از شادی متوسط "جو" تا "جین" بدبخت و "جان" شاد : استفاده از رگرسیون چندک برای تجزیه و تحلیل کامل ذهنی توزیعی بهزیستی

Abstract Standard regression techniques are only able to give an incomplete picture of the relationship between subjective well-being and its determinants since the very idea of conventional estimators such as OLS is the averaging out over the whole distribution: studies based on such regression techniques thus are implicitly only interested in Average Joe's happiness. Using cross-sectional data from the British Household Panel Survey (BHPS) for the year 2006, we apply quantile regressions to analyze effects of a set of explanatory variables on different quantiles of the happiness distribution and compare these results with a standard regression. Among our results we observe a decreasing importance of income, health status and social factors with increasing quantiles of happiness. Another finding is that education has a positive association with happiness at the lower quantiles but a negative association at the upper quantiles. We explore the robustness of our findings in various ways.

Introduction Research into the causes and correlates of human happiness (or synonymously: subjective well-being) has gained momentum in the past years and attracted attention in disciplines such as economics and psychology alike (see recent reviews, e.g. Easterlin, 2003, Frey and Stutzer, 2005 and Dolan et al., 2008). With an increase in interest of researchers from various disciplines, happiness research progressed to a point where many of the initial findings are becoming increasingly qualified, theories become more refined and the statistical tools to analyze the complex relationships between happiness and its determinants become ever more sophisticated. One major theme during the last years was, for example, the introduction of panel data techniques that allow to more reliably identify individual responses to changes in external conditions (via accounting for time-invariant individual-specific components, “fixed effects”, e.g. Ferrer-i Carbonell and Frijters, 2004). What has been neglected so far is the information that is contained in happiness distributions. Thus, what we want to argue for in the present paper is that happiness research should now also start being less concerned with the mean effects of the explanatory variables on happiness but with their effects on different parts of the happiness distribution. Ordinary least squares regression techniques with their focus on the conditional mean of the dependent variable are only able to give an incomplete picture of the relationship between subjective well-being and its determinants since the very idea of OLS regressions is the averaging out of coefficient estimates over the conditional distribution of the dependent variable: studies based on such regression techniques thus are implicitly only interested in the happiness of “Average Joe”, but remain silent on the question of the effects that explanatory variables have on the happiness levels of “Miserable Jane” or “Cheerful John”.1 While average effects certainly are an important feature to examine, from a policy perspective it is often more interesting to understand what happens at the extremes of a distribution. For example, are increases in income as relevant for the happiness of the happiest individuals in a population as they are for the most miserable individuals? Similarly, going beyond the mean is important with regard to individual-specific rates of hedonic adaptation (Diener et al., 2006, p. 311): as recent research on the hedonic treadmill shows, policy makers do have levers to permanently alter individuals’ happiness levels but this seems not to be the case uniformly along the happiness distribution. This type of analysis is long known in welfare economics, where scholars are interested in the distribution of well-being and not just the average (e.g. when analyzing income inequality). This allows to more comprehensively assess policies, where for instance a policy might be ethically acceptable if it has a small positive effect on everyone's well-being, but it would be no longer acceptable, in ethical terms, if some individuals’ gains are counterbalanced by large losses for a minority. In these types of considerations, the focus is no longer on the average effect, but on the full distribution of well-being. We argue that this line of reasoning needs to be extended to happiness research. These considerations become more urgent when one takes into account the findings that happiness distributions are empirically quite skewed: most individuals have positive happiness values, with a mean of 6.33 on a 0 (most unhappy) to 10 (most happy) scale for a sample of 43 nations (Diener and Diener, 1996 and Diener et al., 2006). In heterogeneous distributions, regression methodologies that focus on means might seriously under- or overestimate effects or even fail to identify effects at all (Cade and Noon, 2003). A solution to this lacuna is to extend happiness measurement from ordinary least square regressions to quantile regressions (Koenker and Bassett, 1978 and Koenker and Hallock, 2001). Quantile regression enables the econometrician to analyze effects of the explanatory variables on different quantiles of the happiness distribution as opposed to a (incomplete) focus on the mean of the distribution. It is a pragmatic tool for analyzing extreme effects in the happiness distribution and thus gives the researcher a more complete picture of the effects of the explanatory variables on the dependent variable (in our case happiness). While quantile regressions are starting to be recognized as a helpful technique in the case of skewed (non-normal) distributions in other economic sub-disciplines,2 we are to our knowledge among the first to explore and demonstrate their use in happiness research.3 In order to motivate the usefulness of happiness quantile regressions, the paper proceeds in the following way. Section 2 gives an overview over some relevant knowledge in happiness research in order to justify the later selection of explanatory variables. Section 3 then gives an introduction to quantile regressions and relates them to the standard regression estimators such as OLS (ordinary least squares). In Section 4 we then apply quantile regressions to a fairly standard set of explanatory variables (and their effect on happiness) and compare these results with a standard regression. We explore these relationships by using data from the British Household Panel Survey (BHPS), an extensive data set that covers information on many important life domains of a representative sample of the British populace. We explore the robustness of our results in a number of ways. Section 5 concludes.

Conclusion Research into the causes and correlates of human happiness (or synonymously in this paper: subjective well-being) has increased in momentum in the past years and progressed to a point where many of the initial findings are becoming increasingly qualified, theories become more refined and the statistical tools to analyze the complex relationships between happiness and its determinants become ever more sophisticated. What has been neglected so far is the information that is contained in happiness distributions. We have argued that happiness research should start being more concerned with the effects of explanatory variables on different parts of the happiness distribution. While average effects certainly are an important feature to examine, it is also interesting to understand what happens at the extremes of a distribution. For example, are increases in income as relevant for the happiness of the happiest individuals in a population as they are for the most miserable individuals? If effects are not uniform along the distribution, a standard regression gives the researcher only an incomplete picture of the relationship between dependent and independent variables: in heterogeneous distributions, regression methodologies that focus on means might seriously under- or overestimate effects or even fail to identify effects at all (Cade and Noon, 2003). In this paper, we demonstrated how extending happiness measurement from ordinary least square regressions to quantile regressions can solve this problem (Koenker and Bassett, 1978 and Koenker and Hallock, 2001). Quantile regression enables the analysis of effects of the explanatory variables on different quantiles of the happiness distribution as opposed to a (incomplete) focus on the mean of the distribution. We have applied quantile regressions to a fairly standard set of explanatory variables (and their associations with happiness) and compared these results with a standard (conditional mean) regression. We have explored this relationship by using cross-sectional data from the British Household Panel Survey (BHPS) for the year 2006, an extensive data set that covers information on many important life domains of a representative sample of the British populace. Among our results, we observed that log(income) is positively associated with life satisfaction, which is strongest for the least happy individuals, but not significant for the happiest. Relatedly, social relations and health have their largest impacts for the least happy individuals, with their positive associations being much smaller at the upper end of the happiness distribution. Education is positively associated with happiness for the least happy individuals, while the relationship is negative for the happiest. The good news is that much can be done to alleviate the unhappiness of those individuals at the lower end of the distribution (i.e. the “Miserable Janes”). In contrast, with the factors explored in this study, we have not succeeded in finding the secrets of happiness for the truly happy individuals — at the upper tail of the distribution. These “Cheerful Johns”, it seems, can be found in all situations in life, with little that links them together. Their happiness does not seem to be affected by the external factors identified here, but may come from other sources yet to be uncovered. Future extensions of a quantile regression methodology in happiness research could test whether these relationships found in the present paper generalize to other countries and data sets. Another important step would constitute an application of fixed effects quantile regressions that would exploit the panel properties of a data set, thus being able to take into account time-invariant individual-specific effects. Fixed effects quantile regression would be a suitable tool for exploring differential effects for growth versus decline in happiness, where efforts are made to “homogenize” different individuals, and make them more comparable, by removing time-invariant fixed effects. As such, future work into happiness that applies fixed effect quantile regressions would likely provide an interesting complement to our current findings.