scale economies in education and the brain drain problem

Economics Department of the University of PennsylvaniaInstitute of Social and Economic Research -- Osaka University

Scale Economies in Education and the Brain Drain ProblemAuthor(s): Kaz MiyagiwaSource: International Economic Review, Vol. 32, No. 3 (Aug., 1991), pp. 743-759Published by: Wiley for the Economics Department of the University of Pennsylvania and Instituteof Social and Economic Research -- Osaka UniversityStable URL: http://www.jstor.org/stable/2527117 .

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INTERNATIONAL ECONOMIC REVIEW Vol. 32, No. 3, August 1991

SCALE ECONOMIES IN EDUCATION AND THE BRAIN DRAIN PROBLEM*

BY KAZ MIYAGIWA1

This paper presents a model of brain drain which emphasizes scale economies in advanced education. We demonstrate that brain drain raises the education and income levels of a host country. However, contrary to the presumption that brain drain hurts the unskilled individuals left in a source country, we argue that it is actually those professionals possessing intermediate-level abilities who are hurt by brain drain, regardless of whether they choose to stay or emigrate. We also show that conventional policies designed to stop brain drain may succeed only in retaining those who are mediocre professionals while the brightest continue to emigrate.

1. INTRODUCTION

Brain drain refers to the emigration of skilled and professional personnel from developing countries to advanced industrial nations, and in particular to the United States. A number of studies documenting the magnitude of the brain drain problem are available. For example, according to a 1984 report by the United Nations Conference on Trade and Development (UNCTAD) around 400,000 skilled individuals migrated from developing to developed countries between 1961 and 1972.2 The same report also contains an estimate that between 1977 and 1980 alone Jamaica lost through migration to North America the equivalent of almost 69 percent of those who graduated as professional or skilled workers during the same period.3 Naturally, the countries from which brain drain originates are concerned about both the loss of potential incomes and the detrimental impact of this exodus on the population that remains.

The phenomenon of brain drain has also attracted considerable attention from economists. Two issues have dominated the theoretical work on brain drain.4 The first issue is the question of whether brain drain causes a substantial loss in income for those who continue to reside in the country of emigration. A general conclusion has emerged from this line of inquiry. In the absence of any distortions emigration

* Manuscript submitted March 1989; final revision February 1991. 1 The author wishes to thank anonymous referees for extremely helpful comments for revising the

paper. Special gratitude is due to one referee who kindly provided the author with detailed information on brain drain data and the references on high-tech industries mentioned in the text. Needless to say, any remaining error is the author's responsibility.

2 UNCTAD, Proposals on concrete measures to mitigate the adverse impact of reverse transfer of technology on development countries (TB/B/AC.35/6); July 20 1984. For additional information see Dowty (1987, pp. 148-150), Grubel and Scott (1966a, b) and Rivera-Batiz (1982).

3 This is contained in an address by Edward Seaga, Prime Minster of Jamaica to the Governing Council of UNDP, Geneva, 1984, and is cited in Dowty (1987, p. 149).

4 Bhagwati and Rodriguez (1975) survey early works on brain drain.

743



744 KAZ MIYAGIWA

of skilled individuals, if infinitesimally small in size, does not affect the welfare of the residents in the country of emigration, but a finite level of emigration is welfare-reducing to those left behind.5 Predictably, the presence of distortions would invalidate this proposition.6

The second issue, which stems from the above proposition, is the identification of the appropriate policies to compensate for the welfare losses suffered by those who are left behind. More specifically, the debate centers upon the appropriateness and feasibility, both in terms of economics and legality, of the so-called Bhagwati proposal which calls for income transfers via taxation from the emigrant professionals to those left behind.7

This literature on brain drain is unsatisfactory in at least two respects. Firstly, it typically treats skilled and unskilled labor as two separate factors of production fixed in supply, and analyzes brain drain as a special case in the theory of international factor mobility. This approach therefore ignores the effect of brain drain on the process of skill formation.8

Secondly, the literature has so far focused primarily upon the consequences of brain drain rather than investigating its causes. A recent paper by Kwok and Leland (1982) is an exception.9 Here the authors approach brain drain as a phenomenon arising from asymmetric information on the part of employers in the host and source countries. Their argument is summarized as follows. Source-country employers are assumed to possess imperfect information about the skills of foreign-trained students and hence they can only offer wages based on the average quality of the returnees. By contrast, employers in the host country know the true abilities of the students studying there and pay commensurate wages. In these circumstances, better-skilled students have little or no incentive to return to their home country since they can earn more than the average wage by staying in the host country. Thus, only mediocre students return home, thereby giving rise to brain drain.

The attractiveness Qf the Kwok-Leland model lies in its ability to explain the cause of brain drain. However the model has its own shortcomings. Firstly, as pointed out by Katz and Stark (1984), the result is highly sensitive to which country's employers possess better information about the skills of workers.'0 Secondly, the model is basically a partial-equilibrium framework and hence is not directly amenable to the welfare-theoretic analysis which is the centerpiece of the earlier literature.

The objective of the present paper is to present an alternative theory of brain drain which emphasizes increasing returns to scale in advanced education. The influence of external effects in connection with brain drain has been recognized by earlier writers (e.g. Grubel and Scott, 1966b, pp. 268-274; Johnson, 1967, p. 386)

5See, e.g., Grubel and Scott (1966a, b), Johnson (1967), Rivera-Batiz (1982) and Blomqvist (1986). 6 See, e.g., Bhagwati and Hamada (1974), Hamada and Bhagwati (1976) and Rivera-Batiz (1983). 7Bhagwati and Dellalfar (1976). Hamada (1977) examines the efficiency of the Bhagwati proposal from

the global point of view. 8 There are some exceptions; e.g., Rodriguez (1975). 9 See also Lien (1987). 10 Also see the rejoinder by Kwok and Leland (1984).



SCALE ECONOMIES AND BRAIN DRAIN 745

but the scale effect in education has never been introduced into a formal model as a factor causing brain drain.

The basic idea stems from the observation that the productivity of professional work increases with an increase in the number of similar professionals concentrated in one location. Scholars, scientists and engineers, operating in close propinquity and engaging in constant interactions at seminars, lectures and even informal lunchtime conversations, are able to cooperate with one another more frequently and consequently are in general more productive than those who work alone. This observation is supported by recent empirical work in regional and urban economics. For example, Jaffe (1989) demonstrates the presence of significant spillover effects from university research to the business community which are limited geographically. Hoy (1988) and Dorfman (1988) also confirm that a strong correla- tion exists between the agglomeration of professionals and skilled personnel and the economic growth of the surrounding geographic areas.11 Thus, although it is often asserted that information is a public good which is disseminated freely at no additional cost, this claim is a fiction; in reality not only geographic distances but cultural and linguistic gaps prevent transmission of information among different countries from being as complete as within a country, thereby making "being in the right place" a highly desirable element for professional success.

With this background we present a simple model of brain drain. The model is kept to a bare minimum in order to emphasize the scale effects in advanced education. 12 Hence, it is important to bear in mind from the outset that this view of brain drain is intended to complement rather than replace the existing theories of the brain drain.

The paper is organized as follows. Section 2 presents the basic model of skill acquisition in the presence of increasing returns. Section 3 extends this model to a two-country case in which brain drain appears endogenously. We analyze, in Section 4, the effect of brain drain on skill acquisition and income distribution for the host and source countries. Section 5 explores the nature of an optimal policy whereas in Section 6 we discuss the Bhagwati income tax proposal. Concluding remarks appear in Section 7.

2. THE MODEL

Except for the presence of the scale effect the model of this section is similar to the one of skill formation used in the public finance literature (e.g. Atkinson 1973; Hamada 1974). Thus, we consider an economy endowed with n individuals who possess different levels of (latent) ability denote by q. The abilities are assumed to

" Also see similar studies by Markusen, Hall and Glasmeier (1986) and Henderson (1988, especially, chapter 5).

12 Some authors such as Krugman (1979) and Rivera-Batiz (1989) examine the implications of increasing returns to scale on migration of labor (but not necessarily skilled labor). Furthermore, their models differ from the present one in that the scale effect is based upon monopolistic competition rather than the supply of skilled labor. Markusen (1988) on the other hand models skill formation but assumes homogeneous abilities.



746 KAZ MIYAGIWA

be distributed continuously on the interval [0, 1] with a finite and strictly positive density function f(q):

f(q) dq = 1; f(q) > 0.

In the absence of advanced education, all individuals remain unskilled regardless of their levels of ability. The economy is assumed to produce a single aggregate good with labor alone. We choose units so that one unit of unskilled labor produces one unit of the aggregate good. Thus, the real wage for unskilled labor is equal to unity:

we, = 1.

Suppose that one can acquire advanced education at a constant cost c per individual regardless of individual ability. The acquisition of advanced education enables an individual to perform and earn an income according to his or her ability. The return to higher education is assumed to take the following form which says that an individual with ability j will earn

w(q) = h(s)c

with

h'(s) ah(s)las > 0,

where

(1) s = s(q)n ff(z) dz

indicates the number of individuals who have received education. The term h(s) captures the effect of increasing returns in education: the greater the number of educated individuals in the economy, the greater is the income for each educated individual.

Assuming for now that a student bears the entire cost of education,13 a rational individual will obtain education if and only if the net return from education exceeds or at least equals the unskilled wage. Therefore, higher education will be demanded by all individuals with ability higher than a marginal level q defined by

(2) h(s)q - c = 1.

It is assumed that individuals take h(s) as a parameter so that for a given value of s the net return from education is linear in q. Thus, once educated an individual with a given level of ability earns a proportionately higher level of income than another educated worker who possesses a lower level of ability.

The following assumption ensures an interior solution to the model; h(s) is positive, bounded and satisfies the following inequality:

13 An education subsidy will be examined in Section 5.




(3) h(O) - c > 1.

This inequality states that there exists an economic incentive for the most gifted (with q = 1) to acquire education even when no one else has yet received an education (i.e. s = 0). On the other hand, for the least gifted individuals, q equals zero and so (2) implies - c < 1; hence it never pays for the least gifted to acquire a higher education, regardless of the value s takes.

We show now how the population is divided into the educated and uneducated. Suppose that initially no individuals are educated in the economy, i.e., s = 0. Since q is continuous on [0, 1], by the intermediate value theorem there exists a real number q*, 0 < q* < 1, such that h(O)q* - c = 1. Therefore, all individuals with ability q* or above obtain education and the number of the educated rises from zero to s* = n I 1* f(z) dz. The emergence of the educated in turn raises the return to education so that h(s*)q* - c > 1. That is, it has become attractive for some individuals with ability marginally below q* to obtain education. This new addition to the skilled manpower further increases the returns to education. This process continues until we reach a number qa such that

(4) h[s(qa)]qa -c = 1

where

(5) s(q,1) = nf f(z) dz. J a

Individuals with ability equal to or exceeding qa are educated while those with abilities less than qa remain uneducated. Thus, (4) determines implicitly the division of the labor force n between skilled and unskilled workers.

We turn now to evaluating the impact of education on national income. If individuals with ability in the range (q, 1] receive advanced education, national income (net of education costs) is equal to

(6) y = n h[s(q)]f zf(z) dz + ff(z) dz - cf f(z) dz}

where s(q) is given by (1). The first two terms in (6) represent the skilled and unskilled income, respectively, whereas the third indicates the total costs of education. By setting q = qa in (6) we obtain national income under private decision-making which we denote as y(qa).

Not very surprisingly, increasing returns in education causes the private decision-making process to underproduce skilled labor. This can be seen by considering a social planner who chooses q in order to maximize national income y(q). Differentiating (6) with respect to q yields:

dyldq = nf(q){-nh'f zf(z) dz - hq + 1 + c}.



748 KAZ MIYAGIWA

Setting dyldq = 0 implicitly defines q0, the socially optimal value of q. On the other hand, evaluating dyldq at q = q, and substituting from (4) yields dyldq =

-n2f(q.)h' f 1 zf(z) dz < 0, which indicates that national income can be raised by educating individuals with abilities less than q,. Thus, we have qa, > q0, implying that in the presence of increasing returns in skill acquisition the economy produces too few skilled workers for a social optimum. Standard analysis would suggest that providing an education subsidy increases national income above y(qa). Indeed, a comparison of the above first-order condition with the private decision- making rule in (4) shows that a subsidy equal to nf(q0)h' f 10 zf(z) dz results in the maximal level of national income.

3. BRAIN DRAIN

We now suppose that the world consists of two countries with a structure similar to the one described above. Obviously, if the countries are identical in every respect migration of skilled labor will not take place. Therefore we must assume that there are some differences between the two countries. In this paper we focus upon a size difference, although this assumption is not essential to the analysis.14

Following Kwok and Leland (1982), let us call the two countries in question America and Taiwan. Denote by N and n the size of the population in America and Taiwan, respectively and assume that N > n. Let Qa and qa denote the minimum ability for the educated in America and in Taiwan in the absence of migration, respectively. Qa and qa satisfy the following equations:

(7a) h[s(Qa)]Qa-C = 1

(7b) h[s(qa)]qa- c= 1

where Qa is defined analogously to (5). With identical distribution of q in the two countries, (5) implies that S(Qa) > s(q,) so by (7) a greater number of Americans acquire advanced education than Taiwanese do. Since h'(s) is positive, it follows

(8) h[s(Qa)] > h[s(qa)].

(7) and (8) imply

Qa < qa

That is, not only a greater number but also a greater percentage of the population acquire higher education in America than in Taiwan. (8) also implies that hIs(Qa)]q >

h[s(qa)]q for every q (>0), implying that an individual possessing a certain level of skill earns more income in America than in Taiwan. Hence, there exists an incentive for skilled Taiwanese to migrate to America.

Figure 1 illustrates this situation. There, the horizontal axis represents individual ability q and the vertical line measures individual income. Line ZTa represents the

14 A counterexample to the analysis below is the case in which populous countries like India fail to attract skilled manpower. Such a case may be explained in terms of a difference in the cost of education or the return-to-education function. I am grateful to a referee for this interpretation of the model.




Aa

Ta

0q

Oa qa 1

FIGURE 1

return to advanced education in Taiwan, h(s)q - c, in the absence of migration. Since individuals take h(s) as a parameter, ZTa is linear in q with slope h(s). Line ZAa, the American counterpart, lies above ZTa except at Z. This fact reflects the scale effect which makes the incomes of professionals with identical ability higher in America than in Taiwan. The figure also shows Qa < qa, i.e., a greater proportion of the American labor force obtain advanced education than that of the Taiwanese counterpart.

For modelling the individual's decision whether or not to emigrate, we follow Bhagwati and Hamada (1974) and assume that there is a fixed cost, m, per individual to emigrate. Prior to any migration, the net income for a Taiwanese professional with ability q equals h[s(Q,)]q - m if he emigrates and h[s(qa)]q otherwise. Thus, every Taiwanese professional possessing ability q that satisfies

(9) h[s(Qa)]q - m - h[s(qa)]q

will emigrate to America.15 The inflows of skilled labor increase the return to education h(Q) in America while the outflows depress the Taiwanese counterpart. In Figure 1, a loss of skilled labor in Taiwan has the effect of reducing h(l), thereby rotating line ZTa clockwise while the opposite change occurs in America. The widening difference in professional incomes between the two countries will elicit a

15 To the best of the author's knowledge there exists no model that distinguishes the case in which individuals go abroad to get educated first and decide not to return, from the case in which they get educated in the source country and go abroad to work. As pointed out by Katz and Stark (1984), this comment applies also to the Kwok-Leland model (1982).



750 KAZ MIYAGIWA

second wave of brain drain, which further enlarges the income gap between the two countries. This process of brain drain continues until one of two possible equilibria emerges. Which equilibria occurs depends upon the parameters of the model, in particular, the cost of emigration m, the scale effect captured in the function h(f) and the distribution of ability q. Below we describe the possible outcomes.

Case 1: Complete Brain Drain. Complete brain drain emerges if all skilled Taiwanese emigrate to America. The final equilibrium is characterized by the following equations

(10) h(S)Q - c = 1

(I1) h(S)q -c- m= 1

where

(12) S = N f(z) dz + n f(z) dz.

Here, S equals the total number of educated workers in America after the brain drain from Taiwan is completed. These equations define the minimum abilities of skilled labor for Americans and Taiwanese, denoted by Qe and qe, respectively. (10) indicates that Americans with ability Qe and above acquire education while (11) shows that Taiwanese with ability qe or above acquire education and then emigrate. Finally, for q ? qe we have

h(O)q - c < 1,

implying that no skilled Taiwanese remain in Taiwan; brain drain is complete. Figure 2 illustrates a case of complete brain drain. There, lines ZA and ZT

represent the return to the educated in America and Taiwan in the final equilibrium, respectively. Line Z,A Am is obtained by subtracting the cost of emigration m from ZA and represents the net return to Taiwanese emigrants. The actual income schedule for Taiwanese is outlined by a thick line.

Figure 3 also illustrates another case of complete brain drain. The two cases of complete brain drain are distinguished by the fact that while the thick-lined segment of ZmAin lies entirely above ZTa in Figure 2, the former cuts the latter in Figure 3. The meaning of this distinction is discussed in Section 4.

If qa satisfies (9), complete brain drain necessarily emerges. Even if not, complete brain drain can result if the function h(-) in America increases sufficiently in response to an inflow of Taiwanese skilled manpower and/or the function h(-) in Taiwan decreases sufficiently in response to the outflow. On the other hand, if qa does not satisfy (9) and the function h(-) is not very responsive to the flow of skilled labor in either country, then we may have the following case of brain drain.

Case 2: Incomplete Brain Drain. This case is characterized by equation (10), (12) and also by the following equations which define the triplets (Qj, q2, q3):




A

Am

Ta

W= 1

0 O q e q a1

z 1

FIGURE 2

(13) h(S)q2 - c - m = h(s)q2 - c

(14) h(s)q3 - c = 1

q2

(15) s = n f(z) dz q3

As before, by (10) Americans with ability Q, and above obtain higher education while by (13) Taiwanese with ability exceeding q2 obtain education and emigrate to America. In addition (14) and (15) indicate that there is a segment of the Taiwanese labor force, with ability in the interval [q3, q2), that also acquires education but chooses to remain in Taiwan. The Taiwanese with ability less than q3 remain unskilled. Figure 4 presents the case of incomplete brain drain.

4. EDUCATION AND INDIVIDUAL INCOME

The preceding analysis implies that inflows of skilled foreigners increase national income in America for two reasons. First, economies of scale raises the income for the Americans who are already educated, i.e. h(S) increases. Secondly, a higher professional income induces a segment of Americans previously uneducated to acquire higher education, enabling them to earn higher income as skilled workers.

The effect of brain drain on Taiwanese incomes is more complicated. In the first case of complete brain drain, shown in Figure 2, emigrants will benefit by earning higher incomes while the incomes of those who remain in Taiwan stay constant at



752 KAZ MIYAGIWA

Am

Ta

T

W=1

0

Zm

FIGURE 3

unity. Figure 2 also shows that the opportunity to emigrate induces a greater proportion of the Taiwanese to seek education than when there is no emigration of professional manpower (qe < q). Since benefits to emigrants occur without hurting anyone left in Taiwan, brain drain is clearly beneficial to the Taiwanese community as a whole (i.e., those staying in Taiwan and those residing in America). 16

Figure 3 and 4, however, demonstrates that such a sanguine picture is not the only consequence of brain drain. In Figure 3 which represents Subcase 2 of complete brain drain, line ZmAi, is drawn crossing ZTa above the horizontal line at w 1. If we divide the Taiwanese population into four segments at q 1, q e and qa, as shown in Figure 3, then it is readily verified that only the most gifted Taiwanese, with ability exceeding q 1, absolutely gain from emigration in the sense that their income exceeds the level when emigration is not permitted.

Curious is the fate of the second ablest group, with ability in [qe , q 1). They also emigrate to America as part of the brain drain; however, their net income is lower than when there is no brain drain, and hence they are actually hurt by brain drain! Thus, they may initially object to a policy permitting brain drain but once

16 The fact that brain drain does not hurt unskilled workers is a consequence of the assumption of constant marginal product of unskilled labor.




Am

Ta

T

W=1

Z / qa q3 q 2 q 1 1

zM

FIGURE 4

emigration of the best professionals takes place this group follows the footsteps of the first. This rather paradoxical behavior is clarified by the following; in the presence of scale economies emigration of the most gifted depresses the return to education h(s), and hence the income of the next segment of skilled labor, who in turn emigrate to earn a now relatively greater income in America.

Brain drain also adversely affects the next group of individuals, those with abilities in [ql, q). These individuals would normally have acquired education but choose not to because of the reduced income for skilled labor resulting from brain drain. In short, contrary to Subcase 1, brain drain not only deprives Taiwan of skilled manpower but also reduces the number of educated Taiwanese as a whole.

The effects of incomplete brain drain on individual Taiwanese income levels are similar to those in Subcase 2 of complete brain drain. To see this we divide the population into five segments at q 1 , q2, q3 and qa, as in Figure 4. The opportunity to emigrate benefits only the top group while hurting the second group of emigrants, with q in [q2, qj). Brain drain also has a detrimental effect on the income of the third group on [q3, q2), who acquire education but stay in Taiwan, as well as that of the fourth group, with abilities in [qa, q3), who no longer seek higher education.

The above analysis of brain drain has the following implications. Firstly, brain drain may have a highly inequitable income distributional effect on the Taiwanese population, particularly upon those having intermediate abilities. Secondly, tradi- tional analysis has shown that brain drain, albeit detrimental to those left behind, always increases the aggregate income of the Taiwanese community as a whole,



754 KAZ MIYAGIWA

and hence remittances from emigrants can compensate for any negative effect on those left behind. In contrast the analysis of the present section implies that brain drain may cause an absolute decline in aggregate Taiwanese income, so that remittances will not necessarily improve the collective lot of the Taiwanese. This possibility of an income loss appears in Figures 3 and 4, when an increase in income of best professional emigrants cannot offset a loss in income of individuals having intermediate levels of ability. For example, if outflows of skilled labor results in the second subcase of complete brain drain (see Figure 3), a change in income is written as

n (Wz -haz - m)f(z) dz + n (Wz - haz - m)f(z) dz

rqe

-n i (haz - c - I)f(z) dz Ja

where ha- h[s(qa)] for short, and W denotes the professional wage in America (for simplicity assumed exogenous). While the first term is positive, the next two are negative. Thus, for instance, if a small number of emigrants cause ha to fall significantly, the last two terms can dominate the first, thereby making the resultant level of national income lower than when there is no brain drain. In fact, we show in the next section that in such situations restricting the outflow of skilled personnel is an optimal policy for the Taiwanese community.

5. THE NATURE OF AN OPTIMAL POLICY

As we showed in Section 2 the private economy underproduces skilled labor in the presence of the scale effect in education and hence we have a case for government intervention. This section examines the nature of an optimal policy for the entire Taiwanese community in the presence of brain drain. Suppose that the Taiwanese government can choose how many individuals to educate and how many skilled workers to allow to emigrate. Let a and ,3 ( a + E; E : 0) denote the minimum ability for skilled labor and for skilled emigrant labor, respectively. That is, the Taiwanese government educates individuals with ability a and above and permits emigration of those in the range of [,3, 1] so as to maximize national income of the Taiwanese community. The government's objective is equivalent to maximizing, by the choice of a and 8, the following per capita income:

yin = h(S)zf(z) dz + f h(s)zf(z) dz + f f(z) dz

-c f f(z) dz - m f(z) dz.




Here, the first three integrals on the right-hand side represent (per capita) income for professional emigrants, professionals staying home and unskilled workers, respectively, whereas the last two are the costs of education and migration, respectively. The total number of professionals in America (S) and in Taiwan (s) are given by:

S = N zf(z) dz + n zf(z) dz;

ra + e s = n + zf(z) dz.

The first-order conditions are

(16) a(yln)b8a = -f(,f)[h(S)/3+tfrlf(/3)-h(s)/3-no-m] ?0 (=O if ? > 0)

(17) 3(yln)baa = a(yln)b38 -f(a)[h(s)a + no - c - 1] = 0

where

+--h'(S)[Nf(Q)aQbf83 + nf(3)]f zf(z) dz > 0

-h'(s) Zf(z) dz-0.

The term aQa/38 in tf captures the marginal effect of an inflow of Taiwanese professionals on the proportion of the American population who acquire higher education and is positive.

Suppose that (16) holds with equality so that ? is strictly positive, as in the case of incomplete brain drain. Then (17) implies

(18) h(s**)a + n -c= 1

where s** is the optimal value of s. A comparison of (18) with (14), which holds when there is no government intervention, reveals that an optimal policy calls for an education subsidy n , since n4 is positive. On the other hand, we obtain from (16)

(19) h(S**)13 + /Iff(/3) - m - c = h(s**)13 + no - c

where S** is the value of S under the optimal policy. Taking (19) together with (13) and (18), it follows that an optimal policy calls for an additional policy of subsidizing emigrants at the amount /If(13) - n . However, note that this second subsidy could be negative; i.e., the optimal policy may consist of an education subsidy and an emigration tax. A call for an emigration tax rather than a subsidy results from the fact established in the preceding section that total national income can be decreased by brain drain.



756 KAZ MIYAGIWA

Alternatively, if (16) holds with strict inequality so that 8 = 0, then we have the case of complete brain drain (Case 1). Setting a = ,3 and ? = s = 0, (17) yields

(20) h(S*)13 + /Iff(/3) - c - m = 1

where S* denotes the value of S under an optimal policy. Comparison of (20) with (11), which holds under a noninterventionist policy, shows that an optimal policy requires a subsidy fIf(/3). This subsidy may be either on education or on emigration, which amounts to the same thing under complete brain drain.

We gain further insights into the nature of an optimal policy by examining the small-country case. By definition a small country cannot influence the level of professional income in America so that h(S) is assumed given, say, at W. If the optimal choice of 8 is positive (i.e., incomplete brain drain), we set h'(S) = = 0 in (18) and (19) to obtain:

(21) h(s**)a + no/ - c 1

(22) W,3 - m - c = h(s**)3 + no - c.

Comparing these equations with (13) and (14) indicates that for a small country an optimal policy consists of an education subsidy and a tax on emigration of skilled labor, both at the same rate n ?. An emigration tax is desirable in this case because, with the level of professional income given in America, there will be no scale economies from emigration; the scale effect that exists in Taiwan only works against that country via reduced professional income at home. An emigration tax avoids this possibility of an income loss.

On the other hand, if the first-order conditions imply 8 = 0 (i.e., complete brain drain), we set a = ,3 in (21) and (22) to obtain

Wf3 - m - c = 1.

In other words, an optimal policy for a small country is simply a noninterventionist policy. This result follows because in the case of complete brain drain there no longer remains anywhere the scale effect for the Taiwanese government to manipulate.

6. REFLECTIONS ON THE BHAGWATI TAX PROPOSAL AND OTHER POLICIES

Many countries, for decades, have regarded the human capital embodied in skilled manpower as belonging to the state and consequently have restricted brain drain. A more recent variant of this idea is the Bhagwati tax proposal. This section discusses implications of this tax proposal and other policies designed to stem brain drain. In doing so we assume Taiwan is small in the sense that its brain drain does not affect the level of income of professionals residing in America. This assumption




is not only analytically convenient but also better represents the reality faced by many developing countries.17

First, let us consider the Bhagwati proposal. Here we disregard the well-known legal and technical problems of tax collection and focus on the effect that such a tax has on brain drain and skill acquisition. Suppose that the incomes of professional emigrants are taxed at a proportional rate t so that the after-tax income of an individual possessing ability q becomes (1 - t) Wq. Thus, the after-tax return from emigration can be represented by the line obtained by rotating line ZmA m clockwise around point Zm Starting with the case of complete brain drain then, this tax will discourage emigration of only lower-skilled personnel. If the tax rate is sufficiently high, the tax will move the economy from Case 1 to Case 2, in which case there will be some educated Taiwanes: who choose not to emigrate. However, note that the line representing the after-tax return from emigration is steeper than line ZT, and hence cuts it from below. It follows that the tax in question reduces emigration of lower- to intermediate-skilled workers while the best professionals continue to emigrate. This conclusion remains valid even if we go beyond the impact effect. To see this we note that although the emergence of professionals at home makes line ZT rotate counterclockwise around Z, in the final equilibrium ZT will never be steeper than the line representing the after-tax return from emigration. (Otherwise emigration will cease.) Thus, keeping the most skilled Taiwanese at home will require a highly progressive tax on emigrants.

Our analysis also highlights some equity issues which have not been apparent in previous discussions of the Bhagwati tax proposal. Firstly, the level of emigration will depend on the distribution of tax revenue. For example, tax revenue given to those most likely to emigrate (i.e. relatively gifted individuals) will discourage them from emigrating. On the other hand, distributing revenue to the least talented has little or no effect on the decision of those professionals who contemplate emigration. Consequently, if the government's goal is to prevent emigration, then it will have to pursue a policy of making the rich richer. Secondly, in Subcase 2 of complete brain drain and in the case of incomplete brain drain, there are individuals, having ability q on the interval [q2, q 1 ), who are made worse off by brain drain although they themselves emigrate. It is unclear whether taxing this group of emigrants, which has already suffered income losses, is an "equitable" policy. Thirdly, also in the latter two cases, among those who stay in Taiwan it is those individuals with relatively high incomes who are actually hurt by brain drain. Should the tax proceeds go to those richer individuals who actually are hurt or to those with low incomes who are not hurt by drain drain? These considerations have never surfaced in the previous literature which treats labor as a homogeneous group.

We turn now to examining two other policies commonly used to discourage outflows of professionals. The first of these is an emigration tax. This tax raises the cost of emigration m, thereby lowering ZmAm down, and hence it works much like

17 Grubel and Scott (1966a,b) justify this assumption by arguing that the difference in the stock of human capital in America and developing countries partially explains why brain drain has never become as serious an issue in the United States as in developing countries.



758 KAZ MIYAGIWA

the income tax discussed above. It discourages emigration of intermediate-level individuals while failing to retain the best professionals. However, the analysis from the preceding section shows that imposing an emigration tax may in fact be necessary for maximizing national income especially since advanced education receives some kind of subsidies in most countries.

Another policy pursued by many countries is the provision of scholarships containing a "return" clause to students studying abroad. Since this policy is analytically equivalent to subsidizing all the students at a given rate and taxing emigrating professionals at the same rate, the analysis from the previous section indicates that this policy can be an optimal policy for a small country. Setting aside the goal of reaching a national optimum, it can be seen that the scholarship policy affects the Taiwanese population much like an emigration tax. The initial impact of such scholarships is to raise line ZT upward uniformly, which in turn increases the proportion of Taiwanese who seek education. As under the other two policies, only the individuals with intermediate-level skills stay home whereas emigration of top-level Taiwanese continues.

7. CONCLUDING REMARKS

The present paper has presented an alternative model of brain drain which emphasizes the role of increasing returns to scale in education. Unlike earlier models, the present model provides an explanation as to why an advanced country can offer higher incomes for skilled professionals and also why the country will attract the best individuals from less advanced nations. The model also identifies the presence of some emigrants who are victims of brain drain despite the fact that they themselves emigrate. In such circumstances taxing emigrants so as to rectify the inequity engendered by brain drain cannot produce an equitable result as is typically expected. Furthermore, if applied independently of emigrants' true abilities, the policies employed to reverse the flows of professional emigration actually encourage only the less able individuals to stay at home while the best continue to leave.

The model is kept to a minimum level of complexity in order to focus upon these implications that increasing returns in education has for brain drain. Obviously, future research needs to incorporate scale economies into the earlier models of brain drain mentioned in Section 1 so as to study, for example, the interaction between brain drain and terms of trade, and the effects of commercial policies which influence the latter. Another possible extension would involve examination of the relationship between brain drain and foreign capital inflows into developing countries along the line pioneered by Ramaswami (1968).

University of Washington, U.S.A.

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scale economies in education and the brain drain problem

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