Immigration restriction and the transfer of cultural norms over time and boundaries: the case of religiosity

Abstract

We study the effect of an immigration ban on the self-selection of immigrants along cultural traits, and the transmission of these traits to the second generation. We show theoretically that restricting immigration incentivizes to settle abroad individuals with higher attachment to their origin culture, who, under free mobility, would rather choose circular migration. Once abroad, these individuals tend to convey their cultural traits to their children. As a consequence, restrictive immigration policies can foster the diffusion of cultural traits across boundaries and generations. We focus on religiosity, which is one of the most persistent and distinctive cultural traits, and exploit the 1973 immigration ban in West Germany (Anwerbestopp) as a natural experiment. Through a diff-in-diff analysis, we find that second generations born to parents treated by the Anwerbestopp show higher religiosity.

1. Introduction

An increasing literature studies the transfer of cultural and institutional norms to the countries of origin of returning immigrants (Beine and Sekkat, 2013; Beine et al., 2013; Tuccio and Wahba, 2018; Lodigiani and Salomone, 2020). However, the dissemination of norms and habits is a two-way process, which involves both the sending and receiving countries (Rapoport et al., 2020). In this paper, we study the transfer of norms from the sending to the receiving country with the help of a major natural experiment. Specifically, we exploit the immigration ban in West Germany (henceforth Germany) following the 1973 oil shock to assess how immigration policies affect the transmission of religiosity across countries and between generations of immigrants.¹

According to the Lucas critique, immigration policies —just like any policy— affect the individual behavior. Here, we are interested in the effect of immigration policies on the self-selection of the migrants along cultural characteristics. Self-selection is the crucial mechanism that makes migrants a non-random sample of the population. As a consequence, immigration policies introduce potential distortions into the very fundamental mechanism that determines the characteristics and the structure of the pool of immigrants, which, in turn, is central to the process of norms dissemination (Wahba, 2021).

For instance, in the literature it is known that restrictions on labor mobility alter the optimal duration of immigration. More precisely, authors like Vernon and Zimmermann (2021), Galli and Russo (2019), and Magris and Russo (2009) show theoretically and empirically that restrictions on international mobility incentivize individuals who would otherwise prefer circular or return migration to settle in the destination countries.² Settling permanently into a country entails reproduction and/or family reunion.³ To the extent that these individuals show higher commitment to their origin culture, they are more inclined to convey their cultural traits to their children, spreading their culture across space and time. We describe this process through a simple, micro-founded theoretical model, in which the decision to migrate depends not only on the material benefits of emigration, but also on the cultural dimension, in the form of a preference for consuming in the origin country. Our model proceeds in two steps: (1) self-selection: restrictions on immigration force many individuals with higher commitment to their origin culture to settle in the destination country; (2) cultural transmission: these immigrants tend to convey their customs to the second generation.

This transmission mechanism is, in principle, testable. Unfortunately, finding causal evidence is hard, because it requires an exogenous source of variation in the immigration policy. The 1973 immigration ban in Germany (Anwerbestopp) provides us with a suitable natural experiment, which we use to study the transmission of religiosity to the second generation. In order to understand the functioning of the experiment, let us remark that, before 1973, Germany was very open to immigration. However, after the oil shock, concerns for mass unemployment among immigrants led the government to swiftly reverse this policy through the Anwerbestopp; namely, a ban on the recruitment of workers who did not belong in the European Economic Community (henceforth EEC).⁴ Thus, EEC workers were still allowed free mobility in and out of Germany. This makes it possible to identify a treatment group and a control group, and treat the event as the quasi-experiment that is required to test our theory. Specifically, we expect that: (1) the treated group is more religious than the control group; (2) religiosity, in turn, is conveyed to the second generation, so that children born to treated immigrants show higher religiosity.

In other words, we hypothesize a spillover of the Anwerbestopp treatment to the second generation. Notice that this application of our theoretical model requires that higher commitment to the origin culture is associated with higher religiosity. This happens if religious participation increases the benefits received by the local social network, and these benefits are lost after emigration. In this case, we should observe a negative relationship between the level of religiosity and the probability of migrating. This is confirmed in the literature. For instance, Docquier et al. (2020) find that in Middle East and North Africa countries people who intend to migrate exhibit significantly lower levels of religiosity than the rest of the population. Likewise, using data from the Arab Barometer, Falco and Rotondi (2016) find that radical Islam views are a deterrent to migration. As for the US, Myers (2000) highlights that frequent church attendance and involvement in the social aspects of one's religious organization discourage migration.⁵

In order to study the effect of the Anwerbestopp on the religiosity of second-generation immigrants, we use European Social Survey data; namely, the answer to the question “How religious are you”, on a scale from one to ten. Our results display an increase in the level of religiosity for the treatment group, and hold under several robustness checks. Alternative measures of religiosity provide similar outcomes. These conclusions are in line with our prediction that the Anwerbestopp “forced” to settle in Germany many first-generation immigrants who, on their own, would have preferred circular or return migration.

Generally, our findings illustrate that immigration policies not only affect the share of permanent vs. return immigrants, but also that they influence the characteristics of the second generation. These long-run effects are crucial for the integration of the minorities, but can easily be overlooked by electorally-concerned, short-sighted governments.

Our paper is organized as follows: after this introduction, Section 2 presents our theoretical model; Section 3 reports the natural experiment; Section 4 describes our data; Section 5 discusses the identification strategy and the results; Section 6 is devoted to the robustness checks; Section 7 concludes.

2. Theory

Our theoretical approach is made of two steps. In the first step, we describe the self-selection into permanent or return migration, and illustrate how the immigration policy biases this choice. This part of the model is as in Galli and Russo (2019). In the second part, we improve on Galli and Russo (2019) by presenting a micro-founded model of intergenerational cultural transmission, which shows how the bias induced on the first generation can be conveyed to the second generation.

2.1 Self-selection

We use a simple two-period, two-country model with risk-neutral migrants. The model is extremely simplified in order to focus the attention only on the choice between permanent migration and return migration.⁶ We consider two countries -Origin and Destination- denoted as O and D, respectively. Individuals are endowed with one unit of labor they supply inelastically when young (namely, in the first period). In the second period, individuals are old and do not produce.⁷ In D, one unit of labor produces one unit of a storable good. In O, production is normalized to zero. This shortcut is a convenient way to simplify the algebra without loss of generality, giving everybody an incentive to migrate for at least one period.⁸ However, labor productivity is not the only difference between D and O. Destination and origin countries also differ in economic and political stability. Indeed, economic crises, political turmoils, and climate change are evermore important push factors (Naudé, 2009; Drabo and Linguère, 2015; Beine and Parsons, 2015; Coniglio and Pesce, 2015). We account for this effect by assuming that in O the state of the world is good with probability p, and bad with probability (1 − p). The bad shock drives to zero the utility of staying in O and causes re-migration to D, where consumption of the stored good yields positive utility.⁹ Thus, in our model, the incentive to migrate depends both on the productivity differential and the economic stability. However, entry to D is rationed and requires an entry permit, which is distributed through a lottery that grants a permit with probability π ∈ (0,  1). Only one application per person is allowed. This concludes the description of the incentives to migrate.

Now, we introduce into the model a cultural motivation for return migration; namely, a preference for consuming at home, which we denote as “home-bias”. This is done for taking into account the non-economic factors that affect migration decisions. Actually, if we consider wages alone, migration flows look surprisingly low with respect to what one would expect: given the existing wage differentials, there would be no reason for anyone to live and/or return in countries with lower ones. However, both economic and non-economic factors contribute to curb the outflows and incentivize returns.¹⁰

In our model, the material benefits of emigration are summarized by the productivity differential, while non-economic factors, like differences in language, culture, and, more generally, feelings of uprooting and homesickness are summarized in the concept of home-bias.^{11, 12, 13} For simplicity, the future is not discounted and returning migrants observe the shock in O only after their return.¹⁴ The expected utility of a permanent migrant is given by

(1)$$E[ u_{PM}] = \pi + ( 1-\pi) 0$$

(The migrant is successful with probability π. In that case, she produces and consumes one unit over her lifetime. If the migrant is unsuccessful, she spends both periods in O and consumes zero). The expected utility of returning to O and consuming at home the good produced in D is given by:

(2)

Equation (2) means that, for a successful migrant, if the shock is good, return migration makes it possible to enjoy home-bias augmented consumption. If the shock is bad, re-migration to D is uncertain. In this simplified world, the choice between permanent and return migration only depends on the home-bias θ _j.

2.1.1 Permanent and return migration

We compare the utility under return migration and permanent migration by solving the condition E[u _RM] ≥ E[u _PM] with respect to θ _j. This gives the cutoff value

(3)$$\theta^{\ast}\equiv{( 1-\pi( 1-p) ) \over p}.$$

Thus, individuals for whom θ _j < θ* will be permanent migrants, and individuals for whom θ _j ≥ θ* will be returning migrants.¹⁵

In other words, there exists a critical value of the home-bias θ* that separates permanent migrants from returning migrants. It is crucial to note that the level of home-bias necessary to return depends on the immigration policy π. This happens because the probability of entering D affects the value of return migration through the probability of re-migrating in case of a shock. As we show in the comparative statics analysis below, this is the central finding of our theoretical analysis, and shows how the Lucas critique applies to this aspect of immigration policies. We now present the comparative statics results.

2.1.2 Comparative statics

In this section, we show the comparative statics properties of the model. Computing the derivatives is straightforward. We have

(4)$${\partial\theta^{\ast}\over \partial\pi} < 0$$

and

(5)$${\partial\theta^{\ast}\over \partial p}< 0.$$

Derivative (4) shows that, as π grows, the share of returning migrants increases. This happens because freedom of immigration makes it easier to harbor abroad in the bad state; thus, return migration occurs at a lower θ. Put differently, a restrictive immigration policy fosters permanent migration of immigrants with higher home-bias. This application of the Lucas critique to the self-selection of immigrants is the basis of our empirical analysis.

Derivative (5) shows that improved economic conditions at home incentivize return migration. It is interesting to note that substituting π = 1 into θ* is equivalent to setting p = 1. In both cases, we have θ* = 1. This means that, in presence of free mobility, our simplified model produces no permanent migration at all. This happens because labor mobility also provides insurance against the risk of a crisis in O.

2.2 Cultural transmission

It is very interesting to remark that attempts to curb immigration are mostly targeted at permanent immigration. Temporary immigration is rarely considered a source of concern. What is so special about permanent immigration? There are many obvious differences between temporary and permanent immigration. For instance, the net fiscal impact of immigration can be quite different in the short term than in the long term. However, for our purposes, we argue that what makes permanent immigration important is procreation. Procreation has crucial implications because families carry cultural and ethnic traits from one generation to another. The resilience of cultural traits across generations and the persistence of ethnic minorities are indeed some of the most common observations in heterogeneous societies (see Bisin and Verdier, 2010).¹⁶ In the following, we exemplify a mechanism through which restrictive immigration policies can strengthen the persistence of the foreign culture in the second generation. Our idea is a simple one: according to equation (4), restrictions on immigration push individuals who are more committed to their native culture to settle in the destination country; then, they tend to convey their cultural preferences to their children.¹⁷ In practice, this aim is pursued through educational and socialization effort, which will be the choice variable in our model of cultural transmission. In what follows, we show a simple example of such a mechanism.

Let us suppose that parents value cultural transmission to their children. Thus, we assume that cultural transmission (CT) is a good, which is produced through a Cobb-Douglas technology, with α ∈ (0,  1), whose inputs are educational effort (e ≥ 0), and cultural capital, which is proxied by the home-bias θ _j. We consider a representative household that, in our case, is the household endowed with the average cultural capital of the permanent immigrants, denoted by $\overline {\theta }$. Notice that, by equation (4), $\overline {\theta }$ depends on the immigration policy π, therefore we can write it as $\overline {\theta }( \pi )$, with, as we formally prove in the appendix,

(6)$${\partial\overline{\theta}( \pi) \over \partial\pi}< 0.$$

Thus, cultural transmission is produced according to the following production function:

(7)$$CT = \overline{\theta}^{a}e^{( 1-a) }$$

With quadratic cost of effort, the representative household's utility can be written as

(8)$$\overline{U} = \overline{\theta}^{a}e^{( 1-a) }- {e^{2}\over 2}$$

Maximization yields the optimal effort:

(9)$$\overline{e}^{\ast} = [ ( 1-a) \overline{\theta}^{a}] ^{{1}/( {1 + a}) }$$

It is straightforward to verify that

(10)$${\partial\overline{e}^{\ast}\over \partial\overline\theta}> 0.$$

In other words, the average equilibrium educational effort increases as the average home-bias increases. This is quite not surprising, as the inputs in the production function are complements. However, the closed solution (9) and the comparative statics result (10) provide a convenient way to summarize the transmission mechanism from the immigration policy to the cultural transmission, which is given by the derivative

(11)$${\partial\overline{e}^{\ast}\over {\partial\pi}} = {\partial \overline{e}^{\ast }\over \partial\overline{\theta} } {\partial\overline{\theta}\over \partial\pi}< 0.$$

In other words, relaxing restrictions on immigration reduces the home-bias necessary to incentivize returns. In turn, this reduces the home-bias of the permanent immigrants, who are less committed to their origin, and put less effort in conveying their customs and traditions to the second generation. Of course, the mechanism is reversed in case of restriction. Equation (11) nicely summarizes the story we are telling about the Anwerbestopp.

When religion is part of one's cultural identity, its practice, considered as a set of beliefs and routines, is an important component of the family life. Consequently, it is a preeminent indicator of cultural transmission. If our model is correct, the intergenerational transmission of religiosity can be detected, provided that we find appropriate data and an exogenous source of variation. While data on religious affiliation and practice are available, finding a proper source of variation that ensures causality is harder. We found a suitable natural experiment in the 1973 immigration ban in Germany, which we describe in the next section.

3. The natural experiment

Currently, Germany is the top destination country in the EU for immigrants and for asylum seekers, and the second in the world. In January 2021, according to the Central Register of Foreign Nationals (AZR), around 11.4 million foreign nationals were living in Germany. In addition, 22.3 million people had a migration background, representing 27.2 per cent of the population. However, after World War II, (West) Germany was already the main destination in Europe. The economic boom (Wirtschaftswunder) generated a severe labor shortage, especially for low-skilled workers in construction and industry. At first, immigrants from East Germany and ethnic Germans from Eastern Europe (Aussiedler) were admitted.¹⁸ The recruitment of foreign workers continued via agreements with several countries: first Italy (1953), then Spain, Greece (1960), and Turkey (1961). The foreign population rapidly increased, and, in 1964, the arrival of the millionth guest worker was even celebrated.¹⁹ The building of the Berlin wall in 1961 stopped the flow of immigrants from East Germany, and led to further agreements: Morocco (1963), Portugal (1964), Tunisia (1965), and Yugoslavia (1968). During this period, immigration was considered a resource to support economic growth, albeit permanent settlements were preferably prevented. Recruitment programs were based on a rotation principle (rotationprinzip): migrants would enter Germany for a period of at most two years, returning to their origin country to make room for other guest workers. Between 1961 and 1973, about 14 million foreign workers entered Germany, of whom about 11 million left the country. The oil crisis of the 1970s marked a major change. It ended a period of unprecedented economic growth and opened the new era of stagflation. In order to preserve jobs for natives a halt on recruitment of non-EEC workers (Anwerberstopp) was declared on November 23, 1973. At that time, Germany had 2.6 million of foreign workers, with Turks (23%), Yugoslav (18%) and Italians (16%) representing the main minorities. However, it is important to note that family reunions (with spouses and children under sixteen years old) were still allowed (Heckmann, 1995). Against the government's expectations, the immigrants did not want to lose their jobs and, rather than leaving, they sought to sponsor the entry of their wives and children. As a consequence, the foreign population rose and its composition shifted from workers to dependents (Constant and Massey, 2002). This fostered the creation of a large second-generation. In terms of the theoretical model presented in section 2, the Anwerberstopp fostered permanent settlement, pushing immigrants with stronger commitment to their native culture to stay in Germany, and possibly convey their cultural traits to the second generation.²⁰ Galli and Russo (2019) find evidence of lower cultural integration of second-generation children whose parents were subject to the Anwerberstopp. We now want to test if the Anwerberstopp has affected one of the most relevant aspects of the cultural identity, namely, the religiosity of the second generation.

4. Data

In order to assess the effect of the Anwerbestopp on the religiosity of second-generation immigrants, we use data from the European Social Survey, waves 2-10.²¹ This research initiative, established in 2001, is committed to undertaking cross-national surveys through face-to-face interviews every two years,²² with newly selected samples that represent diverse European populations aged 15 and above. To date, a total of 38 countries have participated in at least one round of the survey. This comprehensive survey addresses a wide spectrum of topics, encompassing living conditions, social structures, public opinions, attitudes, and behavioral tendencies. Furthermore, it collects variables related to ethnicity and religiosity, which are particularly relevant and useful for our analysis. In particular, individuals were asked to rate their religiosity (“How religious are you”) on a scale of 1 to 10, where 1 represents the lowest level and 10 the highest level. Figure (A1) illustrates the methodology employed to generate our sample.

The ban imposed by Germany specifically targeted non-EEC (European Economic Community) immigrants, allowing EEC immigrants to freely travel between Germany and their home countries. Therefore, on the basis of father's country of origin, we distinguish a treatment and a control group. The control group includes Italy, France, United Kingdom, Austria, Netherlands, Belgium, Ireland, Denmark and Luxembourg.²³

Figure A2 reports the major source countries of immigrants to Germany both in the overall sample and in the restricted time window 1963–1983 that we used in most estimations. Poland and Turkey are the countries with the largest number of immigrants. We can see that countries in the control group are substantially balanced before and after 1973, while a slight imbalance is present in the treatment. In particular, European countries like Poland or Czechoslovakia have a larger weight before the Anwerbestopp, while Turkey has a larger weight after. This is quite consistent with the historical evidence that movements from European countries started in the 50's, while Turkey signed a recruitment agreement only in 1961. In the robustness checks section below, we explored the robustness of our results by checking whether they hold when larger countries and when countries with sizeable German minorities are excluded from the sample. Individuals are assigned to the control or treatment group depending on the origin of their fathers. The descriptive statistics for our sample are included in Table (A1). Our proxy for the level of religiosity exhibits a mean value of 4.16. The standard deviation of 3.01 indicates a notable degree of variability in religiosity scores across the sample. The majority of individuals, on average 80%, consists of second-generation individuals with non-EEC fathers. Approximately 44% of the individuals were born after the policy year. Gender distribution is relatively balanced, with an average of 49% males.

5. Empirical evidence

5.1 Identification strategy

To capture the effect of the immigration policy on the second-generation immigrants, we use a diff-in-diff model²⁴:

(12)$$Y_{it} = \alpha + \gamma\ast BornAfter_{it} + \delta\ast extraEEC_{it} + \beta\ast Treatment_{it} + \theta\ast X_{it} + \epsilon_{it}$$

Where Y _it is our proxy of religiosity, “Born after” refers to being born after 1973, “extraEEC” indicates the treated group, “Treatment” is the interaction between “Born after” and “extraEEC”, thus the parameter of interest is β. The specification is completed by $\epsilon _{it}$, the error term, and a vector of exogenous controls X _it; namely, gender, year of birth of respondents,²⁵ and dummies for the round of ESS in which individuals were interviewed. Given that the identification relies on the exogeneity of the policy, in the main regressions presented in Table A2, we decided to be conservative and avoid all possible controls that could theoretically be correlated with the treatment. A richer set of hopefully exogenous controls is proposed in the regressions of Table A5.

To establish support for the parallel trends assumption, we examine the average religiosity based on the year of birth in Figure A3, where the averages of religiosity for EEC and extra EEC countries are interpolated nonparametrically using Loess.²⁶ Before the policy year, both groups exhibit parallel trends.²⁷ After 1973, the trend of the treatment (extra EEC) group is reversed, supporting our identification. The observed declining trend in the control (EEC) group aligns with the overall decrease in religiosity observed in all countries represented in our sample. In Figure A4, we illustrate the average religiosity of the natives, along with the corresponding fitted linear trends, for the main countries included in the analysis. The increasing trend in the religiosity of the treatment group contrasts starkly with the pervasive decline we can observe everywhere else. This is consistent with the theoretical framework we have outlined and suggests that the effects of the Anwerbestopp are indeed visible in the second generation of immigrants.

5.2 Results

For our analysis, our favorite time window is 1963–83. We also ran several checks for symmetric and asymmetric windows around 1973. However, we think that the 1963–83 window gives the best trade-off in terms of closeness to the policy year and sample size (namely, 545 observations). The results of our favorite estimation of equation (12) are presented in table (2). In column (1), we employ an ordered probit model, while in column (2), we use ordinary least squares for a more straightforward interpretation. The reported results include standard errors clustered by the father's country of origin.²⁸ For reference, the same estimations with classic and robust standard errors are presented in Table A11. In both estimates, the treatment demonstrates a positive and statistically significant impact at the 5% level. In the linear model, we observe that belonging in the second generation born to non-EEC fathers implies a marginal effect of approximately 1.5 points on the level of religiosity.²⁹ This outcome is in line with our prediction, namely, the Anwerbestopp “forced” to settle in Germany many first-generation immigrants who would have preferred circular or return migration based on their own cultural tastes. These immigrants were characterized by a higher religiosity, which was conveyed to the second generation.

Interestingly, the OLS results provide an opportunity to explore the magnitude of our estimates. In particular, being part of the non-EEC second generation born after 1973 implies a 1.5-point increase in religiosity. With the mean religiosity score standing at 4.16 (Table 1), this point estimate implies a more than 35 percent increase in the levels of religiosity, which indicates a sizable effect. This coefficient might seem large, yet it must be considered that religiosity displays a high variance (Table 1), and a 1.5 point variation would amount to roughly half a standard deviation. Moreover, the small sample size generates a relatively large confidence interval for the causal effect: the 95% bootstrap-computed interval ranges from 0.28 to 2.83, so the true effect could be from five times smaller to twice as large than the estimated value.

Thus, according to our results, an immigration ban in 1973 has contributed to create a population whose religiosity, after half a century, goes definitely against the trend prevailing in both the origin and the destination countries. This finding shows that immigration policies may have far-reaching effects on the structure of the receiving societies, and they should be carefully used for achieving short-term objectives.

Finally, there is a caveat: our results might be subject to a kind of intertemporal external validity problem. In other words, it must be acknowledged that the story we are telling dates back to half a century ago, when communications were difficult and expensive, border controls were enforced even within Europe, there was no Internet, neither low-cost flights or satellite TV. Even English was far from being the popular lingua franca it is today. This background possibly contributed to exacerbate the difficulty of adaptation to the host society, generating ethnic separation and social marginalization. For this reason, it is difficult to argue that current immigration restrictions would yield the same effect. Today, in a sense, the problem is reversed: it is the ease of communication and transporting cultural consumption across borders that may delay the integration. To be more precise, we do not know the net effect of the ease of traveling and communicating on the incentives to integration. This is an open question both theoretically and empirically, which we are eager to address in future research.

6. Robustness

6.1 Alternative time frames

To ensure the robustness of our findings and demonstrate their independence from the chosen time frame, we estimate Equation (12) applying different window configurations (symmetric and asymmetric) around 1973. Again, we use our baseline regression model, incorporating clustered standard errors based on the father's country of origin. Table (A3) shows a matrix with symmetric windows positioned along the main diagonal. Each cell presents the parameter of interest, sample size, and standard errors. We employ a color-coding system to indicate the significance level (1%, 5%, 10%). It is worth noting that, with a few exceptions, the magnitudes of these parameters remain consistently stable. Most of them exhibit high or medium statistical significance, as indicated by the blue shading.

6.2 Placebo regressions

To assess the significance of the policy year, we conduct placebo regressions by changing the policy year. The results are presented in Table (A4). In column (1) we employ a symmetric window of ±10 years around the counterfactual policy year 1963. In Column (2), we restrict our sample to focus on the period before 1973 and use a symmetrical window spanning ±6 years around 1967. This year provides a suitable alternative, because it corresponds to a recession, which caused a notable decrease in arrivals to Germany (Jennissen, 2014). The estimates on the coefficients of interest are not significant; generally, signs are even negative for the two counterfactual policy years before 1973.

6.3 Religious affiliation and contextual effects

As an additional robustness check, we estimate Equation (12) by including variables for the region of residence (länder), religious affiliation, and their interactions with the policy year. The classification of the treatment and control groups remains based on the father's country of origin. The findings for the coefficient of interest, as presented in Table (A5), consistently align with those in Table (2).

In Column (1), we introduce region-specific interview dummies to account for unobserved regional heterogeneity. Notably, the coefficient associated with the treatment closely resembles our baseline regression in both sign and statistical significance (5%). Column (2) presents the coefficients for religious affiliations, with “non-religious” as the reference category. Remarkably, all coefficients of religious affiliations are positive and statistically significant at the 1% level.

In Column (3), we add region of residence dummies to the religious affiliations. The results remain consistent in terms of sign and significance, keeping significance at the 1% level.

Column (4) examines the interaction between religious affiliation and dummy variables indicating birth before and after 1973. All coefficients are positive and statistically significant at the 1% level, except for ‘other religion”, which is insignificant.

Finally, Column (5) replicates the estimations from Column (4) while incorporating residence dummies. Once again, sign and significance of the coefficients are preserved.

6.4 Alternative rules of inclusion in treatment and control groups

In table A6, we introduce alternative criteria for defining the treatment and control groups. In Column 1, we distinguish second-generation immigrants on the basis of the mother's country of origin. The coefficient of interest is very similar to the one obtained by using the father's country of origin and is strongly significant. In this estimation we clustered on the mother's country of origin.

In Column 2, we further refine our analysis by restricting the sample to households with both parents coming from the same country. Despite a considerable reduction in the sample size, the results are confirmed, though significant at the 10% level. Remarkably, the estimated coefficient is almost twice as large than in the cases when only one parent is considered, suggesting, as one can expect, that cultural transmission is more effective when both parents share the same background.

Finally, in Column 3, we include in our sample all the individuals with at least one parent of foreign origin.³⁰ The sample is larger than the one used in the main estimations. The coefficient of interest does not change substantially and is highly significant.

6.5 Ethnic Germans

In Column 4 of table A6, we run an estimation excluding countries with sizeable German minorities³¹ to check whether our results depend on the repatriation of ethnic Germans. The estimated effect is slightly reduced, but significant at the 5% level.

6.6 Pre-treatment effect

A possible source of bias in the estimated causal effect of the Anwerbestopp could be due to some sort of “pre-treatment” effect in our data.³² It is in fact possible that some immigrants whose children were born before 1973 were planning to return to their origin country, but changed their mind after the Anwerbestopp. Due to this phenomenon, though the immigrants’ decision was actually affected by the policy in 1973, our identification strategy, based on the year of birth of their offspring, could lead to observe a change in the response up to a few years before.

In principle, this possibility does not invalidate our strategy, which only requires that the Anwerbestopp affects the average home-bias of the treatment group. However, this pre-treatment effect could introduce some downward bias in our estimates, as some treated units are coded before the policy year.

It is difficult to assess how important this problem is in practice. In the first place, we notice that, as mentioned in section 3, the guest workers were initially subject to the rotation principle, under which they were assigned renewable yearly work permits tied to a specific job and employer. At the beginning, these workers were mostly unaccompanied young men. In the 60's, as the labor shortage became permanent, the rotationprinzip was basically dismissed. Work permits were extended, and those who wanted to settle permanently raised their families in Germany, attesting their integration into the German society (Constant and Massey, 2002). However, just because mobility was free, it is still possible that some families who were planning to return were locked in by the Anwerbestopp.

If we assume that families with children older than 6–7 had decided to settle in Germany many years before, we can guess that this effect mostly concerned families with children no older than 5–6 years in 1973. Thus, we ran an estimation excluding individuals born from 1968 to 1973. This robustness check should hopefully eliminate most of the pre-treatment effect due to this mismatch. Results are shown in column 5 of table A6. The estimated treatment effect is very similar to the one resulting from the full sample suggesting that this pre-treatment effect either is of limited magnitude or not present at all.

6.7 Effects of single countries

As shown in figure A2, the distribution of origin countries in our sample is uneven, with a few countries representing a large proportion of the individuals. To ensure that our results are not influenced by the immigration from a single major country, we removed the six most frequent origin countries one at the time in the ordered probit regressions of table A7. Though of course sample sizes and estimates display some variation, the sign of the estimated effect is unchanged and there does not seem to be a single country that drives our results, which look robust from this point of view.

6.8 Alternative measures of religiosity

Finally, we used questions about participation in religious events and the frequency of pray to obtain two alternative measures of religiosity. On a scale ranging from 1 to 7, individuals were asked two questions: “how often do you attend religious services?” and “how often do you pray?”. The response options are: never (1); less often (2); only on special holy days (3); at least once a month (4); once a week (5); more than once a week (6); every day (7). The alternative measures are named, respectively, “Participation” and “Pray”.

In Table (A8), we present the correlation coefficients (Spearman's correlation) among the three indicators of religiosity. There exists a moderate positive relationship between personal religiosity and the frequency of participation in religious events, with a correlation coefficient of 0.633. Furthermore, the correlation between religiosity and the frequency of prayer is even stronger, measuring 0.740.

Table (A9) presents estimations of equation (11) with “Participation” and “Pray” as dependent variables, using the same format as in the baseline estimation (Table A2). The coefficients of interest show positive and statistically significant results at the 5% level for both variables.

6.9 Different clustering variables

In most of our estimations, we decided to cluster on the father origin because we assumed that the unobservables which drive both religiosity and the intensity of cultural transmission can strongly depend on the cultural background of the immigrant. The country effect based on the origin of the father seems a suitable proxy for this cultural background. In table A10, we cluster on other possibly relevant sources of group correlation in the residuals, such as the mother's country of origin, the religious affiliation of respondents, their year and decade of birth and the ESS round. Results of course vary, but the significance of the treatment estimates is comparable. A possible exception is given by the clustering performed on birth year and ESS round. Here, we obtained suspiciously low p-values for the significance of the treatment. Though we present these results anyway, we think they are unreliable, possibly due to a failure or the bootstrap algorythm.

7. Conclusions

The socioeconomic integration of the second generations is crucial for supporting the welfare state, the economic growth, and the long-term social cohesion of the multi-cultural societies of most OECD countries. In this view, cultural integration is not only a necessary complement of economic integration, but even a prerequisite. What is the effect of immigration policies on this process? The cultural integration of foreign-born children crucially depends on parental decisions. By a straightforward application of the Lucas critique, we showed that immigration policies affect the size and the characteristics of the pool of immigrants. In particular, theoretical considerations and empirical findings suggest that restrictions on immigration push individuals with a stronger commitment to their native culture to settle and reproduce abroad. To the extent that these individuals convey their culture to the second generation, restrictive immigration policies foster the diffusion of cultural traits and bias the intergenerational process of cultural integration. We exploited the major natural experiment occurred in Germany in 1973, which provides a unique opportunity to investigate the consequences of immigration restriction. We found that the descendants of treated immigrants show higher religiosity. This adds further evidence to the initial results in Galli and Russo (2019) and is important for two reasons: (1) in the literature, religiosity is associated with lower propensity to migrate (Docquier et al., 2020; Falco and Rotondi, 2016; Myers, 2000). Higher religiosity in the second generation confirms that first-generation immigrants who suddenly lost the possibility of moving back and forth were somewhat “forced” to settle in Germany. (2) Religiosity is a major component of the cultural identity, and its transmission confirms the immigrants’ will to preserve the origin culture. Though this does not imply any antagonism with the receiving society, it shows a distortionary long-term effect of restrictive immigration policies.

We are aware that the social and economic conditions in 1973 were quite different than today —not to mention the ease of movement and communication- and that our results cannot be generalized to the present times. However, at least they show that immigration policies can have very far-reaching effects, which can be unexpected to short-sighted policymakers, and show up after decades. In a globalized labor market, more open immigration can reduce distortions in the self-selection of immigrants and, possibly, in the intergenerational integration process. Similar policies were successfully used in the past, and include for instance, free movement agreements between countries,³³ dual citizenship, and permanent or indefinitely renewable residence permits.