Rethinking the Brain Drain

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1 Deartment of Economics Discussion Paer Rethining the Brain Drain Oded Star, University of Bonn; University of Vienna; and ESCE Economic and Social Research Center, Cologne and Eisenstadt May 003 Deartment of Economics University of Calgary Calgary, Alberta, Canada T 4 This aer can be downloaded without charge from htt://

2 Rethining the Brain Drain by Oded Star University of Bonn; University of Vienna; and ESCE Economic and Social Research Center, Cologne and Eisenstadt Mailing Address: ZEF, University of Bonn May 003 Walter-Flex-Strasse 3 D-533 Bonn Germany Address: This aer is the text of the Tjalling Koomans Distinguished Lecture delivered by the author at the International Institute for Advanced Systems Analysis IIASA in March 003. The aer draws on University of Bonn, Center for Develoment Research, Discussion Paers on Develoment Policy, Paer o. 999, and on Institute for Advanced Studies, Vienna, Economics Series, Paer o Partial financial

3 suort from the Humboldt Foundation, the Sohmen Foundation, and the School of Economics and Finance at the University of Hong Kong is gratefully acnowledged.

4 Abstract When roductivity is fostered by both the individual s human caital and by the average level of human caital in the economy, individuals under-invest in human caital. A strictly ositive robability of migration to a richer country, by raising both the level of human caital formed by otimizing individuals in the home country and the average level of human caital of non-migrants in the country, can enhance welfare and nudge the economy toward the social otimum. Under a well-controlled restrictive migration olicy the welfare of all worers is higher than in the absence of this olicy. Keywords: Migration; Human caital formation; Externalities; Social welfare

5 . ITRODUCTIO There is a strong consensus that deficiency in human caital is a major reason why oor countries remain oor. Much though not all of the human caital in a country is a result of decisions made by individuals. But individual choices seldom add u to the social otimum. In articular, individuals do not consider the ositive externalities that human caital confers in roduction. The result is that they acquire less human caital than is desirable. If individuals could be ersuaded to form more human caital, the human caital in an economy could rise to the socially otimal level. What maes an unfortunate state of affairs worse is that whatever quantities of human caital are formed, some and often more than a mere some are lost through the migration leaage. It comes as little surrise then that the concern heretofore has been to contain this leaage. In the words of a recent World Develoment Reort: Can something be done to sto the exodus of trained worers from oorer countries? World Ban 995,.64. This concern follows, and is in congruence with, the large brain drain literature for a systematic review see Bhagwati and Wilson 989. The concern is regularly echoed by the informed ress. In a May 6, 000 lead article that addresses the issue of migration to the Euroean Union, The Economist magazine states: [A]ny regime that concentrated on luring the highly silled would run the ris of robbing oor countries of the eole they are least able to do without. In its May 3, 00 lead article, while advocating the entry of migrants into Euroe, The Economist hastens to add: There is a ris, esecially when immigration olicies target only the highly silled, that the best talent will be drained from oor countries to rich ones. Similar exressions of alarm are voiced by students of

6 migration. Sholniov 995 writes: If able younger scientists leave Russia, their older colleagues would have fewer talented eole to whom they can ass their nowledge. This could lead to a decline in the quality of research in those scientific discilines where Russia is currently raned high internationally. Although exressed more cautiously, the viewoint of Carrington and Detragiache 999 resented in a recent bulletin of the International Monetary Fund is quite similar: Another imortant issue is the extent to which the benefits of education acquired by citizens of develoing countries are externalities that individuals cannot be exected to tae into account when maing their rivate decisions. If such externalities are substantial, as is emhasized by the new growth theory, then olicies to curb the brain drain may be warranted. In this aer we turn this concern on its head. We argue that the rosect of migration can well be harnessed to induce individuals to form a socially desirable level of human caital. Our oint is that comared to a closed economy, an economy oen to migration differs not only in the oortunities that worers face but also in the structure of the incentives they confront; higher rosective returns to human caital in a foreign country iminge on human caital formation decisions at home. We consider a setting in which an individual s roductivity is fostered by his own human caital as well as by the economy-wide average level of human caital. We examine the relationshi between the actual formation of human caital in an economy and the socially otimal formation of human caital in the economy. We identify conditions under which, from a social oint of view, there is too little human caital formation in the economy, and examine the relationshi between the actual formation of human caital and the otimal formation of

7 human caital in the resence of a ossibility of migration. We identify conditions under which er caita outut and the level of welfare of all worers are higher with migration than in its absence, and show that a controlled and restrictive migration olicy can enhance welfare and nudge the economy toward the social otimum. We derive this result first when all worers are alie and are equally caable of resonding to the migration rosect, and second when worers differ both in their sills and in their ability to resond. We conclude that migration is conducive to the formation of human caital. Thus, we cast migration as a harbinger of human caital gain, not as the culrit of human caital drain. An interesting imlication of our ercetion of what migration entails is that the gains from migration to the home country accrue neither from migrants remittances nor from migrants return home with amlified sills acquired abroad. The resent aer builds on earlier aers by Star, Helmenstein, and Prsawetz 997, 998. The main urose of those aers was to establish a ositive causal relationshi between the robability of migration by silled worers from a develoing country and human caital formation within the country. The resent aer taes several major stes that go beyond the analysis erformed in the earlier aers: it defines the socially otimal level of human caital er worer, it measures the difference between that level and the actual level of human caital er worer, it exlains the ga between these two levels, it shows that a sillfully managed migration olicy serves to eliminate the ga, it identifies a concrete olicy tool, it erforms exlicit welfare analysis, and it resents and investigates the case of a heterogeneous worforce.

8 . HUMA CAPITAL FORMATIO I A ECOOMY WITHOUT MIGRATIO Consider a closed economy or a small oen economy without migration. The economy roduces a single commodity. There are identical worers in the economy. The single roduction inut is labor. The worer s cost function of forming human caital is linear in, where is the worer s human caital the sum total of his efficiency units of labor. The economy-wide level of outut is times the er-worer concave roduction function. This roduction function is a weighted sum of and of, the economywide average level of human caital. The reason for the deendence of the worer s outut on is the revalence of externalities that accrue from the average level of human caital. Externalities in roduction arise when as a result of individuals acquiring human caital, they not only mae themselves more roductive but also mae each other more roductive. Conversely, when individuals fail to form human caital, they not only mae themselves less roductive but also mae each other less roductive. A simle way of conditioning a worer s outut not only on his own human caital but also on the human caital of others is to have the worer s outut deend on the average level of human caital. Worers suly their human caital inelastically, having acquired it instantly, though not costlessly, at the beginning of their single-eriod life. Worers borrow the requisite funds to suort the human caital formation at a zero rate of interest. Since labor is the only roduction inut, the gross earnings er worer are simly equal to the outut er worer. The worer sees to maximize his net earnings,

9 that is, his outut minus the cost of forming human caital. Let us refer to the solution to the worer s otimization roblem as. It turns out that is fully secified by the arameters of the cost function of forming human caital and of the roduction function. Since there are identical worers in the economy, the average level of human caital in the economy is also. Therefore, net earnings er worer are fully secified by the model s arameters. Let us refer to these earnings as W. Since the social returns of human caital are not internalized by the individual worer, is not the socially otimal level of human caital. et earnings er worer are maximized when the externalities from the economy-wide average level of human caital are taen into account. The that aears in the worer s maximand is substituted by in the social lanner s maximand. Let us refer to the solution of the social lanner s otimization roblem as results emerge.. Two First, >. Second, if worers choose to form the socially otimal level of human caital,, the net earnings er worer will become W. It is easily shown that W > W. et earnings er worer attained under the social lanner s choice of are higher than those achieved when worers choose how much human caital to form without taing into consideration the human caital externality. By construction, W reresents the highest net earnings er worer achievable, given the roduction technology. Unfortunately, when choosing how much human caital to form, an individual worer will not ay heed to the economy-wide average level of human caital,

10 excet as a arameter. In a large economy no individual can affect the economy s average level of human caital. Thus, the revailing level of human caital will be.

11 3. HUMA CAPITAL FORMATIO I A ECOOMY WITH MIGRATIO In this section we cast migration olicy as a tool to mitigate the inefficiency arising from human caital externalities. Assume that an oortunity to migrate to another, suerior technology country, D, resents itself. Assume further that human caital neither dereciates nor areciates across countries, and that the human caital of individual migrant worers is decihered in D fully and immediately uon the migrants arrival. The returns to human caital in D are higher than in the home country, H. A worer s outut, and thus his gross earnings, in D are again a concave function of the worer s level of human caital. Suose that worers in H face a robability, > 0, of obtaining the gross earnings from an emloyment in D. With robability they do not secure such an emloyment, in which case they wor in H for the home country s gross earnings. Again, the worer s decision roblem is how much human caital to form. ot surrisingly, the worer s chosen level of human caital, Several results follow., deends ositively on. First, > ; in the resence of the ossibility of migration, worers choose to form more human caital than in the absence of the ossibility of migration. The inducement effect of migration raises the level of human caital of all worers including the worers who stay in H. Thus, the inadequacy of human caital formation due to the externalities is mitigated and consequently welfare can otentially be imroved by the

12 ossibility of migration. If the inducement is strong enough, the home country could even be left with more total human caital in the wae of migration. The brain gain could then exceed the brain drain for the home country s total human caital. Second, we are able to erform a comlete welfare analysis. To this end, we reason as follows. Since the returns to human caital in D are higher than the returns to human caital in the home country, the net earnings of the worers who migrate to D are higher than the net returns of those who stay behind. After all, the worers who migrate had incurred exactly the same cost of acquiring human caital as the worers who stay behind, yet the gross earnings of the former are higher than the gross earnings of the latter. Therefore, the ossibility of migration would mae every home country worer better off if it maes the non-migrants better off. To examine whether the ossibility of migration made the non-migrants better off we therefore comare W and W. Viewing the robability of migration,, as a olicy variable, we can show that the difference between W and W attains a unique maximum at a level of to which we refer as, 0 < <, and that the difference between W and W evaluated at is ositive. This result reveals that a carefully designed migration olicy can be welfare enhancing and that the welfare gain of the non-migrants is maximized when the robability of migration is equal to the feasible level. It further follows that when we insert the value of into, we get that the level of is equal to. Therefore, when the robability

13 of migration is, the level of human caital that worers choose to form is exactly the level chosen by the social lanner in the absence of migration. Thus, the welfare of the worers who stay behind is inadvertently maximized by the inducement effect of the ossibility of migration. It is in this sense that a migration olicy can correct for the human caital externality and restore the social otimum. A setic could argue that the otimal robability is a mere theoretical concet; in ractice it would be difficult, if not imossible, for the government of the home country to now the exact level of. This may call into question the usefulness of migration as a tool to imrove welfare and to correct for the disregard of the human caital externalities. To address this concern we examine the difference between W and W as a function of. We can show that this difference is ositive for any 0 <. Thus, as long as the robability of migration is not greater than, the net earnings of a worer who stays in H under migration are higher than the net earnings er worer without migration. This suggests the ractical use of migration as a welfareenhancing olicy tool even when the government of H does not now the exact level of the otimal robability. To sum u, our analysis suggests that a controlled and restrictive migration olicy can be welfare enhancing for non-migrants. In articular, in the resence of a controlled migration olicy with the robability of migration set at, the level of human caital

14 that the worers are induced to form turns out to be the socially otimal level of human caital had the worers not migrated. 4. HETEROGEEOUS WORKFORCE, HUMA CAPITAL FORMATIO, AD MIGRATIO The intersection of migration with the resence of externalities could give rise to a concern that those who leave adversely affect the roductivity of those who stay behind. If the human caital of the worers who migrate is higher than the human caital of the worers who stay behind, and if a worer s outut is an increasing function of the average level of human caital, the non-migrants will end u worse off; the worers who migrate imose a negative externality on the worers who remain. To address this concern, we examine what might be exected to constitute the worst ossible case from the ersective of the low sill worers the case in which these worers cannot articiate in migration at all. We can show that even in such a harsh environment, the human caital formation resonse of the high sill worers to the migration rosect can still lead to the low sill worers being better off. The essence of the argument is as follows. Let us relax the assumtion that the worforce is homogeneous, and let us suose that there are two tyes of worers in H: Low-ability, tye- worers and highability, tye- worers. Human caital formation is costlier for tye- worers. Let the cost of forming human caital by a tye- worer be such that this worer cannot ossibly form a level of human caital that is higher than. The tye- worers do not

15 face such a constraint and otimally choose to form human caital at the level. If and are the numbers of tye- and tye- worers, resectively, then in the absence of migration the average level of human caital in H is =. Let the robability of being selected into emloyment in D for an H country worer whose human caital is be if >, and 0 otherwise. The resence of an oortunity to migrate and earn higher wages in D induces the tye- worers to form more human caital. However, the tye- worers are immune to this inducement effect because of their inability to form more human caital than the minimal level required for the robable emloyment in D. Therefore, under the ossibility of migration, the levels of human caital formed by tye- and tye- worers are, resectively, and, where is an increasing function of. Hence, the average level of human caital of the worers who remain in H is m =. We can, first, comare m and and derive a reasonable sufficient condition under which the average level of human caital of the non-migrants in the wae of migration, migration,. m, is higher than the average level of human caital in the absence of Second, and more imortant, we can once again erform a comlete welfare analysis. When the migration rosect leads to a higher average human caital, tye-

16 worers are obviously better off, benefitting from a greater human caital externality. Whether the remaining tye- worers are also better off under migration is less clear. Yet, when is small and the reasonable sufficient condition yielding m > holds, we are able to show that the tye- worers who remain in H are also better off when the robability of migration is small enough. This result reaffirms the main result of the revious section: a restrictive migration olicy can stimulate human caital formation and imrove the welfare of all worers. In addition, the ossibility of a brain drain of highability worers from H can confer a ositive externality on low-ability worers in H. 5. COCLUSIOS When the roductivity of an individual in a closed economy or in a small oen economy without migration is fostered not only by his own human caital but also by the average level of human caital, the individual who otimally chooses how much to invest in costly human caital formation will, from a social oint of view, under-invest. Consequently, social welfare is affected adversely. Somewhat surrisingly, the facility of migration can mitigate this undesirable outcome. In fact, a well-secified migration olicy can ameliorate the tendency to under-invest in human caital and ermit the formation of a socially desirable level of human caital. The favorable effect of migration and the associated welfare gain aly not only when all individuals can resond to the migration rosect but also when only a subset of individuals are affected. In the latter case, even those who cannot gain from migration by articiating in it stand to gain from the resonse of others.

17 The roensity to acquire sills is not invariant to the ossibility that the sills will be highly rewarded. This consideration aears to have escaed the attention of scholars of migration for many years. The ioneering wor of Grubel and Scott 966 rovides a careful account of why a country need not lose by the emigration of highly silled individuals. In Grubel s and Scott s words [E]migration should be welcomed whenever two conditions are met. These are, first, that the emigrant imroves his own income and, second, that the migrant s dearture does not reduce the income of those remaining behind. 70. That the rosect of migration modifies the human caital formation calculus, thereby entailing a welfare gain for the non-migrants rather than being inconsistent with a welfare loss has neither been mentioned by Grubel and Scott, nor by those who followed in their stes. This aer draws attention to this ossible relationshi. We have shown that the behavioral resonse to the rosect of migration nourishes both a brain drain and a brain gain, and that a sillfully executed migration olicy can confine and utilize the resonse to secure a welfare gain for all worers. 6. COMPLEMETARY REFLECTIOS Building on the foregoing analysis it could be of interest to assess the sensitivity of our results to alternative secifications, to inquire whether our aroach can be extended to incororate welfare analysis in the destination country, and to consider the olicy role that the government of the destination country can lay.

18 In the existing model, human caital is erfectly transferable across economies moving it does not detract from its roductivity it is erfectly general. The existing framewor also assumes full emloyment. Suose, alternatively, that there are two tyes of human caital: general, and destination-secific henceforth secific. The latter tye is roductive abroad but useless at home. The returns to general human caital abroad are considerably higher than the returns to general human caital at home, and the returns to secific human caital are higher still that is, they are higher than the returns to general human caital abroad. When migration is not a ossibility, no worer will acquire secific human caital. Suose that in such a case every worer otimally acquires ˆ of general human caital. When migration is ossible and the robability of obtaining gainful emloyment abroad is π > 0, and migration into unemloyment abroad is not ossible, and when the two tyes of human caital are equally costly to acquire, it should be ossible to show that while worers acquire some quantity of secific human caital, because they now that π < they also acquire a strictly ositive quantity of general human caital. If no general human caital is acquired then, with robability π, worers will end u unemloyed at home, which would confer an infinite negative utility. It will be worthwhile to rovide conditions under which the level of general human caital that a worer otimally chooses to form in such an environment, ˆ, is greater than ˆ, and that welfare, measured by outut er worer remaining at home, is also higher. Concerning the general equilibrium analysis suose, for examle, that the destination country s roduction environment is ain to the home country s roduction

19 environment. If the level of human caital of the incoming silled migrant is higher than the average level of human caital in the host country, the effect of human caital externalities in that country will bring about a welfare gain to all the worers there. The model s insight is not contingent on migration olicy formation being exclusively in the hands of the government of the home country, H. Suose, alternatively, that the enactment of migration olicy is in the hands of the government of the destination country, D. Consider a world in which D is eenly interested in raising the level of welfare of the worers of H, can exercise comlete discretion as to whether to admit none, few, or many of H s silled worers, and searches for a migration olicy that will raise the welfare of the worers of H by most. Our analysis oints to that olicy. Moreover, if the welfare gain of the worers of D, to which we referred in the receding aragrah alies, the choice of its own worers. by the government of D will not be at the exense of

20 ote In the informed ress and in ublic debate, these two counter flows are regularly referred to as the sources of gain that could comensate for the drain. The Economist s May 6, 000 lead article states: Yet even oor countries can benefit when émigrés send home the remittances they earn in the rich world. In an interview held uon assuming the residency of Harvard University and ublished in the March 6, 00 issue of ewswee magazine, Lawrence Summers remars: Brain-drain questions are very difficult, but I m inclined to thin that large arts of the answer lie in countries creating economic environments that lead their most able citizens to return home.

21 References Bhagwati, Jagdish and Wilson, John D Income Taxation and International Mobility. Cambridge, MA.: MIT Press. Carrington, William J. and Detragiache, Enrica How Extensive Is the Brain Drain? Finance and Develoment 36: Grubel, Herbert B. and Scott, Anthony D The international flow of human caital. American Economic Review 56: Sholniov, Vladimir D Potential Energy: Emergent Emigration of highly Qualified Manower from the Former Soviet Union. Santa Monica: Rand. Star, Oded, Helmenstein, Christian, and Prsawetz Alexia A Brain Gain with a Brain Drain. Economics Letters 55: Star, Oded, Helmenstein, Christian, and Prsawetz Alexia Human Caital Deletion, Human Caital Formation, and Migration: a Blessing or a Curse? Economics Letters 60: World Ban 995. World Develoment Reort 995. ew Yor: Oxford University Press.

22 Aendix The urose of this Aendix is to derive the otimal levels of human caital in different settings and to erform comarisons of the measures of welfare that are associated with these levels. Derivation of Let the worer s cost function of forming human caital be C = where > 0 is a constant, and let the worer s roduction function be f = ln η ln for > 0, where > and η > 0 are coefficients that measure, resectively, the rivate returns of human caital and the social returns of human caital. The net earnings er worer function associated with human caital is then W = η ln ln for > 0. Since W = and W = < 0, the worer s chosen level of human caital is =. Thus, W = η ln. Derivation of

23 Taing the externalities from the economy-wide average level of human caital into account, consider the function W = η ln ln for > 0. Since W η =, η =. Thus, η = η ln η W. A comarison of with, and of W with W η Since η > 0, >. Since W W = ηln η, and since for any η x >, x ln x > x, it follows, uon substituting x = >, that W W > 0. Derivation of Let the returns to human caital in D to an H country worer whose level of human caital is be ln C where > η and C 0 are constant and exogenous to the model. The exected net earnings er worer function is W [ C] [ ln η ln ] ln =.

24 Since W = = and 0 < = W, the worer s chosen level of human caital is =. Thus, the level of social welfare, measured by net earnings of the worers who remain in H, is. ] [ ln W = η A comarison of with, and of W with W Let ln η = W W G. Claim: has a unique maximum at G, < = η and G. 0 > Proof: Since is concave, it has a unique maximum. Since G η G =, η =. Since η >,. Inserting into entails < G η η η = ln G. Uon substituting =, > η x it follows that. 0 > G

25 η otice that = = =. A comarison of W with W when 0 < Claim: G > 0 for any 0 <. Proof: Since for any 0 <, η. Thus, G [ ] ln = x ln x x = where x = >. [ x ln x ] > 0 A comarison of m with A sufficient condition for m > to hold is that >, which in turn is true if >. But = [ ] > if > 0, or if 0 < <. To ensure that 0 < <, we assume that >.

26 A comarison of W with W Let the cost of forming human caital for a tye- worer be C =,. 0 < < Then,, =, ln ln W = η and. ] [ ln ln W m = η It follows, then, that. ln ln η = W W G m Since [ ] [ ], / m = we have that 0, / 0 > = = m where the inequality follows from the assumtion that >. Drawing on this inequality, we differentiate with G

27 G resect to and evaluate the result at = 0 to obtain that > 0 = 0. By continuity, G > 0 holds for in a small ositive neighborhood of zero.