The Dynamics of Return Migration, Human Capital Accumulation, and Wage Assimilation 1

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1 The Dynamics of Return Migration, Human Capital Accumulation, and Wage Assimilation 1 Jérôme Adda 2 Christian Dustmann 3 Joseph-Simon Görlach 4 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 , 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.

2 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 percent ratio to the inflow of immigrants in the major European destination countries (OECD, 2013). For the U.S., Renuka Bhaskar,Belkinés Arenas- Germosén, 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

3 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

4 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

5 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

6 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

7 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

8 includes age, ௧ ; years since immigration, ݏݕ ௧ ; work experience, ௧ ; social capital in ௪ the host country, Γ ௧ ; assets, ܣ ௧ ; prior employment status, ॴ ௧ ଵ ; and prior location,, where E stands for emigration (or home) country and I stands for {ܫ,ܧ} ௧ ଵ ܮ 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 ௧ ଵ. ߨ = ߨ, with ߨ ൯= ݔ = 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 ௪ Ω ௧ = ௧, ݏݕ ௧, ௧, Γ ௧, ܣ ௧, ॴ ௧ ଵ, ܮ ௧ ଵ, ߙ, Ψ ௧, Υ ௧. (1) A. Model Setup ) ) Human Capital. The two forms of human capital considered work experience and social capital ( ડ ) 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

9 experience, which is acquired through learning-by-doing, increases by one unit in each period in which the individual is working: ௪ ௧ ଵ = ௧ + ॴ ௧, (2) ௪ where ॴ ௧ takes the value one if individual works in period andݐ 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 ௧ ଵ = Γ ௧ + ॴ ௧, (3) ݐ with ॴ ௧ being an indicator variable that equals one if investment takes place in period 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

10 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 ॴ to denote an indicator variable equal to one if the individual is located in country, =. Log gross annual wages are expressed as log ݕ ௧ = ߙ + ௬( ௧ ) + ߙ Γ ௧ ॴ + ॴߩ + 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 ߪ ఢ ଶ. 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: ௪ ௪ ௧ ଵ + ॴ ௧ ܣ = ௧ ܣ ݕ)ݐ ௧, ܮ ௧ ) + ൫1 ॴ ௧ ൯ ௧ ௧, (5) 0, ௧ ܣ 0, = ܣ 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

11 ௪ where ॴ ௧ is an indicator function equal to one if the individual is working and net() is a function that relates gross earnings ݕ ௧ to 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 = Ω )ݎ ௧ ). 12 Once migrants return, their assets are converted by a factor ݔ ௧ (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 Ω )ߜ ௧ ), while individuals who are unemployed receive a job offer with probability Ω )ߣ 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 )൯ ௧ + ఋ ( ௧ ߁ ௰ ߜ + ௧ ߜ + ߜΦ൫ Ω )ߜ ୧୲ ) = (6-a) and )൯, ௧ + ఒ ( ௧ ߁ ௰ ߣ + ௧ ߣ + ߣΦ൫ Ω )ߣ ୧୲ ) = (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 ߗ)ߜ ௧ ) = ఋ ( ௧ ) and ߗ)ߣ ௧ ) = ఒ ( ௧ ), with age-specific job loss and job 11 See the appendix for details. 12 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. 10

12 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 ௪ (1 h), where h [0,1] is the labor supply. We again use ॴ 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, =.ܫ,ܧ 14 Utility then takes the following form: ௧ ൫ ௧, ॴ ௪ ݑ ௧, ܮ ௧, ॴ ௧ ; Ω ௧ ൯= (Ψ ௧ (Γ ௧ + 1) థ బ) ॴ ಽ థ భ స ௧ (1 h) ॴ ( ௧ )ॴ ௧ + ߟ ௧ ॴ + ߟ ௧ ॴ. (7) As discussed above, we allow for an individual s initial locational preference Ψ to be correlated with unobserved productivity ߙ. 13 We specify the effort function to be linear in age: ( ௧ ) = + ଵ ௧. 14 These persistent and transitory shocks capture aspects such as family events that are important for return decisions but which we do not model explicitly. 11

13 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 ௧ )ݑ, ॴ ௪ ௧, ܮ ௧, ॴ ௧ ; Ω ௧ ) + ܧߚ ௧ (Ω ௧ ଵ ), (8),,ॴ,ॴ where ߚ is the discount factor and ܧ ௧ 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 ௧ ଵ = ܧ whenever ܮ ௧ =.ܧ 15 Because social capital in the host country is not productive in the home country, migrants that have returned always choose ॴ Γ 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

14 ௧, Γ ௧, and Ψ ௧ fixed at their values at age (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 = 0.5ywith y= ቀ ଡ଼/ସ ଵ.ହஞ ቁy + ቆ1 ቀ ଡ଼/ସ ଵ.ହஞ ቁቇy, 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

15 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 the state Ω ௧ at time ݐ is (Ω ௧ ) = such that ଵ ହ, ݐ ௦[return at t + Ω ௧ ] ൧= ଵ ௦ ଵ, where at time ଶ 1 ௦ [return at +ݐ Ω ௧ ] indicates whether simulation predictsݏ 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 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

16 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,ܭ, 1, =, ௧ ߡ We identify social capital, Γ ௧, by linking it to a number of variables 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, = ܧ,ܫ is ߟ൫ ௧ = ൯ݔ, ൯ (ݔ )ݔ ൫ݔ but individuals perceive it to be ߟ൫ ௧. 6 /ߨ. ൯ ( /ݔ )ݔ ൫ݔ The standard deviation for this distribution is = ൯ݔ 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

17 (9),ܭ, 1, k= ଵ Γ ௧ + ௧ ൯, ߛ + ߛΦ൫ ௧ = ߡ where the ߛ ଵ 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 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 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 The authors own calculations based on OECD data, available at 22 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). 16

18 A. Data and Sample Our analysis is based on 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

19 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 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. 26 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 ( 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 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

20 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 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

21 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

22 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 ߛ ଵ ଵ 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 Γ ୧୲ 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

23 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. Results A. 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

24 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

25 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 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 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). 24

26 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

27 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, 33 Because the value of ߖ ௧ for immigrants with a strong preference for the host country is not identified, we set it to 1. 26

28 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

29 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

30 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

31 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

32 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

33 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 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

34 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 ( Similar possibilities exist for non-eu immigrants in Germany ( and EU15 and EFTA immigrants to Switzerland ( 33

35 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

36 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

37 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

38 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

39 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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42 Colussi, Aldo Migrants Networks: An Estimable Model of Illegal Mexican Migration. University of Pennsylvania Job Market Paper, Philadelphia, PA. Cortes, Kalena E Are Refugees Different from Economic Immigrants? Some Empirical Evidence on the Heterogeneity of Immigrant Groups in the United States. Review of Economics and Statistics, 86(2): Cortés, Patricia, and Jessica Pan Relative Quality of Foreign Nurses in the United States. CReAM Discussion Paper 31/12, Centre for Research and Analysis of Migration, Department of Economics, University College London. Duffie, Darrell, and Kenneth J. Singleton Simulated Moments Estimation of Markov Models of Asset Prices. Econometrica, 61: Dustmann, Christian Earnings Adjustment of Temporary Migrants. Journal of Population Economics, 6(2): Eckstein, Zvi, and Yoram Weiss On the Wage Growth of Immigrants: Israel, Journal of the European Economic Association, 2(4): Eckstein, Zvi, and Kenneth I. Wolpin Dynamic Labour Force Participation of Married Women and Endogenous Work Experience. Review of Economic Studies, 56(3): Edin, Per-Anders, Robert J. LaLonde, and Olof Åslund Emigration of Immigrants and Measures of Immigrant Assimilation: Evidence from Sweden. Swedish Economic Policy Review, European Commission Economic and Financial Affairs: AMECO Database. Aviailable at Fernández-Huertas Moraga, Jésus New Evidence on Emigrant Selection. Review of Economics and Statistics, 93(1):

43 Friedberg, Rachel M The Labor Market Assimilation of Immigrants in the United States: The Role of Age at Arrival. Brown University Working Paper, Providence, RI. Green, David A., and Christopher Worswick Entry Earnings of Immigrant Men in Canada: The Roles of Labour Market Entry Effects and Returns to Foreign Experience. Research Paper, Strategic Research and Review, Citizenship and Immigration Canada. Hu, Wei-Yin Immigrant Earnings Assimilation: Estimates from Longitudinal Data. American Economic Review, 90(2): Hunn, Katrin Nächstes Jahr kehren wir zurück: die Geschichte der türkischen Gastarbeiter in der Bundesrepublik. Göttingen: Wallstein Verlag. Imai, Susumu, and Michael P. Keane Intertemporal Labor Supply and Human Capital Accumulation. International Economic Review, 45(2): Keane, Michael P., and Kenneth I. Wolpin The Effect of Parental Transfers and Borrowing Constraints on Educational Attainment. International Economic Review, 42(4): Khan, Aliya Hashmi Post-Migration Investment in Education by Immigrants in the United States. Quarterly Review of Economics and Finance, 37: Kırdar, Murat G Estimating the Impact of Immigrants on the Host Country Social System when Return Migration Is an Endogenous Choice. International Economic Review, 53(2): 453_86. Lessem, Rebecca Mexico-U.S. Immigration: Effects of Wages and Border Enforcement. Tepper School of Business Working Paper, Carnegie-Mellon University, Pittsburgh, PA. 42

44 Long, James E The Effect of Americanization on Earnings: Some Evidence for Women. Journal of Political Economy, 88(3): Low, Low, Hamish, Costas Meghir, and Luigi Pistaferri Wage Risk and Employment Risk over the Life Cycle. American Economic Review, 100(4): Lubotsky, Darren Chutes or Ladders? A Longitudinal Analysis of Immigrant Earnings. Journal of Political Economy, 115(5): Martin, Philip Guest or Temporary Foreign Worker Programs. In The Handbook of the Economics of International Migration, Vol. 1A, ed. Barry R. Chiswick and Paul W. Miller, Amsterdam: North Holland. Nakajima, Kayuna The Fiscal Impact of Border Tightening. University of Wisconsin-Madison Job Market Paper, Madison, WI. Organisation for Economic Cooperation and Development International Migration Outlook Paris: OECD Publishing. Organisation for Economic Cooperation and Development. 2013a. International Migration Outlook Paris: OECD Publishing. Organisation for Economic Cooperation and Development. 2013b. OECD.Stat Web Browser. Pakes, Ariel, and David Pollard Simulation and the Asymptotics of Optimization Estimators. Econometrica, 57, Picot, Garnett, and Patrizio Piraino Immigrant Earnings Growth: Selection Bias or Real Progress? Canadian Journal of Economics/Revue canadienne d'économique, 46(4): Pischke, Jörn-Steffen Assimilation and the Earnings of Guestworkers in Germany. ZEW Discussion Paper 92 17, Centre for European Economic Research, University of Mannheim. 43

45 Rendon, Silvio, and Alfredo Cuecuecha International Job Search: Mexicans In and Out of the U.S. Review of Economics of the Household, 8(1): Sarvimäki, Matti Assimilation to a Welfare State: Labor Market Performance and Use of Social Benefits by Immigrants to Finland. Scandinavian Journal of Economics, 113(3): Skuterud, Mikal, and Mingcui Su The Influence of Measurement Error and Unobserved Heterogeneity in Estimating Immigrant Returns to Foreign and Host- Country Sources of Human Capital. Empirical Economics, 43(3): Tansel, Aysit, and H. Mehmet Taşçı Hazard Analysis of Unemployment Duration by Gender in a Developing Country: The Case of Turkey. Labour, 24(4): Thom, Kevin Repeated Circular Migration: Theory and Evidence from Undocumented Migrants. Mimeo, New York University. TurkStat Structure of Earnings Survey. U.S. Census Bureau Statistical Abstract of the United States: Washington, DC. Van Baalen, Brigitte, and Tobias Müller Return Intentions of Temporary Migrants: The Case of Germany. Mimeo. Van der Klaauw, Wilbert On the Use of Expectations Data in Estimating Structural Dynamic Choice Models. Journal of Labor Economics, 30(3): Van der Klaauw, Wilbert, and Kenneth I. Wolpin Social Security and the Retirement and Savings Behavior of Low-Income Households. Journal of Econometrics, 145(1): World Bank World Development Indicators, Washington, D.C. 44

46 Figures and Tables 45

47 46

48 47

49 48

50 49

51 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 Bundesbank 41 and the OECD 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 ( 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

52 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 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 sinceݐ 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 ߩ ௧ = ଶ and relative price levels at which assets are converted after ݐ ݐ return by a factor ݔ ௧ ݐ ݐ = ଶ, where isݐ time since 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 ݎ ௧ = ଶ ݐ ݐ = ௧ ݎ ଶ and ݐ ݐ

53 Earnings tax schedules and unemployment benefits. For Germany, unemployment benefits ()ݎ are 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:, ) ଷ ݕ ) ) ଶ ݕ ) ) ݕ Φ( ݕ)ݎ ) = where ݕ are previous earnings, aggregated to bins of 10,000 euros ( ଶ = ). In Turkey, during the period of our analysis, no unemployment insurance was in place, so we set = ) )ݎ 0. To calibrate the function ()ݐ for 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 in ݕ as + ଶ ) ݕ ) ݕ Φ( (1 ݕ = ) ݕ)ݐ ) ଷ )), ( ଶ = ), where Φ() denotes the standard normal distribution ݕ ) 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. 45 The authors own calculations based on the German tax schedule in 1999 ( 52

54 assume 40 hours of work per week and 48 weeks of work per year if an individual works, and correspondingly calibrate h to ସ ସ ଵ ହଶ =ߚ We further let time preference = 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 ) = max ௧ )ݑ, ॴ ௪ ௧, ܮ ௧, ॴ ௧ ; Ω ௧ ) + ܧߚ ௧ (Ω ௧ ଵ ), (A1),,ॴ,ॴ 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 ௐ (Ω ௧ ) = max,ॴ ൫ ௧ݑ, ॴ ௪ ௧, ܮ ௧ =,ܫ ॴ ௧ = 1; Ω ௧ ൯ )൧, ௧ ଵ ߗ) ௧ ଵ ) ߗ)ߜ + ) ௧ ଵ ߗ) Ω )ߜ ௧ ଵ )൯ ௐ ൫1 ܧߚ+ (A2) where ௐ ߗ) ௧ ) and ߗ) ௧ ) denote the value functions of working or not working prior to deciding where to locate (defined below). The individual faces a probability ߗ)ߜ ௧ ଵ ) 53

55 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 ൫ ௧ݑ, ॴ ௪ ௧, ܮ ௧ =,ܫ ॴ ௧ = 0; Ω ௧ ൯ (A3) )൧, Ω )ߣ ௧ ଵ )൯ (Ω ௧ ଵ ൫1 Ω )ߣ ܧߚ+ ௧ ଵ ) max{ (Ω ௧ ଵ ), ௐ (Ω ௧ ଵ )} + where Ω )ߣ ௧ ଵ ) 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 ௧ ଵ. For those who decide to return to the home country, if working, the consumption decision is ௐ (Ω ௧ ) = max ൫ ௧ݑ, ॴ ௪ ௧ = 0, ܮ ௧ =,ܧ ॴ ௧ = 1; Ω ௧ ൯ (A4) )൧. ௧ ଵ ߗ) ௧ ଵ ) ߗ)ߜ + ) ௧ ଵ ߗ) Ω )ߜ ௧ ଵ )൯ ௐ ൫1 ܧߚ+ If not working, the decision is expressed by the following Bellman equation: (Ω ௧ ) = max ൫ ௧ݑ, ॴ ௪ ௧ = 0, ܮ ௧ =,ܧ ॴ ௧ = 0; Ω ௧ ൯ (A5) )൧. Ω )ߣ ௧ ଵ )൯ (Ω ௧ ଵ ൫1 Ω )ߣ ܧߚ+ ௧ ଵ ) max{ (Ω ௧ ଵ ), ௐ (Ω ௧ ଵ )} + 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): (Ω ௧ ) = max{ (Ω ௧ ), (Ω ௧ )}, ܮ =,. (A6) 54

56 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. 55

57 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. 56

58 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 ߛ) ଵ ). 57

59 58

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