WPS4614
Policy ReseaRch WoRking PaPeR 4614
Is Migration a Good Substitute for
Education Subsidies?
Frédéric Docquier
Ousmane Faye
Pierre Pestieau
The World Bank
Development Research Group
Trade Team
May 2008
Policy ReseaRch WoRking PaPeR 4614
Abstract
Assuming a given educational policy, the recent brain distortionary, it is desirable to impede emigration and
drain literature reveals that skilled migration can boost subsidize education. The authors investigate the empirical
the average level of schooling in developing countries. relationship between educational subsidies and migration
This paper introduces educational subsidies determined prospects, obtaining a negative relationship for 105
by governments concerned by the number of skilled countries. Based on this result, the analysis revisits the
workers remaining in the country. The theoretical country specific effects of skilled migration upon human
analysis shows that developing countries can benefit from capital. The findings show that the endogeneity of public
skilled emigration when educational subsidies entail subsidies reduces the number of winners and increases
high .fiscal distortions. However when taxes are not too the magnitude of the losses.
This paper--a product of the Trade Team, Development Research Group--is part of a larger effort in the department to
analyze the impact of migration on poverty and economic development.. Policy Research Working Papers are also posted
on the Web at http://econ.worldbank.org. The author may be contacted at frederic.docquier@uclouvain.be.
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development
issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the
names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those
of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and
its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.
Produced by the Research Support Team
Is Migration a Good Substitute for
Education Subsidies?
Frédéric Docquiera, Ousmane Fayeb;c and Pierre Pestieaub;d
a
FNRS and IRES, Catholic University of Louvain (Belgium), and World Bank (USA).
b c
CREPP, University of Liège (Belgium) APHRC, Nairobi (Kenya).
d
CORE, Catholic University of Louvain (Belgium), PSE-Paris (France), and CEPR (UK).
March 2008
Abstract
Assuming a given educational policy, the recent brain drain literature re-
veals that skilled migration can boost the average level of schooling in de-
veloping countries. This paper introduces educational subsidies determined
by governments concerned by the number of skilled workers remaining in the
country. The theoretical analysis shows that developing countries can bene...t
from skilled emigration when educational subsidies entail high ...scal distor-
tions. However when taxes are not too distortionary, it is desirable to impede
emigration and subsidize education. The authors investigate the empirical re-
lationship between educational subsidies and migration prospects, obtaining a
negative relationship for 105 countries. Based on this result, the analysis re-
visits the country speci...c e¤ects of skilled migration upon human capital. The
...ndings show that the endogeneity of public subsidies reduces the number of
winners and increases the magnitude of the losses.
JEL Classi...cations: F22, J24, O15.
Keywords: Brain drain, human capital, immigration policy, development.
2Acknowledgement. We thank Raouf Boucekkine, Simon Commander, David De la
Croix, Saul Estrin, Gordon Hanson, Omar Licandro, Fabio Mariani, Christopher Parsons,
Sergio Perelman and Hillel Rapoport for their comments. Helpful remarks and sugges-
tions from referees were appreciated. A previous version of this paper was presented at
the workshop in Development Economics (Louvain-La-Neuve, Sept 2005) and the CNEM
seminar (London Business School, Nov 2005). Ousmane Faye gratefully acknowledges ...nan-
cial support from the Government of Luxemburg ("Bourse Formation-Recherche, BFR").
The usual disclaimers apply. Corresponding author: Frédéric Docquier, IRES, Catholic
University of Louvain, 3 Place Montesquieu, B-1348 Louvain-La-Neuve, Belgium. Email:
frederic.docquier@uclouvain.be. Tel: +32 10 47 41 49. Fax: +32 10 47 39 45.
1
1 Introduction
The recent literature on the the brain drain asserts that the migration of the highly
skilled may entail bene...cial feedback e¤ects for source countries. Remittances, return
migration and diaspora externalities are potentially important feedback channels.
In addition, several authors such as Vidal (1998), Mountford (1999), Beine et al.
(2001) and Stark and Wang (2002) have recently argued that migration prospects
increase the expected returns to education and may foster educational investments
in developing countries, therefore making it possible for a brain drain to be bene...cial
to the source country (i.e., the country may end up with a higher level of human
capital after emigration is netted out). Obviously, causality is hard to establish in
cross-sectional regressions and the "brain gain" concept deserves further empirical
investigations based on richer data. However, Beine et al. (2001, 2007a) found
evidence in support of such an incentive mechanism.1
In this paper, we analyze the policy implications of the brain gain hypothesis,
especially the interactions between skilled migration and education policies. These
interactions were studied by Stark and Wang (2002) who demonstrated that, by
allowing a controlled proportion of skilled individuals to emigrate to a richer country,
the government can stimulate the expected returns to schooling so as to obtain the
socially desirable level of human capital without subsidies. Although it can be refuted
that sending countries (except perhaps totalitarian regimes) have no perfect control
over emigration rates, Stark and Wang's analysis suggests that the emigration policy
acts as a perfect substitute for public subsidies (i.e. that the higher the skilled
emigration rate, the lower is the rate of subsidy required to decentralize the social
optimum). The purpose of our paper is to theoretically and empirically revisit the
1See also Kangasniemi et al. (2004), Commander et al. (2004), Lucas (2004) or Batista et al.
(2007).
2
migration-subsidy policy mix in a more realistic framework where distortions and
e¢ ciency costs are factored in.
Theoretically, we use a normative approach and derive the optimal emigration and
education policies when social costs and distortions are linked to both instruments.
The ...nancing of public subsidies usually induces many costs such as tax evasion,
distortive e¤ects on labor supply, exit to the informal sector, administrative costs and
corruption. Emigration also entails some costs to the government. It can reasonably
be argued that emigration causes social welfare losses for the domestic country when
the government is concerned by the aggregate stock of residents'human capital or has
ethical opposition against skilled emigration.2 In such cases, our model shows that the
...rst best emigration rate is zero. With non-distortive taxes or at low e¢ ciency costs,
an appropriate education policy always dominates a controlled emigration policy.
When tax distortions are su¢ ciently large, a controlled and rationed emigration rate
can be second best. Skilled migration becomes a substitute to public subsidies, i.e.
a negative correlation exists between the second best subsidy and the controlled
emigration rate. Interestingly, such a negative relationship is also obtained in a
"third-best" framework when the emigration rate is exogenously determined (i.e.
when the planner has no control on emigration).
Such "crowding out" e¤ects of skilled migration upon subsidies have been disre-
garded in the empirical literature, thereby overestimating the magnitude of incentive
mechanisms. Empirically, we use a large sample of middle and low-income countries,
and con...rm the existence of a negative relationship between education subsidies and
skilled migration rates. The elasticity of public subsidies to migration equals -0.20.
2These can be related to population size acting as a cultural public good creating social capital,
or to externalities associated with the total stock of human capital. Authors such as Kremer (1993),
Lagerloef (2001) and Becker et al. (1999) have stressed the role of population growth and population
density in the economic/demographic transition. Galor and Weil (1999) argued that a larger stock
of human capital generates greater numbers of innovations.
3
We then revisit the country speci...c e¤ects of skilled migration on human capital by
considering public subsidies as endogenous. Our counterfactual experiment consists
of equating the skilled emigration rate to the unskilled emigration rate (considered
as the minimal rate of emigration given colonial ties, distance, etc.) and computing
the hypothetical human capital change between 1990 and 2000. Unsurprisingly, the
endogeneity of public subsidies decreases the relative number of winners, reduces the
size of the gains and increases the size of the losses in other countries. It is notewor-
thy that although a brain gain is observed in the largest developing countries, skilled
emigration reduces the number of post-secondary educated in the developing world
by about 2.7 percent.
The remainder of the paper is organized as follows. Section 2 describes the theo-
retical model and compares the ...rst best and second best solutions. Section 3 provides
the empirical analysis and its implications. The ...nal section concludes.
2 Migration as a second best policy option
To analyze the optimal migration-subsidy mix, we consider a small open economy
populated by two overlapping generations. As in Stark and Wang (2002), agents are
homogenous within generations and there are no credit market imperfections. The
number of young individuals living at time t is denoted by Nt and the number of adults
is denoted by At. Each adult gives birth to n > 1 children. At each period, a composite
good (Yt) is produced using capital (Kt) and labor measured in e¢ ciency units (Ht)
according to a neoclassical technology, F(Kt;Ht). This good can be consumed, saved
or used as an input for the formation of human capital. Young agents inherit a
fraction a 2 [0;1] of adults'human capital, ht. Labor in e¢ ciency units is given by
Ht = Ntaht + Atht = At(1 + na)ht
4
The production function exhibits constant returns to scale and is time invariant.
Assuming physical capital is perfectly mobile across countries, the time-invariant
world interest rate R determines the wage rate per e¢ ciency unit of labor w. Our
economy is assumed to be poor. Due to a technological gap, the wage rate per
e¢ ciency unit of labor is lower than it is in the rich world: w < w . We assume no
migration costs. Hence, each worker has an incentive to emigrate to rich countries.
Individuals are only concerned about their level of consumption in the second
period of life, Ct+1. They are risk neutral and maximize their expected consumption
level. Every young individual has the possibility to invest an amount et in education,
to increase their second period stock of human capital. Individuals face a common
training technology:
ht+1 = et ht (1)
with + < 1 (decreasing returns to scale). The latter condition will ensure the
convergence of the human capital stock to a steady state.
A fraction tof education expenditures is subsidized by the government ( t is a
Pigouvian policy instrument). The public budget constraint is balanced by levying
lump-sum taxes on the young ( ) and adults ( ). This implies: n e = n
y a y+ a.
t t t t t t
Individuals'saving if given by St = waht et(1 y
t) . Young agents make
t
their education decision by anticipating a probability mt+1 of emigrating to a rich
country when reaching adulthood. Their second period consumption equals Ct+1 =
RSt +w ht+1 with probability mt+1, and Ct+1 = RSt +wht+1 a with probability
t+1
(1 mt+1). Young individuals maximize their expected (linear) utility
E (Ct+1) = R [waht et(1 y a
t)
t] + mt+1w ht+1 + (1 mt+1) wht+1 t+1
Given our assumptions concerning the training technology, there exists a unique
5
and interior solution to the individuals'maximization problem:
1
ht [w + mt+1(w w)] 1
et = (2)
R(1 t)
and the dynamics of human capital is governed by the equation:
[w + mt+1(w w)] 1
ht+1 = ht
1 (3)
R(1 t)
Given decreasing returns to scale in the human capital technology, this function
is concave and there is a unique interior steady state level of human capital:
[w + m(w w)] 1
hss = (4)
R(1 )
Hence, our model is compatible with the analysis of Vidal (1998) and Stark and
Wang (2002). When individuals are equally capable of responding to emigration
incentives, migration prospects have an unambiguously positive impact on human
capital. In the absence of distortions, public subsidies and a properly controlled
emigration policy can be used to reach any level of human capital. Would this result
resist a normative analysis?
2.1 The ...rst best utilitarian solution
Except in totalitarian regimes, it is fairly obvious that sending countries have little
control over emigration. Nevertheless, in line with the new literature on the brain
drain, it is worth analyzing whether developing countries can bene...t from a positive
skilled emigration rates: i.e. what would be their optimal choice if they could perfectly
control their skilled emigration rate? To address this question, we suppose that the
government is concerned by the total welfare of residents. The social welfare function
is of the Benthamite utiltarian form: it sums utilities of all remaining adults. This
speci...cation implies that the government is concerned by the resident population
6
size. Through this channel, we summarize all the social costs of emigration for the
sending country. Given (R;w;A0;S0;h0), the planner's problem involves maximizing
the social welfare function subject to the production technology of human capital. At
time 0, the Lagrangian can be written as
A0c0
$FB = + X1
t At+1 [Rwaht Ret + wht+1] + t t+1
A et ht ht+1 (5)
t=0
where is the factor of social time preference such that n < 1.
In the ...rst-best problem, the planner has a perfect control on all individual deci-
sions. Using the ...rst order conditions with respect to ht+1, et and mt+1 (see Appendix
6.1), we have:
Proposition 1 Decentralizing the ...rst best solution requires setting the emigration
rate to zero and using both education subsidies and lump-sum taxes.
The intuition is straightforward. There are two sources of intergenerational exter-
nalities in the model: individual education decisions impact upon the next generation
income ( nRwa) and a¤ect the future productivity of education investments ( n ).
The long-run level of human capital at the ...rst best is given by:
w [1 + nRwa] 1
hFB = (6)
ss R [1 n ]
From (4), two instruments (emigration and subsidies) can be used to increase
human capital. Resorting to emigration induces a social loss: the number of skilled
residents decreases. Consequently, with no tax distortion, educational subsidy is to
be preferred over emigration as it keeps all skilled individuals at home.
Comparing (6) to (4), the ...rst best solution can be obtained as a market outcome
if the government chooses a subsidy rate that corrects for both externalities:
nRwa + n
FB = (7)
ss 1 + nRwa
7
It can be easily shown that the unique tax-mix that balances the budget con-
straint and veri...es the optimality conditions requires y;FB = e and a;FB = 0.
ss ss ss ss
When the capital stock is exogenous and saving does not matter, there is no need
for intergenerational transfers. For simplicity, in the remainder of this paper, we will
only consider taxes on the young.
2.2 The second-best utilitarian solution
Let us now assume that levying taxes induces some distortions. E¢ ciency costs are
denoted by c( y): levying y dollars induces a ...scal revenue of y c( y ). The
t t t t
idea that revenue collection entails a loss in e¢ ciency is traditionally associated with
labor/leisure choices, but they can also be linked to administrative costs of running
programs, which in turn can be linked to the quality of governance and rent-seeking
activities in developing countries. The planner now faces a second-best problem in
that he has perfect control of policy instruments, which indirectly a¤ect individual
decisions. Hence, the government takes into account that individuals will maximize
their own utility taking taxes and subsidies as given. The second-best problem now
consists of maximizing the utilitarian social welfare function subject to the production
technology of human capital (with multiplier t), the government budget constraint
including e¢ ciency costs (with multiplier ), and the individual ...rst order condition
t
(eq. (2) with multiplier ). At time 0, the Lagrangian can be written as:
t
A0c0
$SB = + X1
tAt+1 Rwaht R(1 y a
t)et R (8)
t + wht+1 t+1
t=0
+ y y
t et ht ht+1 + [ c( ) e ]
t t t t t
+ w)] R(1
t ht [w + mt+1(w t)e1t
and must be maximized with respect to ht+1, et; ; y
t t and mt+1.
In Appendix 6.2, we provide the ...rst order conditions expressed at the steady
8
state. In the absence of any perception cost (c0( y ) = 0), the optimal emigration rate
is zero and the optimal level of human capital is naturally identical to hFB. This is
ss
the ...rst best solution.
When perception costs are positive (c0( y) > 0), the optimal migration rate can
be positive. For the sake of simplicity, we consider the case of linear e¢ ciency costs:
c0( y) = .3 The optimal level of human capital becomes:
w ( ;m) 1
hSB = (9)
ss R
where ( ;m), as detailed in appendix 6.2, is a decreasing function of and m.
We have:
Proposition 2 In the case of exogenous emigration rates and linear perception costs,
the optimal level of human capital and the subsidy rate are decreasing in m.
From (6) and (9), decentralizing the second best solution requires a subsidy rate
equal to
( ;m) 1 m(w w)
SB = w ; (10)
ss ( ;m)
which is, for reasonable values of the parameters, a decreasing function of and m.
The interpretation is intuitive. On the one hand, the probability of migration
reduces the social return to education (fewer remaining adults induces fewer exter-
nalities), and the optimal level of education decreases. On the other hand, migration
stimulates the laissez-faire investment in education. Consequently, the gap between
private and social returns to education decreases.
The above results characterize the "third best" solution with exogenous emigration
rates, i.e. when the domestic government has no control on the migration rate (or
when the ...rst order condition with respect to mt+1 is not used).
3Although perception costs in public ...nance are usually convex, the assumption of linear costs
was made for simplicity. The introduction of convex costs would yield similar results.
9
Is migration good or bad for the sending country? Using the ...rst order condition
with respect to mt+1, we can determine whether or not a positive migration rate is
desirable from the perspective of the sending country. The condition for a positive
emigration rate is @$SB > 0 evaluated at m = 0. This requires
@m
h (w w) > wh(1 + aR) e (11)
1
We have:
Proposition 3 There is a cuto¤ level in the distortion parameter above which the
c
optimal migration rate is positive.
Indeed, the right hand side term in (11) is decreasing in : from (9), a rise in
reduces the level of human capital. The left hand side term is increasing in (it
tends to in...nity when tends to one and is equal to zero when = 0).
Figure 1 below describes the impact of distortion costs on emigration and subsidy
rates. As in the exogenous migration case, SB falls to zero when perception costs
ss
are su¢ ciently high (when ( ;m) < 1 + m(w w)). Then perception costs vanish
w
and there is no room for increasing the emigration rate.
Assuming exogenous educational policies and abstracting from any normative
consideration, the recent literature on the brain drain reveals that skilled migration
can stimulate human capital accumulation in the sending country. Endogenizing
education subsidies, our analysis shows that emigration can be desirable if and only
if tax distortions are su¢ ciently high. On the contrary, when tax distortions are low,
impeding emigration and using domestic education policies is preferable. Hence, a
welfare improving brain drain can only be obtained in particular circumstances (high
...scal distortions and limited emigration rates). When e¢ ciency costs are low, the
bene...cial brain drain hypothesis hardly resists a normative analysis.
10
Fig 1. Perception costs, optimal subsidy and emigration rates
mss, ss
Subsidy rate
Emigration rate
c
3 Empirical analysis
A central prediction of our theoretical model is that, whether an ine¢ cient govern-
ment can control emigration or not, there should exist a negative relationship between
skilled emigration rates and public education subsidies. In this section, we use a re-
cent data set on emigration to address two empirical issues. Firstly, do human capital
accumulation and public subsidies e¤ectively respond to skilled migration rates? Sec-
ondly, does the endogeneity of public subsidies modify the gains and losses of skilled
migration compared to previous studies? We address these questions in a sample of
108 countries. We eliminate high-income countries (we select nations for which mi-
gration is likely to induce a clear incentive e¤ect), countries for which data on public
expenditures in education are not available and countries that experienced civil war
and political turmoil during the 1990s.4
4 Among countries for which data is available, we exclude Afghanistan, Armenia, Bosnia and
Herzegovina, Dem. Rep. of Congo, Croatia, Eritrea, Georgia, Guinea-Bissau, Iraq, Liberia, Mace-
donia, the Federated States of Micronesia, Rwanda, Serbia and Montenegro, Sierra Leone and
Somalia.
11
3.1 Data on skilled migration
Our empirical analysis is based on a recent data set on international migration by
educational attainment detailed in Docquier and Marfouk (2006) (henceforth DM).
DM use the receiving country r0s census or population register to extract information
on immigrants country of birth, age, and skill level. Such statistics were collected
for all OECD countries (Organization for Economic Cooperation and Development).
Let Mt;s denote the stock of working-age individuals born in a given country, of skill
r
level s = l; h (h stands for individuals with post-secondary certi...cates, l stands for
those with less than post-secondary schooling) and living in country r at time t. The
stock of emigrants from a given country for a given education level, Mt;s = Pr Mt;s;
r
is then obtained by summing over receiving countries. Emigration rates by education
levels are then obtained by comparing the number of emigrants to the population
at origin with similar characteristics, Nt;s. Skilled and unskilled emigration rates
are denoted by mt = Mt;h Mt;l respectively. The data set also
Nt;h+Mt;h and mt = Nt;l+Mt;l
allows us to compute the proportion of post-secondary educated among natives (Ht =
PN(Nt;s+Mt;s)
t;h+Mt;h
s The DM estimates are built accordingPto a broad de...nition of "skilled migrants"
) and among residents (ht = Nt;h ).
sNt;s
in that they include all foreign-born workers with post-secondary schooling wherever
they acquired education.5 Beine et al. (2007b) use immigrants' age of entry as
a proxy for where education has been acquired. They provide alternative measures
of the brain drain by de...ning skilled immigrants as those arrived in the receiving
country after age 12, 18 or 22. These corrected skilled emigration rates, which can
be seen as intermediate bounds to the brain drain estimates, are by construction
lower than those computed without age-of-entry restrictions by DM. Let us denote
5For example, Mexican-born individuals who arrived in the US at age 5 or 10 and later graduated
from US high-education institutions are counted as highly-skilled Mexican immigrants.
12
by mJ;t the skilled emigration rate based on migrants who left their country after
age J (J = 12;18;22), i.e. on restrictive measures of Mt;h. We denote by HJ;t the
corresponding proportion of educated among natives. These alternative measures
are only available for migrants with post-secondary level education. We use them to
evaluate the robustness of our empirical model in Appendix 6.3.
3.2 Empirical model and econometric issues
The theoretical model predicts (i) a negative relationship between skilled emigration
and subsidy rates and (ii) a positive e¤ect of migration prospects and subsidies on
human capital formation. In the theoretical model, individuals live a single adult
period. Hence, the stock of human capital is equal to the lagged investment of the
young. In the real world, the ow of investment in human capital can be approx-
imated by the change in the stock. Hence, our empirical analysis distinguishes two
dependent variables, the growth rate of human capital between 1990 and 2000 and the
logarithm of the education subsidy rate in 1990. Human capital is measured as the
proportion of post-secondary educated natives (including emigrants). The education
subsidy rate is measured as the amount of public expenditure in tertiary education
per student as percentage of GDP per capita (provided by the United Nations Ed-
ucational, Scienti...c and Cultural Organization - UNESCO).6 We consider these two
variables as endogenous and estimate two empirical equations.
Regarding human capital accumulation, we use a " -convergence" equation and
regress the log-ratio of human capital, ln(H00=H90), on:
- the log of the skilled emigration rate in 1990, ln(m90), so as to capture the incentive
e¤ect of migration prospects. Note that in our estimates, we ...rst use as a benchmark
the skilled emigration rate of all foreign born individuals regardless of whether they
6There is a high correlation between public expenditure in secondary and tertiary education (67
percent). This is not the case between the primary and tertiary levels.
13
acquire their education in their origin or host country;7
- the log of tertiary educated in 1990, ln(H90), so as to capture convergence or diver-
gence forces;
- the log of public subsidy per student as percentage of GDP per capita in 1990,
ln( 90); so as to control for the local education policy;
- the age structure of the population within a country. It can be argued that the
growth rate of human capital is stronger in countries where the population turnover
(replacement of old cohorts by young ones) is important. Since migrants usually be-
long to young cohorts, it is important to control for the population structure in our
regressions. We account for that possibility by using the demographic share of in-
dividuals aged 15 to 24, S15=24, and the share of those 49 to 55, S49=55 (Source:
United Nations Population Division);
- the urbanization rate, UR90; which accounts for access to schooling facilities within
a country (Source: World Development Indicators);
- the level of remittances in 1990, R90; which potentially alleviates liquidity constraints
impeding human capital investments (Source: World Development Indicators);
- a set of regional dummies REGDi (Sub-Saharan Africa, Latin America, Middle
East and North Africa, East Asia and Paci...c, Eastern Europe and Central Asia)
capturing regional unobserved characteristics. South Asia is used as reference.
This speci...cation is similar to that used in Beine et al (2007a) but is more general
it in several respects. We add new control variables (including regional ...xed e¤ects)
and use new UNESCO estimates of public expenditures in tertiary education. We
expect the inclusion of the latter variable to improve our assessment of the incentive
mechanism.
7In Appendix 6.3, we estimate our model using alternative measures of the skilled emigration
rate (mJ;t) and human capital stock (HJ;t) which control for the age of entry of migrants.
14
Regarding education subsidies, we estimate the log of public expenditure per stu-
dent as percent of GDP per capita in 1990, ln( 90); as a function of:
- the log of the high skilled emigration rate, ln(m90); so as to capture the policy
trade-o¤ predicted by our theoretical model;
- the investment rate in 1990, I90; since investments in public education are mainly
pro...table where there are machines to complement skills;
- the "rule of law" dimension of governance measuring the extent to which agents
have con...dence in and abide the rules of society, RLAW. It ranges from -2.5 (bad
governance) to 2.5 (good governance). We average the annual scores provided in Kauf-
mann et al. (2003);
- dummies for middle-income (MINC) countries based on the World Bank classi...-
cation;
- the level of remittances in 1990, R90; so as to capture the political demand for public
transfers (as remittances are potential determinants of liquidity constraints);
- the same set of regional dummies, REGDi, as above.
Our speci...cations are:
ln(H00) = a0 + a1: ln(m90) + a2: ln(H90) + a3 ln( 90) + a4S15=24 (12)
H90
+a5S49=55 + a6UR90 + a7R90 + X12 aiREGDi + H
i=8
ln( 90) = b0 + b1: ln(m90) + b2:I90 + b3:RLAW + b4:MINC + (13)
+b5:R90 + X10 biREGDi +
i=6
where H and are error terms.
The potential correlation between unobserved characteristics and the emigration
rate can a¤ect both the growth rate of human capital and level of public subsidies
15
per student. Therefore, the OLS method can generate inconsistent estimates. To
address such a problem, we use the instrumental variable (IV) method and estimate
the two equations with the two-stage least square procedure (2SLS). We consider
ln(m90) as the instrumented variable. The recent empirical growth literature (Barro
and Sala-i-Martin, 1995; Hall and Jones, 1999) paid attention to the determinants of
instruments when estimating a migration equation. However, it is di¢ cult to select
excluded instruments for migration due to an obvious presumption of correlation with
human capital. Here, the ...rst-stage migration equation uses geographical proximity
with developed countries (minimal distance to OECD countries), and two indicators
of disadvantageous location (dummies for landlocked countries and small islands).
In previous versions of the paper, we ran many regressions with di¤erent sets of
instruments and obtained similar results.
In our estimation strategy, several diagnostic tests are conducted to assess the
reliability of the IV estimates. We ...rst check whether our instruments are relevant
and valid using the ...rst-stage F-statistic of joint signi...cance of the instruments (the
rule of thumb in Staiger and Stock (1997) is that F-statistic should exceed 10), An-
derson's canonical correlations likelihood ratio test statistic, and the Cragg-Donald
statistic for weak instruments. The instruments'strength is analyzed against the null
hypothesis of weak instruments, as suggested in Stock and Yogo (2002). The valid-
ity of our instruments is assessed using the Hansen J-statistic for overidenti...cation.
Finally, provided that our instruments satisfy the relevance and validity conditions,
IV estimates can be consistent but ine¢ cient. Therefore, if regressors are exogenous,
consistent and more e¢ cient estimates produced by OLS are preferred. Thus, we
test for exogeneity of ln(m90) using a C-test. We also correct for the presence of
heteroscedasticity in the data and checked for multicollinearity.
16
3.3 Results for the human capital equation
Table 1 reports the OLS and IV estimation results for human capital accumulation
using the overall skilled emigration rate regardless of the age of entry of individuals.
For each method, the ...rst column corresponds to the full speci...cation of the equation
of human capital accumulation; the second column gives a parsimonious speci...cation
in which unsigni...cant or weakly signi...cant variables such as I90 and R90 are excluded.
Note that dropping these variables increases the size of our sample. For IV regressions,
we report ...rst and second stage diagnostic tests.
The results in Table 1 show a positive and signi...cant association between skilled
migration rates and human capital accumulation. This e¤ect is robust across dif-
ferent speci...cations and estimation methods. However, the magnitude di¤ers across
methods. The size of the IV estimate is twice as large as the one obtained with OLS.
Our estimates also indicate that an increase in public subsidies has a positive and
stable impact on human capital formation. Another ...nding worth emphasizing is the
negative and signi...cant impact of the initial human capital stock. This suggests the
existence of a conditional convergence process between 1990 and 2000. The share of
the young cohort S15=24 has negative sign. This can be explained by the fact that
human capital formation is lower in poor countries with high fertility and population
growth rates. The share of the older cohort S49=55 has negative sign, indicating that
a lower turnover of the population reduces the growth rate of human capital. Urban-
ization has a positive and signi...cant impact on human capital formation. Regional
dummies are not reported in the table. In all speci...cations, the sub-Saharan dummy
is signi...cant and negative. The dummies for East-Asia and Paci...c and Eastern Eu-
rope and Central Asia are signi...cant and positive. There is no signi...cant e¤ect for
Latin America and Middle East and North Africa.
17
In every IV regression, the instruments satisfy the relevance and validity con-
ditions. Indeed, the Hansen statistic has high p-values, suggesting that the null
hypothesis is not rejected and the instrument excludability requirement is satis...ed.
The ...rst-stage statistics support instrument relevance and strength: the F-statistics
are above 10; the low p-values of the Anderson canonical correlation likelihood ratio
test, indicate rejection of the irrelevance hypothesis. The Cragg-Donald weak identi-
...cation test rejects the weakness of the instruments. However, the C-tests strongly
suggest rejection of endogeneity. This indicates that the variable ln(m90) can be
treated as exogenous. It follows that the OLS method is the most appropriate esti-
mation technique. Thus, based on the F-Statistic, the OLS 2 model appears to be
the superior speci...cation. The growth rate of human capital between 1990 and 2000
exhibits an elasticity between 3.2 and 4.2 percent with respect to skilled migration
(Beine et al (2007a) found 4.8 percent) and an elasticity of 12 percent with respect
to public subsidies. Appendix 6.3 discusses the robustness of these results.
3.4 Results for the subsidy equation
Table 2 gives the OLS and IV estimates for education expenditures per student. In
all regressions, we obtain a negative and signi...cant impact of ln(m90) on the sub-
sidy rate. We note that the coe¢ cients of ln(m90) are biased downward in OLS
estimations models compared to their magnitudes in IV models. The quality of gov-
ernance (RLAW) is an important factor, signi...cantly and positively a¤ecting public
education subsidies. Subsidies are signi...cantly higher in middle-income countries;
remittances and investments have no e¤ect on education expenditures per student.
All regional dummies proved to be signi...cant and positive (compared to the reference
region, South Asia).
18
Table 1. Log Ratio of Human Capital (H00=H90)
OLS 1 OLS 2 IV 1 IV 2
ln(m90) 0.042** 0.032** 0.082** 0.077**
(0.021) (0.006) (0.036) (0.037)
ln(H90) -0.285*** -0.273*** -0.278*** -0.278***
(0.039) (0.038) (0.040) (0.040)
ln( 90) 0.119** 0.121** 0.125** 0.116**
(0.058) (0.049) (0.060) (0.053)
S15=24 -2.227*** -2.346*** -1.897** -1.907**
(0.860) (0.792) (0.821) (0.807)
S49=55 -10.44*** -10.11*** -10.57*** -10.37***
(3.215) (2.972) (3.112) (3.086)
UR90 0.228* 0.263** 0.410*** 0.380***
(0.137) (0.117) (0.148) (0.147)
R90 -0.000* -0.000*
(0.000) (0.000)
I90 -0.000 -0.000
(0.000) (0.000)
REGD yes yes yes yes
F-statistic 32.255 41.265 36.438 40.021
N. Obs 88 105 104 105
Hansen test (i) 4.622 3.567
p-value 0.099 0.168
First-stage F stat.(ii) 15.52 16.43
Anderson test (iii) 38.398 38.793
p-value 0.000 0.000
Cragg-Donald test (iv) 13.398 13.707
C-test (v) 1.763 1.319
p-value 0.184 0.251
Between brackets, Standard errors. Reported heteroskedastic-robust.
IV excluded instruments: distance to OECD, dummies for landlocked and small island.
p<0.1, ** p<0.05, *** p<0.01
(i) Hansen J statistics - Over-identi...cation test.
(ii) F statistics for ...rst stage regression - Instrument relevance.
(iii) Anderson LR statistics - Instrument relevance.
(iv) Cragg-Donald statistics Instrument relevance.
(v) C-test - Exogeneity of ln(m90).
19
The p-values associated with the Chi-square statistics of the C-test suggests the
variable ln(m90) is not exogenous. The implication is that OLS estimates are not
consistent and that the IV estimation technique is therefore more appropriate. Thus,
the estimated coe¢ cients of model IV2 (the best speci...cation in the table given the
F Statistic) indicate a strong and highly signi...cant relationship between these two
variables: the average elasticity of public education subsidies to skilled migration
rates amounts to -0.20. Such a result is consistent with the main prediction of our
theoretical model. For IV regressions, F-tests on excluded instruments indicate that
these are jointly signi...cant in predicting the endogenous regressor, ln(m90). The
Anderson relevance tests suggest that these instruments as a set are relevant and
strong predictors of ln(m90). The Cragg-Donald statistics exceed the critical value
of 9.08 (at least in model IV2), which imply a bias relative to OLS of less than 10
percent (Stock and Yogo, 2002). The overidenti...cation tests (Hansen J statistic) do
not reject the null hypothesis that the instruments are independent of the second-
stage disturbance terms at the 5 percent level of signi...cance.
20
Table 2. Public education subsidy, ln( 90)
OLS 1 IV 1 OLS 2 IV 2
ln(m90) -0.039* -0.232*** -0.051* -0.201***
(0.041) (0.075) (0.032) (0.057)
I90 0.000** 0.000** 0.000** 0.000**
(0.000) (0.000) (0.000) (0.000)
RLAW 0.494*** 0.407*** 0.420*** 0.363***
(0.117) (0.138) (0.109) (0.124)
MINC 0.503*** 0.333** 0.512*** 0.391***
(0.136) (0.148) (0.130) (0.125)
R90 -0.000 -0.000
(0.000) (0.000)
REGD Yes Yes Yes Yes
F-statistic 80.80 52.34 101.63 72.51
N. obs 92 92 107 107
Hansen test (i) 1.827 1.410
p-value 0.176 0.235
First-stage F stat.(ii) 13.47 18.07
Anderson test (iii) 26.65 32.32
p-value 0.000 0.000
Cragg-Donald test (iv) 13.44 16.93
C-test (v) 7.86 7.856
p-value 0.005 0.005
Between brackets, Standard errors. Reported heteroskedastic-robust.
IV excluded instruments: distance to OECD, landlocked dummy
p<0.1, ** p<0.05, *** p<0.01
(i) Hansen J statistics - Over-identi...cation test.
(ii) F statistics for ...rst stage regression - Instrument relevance.
(iii) Anderson LR statistics - Instrument relevance.
(iv) Cragg-Donald statistics Instrument relevance.
(v) C-test - Exogeneity of ln(m90).
21
3.5 Brain drain and human capital accumulation
Let us now use our empirical ...ndings to simulate the e¤ect of skilled migration on
human capital accumulation. We use a counterfactual experiment, which consists
of setting the 1990 skilled emigration rate to the level of the unskilled rate, m90.8
The unskilled migration rate may be considered as a minimal emigration rate given
country characteristics such as size, geographic proximity, colonial and linguistic links
with OECD members and political factors at origin. Hence, our experiment consists
of minimizing the size of the brain drain. We ...rst use (13) to simulate the impact
on education susbsidies, b90, and then use (12) to predict the 2000 level of human
capital among natives, H00. Note that a similar method is used in Beine et al (2007a)
to compute the e¤ect ofb skilled migration on human capital accumulation between
1990 and 2000. However, taking education subsidies as exogenous (BDR method)
potentially overestimates the size of the incentive e¤ect on human capital formation.
We compare the observed and hypothetical proportions/numbers of skilled resi-
dents. Figure 2 gives the simulated impact of skilled emigration on the proportion
of skilled among residents (intensive measure of human capital) and Figure 3 gives
the impact on the number of skilled residents (extensive measure). A positive amount
means that the country bene...t from skilled migration, i.e. has more human capital
than in the counterfactual scenario where the brain drain is reduced. The grey lines
reports simulations with exogenous subsidies (BDR method).
8For a couple of countries where the unskilled emigration is very close to zero, we impose a lower
bound equal to one tenth of the skilled emigration rate. Since we use a log speci...cation, this avoids
unrealistic e¤ects.
22
Fig 2. Net e¤ect of skilled migration on the proportion of skilled
residents
2.00
1.00
0.00
India
-1.00 Mongolia Brazil China
Bangladesh Indonesia Pakistan Nigeria Turkey
Mexico Kenya fricaA
-2.00
South
-3.00 Philippines
-4.00
-5.00 Nevis
nda
-6.00
Kitts
-7.00 Saint
Brain gain (endogenous subsidies) Brain gain (exogenous subsidies)
-8.00
Fig 3. Net e¤ect of skilled emigration on the number of skilled residents
1400000
1200000
1000000
800000
600000
400000
200000 Brazil
India
0 h
-200000 China
Pakistan Kenya
Banglades Nigeria
Indonesia Turkey Africa
-400000 Mexico
Brain gain (endogenous subsidies) Brain gain (exogenous subsidies) South
Philippines
-600000
23
Setting skilled migration rates to unskilled migration rates induces a rise in the
subsidy rate in almost all countries.9 On average the rate is multiplied by about
1.48. Notwithstanding the rise in education subsidies, reducing skilled migration
rates would have a negative impact on the proportion of educated in 20 countries and
a negative impact on the number of educated in 18 countries (out of 108 countries).
Such brain gain or bene...cial brain drain cases are obtained in large countries combin-
ing relatively low levels of human capital and low skilled emigration rates, con...rming
the BDR results.
The group of winners includes large countries (e.g., China, India, Brazil, Bangladesh)
which represent a large fraction of the population residing in developing countries.
Our results are more pessimistic than those of Beine et al (2007a) who treat educa-
tion subsidies as exogenous (see grey line on Figures 2 and 3). The BDR method
gives 51 winners, larger gains or smaller losses. In addition, BDR predict that the
brain drain generates a positive net gain for developing countries as a whole (+2.2
percent of post-secondary graduates). Endogenizing education subsidies increases the
number of losers and the size of the losses. On the whole, the brain drain induces a
net negative e¤ect on the total number of post-secondary educated in the developing
world (-2.7 percent).
4 Conclusion
One of the arguments levelled at the brain drain is the loss of investment of public
spending in the education of emigrants. How do developing countries adjust their
education policies to skilled migration? What is the resulting e¤ect of their policy on
human capital accumulation? Our paper addresses these questions both theoretically
9The only exception is Bulgaria where the unskilled emigration rate exceeds the skilled emigration
rate.
24
and empirically.
Assuming exogenous education policies, the new literature on the brain drain as-
serts that high-skill migration entails bene...cial feedback e¤ects for the source coun-
tries. Authors such as Vidal (1998), Mountford (1999) and Stark and Wang (2002)
argue that migration prospects may foster education investments in developing coun-
tries, thus making it possible for a brain drain to be bene...cial to the source country.
Survey data and macroeconometric studies con...rm that possibility. Endogenizing
education subsidies, our theoretical analysis reveals that a positive emigration can be
desirable if, and only if, tax distortions are su¢ ciently high, i.e. if the local govern-
ment is unable to decentralize the ...rst best solution with non distortive tax-transfers.
Conversely, when tax distortions are low, impeding skilled emigration would be so-
cially better. The optimal emigration rate is zero. Hence, resorting to the brain drain
must be considered as a second-best policy option that reects the inability of the
government to costlessly use domestic instruments.
Some recent studies such as Beine et al. (2001, 2007a) provide empirical support
for the bene...cial brain drain hypothesis, abstracting from various indirect e¤ects on
skill premia, ...scal policies, etc. In particular, they disregard possible "crowding-out"
...scal e¤ects on public subsidies. Investigating the empirical relationship between
education subsidies and migration prospects, we obtain a signi...cant and negative
relationship in a cross-section of 108 countries. Skilled migration and public subsi-
dies are empirical substitutes. We then revisit the country speci...c e¤ects of skilled
migration on human capital by considering public subsidies as endogenous. Our
counterfactual experiment consists in setting the skilled emigration rate to the un-
skilled rate. We then compute the hypothetical human capital change between 1990
and 2000. The endogeneity of public subsidies strongly reduces the relative number
of losers, increases the size of the losses and reduces the size of the gains in other
25
countries. Obviously, focusing on human capital formation, our analysis abstracts
from all other indirect channels though which migration a¤ects the sending country
(through return migration, remittances, network e¤ects, etc.) or the domestic return
to education (wage rate, skill premium, etc.). Although the perspective of a ben-
e...cial brain drain appears more limited than in previous studies, we still obtained
"winning" countries. However, the net e¤ect on the total number of educated workers
residing in the developing world becomes negative.
5 References
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of Monetary Economics, 32, 363-394.
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Becker, G.S., E.L. Glaeser and K.M. Murphy (1999): Population and economic growth,
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Beine, M., F. Docquier and Hillel Rapoport (2001): Brain Drain and Economic Growth:
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Kangasniemi, M., L.A. Winters and S. Commander (2004): Is the medical brain drain
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Lagerloef, N.P. (2000), "From Malthus to modern growth: the three regimes revisited",
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Mountford, A. (1997): Can a brain drain be good for growth in the source economy?,
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6 Appendix
6.1 Proof of Proposition 1
Using At+1 = nAt(1 mt+1), the planner maximizes $FB in (5) with respect to ht+1,
et and mt+1. This gives the following ...rst order conditions:
@$FB
= tAt+1w + t+1At+2Rwa tAt+1 t+1 1
t+ At+2 t+1et+1 ht+1 = 0
@ht+1
@$FB
= tAt+1R + tAt+1 1
t et ht = 0
@et
@$FB
= tAtnCt+1 < 0
@mt+1
Focusing on the steady state, the social return to human capital, FB = w[1+ nRwa],
ss 1 n
exceeds the private return on human capital, w.
From the ...rst order condition with respect to mt+1, emigration deteriorates social
welfare. The optimal emigration rate is therefore zero.
6.2 Proof of Proposition 2
At the steady state, the ...rst order conditions of (8) are:
28
(i) 0 = w [1 + n(1 m)Rwa] [1 n(1 m) ]
+ n(1 m) [w + m(w w)] h 1
(ii) 0 = R(1 1
t) + e h n R(1 )(1 )e
(iii) 0 = R n + Re
(iv) 0 = R + n[1 c0( y)]
(v) 0 C + (1 m) h (w w)
Clearly, when c0( y) = 0, conditions (iii)-(iv) imply n = R and = 0. From
condition (v), the optimal migration rate is zero. From condition (i), the social return
on human capital is identical to the ...rst best value, FB . Consequently, the ...rst
ss
best solution emerges.
When perception costs are positive, c0( y) > 0, we have n > R, > 0 so that the
optimal migration rate can be positive. Assuming linear e¢ ciency costs (c0( y ) = )
and combining conditions (i), (iii) and (iv), the social return on human capital is
given by:
m)1 + m(w w)
SB w
=
ss w n1 + n(1 m)Rwa + n(1
1 n(1 m) h1 io
From condition (ii), the optimal level of education amounts to:
SB + (w + m(w w))
eSB =
ss " h (1 )
ss
R #11
Combining these results and using (1) yields:
w ( ;m) 1
hSB =
ss R
(1 )[1+ n(1 m)Rwa]+ n(1 m)
with ( ;m) ; which
1h1+m(w w)
w
n(1 m) i+ h1+m(w w)
w i[1 n(1 m) ]
is, for reasonable values of the parameters, a decreasing function of and m (at
29
least for ranging from 0 to 0.5 and for any m). Note that, we have w (0;0) =
w[1+ nRwa] = FB.
1 n ss
Decentralizing the second best solution requires a subsidy rate equal to:
( ;m) 1 m(w w)
SB = w
ss ( ;m)
such that the subsidy rate is a decreasing function of both and m:
@ (1 + m(w w) ) 0 (w w)
= w m w < 0
@m 2
w)
@ (1 + m(w ) 0
w
= < 0
@ 2
It should be noted that SB can be negative for high emigration rates (when ( ;m) <
ss
1 + m(w w) ). The budget constraint requires y = SB SB ).
w ss ss ess =(1
6.3 Human capital regressions - Robustness check
The incentive e¤ect of skilled emigration on human capital accumulation remains
positive and signi...cant whatever the measures of brain drain used. Table A reports
replications of the speci...cations OLS2 and IV2 of Table 1 distinguishing di¤erent
ages of entry. We only report estimates for the three main explanatory variables
although results for other controls and diagnostic tests are almost identical to those
in Table 1. Clearly, Table A supports the robustness of the incentive mechanism and
the positive e¤ect of public education subsidies.
In previous version of the paper, we investigated the robustness of this mechanism
using functional forms other than the log-linear speci...cation we have adopted here.
The incentive mechanism depicted in Table 1 is robust to the alternative speci...ca-
tions: results with m90 or ln(1 + m90); rather than ln(m90), can be obtained upon
request. It could also be argued that further e¢ ciency gains would be obtained by
30
estimating both equations simultaneously as a system. We tested our model using a
three-stage least squares (3SLS) system and obtained similar results.10
Table A. Log Ratio of Human Capital (HJ;00=HJ;90), controlling for age of
entry
J = 12 J = 18 J = 22
OLS IV OLS IV OLS IV
ln(mJ;90) 0.032** 0.077** 0.033** 0.077** 0.033** 0.077**
(0.015) (0.036) (0.016) (0.036) (0.016) (0.036)
ln(HJ;90) -0.273*** -0.279*** -0.273*** -0.277*** -0.273*** -0.277***
(0.038) (0.040) (0.038) (0.040) (0.038) (0.040)
ln( 90) 0.121** 0.116** 0.121** 0.116** 0.120** 0.115**
(0.049) (0.053) (0.048) (0.051) (0.048) (0.051)
Other controls Yes Yes Yes Yes Yes Yes
F-statistic 41.45 40.11 41.29 40.28 41.37 40.24
N. Obs 104 104 104 104 104 104
Between brackets, Standard errors. Reported heteroskedastic-robust.
p<0.1, ** p<0.05, *** p<0.01
10 These results can be obtained upon request to the authors.
31