Most models that are concerned with the effect of migration on human capital investments and a possible brain gain are built on the premise that wage differentials are the main determinant of migration (e.g., Stark et al. 1997, Mountford 1997, Vidal 1998, Beine et al. 2001). A problem with this setup is that it does not account for the intrinsic value of education (see Bénabou and Tirole 2003 for a detailed discussion). The present framework intends to clarify the relationship between aspirations and human capital investments. To allow an accessible interpretation, matters are kept as parsimonious as possible. A simple static model with no general equilibrium effects based on Stark et al. (1997) shows that the exclusion of the intrinsic value of human capital can lead to underestimating the effects of migration on human capital investments. The presentation of the framework proceeds in three steps looking at investments (1) under autarky; (2) with migration; and (3) with dynastic migration.
Assume individuals live for two periods, childhood and working age. Individuals derive utility from consumption c
t
in both periods and from the intrinsic value of human capital θ in the first period in each dynasty d. In the first period, individuals can invest in human capital θ or work to finance consumption c
1. In the second period, individuals can only work to finance consumption c
2. Their objective function is given by:
$$ {U}_d\equiv U\left({c}_1,\psi \left(\theta \right),{c}_2\right) $$
(1)
Consumption is financed only by wages. Individuals can earn wage W
H(θ) in their home country. Labor demand and the wage function are exogenously determined and identical for all individuals. To keep matters simple, a linear wage function will be used such that \( {W}^H\left(\theta \right)={w}_0^H+{w}_1^H\theta \), where \( {w}_1^H \) is the education premium which is time invariant. Individuals face an exponentially increasing human capital cost function C(θ) = γθ
2 were γ > 1. Human capital is acquired instantly in the home country in period one and remains unchanged in period two. For ease of exposition, no restrictions are imposed on the total amount of human capital that can be accumulated. Also, there is no capital market. The individual faces the following resource constraints in the first and second period, respectively:
$$ {c}_1 = {W}^H\left(\theta \right) - C\left(\theta \right) = {w}_0^H+{w}_1^H\theta - \gamma {\theta}^2 $$
(2)
$$ {c}_2 = {W}^H\left(\theta \right)={w}_0^H+{w}_1^H\theta $$
(3)
In addition to these standard elements, the model contains a reference point dependent disutility, following the discussion by Kogszegi and Rabin (2006), which is represented by ψ(θ). The individual will choose the education of a certain reference group θ
R that acts as a benchmark to evaluate her own household’s education level1. This reference point, or aspiration level of education, will most likely be influenced by the environment the individual is exposed to, e.g., family, neighborhood, co-workers. This relates to the results by Mookherjee et al. (2010), who have argued that spatial segregation will lead to persistent reference points, i.e., aspirations traps. The individual will aspire to this reference point and experience increasing disutility the further away she is from this benchmark. Let ψ(θ) = (θ
R − θ)2. It is reasonable to assume that individuals aspire to higher goals and therefore – if it is possible – choose a higher reference group than their current educational level such that θ
R ≥ θ.
Before introducing migration, let us consider the optimal human capital investment in autarky. By substitution it can be shown that the individual will maximize the following objective function:
$$ {U}_d\equiv U\left({c}_1,\psi \left(\theta \right),{c}_2\right) = {w}_0^H+{w}_1^H\theta - \gamma {\theta}^2 - {\left({\theta}^R-\theta \right)}^2+{w}_0^H+{w}_1^H\theta $$
(4)
Solving for θ, it can be observed that the optimal autarky level of human capital θ* is:
$$ {\theta}^{*} = \frac{w_1^H+{\theta}^R}{\gamma +1} $$
(5)
In autarky human capital accumulation will be driven by the education premium \( {w}_1^H \), by the reference level θ
R, and by the cost of education γ. The next step is to allow for the possibility to migrate temporarily in the second period to work abroad. Assume at the probability to migrate p is exogenous and applies equally to all individuals. In the foreign country, individuals can earn a wage W
F(θ) where \( {W}^F\left(\theta \right)={w}_0^F+{w}_1^F\theta \). Let the education premium in the foreign country be bigger than the education premium in the home country, i.e., \( {w}_1^F>{w}_1^H \). Migration will be costly such that migrants will earn κW
F(θ) in the foreign country where 0 < κ ≤ 1 is a cost factor. The resource constraint in the second period will therefore take the following form:
$$ {c}_2 = p\kappa {W}^F\left(\theta \right)+\left(1-p\right){W}^H\left(\theta \right)=p\kappa \left[{w}_0^F+{w}_1^F\theta \right]+\left(1-p\right)\left[{w}_0^H+{w}_1^H\theta \right] $$
(6)
By substituting the second period consumption of equation (6) into equation (4), the objective function reads:
$$ U\left({c}_1,\psi \left(\theta \right),{c}_2\right)={w}_0^H+{w}_1^H\theta -\gamma {\theta}^2-{\left({\theta}^R-\theta \right)}^2+p\kappa \left[{w}_0^F+{w}_1^F\theta \right]+\left(1-p\right)\left[{w}_0^H+{w}_1^H\theta \right] $$
(7)
The optimal level of human capital θ* given the probability to migrate p thus becomes:
$$ {\theta}^{*} = \frac{2\left({w}_1^H+{\theta}^R\right)+p\left(\kappa {w}_1^F-{w}_1^H\right)}{2\left(\gamma +1\right)} $$
(8)
Notice that the only difference between equations (5) and (8) is that the latter contains the probability weighted wage difference term (\( \kappa {w}_1^F-{w}_1^H \)). It is readily observable that a higher probability to migrate and/or a higher wage differential will increase the investments in education in the first period. Given that migrants are only temporarily permitted to work abroad, each generation faces the same decision. This dynamic represents the standard brain gain argument.
In a dynastic migration setting, the implications of the reference point θ
R become even more pronounced. Let the migration of the last generation only have an effect on two variables: the migration cost κ and the reference point θ
R. To emphasize the intergenerational transmission of these two variables, the subscript d will be used.
First, migration might decrease the migration cost. This effect reflects the strong evidence on the importance of migrations networks (e.g., Munshi 2003). By introducing the indicator variable m
d
= {0, 1} — where m
d − 1 = 1 if the last dynasty migrated and zero if not — this can be written as κ
d
= κ
d − 1 + α(1 − κ
d − 1)m
d − 1. Alpha (α) is a deterministic indicator reflecting how much the migration experience reduces migration costs and is defined as 0 < α < 1. Thus, if the probability of migration is non-zero (p > 0) and the last generation also migrated (m
d − 1 = 1), one would observe increased human capital investment compared to a scenario where there is no connection between dynasties.
Second, the migration in the last generation could also raise the reference point the dynasty uses. This change could come about through either externalities in the labor market in the destination country due to the matching of the migrant with a certain sector or other market interactions, or through externalities in social surroundings, i.e., interactions with co-workers, friends or neighbors. Let λ represent the difference between the home and the foreign reference group such that \( \lambda = {\theta}^{R_F}-{\theta}^{R_H}\ge 0 \). The link of the reference point between dynasties can be thought of as:
$$ {\theta}_d^R={\theta}_{d-1}^R+\lambda {m}_{d-1} $$
(9)
If the last generation has migrated (m
d − 1 = 1) and the migrants have adopted a higher reference point (λ > 0), then the aspired level of education \( {\theta}_d^R \) will increase compared to migration without dynasties.