The time structure of the model is as follows. First, the governments of two countriesiand j, which are identical in all respects, simultaneously set tax rates tx and an education policy represented by expendituresx per student,x∈ {i, j}.
The education expenditure can either be positive, in which case we refer to it as an amenity, or negative, in which case it can be interpreted as tuition fees per student. The term ‘amenity’ captures governmental expenditures that potentially attract students.4 As these expenditures and tuition fees are basically two sides of the same coin within the present model, most of the time we only refer to amenities when considering education policy. Lange (2009) presents a comparable migration model with endogenous wage rates and education expenditures which increase individual wages. If the (negative) wage-rate effect of immigration is not too large, the effect of education policy on the number of students in a country is, as in the present model, clearly positive (Lange, 2009, equ. (10), p. 184).
Investments in education quality, however, imply additional regional spillovers from migration which complicate the analysis and are not central to the main argument in the present paper, so we prefer to maintain the amenity approach.
Students who are aware of their migration costsm0 when leaving their country of origin then decide on the location of education. ‘Migration costs’ in our model not only capture monetary costs (such as moving expenses) but also non-monetary costs or benefits that are related to the psychological, social and cultural aspects of migration and therefore also describe a student’s country-specific preferences.5
4 These could include subsidies (scholarships, housing support, travel tickets, medical benefits, book grants etc.), special student loans, hospitality services, leisure and sports facilities, child care, housing offices and health centers. In many OECD countries, subsidies for tertiary education as a percentage of total public expenditure on education are considerable (e.g., Germany 19.1%, U.S. 23.5%, UK 25.8%, Australia 32.3%, New Zealand 41.5%, Norway 42.6%; data from 2005; source: OECD, 2008, p. 290).
5 See e.g. Beckmann and Papageorgiou (1989), Mansoorian and Myers (1993) and Haupt and Peters (2003) who use the concept of ‘home attachment’, or Boneva and Frieze (2001) as an
After graduation, nature reveals the individual migration costsmof leaving one’s location of education, if the individual studied in their home country, and (1− α)m with α ∈ [0,1[ if the individual graduated from a foreign university before returning to their place of origin. A non-zero α captures the migration cost advantage of a repatriate compared to a graduate who leaves their home country for the first time. This cost advantage can for example be due to linguistic proficiency, existing social networks in the home country, faster (re)familiarization etc.
Finally, university graduates decide on the location of labor supply. It seems reasonable to assume that individuals as students are not aware of the migration costs they will face upon graduation. There is some uncertainty with respect to the social networks and ties they built and/or maintained while at college, which are included in non-economic costs and represent a crucial migration/return determinant. In addition, foreign students can barely judge whether they will be able to successfully integrate in their host country. Therefore students can only form expectations about future migration costs.
If tax rates were set after the student-migration and before the labor-migration decision, the government could attract students by announcing low tax rates for the future, but later deviate from this policy after students find themselves unable to leave the country due to high individual migration costs (‘lock-in’). Following Poutvaara’s (2001) argument, we abstain from this hold-up problem, since in a repeated game or rather OLG setting future generations would adjust their behavior in response to deviations from announced policy.6
Mobility costs m0 ∈ [m0, m0] and m ∈ [m, m] are assumed to be uniformly dis-tributed among students and graduates, respectively. We assume that the upper limit of each distribution is positive, implying that there are always individu-als with positive migration costs. Furthermore, it seems reasonable to believe that there are at least some individuals (students and graduates) with negative
example of the socio-psychological approach.
6 Our assumption thatall individuals decide to obtain an education (and exert an identical and exogenously fixed level of effort) directly implies that we disregarded the hold-up prob-lem, which arises in settings with time-consistent taxation and which may be mitigated by interregional competition for human capital (see, e.g., Boadway, Marceau and Marchand, 1996; Andersson and Konrad, 2003a; and Haupt and Janeba, 2009).
migration costs, implying a strong desire for migration; i.e. m, m0 < 0.7 The corresponding density functions are f(m0) = 1/∆m0 and f(m) = 1/∆m with
∆m0 = (m0 −m0) and ∆m = (m−m). In what follows, we also assume that m > |m|, implying that the expected value of m or rather the average mobility cost is positive:
E{m}= Z m
m
mf(m)dm= 1
2(m+m)>0.
Hence, a student expects to face positive migration costs when they want to leave their location of education (the home or the foreign country) upon graduation. A positivem representing an individual’s attachment with respect to their location of education can be due for example to social ties – especially family ties – and the acquisition of country-specific human capital during the course of their studies.8 The individual decision-making process consisting of (i) a student-migration de-cision and (ii) a migration dede-cision upon graduation (labor-migration dede-cision), is solved recursively.
Labor migration At the labor-migration stage, a student who was born and educated in countryi, decides to stay in i(leave i) upon graduation if
m >(ti−tj)w (m <(ti−tj)w), (3.1) i.e. if mobility costs exceed (fall short of) the tax differential between the two countries. The gross-wage income for inelastically supplied labor, which could be interpreted as the return to education, is exogenously given and denoted by w.9
7 A repatriate’s negative cost could for example be interpreted as homesickness, while a first-time migrant’s negative cost reflects a sense of adventure, which not only captures risk-loving behavior but also aspects such as career concerns or intercultural interests.
8 Baruch, Budhwar and Khatri (2007) and Henseler and Plesch (2009) present empirical analy-ses of return/non-return determinants of foreign students. Tremblay (2005) provides a more general overview with respect to the relationship between student and high-skilled labor mobility. Finn (2003) reports high stay rates for foreign doctorate recipients from U.S. uni-versities (about 2/3). Estimated stay rates for foreign students in the U.S. range from 1/5 (Rosenzweig, 2006) to 1/3 (Lowell, Bump and Martin, 2007).
9 The assumption of exogenous wage rates is not too restrictive. If the magnitude of migration-induced wage-rate effects is only secondary, they have a quantitative but no qualitative effect on migration flows (see Lange, 2009).
A graduate ini, if born in j, stays in i (repatriates) if
(1−α)m >(ti−tj)w ((1−α)m <(ti−tj)w). (3.2)
The labor-migration decision has two basic dimensions. First, individuals con-sider net income differentials as a migration motive. Second, non-economic mi-gration incentives or disincentives are incorporated in the m’s that vary across individuals. Individuals with negative migration costs, having a strong desire to emigrate, do so even if there is nothing to gain in terms of net income. This two-dimensional approach applies by analogy to the student migration decision.
While most of the time we refer to migration costs when describing individuals’
migration behavior (which is quite illustrative as we use money equivalents for migration preferences in individuals’ decision making),mandm0 can in fact also represent individuals’ country-specific preferences, i.e. preferences concerning where to live.
Student migration Whether a student born in countryialso attends university in countryi depends on the international education expenditure and net income differential, individual migration costsm0and expectations about migration costs m that are revealed at the next stage. Here, we assume risk-neutral individuals.
An individual in country i compares the expected net payoff from studying in i (πii) with the expected payoff if they study abroad (πij). Studying in i yields the following expected net payoff:10
E{πii} = Pr{m >(ti−tj)w}(1−ti)w
+ Pr{m <(ti−tj)w}[(1−tj)w−E{m|m <(ti−tj)w}]
+si. (3.3)
With probability Pr{m > (ti −tj)w}, the individual works in country i upon graduation and earns net labor income (1−ti)w. With probability Pr{m <
(ti−tj)w}, the individual leavesito work in j where they earn net labor income (1−tj)w. The corresponding expected migration costs are E{m|m <(ti−tj)w}.
10 To simplify matters we assume that there is no discounting between periods. This assumption has no qualitative impact on our results.
When studying in i, the individual benefits from education expenditure si > 0 (or has to pay tuition fees |si| when si <0).
Analogously, studying in j yields
E{πji} = Pr{(1−α)m >(tj −ti)w}(1−tj)w + Pr{(1−α)m <(tj−ti)w}
×[(1−ti)w−E{(1−α)m|(1−α)m <(tj−ti)w}]
+sj −m0. (3.4)
With probability Pr{(1−α)m >(tj−ti)w}, the individual stays injafter studying there. With probability Pr{(1−α)m < (tj −ti)w} they return to their country of origin. The student incurs migration costsm0 at the student-migration stage.
A student born in i attends university in countryi if E{πii}>E{πji}. Using the probabilities and expected migration costs11 in (3.3) and (3.4) and solving form0 yields the following condition:
m0 >(sj−si) + (m+m)w
∆m (ti−tj)−r(α), (3.5) where
r(α) :=
αh
m2− (ti−t1−αj)2w2i
2∆m , r(0) = 0. (3.6)
The less generous the amenities in the country of origin relative to those abroad, the more students leave the country (first term on the RHS in (3.5)). The second term represents the fact that the higher the tax rate in the country of origin relative to the foreign tax rate, the higher the rate of student emigration. This holds for the assumed positive expected value of migration costs m. This is because students anticipate that they may not be able to escape unfavorable
11 The expected migration costs are
E{m|m <(ti−tj)w} = 1
2[(ti−tj)w+m], E{m(1−α)|m(1−α)<(tj−ti)w} = 1−α
2
(tj−ti)w 1−α +m
.
taxation at the next stage, so they will tend to do so already at the first stage.
Furthermore, the lower expected labor-mobility costs at the second stage, i.e. the higher expected labor mobility, the weaker the impact on the student migration decision, implying lower student mobility. The third term r(α) relates to the difference in graduate migration between a repatriate and a first-time migrant forα >0.