Building Weighted-Domain Composite Indices of Life Satisfaction with Data Envelopment Analysis

Choosing the domains to describe life satisfaction is not, therefore, an easy task. Rojas (2006) proposed three criteria to choose domains: parsimony (the number of domains must be manageable and represent separate information), meaning (they should be related to the way people think about their lives) and usefulness (they must contribute to the understanding of the subject). Beyond the criteria of the researcher or data limitations to choose the domains, techniques such as factor analysis can be used to group domains when they become too numerous.

Computer-based methods using econometric regressions normally employ bottom-up approaches, while structural equation modelling can take into account both bottom-up and top-down approaches.

Other weighting measures have also been proposed, such as rating the direct have–want discrepancy; e.g., Wu (2009) rates the have–want discrepancy for several domains using a 5-point Likert-type scale ranging from −4 (marked discrepancy from the want status) to 0 (the same as the want status).

Zhou et al. (2007) highlight the ability of DEA techniques to build composite indicators reflecting a variety of economic, social and environmental factors (see also Zaim et al. 2001). Furthermore, some researchers have used several variants of these techniques to compute quality of life indicators, including Hashimoto and Kodama (1997); Zhu (2001); Murias et al. (2006); Jurado and Perez-Mayo (2012); Domíguez-Serrano and Blancas (2011).

Allen and Thanassoulis (2004) review the techniques available to incorporate weighting restrictions into the framework of DEA-based models.

This model is closely related to Russell’s non-radial efficiency model (Färe and Lovell 1978).

In practice, such integration procedures have been carried out by computing a series of 101 composite life satisfaction indicators for each individual allowing the parameter t to vary between 0 and 1 at intervals of 0.01. Then, these estimates of life satisfaction and the corresponding estimates of common weights have been averaged into a single life satisfaction indicator and a single set of common weights, respectively (see Reig-Martínez et al. 2011 for details).

Additionally, we have computed a DEA-Benefit-of-the-doubt composite indicator of life satisfaction using proportional or radial measures, as in Bernini et al. (2012), with the result of 138 individuals (77 % of the sample) scoring full satisfaction, i.e., with composite indicators equal to one. These results are available upon request and strongly justify our choice of a slack-based approach to improve the capacity of our basic DEA model to discriminate among individuals.

For example, Bernini et al. (2012) computed a common-weight subjective community well-being indicator for people in the European areas of Romagna and San Marino, finding that personal life features are the most important domain in determining well-being in the collective optimum. However, these features drop third and last place in the most penalised individual optimum.

Following the suggestion made by an anonymous referee, we have calculated the weightings that would result from regressing self-reported life satisfaction on life domains by OLS. The results are in the “Appendix” and show that only the health and work life domains are statistically significant at standard confidence levels. Moreover, estimated life satisfaction for an average individual is 8.2. Furthermore, we have run some additional regressions excluding certain life domains in order to avoid problems of multicollinearity, with no different results. We would nevertheless like to highlight that econometric and DEA-MCDM-based techniques are different approaches to assessing life satisfaction and weightings for life domains, and that the choice of one over the other depends on issues such as the availability of information or the theoretical assumptions the researcher is willing to accept. In our opinion, one of the contributions of our paper is suggesting DEA-MCDM techniques as an alternative computer-based approach to assessing life satisfaction and the importance of life domains.