Brain Drain, Fiscal Competition, and Public Education Expenditure
Abstract
A two-country model is developed in this paper to examine the implications of fiscal competition in public education expenditure under international mobility of high-skilled labor. The authors allow for educational choice, asymmetry of countries with respect to total factor productivity, and tax base effects of migration in source and host country. As the latter may give rise to multiplicity of equilibrium, alternative belief structures of mobile high-skilled workers are carefully taken into account. The paper also looks at the consequences of bilateral policy coordination. While in line with other studies on tax competition, bilateral coordination can reduce the under-investment problem in public education spending, it also tends to hinder migration or may even reverse the direction of the migration flow that materializes under non-cooperative policy setting. As a result of its potentially adverse effects on migration patterns, bilateral coordination may therefore reduce global welfare and bring the world economy further away from the social planner's solution.
1. Introduction
Skilled labor has become increasingly mobile. The bulk of skilled immigrants acquired publicly financed education in their home country.1 This potentially creates severe problems in the source countries of migrants and the consequence may be detrimental fiscal competition, with countries underinvesting in higher education in order to avoid brain drain and to attract high-skilled foreign immigrants (Justman and Thisse, 1997, 2000). This raises the question whether policy coordination could improve social welfare when skilled labor is mobile and how it changes the migration flows.2
In this paper, we develop and analyze a two-country model to examine the implications of fiscal competition in public education expenditures under international mobility of high-skilled labor. To capture the idea of higher education (instead of basic, compulsory education), we model education as the outcome of individual choice. With education being publicly financed, our model generates “agglomeration” effects from migration on the tax base in both source and host country; that is, higher emigration reduces the tax base in the source country and increases it in the host country, thereby further reinforcing migration incentives.3 Because of the existence of agglomeration effects, it may be the case that, for given public spending levels and depending on the belief structure in the economy, migration may or may not occur in equilibrium, thereby potentially creating the problem of multiplicity of equilibria. We carefully address the issue in our analysis in a way which may be useful also in other political games with multiple equilibria.
Motivated by the recent endeavor in Europe to reach a higher degree of coordination in tertiary education (for instance, because of the Bologna process), we study potential gains from coordinated policy setting in the context of public education and international migration. We analyze the behavior of cooperative governments which aim to maximize the aggregate welfare of non-migrants (with transfers across countries to compensate losers), whereas a social planner would also consider the utility of migrants. The justification for this approach is that national governments target the median voter in their country, who is most likely a non-migrant. We show that from the perspective of a utilitarian social planner, bilateral coordination of education policies does not necessarily solve the problem arising from fiscal competition. On the one hand, bilateral coordination tends to increase public education expenditure compared to the non-cooperative levels. On the other hand, however, bilaterally coordinated policies have consequences for the desired migration pattern. While coordination favors non-migration, the social planner may prefer brain drain in order to extract migration gains. In fact, we demonstrate that an endeavor to stop migration through a bilateral contract may even reduce welfare compared to a non-cooperative equilibrium. Moreover, we show that policy coordination may not always be successful in preventing brain drain, depending on the belief structure and migration costs. In this case, government cooperation may reverse the direction of the migration flow compared to both non-cooperative policy setting and the social optimum.
The remainder of the paper is organized as follows. Section 2 presents the model. Section 3 analyzes the equilibrium for a given public education policy. In section 4, we examine how governments have to adjust their education expenditure in order to avoid brain drain when labor market integration reduces migration costs for high-skilled workers. Section 5 analyzes non-cooperative policy setting. In section 6 we explore the consequences of cooperation between governments for public education expenditure and migration patterns; these patterns are compared with both non-cooperative policy setting and the social planner solution. The last section presents our conclusions. Owing to space constraints, we do not present formal proofs of lemmata and propositions in this paper but refer the interested reader to the working paper version of our manuscript in Egger et al. (2007).
2. The Model
(1)In either country, there is a unit mass of workers, indexed i ∈ [0, 1], who make two decisions: first, whether or not to acquire higher education; and, second, if high-skilled, whether or not to migrate to the other country in order to live and work there. Individuals take the migration decision into account when deciding whether or not to acquire education. That is, individuals are aware of earning opportunities abroad as well as at home. They are endowed with one unit of time. Acquisition of education requires ē ∈ [0, 1) units of time, so that 1 − ē is the residual working time of an educated individual.
Utility of an individual i living at home is simply given by the level of consumption, C(i). Living abroad implies that utility is given by a discounted value of consumption which reflects the social costs of living in a foreign environment. Formally, the utility of migrant i is given by C(i)/(1 + θa(i)), where a(i) = 1 for a mass q ∈ (0, 1) of high-skilled workers and a(i) prohibitively high for the rest of them.5 Parameter θ reflects the degree of international integration. A decline in θ means a more mobile high-skilled labor force.
(2)3. Equilibrium Patterns of Brain Drain
and 
denote country j's wage rate per efficiency unit of high-skilled and low-skilled labor, respectively. Education is financed by a proportional wage income tax, with tax rate τj ∈ [0,1) in j = H, F. Then, the consumption of a native individual from H is given by
(3)
(4)
is the relative wage rate of high-skilled to low-skilled labor in country H in terms of efficiency units.6 For the migration decision of high-skilled individuals, consumption level 
when staying at home has to be compared with the discounted consumption level when migrating, 
. A high-skilled worker born and educated in H moves to F if and only if
(5)
(6)
, 
, and the relative net wage is given by:
(7)The further analysis assumes that Gj is smaller than the exogenous level 
, j = H, F. Thus, as q is the maximal emigration rate, condition (6) is satisfied. χH(µH) represents the incentives to migrate from H to F, which—according to (5)—have to be compared with the cost 1 + θ. For µH = 0, µF ≥ 0, an analogous expression χF(µF) describes the incentives to migrate from F to H.
As migrants take their education level with them to the foreign country, the (relative) wage rate per efficiency unit of skilled labor is decisive for the migration decision. However, the wage per efficiency unit in H, 
, is decreasing in GH. The reason is that higher education finance raises the supply of skills for a given fraction of individuals that choose higher education. Thus, an increase in GH makes the home country more prone to brain drain. Furthermore, the government in H must increase its tax revenues in order to finance the additional expenditures associated with an increase in GH. While in an economy without migration the tax burden per efficiency unit of high-skilled workers, 
, stays constant when the government increases GH, the resepective burden rises from φ to φ/(1 − µH) if there is brain drain from H to F, that is, if µH > 0 and µF = 0. The tax payment per efficiency unit of high-skilled labor in F is φ/(1 + µHGH/GF). Inflow µH of high-skilled labor from H broadens F's tax base so that the tax burden per individual declines. Thus, the tax channel strengthens the incentives of high-skilled workers to leave H, and it generates agglomeration effects in favor of the receiver country.
(8)
implies µj ≤ q < mj and thus restricts the analysis to feasible education levels.
Migration Incentives and Migration Equilibria: GH/GF ≥ (AH/AF)1/(1−β)
Comparing the returns to migration to the cost of working in a foreign country, we see that the following patterns of brain drain hold in equilibrium. If migration costs are high (1 + θ″ in Figure 1), then χj(µj) ≤ χj(q) < 1 + θ″ for all µj ≤ q. Thus, according to (5), no educated worker will leave his/her home country and only non-migration can hold in equilibrium in this case. At cost 1 + θ′, non-migration is still an equilibrium since χF(0) < χH(0) < 1 + θ′. However, 
and BH are also equilibria. At 
, individuals are indifferent as to whether they will work abroad or in their home country, but any deviation to the left eliminates migration (χH(µH) < 1 + θ′ for 
), whereas any deviation to the right induces more migration (χH(µH) > 1 + θ′ for 
). We call such an equilibrium unstable. In contrast, BH is a stable equilibrium since χH(q) > 1 + θ′ and all mobile workers have gone from H to F. If migration costs diminish further, migration from F to H can also be an equilibrium. For instance, at cost 1 + θ, we have an unstable equilibrium 
and a stable equilibrium BF, in addition to equilibrium BH. Throughout the following analysis, we focus on the stable equilibria, that is, either µH = µF = 0, µH = q, or µF = q.
In the next section, we examine for given education policies GH, GF whether a non-migration equilibrium can be sustained when international labor markets for high-skilled workers become more integrated. We also explain how we deal with policy combinations that give rise to multiple migration equilibria.
4. Opening up the Labor Market for Given Policy
Suppose that up to now, high-skilled workers have worked where they were educated. As in Figure 1, let χF(0) < χH(0). Now suppose migration costs decline from θ″ to θ (such that χH(0) > 1 + θ > χF(0)). In this case, as χH is increasing in GH, domestic education policy is too ambitious relative to total factor productivity and mobile high-skilled workers of country H benefit from leaving their home country and working abroad. The resulting brain drain from H to F has detrimental consequences for immobile workers in H, whose tax burden increases. Therefore, a crucial question facing national policymakers is how education expenditure can be adjusted in order to prevent this brain drain.
If θ approaches zero, an outcome without migration is feasible only if countries H and F choose their policies in such a way that χH(0) = χF(0) = 1. In this case, locations H and F are equally attractive for high-skilled workers. According to (7), this requires GH/GF = (AH/AF)1/(1−β). In Figure 2, line EA with slope (AH/AF)1/(1−β) represents the locus of equal attractiveness.
Scope for Policy
(9)
in Figure 2. According to (6), (GF)1−β < bAF/φβ. Thus, for θ > 0, 
and 
lies above the EA line. Moreover, as GF increases, 
decreases from (1 + θ)1/(1−β), for GF = 0, to one, for 
(use (6)). This explains the concave shape of 
as shown in Figure 2.Policy combinations on line 
fulfill the condition that χH(0) = 1 + θ and, therefore, render mobile high-skilled workers indifferent as to whether they should stay at home or work abroad. 
describes country H's scope for µH = 0 supporting policy. When θ declines, the scope for raising education expenditure above the EA line narrows. To determine which policy combinations are consistent with µF = 0, we have added locus 
in Figure 2. The set of policy combinations that are consistent with non-migration is bounded by 
and 
.
and 
? We know from Figure 1 that—because of the agglomeration effects of brain drain—the equilibrium migration pattern is not necessarily unique. This implies that certain policy combinations in the lens bounded by the two incentive constraints 
and 
, although consistent with non-migration, may be consistent with brain drain as well, say from H to F. To determine the policy domain associated with multiple migration patterns, we consider the constraint for policy combinations that prevent brain drain from H to F. This constraint is given by χH(q) ≤ 1 + θ. In analogy to (9), it can be written in the form
(10)
. The upper bound of policy combinations preventing brain drain from H to F is represented by the curve IH→F in Figure 2. Since 
, the incentive constraint IH→F lies below the incentive constraint 
. Only relatively strong expenditure and tax cuts in the source country can outweigh the agglomeration advantages of the receiver country. Like 
, the incentive constraint IH→F rotates downward when migration costs decline: 
(see Egger et al., 2007).Policy pairs in the region bounded by 
and IH→F are associated with multiple migration patterns. This multiplicity of migration equilibria constitutes a problem for the characterization of optimal non-cooperative education policies in Section 5. The reason is that national governments base their expenditure decisions on certain expectations concerning the equilibrium migration pattern. However, it is not clear how these expectations are formed if multiple migration patterns are possible. To overcome this problem, we introduce a selection criterion that is based on a publicly known (and identical) belief of mobile high-skilled workers about the equilibrium (µH, µF) pattern.
We distinguish between two types of beliefs. As the baseline scenario, we consider “stay-home beliefs”. Under stay-home beliefs, mobile high-skilled workers do not migrate whenever an outcome with µH = µF = 0 is consistent with rational behavior. In this case, the the scope for policies avoiding brain drain from H to F is given by 
, that is, (9) is the relevant constraint. In addition to the baseline case of stay-home beliefs, we also consider the alternative case that migration decisions are based on “go-abroad beliefs”. Under go-abroad beliefs, mobile high-skilled workers migrate from H to F whenever µH = q, µF = 0 is consistent with rational behavior. In this case, mobile high-skilled workers of country H anticipate the agglomeration effects of migration and the scope for policies avoiding brain drain from H to F shrinks from 
to 
, that is, (10) instead of (9) becomes the relevant constraint.
5. National Education Policies
In order to shed light on optimal education policies from a national point of view, we first have to specify the national policy goal. Under the reasonable assumption that the median voter does not migrate, the workers who stay are decisive for national governments. Therefore, we look at the impact of Gj on the low-skilled workers and on the high-skilled workers who work in j. By virtue of (3) and (4), the consumption levels of the low-skilled and the non-migrating high-skilled workers are identical and given by net wage 
. Thus, we can take Wj as an objective function of the government.
(11)For any given µj, µk ∈ [0,q], objective function Wj has a unique maximum at
, j ≠ k. We have (i)
, (ii)
, and (iii)
if µk > 0, else
. Moreover, (iv)
.
For any given migration pattern, Lemma 2 characterizes j's best reply to policy Gk. We use the following notation: 
denotes j's best reply function conditional on non-migration, while 
is j's best reply function conditional on brain drain from j to k. However, the best reply functions determined in Lemma 2 are not necessarily consistent with the incentive constraints of mobile high-skilled workers. If an incentive constraint is binding, education expenditure has to be adjusted in order to sustain the assumed migration pattern. Hence, migration incentives limit the scope of national education policy.
Furthermore, a country may have an incentive to undercut education expenditures that are optimal for a certain migration pattern in order to shift brain drain in its own favor. The costs of deviating from optimal adaptation to a given migration pattern as well as the benefits of changing the pattern of migration can be evaluated by comparing the net wage function Wj for different µj, µk constellations. Figure 3 illustrates for the three possible equilibria identified in section 3 the objective function WH and the best responses of H to a given foreign education policy. Subscripts H → F, 0, F → H refer to migration from H to F, non-migration, and migration from F to H, respectively.
Optimal Education Policies for Different Migration Patterns and Deviation Incentives
The ranking 
follows from (11), and 
follows from Lemma 2. Figure 3 shows that deviation from 
within range (
, 
) would be beneficial if such a deviation induced a switch from non-migration to brain drain from F to H. Analogous bounds 
, 
for attractive deviations exist to the left of 
. If H succeeds in preventing the outflow of high-skilled labor (or even induces inflow from F) by lowering GH to below GH→F, this is beneficial as long as GH remains within the range marked by 
(
, respectively). Since, according to (11), an increase in GF moves the WH curve for µH = 0, µF = q upward, whereas the WH curves for (µH, µF) ∈ {(0, 0), (q, 0)} are unaffected, 
and 
are decreasing in GF, while 
is constant.
As outlined in detail in the working paper version of this manuscript, Egger, et al. (2007), the outcome of the policy game (in pure strategies) depends on the belief structure and it is inconsistent with a binding incentive constraint of mobile high-skilled workers. Let us first consider the case of stay-home beliefs. In this case, only a policy pair with 
—and thus non-migration—is consistent with a best response of both governments.7Figure 4 shows the relevant deviation bound 
from conditional equilibrium policy 
. Deviation successfully triggers brain drain from F to H if incentive constraint 
is crossed. Thus, for high migration costs (θ2), the shaded area DC (“deviation cone”) to the right of intersection point T0 describes the range of deviations from 
that change the pattern of migration in favor of H and increase WH. There is no policy GH such that 
. Thus, for θ2, H will not deviate from 
and N0 is an equilibrium under rational policy setting. However, if migration cost θ decreases, incentive constraint 
moves closer to the EA line. If θ is sufficiently low (θ1), we have an incentive constraint which intersects 
at a point (
) to the left of 
. Then the deviation cone DC′ contains (
, GH), for some GH and H will deviate from 
. Hence, for sufficiently low migration costs, non-migration cannot be sustained in a Nash equilibrium under rational policy setting.
Deviation Cones (DC) from Conditional Non-migration Equilibrium (θ1, θ2)
Under go-abroad beliefs, both 
as well as 
, with 
,
being determined by the intersection of best response function 
, 
in (GH,GF) space, are candidates for a non-cooperative equilibrium of rational governments. For N0, the deviation incentives are analogous to the situation discussed for stay-home beliefs. If N1 is realized, then the question is: Will H deviate from conditional best reply 
to change the pattern of migration in its favor? If H wants to avoid brain drain from H to F, it must cross incentive constraint IH→F. Figure 5 shows constraints IH→F as well as deviation bound 
(which is independent of GF) for two values of migration costs θ1, 
, with 
. While IH→F rotates downward when θ declines, conditional best replies and deviation bounds do not vary with θ.
Deviation Cones for Return Migration (
)
If migration costs are sufficiently low (
), country H has no possibility to reach the relevant deviation cone (
) by deviating from 
. Given that high-skilled migrants suffer a low burden as a result of working abroad, the expenditure and tax cuts required to prevent migration are too high to be an attractive option for H. In contrast, if the burden of working abroad were more severe (θ1), then it would be in H's national interest to induce migrants to stay at home by deviating from N1 to DC1, that is, by reducing education expenditure.8
Summarizing the insights from above, we can formulate the following proposition.
Proposition 1. A non-cooperative equilibrium (in pure strategies) may not exist. In particular, if θ is sufficiently low, an equilibrium without migration is excluded. Furthermore, an equilibrium with brain drain requires that individual migration decisions are based on go-abroad beliefs and that θ is sufficiently low.
6. Coordination of National Policies
(12)Proposition 2. For any given education policies GH, GF > 0, Wc is higher at µj = µk = 0 than at µj = q, µk = 0, j ≠ k ∈ {H, F}. The optimal bilateral contract depends on the beliefs of mobile high-skilled workers. (i) Under stay-home beliefs, the optimal bilateral contract supports non-migration by coordinating on
, 
. (ii) Under go-abroad beliefs, policies
, 
are not optimal if migration costs θ are sufficiently low. In this case, governments may want to coordinate on policies that trigger brain drain. (iii) If non-cooperative policy setting of rational governments leads to an equilibrium with brain drain, then coordination increases Wc and the direction of brain drain may be reversed.
The proposition shows that national governments that serve the interests of the workers who stay in their country have a preference for non-migration. The reason is that even though the median voter in the host country of migrated labor would gain, this gain is lower than the loss suffered by the median voter in the source country. Therefore, the country threatened by losses from brain drain is willing to pay the other country for not triggering the drain.
If mobile high-skilled workers base their migration decision on stay-home beliefs, coordination definitely supports non-migration. This may or may not require signing a contract. If non-migration is also the outcome of non-cooperative education policies, there is no role for coordination because the best contract would just reproduce the non-cooperative solution. However, according to Proposition 1, reduced migration costs tend to provoke fiscal competition for foreign high-skilled workers. In this case, bilateral coordination has the role of preventing fiscal competition for high-skilled labor and is definitely in the interest of the national median voters.
If migration decisions are based on go-abroad beliefs, coordinating on 
, 
may be less successful in establishing an equilibrium without migration. However, a bilateral contract can stop the possibly ongoing struggle for mobile high-skilled workers under non-cooperative policy setting. Furthermore, if non-cooperative policy setting leads to an equilibrium with brain drain from H to F, bilateral coordination is definitely beneficial for the national median voters. The coordination may imply education policies that reverse the direction of brain drain, leading to a factor flow from F to H. This result may be surprising at first glance because non-migration is the preferred pattern under bilateral coordination. However, non-migration is possibly inconsistent with the optimal bilateral agreements that satisfy the incentive constraints for mobile high-skilled workers.
The bilateral coordination perspective considered here must be clearly distinguished from the social planner solution. National governments care about the utility of median voters but ignore the gains of migrants. In the following, we compare education policies implemented by a utilitarian social planner with the contract resulting from bilateral coordination of education policies.
(13)In the working paper version of this manuscript, we undertake two numerical simulation exercises in order to shed further light on how the social planner solution deviates from non-cooperative policies and the bilateral contract. However, in the interest of brevity, we do not present these exercises here. Instead, we summarize the main insights from these exercises as follows and refer the reader, who is interested in further details, to Egger et al. (2007):
Proposition 3. Bilateral coordination can help to increase public education expenditure to above suboptimal non-cooperative levels. Moreover, it is useful for overcoming an ongoing battle for mobile high-skilled workers. However, (i) bilateral coordination is biased toward non-migration, and (ii) it may reverse the direction of brain drain compared to both the non-cooperative policy game and the social planner solution; (iii) from a social planner's point of view, non-cooperative education policies can be better than bilateral coordination.
7. Concluding Remarks
This paper aimed at shedding light on opportunities of and incentives for national governments to provide public finance for higher education and to compete for educated workers. For this purpose we analyzed a simple two-country model in which countries may differ in TFP and where brain drain has agglomeration effects because it affects the tax base in both source and receiver country. Within this framework, we compared public education expenditure levels, migration patterns, and welfare in non-cooperative political equilibria with the outcomes under bilateral coordination and the social planner solution. As a key result we found that bilateral coordination can reduce the under-investment problem in public education spending but at the same time it tends to hinder migration or may even reverse the direction of the migration flow that materializes under non-cooperative policy setting. Because of its potentially adverse effects on migration patterns, bilateral coordination may therefore reduce global welfare and bring the world economy further away from the social planner's solution.
In the interest of analytical tractability, we had to impose several simplifying assumptions which might limit the practical relevance of our analysis. For instance, we have ignored intertemporal externalities from migration of high-skilled labor—such as changes in productivity. Furthermore, we have not allowed for other forms of policy coordination, like international agreements on taxing graduates.10 While both of these extensions would be worthwhile to consider in our framework, they are clearly beyond the scope of this paper.
References
Notes
, 
. Hence, a pure strategy equilibrium with migration is inconsistent with stay-home beliefs.
