The Dynamics of Return Migration, Human
Capital Accumulation, and Wage Assimilation1
Jérôme Adda2
Christian Dustmann3
Joseph-Simon Görlach4
July 2015
Abstract: To assess the implications of the interplay between anticipated migration
durations and immigrants’ behavior, we develop a lifecycle model in which immigrants
decide labor market participation, consumption, and investment in human capital
together with the optimal length of migration. We estimate this model using panel data
that provide repeated information on immigrants’ return intentions and realized return
migrations. We show that the relation between return intentions and human capital
investment leads to behavior-based selective outmigration, and that policies that
influence migrants’ return decisions may lead to suboptimal career profiles, inducing
welfare losses for both immigrants and the host country’s population.
JEL F22, J24, J61
Keywords: International migration, human capital, immigrant workers.
1
Dustmann acknowledges funding by the European Research Council (ERC) Advanced Grant No 323992,
and Görlach acknowledges funding from the NORFACE program on migration.
2
Bocconi University and IGIER.
3
University College London and Centre for Research and Analysis of Migration (CReAM).
4
University College London and CReAM.
For most migrants, the length of migration is a choice and the outcome of
maximizing welfare over the lifecycle.
5
However, to understand all aspects of
immigrants’ lifecycle behavior, we must know how optimal migration duration is
determined, how return plans may change over the migration cycle as new information
becomes available, and how this decision interacts with other lifecycle choices. For
instance, the expected migration duration affects the period over which investments in
host country-specific human capital is productive and thus influences immigrants’ career
and earnings profiles. Similarly, because policies that interfere with immigrants’ optimal
choice of migration duration may impact other margins of behavior, including economic
performance and social integration, they have important welfare consequences for both
the immigrants and the host country alike.
In this paper, we study the implications of uncertain and changing return plans on the
selection through outmigration, the estimation of earnings profiles, and the design of
optimal migration policies. In particular, we analyze immigrants’ return plans, their
responses to economic shocks and new information, and the interaction of these
responses with other decisions such as human capital investments and savings. To do so,
we develop an estimable lifecycle model of return migration in which individuals decide
simultaneously on whether or not to return to their country of origin and their investment
5
That many—and possibly most—migrations are temporary is well documented in a number of recent
studies. For example, the OECD (2008) estimates that, depending on the countries and time periods
considered, 20 to 50 percent of immigrants leave the host country within the first five years after arrival.
In 2011, foreign-born outflows stood at a 40–80 percent ratio to the inflow of immigrants in the major
European destination countries (OECD, 2013). For the U.S., Renuka Bhaskar,Belkinés ArenasGermosén, and Christopher Dick (2013) estimate that 2.1 million foreign-born individuals left the country
between 2000 and 2010, as compared with 13.1 million immigrants during the same period counted by
the U.S. Census Bureau (2012).
1
in human capital, labor force participation, and savings. A key feature of our model is
that it allows individuals’ return plans to change over the migration cycle as new
information becomes available. Thus, immigrants may adjust their investment decisions
according to the changes in their expected optimal migration duration. We estimate this
model and use it to reevaluate the different mechanisms that affect the evolution of
immigrants’ career profiles, and show the consequences of this evolution for the
estimation of immigrants’ earnings profiles and the assessment of selective outmigration
in standard reduced form settings.
Our analysis provides a new perspective on the interpretation of selective
outmigration. In particular, it shows that when migrations are temporary, career decisions
depend on intended migration duration. Outmigration therefore creates a “behavioral
selection” in which immigrants’ investment in human capital may be lower when they
intend to return home earlier. Such selection along the achievement distribution results
not from heterogeneity in productivity but from different investment intensities based on
the future intended length of migration. Thus, the negatively selective outmigration
estimated in a number of studies (e.g., Wei-Yin Hu 2000; Darren Lubotsky 2007; Ran
Abramitzky, Leah Platt Boustan, and Katherine Eriksson 2014) may in fact be due not to
selection in unobserved ability but to those who intended to stay longer and thus invested
more in human capital, thereby generating steeper career profiles. In our case, this effect
dominates the pure selection effect through unobserved productivity, which we estimate
to be positive rather than negative. This finding gives a new spin to the interpretation of
reduced form estimates of selective outmigration when negative selection results not
2
from low-productivity migrants leaving the country but from those who wish to stay
longer investing more in human capital.
Our model also allows us to investigate the consequences of immigrants’
expectations about a possible return for their career profiles and savings decisions. By
manipulating these expectations, we can simulate the impact that immigration policies
have on immigrant behavior, how they affect selection, and what their consequences are
for welfare. In particular, we demonstrate that important investment decisions are made
in the early years after arrival and that initial beliefs about the migration being temporary
may lead to large earnings losses over the lifecycle if such expectations are revised at a
later stage. We further show that migration policies that manipulate such expectations
(e.g., by offering the probability of permanent residence after some years in the host
country) may lead to welfare losses for both the immigrants and the population of the
receiving country.
In the dynamic life-cycle model we develop, migrants decide in every period not only
whether to return to their home country but upon their labor market status, consumption,
and investment in human capital. At the same time, they accumulate precautionary
savings in response to two different uncertainties: the risk of a bad labor market outcome
and uncertainty about preferences for the host country that may trigger a return to the
home country. Human capital is composed of two separate stocks: work experience and
social capital. This latter, which comprises such host country-specific components as
language proficiency and knowledge about and social contacts in this country, not only
affects wages but determines the migrant’s social assimilation. It thus enters into the
3
utility function in that individuals who are socially better integrated may find life in the
host country more desirable. When investing in social capital, migrants take into account
their planned length of stay.
It is this planned length of stay at any given period, rather than the actual ex post
migration duration, that is key to understanding investment decisions for both forms of
human capital. That is, return plans may be amended over time because of shocks to
preferences or labor market status, thereby also changing future investment paths. This
dynamic relation in which perceived duration in the host country drives future
investments that in turn change the migrant’s horizon can only be analyzed within a
structural dynamic model such as that developed here. 6 This model allows optimal
behavior to be computed in terms of labor supply, savings and consumption, investment
in social capital and ensuing earnings, and potential return migration. It also allows for
heterogeneity not only in ability but also in preferences for the host country, enabling us
to distinguish between selective returns based on productivity and those based on
preference differences.
To the extent that the planned migration duration deviates from the actual stay, the
estimation of immigrants’ dynamic behavior over their migration cycle requires
information not only about the migration’s final duration but also about return plans at
any point over the migration cycle, information that is rarely available in surveys.
Fortunately, we are able to derive such information from the German Socio-Economic
6
Aliya Hashmi Khan (1997) and Kalena E. Cortes (2004) provide empirical support for the argument that
expected migration duration should affect human capital investment decisions in a static framework that
compares postmigration investment in education and the earnings paths of refugee and labor migrants in
the U.S. George J. Borjas (1982) makes this point in a comparison of earnings profiles of Cuban and
other Hispanic immigrants to the United States.
4
Panel (SOEP), a dataset that oversamples immigrants to Germany. Each wave of this
survey includes a measure of immigrants’ planned migration durations, which serves as
an important variable in our estimation.7 In addition, by using a factor model, we are able
to link social capital (which is generally unobserved by econometricians) to a number of
observed outcomes.
Our paper contributes to the large body of literature on immigrants’ earnings
assimilation by providing a structural framework that identifies both the channels
through which selective outmigration may bias estimates and their direction.8 It also adds
to this literature by highlighting a form of selection that is induced through the interplay
of human capital investment and return plans. That is, rather than being based on
unobserved productivity, this selection is a natural consequence of human capital
investments being determined jointly with return plans. It thus affects the estimation of
earnings profiles over and above selection based on unobservable fixed productivity and
is typically difficult to address.
The analysis also contributes to the small but growing literature on structural models
that take temporary migrations into account, much of which focuses on the effect of
border enforcement on Mexico-U.S. migration (Aldo Colussi, 2003; Kevin Thom, 2010;
Rebecca Lessem, 2013). Other related papers include the work of Charles Bellemare
(2007) and Silvio Rendon and Alfredo Cuecuecha (2010), who analyze the job search
7
See Wilbert Van der Klaauw and Kenneth L. Wolpin (2008) and Van der Klaauw (2012) for a discussion
of the value of such information for identification.
8
See, for example, Barry Chiswick (1978), James E. Long (1980), Borjas (1985), Jörn-Steffen Pischke
(1992), Christian Dustmann (1993), Hu (2000), Erling Barth, Bernt Bratsberg, and Oddbjorn Raaum
(2004), Bratsberg, Barth, and Raaum (2006), Lubotsky (2007), and Abramitzky, Platt Boustan and
Eriksson (2014).
5
and outmigration behavior of immigrants in Germany and the U.S., respectively, and that
by Murat G. Kırdar (2012) and Kayuna Nakajima (2014), who evaluate the social
insurance and fiscal contributions of temporary migrants, again for Germany and the
U.S. All these papers, however, rely on data for actual migration durations rather than
anticipated stays. Hence, in these papers, identification of the parameters governing
individual choices critically depends on the assumption of fully rational forward-looking
individuals, an assumption that we relax. Our model also focuses on the accumulation of
a latent social capital variable that affects immigrants’ locational preferences and
economic outcomes. Because the level of this stock variable is determined by an
individual’s earlier attitudes toward the destination country (or by migration policyimposed restrictions that constrain such attitudes), it introduces a behavioral persistence
in preferences that is endogenous to new information arriving throughout an immigrant’s
stay. Both this endogenous preference and this estimation of the accumulation of a latent
variable are novel in this literature, which so far has restricted attention to observed
choices such as consumption and location decisions.
I. Model
We model immigrants’ outcomes from the time they arrive in the new location until
retirement in either the emigration or immigration country. Time is discrete and each
period lasts one year. In each period, individuals make decisions about their labor market
status, their investment in human capital or savings, and whether or not to return to their
home country. These decisions are made conditional on the state space Ω௜௧, which
6
includes age, ܽ௜௧; years since immigration, ‫ ݉ݏݕ‬௜௧; work experience, ܺ௜௧; social capital in
௢௥௞
the host country, Γ௜௧; assets, ‫ܣ‬௜௧; prior employment status, ॴ௪௜௧ିଵ
; and prior location,
‫ܮ‬௜௧ିଵ ∈ {‫ܧ‬, ‫ }ܫ‬, where E stands for emigration (or home) country and I stands for
immigration (or host) country.
We also allow for fixed and time variant unobserved heterogeneity along two
dimensions. First, individuals differ ex ante in their labor market productivity (or ability),
denoted by ߙ௜. Second, preferences across individuals for a particular location vary and
consist of a persistent shock, Ψ௜௟௧, ݈= ‫ܫ‬, ‫ܧ‬, which is autocorrelated over time and
modeled as a first order Markov process.9 We assume a symmetric transition matrix with
the elements
ܲ൫Ψ௜௟௧ = ‫ݔ‬௝หΨ௜௟௧ିଵ = ‫ݔ‬௞൯= ߨ௝௞ , with ߨ௝௞ = ߨ௞௝.
We model the joint distribution of ߙ௜ and Ψ௜ூ଴ in terms of discrete mass points. We further
allow for iid shocks to preferences, denoted by ߟ௜௟௧, ݈= ‫ܫ‬, ‫ܧ‬, which we assume follow an
extreme value distribution.
௝
We combine the stochastic shocks ߟ௜௧ and an iid shock affecting income (ߝ௜௧) in a
vector denoted Υ௜௧. The state vector is therefore written as
௢௥௞
Ω௜௧ = ൛ܽ௜௧, ‫ ݉ݏݕ‬௜௧, ܺ௜௧, Γ௜௧, ‫ܣ‬௜௧, ॴ௪௜௧ିଵ
, ‫ܮ‬௜௧ିଵ, ߙ௜, Ψ௜௟௧, Υ௜௧ൟ.
(1)
A. Model Setup
Human Capital. The two forms of human capital considered—work experience (ࢄ ࢏࢚)
and social capital ( ડ࢏࢚) —affect both wages and labor market transitions. Work
9
We normalize Ψ௜ா௧ to one so that Ψ௜ூ௧ represents the relative taste for the immigration country.
7
experience, which is acquired through learning-by-doing, increases by one unit in each
period in which the individual is working:
ܺ௜௧ାଵ = ܺ௜௧ + ॴ௪௜௧௢௥௞ ,
(2)
where ॴ௪௜௧௢௥௞ takes the value one if individual ݅works in period ‫ݐ‬and zero otherwise.
Work experience is partly portable across countries. When immigrants initially move
from the home to the host country, their experience depreciates by a factor ߦ. Upon
return to the home country, however, their experience is fully portable, although as
explained below, overall productivity in the home country is lower.
Social capital, on the other hand, is a country-specific skill that includes knowledge
of the country, social contact with the majority population, and communication skills. It
thus not only impacts labor market productivity by enhancing the productivity of the
work experience collected in ܺ௜௧ but affects social integration and contacts that may help
the immigrant locate better matches. Such capital is acquired through active investment
(as in Yoram Ben-Porath 1967). We therefore assume that upon arrival, the immigrants’
stock of host country-specific social capital is zero but that they are endowed with a
maximum amount of home country-specific social capital, which does not depreciate.
Social capital in the host country then evolves as
Γ௜௧ାଵ = Γ௜௧ + ݀୻ॴ୻௜௧ ,
(3)
with ॴ୻௜௧ being an indicator variable that equals one if investment takes place in period ‫ݐ‬
and the initial stock Γ௜଴ is normalized to zero. It should be noted that although experience
capital accumulates without requiring any other investment than working (as in, e.g., Zvi
Eckstein and Kenneth I.Wolpin 1989), investments in social capital are active and create
8
a cost in disutility. Moreover, because host country social capital has no value back in the
home country, investments in any period depend on the expected future duration in the
host country (cf. Ben Porath 1967).
Wages and Unemployment Benefits. We use ॴࡸ࢏࢚ୀ࢒ to denote an indicator variable
equal to one if the individual is located in country ࢒= ࡱ, ࡵ. Log gross annual wages are
expressed as
log ‫ݕ‬௜௧ = ߙ௜ + ݂௬ (ܺ௜௧) + ߙ୻Γ௜௧ॴ௅೔೟ୀூ + ߩॴ௅೔೟ୀா + ߝ௜௧,
(4)
where ߙ௜ is individual specific productivity, and ݂௬ (. ) is a piecewise linear function of
work experience with nodes at 2, 5, 10, and 20 years of experience. Social capital in the
host country, Γ௜௧, affects log wages linearly with return ߙ୻ but has no value in the home
country.10 In fact, after return to the home country, wages are lower by a factor ߩ, which
incorporates the differences in productivity between the two countries. The error term ߝ௜௧
is normal and iid across time and individuals, with a mean of zero and variance ߪఢଶ.
Budget Constraint. We assume a standard intertemporal budget constraint under
which assets ‫ܣ‬௜௧ depend on past assets, net income (or unemployment benefits if the
individual is not working), and consumption:
‫ܣ‬௜௧ = ܴ‫ܣ‬௜௧ିଵ + ॴ௪௜௧௢௥௞݊݁‫ݕ(ݐ‬௜௧, ‫ܮ‬௜௧) + ൫1 − ॴ௪௜௧௢௥௞൯ܾ௜௧ − ܿ௜௧,
(5)
‫ܣ‬௜଴ = 0, ‫ܣ‬௜௧ ≥ 0,
10
We impose a log linear relation between social capital and wage, but because social capital is a latent
factor, it is difficult to distinguish between nonlinear returns and a rate of social capital growth that
changes with age. Our model does, however, allow the cost of investment in social capital to vary with
age.
9
where ॴ௪௜௧௢௥௞ is an indicator function equal to one if the individual is working and net() is
a function that relates gross earnings ‫ݕ‬௜௧to net earnings and models the tax schedule in
each country.11 To approximate the unemployment compensation scheme in place over
the period of study, we specify unemployment benefits ܾ௜௧ as a function of the expected
wage the individual would receive if working, so that ܾ௜௧ = ܾ‫(ݎ‬Ω௜௧).12 Once migrants
return, their assets are converted by a factor ‫ݔ‬௧ (see the appendix for the exact
specification), which depends on the purchasing power of the host country currency in
the home country.
Labor Market Transitions. In each period, employed workers are laid off with
probability ߜ(Ω௜௧) , while individuals who are unemployed receive a job offer with
probability ߣ(Ω௜௧) and decide whether to accept the job or remain unemployed (we
explain how this choice is made below). The rates at which jobs are lost and new job
offers arrive are functions of labor market experience, age, and social capital, which for
the host country are specified as
and
ߜ(Ω୧୲) = Φ൫ߜ଴ + ߜ௑ ܺ௜௧ + ߜ௰ ߁௜௧ + ݂ఋூ(ܽ௜௧)൯
(6-a)
ߣ(Ω୧୲) = Φ൫ߣ଴ + ߣ௑ ܺ௜௧ + ߣ௰ ߁௜௧ + ݂ఒூ(ܽ௜௧)൯,
(6-b)
where ݂ఋ(ܽ௜௧) and ݂ఒ(ܽ௜௧) are a spline function of age, and Φ( ) denotes the standard
normal distribution function. For Turkey, the home country in our implementation, we
define ߜ(ߗ௜௧) = ݂ఋா (ܽ௜௧) and ߣ(ߗ௜௧) = ݂ఒா (ܽ௜௧) , with age-specific job loss and job
11
See the appendix for details.
See the appendix for details. Because Turkey offered no unemployment benefits during most of our
period of analysis (they were introduced in 2002 by Unemployment Insurance Law no. 4447, with a fairly
low replacement ratio of 9%), we set ܾ௜௧ = 0 for individuals who have returned home.
12
10
finding probabilities derived from unemployment rates and unemployment durations as
estimated by Aysit Tansel and H. Mehmet Taşçı (2010).
Preferences. The individual derives utility from consumption ܿ௜௧ and from leisure
(1 − ℎ), where ℎ ∈ [0,1] is the labor supply. We again use ॴ௪௜௧௢௥௞ to denote an indicator
function equal to one if the individual is working in period ‫ݐ‬. Utility also depends on
social capital, which enhances the utility from living in the host country relative to the
home country. This dependence allows for habit formation and implies that short-term
events that keep migrants in the host country for an additional period may have
permanent effects on their future choices. The utility function also incorporates a cost of
investment in social capital, ݁(ܽ௜௧) , which is age dependent. 13 This cost takes into
account that older individuals may find it more difficult to acquire new language skills or
to form social contacts. Finally, we allow the utility to be stochastic, depending both on a
persistent shock, Ψ௜௟௧, and an iid shock, ߟ௜௟௧, ݈= ‫ܧ‬, ‫ܫ‬.14 Utility then takes the following
form:
௅
ೢ ೚ೝೖ
‫ݑ‬௜௧൫ܿ௜௧, ॴ୻௜௧, ‫ܮ‬௜௧, ॴ௪௜௧௢௥௞; Ω௜௧൯= (Ψ௜௧೔೟(Γ௜௧ + 1)థ బ )ॴಽ೔೟స ಺ܿ௜௧థ భ (1 − ℎ)ॴ೔೟
−݁(ܽ௜௧)ॴ୻௜௧ + ߟ௜ூ௧ॴ௅೔೟ୀூ + ߟ௜ா௧ॴ௅೔೟ୀா .
(7)
As discussed above, we allow for an individual’s initial locational preference Ψ௜ூ଴ to be
correlated with unobserved productivity ߙ௜.
We specify the effort function to be linear in age: ݁(ܽ௜௧) = ݁଴ + ݁ଵܽ௜௧.
These persistent and transitory shocks capture aspects such as family events that are important for return
decisions but which we do not model explicitly.
13
14
11
B. Dynamic Specification of the Model
In each period, individuals choose their consumption level, labor supply, and whether
to invest in social capital and/or change location. The value function is defined by the
following Bellman equation, which describes how these choices affect the
contemporaneous and future utility:
ܸ(Ω௜௧) =
max
‫ܿ(ݑ‬௜௧, ॴ୻௜௧, ‫ܮ‬௜௧, ॴ௪௜௧௢௥௞; Ω௜௧) + ߚ‫ܧ‬௧ܸ(Ω௜௧ାଵ),
(8)
ೢ ೚ೝೖ
௖೔೟,ॴ౳
,௅೔೟
೔೟,ॴ೔೟
where ߚ is the discount factor and ‫ܧ‬௧ is the expectation operator conditional on
information in period t. The expectation for the individual is over the vector of shocks to
preferences for location, future income shocks, and future labor market shocks. These
choices are made subject to the constraint explained above. As to location, we model
migrants from the time they arrive in the host country but take the decision to return to
the home country as final; hence, ‫ܮ‬௜௧ାଵ = ‫ ܧ‬whenever ‫ܮ‬௜௧ = ‫ܧ‬.15 Because social capital
in the host country is not productive in the home country, migrants that have returned
always choose ॴΓ
௜௧ = 0 . Hence, once migrants have returned, they only choose
consumption and labor supply. We further assume that individuals who quit work do so
involuntarily. However, out-of-work individuals choose whether to work or not if they
receive an offer. Finally, we set retirement age at 65, from which point until age 80 (end
of life in our model) individuals only make consumption decisions, with state variables
15
This specification corresponds to the context studied in which return migrations are final. It is
straightforward to extend the model to accommodate circular migrations as in Colussi (2003), Thom
(2010), Lessem (2013), and Nakajima (2014).
12
ܺ௜௧, Γ௜௧, and Ψ௜ூ௧ fixed at their values at age 6416 (see Appendix A for more details on the
model’s dynamic specification and how we solve it).
C. Intended Length of Stay
Given the stochastic nature of the model, migrants have no fixed duration of stay in
mind. Rather, in every period ahead, they face a probability of returning to their home
country dependent on their own characteristics, the choices they have made, and future
choices. The survey data we use include forecasts of stay duration, which is important
information given that migrants condition their investments and labor market choices on
their expectations of migration length. Hence, to match the model with these reported
intentions, we must construct a model counterpart, a complex object that depends on the
value function and state space at a given time, as well as the distribution of future shocks
and future paths of endogenous variables such as assets, work experience, and social
capital. We achieve this task by simulating for each individual at given ages sequences of
future shocks and corresponding choices, which allows us to calculate the likelihood of
returning in any of the years ahead.
The first step in this simulation focuses on the probability that a migrant returns to
the home country in the current period. This probability is conditional on age, time since
immigration, prior labor market status, work experience, assets, ability, social capital,
16
During this period, individuals receive retirement benefits. Because we keep track only of effective
experience (a composite of the years individuals have been working in the emigration and immigration
countries), we approximate pension entitlements by y ୖ = 0.5y෤ with y෤ = ቀ
ଡ଼/ସ଴
ቁy ୍ + ቆ1 − ቀ
ଵା଴.ହஞ
ଡ଼/ସ଴
ቁቇy ୉ ,
ଵା଴.ହஞ
which corresponds to the individual working for 40 years (excluding nonworking spells) and
accumulating 1/3 of this total experience in the country of origin.
13
and current location preferences. Given the assumption of an extreme value distribution
௝
for location preference shocks ߟ௜௧, the probability of returning in the current period has a
closed form solution, which takes a logistic form involving the value functions defined in
(8). Next, to determine the conditional probabilities of returning in all future periods, we
simulate ܵ future paths for shocks to earnings, employment, and preferences, and
determine the optimal consumption, labor supply, and investment in human capital.
These in turn determine the future (conditional) probability of returning to the home
country. This procedure allows us to construct the density of future return dates,
conditional on the current state vector. We define the median of these return dates as the
intention stated by an individual at a given time and observed by us in the data. We opt
for the median because it produces a more robust measure of intentions than does the
mean, which is sensitive to outliers.17 Individuals are assumed to intend to stay forever if
their intended age at return exceeds age 64. More formally, the intended length of stay ߫
given
ଵ
ௌ
the
state
Ω௜௧
at
time
∑ௌ௦ୀଵ ૚ൣ∑଺ହ
૚௦[return at t + ݆|Ω௜௧] ≤ ݉ ൧=
௝ୀ଴ ݆
ଵ
ଶ
‫ݐ‬
is
,
߫(Ω௜௧) = ݉
where
at
such
that
‫ݐ‬
time
,
1௦[return at ‫ݐ‬+ ݆|Ω௜௧] indicates whether simulation ‫ݏ‬predicts that the migrant will return
at time ‫ݐ‬+ ݆given current states. This formula allows us to have a theoretical counterpart
to the stated return intentions of the individuals observed.18
17
Van der Klaauw and Wolpin (2008) also use intentions to identify a dynamic model but equate them
with the mean rather than the median of the distribution. They build their model of labor supply and
retirement using data on life expectancy and the likelihood of work at older ages. Our approach, which
includes repeated intentions for each individual in our data, thus adds to their contribution by allowing for
revised intentions as individuals age and experience new shocks.
18
Because the simulation of intentions is computationally intensive, we do it only for ages 25 and 35 rather
than simulating intentions for every point in time. We choose these relatively young ages because it is at
14
In the data, the distribution of the migrants’ intended length of stay stated on arrival
differs from the realized durations. This feature is one that our model is able to match as
new realizations of shocks to income or preferences change the migrant’s horizon. As
previously explained, however, our model also implies that, on average, migrants should
be able to forecast their length of stay. Yet a feature of the data is that migrants tend to
underestimate duration when they arrive and on average end up staying slightly longer.
To reflect this reality, we allow individuals to systematically misperceive the actual
variance in preference shocks to location ( ߟ௜ா௧, ߟ௜ூ௧) as ߭ times larger than its actual
value. 19 Doing so introduces the possibility that intended migration durations may
systematically deviate from the actual time spent in the host country. For ߭ > 1 ,
perceived shock variances are larger than true variances so that per period return
probabilities are biased toward 0.5. This bias implies that immigrants overestimate the
probability of returning.20
D. Social Capital and Assimilation
We identify social capital, Γ௜௧, by linking it to a number of variables ߡ௜௞௧, ݇ = 1, … , ‫ܭ‬,
observed in the data that measure (social) assimilation, such as language skills or the
propensity to befriend natives. We do so using the following factor model:
this life stage that most social capital investment takes place and many immigrants in our sample arrive.
In any case, considering intentions at only two points in time is sufficient to allow us to construct
dynamic moments involving intentions.
19
The true cdf of ߟ௜௟௧, ݈= ‫ܫ‬, ‫ ܧ‬is ܲ൫ߟ௜௟௧ ≤ ‫ݔ‬൯= ݁‫݌ݔ‬൫−݁‫(݌ݔ‬−‫)ݔ‬൯, but individuals perceive it to be ܲ൫ߟ௜௟௧ ≤
‫ݔ‬൯= ݁‫݌ݔ‬൫−݁‫(݌ݔ‬−‫ݔ‬/߭)൯. The standard deviation for this distribution is ߭ߨ/√6.
20
Brigitte van Baalen and Tobias Müller (2008) calibrate a model of return migration under quasihyperbolic time preferences to replicate the discrepancy between anticipated and actual migration
durations.
15
ߡ௜௞௧ = Φ൫ߛ଴௞ + ߛଵ௞Γ௜௧ + ߱ ௜௞௧൯, k= 1, … , ‫ܭ‬,
(9)
where the ߛଵ௞ ’s are factor loadings and Φ() denotes the standard normal cumulative
distribution function. In our setting, individuals do not derive utility directly from
individual measures of assimilation but from the common factor Γ௜௧, which considerably
reduces the dimensionality of the model and allows us to solve and estimate it. We
assume that the shocks ߱ ௜௞௧ arise from measurement error and are iid.
II.
Background, Data, Sample, and Descriptives
The strong upward swing in the West-German economy after 1955 drew an
unprecedented flow of (mainly unskilled) immigrants from Southern Europe and Turkey
into Germany, with the percentage of foreign-born workers employed increasing from
0.6 percent in 1957 to 11.2 percent in 1973. This early migration movement created
subsequent immigrant movements into Germany, particularly from Turkey, the main
sending country today, which supplied 14 percent of the overall immigrant population in
2011.21 Our analysis thus focuses on migrants from Turkey who arrived in Germany after
1961, the year in which Germany signed a bilateral guest worker agreement with
Turkey.22
21
The authors’ own calculations based on OECD data, available at http://stats.oecd.org/.
A 1964 amendment to the initial agreement signed in 1961 guaranteed equal treatment of guest workers
and German workers in terms of social insurance and ensured that retirement benefits could be claimed
even after a return to Turkey. It also repealed an earlier two-year restriction on work permits, thus making
migration duration a matter of individual choice (see Katrin Hunn 2005, for a detailed historical account).
22
16
A.
Data and Sample
Our analysis is based on 1984–2011 panel data from the German Socio-Economic
Panel (SOEP), a household-based panel survey similar to the Panel Study of Income
Dynamics in the U.S. or the British Household Panel Survey in the UK. The SOEP was
initiated in 1984, when it oversampled the then resident migrant population in West
Germany. Its first wave encompasses interviews with about 4,500 households with a
German-born household head and an additional 1,500 households with a foreign-born
household head, who were subsequently re-interviewed yearly. The foreign-born
households selected came from the five largest immigrant communities at the time:
Turkey, the former Yugoslavia, Italy, Greece, and Spain. When needed, the
questionnaires used for these interviews were available in the home country language.
These data are unique not only in that they provide repeated information on a large
sample of immigrants over a long period of time but that they record the updated return
plans of immigrants at different points over their lifecycle. Such information is rarely
available, particularly in longitudinal format. Specifically, the immigrants were asked
whether they wished to stay in Germany forever, and if not, for how many more years
they intended to stay.23 In addition to planned length of stay, the survey recorded returns
realized, 24 as well as a large array of information on personal and household
characteristics, including employment histories, income, and in some waves, household
23
The exact wording of the question is as follows: “How long do you want to live in Germany? [1] I want
to return within the next 12 months _____ [2] I want to stay several more years in Germany _____
number of years _____ [3] I want to remain in Germany permanently _____" (German Socio-Economic
Panel, 1984).
24
The SOEP follows up on households throughout the year by checking mail and phone registers, as well
as administrative records if an address is no longer valid or respondents die.
17
assets and annual savings and remittances. To identify the integration process, we also
use variables that measure spoken and written proficiency in the German language and
others that indicate degree of integration.
To ensure a homogeneous immigrant sample, we restrict our analysis to males
without a tertiary education, 25 who were born in Turkey, were aged 16 or older at
immigration, and arrived in West Germany after 1961. The result is an unbalanced panel
of 4,144 observations for 402 individuals. We augment this SOEP data with information
obtained from the Turkish statistical office (TurkStat 2006) on the 2006 median gross
income for male workers without a tertiary education in Turkey. We then extrapolate to
other years using time series on nominal compensation per employee provided by the
European Commission (2015) and gross national income from the World Development
Indicators. 26 All monetary variables are adjusted to 2005 euros using consumer price
indices and exchange rates from the Bundesbank 27 and the OECD. 28 We obtain
unemployment rates and unemployment durations in Turkey from Tansel and Taşçı
(2010).
We also take into consideration that economic trends over the time period
investigated are very different for Germany and Turkey. In particular, earnings in Turkey
25
Only 5.4 percent of individuals in our sample have a tertiary education.
The European Commission’s AMECO database provides series of average nominal compensation per
employee
back
to
1960
for
West
Germany
and
to
1988
for
Turkey
(http://ec.europa.eu/economy_finance/ameco/user/serie/ResultSerie.cfm). To extrapolate to earlier
income levels in Turkey, we use gross national income from the World Bank’s (2014) World
Development Indicators.
27
Available at http://www.bundesbank.de/Navigation/EN/Statistics/Time_series_databases/
Macro_economic_time_series/its_details_value_node.html?nsc=true&listId=www_s311_lr_vpi&tsId=B
BDP1.A.DE.N.VPI.C.A00000.I10.L.
28
http://stats.oecd.org/.
26
18
have risen strongly relative to those in Germany, with median real net earnings of
workers with no tertiary education increasing from 5.9% to 28.4% of the corresponding
level in Germany between 1970 and 2010. As explained previously, calendar time is not
a state variable in our model. We account for such macroeconomic differences by
assuming that immigrants arrive in 1973, which is both the median and the mode year of
immigration in our sample. The attractiveness of returning to Turkey as determined by
expected earnings there and by the relative price level then changes according to the
development of these variables over time.29
B. Descriptives
In Table 1, we list the means of the main variables used in the analysis, with
realizations reported separately for intentions to stay permanently versus a wish to return
at some future point in time. As expected, the age at which individuals arrive is
positively associated with the intention to return, suggesting a stronger attachment to the
country of origin when the migration takes place at a later age. Interestingly, individuals
who consider themselves temporary migrants are more likely to be employed, with two
counteracting factors relating temporariness and labor force participation. On the one
hand, temporary migrants may have less incentive to invest in host country-specific
capital and socially integrate; on the other, if the primary purpose of a temporary
migration is the accumulation of savings and a migrant’s marginal utilities of
consumption and leisure are higher in the country of origin, intertemporal substitution of
leisure may make temporary migrants more likely to work. This interpretation is
29
See the appendix for details.
19
supported by on average higher annual savings and remittances by those with temporary
intentions. The data also suggest that the differences in employment are partly driven by
more frequent job matches for temporary immigrants, consistent with lower reservation
wages among migrants who value consumption and leisure in their home country more
than in the country of destination. On the other hand, individuals with permanent
intentions not only score more highly on mean earnings but also on German language
proficiency, the frequency of reading German newspapers, and reported feelings of being
German, all variables used to characterize social capital.
As previously emphasized, however, migration plans respond to unforeseen events
and may thus change over time. For this reason, analyses of the interaction between
migration duration and economic behavior that rely on completed migration durations
(rather than expected migration duration when decisions are made) may be misleading.
We illustrate the deviation of actual from intended return migration plans in Figure 1a,
which shows the mean age at return by intended age for the subsample of individuals that
left the country during the panel period. Although the figure suggests a strong link
between reported intentions and actual migration durations, it also shows a tendency for
individuals to stay for longer than intended in earlier periods. In Figure 1b, which
illustrates the distribution of this deviation, the underestimation (on average) of migration
duration is reflected by the slight right skewedness of the distribution. As explained
above, our model allows for such skewedness and matches the distribution of the
difference between actual and intended migration durations well (see Appendix Figure
A1b).
20
III.
Estimation and Model Fit
A. Method of Moments
We estimate our model using a simulated method of moments estimator that
minimizes the distance between moments from the data and the equivalent moments
simulated using the model (see Ariel Pakes and David Pollard 1989; Darrell Duffie and
Kenneth J. Singleton 1993). We implement this method by simulating a population of
immigrants and by comparing it with the population followed in the SOEP. Identification
then relies on static, conditional, and dynamic data moments obtained from the data,
usually through auxiliary regressions. We match the moments pertaining to the
determinants with the evolution of earnings, transitions between work and non-work, the
evolution of savings and social integration, and actual and intended returns. We list the
type of moments used for identifying several sets of parameters of our model in Table A1
and provide the full set of matched moments in Tables A2–A10 in Appendix C. Certain
other parameters, however, have to be normalized because they are not separately
identified. For example, because social capital has no scale, we normalize ߛଵଵ in equation
(9) to one. Similarly, because the relative preference for the host country in utility
function ߖ ௜ூ௧ and the level of social integration are not separately identified, we normalize
the initial stock of Γ୧୲ to zero.
B. Model Fit
The first panel of Figure 2 shows the log of annual earnings against time passed since
immigration as observed in our sample (grey line) together with the profile predicted by
21
the model (black line). The specification chosen for the earnings function, with a linear
spline over five experience intervals, seems well fitted to the mean of log annual earnings
by age. The second and third panels display the fit with respect to annual savings and
planned migration durations. The latter includes immigrants reporting an intention to stay
in the host country permanently, with their intended length of stay set to the time until
they reach retirement age at 65. The model predicts slightly higher perceived migration
durations and overestimates savings at older ages.
An important, and observed, source of risk faced by individuals in our model comes
from employment transitions as jobs held are lost and new ones found. These rates vary
strongly with age, with very few individuals switching into employment after age 50 but
job separation rates increasing. As Figure 3 shows, the model reproduces the hump
shaped profile of job finding rates and the increasing probability of layoff as a function
of age. In Appendix C, we provide further evidence of the model’s fit, including
moments not used in the estimation but that are nevertheless reproducible.
IV.
A.
Results
Estimated Parameters
The model has 40 parameters that we estimate. We focus here on a subset of key
parameters relating to earnings, the utility function, and social capital accumulation (see
Tables 2–4). Specifically, our discussion addresses earnings, employment transitions,
utility, and unobserved heterogeneity. All remaining parameters are examined in
Appendix D.
22
Earnings Equation. The (log) earnings equation (4) is characterized by parameters
that measure the slope and concavity of log earnings with respect to accumulated work
experience and the return to social capital. The estimates are displayed in Table 2. The
returns to social capital (denoted ߙ୻) are substantial, leading to an increase in earnings of
about 9 percent on average over a period of 20 years in the host country. 30 These
estimates also imply a steeper profile for immigrants who at immigration intend to stay
permanently (as compared to immigrants planning to return home). Hence, social capital
is an important determinant of wage growth, one that has implications for the
interpretation of observed wages and return migration.
The estimates further suggest a concave profile with respect to work experience, with
high returns of about 0.2 log points early on, about 0.04 percent at 2 to 5 years, and much
lower returns for higher levels of experience. Working experience accumulated in the
home country prior to immigration has close to no value in the destination country, as
indicated by the estimated parameter ߦ. Hence, returns to home country experience are
only 5.8 percent of returns to experience accumulated in the destination country with an
estimate that is not significantly different from zero. This finding is in line with evidence
of low returns to home country experience in many other migrations; for example, USSR
immigrants to Israel (Eckstein and Yoram Weiss 2004) and post-1990s immigrants to
Canada (David A. Green and Christopher Worswick 2009).
Employment Transitions. As explained in Section 2.1, the stock of social capital
affects not just earnings and utility but also job finding and job destruction probabilities.
30
Because social capital itself has no meaningful scale, we evaluate its effect on earnings by simulating
average social capital accumulation by initial intentions and calculate its contribution to log earnings.
23
This influence reflects the fact that social capital may impact immigrants’ search
networks or the value of an employment match. In fact, the estimates for the employment
transition parameters (equation (6)) in Table 3 do indeed suggest that social capital, while
slightly increasing the rate at which job offers are received (ߣ୻), reduces the probability
of losing a current job (ߜ୻), meaning that migrants who accumulate more social capital
receive slightly more job offers and the jobs they take are more stable and pay higher
wages. These parameters, however, are small in magnitude.
Utility Function. Among the parameters characterizing preferences (see equation (7),
and further details in the appendix), the curvature of the utility function with regards to
consumption (߶ଵ) is a measure of relative risk aversion (see Table 4). Here, our estimate
of 0.40 implies a concave profile and a relatively low relative risk aversion of 0.60.31 We
also find evidence of habit formation as social capital positively influences the utility in
the host country, which is reflected by the parameter ߶଴. The estimated value of this
parameter implies that over 20 years, the relative preference for the host country
increases on average by about 13 percent. Such habit formation implies that temporary
shocks to preferences or temporary changes in policies can have long-term effects
because they change the stock of social capital and hence relative preferences for the host
country. We discuss this mechanism in the context of a counterfactual policy in Section
5.4.
Our specification of the utility function implies a constant relative risk aversion equal to 1 − ߶ଵ. Our
estimate is comparable to Rendon and Cuecuecha (2010), who find this parameter to be 0.56, although
Michael P. Keane and Wolpin (2001) and Susumu Imai and Keane (2004) estimate it at 0.48 and 0.74,
respectively. Others, such as Hamish Low, Costas Meghir, and Luigi Pistaferri (2010), set it to 1.5 based
on estimates by Orazio Attanasio and Guglielmo Weber (1995).
31
24
The utility function also includes an effort cost of investment (parameters ݁଴ and ݁ଵ)
in social capital, which is allowed to vary with age. Based on our estimates, a 20-year-old
immigrant faces a 42 percent lower cost of investing in social capital than an immigrant
aged 40. Thus, our model suggests that age of arrival plays an important role in
explaining immigrants’ career profiles, as demonstrated in a reduced form context by
Friedberg (1992). In addition, as previously explained, we allow for a systematic bias in
individuals’ expected migration duration through a misperception of the variance of
location shocks ߟ௜ூ௧ and ߟ௜ா௧. Our estimate for the misperception ߭ regarding the spread of
the distribution of transitory preference shocks suggests that immigrants slightly
overestimate the standard deviation of this distribution (by 4.6 percent, see Table 4).
Unobserved Heterogeneity. Our model allows for two types of unobserved
heterogeneity that affect preferences for the host country and productivity, respectively.
Table 4 displays the relative preference for the host country (lower support point of ߖ ௜ூ௧)
and the estimated fraction of immigrants with an initially low preference. Our estimates
imply considerable ex ante heterogeneity in preferences at arrival before any further
choices are made through the initial realization of the taste shock ߖ ௜ூ଴. This taste shock,
modeled as a first order Markov process, has a fairly strong persistence, with only 1.8
percent of individuals switching in each period from a strong preference for the host
country to a lower one and vice versa.32 This observation implies that those who arrive in
Germany with a low realization of the taste shock expect a shorter stay in the country
because they anticipate this high persistence and an implied lower chance of receiving a
32
Over a period of 20 years, the probability of switching from one state to the other is close to 30 percent.
25
high preference shock later on. Immigrants with a strong attachment to the origin
country, in contrast, initially incur a utility loss of about 50 percent (relative to high
preference individuals) by spending time in the host country rather than in their home
country.33 Depending on the level of social capital accumulated, this loss may be reduced
by up to 13 percentage points after 10 years, and 27 percentage points after 20 years in
the host country. One implication of this finding is that immigrants with a strong
attachment to their country of origin, in which the benefit of consumption is higher (see
the complementarity of Ψ௜௧ and consumption in the utility function in (7)), are likely to
save a larger fraction of their incomes while residing in the host country. Similarly, since
the value of leisure (1-h) is lower for these immigrants, they will be more inclined to
accept job offers at a given wage rate. Both these implications are compatible with the
descriptive figures in Table 1, which suggest higher savings for immigrants with return
intentions, higher probabilities of being employed, and higher non-work to work
transitions. Finally, the estimated weights for the unobserved types of individuals imply a
positive correlation between the preference for the host country and productivity.
B. Immigrant Career Profiles
We now analyze the evolution of key aspects of individual careers, such as social
capital accumulation and the evolution of wages, and how these are related to return
plans. We do so by simulating our model while distinguishing between two types of
immigrants: those who, at the start of their migration history, intend to stay permanently,
Because the value of ߖ ௜ூ௧ for immigrants with a strong preference for the host country is not identified,
we set it to 1.
33
26
and those who intend to stay only temporarily. This distinction corresponds to
immigrants with a high or low initial preference for the host country, Ψ௜ூ଴.34 Within each
of these groups, we distinguish between high and low productivity immigrants based on
the realization of ߙ௜.
Length of Stay, Accumulation of Social Capital, and Migrant Selection. In Figure 4,
we consider the survival rates of immigrants in the host country, with solid and dashed
lines representing low and high productivity individuals, respectively, and grey and black
lines designating those with a low versus high preference for the host country. As the
figure clearly shows, those with an initially permanent migration intention remain longer
on average than those with an initially temporary intention. However, within each of the
two groups, high productivity migrants tend to return sooner, suggesting that the income
effect, which raises the demand for time spent in a migrant’s home country, dominates
the substitution effect (i.e., the increase in opportunity cost of staying and earning in the
destination country).
Taken together, these survival estimates indicate that selection on unobservable
productivity differences is negative in the sense that those who remain in the host country
longer are less productive. This is not to say, however, that those who remain necessarily
earn lower wages, conditional on experience, because they may accumulate social
capital, Γ௜௧, at a different rate. In fact, as shown in the previous section, the return to
social capital is positive and quite substantial. Hence, to understand the relation between
34
Of course, as time passes, individuals experience new taste shocks and adjust behavior and intentions
accordingly, so that those who initially believed they would stay permanently may eventually return.
27
return migration and earnings, it is important to understand how social capital is
accumulated over the lifecycle.
We illustrate this accumulation in Figure 5, in which the grey lines designate
immigrants who at the time of immigration planned to return during their working lives
(i.e., those with a low preference for the host country Ψ௜ூ଴ ) and the black lines,
immigrants who expected to stay permanently. The solid lines represent the means of Γ௜௧
for those observed in the host country at any duration of migration, a group whose
composition changes because of outmigration. These lines suggest a stronger
accumulation of social capital during the first years after arrival by migrants with an
initial intention to stay permanently who expect to reap the benefits of higher social
capital over a longer period of time. At the same time, the dashed lines, which plot the
selection-corrected means for the entire initial immigrant cohort (i.e., the paths of social
capital for the counterfactual situation that no one out-migrates), indicate that the largest
part of this difference is not driven by compositional effects and/or selective
outmigration. Rather, the difference between the solid and dashed lines is a measure of
the selection of returnees with respect to social capital. Our comparison also shows that
outmigration is slightly negatively selective in terms of social capital (Γ௜௧); that is, within
each of the two groups, those who have accumulated less social capital are more likely to
leave earlier.
Hence, in our framework, the selection of immigrants through return migration has
two distinct sources. First, immigrants select according to fixed productivity differences,
with our results pointing to those who return earlier being positively selected with respect
28
to their unobserved productivity, due to the income effect described above.35 Second,
migrants accumulate social capital at different rates, which generates the second source
of selection, referred to here as “behavioral selection.” This type of selection prompts
immigrants who invest more in human capital because of an intention to stay longer to
actually stay longer on average. These two forms of selection, however, cannot easily be
disentangled by a simple reduced form analysis because the heterogeneity across
immigrants in human capital investments based on different return intentions is
unobservable. Reduced form analysis may thus generate misleading conclusions about
selection on unobservable productivity. Even when return migration is positively
selective in the sense that individuals with higher unobserved productivity return earlier,
the presence of behavioral selection may lead researchers using standard reduced form
selection models to draw the opposite conclusion (i.e., a positive selection of stayers).
Estimation of Earnings Profiles. What then do the above findings imply for the
estimation of immigrants’ earnings profiles? We answer this question by examining the
earnings profiles in Figure 6, which are plotted for each of the four types separately (i.e.,
high/low productivity, high/low preference at arrival). Here, the vertical axis carries the
log wage, while the horizontal axis carries age. Each earnings graph is plotted up to the
median of the group specific durations, thereby revealing the differences in the return
migration across the groups. In particular, this figure illustrates two separate sources of
35
This type of selection is usually discussed in the literature in the context of a Roy type model (see, e.g.,
Borjas and Bratsberg 1996). A simple one factor Roy model provides predictions, which depend on the
price of skills in the home and host countries, and assumes that migration choices are based only on
income maximization. In our framework, individuals maximize utility, which is a function of both income
and location, so the selection of return migrants depends on whether income or substitution effects
dominate.
29
bias in OLS estimates of log wage, which pertain to the immigrants’ experience profiles.
First, the positive selection of return migrants (i.e., those who return home earlier on
average have higher productivity) is reflected by the difference in length and levels of the
grey lines in Figure 6. Ignoring high preference individuals for the moment, this
difference biases OLS estimates downward in that those who stay longer have a lower
earnings profile. This distortion is the classic selection bias addressed in the literature.
Second, when calculated using conventional reduced-form estimators, the difference in
earnings growth from differential human capital investment between those with initially
temporary and permanent intentions (the difference in length and slope between the grey
and black profiles) generates an upward bias. This bias is obviously present even when
there is no heterogeneity in unobserved productivity between the two groups of
individuals.
It is the first of these two effects that has received much attention in the literature
(e.g., Borjas 1989; Per-Anders Edin, Robert LaLonde, and Olof Åslund 2000; Hu 2000;
Lubotsky 2007; Matti Sarvimäki 2011; Mikal Skuterud and Mingcui Su 2012; Garnett
Picot and Patrizio Piraino 2013; Abramitzky, Platt Boustan, and Erkisson 2014), which
suggests that the difference in levels, and thus the bias within the temporary and
permanent intention groups, can be eliminated by within-group estimation. Such
estimation would still, however, lead to upwardly biased estimates because it does not
eliminate the bias from those with permanent intentions having steeper earnings profiles
and staying longer. In our model, eliminating this bias requires observing the typically
30
unobserved social capital Γ, more of which is accumulated by immigrants who stay
longer.
To illustrate this point further, in Figure 7, we show how the difference in social
capital accumulation translates into earnings profiles within productivity types. As in
Figure 5, the black and grey lines, respectively, represent initial intentions to stay
permanently or return home, while the solid and dashed lines represent those in the host
country at any duration versus the counterfactual profile of the initial cohort if nobody
had left. The graphs reveal a considerably steeper earnings growth for immigrants who
plan to stay, a difference that is present within immigrant groups with the same ex ante
productivity. The difference between the solid and dashed lines further indicates that
within productivity types, migrants leaving the host country tend to have slightly lower
earnings than stayers, a selection effect that is more pronounced among high productivity
and older immigrants. This pattern, which is consistent with that in Figure 5, is driven by
immigrants who have accumulated lower levels of social capital being more likely to
leave.
These two selection effects (on productivity, and behavioral selection through
preference-based differential investment patterns) are easily confounded, and a priori the
overall direction is unclear. In our case, we find that their effect on earnings is in fact
non-monotonic, with those leaving first and those staying permanently having the highest
earnings—but for different reasons. Whereas short-term temporary migrants are
predominantly drawn from high productivity levels, permanent migrants accumulate
higher levels of social capital. Longer term temporary migrants, on the other hand, tend
31
to have both lower productivity levels and lower incentives to accumulate social capital.
We illustrate this situation in Figure 8 by simulating different stock-based samples of an
initial entry cohort of immigrants; that is, all those observed in the host country for
between 10–20, 20–30, 30–40, and more than 40 years. The figure clearly shows that the
selection of out-migrants is non-monotonic in earnings: those leaving earliest, who
mostly have a low preference for the host country but are highly productive, have the
highest profiles. Those with intermediate durations, who are a mix of mostly low
preference and low productivity individuals, have lower profiles, while those who stay
longest or permanently, who show a high preference but are a mix of low and high
productivity, have steeper profiles.
V.
Immigration Policy: Conditional Permanence Permits
The observation that immigrants’ economic choices may depend on anticipated
migration durations has important implications for immigration policies. Not
surprisingly, temporary migration schemes are appealing for policy makers because they
seemingly address employers’ needs to fill skill gaps while speaking to wider public
concerns about immigration. 36 However, the impact of various schemes on migrants’
optimal choices through restriction of migration duration or uncertain opportunities for
permanent migration may lead to inefficiencies in the immigrants’ investment in human
capital and thus to losses in their lifetime earnings and welfare and potential reductions in
36
These policies not only include schemes to attract seasonal agricultural workers (e.g., the U.S.’s large
scale 1942–64 Bracero program for Mexicans) but also high-skill oriented visa categories like the U.S.
H1-B visa. Similar programs were and are in place in Canada and other traditional immigration countries.
For details on these and temporary worker schemes in more recent migrant destinations like the Gulf
Cooperation Council countries, see Philip Martin (2015).
32
tax revenues for the host country. Such negative aspects of temporary migration schemes
are typically neglected in the policy debate. Hence, to better understand the implications
of such policies on immigrants’ career paths, we now use our model to simulate a policy
environment in which immigrants face the possibility of not being granted permanent
residence.
A. Residence Permits and Migrants’ Career Profiles
In many destination countries, a permanent permit is granted only after a certain
period of residence and only for a fraction of each cohort. 37 We therefore assume a
cohort of immigrants who arrive in the destination country at age 20 and face the odds of
being granted permanence after five years. We assume that this probability is
independent of individual characteristics; extensions where this probability is affected by
fixed characteristics (e.g., age and gender) or that can be influenced by the factors under
the migrant’s control (e.g., absolute earnings) are straightforward. The uncertainty,
therefore, comes either from the policy itself (i.e., it only allows some migrants to stay)
or from political uncertainty when different political parties have differing views on
immigration. This probability of being granted permanent residence inherently affects
new immigrants’ investments in human and social capital because an increased risk of
having to leave the host country reduces the expected returns to any location-specific
dimensions of human capital.
37
Immigrants to the UK, for instance, can apply for a permanent residence card after five years
(https://www.gov.uk/apply-for-a-uk-residence-card/). Similar possibilities exist for non-EU immigrants in
Germany (http://www.bamf.de/EN/DasBAMF/Aufgaben/Daueraufenthalt/daueraufenthalt-node.html) and
EU15 and EFTA immigrants to Switzerland (http://www.swissinfo.ch/eng/work-permits/29191706).
33
We illustrate this policy scheme in Figure 9, which plots a number of outcomes under
different admission probabilities relative to a situation with no visa restrictions. Figure 9a
illustrates the loss in discounted lifetime utility, ܸ(Ω௜଴), for different probabilities of
receiving permanent residence after five years. As the figure shows, if the probability of
obtaining permanence is only about 10%, the implied loss in lifetime utility amounts to
around 35%. This loss decreases when the probability of obtaining permanence after five
years increases but still amounts to about 5% of lifetime utility given a 90% probability
of obtaining a permanent visa.
There are two reasons for this welfare loss: First, a positive probability of having to
return to the home country has a direct effect on welfare because utility flows differ
across locations, e.g. because individuals can afford different consumption levels.
Second, anticipation of potential relocation leads individuals to adjust their economic
choices. For instance, different policy environments (e.g., an environment in which a
permit might be granted after five years versus one that offers permanent status
immediately) produce sizeable variation in initial savings rates and human capital
investments. As Figure 9b shows, immigrants adjust their human capital investment
downward, with a lasting effect on individual earnings. Figure 9c then demonstrates that
discounted lifetime earnings of immigrants who stay until retirement are reduced by up
to 6 percent (58,000 euros deflated to the 2005 rate) over the migration cycle.
This reduction in earnings capacity implies not only a welfare loss for migrants but
also for the receiving country via the immigrants’ fiscal contributions. For example,
considering only the income and value added taxes of immigrants who stay until
34
retirement age, a 5% reduction in discounted lifecycle earnings amounts to a diminution
in discounted taxes paid over an immigrant’s working life of almost 20,000 euros (Figure
9d). Moreover, this estimate is likely to be a lower bound because it does not consider
such aspects as reductions in value added taxes from reduced consumption, some of
which may be repatriated to the home country in the form of remittances.
Taken together, Figures 9b–9d suggest that an increase in the probability of being
granted residency has a persistent and non-monotonic impact on the outcomes considered
here. This impact results from two counteracting effects when the reduction in human
capital accumulation is partly offset by the impact of a less negative selection of stayers
on unobserved productivity and a more positive selection on social capital. The latter two
are induced by the effect on return decisions of initial uncertainty about being granted
permanent residency and its consequence for asset and human capital accumulation even
when an immigrant is in fact finally granted such a permit. In our case, the positive
selection of out-migrants on unobserved productivity is less pronounced at high
probabilities of being granted residency than when immigrants are free to choose their
length of stay, which overcompensates for the lower social capital investment from
forced leaving. Hence, among immigrants who are both permitted to stay and choose not
to return, average cumulative earnings are slightly higher than under a regime of entirely
free migration duration choice (see the last bin in panel (c)). Moreover, and as shown in
Figure 5, return migration is negatively selective on social capital, a particularly strong
effect if immigrants face very low probabilities of permanent residency. Under such a
policy, the strongly negative effect on cumulative earnings from lower social capital
35
accumulation is slightly counteracted by a selection effect in the opposite direction,
which explains the non-monotonicity at the left end in panels (b)–(d) of Figure 9.
B. Migration Policy and Immigrant Selection
Policy regimes of the type described above affect not only the welfare of immigrants
already in the host country but also the emigration decisions of those who are not,
thereby influencing the population of potential emigrants. Although the absence of such a
population in our data prevents us from modeling this effect on selection, we are able to
assess the relative attractiveness of a destination country to different groups of potential
migrants under different permit regimes. Hence, in Figure 10, by again comparing two
situations in which a permanent permit is either granted from the start or may be obtained
after five years with the probabilities shown on the horizontal axis, we illustrate the
difference in relative lifetime utility changes between individuals of high and low
productivity (ߙ௜). The figure shows that in our model specification, the attractiveness of a
destination that offers immigrants a 50% probability of a permanent residency permit is
about 12 percent lower for high productivity immigrants than for low productivity
immigrants.38
These observations clearly imply that the relation between immigrants’ decisions in
the host country and their planned duration of residence may cause immigration policies
of the type discussed above to affect migrant selection through at least two channels.
38
This outcome results from the complementarity between social capital and consumption in the utility
function, which implies that reducing social capital accumulation impacts high ability individuals more
strongly. Given our specification and the discretization of unobserved heterogeneity, the difference in
mean productivity between these groups is 0.43 log points.
36
First, such a policy may change immigrants’ investment in human capital and thus their
earnings potential, which in turns affects outmigration selection. Second, it may affect
the type of immigrants that are drawn to the country. In our simulations, for example,
uncertainty about being granted residency renders a migration less attractive to high
ability immigrants relative to low ability immigrants. Hence, although the degree to
which these channels affect immigrant selection depends on the circumstances in the
sending country, this example illustrates an important yet so far ignored aspect of the
complex relation between a host country’s immigration policies and the type of
immigrants it attracts.39
VI. Discussion and Conclusions
The decision to leave the host country before the end of one’s productive life is an
aspect of migrations as fundamental as the emigration decision itself. Yet although
emigration decisions have been studied extensively, far less is known about migrants’
decisions to return and how these affect other aspects of their behavior. In this paper,
therefore, we develop a framework that models this decision in a context of uncertainty,
and in which individuals can revise their migration plans over the migration cycle. By
estimating the model using panel data that capture both the immigrant’s economic
decisions and their migration duration intentions at multiple stages over the lifecycle, we
show that return plans are an important source of heterogeneity in immigrants’ earnings
39
Studies that are more directly concerned with immigrant selection from their countries of origin include
George Borjas (1987), Daniel Chiquiar and Gordon H. Hanson (2005), Abramitzky et al. (2012, 2013),
Fernández-Huertas (2011), Patricia Cortés and Jessica Pan (2012), and Manuela Angelucci (2015),
among many others.
37
and career profiles, and an essential driver for a type of selective outmigration that is
unrelated to unobserved ability. The relation between behavior/career path and expected
duration in the host country also implies that migration policies that add uncertainty to
the possibility of permanent residency affect not only immigrants’ career paths and
welfare but also the welfare of the receiving population by leading immigrants to invest
less in their human capital than they would have done otherwise. Such policies may also
have different effects on the overall migration benefit for immigrant groups with diverse
productivities and hence may potentially influence the type of individuals that immigrate.
Admittedly, however, our analysis is limited to a fairly homogeneous group of
immigrants who all arrived from the same country and had similar observable
characteristics. Hence, studying immigrant populations composed of individuals from a
variety of origin countries with different institutions and opportunity distributions would
add additional challenges. Nevertheless, we believe that careful consideration of the
implications for immigrant behavior of the non-permanency of many migrations should
be a key element in immigration studies. Therefore, although we restrict our discussion
to particularly relevant aspects and consequences of the interplay between return plans
and economic choices, our findings could also inform other dimensions of immigration
research. For example, as regards immigration’s impact on wages and employment, the
heterogeneity in career profiles and skill accumulation induced through the mechanisms
identified above may imply that different immigrant groups induce different dynamic
labor supply shocks along the distribution of native skills and that outmigration itself
may cause negative labor supply shocks.
38
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Figures and Tables
45
46
47
48
49
Appendix (For Online Publication)
A. Data Description
The estimates of our model parameters are based on sample moments from the
German Socio-Economic Panel (SOEP). We reduce heterogeneity along dimensions not
modeled by restricting the sample to males without tertiary education, who were born in
Turkey and aged 16 or older at immigration, and who arrived in West Germany after
1961, when Germany signed the bilateral guest worker agreement with Turkey. We use
additional data sources to calibrate several parameters that capture the economic
conditions in Turkey. In particular, earnings conversion factors are computed based on
the median gross income of male workers without tertiary education in Turkey, obtained
from the Turkish statistical office (TurkStat 2006) and then extrapolated to other years
using time series on nominal compensation per employee provided by the European
Commission and gross national income from the World Development Indicators.40 All
monetary variables are adjusted to 2005 Euros using consumer price indices and
exchange rates from the Bundesbank41 and the OECD.42
40
The European Commission’s AMECO database provides series of average nominal compensation per
employee
back
to
1960
for
West
Germany
and
to
1988
for
Turkey
(http://ec.europa.eu/economy_finance/ameco/user/serie/ResultSerie.cfm). To extrapolate to earlier
income levels in Turkey, we use gross national income from the World Bank’s (2015) World
Development Indicators.
41
Available
at
Macro_economic_time_series/its_details_value_node.html?nsc=true&listId=www_s311_lr_vpi&tsId=BB
DP1.A.DE.N.VPI.C.A00000.I10.L.
42
http://stats.oecd.org/.
50
B Model Description
B.1 Specification Details
Real exchange rate, interest rate and earnings conversion factor. To account for the
diverging macro trends between Germany and Turkey that affect immigrants’ return
decisions, we restrict the sample to immigrants who arrived after 1961. The model
assumes that immigrants arrive in 1973, which corresponds to both the median and the
mode in this sample. The simulation is based on gross earnings conversion factors and
purchasing power parities as predicted by second order polynomials of years ‫ݐ‬since
1973. For this calculation, we use the median gross income of male workers without
tertiary education in Turkey, obtained from the Turkish statistical office (TurkStat 2006).
We extrapolate to other years using time series on nominal compensation per employee
provided by the European Commission and gross national income from the World
Development Indicators. Real exchange rates are taken from the OECD’s online
database. 43 The outcomes lead us to convert net earnings by a factor ߩ௧ = 0.04105 +
0.00873‫ݐ‬− 0.000067‫ݐ‬ଶ and relative price levels at which assets are converted after
return by a factor ‫ݔ‬௧ = 0.67453 − 0.02589‫ݐ‬+ 0.00066‫ݐ‬ଶ, where ‫ݐ‬is time since 1973.
Similarly, using nominal interest and inflation rate series for Germany and Turkey from
the World Bank’s (2015) World Development Indicators and the OECD, we approximate
the real returns to capital in Germany and Turkey, respectively, as ‫ݎ‬௧ூ = 0.00044 +
0.00146‫ݐ‬− 0.0000405‫ݐ‬ଶ and ‫ݎ‬௧ா = −0.00619 + 0.00155‫ݐ‬+ 0.0000092‫ݐ‬ଶ.
43
http://stats.oecd.org/.
51
Earnings tax schedules and unemployment benefits. For Germany, unemployment
benefits ܾ‫ )(ݎ‬are calibrated based on mean benefits and mean previous annual earnings
within bins of 10,000 euros as observed for nontertiary educated Turkish males in the
SOEP. To set a bound on the predicted benefit ratio, we adjust the benefit ratio for these
observations by the inverted standard normal cdf and regress the result on a third order
polynomial of log earnings:
ܾ‫ݕ(ݎ‬
෤ீ ) = Φ(98.1756 − 30.8281 ݈‫ݕ ݃݋‬
෤ீ + 3.2219(݈‫ݕ ݃݋‬
෤ீ )ଶ − 0.1122(݈‫ݕ ݃݋‬
෤ீ )ଷ) ,
where ‫ݕ‬
෤ீ are previous earnings, aggregated to bins of 10,000 euros (ܴଶ = 0.9488).
In Turkey, during the period of our analysis, no unemployment insurance was in
place, so we set ܾ‫ = ) (ݎ‬0. To calibrate the function ݊݁‫ )(ݐ‬for Germany, we use the tax
schedule prevalent in 1999 and assume that the individual is married.44 The tax schedule
also depends on the number of children, although the differences in taxation with respect
to this variable are small. The tax schedule is approximated by a third order polynomial
݈‫ீݕ ݃݋‬
in
as
݊݁‫( ீݕ = ) ீݕ(ݐ‬1 − Φ(−544.3878 + 149.5174 ݈‫ ீݕ ݃݋‬− 13.7412(݈‫) ீݕ ݃݋‬ଶ +
0.4220(݈‫) ீݕ ݃݋‬ଷ)), (ܴଶ = 0.9983), where Φ() denotes the standard normal distribution
function.45
Preferences. We assume that individuals can choose between full-time employment
and not working. In the latter case, the fraction of time worked, ℎ, takes value zero. We
44
In our sample, 83.2 percent of respondents are married, and 73.1 percent of wives do not work for pay.
The authors’ own calculations based on the German tax schedule in 1999
(http://www.parmentier.de/steuer/incometax.htm).
45
52
assume 40 hours of work per week and 48 weeks of work per year if an individual works,
ସ଴ ସ଼
and correspondingly calibrate ℎ to ଵ଺଼ ହଶ = 0.22. We further let time preference ߚ=0.95.
B.2 Dynamic Specification of the Model
We now describe in more detail the dynamic choices of individual immigrants,
described in the main text in Section 2.2 in terms of the generic Bellman equation:
ܸ(Ω௜௧) =
‫ܿ(ݑ‬௜௧, ॴ୻௜௧, ‫ܮ‬௜௧, ॴ௪௜௧௢௥௞; Ω௜௧) + ߚ‫ܧ‬௧ܸ(Ω௜௧ାଵ),
max
ೢ ೚ೝೖ ,௅
௖೔೟,ॴ౳
೔೟
೔೟,ॴ೔೟
(A1)
This Bellman equation can be decomposed into a sequence of choices involving
conditional value functions conditioned on employment status and the decision of
whether or not to return to the home country. We make the distinction between being in
work or being unemployed because individuals face different choice sets. For instance,
individuals who are unemployed can accept a job if they are offered one. Individuals who
are working may be fired but cannot choose to be unemployed. Similarly, the return to
the home country is an absorbing state in that we neither allow (nor observe) individuals
to come back to Germany. Hence, these conditional value functions explicitly model
constraints that are only implicit in (A1).
We begin with the value functions for those who have decided to stay in the
immigration country. The value of working can be expressed by
ܸௐூ (Ω௜௧) = max௖೔೟,ॴ౳ ‫ ݑ‬൫ܿ௜௧, ॴ୻௜௧, ‫ܮ‬௜௧ = ‫ܫ‬, ॴ௪௜௧௢௥௞ = 1; Ω௜௧൯
೔೟
+ߚ‫ܧ‬ൣ൫1 − ߜ(Ω௜௧ାଵ)൯ܸ෨ௐூ (ߗ௜௧ାଵ) + ߜ(ߗ௜௧ାଵ)ܸ෨ேூ(ߗ௜௧ାଵ)൧,
(A2)
where ܸ෨ௐூ (ߗ௜௧) and ܸ෨ேூ(ߗ௜௧) denote the value functions of working or not working prior
to deciding where to locate (defined below). The individual faces a probability ߜ(ߗ௜௧ାଵ)
53
of being fired and start the next period as unemployed. Individuals who are currently
unemployed make choices according to the following Bellman equation:
ܸேூ(Ω௜௧) = max௖೔೟,ॴ౳ ‫ ݑ‬൫ܿ௜௧, ॴ୻௜௧, ‫ܮ‬௜௧ = ‫ܫ‬, ॴ௪௜௧௢௥௞ = 0; Ω௜௧൯
೔೟
(A3)
+ߚ‫ܧ‬ൣߣ(Ω௜௧ାଵ) max{ܸ෨ே (Ω௜௧ାଵ), ܸ෨ௐ (Ω௜௧ାଵ)} + ൫1 − ߣ(Ω௜௧ାଵ)൯ܸ෨ே (Ω௜௧ାଵ)൧,
where ߣ(Ω௜௧ାଵ) is the probability of a job offer. When offered a job, individuals decide
whether or not to accept it, depending in particular on the income shock ߝ௜௧ାଵ.
For those who decide to return to the home country, if working, the consumption
decision is
ܸௐா (Ω௜௧) = max௖೔೟ ‫ ݑ‬൫ܿ௜௧, ॴ୻௜௧ = 0, ‫ܮ‬௜௧ = ‫ܧ‬, ॴ௪௜௧௢௥௞ = 1; Ω௜௧൯
(A4)
+ߚ‫ܧ‬ൣ൫1 − ߜ(Ω௜௧ାଵ)൯ܸௐா (ߗ௜௧ାଵ) + ߜ(ߗ௜௧ାଵ)ܸோ (ߗ௜௧ାଵ)൧.
If not working, the decision is expressed by the following Bellman equation:
ܸோ (Ω௜௧) = max௖೔೟ ‫ ݑ‬൫ܿ௜௧, ॴ୻௜௧ = 0, ‫ܮ‬௜௧ = ‫ܧ‬, ॴ௪௜௧௢௥௞ = 0; Ω௜௧൯
(A5)
+ߚ‫ܧ‬ൣߣ(Ω௜௧ାଵ) max{ܸோ (Ω௜௧ାଵ), ܸௐா (Ω௜௧ାଵ)} + ൫1 − ߣ(Ω௜௧ାଵ)൯ܸோ (Ω௜௧ାଵ)൧.
Finally, individuals still in the immigration country make a location decision by
comparing the value of staying an additional year in the immigration country, defined in
(A2) and (A3), with the value of returning to the home country, defined in (A4) and
(A5):
ܸ෨௟ூ(Ω௜௧) = max{ܸ௟ூ(Ω௜௧), ܸோ (Ω௜௧)} , ‫ ܰ = ܮ‬, ܹ .
(A6)
54
C. Identification of the Model and Model Fit
[Table A1 here]
In Table A1, we provide a complete description of the moments used to estimate the
model. Figure A1 shows the model fit on second moments of some core variables in our
analysis. In particular, the top left panel of this figure shows the distribution of the error
in anticipated migration durations as predicted by the model. The figure is thus the
simulated counterpart to Figure 1. It should be noted that we do not use any moment of
this distribution directly in the estimation. Nevertheless, both the location and the
variation—particularly, the slight right skewedness of the distribution—are well
replicated. Finally, Tables A2–A10 show the goodness of fit with respect to the full set of
moments used in the estimation.
[Figure A1 here]
[Tables A2–A10 here]
To measure the process of social capital accumulation and some core parameters of
the utility function (e.g., those related to leisure and those that determine job acceptance
decisions), we regress employment transitions and log annual earnings on these observed
integration variables. We also use auxiliary regressions of the integration variables on
time spent in Germany, the intention to stay permanently, and an interaction of the two.
We identify the parameters in the wage and employment transition equations by
matching the coefficients in the regressions of log earnings and employment and
employment transitions on work experience in Turkey and on spline functions of work
experience in Germany and age.
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The exponent ߶ଵ on consumption in the utility function is determined using
information on correlations between annual savings and employment, income and the
reported intention to stay permanently. Similarly, the exponent ߶଴ on social integration
and the relative preference for the host country versus the country of origin are derived
using auxiliary regressions of intended length of stay on employment, income, and years
since immigration.
To identify the parameters governing the deviation of actual return migration from
earlier migration plans, we further include information on actual return migration
conditional on such observables as age and employment status and on coefficients from
an autoregression of intended length of stay. We also determine distributional parameters
like variances in unobserved earnings shocks using the residual variances in some of
these auxiliary regressions. Finally, to identify unobserved individual heterogeneity in
earnings and relative preferences, we include in our set of moments the standard
deviations of the within-individual mean residuals from the earnings and intentions
regressions and their correlation.
The age at which immigrants arrive in Germany and their prior work experience
accumulated in the home country are taken from the joint distribution of age at
immigration and home country experience in our data. Similarly, because the model
begins at age 18, we draw the working experience in Germany that individuals may have
accumulated between ages 16 and 18 from the empirical distribution.
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D. Additional Estimation Results
[Table A11 here]
Table A11 reports additional estimated parameters that refer to the factor model of social
capital used to determine a number of observed integration outcomes, as well as the
magnitude by which social capital in the model increases if an individual chooses to
invest in a given period (݀Γ ). Because the stock of social capital is unobserved, a
normalization on either ݀୻ or on one of the slope coefficients in the factor model is
required. We choose to normalize to one the effect of social capital on knowledge of the
host country language (ߛଵ௅).
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