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.Footnote 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.Footnote 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.Footnote 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.Footnote 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.Footnote 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.Footnote ^11, Footnote ^12, Footnote ¹³ For simplicity, the future is not discounted and returning migrants observe the shock in O only after their return.Footnote 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.Footnote 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).Footnote 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.Footnote 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.

5.1 Identification strategy

To capture the effect of the immigration policy on the second-generation immigrants, we use a diff-in-diff modelFootnote ²⁴:

(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,Footnote 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.Footnote ²⁶ Before the policy year, both groups exhibit parallel trends.Footnote 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.

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, Reference Jennissen2014). 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.Footnote 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 minoritiesFootnote ³¹ 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.Footnote 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, Reference Constant and Massey2002). 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.