Immigration restrictions and second-generation cultural assimilation: theory and quasi-experimental evidence


We study the effects of immigration restrictions on the cultural assimilation of second-generation migrants. In our theoretical model, when mobility is free, individuals with a stronger taste for their native culture migrate temporarily. When immigration is restricted, however, these individuals are incentivized to relocate permanently. Permanent emigrants procreate in the destination country and convey their cultural traits to the second generation, who will therefore find assimilation harder. We test this prediction by using the 1973 immigration ban in Germany (Anwerbestopp) as a quasi-experiment. Since the ban only concerned immigrants from countries outside the European Economic Community, they act as a treatment group. According to our estimates, the Anwerbestopp has reduced the cultural assimilation of the second generation. This result demonstrated robustness to several checks. We conclude that restrictive immigration policies may have the unintended consequence of delaying the intergenerational process of cultural assimilation.

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  1. 1.

    An often cited example is the referendum that has forbidden the construction of new mosques in Switzerland.

  2. 2.

    See Jaitman and Machin (2013) for recent results and other references.

  3. 3.

    According to Razin (2012), ’restrictions on international mobility of labor are arguably the single most important policy distortion that besets the international economy’.

  4. 4.

    In this vast literature, see, for example, Herberg (1955); Chiswick (1978); Carliner (1980); Hughes and Thomas (1998); Rumbaut (1994); Dustmann (1996); Casey and Dustmann (2010); Abramitzky et al. (2014); Schueller (2015).

  5. 5.

    There is a considerable debate over the term that correctly depicts the process of inclusion and acceptance of migrants in the receiving societies. While most US authors use “assimilation,” European authors prefer “integration” (see Algan et al. 2012; Constant et al. 2009; Blau 2015). The concepts of “incorporation,” “acculturation,” and “adaptation” have also been prompted to highlight different facets of the process. However, the new assimilation theory of Alba and Nee (2003) bridges the US and the European approaches; thus, we adopt their definition.

  6. 6.

    The phenomenon that some ethnic groups can be incorporated into a society as permanently disadvantaged minorities is defined as “segmented assimilation” or “downward assimilation” (Alba and Nee 2003; Portes and Rumbaut 2001). This issue is well-known since Chiswick (1978) and Carliner (1980). Borjas (1993) reports evidence of the downward assimilation of Mexican immigrants. Further examples concern African Americans or Native Americans (Hughes and Thomas 1998). Angelini et al. (2015) show that cultural assimilation is crucial for the perceived well-being of immigrants. See Vega and Rumbaut (1991) for mental health issues.

  7. 7.

    The recent findings by Amuedo-Dorantes and Lopez (2015) show that anti-immigration measures worsen the school performance of unauthorized immigrants’ children.

  8. 8.

    See Hill (1987); Magris and Russo (2009); Kirdar (2012).

  9. 9.

    See, among others, Reichert and Massey (1984); Koussodji (1992); Porter (2003); Constant and Zimmermann (2011); Massey and Pren (2012); Borodak and Tichit (2013); Amuedo-Dorantes et al. (2013); Massey et al. (2016). Quite interestingly, Baines (1991) remarks that even at the end of the 19th century circular migration spells of 3–4 years from Europe to the Americas were the norm.

  10. 10.

    The European Economic Community was the free-trade agreement replaced by the European Union in 1993.

  11. 11.

    Generally speaking, the time spent abroad is a continuous variable: an individual may decide to migrate for a year, 10 years, or for her whole life; from this point of view, permanent migration is a corner solution. For this reason, national statistical offices find it difficult to categorize the different types of migration. We observe so many sources and so many different migration patterns (permanent migration, temporary migration, repeat migration, seasonal migration, circular migration) that Willekens (1984) remarked “migration is a fuzzy concept, with many definitional problems.” According to the UN (1991, p. 99), international migration “remains the most difficult of demographic phenomena to define and measure correctly.” Attempts to achieve greater homogeneity and comparability in the available statistics are still ongoing (see the monographic issue n. 4-1987 of the International Migration Review, and more recently, the efforts to build the IMPALA database by a consortium of US, European, and Australian universities). Fortunately, for our purposes, we only need to define the concept of “permanent migration.” According to OECD (2007), a permanent migrant is a person who is on a “migration track” that normally leads to permanent residency in the host country. These migrants include persons with permanent residence permits, persons with limited but indefinitely renewable permits, and persons with the right of free movement (such as EU citizens within the European Union). Thus, the OECD definition is focused on the intention of settling abroad permanently. This focus fits our model very well; therefore, in the following, we adopt the OECD definition. In terms of our model, immigrants who settle abroad for two periods are permanent migrants, and immigrants who return home after a period are temporary migrants.

  12. 12.

    For our results to hold, we only need labor productivity to be higher in D.

  13. 13.

    Since the crisis drives utility to zero, only returning migrants re-migrate (those who were unable to migrate in the first period are now old and do not produce; thus, their utility would be zero in both countries).

  14. 14.

    Introducing a home bias is common in the literature (see, for instance, Dustmann 1997; Dustmann and Kirchkamp 2002; Li 2016). According to Borjas (1999), important non-economic factors, such as differences in language, culture, and the costs of entering an alien environment reduce migration flows.

    “With soft seductive speech she (the nymph Calypso) keeps tempting him, urging him to forget his Ithaca. But Odysseus yearns to see even the smoke rising from his native land and longs for death” (Homer, The Odyssey, I, 75-79).

  15. 15.

    We have chosen unity as the lower bound of 𝜃j because 𝜃j < 1 would indicate a preference for consuming abroad, which contradicts home bias. This is by no means restrictive: we would simply observe permanent emigration for all 𝜃j < 1.

  16. 16.

    Though this assumption may look restrictive, it can be dropped by using a three-period model. This would complicate the algebra without changing our results. The intuition is as follows: consider a three-period model, and suppose that a migrant wants to return after just one period. Such an immigrant exists because it is always possible to find 𝜃j high enough to prompt an individual to migrate for a single period. This immigrant observes a good state of the world in O and wants to return for the remaining two periods. However the possibility of a bad shock in the third period and the uncertainty about the ability to re-migrate will bias her decision exactly as it happens in the two-period model.

  17. 17.

    In both cases, we have 𝜃 = 1. This means that in our simplified model, there will be no permanent migrants.

  18. 18.

    According to Borjas (1994, p.1711), “the evidence suggests that the ethnic skill differentials will persist into the third generation and perhaps even into the fourth.[. . .] Ethnicity matters, and it seems to matter for a very long time.”

  19. 19.

    In the literature, the acquisition of cultural traits is explained through family efforts (vertical socialization) and social interactions (horizontal socialization). Since the choice of neighborhood and schools is generally a part of the family’s vertical socialization effort (Ioannides and Zanella 2008; Kremer and Sarychev 2000), for our purposes, it is sufficient to focus on the role of the family.

  20. 20.

    This process echoes the transmission of diseases from parents to children in the medical literature, where it is known as “vertical infection transmission.”

  21. 21.

    For simplicity, we do not model the parents’ decision concerning the intergenerational cultural transmission. Our argument can be seen as a reduced form of the elegant formalization by Epstein (2007), which models cultural transmission within the family. See Casey and Dustmann (2010) for another simple model of cultural transmission.

  22. 22.

    We have chosen this functional form for its simplicity. Other decreasing functions of 𝜃j would be equivalent.

  23. 23.

    It is important to remark that these effects can be carried over to many generations before they fade out.

  24. 24.

    This is true of Germany, France, Luxembourg, Switzerland, and the Nordic countries, albeit under different rules and degrees of enforcement. These measures, together with the severe border controls that in the 1970s still restricted the movement of workers across Europe, minimize the risk of immigrants flowing from Germany to the neighboring countries, and that the immigrant pools in Germany before and after 1973 are affected by policies put in place by other European countries.

  25. 25.

    Throughout the paper we use the term “Germany” to refer to the Federal Republic of Germany, thereby excluding the Eastern Laender before reunification and including them afterwards.

  26. 26.

    Similar patterns have been observed in other countries: Massey et al. (2016) point out that the militarization of the US-Mexico border transformed a circular flow of male workers going to a handful of states into settled families living in 50 states with a population of 11 million people. See Zimmermann (2014) for further examples.

  27. 27.

    Note that family reunions contribute to creating ethnic networks that, in turn, favor the settlement of more home-biased immigrants. Models of cultural transmission that allow for network effects can be found in Patacchini and Zenou (2011, 2016).

  28. 28.

    In order to apply a difference-in-differences approach to these immigrants, we would need proxies of assimilation collected before 1973.

  29. 29.

    The first wave has been discarded because respondents were not asked their father’s nationality. The lack of information about the country of origin of the respondent’s father prevented us from using the larger database provided by the German Socio-Economic Panel (GSOEP).

  30. 30.

    It is worth noting that the remaining countries in the control pool entered the EEC after 1973; thus, their immigrants were considered non-EEC citizens before entrance and EEC citizens afterwards. This is true of Greece, which joined the EEC in 1981, and of Spain and Portugal, which joined in 1986.

  31. 31.

    Depending on the authors, these indicators include, for instance, identification with the host country’s values, education, political satisfaction, mental health, economic success, political participation.

  32. 32.

    A quadratic trend was also included but the results were similar, so we only present the linear trend specification.

  33. 33.

    See the discussion in Section 3.

  34. 34.

    Only respondents born in Germany were considered.

  35. 35.

    See the list in Section 4.

  36. 36.

    We thank an anonymous reviewer for this suggestion.

  37. 37.

    ESS respondents are identified at the NUTS 1 level; thus, we cannot go further in searching for local effects. According to NUTS 1 subdivision, Germany is composed of 16 regions (Laender). At the time of the Anwerbestopp, the Federal Republic of Germany was formed by 10 Laender plus West Berlin, which officially was not a Land but was treated as such by the Federal Statistical Office.

  38. 38.

    This proxy is constructed as follows. First, we obtained a proxy for the stocks of immigrants by summing the regional net inflows over the 1955–1972 period (data have been provided by the Federal Statistical Office of Germany). Then, we computed the percentage of immigrants from each origin country over the Land population.

  39. 39.

    Estimates mentioned in this last paragraph are not shown but available upon request.

  40. 40.

    Source: Pew Research Center 2013, and our elaborations on Eurostat data, Labour Force Survey ad hoc 2014 module on the labor market situation of immigrants.

  41. 41.

    Assimilation is even more compelling in order to prevent the radicalization and the enrollment of terrorists among the foreign born.

  42. 42.

    See O’Rourke (2009); Massey and Pren (2012); Constant et al. (2013); Zimmermann (2014); Amuedo-Dorantes and Lopez (2015); Massey et al. (2016).

  43. 43.

    See Constant et al. (2013) for a survey of major mobility partnerships worldwide.


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We are grateful to the Editor-in-Chief, Klaus F. Zimmermann, and two anonymous referees who helped us to greatly improve our paper with their remarks. We acknowledge participants to the XIII Brucchi Luchino Workshop, the IX CSEF-IGIER Symposium on Economics and Institutions, and the Petralia Applied Economics Workshop. We also thank Toke Aidt, Alberto Bennardo, Gaetano Bloise, Michel Beine, François Bourguignon, Vincenzo Carrieri, Andrew Clark, Francesco Magris, Claire Naiditch, Dimitri Paolini, Eleonora Patacchini, Nicola Persico, Giovanni Pica, Vincenzo Pierro, Shanker Satyanath, and Filippo Taddei. The usual disclaimer applies.


The authors acknowledge financial support from the University of Salerno Giuseppe Russo: FARB project ORSA 163317; Fausto Galli: FARB project 160472.

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Responsible editor: Klaus F. Zimmermann



In order to obtain a suitable sample, we pruned the initial set of data further. In particular:

  • We discarded the first ESS round because the question regarding the country of birth of respondents’ fathers was introduced in the second round.

  • We discarded respondents with fathers born in Germany and the Netherlands in all regressions except the robustness checks in Table 4.

  • We discarded the negligible share (less than 3%) of respondents who either did not answer the question “In which country was your father born?” or claimed to ignore it.

  • We discarded respondents that did not declare their year of birth (less than 1%).

  • Proof of proposition 2

$$ \bar{a}(\pi)=\frac{{\int}_{1}^{\theta^{\ast}(\pi)}\frac{f\left( \theta_{j}\right)} {\theta_{j}}d\theta_{j}}{{\int}_{1}^{\theta^{\ast}(\pi)}f\left( \theta_{j}\right) d\theta_{j}} $$

The derivative of \({\int }_{1}^{\theta ^{\ast }(\pi )}f\left (\theta _{j}\right ) d\theta _{j}\) with respect to π is:

$$ \frac{\partial{\int}_{1}^{\theta^{\ast}(\pi)}f\left( \theta_{j}\right) d\theta_{j}}{\partial\pi}=f(\theta^{\ast}(\pi))\frac{\partial\theta^{\ast}} {\partial\pi}<0 $$

(see (4)). The derivative \(\partial \bar {a}/\partial \pi \) is given by:

$$ \frac{\partial\bar{a}}{\partial\pi}=\frac{f(\theta^{\ast}(\pi))\frac{\partial\theta^{\ast}}{\partial\pi}\left[ {\int}_{1}^{\theta^{\ast}(\pi)} \frac{f\left( \theta_{j}\right)} {\theta^{\ast}(\pi)}d\theta_{j}-{\int}_{1}^{\theta^{\ast}(\pi)}\frac{f\left( \theta_{j}\right)} {\theta_{j}} d\theta_{j}\right]} {\left[ {\int}_{1}^{\theta^{\ast}}f\left( \theta_{j}\right) d\theta_{j}\right]^{2}}. $$


$$\frac{f\left( \theta_{j}\right)} {\theta^{\ast}(\pi)}<\frac{f\left( \theta_{j}\right)} {\theta_{j}}\ \text{for any\ } \theta_{j}\in\left[ 1,\theta^{\ast}\right] , $$

the term in square brackets on the numerator is negative, and \(\frac {\partial \bar {a}}{\partial \pi }>0.\)

Table 2 Difference in differences estimation results for (10) on the window 1963-1983 centered around 1973. Parameters are estimated by linear probability model with two-way clustered standard errors on year of birth and father’s origin country (column 1), heteroskedasticity consistent standard errors (column 2) and with logistic regression (column 3). Inclusion in the treatment group (extraEEC) on the basis of the country of birth of the father
Table 3 Sample sizes (italics), experimental parameters and two-way clustered standard errors (in parentheses) of the estimations of the difference in differences model in (10) performed on various symmetric and asymmetric windows centered around 1973. Inclusion in the treatment group on the basis of the father’s country of birth
Table 4 Robustness checks. Columns 1 to 3 display results for (10) with different criteria for the inclusion in the treatment group (extraEEC). Column 1 reports the results when the inclusion in the treatment group depends on the mother’s origin country; column 2 when inclusion depends on the father’s country of birth and both parents were born abroad; column 3 when at least one parent is foreign born. Finally, column 4 reports the results when countries with significant historical German minorities were excluded from the sample (Poland, Czechoslovakia, Austria, Russian Federation, Ukraine, Belarus, Latvia, Lithuania, Kazakhstan, Czech Republic and Slovakia). ± 10 years windows centered around different years. Parameters estimated by linear probability model with two-way clustered standard errors
Table 5 Robustness checks. Results for equation 10 with the addition of contextual controls. Column 1 includes an estimate of the percentage of immigrants of the same country of individuals in our sample in 1972. Column 2 includes dummies for their Land of residence at the time of the ESS interwiew. Column 3 includes both (former eastern Laender are not included). Parameters are estimated by linear probability model with two-way clustering on year of birth and father’s origin country
Table 6 Placebo regressions. Results for (10) on various windows centered around different treatment years. Column 1 presents the results a window of ± 6 years around 1967, column 2 and 3 the results of placebo regressions with ± 10 years windows considering 1963 and 1983 respectively as the treatment year. Parameters estimated by linear probability model with two-way clustered standard errors. Inclusion in the treatment group (extraEEC) on the basis of the country of birth of the father
Table 7 Triple difference estimation results for equation 11 on the windows 1968-1978 (column 1), 1963-1983 (column 2) and 1958-1988 (column 3). Parameters are estimated by linear probability model with two-way clustered standard errors. Inclusion in the treatment group (extraEEC) on the basis of the country of birth of the father

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Galli, F., Russo, G. Immigration restrictions and second-generation cultural assimilation: theory and quasi-experimental evidence. J Popul Econ 32, 23–51 (2019).

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  • Second-generation immigration
  • Intergenerational assimilation
  • Cultural transmission
  • Social and economic stratification

JEL Classification

  • D91
  • F22
  • J15
  • K37
  • Z13