A major methodological concern with the empirical analysis of the impact of labour market experience and marriage formation in the host country on return migration decisions is that all these processes depend on student characteristics. This implies that any observed relationship between individual labour market changes or marriage formation and return migration may be caused by unobserved factors that influence both the labour market dynamics, the marriage formation and the return migration decision. For example, a finding that female students have shorter migration durations in the host country may not imply that gender causes students to leave fast. Rather, it may be induced by other factors of female students which make them to stay for a shorter period. Labour market behaviour in the host country plays here a central role. Unemployment has been shown to affect the return decision (Bijwaard et al. 2014; Kırdar 2009). It is therefore imperative to account for interdependence between labour market changes (and marriage formation) and return. We use a ‘timing-of-events model’ (Abbring and Berg 2003), which explicitly controls for the strong correlation between labour market changes and the decision to return (Bijwaard et al. 2014), to account for this interdependence.
Thus, we seek to identify the effect of labour market and family formation dynamics on foreign students’ decision to leave. Let \(T_{\mathrm{m}}\) denote the time (since entry into the Netherlands) the immigrant emigrates from the host country, \(T_{\mathrm{s}}\) the time a study spell ends in the host country, \(T_{\mathrm{e}}\) the time an employment spell ends, \(T_{\mathrm{u}}\) the time an unemployment spell ends, and \(T_{\mathrm{mar}}\) the time a migrant marries in the host country (all students are single at entry). A study spell can end in either employment or unemployment (or departure).
The durations of a study spell ending in employment and unemployment spells are denoted by \(\delta _{\mathrm{se}}(t)\) and \(\delta _{\mathrm{su}}(t)\). Similarly, the durations from employment to unemployment is denoted by \(\delta _{\mathrm{eu}}(t)\) and from unemployment to employment by \(\delta _{\mathrm{ue}}(t)\). In order to keep track of labour market and marriage events, we also define the associated time-varying indicators: the indicator \(I_{\mathrm{u}}{(t)}\) takes value one if the migrant is unemployed at time t,Footnote 4
\(I_{\mathrm{e}}(t)\) indicates that the immigrant is employed, and \(I_{\mathrm{mar}}(t)\) indicates that the immigrant is married.
In Fig. 4 we depict the labour market, marriage and migration dynamics of an arbitrary foreign student. The student is (by definition) studying and single at entry. After a study period of \(t_{\mathrm{s}}\) the student finds a job in the Netherlands. This implies that the time till employment is \(\delta _{\mathrm{se}}(t)=t_{\mathrm{s}}\), which is equal to the (censored) time till unemployment, \(\delta _{\mathrm{su}}(t)=t_{\mathrm{s}}\). The student is fired at \(t_{\mathrm{e}}\). Thus the (first) job lasts for \(\delta _{\mathrm{eu}}(t)=t_{\mathrm{e}}-t_{\mathrm{s}}\). After a period of unemployment \(\delta _{\mathrm{ue}}(t)=t_{\mathrm{u}}-t_{\mathrm{e}}\), the student finds a new job at time \(t_{\mathrm{u}}\). In the meantime the student got married at time \(t_{\mathrm{mar}}\), which implies that he/she has been single for \(t_{\mathrm{mar}}\). At the moment the student leaves the country, at \(t_{\mathrm{m}}\), the employment spell (and the marriage spell) in the Netherlands ends. This implies that the second employment spell was censored and of length \(\delta _{\mathrm{eu}}(t)=t_{\mathrm{m}}-t_{\mathrm{u}}\). We assume that all these events also change the incidence of the other events and that the incidence depends on (un)observed individual factors that influence all the events simultaneously.
We consider three different processes: (1) the labour market process, including studying; (2) the process of getting married; and (3) the main process of leaving the country. As the migrant is either studying, employed or unemployed, the labour market process has four possible transitions: study to employment (se), study to unemployment (su), employment to unemployment (eu) and unemployment to employment (ue). Note that all the students are, by definition, studying at entry. So, there is no need to model any initial conditions to enter the first state. The conditional hazards for these transitions all follow mixed proportional hazard (MPH) models and are allowed to be correlated through unobservable heterogeneity terms:
$$ \theta _{k}\left. \left( \delta _{k}(t)|t_{\mathrm{mar}}, x_{k}(t), v_{k}\right) = v_{k} \lambda _{k}\left( \delta _{k}(t)\right) \exp \left( x_{k}(t)\beta _{x}^{k} +I_{\mathrm{mar}}(t)\gamma _{\mathrm{mar},k}\right) \right., $$
(1)
with \(k=\{ \hbox {se}, \hbox {su}, \hbox {eu}, \hbox {ue} \}\). The baseline hazard \(\lambda _{k}(\cdot )\), which is common to all individuals, reflects the duration dependence of the particular hazard rate. The exogenous (control) covariates that may explain the labour market transition, \(x_{k}(t)\), are possibly time-varying and enter the hazard exponentially, \(\exp (x_{k}(t)\beta _{x}^{k})\), which accelerates exits. To accommodate unobserved heterogeneity a positive time-invariant individual-specific random term, \(v_k\), multiplies the hazard. Two additional terms are included: \(I_{\mathrm{mar}}(t)\) indicates that a student is married at t and \(\gamma _{{\mathrm{mar}},k}\) captures the effect of marriage on these labour market transition hazards.
Most students are in their 20s, and this age period is generally the onset of family formation. Students at campus or starting their career are prone to find their partner. The hazard of marrying is also of the MPH form and we allow for a direct effect of (un)employment on this transition:Footnote 5
$$ \theta _{\mathrm{mar}}\left( t| t_{\mathrm{e}}, t_{\mathrm{u}}, x_{\mathrm{mar}}(t), v_{\mathrm{mar}}\right) =v_{\mathrm{mar}} \lambda _{\mathrm{mar}}( t)\exp \left( x_{\mathrm{mar}}(t)\beta _{x}^{\mathrm{mar}} +I_{\mathrm{e}}(t)\gamma _{e,\mathrm{mar}}+I_{\mathrm{u}}(t)\gamma _{u,\mathrm{mar}}\right) ,$$
(2)
with \(I_{\mathrm{u}}(t)\) and \(I_{\mathrm{e}}(t)\) are the indicators of (un)employment of the student and \(\gamma _{e,\mathrm{mar}}\) and \(\gamma _{u,\mathrm{mar}}\) capture the effect of these labour market changes on the hazard to get married. Again \(\lambda _{\mathrm{mar}}(\cdot )\) captures the duration dependence, \(x_{\mathrm{mar}}(t)\) are (possibly time-varying) control variables explaining the hazard of marrying and, \(v_{\mathrm{mar}}\) is a positive time-invariant individual-specific random term capturing unobserved heterogeneity.
Finally, the return migration hazard also has an MPH form. The migration hazard is a function of (possibly time-varying) control variables \(x_{m}(t)\), labour market changes, \(I_{\mathrm{u}}(t)\) and \(I_{\mathrm{e}}(t)\), and getting married \(I_{\mathrm{mar}}(t)\)
$$ \theta _m\left( t|t_{\mathrm{u}}, t_{\mathrm{e}}, t_{\mathrm{mar}}, x_m(t), v_m\right) = v_m \lambda _{m}(t)\exp \left( x_m(t)\beta _{x}^m + I_{\mathrm{u}}(t)\gamma _u +I_{\mathrm{e}}(t)\gamma _e + I_{\mathrm{mar}}(t) \gamma _{\mathrm{mar}} \right). $$
(3)
Again \(\lambda _{m}(\cdot )\) captures the duration dependence and \(v_{\mathrm{m}}\) is a positive time-invariant individual-specific random term capturing unobserved heterogeneity.
It is well known that, due to dynamic sorting effects, the distribution of the unobserved heterogeneity among those students who become (un)employed or married at a particular time will differ from its population distribution. Consider, for example, the student to employment process. Students with high \(v_{\mathrm{se}}\), e.g. high motivation to become employed, will tend to enter employment earlier than individuals with low \(v_{\mathrm{se}}\). If \(v_{\mathrm{se}}\) and \( v_{\mathrm{m}}\), the unobserved heterogeneity of the return migration hazard, are dependent, then the distribution of \(v_{\mathrm{m}}\) for employed students at a given time in the country will differ from the distribution of \(v_{\mathrm{m}}\) for students still studying. Similarly, if \(v_{\mathrm{m}}\) and \(v_{\mathrm{mar}}\) are dependent, then the distribution of \(v_{\mathrm{m}}\) among married students will differ from its population distribution. Therefore, one cannot infer the effect of (un)employment or marriage on the return migration from a comparison of the realised durations of those who became (un)employed/married at a particular time with the rest of the population, because one would then mix the effect of (un)employment/marriage on the duration with the difference in the distribution of \(v_{\mathrm{m}}\) between these migrants. In this case \(I_{\mathrm{e}}(t), I_{\mathrm{u}}(t)\) and \(I_{\mathrm{mar}}(t)\) will be endogenous. The same holds for the inclusion of the marriage in the labour market processes and for the inclusion of (un)employment in the marriage process, and therefore all the durations \(T_{\mathrm{se}},\ldots , T_{\mathrm{mar}}\) and \(T_{\mathrm{m}}\) should be modelled jointly to account for dependence of the unobserved heterogeneity terms.
For the sake of parsimoniousness, we assume that each of the unobserved heterogeneity terms remains the same for recurrent durations of the same type, and we adopt a discrete distribution, i.e. v has discrete support \((v_1, \ldots , v_K)\), with \(v_{\mathrm{r}}=(v_{\mathrm{se,r}},\ldots ,v_{\mathrm{m,r}})\) and \(p_{\mathrm{r}}= \Pr (v=v_{\mathrm{r}})\).Footnote 6
The “timing-of-events” method of Abbring and Berg (2003) implies that the full effects of labour market changes and marriage formation on the return migration hazard, \(\gamma _{e}\), \(\gamma _{u}\) and \(\gamma _{\mathrm{mar}}\) in our framework, have a causal interpretation. This requires that all transition rates are modelled parametrically as mixed proportional hazards, as we have. Identification of the causal effect additionally requires that the so-called no-anticipation assumption holds. The (untestable) no-anticipation assumption requires that migrants do not anticipate entering the labour market (or marriage) by migrating before the anticipated event would occur. Although it can be argued that the no-anticipation assumption is valid, we are cautious in using a casual interpretation of the our effects. Still, the timing-of-events method corrects for possible endogeneity of the labour market and marriage formation processes.
Although in principle the exact date of emigration is known, some migrants do not officially inform the authorities that they are about to leave the Netherlands. However, all citizens (immigrants and natives) are required to register with their municipalities (this is a pre-requisite for many social services and for tax-benefit matters). It is thus clear that any migrant who has no entries in the tax-benefit register and does not appear in the register of another municipality must have left the country. Only the exact date of the departure is unknown. Such non-compliers are periodically identified and removed from the registers by the authorities in a step labelled “administrative removal”. These administrative removals are included among the emigrations. In our data the percentage of administrative removals among the emigrants runs from 14 % for students from Antilles and Surinam to 46 % for students from developed countries (EU 15: 33 %; new EU: 37 % and LDC: 40 %).
We assume that when a migrant is “administrative removed” and has “zero income at the last observed time” implies that the migrant has left before the date the administrative removal is recorded and after the last date of any observed change in the observed characteristics (e.g. labour market status, housing and marital status). Such limited information is equivalent to interval-censored data. For interval-censored data the exact timing of an event is unknown, but it is known that the duration ended in some period of time.