1. R. Aísa, J. Cabeza and G. Larramona University of Zaragoza
XXXIII SIMPOSIO DE ANÁLISIS ECONÓMICO ZARAGOZA 2008
                                  
THE INFLUENCE OF HUMAN CAPITAL ON MIGRANTS’ CHOICE OF TIMING FOR MIGRATION
R. Aísa, J. Cabeza and G. Larramona
University of Zaragoza

2. SAE 2008, Zaragoza THE INFLUENCE OF HUMAN CAPITAL ON MIGRANTS’ CHOICE OF TIMING FOR MIGRATION
MOTIVATION
How to implement appropriate policies to ease the assimilation of migratory flows?
To design suitable policies we need to ascertain the characteristics of these migrants.
Two relevant feature of migrants’ distinctiveness:
Education
Age

3. SAE 2008, Zaragoza THE INFLUENCE OF HUMAN CAPITAL ON MIGRANTS’ CHOICE OF TIMING FOR MIGRATION
MOTIVATION
Education has been especially studied (Borjas, 1987; Antolin and Bover, 1997; Beine, Docquier and Rapoport, 2001; Chiquiar and Hanson, 2005)
Less attention to age (Lewis, 1977; Scholottmann and Herzog, 1984; Goss and Paul, 1986; Pissarides and Wadsworth, 1989) Impact of age on the decision to migrate

4. MOTIVATION What age do migrants choose to migrate at?
SAE 2008, Zaragoza THE INFLUENCE OF HUMAN CAPITAL ON MIGRANTS’ CHOICE OF TIMING FOR MIGRATION
MOTIVATION
What age do migrants choose to migrate at?
What does theoretical work answer?
The best decision is to migrate immediately (Hartog and Winkelmann, 2003)
They compare the estimated marginal benefit of increasing age at migration with the marginal cost of later migration

5. MOTIVATION What does empirical evidence show?
SAE 2008, Zaragoza THE INFLUENCE OF HUMAN CAPITAL ON MIGRANTS’ CHOICE OF TIMING FOR MIGRATION
MOTIVATION
What does empirical evidence show?
Most migrants decide to migrate within the range of years in the case of USA and Spain

6. SAE 2008, Zaragoza THE INFLUENCE OF HUMAN CAPITAL ON MIGRANTS’ CHOICE OF TIMING FOR MIGRATION
MOTIVATION
The divergence between the data and theory is that they only consider the stream of incomes associated with migration and one monetary cost of migrating, without taken into account other relevant elements.
In order to avoid the discrepancy with data our framework also integrates education and social factors in the home and host countries.

7. SAE 2008, Zaragoza THE INFLUENCE OF HUMAN CAPITAL ON MIGRANTS’ CHOICE OF TIMING FOR MIGRATION
MOTIVATION

8. SAE 2008, Zaragoza THE INFLUENCE OF HUMAN CAPITAL ON MIGRANTS’ CHOICE OF TIMING FOR MIGRATION
MOTIVATION
Economic dimension: The immediate gain of migrating is the difference between salaries in the host and home countries (Harris and Todaro, 1970)
Educational dimension: We introduce qualifications in order to capture the heterogeneous population and their different earnings in the host country (Grogger and Trejo, 2002, Van Ours and Veenman, 2006)
Effect of Migration age in education vs. effect of education on migration age
Social dimension: The individual who emigrates suffers a loss of relationships in his homeland and must make a great deal of effort to adapt to the new culture (Faini, 1996)

9. CONTRIBUTION OF THE PAPER
SAE 2008, Zaragoza THE INFLUENCE OF HUMAN CAPITAL ON MIGRANTS’ CHOICE OF TIMING FOR MIGRATION
CONTRIBUTION OF THE PAPER
First contribution: We use a two-stage optimal control technique with an explicit switch point dependency, enabling us to endogenize optimal timing for migration, taking into account education, earnings and social factors.
Second contribution: The choice of migration age by each individual establishes a novel mechanism that makes social migration costs endogenous (Carrington et. al., 1996, Spilimbergo and Ubeda, 2004)

10. SAE 2008, Zaragoza THE INFLUENCE OF HUMAN CAPITAL ON MIGRANTS’ CHOICE OF TIMING FOR MIGRATION
MAIN RESULTS
The calibration of the model shows a pattern for migration age similar to Spanish data.
The optimal migration age will be lower for more highly educated individuals than for the unskilled, a result supported by Spanish data.

11. STRUCTURE The model Calibration Conclusions
SAE 2008, Zaragoza THE INFLUENCE OF HUMAN CAPITAL ON MIGRANTS’ CHOICE OF TIMING FOR MIGRATION
STRUCTURE
The model
Calibration
Conclusions

12. THE MODEL Continuos time. Preferences of the emigrant born in t=0:
SAE 2008, Zaragoza THE INFLUENCE OF HUMAN CAPITAL ON MIGRANTS’ CHOICE OF TIMING FOR MIGRATION
THE MODEL
Continuos time.
Preferences of the emigrant born in t=0:
c(t) is the consumption of this individual in t
T is the longevity of this individual
 is the intertemporal discount rate of the utility
preference for the country of origin

13. SAE 2008, Zaragoza THE INFLUENCE OF HUMAN CAPITAL ON MIGRANTS’ CHOICE OF TIMING FOR MIGRATION
THE MODEL
We assume that this parameter takes the following form:
t1 denotes the departure time of the emigrant
There is always a loss in utility associated with migration (social moving costs)
The age of the potential emigrant affects the reduction of utility associated with migration

14. SAE 2008, Zaragoza THE INFLUENCE OF HUMAN CAPITAL ON MIGRANTS’ CHOICE OF TIMING FOR MIGRATION
THE MODEL
Faini (1996) considers that the loss of utility is exogenous and constant
Spilimbergo and Ubeda (2004) assume that the loss of utility depends exogenously on integration of the worker within the society
In this work: Delay in the timing of migration helps the integration and reduce the loss of utility related to migration.
JOB IN HAND, time is necessary to get information of the job market BETTER-KNOW ENVIRONMENT

15. SAE 2008, Zaragoza THE INFLUENCE OF HUMAN CAPITAL ON MIGRANTS’ CHOICE OF TIMING FOR MIGRATION
THE MODEL
The objective function: Migration to obtain a better standard.
c(t) is the consumption of this individual in t
T is the longevity of this individual
 is the intertemporal discount rate of the utility
is the loss of utility associated with migration

16. THE MODEL k(t) is the capital in t of this individual
SAE 2008, Zaragoza THE INFLUENCE OF HUMAN CAPITAL ON MIGRANTS’ CHOICE OF TIMING FOR MIGRATION
THE MODEL
The budget constraint for this emigrant:
k(t) is the capital in t of this individual
h is his human capital which depends positively on the period of education, s
r1 and r2 are the interest rates in the birth and host countries
w1 and w2 are the rates of return of human capital in the birth and host countries: w2 > w1 , w2 grows at a positive rate 2

17. THE MODEL Max preferences s.t. budget constraint
SAE 2008, Zaragoza THE INFLUENCE OF HUMAN CAPITAL ON MIGRANTS’ CHOICE OF TIMING FOR MIGRATION
THE MODEL
Max preferences s.t. budget constraint
Endogenous variables: c(t), t1
Exogenous variables: s, r1, r2, w1 w2(t) and 2
This problem can be solved by applying the conditions developed by Tomiyama and Rossana (1989) for two-stage control problems, where the switch point t1, is a choice variable and appears as an argument of the integrands
We decompose the problem into two auxiliary problems.

18. THE MODEL Auxiliary Problem II Auxiliary Problem I
SAE 2008, Zaragoza THE INFLUENCE OF HUMAN CAPITAL ON MIGRANTS’ CHOICE OF TIMING FOR MIGRATION
THE MODEL
Auxiliary Problem II
Auxiliary Problem I

19. THE MODEL Matching conditions at t1*
SAE 2008, Zaragoza THE INFLUENCE OF HUMAN CAPITAL ON MIGRANTS’ CHOICE OF TIMING FOR MIGRATION
THE MODEL
Matching conditions at t1*
continuity of costate variable corresponding to k
the continuity of the path of assets
Tomiyama and Rossana condition
We deduce that there is an interior solution for t1* with , if and only if

20. CALIBRATION h = Bils and Klenov, 2000
SAE 2008, Zaragoza THE INFLUENCE OF HUMAN CAPITAL ON MIGRANTS’ CHOICE OF TIMING FOR MIGRATION
CALIBRATION
h = Bils and Klenov, 2000

21. SAE 2008, Zaragoza THE INFLUENCE OF HUMAN CAPITAL ON MIGRANTS’ CHOICE OF TIMING FOR MIGRATION
CALIBRATION

22. CALIBRATION The intuition of this solution is the following:
SAE 2008, Zaragoza THE INFLUENCE OF HUMAN CAPITAL ON MIGRANTS’ CHOICE OF TIMING FOR MIGRATION
CALIBRATION
The intuition of this solution is the following:
There exist two forces which act in opposite directions.
An economic force leads to emigrate as soon as possible. The sooner the timing of migration the longer the period of high income.
The second force is social and leads to delay the timing of migration. By postponing this moment, the emigrant could reach a better adaptation reducing the social migration costs.
Therefore, more educated migrants will have more incentive to migrate sooner than less educated migrants because the economic force depends positively on the human capital level.

23. SAE 2008, Zaragoza THE INFLUENCE OF HUMAN CAPITAL ON MIGRANTS’ CHOICE OF TIMING FOR MIGRATION
CONCLUSIONS
A framework which endogenously determines the timing of migration has
been constructed.
The combination of social, educational and economic factors related
to migration allows us to detect different effects on the age of migration:
some bring forward the timing and others delay it.
The longer the period of education, the earlier the timing of migration.

24. SAE 2008, Zaragoza THE INFLUENCE OF HUMAN CAPITAL ON MIGRANTS’ CHOICE OF TIMING FOR MIGRATION
CONCLUSIONS
Immigration policies based on human capital selection provide younger and more qualified workers:
more productive,
contribute longer to the production system.