1 Introduction

Ten years ago Putnam (2000) stired the American social and political debate describing the changes of several indicators of US social capital (SC) across the previous 30 years. Putnam claims that, since the 70s, the American society has been experiencing a drop in social relationships and in its system of shared values and beliefs.

These findings raised a considerable debate involving the media, politicians, the public opinion as well as the academic world. Indeed, much of the subsequent research aimed at testing Putnam’s evidence. Although the debate is still open, the current state of the literature confirms the decline of US SC.Footnote 1

This evidence raises an urgent question for modern societies: is this erosion a general feature of western societies or is it rather a characteristic aspect of the American one? The answer is controversial. Some recent contributions suggest that the trends of SC in European countries are following various patterns (Morales 2004; Adam 2008; Sarracino 2010, 2011).

Looking at trends between 1980 and 2002 from the World Values Survey (WVS) and the European Social Survey (ESS), Morales (2004) concludes that it is not possible to clearly state whether the general levels of SC have been increasing or decreasing.

Adam (2008) uses trends of generalized trust and membership in voluntary organizations as proxies of SC. He adopts data from WVS in the period 1980–2000. The author finds evidence of a non eroding SC in Europe even if he warns about signs of decline as well as improvement: Adam highlights a decline in trust in individuals and a more complex, but on average positive trend of associational involvement.

Finally, Sarracino (2010) studies the relationship between SC and subjective well-being trends across Europe using data from the WVS and the European Values Study (EVS). The trends from 1980 to 2000 of four different set of proxies of SC observed in eleven western European countries show a persistent loss of confidence in the judicial system, in religious institutions, in armed forces and in police. In the same period, participation in various kind of groups and associations and trust in others increased in many countries.

These results confirm previous findings suggesting that SC follows various patterns across time. In this framework the evidence about Great Britain is worth mentioning. Results suggest that this is the European country—among the considered ones—with the worst trends of SC: 14 out of the 15 adopted proxies have been declining between 1980 and 2000 (Sarracino 2010). This evidence has been further confirmed in subsequent analysis adopting longer time series and a larger sample of countries (Sarracino 2011).

Figures about the trends of SC suggest that two of the richest countries in the world, US and Great Britain, are following negative and significantly different trends of SC than other western societies. Hence, my first research issue is whether this erosion is a legacy of the richest countries in the world.

But this point raises also a second related research question. Some recent works by Bartolini et al. (2011, 2012) and Bartolini and Sarracino (2011) show that the erosion of SC in US resulted in a significant shrinking of people’s well-being. The decomposition of the effects of several variables over subjective well-being (SWB) points out that SC—and particularly relational SC—accounts for a large share of the overall SWB variation. Data from the US General Social SurveyFootnote 2 reveal that, to compensate for the negative effect of the erosion of SC on SWB (keeping SC stable at its 1975 level), the yearly growth rate of US GDP had to be over 10 %. This evidence explains the Easterlin paradox giving SC a new role: a higher income increases happiness as long as it does not undermine SC.

Moreover, Bartolini and Sarracino (2011) show that the correlation between SC and SWB trends is stronger than the one between SWB trends and GDP growth. This evidence makes present research question more intriguing: if the richest countries in the world are characterized by eroding SC and stagnating SWB (Easterlin 1974; Easterlin and Angelescu 2009; Easterlin et al. 2010), is economic growth failing to provide a higher well-being? In other words, my second question is: are people in richest countries destined to unsatisfactory, but rich lives?

To answer my questions, this article explores the relationship between SC and SWB trends in Luxembourg. Despite its small dimensions and its many peculiarities (the small population size, the high share of migrant workers as well as its special status of city-state), Luxembourg is one of the countries with the highest income per capita.Footnote 3 It is, therefore, an interesting subject to test whether the erosion of social capital is a common feature of the wealthiest countries in the world.

But there are also other aspects making Luxembourg an interesting case for study. First, because of the scarcity of data and probably the small dimensions of this country, the literature neglected it and we do not know much about its SC. Present study tries to fill this gap. Second, Luxembourg represents a peculiar experimental case because it is a country in which 40 % of the population is immigrant, with a highly heterogeneous economic, social and cultural background. About 50 % of the total labor force comes from neighboring countries crossing Luxembourg’s borders every day. The mix of these elements raises strives and tensions that are currently common to many other European countries and that are liable to hinder both people’s well-being and the accumulation of social capital. Therefore, although Luxembourg is in many regards an exception, it is an interesting experimental case to test whether people in rich countries are destined to wealthy but unsatisfactory lives. Its various social fabric—and particularly the high percentage of migrants with their different backgrounds (blue and white collars, low and high skilled, European and non European)—allows us to test the relationship between SC and SWB in more detail.

Finally, the recently released EVS 2008 data, containing observations on SWB in Luxembourg, allows the first assessment of how well-being changed in this country between 1999 and 2008.

To answer my questions I will contrast the trends of SC and SWB in Luxembourg with the ones from a set of other Western European countries. The comparison has a twofold goal: first, to interpret the figures about Luxembourg in relation to the broader picture offered by other European countries;Footnote 4 second, checking whether the trends for Luxembourg are an exception in the European landscape. In case the erosions of SC and of SWB are a specific feature of the richest countries in the world, I expect to find stark contrasts between the trends for Luxembourg and its neighbouring countries. Alternatively, if the decline in SC and SWB is just a feature of some societies, I do not expect to find significant differences among European countries and Luxembourg. However, the features characterizing Luxembourg require prudence in drawing conclusions from these comparisons.

The main results of my research are the following:

  • between 1999 and 2008, Luxembourg experienced a substantial increase in almost every proxy of SC. These trends are largely in line with those characterizing other western European countries;

  • the erosion of SC is not a legacy of the richest countries in the world: the way economic systems are organized affect their social and well-being outcomes. Therefore, economic performance can be compatible with a rich social environment and well-being;

  • considering the relationship between SC and SWB within Luxembourg, both endowments and trends of the various proxies differ significantly between nationals and immigrantsFootnote 5:

    • immigrants report rising trends of trust in other people, while natives report stagnating trends. However, differences in levels between the two groups are not significantly different when compared with the average EU levels;

    • Luxembourg is characterized by high levels of confidence in institutions such as: social security system, education, judicial system and police. However, nationals report lower levels of trust in religious institutions, armed forces and labour unions than other EU citizens. Levels of confidence in press, the parliament and major companies are in line with the European average;

    • Luxemburgian people share a substantially higher participation in groups and associations than immigrants;

    • the vast majority of the positive trends of confidence in institutions in Luxembourg is driven by immigrants;

    • nationals report on average higher levels of satisfaction with their life than immigrants. Accordingly, trends of subjective well-being are growing for the first group, while decreasing for the second one.

The paper is organized as follows. The next section describes the data adopted for the research, whereas some methodological aspects are presented in Sect. 3. Section 4 describes the changes over time of SC and SWB for Luxembourg and contrasts these results with the average trends of other Western European countries. Subsequently, the relationship between SC and SWB is further explored within Luxembourg distinguishing between natives and immigrants. This issue is the topic of Sect. 5, while the last one will draw some concluding remarks.

2 Data

The main limit of present work is the availability of comparable data on SC and well-being over time for Luxembourg. Only a few data-sets provide repeated and cross-country comparable observations for a wide range of proxies of SC over time and only one contains information about Luxembourg over a reasonable time span. Therefore, for the purposes of present study I adopt data from the European Values StudyFootnote 6 (EVS), a rich source of data on SC and SWB allowing an assessment of the evolution of these two variables for Luxembourg over a period of 9 years—from 1999, when this country was first surveyed, to 2008. The sample size in this case amounts to 1,211 people in 1999 and to 1,610 people in 2008. To avoid sample size bias, data are weighted by the population weight thus making the two waves comparable.

An important feature of the EVS is that it provides comparable information also for other western European countries thus allowing to compare Luxemburgian trends with the European ones. Given the focus of the present study, the sample available for the analysis is limited to the two waves when both SC and SWB proxies have been surveyed in Luxembourg—i.e. the fourth (1999–2001) and the fifth (2005–2009) waves. Countries satisfying this requirement are: Austria, Belgium, Denmark, Finland, France, Germany, Great Britain, Greece, Ireland, Italy, Malta, The Netherlands, Portugal, Spain and Sweden. The last wave of the EVS does not contain any information about Great Britain, Italy and Sweden. To include these three countries, data have been retrieved from the fifth wave of the World Values SurveyFootnote 7 (WVS). EVS and WVS are two wide compilations of surveys collected in more than 80 countries representing more than 80 % of the world’s population. They collect information about socio-cultural and political changes on randomly selected samples of 300 to 4,000 individuals per country. In particular the two data-sets provide information on “individual beliefs about politics, the economy, religious, social and ethical topics, personal finances, familiar and social relationships, happiness and life satisfaction”.Footnote 8 EVS data have been collected in four waves from 1981 to 2008 every 9 years, while WVS has been administered in five waves (1981–1984; 1989–1993; 1994–1999; 1999–2004 and 2005–2007).

Descriptive statistics concerning the observed countries and the missing observations about SC and SWB proxies are available in Table 2, Table 3, Table 5 and Table 6 in the “Appendix”.Footnote 9

In present work I refer to SC as “the stock of both non-market relations and beliefs concerning institutions that affect either utility or production functions.” Footnote 10 which is an operating definition in line with the one adopted by Putnam (2000) and the OECD (2001). Indeed, the authors adopt Putnam’s framework (i.e. networks, norms and trust) comprising all those aspects—material and immaterial—that can contribute to develop mutual trust and co-operation. They emphasize two main features of SC. The first one is non-market relationships among individuals that allow people to communicate with each other and to develop mutual trust. This aspect is referred to as relational SC and can be further articulated in intrinsically and extrinsically motivated relational SC. They define intrinsic SC (alternatively defined as relational goods) those elements “that enter into people’s utility function”; and extrinsic SC those components that do not “directly enter into people’s utility functions but are instrumental to something else that may be considered valuable”.Footnote 11

The second one is the system of values or beliefs that makes people act consistently and that is usually labelled non relational SC. Table 1 provides a summarizing scheme of the various components of SC.

Table 1 Summarizing scheme of the different constituents of social capital
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Accordingly, and in line with the majority of the empirical literature on SC (Paxton 1999; Costa and Kahn 2003; Van Schaik 2002), I proxy the beliefs component through several reports of confidence in institutions, namely armed forces, police, parliament, civil services, press, religious, judicial system, education system, labour unions and major companies. Answers to these questions range on a 1–4 points scale going from none at all to a great deal. To measure non-market relations, I use trust in individuals, membership and unpaid voluntary work in various groups and organizations.Footnote 12 Detailed descriptive statistics on membership and unpaid voluntary work by year and by country are provided in the “Appendix” (see Tables 7, 8, 9 and 10). Two new dummy variables have been created: one for group membership and the other one for unpaid voluntary work. Both variables are set equal to 1 if the respondent performs at least one of the mentioned activities and 0 otherwise.

SWB is proxied by reported life satisfaction, a variable ranging from 1 = “dissatisfied” to 10 = “satisfied” depending on the answers to the following question: “all things considered, how satisfied are you with your life as a whole these days?”. In principle, these data-sets provide also another proxy of subjective well-being, namely reported feelings of happiness. However, for the purposes of this article I will focus only on life satisfaction. The reasons are mainly two: first, life satisfaction is reported on a ten points scale, whereas happiness is on a four point scale. The former is supposed to provide a better and more differentiated information than the second one. Second, although the evidence from the two variables is usually consistent, it is commonly held that happiness provides a more emotional measure of well-being. On the contrary, life satisfaction reflects a more cognitive evaluation of well-being and is therefore regarded as more reliable (Diener 2006).

A major issue in this context is the availability of some of the proxies of SC and missing data. Information about confidence in political parties are completely missing for the fourth wave. The same survey misses data on confidence in political parties, educational system, social security system, judicial system and major companies for Sweden. This aspect reduces the possibilities to compare SC in Luxembourg with the one in other European countries, but does not hinder present econometric analysis since these data are missing completely at random.Footnote 13 As such, they are not liable to bias estimates.

Tables 2 and 3 inform that in 1999 some data for Luxembourg are missing. The problem concerns mainly proxies of non-relational SC: the last column on the right reports percentages of missing data. It informs that 10–12 % of the respondents didn’t provide data on confidence in political parties, labor unions, civil service, parliament and major companies. Unfortunately, given the subjective character of such variables, imputing the missing data requires strong assumptions that may easily result arbitrary. For that reason and considering the limited number of variables involved, I consider a safe choice using data as such, being prudent in drawing conclusions.

Table 2 Descriptive statistics for Luxembourg—1999
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Table 3 Descriptive statistics for Luxembourg—2008
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For what concerns remaining variables, the percentages of missing observations are much smaller and, according to the majority of the literature on missing data,Footnote 14 they are negligible.

3 Methodological Aspects

To study SC and SWB trends between 1999 and 2008 in Luxembourg, I adopt a very simple methodology regressing the proxies of SC on a “time” variable containing the years 1999 and 2008 (Aguiar and Hurst 2006).

Regression techniques to estimate the coefficient of time change depending on the nature of the dependent variable. Provided that the aim of present work is to evaluate the evolution of SC and SWB in Luxembourg and to compare it with other western European countries, I adopt a probit model with robust standard errors reporting marginal effects. Hence, in case of a dummy variable (i.e. trust in others and membership or unpaid voluntary work in groups and organizations) the resulting equation is:

$$ SC_{i} = \left\{ \begin{array}{ll} 1 & \hbox{if } z_{i} > 0, \\ 0 & \hbox{if } z_{i} < 0, \end{array}\right.\\ $$
(1)

where the index i stands for individuals; SC i are the individual dichotomous proxies of SC; and \(z_i = TIME_{i} \cdot \beta + \epsilon_{i}, \epsilon_{i} \sim N(0,1)\).

This model is repeated for each country separately.

In case of an ordered dependent variable taking discrete values [i.e. confidence in institutions (from 1 to 4) and satisfaction with life (from 1 to 10)] the most suited regression techniques are ordered probit or logit (see Ferrer-i Carbonell 2005). In this case I opt for an ordered probit model with robust standard errors reporting marginal effects. Assuming that the dependent variable is ordered in K different categories, the resulting model is:

$$ Y_{i} = \left\{ \begin{array}{ll} 1 &\hbox{if } z_{i} \leq 0, \\ 2 &\hbox{if } 0 < z_{i} \leq c_1, \\ 3 &\hbox{if } c_1 < z_{i} \leq c_2, \\ \vdots &\\ K & \hbox{if } c_{K-1} < z_{i}. \\ \end{array}\right. $$
(2)

where 0 \(< c_1 < c_2 < \cdots < c_{K-1}\); the index i stands for individuals; Y i stands for the various ordered dependent variables; \(z_{i}=TIME_{i} \cdot \beta+\epsilon_{i}, \epsilon_{i} \thicksim N(0,1)\) and c K−1 are unknown parameters to be estimated.

Also in this case, I run a separate regression for each country.

In both models 1 and 2 I have included population weights to allow the comparability of samples in the two waves. Marginal effect of the coefficient of the TIME variable reflects the slope of the line that best fits the distribution over time of its observations. Hence, they can be interpreted as the average yearly change of the dependent variable.

To check whether the trends from Eqs. 1 and 2 are not the outcome of peculiar unobserved individual or social features, I run a further set of regressions including different groups of socio-demographic control variables. These are: age and age squared/100; gender; number of children; religiosity; marital and professional status and educational level. This is a standard set of control variables in this kind of studies. Their effects on SWB have been largely studied in previous works (Blanchflower and Oswald 2008, 2004; Oswald 1997; Clark and Oswald 1994) and they are usually included to account for individual unobserved heterogeneity. In particular, age squared/100 is included to control for eventual non-linearities in the relationship between age and well-being. Dividing the squared term by 100 makes the interpretation more intuitive: whenever the coefficients of the two age variables are equal and of opposite sign, than the low point of the U-curve happens to be at age 50. A control for the religiosity of the respondent is included because, as clearly put forward by Lim and Putnam (2009), attending the church enhances people’s well-being by promoting participation in religion related groups. To account for these differences I included a dummy variable set to 1 if the respondent declares to attend religious services at least once per month, 0 otherwise.

Overall, results from the univariate regressions are robust to the inclusion of all the listed variables.Footnote 15 This evidence suggests that the trends of SC and SWB are independent from the specific socio-demographic composition of the sample.

4 Results

I report and discuss results from several regressions relative to Eqs. 1 and 2. Marginal effects of the TIME variable over SC and SWB proxies are summarized in Table 4, while detailed estimates are reported in Tables 11–26 in the “Appendix”.

4.1 Trends of Relational Social Capital

The first three lines of Table 4 report marginal effects of coefficients for three proxies of relational SC in Luxembourg and for a sample of western European countries. Figures suggest that between 1999 and 2008 Luxembourgians increased their participation in groups and associations and trust in others raised. However, a more careful analysis unveals some peculiar patterns.

Between 1999 and 2008 the number of people in Luxembourg declaring to trust other people increased on average by 0.005 points on a 0–1 scale. That is to say a 0.5 % increase each year. This result is in line with what has been happening on average in western Europe: in the same period, the percentage of European citizens declaring to trust others increased by 0.4 % on an yearly basis.

Figure 1 reports average levels of the three proxies of relational SC in 1999 and 2008 showing that levels of trust in others in Luxembourg are steadily lower than the average European one: in 1999 25 % of people in Luxembourg declared to trust other people and in 2008 this amount increased to 31 %. These levels are significantly lower than the European average: 36 % in 1999 and 39 % in 2008.

Fig. 1
figure 1

Average levels of relational social capital proxies for Luxembourg and western European countries. Proxies are listed on the x-axis. From left to right, the chart reports membership in groups and associations, unpaid voluntary work in groups and associations and trust in others. The y-axis ranges on a 0–1 scale reflecting the original scaling of each variable

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Table 4 Trends of SC and SWB proxies for Luxembourg and for a sample of western European countries
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Overall, trust in others has been increasing in all western Europe. In this context, Luxembourg shows lower endowments, but stronger growth rates.

At the same time, people in Luxembourg increased their participation in groups and associations: both variables of membership and unpaid voluntary work in groups and associations increased in the considered period (+0.5 and +1.3 % respectively). This figure is at odds with what other European countries have been experiencing. Coefficients in the second and third line of Table 4 suggest that in the same period European countries experienced a decrease in membership (−0.8 %) and in involvement in unpaid voluntary work (−0.4 %). In 1999 the levels of both variables for Luxembourg and, on average, for Europe were very close: 58 % of people in Luxembourg declared to be member of at least one group or organization versus an European average of 56 %. Similarly, 30 % of Luxemburgian people were performing unpaid voluntary work versus an average of 32 %. From this point onward, the trends diverged: they have been shrinking for most western European countries and increasing for Luxembourg (see Fig. 1).

Between 1999 and 2008 Luxemburgian active participation in groups and associations grew up about three times faster than the European one. In a period of widespread decline of involvement in groups and associations, Luxembourg is characterized by positive trends.

4.2 Trends of Non-relational Social Capital

The remaining lines of Table 4 consider the evolution in time of non-relational SC as proxied by confidence in institutions.

Data suggest that confidence in religious institutions significantly declined all over western Europe. The rate of this decrease appears to be higher in Luxembourg than in other European countries. It is worth recalling that variables about confidence in institutions vary on a 1 to 4 point scale. In this case an yearly decrease by −0.013 points means a drop by −0.32 % per year.

In the same period, confidence in armed forces, educational system and labor unions stagnated. In all these cases variations across time are not significantly different from zero, suggesting a flat trend. However, this doesn’t lead to the conclusion that Luxemburgian people have low levels of trust in these institutions. Figures 2 and 3 show that levels of confidence in armed forces and in labour unions are generally low, while people reveal to have quite high levels of confidence in the educational system. This figure is in line with the western European average.

Fig. 2
figure 2

Average levels of non-relational social capital proxies for Luxembourg and western European countries. Proxies are listed on the x-axis. From left to right, the chart reports confidence in: religious institutions, armed forces, police and educational institutions. The y-axis ranges from 1 (not at all) to 4 (a great deal) following the original scaling of each variable

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Fig. 3
figure 3

Average levels of non-relational social capital proxies for Luxembourg and western European countries. Proxies are listed on the x-axis. From left to right, the chart reports confidence in: press, labor unions, political parties and parliament. The y-axis ranges from 1 (not at all) to 4 (a great deal) following the original scaling of each variable

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On the other side, between 1999 and 2008 confidence of Luxemburgian people in political parties raised by 0.023 points per year, an increase of about 0.57 %.Footnote 16

Finally, all the remaining institutions report positive and significant trends. In particular, the most impressive trend is the one of confidence in social security system. This institution is by far the most successful in Luxembourg ranking well above the European average: in 1999 17.4 % of respondents declared to be highly confident in social security system. This percentage jumped to 32 % in 2008. At the same time the percentage of those declaring to have only a few or not at all confidence in this institution dropped by 25 % in 1999 to 13 % in 2008. Overall, the average annual growth of confidence in social security system is about 1.15 %, almost three time higher than the European average (0.35 %).

At the same time also confidence in civil service, judicial system and political parties have been increasing significantly and well beyond the average European growth rate. The percentage of people declaring to be very confident in Luxemburgian civil service rose from 58 % in 1999 to 70 % in 2008, while those declaring to have low levels of confidence went from 40 to 29 %. Overall, confidence in this institution has been growing by 0.65 % on a yearly basis (Fig. 4).

The years between 1999 and 2008 in Luxembourg are also characterized by a strong growth of confidence in the judicial system (on average 0.67 % per year). In this case, the growth rate is almost two times higher than the European average. Furthermore, in 1999 the percentage of respondents declaring to trust a lot or quite a lot the judicial system was 60 % versus an European average of about 49 %. In the same period those declaring to have low levels of trust in justice were 40 % in Luxembourg and 41 % in Europe. Almost ten years later, the group of people trusting this institution increased to 70 % in Luxembourg and 57 % in Europe, while those not trusting it reduced to 30 and 49 %, respectively.

In line with the trends of other European countries, Luxembourg experiences also an increase of confidence in police with an annual growth of about 0.35 %. This growth is only slightly lower than the European average (0.42 %).

Finally, in a period characterized by declining European trends of confidence in major companies and in press, Luxemburgian trends increase on average by 0.26 % per year.

Following some recent results from SWB literature pointing to a positive correlation between SC, particularly relational SC, and SWB trends, we should expect that also Luxemburgian SWB should have increased over time (Helliwell 2008; Helliwell et al. 2009; Becchetti et al. 2008, 2009; Bartolini et al. 2012).

Surprisingly, the evidence contradicts this hypothesis: the last line of Table 4 shows that the trend of SWB in Luxembourg is not significantly different from zero. This seems to confirm that rich countries are destined to stagnating trends of well-being and that SWB trend is independent from SC trends. However, this is not all the story: while the literature suggests that economic growth is accompanied by the decline of SWB and the erosion of SC, Luxemburgian SC flourishes. There is something more here to be explained.

5 Differences Between Immigrants and Luxemburgian People

Figures from Tables 11–26 provide some information to look deeper into this puzzle. Besides the coefficient of the time variable, some control variables are showing peculiar patterns common to all the proxies of SC and SWB.

In many cases we find a U-shaped relationship between some proxies of SC and age. This is the case of trust in others, membership and unpaid voluntary work in groups and associations, confidence in religious institutions, in armed forces, in educational system, in major companies and judicial system. These figures suggest that SC reduces during the early stages of life reverting in late adulthood.

Consistently with the literature, the same relationship arises between SWB and age. Indeed, even if the age variable in Table 26 is not significant, its squared term/100 is significant confirming the U-shaped relationship. This result is summarized in Fig. 5 reporting the scatterplot of predicted values of SWB and age and their curvilinear relationship.

Fig. 4
figure 4

Average levels of non-relational social capital proxies for Luxembourg and western European countries. Proxies are listed on the x-axis. From left to right, the chart reports confidence in: civil services, social security system, justice system and major companies. The y-axis ranges from 1 (not at all) to 4 (a great deal) following the original scaling of each variable

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Fig. 5
figure 5

U-shaped relationship between predicted values of life satisfaction and age

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Moreover, being a woman is significantly and negatively correlated with participation in groups and associations and confidence in civic service, major companies and political parties.

The educational level of the respondent is in many cases significantly correlated with SC proxies. For example, people with secondary or higher level of education report on average higher trust in others and participation in associational life (see Tables 11, 12 and 13). By the same token, education is often negatively correlated with confidence in institutions. More educated people are less confident in armed forces and in religious institutions, while reporting higher trust in the parliament. Education is negatively correlated with confidence in labour unions, police and major companies. People with lower levels of education are less confident in the judicial and the social security systems. Interestingly, confidence in educational system is negatively correlated with the educational level of the respondent. The higher the educational attainment, the less negative is the confidence.

Among the proxies of professional status, belonging to military professions or being a student is highly and negatively correlated with confidence in educational system (see Table 16). Similarly, being a student, a white collar or a trader is positively correlated with trust in others and membership in groups and associations, while only being a student is correlated with voluntary activities. People with handicap report less confidence in religious institutions, while being an unskilled worker is positively correlated with higher confidence in armed forces. Civil servants, students and unskilled workers report higher confidence in civic service. Finally, almost all categories excluding military professions are positively correlated with confidence in major companies and subjective well-being.

A more interesting pattern arises if we consider correlations between being immigrant, SC and SWB. In this case, data suggest that there aren’t significant differences between nationals and immigrants in the endowments of trust in others and confidence in labour unions. On the contrary, being immigrant is significantly and negatively correlated with participation in groups and associations (−0.24), unpaid voluntary work (−0.22), confidence in political parties (−0.14) and SWB (−0.26). These relationships hold even after including control variables.

Correlation with lower levels of relational SC can be explained in many ways. A plausible one is that people coming from abroad have more difficulties in building networks of relationships and actively participating in the social life of a new country. Also the result about political parties may reflect the fact that immigrants are less involved in local social and political life.

Some other patterns are also worth mentioning: being immigrant is positively correlated with 11 out of 12 variables of confidence in institutions. Immigrants are significantly more confident than natives in religious institutions, armed forces, educational system, press, police, parliament, civic service, social security system, major companies and judicial systems.

Summarizing, being immigrant is positively correlated with confidence in institutions and negatively correlated with relational proxies of SC and with SWB.

These differences cast the doubt that the evolution of SC and SWB over time might be different between natives and immigrants. Differences in levels may imply differences in trends.

To provide some insights in this regard I run a further set of regressions in which I include among the regressors the interaction between the time variable and the immigrant dummy variable.Footnote 17 My aim is to test the hypothesis that the trends of SC and SWB proxies for immigrants are significantly different from the Luxemburgian ones. Formally, I estimate a probit model:

$$ SC_{i} = \left\{ \begin{array}{ll} 1 &\hbox{if } z_{i} > 0, \\ 0 &\hbox{if } z_{i} < 0, \\ \end{array}\right. $$
(3)

where \(z_i=TIME_{i} \cdot \beta+non-Lux_{i} \cdot \beta_{2}+TIME_{i} \cdot \beta_{3} \cdot non-Lux_{i} + X_{i} \cdot \gamma+\epsilon_{i}, \epsilon_{i} \sim N(0,1)\). and an ordered probit model:

$$ Y_{i} = \left\{ \begin{array}{ll} 1 & \hbox{if } z_{i} \leq0, \\ 2 & \hbox{if } 0 < z_{i} \leq c_1, \\ 3 & \hbox{if }c_1 < z_{i} \leq c_2, \\ \vdots & \\ K & \hbox{if } c_{K-1}< z_{i}. \\ \end{array}\right. $$
(4)

  • where 0 \(< c_1 < c_2 < \cdots < c_{K-1}.\)

  • \(z_{i}=TIME_{i} \cdot \beta+non-Lux_{i} \cdot \beta_{2}+TIME_{i} \cdot \beta_{3} \cdot non-Lux_{i} + X_{i} \cdot \gamma+\epsilon_{i}, \epsilon_{i} \thicksim N(0,1) \)

  • \(c_{K-1}\) are unknown parameters to be estimated.

The choice of the model depends on the quality of the dependent variables, X i is a vector of control variables as listed in Sect. 3 and index i stands for individuals. Each model from Eqs. 3 and 4 is run for each country separately. Results are reported from Tables 27–32 in the “Appendix”.

The picture arising is significantly richer than the one resulting from Sect. 4. The interaction term shows that trends of 8 variables out of 16 change their sign. The positive trend of trust in others is entirely driven by immigrants. Similarly, immigrants report increasing confidence in religious institutions, police, press, parliament, civil service and major companies. Between 1999 and 2008, confidence of natives in the same institutions either didn’t significantly change or declined. This is the case, for example, of confidence in educational system whose trend didn’t grow up over time: results in the third and fourth column of Table 29 show that natives’ confidence in this institution has been decreasing from 1999 to 2008, while both the interaction term and the dummy on nationality suggest that immigrants report both positive trends and higher levels of confidence.

This new set of regressions brings about further evidence informing that much of the positive Luxemburgian trends of confidence in institutions is driven by immigrants. This conclusion is contraddicted in mainly two cases: (1) people in Luxembourg, and particularly nationals, experienced an increase in confidence in political parties, social security system and judicial system; (2) membership and unpaid voluntary work show that immigrants have significantly lower levels of participation in social life than Luxemburgian people and, as reported by the interaction term, their trends are not significantly different from zero.

Hence, after controlling for immigrants, the evolution of SC between 1999 and 2008 appears significantly different than before: the various proxies of SC followed different trajectories in different groups of the population. Non relational proxies of SC are performing particularly well among immigrants, while relational SC proxies are considerably growing among natives.

What has been happening to SWB?

Table 32 shows that SWB of natives turns out to be increasing over time. Both the equation with and without controls (columns 1 and 2, respectively) reveal that well-being has been growing up by 1.1 % yearly. Indeed, in 1999 natives declaring to be very satisfied with their life (the top 2 categories) where about 40 % of the total sample. In 2008 this percentage rose to 49 %. At the same time the percentage of those reporting less satisfaction with their life (the bottom 2 categories) basically remained constant (about 1.8 % of the sample).

On the other hand, immigrants have not significantly different levels of satisfaction with their own life, but their trend of SWB is about 1.8 % lower than the Luxembourgian one with a net decreasing trend of about 0.6 % per year.

This evidence suggests a different conclusion. According to the hypothesis formulated at the beginning from the literature on SC and SWB, nationals report growing participation in groups, associations and unpaid voluntary work and, consistently, rising SWB. Immigrants, who are characterized by both lower levels and trends of relational SC, but growing trends of confidence in institutions, report slightly negative trends of satisfaction with their lives. This evidence is compatible with previous results from the literature on SWB pointing out a positive relationship between social connections and SWB. Immigrants may have been enjoying their lives less than their fellow citizens in Luxembourg because they are less involved in the social life of the country.

6 Conclusions

This paper describes the evolution of several proxies of SC and SWB in Luxembourg between 1999 and 2008 using the available information from EVS-WVS data-base. Adopting a very simple regression technique, it contributes to the literature in several ways: (1) it explores the relationship between SC and SWB trends in rich countries testing: (a) whether the erosion of SC is an unavoidable feature of the richest and most modern countries in the world and (b) whether people in rich countries shouldn’t expect any well-being improvements in their lives; (2) providing figures about what happened to the Luxemburgian SC and SWB. Beside these two main aspects, present research provides fruitful information about the Luxembourgian society in several ways: it informs policies aimed at improving people’s well-being; it highlights what are people’s feelings about many fields of social life: schooling, justice, social security, politics and religion. Furthermore, it informs about the differences among all these dimensions within the Luxembourgian society. Finally, even if Luxembourg is in many regards an exception in the international landscape, these results are consistent with the interpretation that the quality of the chosen development path matters for people’s quality of life. In other words, positive economic performances do not necessarily come at expenses of SC and well-being.

The overall result from the analysis of available data betwen 1999 and 2008 depicts Luxemburgian society as rich in various forms of SC, from involvement in social life and activities to trust in others and confidence in institutions. Across the investigated nine years almost every proxy of SC has been increasing, confidence in religious institutions being the only proxy with a negative evolution.

Luxemburgian SC performs very well also when considered in an international perspective. The same analysis run over a sample of 15 western European countries reveals that in the same period various proxies of SC have been following mixed patterns: on average, proxies of participation and social involvement have been decreasing and European citizens have been loosing confidence in religious institutions, press, political parties and major companies.

In the same period, people’s perceived well-being has been decreasing across western Europe, while, for what concerns Luxembourg, the trend doesn’t appear to be significantly different from zero. At a first glance, this evidence stands at odds with previous results from the literature. While European average trends of SC are compatible with worsening people’s well-being, the flourishing Luxemburgian SC should be accompanied by increasing subjective well-being. Unfortunately, this doesn’t seem to be the case.

A deeper analysis accounting for the large percentage of immigrants within the Luxembourgian society reveals that this picture is partial and that SC and SWB trends have to be evaluated in the light of the specific composition of the society. Indeed, both trends and levels of various forms of SC and SWB are substantially different between natives and immigrants. Present results suggest that:

  1. 1.

    the positive evolution of trust in others in Luxembourg is entirely driven by immigrants. Natives do not show any significant increase in this respect;

  2. 2.

    on the contrary, natives have been significantly increasing their participation in social activities and voluntary groups and associations, while immigrants report both lower endowments and non-varying trends of this form of relational SC;

  3. 3.

    the positive trends of confidence in police, press, parliament, civic service and major companies are led by immigrants. Political parties, social security system and judicial system have been gaining increasing trust from both natives and immigrants, with the last group reporting higher coefficients. Two further cases are worth highlighting:

    1. (a)

      confidence in educational system grows up only for immigrants, while the trend turns out to be negative for natives;

    2. (b)

      negative trend of confidence in religious institutions is mainly driven by natives, while immigrants report slightly positive trends.

  4. 4.

    natives enjoy higher levels and growing trends of satisfaction with their lives, whereas immigrants are experiencing decreasing trends.

These results hold also after controlling for differences in the countries of origin and in the patterns of the time profile of migration.

A first conclusion of this work is that various forms of SC grew up in a non uniform way across people in Luxembourg. With the only exception of trust in others, natives enjoy higher participation in relational SC, while immigrants report high levels of trust in institutions, that is to say non-relational SC.

Secondly, this research found further evidence about the positive relationship between trends of SC and SWB. Consistently with previous results from the literature, positive trends of relational SC are associated with growing trends of well-being, while non-relational SC trends are less correlated with SWB trends.

At any rate, the availability of limited time-series data prevents a comparison over a longer time-period and does not allow an analysis of the causes of the variations. Indeed, there can be many possible factors affecting SC: the small dimensions of the country, the low number of inhabitants, its opulence, the institutional framework or even the presence of European institutions. Unfortunately, available data are not sufficient to explore these causal links.

Independently from these constraints, present research pointed out some peculiar features of the Luxemburgian society that are not immediately apparent and provided some evidence compatible with the hypothesis that richer societies are not destined to SC erosion and to unhappy lives. It is possible to envisage social and economic organizations compatible with high economic performances, enjoyable lives and a good social environment.

Still, Luxembourgian system turns out to be imperfect since this society seems to be not inclusive showing a sort of polarization between immigrants and residents. Whether this is a real social issue or just a matter of time is a question requiring a separate analysis. The future availability of longer and possibly richer time-series data will allow researchers to deal with this issue.

Present work just set the scene for broader research questions and provided evidence that Luxembourg represents a peculiar case that is worth studying for the insights it can provide for policy-making.