > π ≡ ηt −1 which
is lower than one.
There is no saving so that the utility depends on the first and expected second-period incomes.
For simplicity, utility is log-linear and there is no time-discount rate. We have
e
)
uec,t = ln(y1,t − µ) + ln(y2,t+1
(4)
where µ is the level of subsistence when young.
2.1
Human capital diasparities across countries
Individuals choose their education so as to maximize their expected utility. The expected lifetime
income for an uneducated agent is
e
uec,t = ln(wt − µ) + ln(wt+1
).
(5)
By contrast, the lifetime income for an educated agent is
e
e
uec,t = ln(wt − cαt wt ηt − µ) + ln(wt+1
ηt+1
).
(6)
Clearly, education is worthwhile for individuals whose education cost is lower than a critical value.
The condition for investing in education in an economy with no migration (henceforth denoted
using the subscript n) is:
c < cn,t ≡
e
−1
wt − µ ηt+1
×
e
αt wt
ηt ηt+1
(7)
e
,
which is an increasing function of the local wage rate wt and of the expected skill premium ηt+1
but a decreasing function of the current skill premium ηt and of the share of education supported
by individual αt (one minus the subsidy rate). Note thqt in the steady state, cn,t increases in η
when η is lower than 2. We then assume ηt ∈ [1, 2] in what follows. Moreover, the proportion of
e
educated is independent on the expected wage rate wt+1
Without migration, the proportion of educated adults is given by the lagged proportion of the
young opting for education, πt = cn,t−1 and the average level of human capital is given by
ht = 1 +
wt−1 − µ
ηe − 1
× t
× (ηt − 1)
αt−1 wt−1
ηt−1 ηte
(8)
Since wt−1 is determined by ht−1 at least in countries where the lagged level of human capital
exceeds h∗ , the previous equation determines the dynamics of human capital. For constant skill
premia and subsidy rates, we have:
ht =
© 1+
1+
ξt−1 −µ
αξt−1
³
×
w(ht−1 )−µ
αw(ht−1 )
η−1
ηη
³
×
5
´2
η−1
ηη
´2
if ht−1 < h∗
if ht−1 ≥ h∗
(9)
Figure 1: Multiple steady states without migration.
This dynamic function is likely to give rise to multiple steady states. Two steady states can
be observed: a poverty trap with ht −→ hss (South equilibrium) and a high steady state with
ht −→ hss (North equilibrium). If w(h∗ ) = 1 and if South and North countries exhibit the same
education policies and skill premia, then the threshold h∗ determines the basins of attraction
of both equilibria (see Case1 on the left panel). If w(h∗ ) > 1 or if South and North countries
exhibit different characteristics, there can be a jump in the dynamic function so that the basin of
attraction of the South equilibrium (under w(h∗ ) = 1, we had h0 = h∗ )
Given the random shock ξt , countries are not deterministically stuck in the poverty trap. Even
when ht−1 < h∗ , a poor country can exit out a poverty trap by experiencing a large productivity
³
´2
0
t −µ
× η−1
> h . Such a take-off (growth miracle) occurs with a probability
shock such that 1+ ξαξ
ηη
t


³
´2
η−1
µ
ηη


1 − F ³

´2
0
η−1
−
α(h
−
1)
ηη
(10)
0
which is increasing in η but decreasing in h , α and µ.
Except for large random shocks, there are sell-reinforcing mechanisms which cause poverty to
persists. Realistically, poverty traps in human capital formation are likely to be the rule and one
should not expect human capital disparities to vanish in the long-run.
2.2
Human capital convergence
Although long-run disparities are clearly predicted by our model, the magnitude of these disparities
is clearly endogenous and can vary over time. How can we explain that despite considerable
progress in educational attainment, the poorest countries of the world did not catch up with highincome nations? Our model provides several explanations to that paradox: some are valid in the
long-run, others are valid in the short-run. Let us denote the leading countries by a upper bar
ss −µ
≈ α1 (the
and suppose that their wage rate wss is much larger than µ so that we can write wαw
ss
minimum of subsistence does not matter in the North).
In the long run, i.e. without random shock and under constant policy and skill premia, the
6
North-South ratio in the proportion of educated are given by:
³
´2
η−1
1
µ
¶
1
+
×
α
η
hss
E
≡
³
´2
hss
1−µ
η−1
1+ α × η
While the ratio of GDP per capita is given by
µ
¶
µ
¶
y ss
hss
E
= w(hss )E
yss
hss
(11)
(12)
In the long-run, both ratios evolve in the same way. The GDP per capita gap is higher than the
human capital gap as w(hss is higher than one. Long-run partial convergence in human capital
occurs when η and α increase or when η and α decrease. In other words, partial convergence is
obtained when the education policy becomes more generous and when the skill premium increases
in the South (relatively to the North). Opposite changes lead to higher disparities. Note that the
ratio of
a decrease in the ratio of human capital. We have
³ despite
³ GDP
´ per capita can increase
´
ss
d ln E yyss
= d ln w(hss ) + d ln E hhss
.
Suppose
a rise in both levels of human capital but a
ss
³ ´
is negative but d ln w(hss ) is positive. If the wage
stronger rise in the South. Then d ln E hhss
ss
externality d ln w(hss ) is sufficiently high, the ratio of GDP per capita increases.
In the short-run, many shocks can generate a temporary convergence in human capital while
increasing the long-run disparities. For illustrative purpose, assume that the skill premium in the
North follows a random walk with unexpected shocks. North shocks are then partly diffused to
the South with a lag of one period. Hence, although technological shocks are unexpected in the
North, they can be expected in the South. The dynamics of skill premium can be described by
ηt
=
η t−1 + ²t
ηt
=
ηt−1 + δ²t−1 + ²t
with ²t and ²t , two iid processes of zero mean and constant variance.
Assume a positive shock in period 1, ²1 > 0. From period 2 onwards, the level of human capital
increases and wages increase in the North (as the expected return to education increases at time
1). In period 1, a moderate effect is also observed on GDP per capita since the productivity of the
educated rises. In the South, the rise in investment is stronger in period 1 since the young expect
a higher return to education but pay the same cost (teachers’ wage are low at time 1). Hence,
a temporary convergence in human capital can be observed in period 2 although divergence is
observed in the long-run (as the rise in skill premium is partly diffused in the South country).
Here again, the disparities in human capital and GDP per capita are likely to evolve differently
on the transition path.
2.3
Skilled migration and human capital convergence
It is usually argued that the brain drain (from poor to rich countries) makes rich countries richer
at the expense of the poor. Although skilled migration is likely to generate multiple effects on the
sending economy4 , we focus here on the impact of the brain drain on human capital disparities.
4 The total impact of the brain drain depends (i) on the fiscal impact of emigration (skilled emigrants are likely
to be the net contributors to the government budget), (ii) on the likelihood of future return migration, (iii) on the
7
In poor countries, the incentives to educate are low. The main reason is that, due to technological and institutional characteristics, domestic returns to education are small. However, given the
recent evolution of immigration policies in rich countries, education is more and more considered as
a passport for emigration. As candidates leave nothing to chance, migration prospects may affect
the expected return to education and induce them to educate more. Then, given quota systems
and various types of requirements and restrictions imposed by immigration authorities (such as
the point systems), there is a probability that the migration project will have to be postponed or
abandoned at all stages of the immigration process. Individuals engaging in education investments
with the prospect of migration must therefore factor in this uncertainty, creating the possibility
of a net gain for the source country.
Let us now examine the impact of skilled migration on poor economies. Indeed, if the economy
is at the good equilibrium, nobody wants to emigrate. Suppose the sending country is stuck in
the poverty trap but agents have now the possibility to emigrate to a rich economy where w = w.
The sending country is small and cannot affect the wage rate in the North.
Due to immigration restrictions, the receiving country is willing to accept a number Qt of educated immigrants at time t. Every educated adult is a candidate to emigration. The immigration
quota Qt represents a fraction qt of the adult population at time t. For simplicity, we assume a
constant skill premium across countries and periods.
Young agents now educate by anticipating a probability pet+1 of emigrating to the rich country.
The expected lifetime income for an uneducated agent is
uec,t = ln(ξt − µ) + ln(1).
(13)
The lifetime income for an educated agent now becomes
uec,t = ln(ξt − cαξt η − µ) + (1 − pet+1 ) ln(η) + pet+1 ln(wη).
(14)
Clearly, education is worthwhile for individuals whose education cost is lower than a critical value.
The condition for investing in education in an economy with migration (henceforth denoted using
the subscript q) is:
e
c < cq,t
ξt − µ wpt+1 η − 1
≡
×
e
αt wt
wpt+1 η 2
(15)
which is an increasing function of the local wage rate ξt , of the expected skill premium η, of the
foreign wage w and of the probability of emigration pet+1 . Clearly, we have cq,t = cn,t if pet+1 = 0.
e
Suppose individuals form rational expectations on pet+1 , i.e. they anticipate pet+1 = qt+1
/cq 5 .
Endogenizing the probability of emigration, the equilibrium proportion of educated among natives
is determined by the following implicit equation
e
cq,t =
ξt − µ wqt+1 /cq,t η − 1
e
×
≡ g(w, xit , η, qt+1
, cq,t )
e
αt ξt
wqt+1 /cq,t η 2
(16)
magnitude of remittances, (iv) on the network impact on FDI inflows and trade with receiving countries, (v) on
the complementarity/substitutability between skilled and unskilled workers on the labor market, (vi) on the consequences on wage bargaining and income sharing in the home country, etc. The only difference is that the convergence
is slower than with rational expectations (under rational expectations, the convergence is instantaneous).
5 Note that in the case of myopic expectation (i.e. pe
t+1 = pt = qt /cp,t−1 ), we would have the same long-run
equilibrium. The only difference is that the convergence is slower than with rational expectations (under rational
expectations, the convergence is instantaneous).
8
Figure 2: Skilled migration and human capital: intermediate country case.
Using the implicit function theorem, it can easily be shown that the equilibrium value for cq,t
e
(brain gain), in the skill premium η and the expected
is increasing in the expected quota qt+1
migration premium w.
The proportion of educated among remaining adults is now given by
πt =
cq,t−1 (1 − pt )
cq,t−1 − qt
=
= π(qt ; cq,t−1 )
1 − pt cq,t−1
1 − qt
(17)
Clearly, for a given cq,t−1 , the remaining proportion of educated decreases in qt (brain drain)6 .
However, cq,t−1 increases in qt . Consequently, the global impact of skilled migration on human
capital is ambiguous.
In the long-run, we have qt = q, cq,t = cq and pt = cqq . It follows that the steady state
cq −q
proportion of educated residents amounts to πss = 1−q
. The marginal impact of q on πss is given
by
h
i
0
dπss
2
= (1 − q) cq + cq (1 − q) − 1
(18)
dq
0
where cq is the positive derivative of cq with respect to q.
A limited degree of openness is desirable when dπdqss > 0 at q = 0. This requires that ln w is
sufficiently high. Otherwise, migration decreases the average level of human capital among adults.
0
1−c
For positive q, increasing skilled migration is desirable if cq > 1−qq , i.e. when the brain gain effect
dominates the brain drain. This condition is more restrictive as q increases. Hence, the higher the
brain drain, the lower is the probability of obtaining a beneficial effect on human capital.
Case 1 on Figure 1 illustrate the effect of skilled emigration on the long-run level of human
capital when the country is not too poor, i.e. when the local wage is far above the subsistence
level µ.
• the right panel illustrates the long-run impact of skilled emigration on the native proportion
of educated, cq . The equilibrium proportion of educated is the intersection between cq and
e
, cq,t ). We distinguish two possible values for the quota q: when the quota
g(w, xit , η, qt+1
6 When p tends to one (or c
t
q,t−1 = qt ), the equilibrium proportion of educated among remaining adults tends
to zero.
9
Figure 3: Skilled migration and human capital: poor country case.
e
increases, the g(w, xit , η, qt+1
, cq,t ) function shifts upwards. The equilibrium moves from A
to B then fostering the proportion of educated among natives;
• the left panel illustrates the long-run impact on the residents’ proportion of educated. We
cq −q
have π(cq , q) = 1−q
. Note that when q = 0, we have π(cq , q) = c (45◦ line). When q is
0
positive, we have πc > 1, π(0, q) < 0 and π(1, q) = 1.
Let us now use the graphical representation. In a closed economy, we have g(w, η, q, cq ) =
× η−1
η 2 and π = c. Hence, point N describes the closed economy ”poverty trap” equilibrium.
The good equilibrium is obtained when π > π ∗ and c > c∗ . In that case, no individual wants to
emigrate. The point T K describes the frontier above with a takeoff is observed. Suppose the economy starts at the ”bad” equilibrium and let us introduce skilled migration prospects. Between N
and T K, educated adults choose to emigrate and the equilibrium proportion of educated residents
may increase or decrease in the relative quota, q. Under positive emigration quotas, the function
(w, η, q, cq ) is decreasing in c and convex; as q increases, (w, η, q, cq ) shifts upwards. On the right
panel, the function π(cq , q) is linear but shifts upwards as well. Point A describes the case of a
beneficial brain drain. The quota is rather small, the proportions of educated natives and residents
reaches c1 and π1 . Point B describes the case of a beneficial brain drain. The quota is larger,
the proportions of educated natives and residents reaches c2 and π2 . Hence, cq is unambiguously
increasing in q a while the effect of q on π is clearly ambiguous.
On Case 2, we represent an economy where the local wage rate is not far above the minimum
of subsistence. On the right panel, the incentive effect of skilled migration is small (from A to N).
ξt −µ
αt ξt
If the proportion of educated natives is below the quota that can be accepted by the receiving
country, all the educated are leaving and the proportion of educated among remaining residents
falls to zero.
When random shocks are introduced, the probability to exit out the poverty trap depends on
the effect of the brain drain on the proportion of educated. When skilled emigration increases πss ,
it also increases the probability to exit out the trap. When skilled migration reduces πss , it also
reduces the probability of a growth miracle.
What should be tested? Our theoretical model predicts that skilled migration has an
unambiguously positive impact on natives’ education decisions, at least when the country is not
10
too poor. In the latter case, the impact is likely to be zero or not significant. The impact on
residents’ human capital formation is ambiguous in intermediate income countries and detrimental
in the poorest countries. These predictions can be empirically tested by computing the human
capital level of natives (including migrants and residents) and regressing the change in human
capital on the skilled emigration rate. In this regression, the effect of the skilled emigration rate
should depend on the country income compared the subsistence level. In a second step, the stock
of human capital among residents can be predicted by dropping out emigrants from the native
group. Such a system allows to simulate the impact of skilled emigration rates on the average level
of human capital remaining in the origin country.
11
3
Empirical tests
Our empirical investigation relies on the standard framework of convergence models. In particular,
we will assess to which extent human capital levels have converged across countries and we will
evaluate the role of migration flows of skilled workers in the convergence process. To account
for the potential incentive effect of migration prospects on human capital formation, we measure
human capital as the proportion of high-skill natives, rather than high-skill residents. In a second
step, the residents’ level of schooling will be predicted by dropping out emigrants from natives.
Before discussing the various convergence processes and their related econometric specifications,
we first expose how the crucial variables at stake here, namely human capital levels and migration
flows, are measured.
3.1
Data issues
Our dependant variable, namely the human capital level, is captured by the resident’s proportion
of tertiary educated people in each country. The tertiary education level corresponds to the one
obtained after more than 13 years of education. The data are mostly based on the well-known
dataset built by Barro and Lee (2000) for developing countries, and De La Fuente and Domenech
(2002) for OECD countries. For countries where Barro and Lee measures are missing, we either
use Cohen and Soto (2001) indicators, or transpose the skill sharing of the neighboring country
with the closest domestic enrollment in tertiary education. This method is used in Docquier and
Marfouk (2005). These data are built on a period ranging from 1975 to 2000 and span periods of
five years.
An important objective of this paper is to measure the impact of the emigration of skilled
workers on the long run level of the human capital level of the countries. For 1990 and 2000,
emigration rates by education attainment are provided by Docquier and Marfouk (2005). This
data set relies on two steps. First, emigration stocks by education level are computed using
census data collected in all OECD countries. Second, these stocks are expressed in percentage of
the total labor force born in the sending country (including migrants themselves) with the same
education attainment. Basically, Docquier and Marfouk (2005) provide estimates of the brain
drain phenomenon for 175 countries in 1990 and 195 countries in 2000. They attempt to improve
the previous estimates provided by Carrington and Detragiache (1998) that were used in previous
empirical evaluation of the incentive hypothesis (Beine et al., 2003 for instance).
Here we follow the same methodology. However, in order to overcome the limitations of the
cross-section approaches, we extend the time series dimension of the data set to cover the period
1975-2000 with data sampled at a five-year frequency. Unfortunately, we have to focus on a more
limited number of host countries. We collect census data on immigration by country of birth and
by education attainment from the 6 major receiving OECD countries, i.e. Canada, Australia, US,
UK, France and Germany. In some cases, reasonable interpolations are required to evaluate the
structure of immigration between two censuses. Compared to Docquier and Marfouk, it should
be stressed that these countries account for more than 75% of the OECD imigration stock. The
skill levels considered are fully consistent with the one used for capturing the human capital level.
12
3.2
Cross-section analysis
Our starting point is based on a cross-section analysis of the convergence in natives’ human capital.
This type of approach, known as β-convergence, has been extensively used in the literature, dating
back to Romer(1989) among many others. The idea is to investigate whether poor countries are
catching up with the richer countries. Along these lines, we estimate first the following equation:
ln(h00,i ) − ln(h75,i )
= α + βln(h75,i ) + ²i
25
(19)
where ht,i denotes the level of human capital of country i observed at year t. This process
assumes a form of absolute convergence in the sense that if β is significantly negative, countries
are supposed to converge to the same long-run level of human capital. This highly irrealistic
assumption has been questioned in subsequent empirical studies of convergence (Barro and SalaI-Martin, 1992, Mankiw, Romer and Weil, 1992). These approaches test whether the countries
converge in a conditional way, i.e. towards long-run levels different across countries. With respect
to the convergence of human capital level, long-run proportion of education are supposed to
depend on a set of factors that will differ in a persistent way across countries. In a first step, we
can account for a conditional type of convergence process by making the long-run level dependent
on a set of observed variables. In line with the theoretical framework developed before, we test
whether these long-run level depend on the migration rates of skilled workers. Since the long-run
impact of migration on human capital accumulation might depend on the country level of income
(which affects both the capacity to pay for education costs and the incentive to emigrate), we split
the migration variable between three groups of countries: rich, intermediate and poor countries.
We classify these countries with respect to the average income per capita over the whole period.
We also add the public expenditures in tertiary education in percent of the GDP per capita as a
potential determinant of human capital level. This is done in extending equation (19):
ln(h00,i ) − ln(h75,i )
= α + γr mri + γi mii + γp mpi + δEi + βln(h75,i ) + ²i
25
(20)
where Ei is the sample average value of the public expenditure on education as a proportion
of GDP in country i. The variables mri , mii and mpi denote sample average emigration rates of
skilled workers of country i (to the six main destination countries) respectively for higher level,
intermediate level and low level income categories.7 If liquidity constraints are binding, we expect
γp to be zero or even negative if the direct effect in terms of brain drain is important. The same
holds for γr as skilled workers of rich countries have few economic incentives to migrate. If the
brain effect dominates the drain effect and if liquidity constraints can be alleviated in intermediate
income level countries, we can observe a positive γi .
Table 1 provides the results of our cross section estimations. Since average education expenditures are unavailable for a subset of countries, accounting for their influences on the long-run
level of human capital results in a significant reduction of the sample size. The same holds to a
much less extent for the emigration rates of skilled workers (loss of 5 observations). Column(1)
provides the results relative to the absolute convergence process. The results provide some support
in favor of a convergence process. Nevertheless, the rate of convergence is quite low, slightly above
7 Our initial categorization leads to have 40 percents, 20 percents and 40 percents of countries classified respectively as rich, intermediate and poor countries. In the panel estimation results (see next section), we show that the
results are to a certain extent robust to marginal changes in these proportions.
13
Table 1: Convergence of human capital : cross-section results
Var
(1)
(2)
(3)
(4)
Coefficient
0.0084b
0.0308b
0.0294a
0.066
(0.0037) (0.0054) (0.0240) (0.0042)
β
-0.0098a -0.0156a -0.0153a -0.0101a
(0.0011) (0.0016) (0.0059) (0.0013)
γr
0.0046
0.0040
0.0054
(0.0082) (0.0094) (0.0071)
γi
0.0299a
0.0299a
0.0139b
(0.0116) (0.0099) (0.0066)
γp
0.0047
0.0048
-0.0121
(0.0104) (0.0145) (0.0129)
δ
-0.0098a -0.0094a
(0.0017) (0.0102)
λ
0.011
0.0198
0.0194
0.0116
Obs
171
126
120
166
R2
0.306
0.536
0.536
0.323
ln(h
)−ln(h
)
00,i
75,i
Note: Estimated equation:
= α + γr mri +
25
p
i
γi mi + γp mi + δEi + βln(h75,i ) + ²i .
a, b, c mean significance of coefficients at respectively 1, 5 et
10 percent significance levels.
Columns (1), (2) and (4), OLS estimates. Results in column
(3) are obtained with IV estimation with expenses on education instrumented by total public expenditures and health
expenditures.λ is the implied rate of annual convergence comln(1+(25β)
puted as
.
25
1 percent per year, meaning that almost a century is necessary for the human capital levels to
converge to the same long run levels. In columns (2) to (4), the assumption of identical steady
states is suppressed, which results is a quicker speed of convergence.
Results in column (2) suggest that the heterogeneity in steady states of human capital is driven
both by migration rates and public expenditures. The long run impact of skilled migration rate
is positive only for intermediate countries, as suggested by the significance of the γi parameter.
This is line with the empirical literature on the beneficial brain drain hypothesis (Beine et al.
2003; Mariani, 2005) showing that a subset of countries might benefit from higher migration rates
of skilled workers. The estimation results suggest that the net effect of migration rates is not
different from zero for rich and poor countries.
The estimated effect of public expenditures is unintuitive, implying that more expenditures
tend to decrease the long run level of education. In order to solve this puzzle, we investigate
whether public expenditures are endogenous with respect to the variation of human capital, leading
to biased coefficient in equation (20).8 Columns (3) report the estimation results with education
expenditures instrumented by total public expenditures (relative to GDP) and health expenditures. These two variables are found to be positively correlated with education expenditures.
Instrumental variable estimation does not lead to different results, either in terms of the impact
of migration and education expenditures on the long-run levels of human capital or in terms of
convergence speed.9 Unsurprisingly, accounting for the heterogeneity of long-run human capital
8 Frederic,
9A
as tu un mecanisme en tete?
Hausman overidentification test as well as a C test fail to reject the erogeneity of public expenditures with
14
levels leads to a quicker rate of convergence close to 2% a year. This remains nevertheless very
modest, given the huge increase of the proportion of highly skilled agents reported in numerous
emerging countries (ref ?).
Finally, we drop the education expenditure variable in equation (20). This stems from two
reasons. First, unintuitive results in terms of its effect raises the question of whether this variable
really captures public effort to boost education. Second, due to missing data for this variable, its
inclusion significantly reduces the sample size, leading to a potential problem of selection bias. The
results are reproduced in columns (4). They confirm the two main findings of these cross-section
results, namely the very slow speed of convergence and the positive long run impact of skilled
agents’ migration rates for intermediate income level countries.
3.3
Panel data analysis
Introducing variables that account for the heterogeneity of long-run human capital levels is obviously a first step towards a better understanding of the convergence process at stake. Nevertheless,
combining the time series dimension and the cross section variation is obviously called for here.
Beyond the mere advantage of using much more observations, there are a set of reasons to overcome
the limitations of a pure cross section analysis.
First, as well documented by Islam (1995) for income levels, cross section results are subject
to important mispecification bias. Failure to control for the factors that influence the human
capital accumulation process leads to some omission variable bias as these factors are likely to be
correlated with the initial level of human capital. While the migration rates of skilled workers
might be one of these factors, a number of unobservable factors are likely to influence human
capital accumulation.10 Assuming that these factors are constant over time, a panel data analysis
can take that into account through the introduction of country specific effects. We will show that
the introduction of these effects results in an estimated equation that behaves particularly well in
an in-sample forecasting exercise.
Second, extending the analysis to a panel dimension allows to account for the effect of shocks
to human capital accumulation common to all countries. This is indeed important for human
capital levels since education levels have obviously improved around the world along with increased
globalization.
Third, as for the role of migration, cross section analysis implicitly assumes a constant rate of
emigration of skilled workers for each country. This is obviously a strong assumption.
We extend equation (20) by introducing the time series dimension, which leads to the following
equation:
p
ln(hi,t ) − ln(hi,t−1 ) = α + αi + δt + γr mri,t + γi mi,t
i + γp mi,t + βln(hi,t−1 ) + ²i,t ; t = 1, ..., 6. (21)
where hi,t denote the level of human capital level for country i at time t (similar notations hold
for the migration rates), αi is the country specific effect capturing the influence on the long-run
respect to human capital levels. These results are not reported here in order to save space but are available upon
request.
10 As for the effect of education expenditures, it is not possible to introduce them in the panel data analysis due
to the highly missing information in most countries for a lot of years. The influence documented in the cross section
could therefore be well captured by the αi .
15
Table 2: Convergence of human capital : panel data
Var
(1)
(2)
(3)
(4)
Coefficient -0.1438a -0.3690a -0.2438a
0.0006
(0.0440) (0.0054) (0.0365) (0.0074)
β
-0.1007a -0.1482a
-0.045a
-0.0129a
(0.0100) (0.0248) (0.0049) (0.0017)
γr
0.0303
-0.0561
0.0089
0.0157
(0.0472) (0.0600) (0.0476) (0.0108)
γi
0.1420a
0.1384c
0.2129a
0.0299a
(0.0385) (0.0786) (0.0482) (0.0118)
γp
0.0677
-0.0487
0.206a
0.0066
(0.0451) (0.0652) (0.0482) (0.0126)
λ
0.1400
0.2702
0.0509
0.0132
Obs
829
664
829
829
R2
0.4883
0.536
0.390
0.1009
results
(5)
0.0006
(0.0053)
-0.0128a
(0.0015)
0.0151
(0.0100)
0.0283a
(0.0110)
0.0031
(0.0118)
0.0132
829
0.092
Note: Estimated equation:ln(hi,t )−ln(hi,t−1 ) = α+αi +δt +γr mri,t +
p
γi mi,t
i + γp mi,t + βln(hi,t−1 ) + ²i,t .
a, b, c mean significance of coefficients at respectively 1, 5 et 10% significance levels.λ is the implied rate of annual convergence computed
ln(1+(5β)
as
. Estimates of αi and δt not reported to save space.
5
In columns (1), (2), fixed (country and period specific) effects estimates. In column (2), ln(hi,t−1 ) is instrumented by ln(hi,t−2 ). Column (3) include the results with fixed αi but without time dummies.
Columns (4) and (5) report estimates with random country specific
effects. In column (4), time dummies are included whereas in column
(5), they are omitted.
level of country specific factors that are constant over time, δt captures the impact of common
shocks across countries specific to year t.11
A big question regarding the estimation of this panel model is whether αi should be considered
random or fixed. The answer depends on whether these αi are correlated with cross section and
time varying variables in the model. As pointed out by Islam (1995), for income convergence, since
physical capital and population growth are likely to be correlated with total factor productivity,
the answer is obvious. It is less obvious for human capital convergence. Therefore, we consider
the two types of estimates. Note that a Hausman test tends to reject random effects estimates in
favour of the fixed effects specification. Nevertheless, for the sake of comparison, we will report
both types of results. The results are gathered in Table (2).
Column(1) report the fixed effect estimates. The results are strikingly different from the cross
section results. A significant part of the long run levels of human capital is captured by the αi . This
leads to more heterogeneous estimates of these long run levels, increasing the rate of convergence
of countries in terms of human capital level. The implied rate of convergence amounts to 14%
a year, suggesting that countries need on average 7 years to reach their long run human capital
level. This result is much in line with the results obtained by Islam (1995) for income per capita
convergence. Having said that, an important result is that migration rates of skilled workers still
influence the long run levels of human capital in a very similar way as the one documented in
cross-section analysis. A higher rate of emigration of skilled workers tend to favor human capital
11 It should be emphasized that the estimates of δ are all highly significant at the 1% level. They suggest that
t
the growth rate of human capital was on average increasing over time.
16
accumulation in the long run for intermediate income level countries.
A potential problem with these fixed effects estimates stems from the dynamic feature of the
convergence model. The use of fixed effects and AR terms leads to inconsistency of estimates,
especially when the number of periods is increasing (Nickell, 1981). While the ratio of the cross
section dimension to the time dimension suggests that the Nickell bias should be limited in our
regressions, it is interesting to look at alternative approaches. This is especially important here
given the seemingly high rate of convergence we get with the fixed effects specification. One way to
overcome this problem is to use IV estimation, as suggested by Barro and Lee (1992) and recently
applied by Coulombe and Tremblay (2005). More precisely, we use ln(hi,t−2 ) as an instrument of
ln(hi,t−1 ).12 Estimates in column (2) suggest that this procedure does not lead to a lower speed of
convergence. The implied λ is even higher, amounting to about 0.27. This suggests that the speed
obtained with the fixed effects specification is not overestimated due to econometric problems.
Finally, we proceed to two additional robustness checks. Since the nature of the countryspecific effects is not obvious, we estimate the model with random αi .13 The two last columns of
Table (2) report the results obtained with and without time specific effects. Estimation results also
support the case of a conditional convergence process, but with a much slower pace of convergence.
Interestingly, the influence of migration rates on the long-rn levels of human capital still prevails
for intermediate income countries. Therefore, this impact is found to be robust to the degree of
correlation between the country specific effects αi and the migration rates of skilled workers.
To discriminate further between the random effects and the fixed effects specification, we will
proceed to forecasting experiments. Basically, starting with the (log of the) initial levels of human
capital (ln(hi,75 )) and using the country-specific effects, the migration rates for the subsequent
periods and the estimated rates of convergence, we compute the value of the (log of the) levels
of human capital in 2000 and draw the implied empirical distribution across countries. For each
regression model, we can compare this implied distribution with the observed one. Figure 4 plots
three implied distributions along with the observed one for ln(hi,00 ). These suggest that the
fixed effects model yields very good results in a forecasting exercise and tends to reproduce fairly
well the observed distribution of human capital in the final period (year 2000). The fixed effects
specification (labelled FE in figure 4) is able to produce the double-hump shape in the distribution.
The fixed effects specification estimated with IV is also able to generate the observed shape , but
with a higher discrepancy with respect to the observed distribution (especially around its mode).
In contrast, the random effects model generates a distribution with modes that significantly depart
from the observed one and produce too a low dispersion in the human capital levels. This sheds
some further doubts on the relevance of the random effect model.
Our results regarding the impact of skilled migrations on the long-run human capital levels
rely on an initial classification of countries into intermediate, rich and poor ones. We look at other
classifications. Our initial classification considered 40% of countries that were rich and 40% poor,
with the 20 remaining % considered intermediate. Let us call that the 40-20-classification.
We look at three alternative classifications : 40-30-30 (10% of poor countries move into the
group of intermediate ones), 40-15-45 (additional 5% of intermediate countries subject to liquidity
constraints) and 35-25-40 (additional 5% of countries with an incentive to migrate). The results
12 The
choice of this instrument procedure leads therefore to a further loss of one cross-section.
that the combination of fixed time specific effects with random country specific ones is not possible in
unbalanced panels. Therefore, the δt are dropped off in the regression.
13 Note
17
Table 3: Robustness of classification of countries: panel data results
Var
(1)
(2)
(3)
Coefficient -0.1429a -0.2308a
-0.1859a
(0.0440) (0.0342)
(0.0301)
β
-0.1005a -0.1015a
-0.1015a
(0.0100) (0.0100)
(0.0099)
γr
0.0294
0.0516
0.0519
(0.0472) (0.0651)
(0.0652)
γi
0.0892a
0.0802b
0.0810b
(0.0422) (0.0338)
(0.0324)
γp
0.0936a
0.0673
0.0658
(0.0469) (0.0425)
(0.0450)
λ
0.1400
0.1416
0.1416
Obs
829
829
829
R2
0.4874
0.4867
0.4867
Note:Estimated equation:ln(hi,t ) − ln(hi,t−1 ) = α +
p
αi + δt + γr mri,t + γi mi,t
i + γp mi,t + βln(hi,t−1 ) + ²i,t .
a, b, c mean significance of coefficients at respectively
1, 5 et 10% significance levels. Estimates of αi and δt
not reported to save space. λ is the implied rate of
ln(1+(5β)
annual convergence computed as
.
5
In column(1), the classification involve 30, 40 and 30%
of respectively rich, intermediate and poor countries.
Results in columns (2) and (3) are based respectively
on 15-40-45 and 25-35-45 classifications.
are reported in Table 3. The results suggest that the positive long-run effect of migration rates on
the human capital level shows up especially for intermediate income countries. The positive effect
obtained for poor countries for a particular classification is not robust to marginal change in the
groups’ weight.
18
0.6
0.5
0.4
0.3
0.2
0.1
0
-8
-7
-6
-5
re
-4
-3
fe
fe_ivh
-2
-1
0
1
obs
Figure 4: Plots of the 3 cross-country distributions of ln(hi,00 ) corresponding to the fixed effects
(fe), random effects (re) and fixed effects with instrumental variable (fe-ivh) specifications of
equation (21) along with the observed distribution of ln(hi,00 ) (obs).
19
4
Counterfactual experiments
Our empirical analysis reveals that skilled migration fosters natives’ human capital formation
in intermediate income countries. In poor and high income countries, migration prospects do no
affect education choices. In this section, we use counterfactual experiments to evaluate the effect of
skilled migration on the average level of schooling remaining in the origin country (i.e. the average
level of schooling among residents). Our experiments consists in setting the skilled emigration rate
to the unskilled emigration rate. Indeed, the unskilled rate captures the minimal level of mobility
of workers, given the country size, distances with the main receiving countries, country-specific
push factors...
Starting from the human capital level observed in 1975, we sequantially use the estimated
equation (21) and compute the dynamics of natives’ human capital between 1975 and 2000:
0
ln hi,t = alpha + (1 + beta) ln h0i,t−1 + deltami,t−1 Ii + ai + bt + varepsiloni,t
(22)
0
where hi,t is the counterfactual proportion of tertiary skilled among natives, mi,t−5 is the lagged
skilled emigration rate (observed or counterfactual), Ii is the dummy capturing inermediate income
countries (α, β, ai , bt ) are estimated coefficients and fixed effects, and εi,t is the residual obtained in
our regression. By intergrating εi,t ,.the simulation with the skilled emigration rate mi,t−1 = msi,t−1
would exactly match observations.
Note that our estimated equation also allow us to simulate the steady state level of human
capital for any skilled emigration rate. We have:
0
ln hi,ss =
alpha + deltami,2000 Ii + ai + b2000 + varepsiloni,2000
−β
(23)
In 2000 or at the steady state, residents’ human capital is then obtained by dropping out the
(observed or counterfactual) proportion mi,2000 of emigrants from the native labor force.
Results are presented in Table Z. We distinguish high-income, intermediate-income and lowincome countries. In each group, the first two columns compare observed and steady state levels
of human capital. It is noteworthy that the steady state level of human capital is usually close
to the observed level in 2000. Some countries will experience a modest rise in human capital
while other will experience a slight decrease. The relative increase is important in some African
countries (Mozambique, Gambia, Burundi, Rwanda, Comoros) or in Solomon islands and Iran. An
important relative decrease is expected in Angola, Somalia, Central Africa or Namibia. However,
in most cases, we should not expect to observe a strong convergence in human capital for the
coming decades.
The last two columns give the results of our counterfactual experiments, i.e. setting the skilled
emigration rate to the unskilled rate.
• In low-income and high-income countries, migration does not induce any incentive effect on
human capital formation. Hence, slowering skilled migration does not affect natives’ choice
and reduces human capital losses. These countries would clearly gain from reducing the
human capital flight. The gains are relatively small in the large majority of cases. However,
strong improvement would be obtained in countries where skilled migration rates reach
international records such as Somalia, Guyana, haiti, Trinidad and Tobago, Grenada, St
20
21
Lucia,, Rwanda, Gambia, Sierra Leone etc. In some of the latter cases, the proportion of
tertiary educated would rise by more than 10 points of percentage In the largest emigration
countries such as China, India, Mexico or Pakistan, the effect is very small.
• In intermediate-income countries, migration prospects stimulate human capital accumulation. The global effect is then ambiguous. Among the 33 medium income countries, reducing
skilled migration would increase the average level of schooling in 10 cases (the detrimental
brain drain cases). On the contrary, it would reduce residents’ human capital in 23 cases
(the beneficial brain drain cases). As shown in previous studies (Beine et al, 2004), the
detrimental cases are small islands in which the skilled emigration rates is particularly high
(on average, 45 percent), or countries in which the brain drain is low but the general level
of education is relatively high (Bulgaria, Romania, Algeria). In the other countries, the
skilled emigration rates is lower (on average, 17 percent). These countries would clearly
loose from reducing the brain drain. The loss would be important in Lebanon, El Salvador,
Iran, Cuba, Belize, Vanuatu or Tunisia. Note that Turkey and Thailand would also belong
the the beneficial brain drain group.
Finally, the impact of skilled migration on the international distribution of human capital
is illustrated on the gaussian densities in figureY. Both 2000 and steady state densities are right
skewed, globally unimodal with mode around 5 percent. Clearly, reducing skilled emigration would
affect two specific segments of the human capital density. First, it would improve the situation
of the poorest countries: we observe a downward shift at very low human capital levels. The
proportion of countries characterized by a proportion of tertiary educated below 7 percent would
then decrease. On the other hand, the proportion of countries characterized by a proportion of
tertiary educated between 17 and 31 percent would increase. Although the tails of the distribution
would be rather unaffected, reducing the brain drain would make the distribution more bimodal.
The same conclusion is obtained at the steady state.
22
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