To verify the robustness of our results, we re-estimate the models presented in Sect. 4 using (A1) a different estimation technique, (A2) different sub-samples, and (A3) more domains.
A1 Variation of the Statistical Model
Although several articles in the field of happiness economics have shown that OLS estimators lead to qualitative similar results as ordered probit models (Ferrer-i-Carbonell and Frijters 2004; Rojas 2007; Ochsen and Welsch 2012; Metcalfe et al. 2011), we re-estimated the models presented in Tables 5.1, 5.3, 5.4, and 5.5 by using ordered probit regressions.10 Apart from slight changes in the levels of significance of a very few coefficients, our ordered probit regression comes to almost identical results. Changes are, for example, observed in the variable for friendship satisfaction in Table 5.1, Model 3, which is now significant at the 1 % level (before: 5 % level). In Table 5.4, the coefficients of health satisfaction (Models 1 and 2) become non-significant (before: 10 % level), which confirms our classification of health as a “relative domain.” Finally, in Table 5.5, Model 2, we see the coefficient of being in a managerial position become significant at the 10 % level (before: not significant). All in all, the results of our ordered probit regression correspond qualitatively to the OLS models presented in Sect. 4.
A2 Variations of the Sample
As a further robustness check, we drop all respondents from the sample who either (a) reported that they consider all five domains important or (b) reported that they consider none of the domains important. After dropping those 377 observations, we are left with 2,521 valid responses, to which we apply the same OLS regressions as reported in Sect. 4. The full results are not reported here, but are available upon request. Similar to the first robustness check, the reported results change only marginally. In Table 5.1, for example, the importance of purpose in life becomes, in both models, statistically significant at the 5 % level, whereas satisfaction with friends loses its significance in Model 4. In Table 5.2, the dominance analysis shows a switch in ranks for financial and family satisfaction (with family taking rank 1). In Table 5.3, Model 3, the importance of purpose in life as well as its interaction term with satisfaction are no longer statistically significant. In Table 5.4, the coefficients for importance of purpose in life as well as for importance of friends become statistically significant at the 1 % (purpose in life) and 5 % (friends) level, while the coefficient of health satisfaction loses its significance in both models.
In a next step, we concentrate on workers in the sample and drop all respondents who are students, housewives, or without work (1,049 observations). After dropping these observations, we are left with 1,847 valid responses to which we apply the same OLS regressions reported in Sect. 4
. We are especially interested in any changes concerning the global interaction model, which is why we focus on changes in the results of Table 5.4
. Results are reported in Table 5.6
. The most remarkable change is observed in the health domain. While importance of health becomes significant at the 5 % level in both models, the interaction effect of health satisfaction and importance loses its statistical significance. This results casts doubt on the classification of health as a “relative domain,” which is why further research is needed to verify the classification scheme we proposed in Sect. 4.2
Global interaction model (OLS) (only working sample)
A3 Variation of the Domains
In a last robustness check, we again focus on workers in the sample (n = 1,847). Concentrating on people who are employed allows us to introduce a number of work-related domains, such as job and workplace. Beside those work-related domains, we also include the region that the respondents are living in as another domain of satisfaction and importance. Adding these three domains to the existing interaction model of Table 5.4 allows us to check whether our results are robust on the selection of domains that are related to the happiness function of the respondents (results are available upon request). We find that neither of the newly added domains shows any significant results (in satisfaction, importance, and interaction). The other results are similar to the five domain model of working respondents (Table 5.6).
Taken together, the robustness checks presented above show that our results are robust to a variety of changes in estimation techniques, sample variation, and domain selection. The only remarkable change in results is observed in the health domain, which is why our classification scheme of Sect. 4.2 should be a subject of further research.