Social Capital and Subjective Well-Being

Abstract

Social capital and especially trust are the foundation of most personal relationships and it is considered a key factor of many economic and social outcomes. The purpose of this study is twofold. First, we investigate the links between social capital (trust and voluntary association membership) and life satisfaction. Then, we analyse the impact of the structure of the country wealth on life satisfaction. Our original empirical approach address simultaneously both questions, using a recursive mixed-process model, with bootstrapped standard errors accounting for the sampling design. The role of social capital regarding the well-being of individuals is preponderant, but we underline that the mechanisms at work are not the same for all countries. The process of well-being improvement corresponds to varying models that depend on the country’s initial stocks of capital.

Appendix

The system includes an ordered probit and two binary probit, i.e.

$$\displaystyle \begin{aligned} \begin{cases} y_1= p\ \text{if}\ \tau_{p-1}<y_1^*<\tau_p\ \text{with}\ p=1,\ldots,10, \tau_{0}=-\infty\ \text{and}\ \tau_{10}=\infty\\ z_j= 1\ \text{if}\ z_j^*>0\ \text{and}\ z_j = 0\ \text{if}\ y_j^* \le 0\ \text{with}\ j=1,2\vspace{12pt} \end{cases} \end{aligned} $$

(16.2)

This system of equations is estimated according to the method of simulation of maximum likelihood based on draws from Halton sequences. Standard errors are obtained through bootstrapping at the cluster (country) level using 100 replications. This procedure has been shown to be a convenient way to address the structure of clustered data without relying on the assumptions of multilevel modeling (Cameron et al. 2008) that although traditionally used for cross-sectional data may lead to intractable models in a case of high-dimensional problems (Bartus and Roodman 2014).

The use of bootstrapped standard errors to improve inference reliability. Three differents methods are used : bootstrap samples are taken independently within each stratum. Using the notation of Steele and Goldstein (2006), we have therefore for an individual i in a country j:

$$\displaystyle \begin{aligned} g(y_{r,i,j})=\beta_{r}X_{r,i,j}+u_{r,j}+e_{r,i,j} \end{aligned} $$

(16.3)

with g(.) the probit function, y _r,i,j the response with r = 1 for trust ans r = 2 for association membership. X _r,i,j a vector of independent variables (that can be specific for each response r). We have

We can establish an ICC (residual (or conditional) intraclass correlation coefficient) for the response r corresponding to the variance explained by the country level:

$$\displaystyle \begin{aligned} ICC_{r}=\frac{Var_{2}(y^{*}_{rij})}{Var_{1}(y^{*}_{rij})} \end{aligned} $$

(16.4)

Where $Var_{1}(y^{*}_{rij})$ is the variance at level 1 (that of the individual) and $Var_{2}(y^{*}_{rij})$ is the variance at level 1 (country level).

This coefficient gives the percentage of the variance in the acceptance taken into consideration by the inclusion of a level. Interpretation of the ICC value differs among researchers, with some arguing that a value less than 5% indicates that multilevel modelling is not needed, whereas others advocate that even small amounts of variance can result in significant differences in model fit, in the presence of categorical variables (Grilli and Rampichini 2007).

Here we will use the same random effects probit model to estimate in which extend the following variables are impacting subjective well-being: total wealth (country), intangible capital (country), % of intangible capital in total wealth, income (individuals), voluntary association membership (individuals), trust (individuals). To deal with potential endogeneity between social capital and subjective well-being, we use the control function approach developed by Wooldridge (2010). The generalized residuals (Gourieroux et al. 1987) estimated thanks to Equation 4 were included in a multilevel ordered probit with subjective well-being as a dependant variable and trust and association membership as explanatory variables.

Using margins effects calculations, we aim to check if social capital has a key role in transforming wealth into subjective wellbeing as well as a resilience effect when wealth is not globally growing in crisis period.