Abstract
There is significant variation in average subjective well-being across countries. What makes people in some countries happier or more miserable than others? In this study, we decompose the difference in average subjective well-being across countries into a comprehensive set of socio-economic factors along with cross-country difference in sensitivity of happiness in order to answer the question. While an individual’s subjective well-being is affected by socio-economic status, every individual does not necessarily draw the same level of subjective well-being from a given condition of life because of different personal characteristics. Sensitivity of happiness is an umbrella term capturing such factors that are not reflected by socio-economic conditions. We introduce Data Envelopment Analysis (DEA) approach to estimate a happiness function and specify the sensitivity score for each country in a sample. We draw on a comprehensive set of well-being indicators released by the Better Life Initiative of the OECD, along with measures of income inequality. We find that the health factor and sensitivity term play the largest role in generating variation in subjective well-being. Even within countries, the average level of subjective well-being varies between different population groups. Drawing on a set of indicators that assess the life circumstances of different groups within each country, our decomposition formulation allows for a full explanation of the differences in average life satisfaction between the groups. We investigate the differences between men and women, and high income earners and low income earners.
This is a preview of subscription content,
to check access.


Notes
See Caselli (2005).
There are multiple measures of happiness. This study adopts the 0–10 point scale of the Cantril Ladder of life.
The terms ‘happiness’, ‘subjective well-being’, and ‘life satisfaction’ are used interchangeably, as is common in the literature.
Helliwell and Wang (2013) and Helliwell et al. (2015) explain three-quarters of the international differences in subjective well-being by using a much smaller number of variables (six) to characterise people’s life circumstances. By comparing people’s lives using more than double this number of variables, we can attribute a higher proportion of the differences in subjective well-being to the differences in life conditions.
The DEA was originally proposed by Charnes et al. (1978) for measuring the productive efficiency of firms.
In the regression approach, the individual or country-specific effect, which corresponds to the sensitivity term, is estimated by exploiting longitudinal data (See Das and van Soest 1999; Ferrer-i-Carbonell and Frijters 2004). However, the DEA approach adopted by the present paper can specify the sensitivity term by simply utilizing cross-sectional data. Clark et al. (2005) model intercept and slope heterogeneity simultaneously. Although our model incorporates only the former, we attribute the differences in the marginal utilities among countries to the differences in socio-economic conditions.
Guardiola and Picazo-Tadeo (2014) utilize DEA to address the problem of relating people’s satisfaction with different domains of their lives to overall life satisfaction. Although the researchers are mainly concerned with overall life satisfaction, which equates to this study’s subjective well-being, they address a different question.
Debnath and Shankar (2014) also estimate the efficiency of happiness based on the DEA approach. However, in their model, the government is responsible for providing people with a higher average subjective well-being. Thus, the authors’ estimated efficiency is interpreted as measuring the performance of the government of each country, which is conceptually different from the idea of the sensitivity of happiness.
See Balk (2008) for a survey of a recent development of index number theory.
For simplicity, the average level of subjective well-being of people in a country is called ‘national average subjective well-being’ or ‘subjective well-being of a country’ in this paper.
For example, the n-th component \(x_{n}^{c}\) corresponds to the n-th socio-economic condition of country c, such as income, jobs, and environment. However, each socio-economic condition is often characterized by a vector consisting of multiple indicators; for example, the environmental quality of country c might be captured by qualities of air and water as well as green spaces. Thus, it is appropriate to adopt a socio-economic vector consisting of N sub-vectors, such as \(\varvec{x}^{c} = (x_{1}^{c} , \ldots ,x_{N}^{c} )\). While our empirical application adopts this framework, it complicates our description of the model and estimation strategy. Thus, for simplicity, we consider the case in which each socio-economic condition is characterized by one indicator, such as \(\varvec{x}^{c} = (x_{1}^{c} , \ldots ,x_{N}^{c} )\).
We find that introducing the concept of sensitivity of happiness is a practical solution to controlling for the uncovered factors because these factors involve subjects which are difficult to measure.
Sensitivity corresponds to efficiency, which is a measure of productive performance and requires the fewest inputs to produce the most outputs. Just as a firm producing more output from the same input is considered to be more efficient, in this study, a country with greater subjective well-being from the same socio-economic vector is considered to be more sensitive. θ is within the range between 0 and 1 because θ is the counterpart to the Farell measure, which is normalized within the same range.
For example, in a simple case of N = 2, the decomposition formula (4) is as follows.
\(\frac{{SWB^{c} }}{{\bar{\theta }H(\bar{\varvec{x}})}} = \frac{{\theta^{c} }}{{\underbrace {{\bar{\theta }}}_{sesitivity}}} \times \underbrace {{\left( {\frac{{H(x_{1}^{c} ,x_{2}^{c} )}}{{H(\bar{x}_{1} ,x_{2}^{c} )}} \cdot \frac{{H(x_{1}^{c} ,\bar{x}_{2} )}}{{H(\bar{x}_{1} ,\bar{x}_{2} )}}} \right)^{1/2} }}_{{1{\text{st}}\,factor}} \times \underbrace {{\left( {\frac{{H(\bar{x}_{1} ,x_{2}^{c} )}}{{H(\bar{x}_{1} ,\bar{x}_{2} )}} \cdot \frac{{H(x_{1}^{c} ,x_{2}^{c} )}}{{H(x_{1}^{c} ,\bar{x}_{2} )}}} \right)^{1/2} }}_{{2{\text{nd}}\,factor}}\).
In this case, the percentage differences in subjective well-being between country c and the reference country are decomposed as follows.
\(\begin{aligned} & \left({\frac{{SWB^{c} - \bar{\theta }H(\bar{\varvec{x}})}}{{\bar{\theta }H(\bar{\varvec{x}})}}} \right) \times 100 \approx \underbrace {{\ln \frac{{SWB^{c} }}{{\bar{\theta }H(\bar{\varvec{x}})}} \times 100}}_{difference \, (\% )} = \underbrace {{\ln \frac{{\theta^{c} }}{\theta } \times 100}}_{sensitivity} \\ & \quad + \underbrace {{\left( {\frac{1}{2}} \right)\ln \left( {\frac{{H(x_{1}^{c} ,x_{2}^{c} )}}{{H(\bar{x}_{1} ,x_{2}^{c} )}} \cdot \frac{{H(x_{1}^{c} ,\bar{x}_{2} )}}{{H(\bar{x}_{1} ,\bar{x}_{2} )}}} \right) \times 100}}_{{1{\text{st}}\,factor \, (\% )}} + \underbrace {{\left( {\frac{1}{2}} \right)\ln \left( {\frac{{H(\bar{x}_{1} ,x_{2}^{c} )}}{{H(\bar{x}_{1} ,\bar{x}_{2} )}} \cdot \frac{{H(x_{1}^{c} ,x_{2}^{c} )}}{{H(x_{1}^{c} ,\bar{x}_{2} )}}} \right) \times 100}}_{{2{\text{nd}}\, factor \, (\% )}}\end{aligned}.\)
Furthermore, the differences in subjective well-being between country c and the reference country are additively decomposed as follows.
\(\begin{aligned} & SWB^{c} - \bar{\theta }H(\bar{\varvec{x}}) \approx \underbrace {{\ln \frac{{SWB^{c} }}{{\bar{\theta }H(\bar{\varvec{x}})}} \times \bar{\theta }H(\bar{\varvec{x}})}}_{difference \, (0 - 10 \, scale)} = \underbrace {{\ln \frac{{\theta^{c} }}{\theta } \times \bar{\theta }H(\bar{\varvec{x}})}}_{sensitivity \, (0 - 10 \, scale)} \\ & \quad + \underbrace {{\left( {\frac{1}{2}} \right)\ln \left( {\frac{{H(x_{1}^{c} ,x_{2}^{c} )}}{{H(\bar{x}_{1} ,x_{2}^{c} )}} \cdot \frac{{H(x_{1}^{c} ,\bar{x}_{2} )}}{{H(\bar{x}_{1} ,\bar{x}_{2} )}}} \right) \times \bar{\theta }H(\bar{\varvec{x}})}}_{{1{\text{st}}\,factor \, (0 - 10 \, scale)}} + \underbrace {{\left( {\frac{1}{2}} \right)\ln \left( {\frac{{H(\bar{x}_{1} ,x_{2}^{c} )}}{{H(\bar{x}_{1} ,\bar{x}_{2} )}} \cdot \frac{{H(x_{1}^{c} ,x_{2}^{c} )}}{{H(x_{1}^{c} ,\bar{x}_{2} )}}} \right) \times \bar{\theta }H(\bar{\varvec{x}})}}_{{2{\text{nd}}\,factor \, (0 - 10 \, scale)}} \end{aligned}.\)
Just as efficiency of a firm is captured by the ratio between its actual output and its maximum output, sensitivity of happiness for a country is captured by the ratio between its actual subjective well-being and maximum subjective well-being SWB/H(x).
The OECD launched the Better Life Initiative on its 50th anniversary, held under the theme ‘Better Policies for Better Lives’. It aims to better understand what drives the well-being of people and what countries need to do to achieve greater progress for all (OECD 2011).
See OECD (2011) for a detailed description of the selection of headline indicators and the construction of well-being indicators.
See Clark and Oswald (1994), Di Tella et al. (2001) and Blanchflower and Oswald (2004) for jobs; Inglehart and Klingemann (2000), Bjørnskov (2003) and Helliwell and Putnam (2004) for community; Ferrer-i-Carbonell and Van Praag (2002) and Powdthavee (2008) for health. Recently, the influence of environmental quality has been examined and utilized for computing the monetary evaluation of non-market goods such as air pollution (Clark and Oswald 1994), noise (Van Praag and Baarsma 2005), and natural environment (Ambrey and Fleming 2011, 2013).
See Peck and Stewart (1985) and Oswald et al. (2003) for housing; Salinas-Jiménez et al. (2011) and Cuñado and de Gracia (2012) for reporting the direct impact of education; Frey and Stutzer (2000, 2002) and Helliwell and Huang (2008) for civic engagement; Powdthavee (2005) for safety; and Pouwels et al. (2008) for work-life balance.
We can compare the variations of different socio-economic indicators based on the coefficient of variation, which is a scale-free, relative measure of variability.
The BLI measure of water quality is the ratio of people who responded they are satisfied with water quality in the Gallup World Poll. Since this indicates individual perceptions of water quality, a smaller value of water quality for high income earners does not necessarily mean worse conditions of the water in their environment. Most likely, high income earners set a higher standard for the water quality than low income earners.
Note that the set of available variables is the same for all countries.
Linear monotone decreasing transformation is applied to seven indicators. The transformed indicators \(\tilde{x}_{1.1}\), \(\tilde{x}_{1.2}\), \(\tilde{x}_{2.3}\), \(\tilde{x}_{3.2}\), \(\tilde{x}_{3.3}\), \(\tilde{x}_{6.1}\), \(\tilde{x}_{9.1}\), \(\tilde{x}_{9.2}\), and \(\tilde{x}_{10.1}\) are used as components of socio-economic vector x. They are defined as follows.
(a) \(\tilde{x}_{1.1} = 100 - x_{1.1}\); (b) \(\tilde{x}_{1.2} = 100 - x_{1.2}\); (c) \(\tilde{x}_{2.3} = 1 - x_{2.3}\); (d) \(\tilde{x}_{3.2} = 100 - x_{3.2}\); (e) \(\tilde{x}_{3.3} = 100 - x_{3.3}\); (f) \(\tilde{x}_{6.1} = \frac{{{\text{World \,highest \,score\,of \,Sudan\,}}\left({ = 156.2} \right) - x_{6.1} }}{{{\text{World \,highest \,score \,of \,Sudan\,}}\left( { = 156.2} \right) - {\text{World \,lowest \,score \,of \,Gabon\,}}\left( { = 6.7} \right)}}\); (g) \(\tilde{x}_{9.1} = 100 - x_{9.1}\); (h) \(\tilde{x}_{9.2} = 100 - x_{9.2}\); and i) \(\tilde{x}_{10.1} = 100 - x_{10.1}\). While Stevenson and Wolfers (2008, 2013) use the natural logarithm of individual income for explaining subjective well-being, we use monetary measures of income and wealth without any transformation. Our non-parametric estimation of the happiness function based on DEA allows us to capture the decreasing marginal utility of income and wealth on subjective well-being, without logarithmic transformations.
See Table 7 in Appendix decomposes the differences in subjective well-being relative to the reference country on a percentage scale. Countries are ordered according to the value of their subjective well-being.
In other words, the subjective well-being of people in Australia is insensitive to their socio-economic conditions.
The subjective well-being of the reference country \(\bar{\theta }H(\bar{\varvec{x}})\) is closest to the average subjective well-being of Germany and the US. Among these two countries, the US can be regarded resembling to the reference country more than Germany based on Fig. 1.
In the previous analysis on the variation of national average subjective well-being, the same reference country is used for every country. However, in the decomposition of the differences in subjective well-being between females and males, a different reference is used for each country. In addition, we note that the happiness function is constructed from 72 data points, which comprise males and females in 36 countries.
See Table 8 in Appendix decomposes the differences in subjective well-being of females relative to males on a percentage scale. Countries are ordered according to the differences in subjective well-being between females and males.
However, it is necessary to aware that the decisive contribution of safety factor is documented only for Brazil, Mexico, and Russia and it plays almost no role for the remaining countries.
It is possible that females’ higher sensitivity reflects dismissed socio-economic conditions such as housing and income factors. However, it is unlikely that females’ life circumstances are generally better than those of males in terms of housing and income factors. Thus, I consider that females’ higher sensitivity of happiness is a more robust result, a finding which holds even after incorporating more socio-economic dimensions.
Estimating a liner happiness function, Arrosa and Gandelman (2016) report that the dummy variable for females has a positive and statistically significant coefficient.
In the previous analysis on the variation of national average subjective well-being, the same reference country is used for every country. However, in the decomposition of the differences in subjective well-being between high and low income earners, a different reference is used for each country. In addition, we note that the happiness function is constructed from 72 data points, which comprise high and low income earners in 36 countries.
See Table 9 in Appendix decomposes the differences in subjective well-being of high income earners relative to low income earners on a percentage scale. Countries are ordered according to the differences in subjective well-being between high and low income earners.
Number of indicators for high and low income earners is even more restricted than that for female and male groups. The life condition of high income earners is likely to be better than low income earners. Thus, once more socio-economic indicators for high and low income earners are incorporated, high income earners’ sensitivity might become smaller.
Robustness check for the selection of variables for different population groups is especially hard because of data limitation. Although our analysis of Cases C and D is rather brief and incomplete, we do the best of the BLI with different population coverage there. Systematic studies on the selection of variables are necessary. We leave it for the future research.
Since Greece is one of few countries in which the community factor significantly affects subjective well-being of their populations. Thus, once Greece is excluded from the sample, the variation of subjective well-being explained by the community factor has been shrunk.
According to Table 1, the coefficient of variation for variables of health is 0.13 on average, which is the second lowest among all socio-economic factors.
In cases where the same improvement in some socio-economic dimensions is possible for two people, the sum of their subjective well-being becomes larger when the improvement occurs to the person with the higher sensitivity of happiness.
For example, variables related to demographics and religions are not used in our analysis.
References
Ambrey, C. L., & Fleming, C. M. (2011). Valuing scenic amenity using life satisfaction data. Ecological Economics, 72, 106–115.
Ambrey, C., & Fleming, C. (2013). Public greenspace and life satisfaction in urban Australia. Urban Studies, 51(6), 1290–1321.
Arrosa, M. L., & Gandelman, N., (2016). Happiness decomposition: Female optimism. Journal of Happiness Studies, 17(2), 731–756.
Balk, B. M. (2008). Price and quantity index numbers. New York, NY: Cambridge University Press.
Binder, M., & Broekel, T. (2012). Happiness no matter the cost? An examination on how efficiently individuals reach their happiness levels. Journal of Happiness Studies, 13(4), 621–645.
Bjørnskov, C. (2003). The happy few: Cross-country evidence on social capital and life satisfaction. Kyklos, 56(1), 3–16.
Bjørnskov, C. (2010). How comparable are the Gallup World Poll life satisfaction data? Journal of Happiness Studies, 11(1), 41–60.
Blanchflower, D. G., & Oswald, A. J. (2004). Well-being over time in Britain and the USA. Journal of Public Economics, 88(7-8), 1359–1386.
Caselli, F. (2005). Accounting for cross-country income differences. In P. Aghion & S. N. Durlauf (Eds.), Handbook of economic growth (Vol. 1A, pp. 679–741). Amsterdam: North-Holland.
Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2(6), 429–444.
Cherchye, L., et al. (2007). An introduction to ‘benefit of the doubt’ composite indicators. Social Indicators Research, 82(1), 111–145.
Clark, A. E., & Oswald, A. J. (1994). Unhappiness and unemployment. Economic Journal, 104(424), 648–659.
Clark, A., et al. (2005). Heterogeneity in Reported Well-Being: Evidence from Twelve European Countries. Economic Journal, 115(502), C118–C132.
Cordero-Ferrera, J.M., Salinas-Jiménez, J., & Salinas-Jiménez, M.D.M., (2014). Assessing the level of happiness across countries: A robust frontier approach. MPRA Paper 57784. Germany: University Library of Munich.
Cuñado, J., & de Gracia, F. P. (2012). Does education affect happiness? Evidence for Spain. Social Indicators Research, 108(1), 185–196.
Das, M., & van Soest, A. (1999). A panel data model for subjective information on household income growth. Journal of Economic Behavior & Organization, 40, 409–426.
De Neve, J.-E., et al. (2012). Genes, economics, and happiness. Journal of Neuroscience, Psychology, and Economics, 5(4), 1–27.
Debnath, R. M., & Shankar, R. (2014). Does good governance enhance happiness: A cross nation study. Social Indicators Research, 116(1), 235–253.
Di Tella, R., MacCulloch, R. J., & Oswald, A. J. (2001). Preferences over inflation and unemployment: Evidence from surveys of happiness. American Economic Review, 91(1), 335–341.
Diener, E., Diener, M., & Diener, C. (1995). Factors predicting the subjective well-being of nations. Journal of Personality and Social Psychology, 69(5), 851–864.
Easterlin, R. A. (1974). Does economic growth improve the human lot? Some empirical evidence. In M. Abramovitz, P. A. David, & M. W. Reder (Eds.), Nations and households in economic growth: Essays in honor of moses abramovitz (pp. 89–125). New York: Academic Press.
Ferrer-i-Carbonell, A., & Frijters, P. (2004). How important is methodology for the estimates of the determinants of happiness? Economic Journal, 114(497), 641–659.
Ferrer-i-Carbonell, A., & Ramos, X., (2013). Inequality and Happiness. Journal of Economic Surveys, 28(5), 1–12.
Ferrer-i-Carbonell, A., & van Praag, B. M. S. (2002). The subjective costs of health losses due to chronic diseases. An alternative model for monetary appraisal. Health Economics, 11(8), 709–722.
Fisher, I. (1922). The making of index numbers: A study of their varieties, tests, and reliability. Boston, MA: Houghton Mifflin.
Fleurbaey, M., & Gaulier, G. (2009). International comparisons of living standards by equivalent incomes. Scandinavian Journal of Economics, 111(3), 597–624.
Fortin, N., Helliwell, J. F., & Wang, S. (2015). How does subjective well-being vary around the world by gender and age? In J. F. Helliwell, R. Layard, & J. Sachs (Eds.), World happiness report 2015 (pp. 42–75). New York, NY: Sustainable Development Solutions Network.
Frey, B. S. (2008). Happiness: A revolution in economics. Cambridge, Massachusetts: MIT Press.
Frey, B. S., & Stutzer, A. (2000). Happiness economy and institutions. Economic Journal, 110(466), 918–938.
Frey, B. S., & Stutzer, A. (2002). Happiness and economics. Princeton, NJ: Princeton University Press.
Graham, C., & Chattopadhyay, S. (2013). Gender and well-being around the world. International Journal of Happiness and Development, 1(2), 212.
Guardiola, J., & Picazo-Tadeo, A. J. (2014). Building weighted-domain composite indices of life satisfaction with data envelopment analysis. Social Indicators Research, 117(1), 257–274.
Helliwell, J. F., & Huang, H. (2008). How’s your government? International evidence linking good government and well-being. British Journal of Political Science, 38(04), 595–619.
Helliwell, J. F., & Putnam, R. D. (2004). The social context of well-being. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, 359(1449), 1435–1446.
Helliwell, J. F., & Wang, S. (2012). The state of world happiness. In J. F. Helliwell, R. Layard, & J. D. Sachs (Eds.), World happiness report (pp. 10–57)., The Earth institute New York, NY: Columbia University.
Helliwell, J. F., & Wang, S. (2013). World happiness: Trends, explanations and distribution. In J. F. Helliwell, R. Layard, & J. D. Sachs (Eds.), World happiness report 2013 (pp. 8–37). New York, NY: Sustainable development solutions network.
Helliwell, J. F., Huang, H., & Harris, A. (2009). International differences in the determinants of life satisfaction. In B. Dutta, T. Ray, & E. Somanathan (Eds.), New and enduring themes in development economics (pp. 3–40). Singapore: World Scientific Publishing Co Pte Ltd.
Helliwell, J. F., Huang, H., & Wang, S. (2015). The geography of world happiness. In J. F. Helliwell, R. Layard, & J. Sachs (Eds.), World happiness report 2015 (p. 172). New York, NY: Sustainable Development Solutions Network.
Inglehart, R., & Klingemann, H.-D. (2000). Cenes, culture, demography, and happiness. In E. Diener & E. M. Suh (Eds.), Culture and subjective well-being (pp. 165–184). Cambridge, Massachusetts: MIT Press.
Jones, C.I., & Klenow, P.J., (2010). Beyond GDP? Welfare across countries and time. NBER Working Paper, No. 16352.
Kahneman, D., & Deaton, A. (2010). High income improves evaluation of life but not emotional well-being. Proceedings of the National Academy of Sciences of the United States of America, 107(38), 16489–16493.
Layard, R., Clark, A., & Senik, C. (2012). The causes of happiness and misery. In J. F. Helliwell, R. Layard, & J. D. Sachs (Eds.), World happiness report (pp. 58–89)., The Earth Institute New York, NY: Columbia University.
Malmquist, S. (1953). Index numbers and indifference surfaces. Trabajos de Estadística y de Investigación Operativa, 4, 209–242.
Mizobuchi, H. (2014). Measuring world better life frontier: A composite indicator for OECD better life index. Social Indicators Research, 118(3), 987–1007.
Mizobuchi, H., (2016). Incorporating Sustainability Concerns in the Better Life Index: Application of Corrected Concave Least Squares Method. Social Indicators Research. doi:10.1007/s11205-016-1282-9.
Oishi, S. (2010). Culture and Well-Being. In E. Diener, J. F. Helliwell, & D. Kahneman (Eds.), International differences in well-being (pp. 34–69). New York, NY: Oxford University Press.
Organisation for Economic Co-operation and Development. (2011). How’s life?. Paris: OECD Publishing.
Oswald, F., et al. (2003). Housing and life satisfaction of older adults in two rural regions in Germany. Research on Aging, 25(2), 122–143.
Peck, C., & Stewart, K. K. (1985). Satisfaction with housing and quality of life. Home Economics Research Journal, 13(4), 363–372.
Pouwels, B., Siegers, J., & Vlasblom, J. D. (2008). Income, working hours, and happiness. Economics Letters, 99(1), 72–74.
Powdthavee, N. (2005). Unhappiness and crime: Evidence from South Africa. Economica, 72(287), 531–547.
Powdthavee, N. (2008). Putting a price tag on friends, relatives, and neighbours: Using surveys of life satisfaction to value social relationships. Journal of Socio-Economics, 37(4), 1459–1480.
Salinas-Jiménez, M. D. M., Artés, J., & Salinas-Jiménez, J. (2011). Education as a positional good: A life satisfaction approach. Social Indicators Research, 103(3), 409–426.
Stevenson, B., & Wolfers, J., (2008). Economic growth and subjective well-being: Reassessing the Easterlin paradox. Brookings Papers on Economic Activity, Spring, 1–87.
Stevenson, B., & Wolfers, J. (2009). The paradox of declining female happiness. American Economic Journal: Economic Policy, 1(2), 190–225.
Stevenson, B., & Wolfers, J. (2013). Subjective well-being and income: Is there any evidence of satiation? American Economic Review, 103(3), 598–604.
Stiglitz, J.E., Sen, A., & Fitoussi, J.-P., (2009). Report by the commission on the measurement of economic performance and social progress. http://www.stiglitz-sen-fitoussi.fr/documents/rapport_anglais.pdf.
Veenhoven, R., & Ehrhardt, J. (1995). The cross-national pattern of happiness: Test of predictions implied in three theories of happiness. Social Indicators Research, 34(1), 33–68.
Acknowledgments
The author is grateful for two anonymous referee referees, Jiro Nemoto, Tomohiro Tasaki, Akiko Kamesaka, and Bernhard Mahlberg for their helpful comments and suggestions. This article was completed when the author visited Center for Efficiency and Productivity Analysis in the School of Economics at the University of Queensland. The good research environment offered by the institute and the department is greatly appreciated. This research was financially supported by Grant-in-Aid for Scientific Research (KAKENHI 25870922). All remaining errors are the author's responsibility.
Author information
Authors and Affiliations
Corresponding author
Appendix: Estimation Procedure of the Happiness Function and Implementation of Decomposition
Appendix: Estimation Procedure of the Happiness Function and Implementation of Decomposition
We graphically illustrate how to implement the decomposition of the differences in subjective well-being based on Eqs. (4) and (5) using a simple case of a single socio-economic variable x and two observations: countries A and B. Points A and B in Fig. 4 correspond to the observation of each country. x A and x B indicate a socio-economic variable for each country, respectively; SWB A and SWB B indicate subjective well-being for each country, respectively.
Since the slope of 0B is higher than that of 0A, country B is considered as being more sensitive to its socio-economic variable than country A. Thus, Eq. (5) constructs a happiness function H(x) by the ray from the origin through point B. H(x) depicts the hypothetical value of subjective well-being that sensitive country B would draw from any given socio-economic variable x. Thus, the ratio of the actual subjective well-being of each country to H(x) indicates each country’s sensitivity of happiness θ. The sensitivity of country B is evaluated at 1, such that θ B = H(x B)/SWB B = 1. On the other hand, H(x A) is smaller than SWB A and, thus, point A is below the happiness function. Therefore, country A’s sensitivity is below 1, such that θ A = SWB A/H(x A) < 1.
Point C indicates the hypothetical reference country for implementing Eq. (4). Both the socio-economic variable and the sensitivity term for country C are the averages of the values of the two countries, such that \(\bar{x} = (x^{A} + x^{B} )/2\) and \(\bar{\theta } = (\theta^{A} + \theta^{B} )/2\). Thus, subjective well-being of country C is calculated by \(SWB^{C} = \bar{\theta }H(\bar{x})\).
We apply Eq. (4) to the data of three countries to investigate the reasons why country A is less happy than the reference county C and country B is happier than reference country C in the ratio form as follows.
Taking the natural logarithm of Eqs. (6) and (7) at both sides, we can additively decompose the differences in subjective well-being on a percentage scale into sensitivity term and socio-economic factor as follows.
Moreover, by multiplying Eqs. (8) and (9) by SWB C, we can additively decompose the differences in subjective well-being in the original 0–10 point scale into differences in sensitivity term and socio-economic factor as follows:
As explained in Sect. 4, we can also apply Eq. (4) to explain the differences in subjective well-being between different population groups. Suppose that country A is the female group and country B is the male group in the same country. If we set country B as the reference rather than country C, Eq. (4) allows us to decompose the differences in subjective well-being between the female and male groups into multiple factors as follows.
Equations (12), (13) and (14) help us to investigate the reasons why females’ subjective well-being is higher than males’ subjective well-being. Similarly, we can also explain the reasons why subjective well-being of high income earners is higher than that of low income earners.
Rights and permissions
About this article
Cite this article
Mizobuchi, H. Measuring Socio-economic Factors and Sensitivity of Happiness. J Happiness Stud 18, 463–504 (2017). https://doi.org/10.1007/s10902-016-9733-1
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10902-016-9733-1