Article Summaries Part 1

Social Science Research 40 (2011) 742–756

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Social Science Research

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / s s r e s e a r c h

Is happiness inequality immune to income inequality? New evidence through instrument-effect-corrected standard deviations

Jan Delhey a,⇑, Ulrich Kohler b a Jacobs University Bremen, School of Humanities and Social Sciences, Campus Ring 1, D-28759 Bremen, Germany b Social Science Research Center Berlin (WZB), Research Unit Inequality and Social Integration, Reichpietschufer 50, D-10715 Berlin, Germany

a r t i c l e i n f o a b s t r a c t

Article history: Received 14 April 2010 Available online 21 December 2010

Keywords: Income distribution Happiness Inequality Well-being Measurement Comparative research

0049-089X/$ - see front matter � 2010 Elsevier Inc doi:10.1016/j.ssresearch.2010.12.004

⇑ Corresponding author. Fax: +49 421 200 3303. E-mail addresses: [email protected]

Previous research has found that a nation’s income inequality does not affect its happiness inequality. This article questions the appropriateness of the standard deviation as measure of happiness inequality used in these studies. Our main criticism concerns structural dependency, i.e. the technical dependency of the standard deviation on a nation’s mean happiness which is induced by measuring happiness with limited rating scales. To over- come this drawback, two new measures are proposed which adjust for the effects of lim- ited instruments. Applying these new measures to the most recent World Values Survey data demonstrates that some countries change their ranking in the league table of happi- ness inequality considerably. Moreover, income inequality does affect corrected happiness inequality, a finding which has significant public policy implications.

� 2010 Elsevier Inc. All rights reserved.

1. The issue

Although happiness – or subjective well-being (SWB), to use a more encompassing term – is currently a major topic among social scientists (Frey and Stutzer, 2002; Layard, 2005) and psychologists (Diener and Biswas-Diener, 2008) alike, little use has been made so far of subjective indicators in inequality research. In particular, the idea of expressing a nation’s overall degree of inequality in terms of happiness is still quite novel. But this is about to change. One indication is that ‘Happiness and Inequality’ received an entry in the recently published Oxford Handbook of Economic Inequality (Van Praag and Ferrer- I-Carbonell, 2009). Dutch scholars have been particularly active in assessing summary measures of happiness distributions, recommending the standard deviation as the most suitable indicator (Kalmijn and Veenhoven, 2005). Research following this recommendation has produced noteworthy findings, and probably the most puzzling one is that happiness inequality is only weakly, if at all, related to the income distribution of nations. The theoretical conclusion drawn is that happiness is ulti- mately based on absolute, not relative, need fulfilment.

This article takes a fresh look at the income inequality–happiness inequality link. A fresh look is necessary, we argue, be- cause the standard approach – measuring happiness inequality as the standard deviation of reported well-being – has its flaws. The problems largely stem from the fact that the standard deviation is, at least to some extent, technically dependent on mean happiness, due to bounded scales. If this bias turns out to be large, the standard deviation gives us an inaccurate picture of the extent of happiness inequality, and of the societal conditions driving them. This article presents evidence that indeed the measurement problem deserves more attention than it currently receives. As a methodological contribution we develop two novel measures of happiness inequality which overcome the measurement problem. The second contribution is substantive: Applying these new measures to data from Wave 5 of the World Values Survey, we find that income inequality does affect happiness inequality, contrary to conventional wisdom.

. All rights reserved.

(J. Delhey), [email protected] (U. Kohler).

J. Delhey, U. Kohler / Social Science Research 40 (2011) 742–756 743

The article is organized as follows: the next section (2) briefly examines the place of SWB measures in inequality research and summarizes key findings from previous studies. The drawbacks of the conventional measure of happiness inequality are discussed (3), and two alternatives presented (4). They are then applied to survey data for 52 nations (5). The last section (6) summarizes our argument and discusses implications for future research.

2. What happiness inequality is and what we know about it

2.1. The case for happiness inequality

Traditionally, central to inequality research are objective disparities in resources such as income and wealth, power, and education (Kerbo, 1996). The only established ‘subjective’ dimension of inequality is occupational prestige (Treiman, 1977), which is still very different from subjective appreciation of one’s own life. For cross-national research in particular, the cur- rent gold standard is to compare income distributions by means of Gini coefficients or similar statistics (Firebaugh, 2003). Some contributions compare overall inequality in nations in terms of education (Thomas et al., 2001), longevity (Hicks, 1997), or human development (Grimm et al., 2010), but these studies are far outnumbered by income studies.

Scholars have been concerned with income for good reasons: it is an important resource in modern market societies and is (relatively) easy to measure; it provides information on the ratio level; and it can be influenced by social policies. Yet in- come has its problems, too. First, it is a means, not an end (UNDP, 1990), and thus gives us insights into life chances rather than life results. Second, income is far from being an encompassing measure of well-being. As Ringen (2006, p. 3) put it, inequality is about everything that is doing good or bad to an individual, not just income. What, then, are the alternatives? One is the ‘level of living’ approach (Erikson, 1993), which collects a wealth of information on objective living conditions of individuals and households. But this approach has its limitations as well. Not only do such encompassing data hardly exist for a great number of countries; there is also the ‘index problem’ (Ringen, 2006, p. 18–21) of how to combine this diverse information into one index of well-being.

Happiness measures promise an easy solution, in particular those targeting life-as-a-whole. Happiness can be defined as the extent to which people evaluate their lives positively, and can be measured, among other indicators, as life satisfaction (Veenhoven, 2007). Life satisfaction yields information on how people experience their overall living conditions, after filter- ing by values and aspirations. This perspective shifts attention from life chances to experienced life results, and the indexing is done by those who should know best – the respondents themselves. Overall happiness can offer insights into what kind of life people are able to get from the resources they command within the broader opportunity structures provided by the fam- ily, community and society in which they live.

Veenhoven argues that for well-being, happiness is ‘possibly a better indicator than the income disparities that are central to comparative inequality research’ (Veenhoven, 2005, p. 352). Yet subjective well-being measures might have their disadvan- tages too. One involves the strong influence by personal and intimate aspects of life in a way that homeostatic control largely buffers it against shifts in personal circumstances and material conditions (Eckersley, 2000), which means that satisfaction and happiness measures are not terribly sensitive to (changing) living conditions. Other critics point to some relativities of the semantics of satisfaction across groups and cultures (Hazelrigg and Hardy, 2000), and to differences in response styles (Kapteyn et al., 2010), which complicates well-being comparisons. However, extensive research has established that these problems do not invalidate subjective measures: self-reported well-being is reasonably valid, reliable and comparable across nations, and meaningfully correlates with privileged/poor living conditions both across individuals and societies (Veenhoven, 2007). The bottom line is that happiness measures provide a useful additional layer of understanding for inequality research, in particular since we are short of an ‘‘objective’’ summary measure of inequality of life-as-a-whole.1

Happiness inequality, then, is the heterogeneity of evaluations of life-as-a-whole within a nation. In recent years a good deal of progress has been achieved in ascertaining which are the most suitable statistics. After extensive tests, Kalmijn and Veenhoven (2005) recommend various measures as suitable, but highlight the standard deviation as the most simple and most informative one. In contrast, statistics known from income distribution such as the Gini coefficient, used e.g. by Easterlin (2009), are less suitable, mainly because the standard survey instruments do not measure happiness at the ratio level. The standard deviation is also the summary measure that has been applied most often; we shall now turn to the in- sights from this previous research.2

2.2. Previous research

2.2.1. Extent According to the World Database of Happiness, disparities in SWB are smallest in the Netherlands, Pakistan, Switzerland,

Iceland and Malta, and largest in Tanzania, Egypt, Algeria, the Dominican Republic and Zimbabwe. The range is between 1.4 and 2.8.

1 See Böhnke & Kohler (2008), pp. 630–635 for a systematic comparison of the relative merits of the two approaches to well-being. 2 We exclusively focus here on happiness inequality. We do not review research investigating how income inequality effects happiness levels, which is a

different area of research (Alesina et al., 2004; Biancotti and D’Allessio, 2007; Van Praag and Ferrer-I-Carbonell, 2009).

w s d R

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2.2.2. Correlates Objective income inequality is the prime candidate tested. Yet the vastly different income distributions (think of Namibia in

contrast to Denmark) leave no trace in happiness inequality. For Europe, literally no association has been found between income Ginis and the standard deviation of life satisfaction (Fahey and Smyth, 2004). In broad international comparisons, only weak cor- relations emerged (Ott, 2005; Veenhoven, 2005), with income distribution turning out to be the weakest correlate among 14 coun- try characteristics examined. The most extensive comparison of 119 nations found a zero-order correlation of .21, which was reduced virtually to zero after controlling for national wealth (Berg and Veenhoven, 2010). Ott (2005) looked at rich and poor countries separately, again finding only a weak correlation for rich countries (.16), and an even weaker one for poor countries. Sim- ilarly, the distribution of SWB is not more equitable in strong welfare states (Veenhoven, 2000). Ott (2005) arrived at the same conclusion for a sample of poor countries, whereas for rich countries he found, surprisingly, that welfare state transfers and sub- sidies were weakly correlated with higher, not lower, life satisfaction dispersion.

2.2.3. Trends When tracked over time, the spheres of income and happiness again seem to be separate worlds, at least in OECD coun-

tries. Whereas for income most of the discussion focussed on the ‘big U-turn’ – that is, the recent rise in inequality after a long period of levelling (Alderson et al., 2005; Alderson and Nielson, 2002; Brandolini and Smeeding, 2006; Firebaugh, 2003; Gustafsson and Johansson, 1999) – there are no such signs for life satisfaction. In Europe, the United States and Japan, dis- persions in life satisfaction have become smaller, not larger, over the past 25 years (Veenhoven, 2005).

Taken together, previous findings suggest that the extent of objective inequality (income) in nations is at best very weakly related to subjective inequality (happiness).3 What, then, matters? Affluence does: the richer a country, the more equally hap- piness is distributed (Berg and Veenhoven, 2010; Delhey, 2004; Fahey and Smyth, 2004; Ott, 2005; Veenhoven, 2005). More generally, socio-economic and political modernization drives happiness inequality down. Because ‘level and inequality of hap- piness depend ultimately on the same institutional conditions’ (Ott, 2005, p. 414), it is concluded that the same public policies that raise levels of happiness alleviate respective inequalities as well. Most generally, the findings have been viewed as evidence for the argument that happiness should be conceptualized as an absolute phenomenon, depending first and foremost on the level of need fulfilment, not on comparisons with relevant others or culturally-colored aspirations (Veenhoven, 1991).

The evidence may well reflect a profound truth about modern societies and social progress (cf. Veenhoven, 2005): Income gaps might hurt less in rich countries because many needs are satisfied, even for the poor (Böhnke and Kohler, 2008; Schyns, 2002), and the taste for post-materialist happiness is greater (Delhey, 2010; Welzel and Inglehart, 2010). In affluent societies people might also be better equipped to lead a satisfactory life because of rising education levels, a greater diversity of so- cially accepted life styles, the successful empowerment of minorities and/or a more even access to crucial resources other than income. Yet previous findings could also reflect, at least partly, a measurement technicality. This potential problem is explained in the next section.

3. Measuring happiness inequality: drawbacks of the conventional approach

All tried and tested global indicators of well-being, from life satisfaction to feeling happy and the ‘ladder of life’, use limited scales. For example, in the World Values Surveys, respondents rate their feelings of happiness on a 1–4 scale, and their life satis- faction on a 1–10 scale. The Gallup World Poll uses a ladder with 10 rungs (Veenhoven, 2007). Consequently, respondents cannot be more happy than a ‘4’, or more satisfied and content than a ‘10’. Whereas income can grow to extreme heights (think of invest- ment bankers and sports stars), observed happiness cannot. A more philosophical question is whether latent happiness is equally limited. Many adopt this view, based on the strong affective component underlying happiness judgements and the limits of the human experiential repertoire. Others point to the cognitive component involved, in particular those activities and virtues which are related to more eudaimonic or spiritual paths to happiness (Seligman, 2002), which would allow for unlimited happiness.

No matter what stance we take on this philosophical question, measures of observed happiness have a lower and upper limit. Empirically, this leads to a close association between mean life satisfaction (level) and the standard deviation (inequality). Cor- relations found are �.41 across 62 studies from 22 countries (Cummins, 2003); �.65 in a global comparison (Ott, 2005); and a startling �.86 in a European comparison (Fahey and Smyth, 2004). One – unproblematic – explanation is intrinsic dependency (Kalmijn and Veenhoven, 2005, p. 373): the presence of socio-economic mechanisms in a society that simultaneously influence the level and distribution of well-being. In short: social progress. Yet the standard deviation is also technically conditioned on average happiness, and this structural dependency (Kalmijn and Veenhoven, 2005, p. 371) is more problematic. For if a popula- tion is very satisfied with life (say, on average ‘8’ on a 1–10 scale), the respective raw standard deviation score is almost inevitable low. If a population is less happy (say, ‘5’ on average), there is more scope for unequal happiness.4

3 This is not to say that within countries having a high or low income is of little importance for well-being. Quite the contrary, the positive effect of income – or material living conditions in general – on life satisfaction is a well-established fact (Headey et al., 2004; Layard et al., 2010). Usually, the income effect is stronger in poorer societies and weaker in richer societies (Böhnke and Kohler, 2008; Schyns, 2002). 4 For income the situation is somewhat different, as it is only limited at the bottom (no income at all). The maximum feasible Gini index therefore increases ith average income (Milanovic, 2006) Another difference is that for income, structural dependency and intrinsic dependency work in different directions,

ince in modern-affluent societies social forces work for a more egalitarian income distribution, as described by (Lenski, 1984). For income, intrinsic ependency is much stronger than structural dependency, since rich countries tend to have indeed smaller Gini coefficients than poor countries (Ferreira and avallion, 2009).

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One crucial point is that the theoretical maximum of the standard deviation depends on the mean. Is this a serious prob- lem? Kalmijn and Veenhoven (2005, p. 372) give the all-clear: ‘Apparently, in this case for 2 6 m 6 8 [population means of happiness between 2 and 8 on a 0–10 scale, JD and UK], the theoretical maximum value of the standard deviation varies be- tween 4 and 5. Although both the mean and the standard deviation are bounded statistics, in practice, these boundaries are (a) only modestly dependent on the value of m and (b) fairly remote from almost all empirical values of the statistic in nation studies (1.3–2.5 on this scale)’. And a few pages later they conclude: ‘Only at very extreme mean values, which usually also give rise to strong skewness might, [sic!] this dependency be a problem. As long as such societies are not found, we can ignore this issue’ (374).

In our view, more caution may be warranted, on at least two counts. First, the argument that real-life standard deviations are far smaller than the theoretical maximums misses the point. The question is rather whether the same standard deviation, irrespective of how happy the average person is, indicates an identical degree of inequality? We argue it does not, since the scope for dispersion is somewhat smaller at the tails (i.e. in very happy and very unhappy citizenries). Secondly, one cannot a priori say whether the technical bias is, in practice, negligible. Such a conclusion would only be justified if accounting for the bias does not make a difference in substantive terms, neither for the league table of happiness inequality, nor for its deter- minants and consequences. Until now, this has been assumed rather than empirically tested.

Do we have any empirical evidence that these measurement technicalities deserve our attention? Structural dependency would predict an inverted U-curve relationship between the central tendency and the dispersion: the standard deviation is zero when everybody reports complete dissatisfaction – all are equally dissatisfied with life. It increases when the average person moves towards neutral satisfaction levels, reaching its (theoretical) maximum value at the mid-point of the scale. If average satisfaction increases further standard deviation begins to decline again, finally reaching zero if everyone is com- pletely satisfied with life. In contrast, intrinsic dependency would suggest a downward-directed regression line: large gaps in unhappy nations, and small gaps in happy nations, since both are essentially driven by the same social forces.

Fig. 1 is based on data of the World Value Survey (WVS) from Wave 5 (which will be introduced in more detail in Section 5.1). It plots mean life satisfaction for over 50 nations against the raw standard deviation (top panel). The inverted U-curve we get is close to the pattern predicted by structural dependency: dispersion of life satisfaction is highest in moderately hap- py populations with means close to the mid-point of the scale; it is somewhat lower in less happy nations, and lowest among the happiest nations, with Mexico and Colombia being partial exceptions.5 This evidence makes it difficult to hold the position that the problem is negligible. Rather, the results suggest the need for (a) a more refined measure that adjusts for structural dependency and (b) empirical evidence whether adjustment makes a difference. Two suggestions are developed and applied in the remainder of this article.

4. Correcting for instrument effects: two suggestions

In order to remove structural dependency let us define as a target quantity the instrument-effect-corrected standard devi- ation as

5 If d pattern

6 The This wa standar

SDIEFF ¼ SDRaw � IEFF ð1Þ

where SDRaw is the standard deviation of an observed variable and IEFF is an ‘‘instrument effect’’ that captures the structural dependency. An instrument effect of 1 leaves the raw measure unchanged, while an instrument effect of, say, 2 leads to a corrected standard deviation that is two times larger than the raw standard deviation. In what follows we suggest two ways to quantify the instrument effect using different assumptions.

Our first suggestions assumes that happiness is not just measured using limited rating scales, but is also conceptually lim- ited in the sense that there is in fact a minimum and a maximum degree of happiness. Consequently, the standard deviation of happiness will be limited between 0 and max ðrÞ where

maxðrÞ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðu � lÞ�ðl � lÞ� N

N � 1

r ð2Þ

The parameters u and l represent the upper and lower boundary of happiness and l is its mean (cf. Kalmijn and Veenhoven, 2005).6 From the formula we see that structural dependency exists in the sense that the maximum standard deviation increases with the mean moving towards the center of the scale. Moreover, the maximum standard deviation also depends on the mini- mum and maximum value of the instrument used to measure happiness. Our first suggestion to remove structural dependency is therefore to define IEFF as

IEFFA ¼ 1

maxðrÞ ð3Þ

ata were available on nations even less happy than Iraq (which probably are difficult to find), we expect an even more ‘‘complete’’ inverted U-curve . formula slightly deviates from the formula presented by (Kalmijn and Veenhoven, 2005) in multiplying the term inside the square root with N/(N � 1). s necessary because the formula of Kalmijn and Veenhoven represents the maximum of the population standard deviation, while we used the sample d variation.

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Fig. 1. Average happiness and happiness dispersion in nations.

746 J. Delhey, U. Kohler / Social Science Research 40 (2011) 742–756

The resulting IEFFA-corrected standard deviation is tantamount to the proportion of the standard deviation from the the- oretical maximum. Hence, the measure will have values between 0 and 1, with 0 meaning that all citizens of the country are equally happy (or unhappy), and 1 meaning that the country reaches the highest standard deviation possible given the aver- age level of happiness in this country. We suggest to name this new measure percent maximum standard deviation. A short example demonstrates how it works in practice. Consider four nations which all have life satisfaction standard deviations of 2.0, but at different levels of mean happiness: 5, 6, 7, and 8 (on a 0–10 scale). These mean levels correspond to varying max- imum standard deviations of 5.00, 4.90, 4.58, and 4.00.7 The logic applied is that the identical dispersion of 2.0 captures dif- ferent proportions of the maximum possible dispersion – to be precise, 40%, 41%, 44%, and 50% (the highest value in our example), respectively. Thus, rather than being identically unequal (the conclusion when we accept the standard deviations of 2.0 at their face value), the four nations in our example are in fact characterized by different degrees of well-being inequality.

The starting point of our second suggestion is the distinction between individuals’ observed happiness and their true – yet unknown – underlying latent happiness. The latter we regard as interval-scaled, continuous, and unlimited. ‘‘Unlimited’’ means that even if a person is very happy, there might be a situation where he becomes even happier. Similarly, even if there is a very unhappy person, he might become even less happy some day. We further regard latent happiness as normally dis- tributed, which is not an unusual assumption in well-being research (e.g. Stevenson and Wolfers, 2008).8

If we measure this kind of latent happiness using a categorical, limited scale the situation illustrated in Fig. 2 arises. The curve shows a fictitious distribution of latent happiness – in this example, a normal distribution with a mean of 7

7 We assume having a large sample, so that N/(N � 1) approximates 1. 8 We also looked at those eight countries from the WVS 5 with average life satisfaction between 5 and 6 (close to the mid-point of the 1–10 scale), and find

that the assumption of a normal distribution is warranted here.

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Latent happiness Observed happiness

Fig. 2. Distribution of latent and observed happiness.

J. Delhey, U. Kohler / Social Science Research 40 (2011) 742–756 747

and a standard deviation of 2. Most individuals have values between 4 and 10, but some score above 10. Now, consider this latent happiness as measured on a scale with 11 categories, from 0 to 10. Each respondent is forced to match his or her ‘true’ degree of happiness to the closest category offered, and we assume that those whose true (latent) happi- ness lies above ‘10’ have no other choice than to choose the ‘10’. The bars in Fig. 2 show the resulting distribution of observed happiness. It is obvious that limited scales result in an inflated proportion of respondents in the highest category.

Another consequence is that the standard deviation s of observed happiness deviates from the ‘‘true’’ standard deviation r of latent happiness. If we knew the amount of difference between the two quantities we could use this information to define the instrument effect as

9 Eac

IEFFB ¼ r s

ð4Þ

IEFFB measures how much larger the latent standard deviation is compared to the one observed. In order to quantify IEFFB

we conducted a simulation-study. In this simulation we created categorical happiness variables by randomly drawing obser- vations from a normal distribution with predefined variances and means between the upper and lower boundary of the sim- ulated scale.9 The reciprocal values of the standard deviation of the variables created are then multiplied with the predefined variance to get an estimate for IEFFB.

How large are the two different instrument effects of commonly used happiness scales? The answer is provided in Figs. 3 and 4, respectively. Fig. 3 shows the values of IEFFA by happiness means, for scales with 11-points (with categories from 0 to 10), 7-points (1–7), and 4-points (1–4). Fig. 4 does the same for IEFFB for two different predefined values of r, namely r = 1 and r = 3. Note that IEFFA involves a rescaling of the standard deviation to a scale between 0 and 1, while IEFFB does not. The values of IEFFA are therefore smaller than 1 even in the center of the distribution, while IEFFB values are always higher than 1 (i.e. raw standard deviations underestimate happiness inequality).

The main point is that, no matter which correction procedure we apply, instrument effects tend to be small and more similar in and around the center of the distribution, and only becomes larger at the edges. Therefore, any correction tends to be large in very happy and very unhappy nations only (where average well-being approaches the lower or upper bound- aries of the scale). As a consequence, correlations of instrument effect-corrected standard deviations with quantities such as income inequality are likely to remain largely unchanged as long as IEFF corrections are small. A second key message is that instrument effects vary stronger with mean happiness when rating scales with only few categories are used, so that correc- tion is generally larger for coarsely SWB measures. These two properties are shared by both procedures, whereas one effect is peculiar to IEFFB: It co-varies with the assumed standard deviation of latent happiness. Generally, the IEFFB correction will be larger the higher the assumed standard deviation is.

At first glance, to say that corrections are usually small as long as mean happiness is not either extremely high or extre- mely low seems to corroborate Kalmijn and Veenhoven (2005), who claim that the raw standard deviation can be taken as it is. However, it should be noted that the instrument effects shown in Figs. 3 and 4 are not constant even in the center of the distribution, and their variation with the mean is systematic. Further, any larger set of countries might include a couple of societies which larger IEFF corrections. We consider it an empirical question to which extent substantial results actually change when these corrections are applied. The answer is given in the next section.

h round of the simulation created 1000 observations of the ‘‘observed’’ happiness variable, and we conducted 200 simulations for each setting.

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Fig. 4. Simulation of instrument effect-B, for three different.

748 J. Delhey, U. Kohler / Social Science Research 40 (2011) 742–756

5. Application to WVS 5

5.1. Data and variables

The World Values Survey (WVS) is the largest project to analyze values and cultural change worldwide. Wave 5, which extents from 2005 to 2007, covers 52 countries from all major world regions. The surveys consist of representative samples of the population aged 18 and older, with sample sizes ranging between 954 in New Zealand and 4030 in Indonesia.10 They contain a tried and tested rating question concerning overall life satisfaction, our measure of happiness:

All things considered, how satisfied are you with your life-as-a-whole these days? Please use this card to help with your answer.

[1 completely dissatisfied 2 3 4 5 6 7 8 9 10 completely satisfied].

10 Survey statistics for all countries participating in the Word Values Survey are available in the section ‘‘Data and Documentation’’ at http:// www.worldvaluessurvey.org/. However, for the time being the information provided are not sufficient for calculating meaningful response rates. E.g., only six of the 51 participating countries in wave five provided information on the total eligible sample, and only four countries provided detailed reasons for non- response (these four are Andorra, Spain, Taiwan, and Trinidad & Tobago). Dividing the final sample (conducted interviews) by the total eligible sample yields response rates ranging between 44% in Taiwan and 100% in Thailand. Yet it is difficult for users of the WVS to assess the quality of these information.

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National means vary between 4.5 and 8.3 (see Fig. 1, any panel, X-axes).11 The happiest places are Colombia and Mexico, the least happy place by far is Iraq. This ranking mirrors very well previous rankings (Bjornskov, 2010; Diener et al., 1995; Inglehart and Klingemann, 2000; Vemuri and Constanza, 2006), which increases our confidence in the WVS 5 data.12

The countries also differ widely with respect to income inequality, as measured with the Gini coefficient, and affluence, our two key independent variables. The Gini can range from 0 to 100, with 0 indicating absolute equality (all incomes being equal) and 100 indicating absolute inequality (all income goes to one single person or household). Japan and Sweden are most equal (Gini of 24), Colombia most unequal (Gini of 58). Gini coefficients are taken from the Human Development Report 2007/08 (UNDP, 2007). Affluence is measured as the logarithm of gross domestic product per capita in purchasing power parity, taken from the recent International Comparison Program of the Worldbank (2008). Our set of nations include high-income countries (a number of OECD countries, including the United States), middle-income countries (among them China and India), and low-income countries (such as Rwanda, Zambia, Ethiopia, Mali and Burkina Faso). Indicators for other country characteristics used are listed in Appendix B.

5.2. Estimating instrument effects for the WVS 5

Employing Eq. (3) above, the percent maximum calibration (IEFFA) is computed. For the 1–10-scale used in the WVS the maximum standard deviation of life satisfaction is 4.51, at a mean of 5.5. For IEFFB (Eq. (4)) the simulation-study described above was re-run for the 10-point scale. A preparatory step here is to predefine the – unfortunately – unknown standard deviation of latent happiness. As a proxy we set it to the value of the raw standard deviation across all WVS 5 observations, which is 2.34.13 The simulated average value of IEFFB for a specific mean was merged back to those countries with exactly that level of mean happiness.14 Appendix A lists raw standard deviations, the two instrument effects and respective corrected standard deviations for all WVS 5 countries. Equipped with two new measures, we can now move on to the findings.

5.3. Country rankings of happiness inequality

We start with the conventional approach (Fig. 1, upper panel, Y-axis). Raw standard deviations vary between 1.4 and 2.8, with gaps in life satisfaction being smallest in the Netherlands, Spain, and Norway. The 10 most equal societies are exclu- sively Western. Gaps are largest in Jordan, Egypt and Ghana. Among the 10 most unequal societies are five from Africa.

The IEFFA-corrected standard deviations range between .34 and .68, in other words between 34% and 68% of maximum dispersion (Fig. 1, middle panel). The most egalitarian countries are the Netherlands (still), Spain and Andorra. New in the top 10 are Morocco and Malaysia. The least egalitarian is still Jordan, now by a wide margin. Newcomers among the most unequal societies are Guatemala and Mexico. The non-parametric regression line (LOWESS) indicates that the corrected standard deviation is related to average life satisfaction to a lesser extent than is the case for the raw standard deviation. Finally, the lower panel of Fig. 1 exhibits scores corrected with IEFFB (simulation-based). Adjusted standard deviations range from a low 1.6 (Netherlands) to a high 3.2 (Jordan). The scatterplot is strikingly similar to the one for the IEFFA correction. Both new measures rank Mexico and Guatemala among the most unequal countries, in contrast to the conventional measure.

Table 1 shows in more detail the re-ranking of countries when we move from uncorrected dispersion (middle column) to IEFF-corrected happiness dispersion (left-hand side columns-percent maximum standard deviation; right-hand side columns-standard deviations corrected with IEFFB). A ‘‘ + ’’ in columns 1 and 5 indicates which countries moved up (towards greater equality) and how many ranks they gained, a ‘‘�’’ indicates which countries moved down (towards greater inequality). The overall rank correlation coefficient (Spearman) between the ‘old’ and the ‘new’ ranking(s) is .91 and .90 for IEFFA and IEFFB, respectively. Some countries change their position only marginally, if at all. Yet a handful of countries do shift by more than 10 ranks, with the greatest change experienced by Colombia (�22 ranks), Mexico (�22), and Guatemala (�15). New Zealand, Fin- land, and Argentina slide down roughly 10 places. Moves towards greater equality are generally less dramatic, with Serbia and Burkina Faso climbing-up 10 ranks each, and Rwanda, Morocco, and Moldova 9 ranks each. When we look at broad world re- gions, the most evident change is the collective descent by Latin America, whereas there is a mild tendency of a collective ascent by Africa and Eastern Europe. Latin America is a region (in)famous for enormous gaps between rich and poor (De Ferranti et al., 2003), which is hardly reflected in raw happiness standard deviations, but leaves more traces in the adjusted scores.

5.4. Correlates and determinants of happiness inequality

We now turn to correlates and determinants of happiness inequality, starting with income distribution and wealth. Descrip- tive scatterplots are provided in Fig. 5. We start with raw happiness dispersion, which is only weakly associated with income

11 The country abbreviations used in the figures are listed in Appendix A. 12 Rankings using the ladder of life look a bit different (Bjornskov, 2010). 13 Thus, our final correction factor will be a conservative estimate, because, given our assumptions about latent happiness, the variance of latent happiness

must always be larger than that of observed happiness. 14 Technically the merge is performed by fitting a regression model of the simulated standard deviation on mean and mean-squared of the simulated

happiness. The results of this regression were then used to predict the standard deviation in the WVS country data. The details of this procedure can be studied in the Stata Do-File ancorrwvs3.do in the online appendix on http://www.wzb.eu/~kohler/publications/happinessinequality/index.html.

Table 1 Happiness inequality rankings (top = low inequality) and rank changes.

D Rank Rank SDIEFF-A Rank SDRaw Rank SDIEFF-B D Rank

0 Netherlands Netherlands Netherlands 0 0 Spain Spain Spain 0

+4 Andorra Norway Andorra +4 �1 Norway Switzerland Morocco +10 +9 Morocco Sweden Norway �2

0 United Kingdom United Kingdom United Kingdom 0 +3 Italy Andorra Italy +3 �3 Sweden Canada Sweden �3 +4 Malaysia United States Malaysia +4 �1 United States Italy United States �1 �7 Switzerland Finland Switzerland �7

0 Germany Germany Germany 0 +3 Japan Malaysia Japan +3 �6 Canada Morocco Canada �6

0 Thailand Thailand Thailand 0 +7 Hong Kong Japan Hong Kong +7 +8 South Korea Australia South Korea +8 �1 Australia New Zealand Australia �1 +2 France Uruguay France +2

0 Viet Nam Viet Nam Ethiopia +8 +7 Ethiopia France Viet Nam �1 �11 Finland Argentina Finland �11 �4 Uruguay Hong Kong Uruguay �4

+10 Serbia Colombia Serbia +10 +1 Slovenia South Korea Rwanda +11 +5 Taiwan Slovenia Taiwan +5 +9 Rwanda Cyprus Slovenia �1 �1 Cyprus Ethiopia Burkina Faso +10 +9 Burkina Faso Chile Cyprus �2 �1 Chile Mexico Chile �1 �13 New Zealand Taiwan New Zealand �13 �10 Argentina Poland Argentina �10 �1 Poland Guatemala Poland �1 +9 Moldova Serbia Moldova +9 +7 Georgia Brazil Georgia +7 +1 Indonesia Rwanda Bulgaria +8 +7 Bulgaria Indonesia Indonesia 0 +7 India Burkina Faso India +7 +7 Ukraine Trinidad and Tobago Ukraine +7 +1 Peru Turkey Romania +7 +6 Romania Peru Peru 0 �7 Brazil Georgia Brazil �7 �4 Trinidad and Tobago Moldova Trinidad and Tobago �4 +5 Iran Bulgaria Iran +5 +7 Russian Federation India Russian Federation +7 �6 Turkey Ukraine Colombia �22 �23 Colombia Romania Iraq +4

+3 Iraq China Turkey �8 �16 Guatemala Iran China �1 �2 China South Africa Guatemala �17 +2 Zambia Iraq Zambia +2 �2 South Africa Russian Federation South Africa �2 �23 Mexico Zambia Mexico �23

0 Mali Mali Mali 0 0 Ghana Ghana Ghana 0 0 Egypt Egypt Egypt 0 0 Jordan Jordan Jordan 0

Note: + = move towards less inequality; � = move towards more inequality.

750 J. Delhey, U. Kohler / Social Science Research 40 (2011) 742–756

inequality (r = .27, p > .05), and the association is not statistically significant at the usually adopted 95% level. Instead, the raw dispersion measure is strongly driven down by per capita income (r = �.73, p < .001): the richer the country, the less unequal subjective life experiences are. When entering both terms into a regression equation (Table 2), it is national income that matters, not income distribution, a finding completely in line with previous research based on uncorrected standard deviations.

With both new measures the outcome is different. For the IEFFA correction, both national affluence (negatively) and income distribution (positively) are strong correlates, very similar in strength (r = �.42, p < .001 for income level; r = .41, p < .01 for the income Gini). The scatterplot (Fig. 5, middle panel) reveals an almost perfect linear relationship between income inequality and the IEFFA-corrected standard deviation. In other words: happiness inequality tends to be larger in places where income gaps are

AD

AR AU

BF BG

BR

CA CH

CL

CN

COCY

DE

EG

ES

ET

FI

FR

GB

GH

GT

HK

ID

IN IR

IT

JO

JP KR

MA

MD

ML

MX

MY

NL

NO

NZ

PE

PL

RO

RS

RU

RW

SE

SI TH

TRTT

TW

UA

US

UYVN

ZA ZM

AD

AR

AU

BF BG

BR

CACH

CL

CN CO

CY

DE

EG

ES

ETFI FR

GB

GH

GT

HK

ID IN

IR

IT

JO

JP KR

MA

MD

ML MX

MY

NL

NO

NZ

PE

PL

RO

RS

RU

RW

SE

SI

TH

TR TT

TW

UA

US

UY VN

ZAZM

AD

AR

AU

BF BG

BR

CACH

CL

CN CO

CY

DE

EG

ES

ETFI FR

GB

GH GT

HK

ID IN

IR

IT

JO

JP KR

MA

MD

ML MX

MY

NL

NO

NZ

PE

PL

RO

RS

RU

RW

SE

SI

TH

TR TT

TW

UA

US

UY VN

ZA ZM

1. 5

2 2.

5 3

.3 .4

.5 .6

.7 1.

5 2

2. 5

3

20 30 40 50 60

Raw SD

IEFF−A

IEFF−B

In eq

ua lit

y of

li fe

s at

is fa

ct io

n

Income inequality (Gini 2005)

Fig. 5. Income inequality and happiness dispersion in nations.

J. Delhey, U. Kohler / Social Science Research 40 (2011) 742–756 751

larger. Jordan is a clear outlier – well-being inequality is large, whereas there is nothing special about Jordan’s income distribu- tion, as far as one can tell from the Gini coefficient. According to the regression analysis, both per capita income and income dis- tribution matter for the corrected happiness inequality, with per capita income being more important (Table 2). Finally, we use IEFFB corrected standard deviations as the dependent variable. The results confirm the findings for the IEFFA correction: both affluence and income distribution – in this order – matter for a nation’s distribution of happiness.

The last analysis deals with a greater variety of societal correlates of happiness inequality, using Ott (2005) as a reference (Fig. 6).15 Again, we want to know whether correction to the dispersion measure makes a difference. Across the board, corre- lations for corrected happiness inequality (both versions) do not differ much from those for uncorrected standard deviations. There is no difference with respect to direction: progress leads to more equal life results (indicated by negative correlations), no matter whether we define progress economically, politically, or socially. Being scaled in the opposite direction, only income inequality leads to more unequal life results as indicated by a positive correlation. The difference lies in the strength of corre- lations. For corrected happiness dispersion, the relation with the progress indicators is somewhat weaker, bar political stability and social security, and the one with income inequality is stronger, as we just pointed out. Provided policy aims at equalizing well-being, progress is certainly of paramount importance, but a bit less so than previously thought, whereas fighting income inequality turned out to be more important than previously thought.

6. Discussion and conclusions

Our point of departure concerned doubts about the conventional statistics for happiness inequality. We find fault with the practice of using the raw observed standard deviation, without correcting for instrument effects. Measured by using bounded

15 The only bigger difference between Ott’s indicators and ours concerns gender equality; we use an attitudinal measure (see Appendix B) instead of the Gender Empowerment Measure.

Table 2 Explaining happiness inequality: OLS regressions.

Raw SD IEFF-A IEFF-B

Income inequality (Gini) 0.112 0.280* 0.291*

(0.99) (2.33) (2.41) Log GDP per capita (in PPP) �0.612*** �0.449*** �0.432***

(�5.42) (�3.74) (�3.57) Observations 52 52 52 R2 0.426 0.352 0.343

Dependent variable: happiness inequality (life satisfaction). Standardized beta coefficients; t statistics in parentheses. Data: WVS 5. * p < 0.05. ⁄⁄ p < 0.01. *** p < 0.001.

Income inequality (Gini) Size of government

Political Stability Social security (% GDP)

Economic Freedom (Fraser) Voice and accountability

Economic Freedom (Heritage) Regulatory Quality

Rule of Law Control of Corruption

Gov effectiveness Wealth (p/c)

Gender Equality Scale

−.75 −.5 −.25 0 .25 .5 .75 Correlation with inequality of life satisfaction

Raw SD IEFFA/IEFFB

Fig. 6. Further correlates of happiness inequality.

752 J. Delhey, U. Kohler / Social Science Research 40 (2011) 742–756

scales, a nation’s standard deviation of happiness is also technically conditioned on average happiness, not only by social mechanisms. Provided this bias is substantial, we get an inaccurate impression of the extent of happiness inequalities and the societal conditions driving them. While widely held, the view of unbiasedness has not been subject to empirical evaluation.

Our research suggests that the bias is not negligible. We developed two procedures to account for instrument effects, a percent maximum calibration, and a simulation-based adjustment. Compared to the conventional approach, both new ap- proaches produce substantial differences in the country ranking of happiness inequality, with Latin American countries in particular exhibiting greater inequality. Further, they lead to new insights about macro-level determinants: where economic resources are unequally distributed, subjective appreciation of life-as-a-whole tends to be rather unequal, too. In other words: happiness inequality is not immune to income inequality. Yet it is important to note that the new evidence is not in every way contradictory to conventional wisdom, e.g. the finding that affluence and other characteristics of a liveable soci- ety (such as rule of law, political freedom etc.) drive happiness inequality down.

Although the two new measures developed here rest on very different assumptions and use different techniques, they yield (almost) the same findings. We take this as evidence for the robustness of our claim. Which of the two new measures, then, is preferable? In the case of life satisfaction measured on a 10-point scale, we argue in favour of the IEFFA correction: it is much easier to compute and rests on assumptions which are more consensual, namely that latent happiness is limited. The interpretation of the scores as the percentage of the maximum possible inequality is very intuitive, and scores from different scales can easily be compared, since they are expressed in a common metric. Thus our recommendation is to use this cor- rection-technique, for which we propose the term Percent Maximum Standard Deviations, in future studies, and to discon- tinue the use of unadjusted standard deviations.16

16 Percent maximum standard deviations pass all the standards proposed by Kalmijn and Veenhoven (2005), with one exception: Since the goal is to reduce structural dependency, they are not (and should not be) independent of the mean, since it tries to retain intrinsic dependency. Further, percent maximum standard deviations pass the criterion of being insensitive to linear scale transformations, a property which gives it an additional advantage over raw standard deviations. A Stata program that calculates percent maximum standard deviations is downloadable from the Statistical Software Components (SSC) Archive using the Stata command ‘‘ssc install sdlim’’.

J. Delhey, U. Kohler / Social Science Research 40 (2011) 742–756 753

What are the policy implications? Conventional wisdom has concluded that, from the perspective of happiness (increas- ing) income inequality does not pose an ethical problem (Berg and Veenhoven, 2010), and that redistributing incomes is not an effective measure to level gaps in well-being (Ott, 2005). The findings presented here suggest the reverse: income inequality does pose an ethical problem because it leads to unequal life results, and redistributing income does have an equalizing effect on well-being. That means that policy makers have an additional tool in the box for equalizing well-being: income redistribution.

The evidence also let us to think anew about the nature of happiness. Previous research on happiness inequality has usu- ally concluded that happiness is absolute, not relative. Yet the sensitivity to income distribution demonstrated in this article indicates that it does not rest entirely on the fulfilment of absolute needs. There is a relative component as well (though prob- ably weaker than the absolute component), so that social comparisons do play a part in how we judge our lives (cf. Michalos, 1985). Comparison effects have been shown in a number of studies, both experimental (Frank, 1997) and survey research (Clark et al., 2008; Delhey and Kohler, 2006; Luttmer, 2005; Offer, 2006).

The main purpose of this study was to refine the measurement of happiness inequality, and to revisit the link with income inequality. An extension would be to systematically apply the new approach to different components of well-being, like mood level or contentment with life (cf. Nettle, 2005; Veenhoven, 2007). It could be that the association with income inequality is stronger for more cognitive components and weaker for more affective ones (cf. Berg and Veenhoven, 2010). A further extension would be to apply the percent maximum calibration to the standard deviation scores assembled together from different surveys worldwide in the World Database of Happiness, and to re-assess the main determinants of happiness inequality worldwide with maximum geographical coverage. In conclusion, our research suggests that previous work on lev- els, trends and correlates of happiness inequality needs to be revisited. The good news, however, is that we have made a step forward towards a better measure.

Acknowledgments

We are very grateful to the anonymous reviewers and the editor for their helpful comments on an earlier version of this article, and to Tom Cusack who kindly helped us with the language check.

Appendix A

Country abbreviations and statistics for life satisfaction dispersion

Code

Country

SDraw

IEFF A

SDIEFF

IEFF

B

SDIEFF

AD

Andorra

1.627

0.238

0.388

1.107

1.801

AR

Argentina

1.920

0.255

0.489

1.187

2.278

AU

Australia

1.817

0.242

0.440

1.124

2.043

BF

Burkina Faso

2.181

0.222

0.484

1.023

2.232

BG

Bulgaria

2.279

0.223

0.507

1.026

2.338

BR

Brazil

2.099

0.253

0.531

1.178

2.473

CA

Canada

1.667

0.257

0.428

1.197

1.996

CH

Switzerland

1.577

0.267

0.422

1.246

1.965

CL

Chile

2.035

0.239

0.486

1.110

2.258

CN

China

2.400

0.231

0.556

1.071

2.572

CO

Colombia

1.936

0.284

0.551

1.320

2.555

CY

Cyprus

1.977

0.244

0.483

1.136

2.246

DE

Germany

1.751

0.242

0.424

1.126

1.972

EG

Egypt

2.689

0.223

0.598

1.025

2.755

ES

Spain

1.500

0.243

0.364

1.130

1.695

ET

Ethiopia

2.014

0.224

0.450

1.031

2.077

FI

Finland

1.746

0.260

0.454

1.211

2.115

FR

France

1.903

0.234

0.445

1.084

2.063

GB

United Kingd.

1.608

0.251

0.404

1.169

1.880

GE

Georgia

2.254

0.224

0.504

1.032

2.327

GH

Ghana

2.630

0.224

0.590

1.034

2.720

GT

Guatemala

2.086

0.265

0.552

1.234

2.574

HK

Hong Kong

1.928

0.227

0.437

1.047

2.020

ID

Indonesia

2.157

0.234

0.505

1.084

2.338

(continued on next page)

754 J. Delhey, U. Kohler / Social Science Research 40 (2011) 742–756

Appendix A (continued)

Code

Country

SDraw

IEFF A

SDIEFF

IEFF

B

SDIEFF

IN

India

2.351

0.223

0.523

1.026

2.411

IQ

Iraq

2.419

0.228

0.552

1.057

2.556

IR

Iran

2.401

0.227

0.545

1.049

2.517

IT

Italy

1.742

0.233

0.407

1.082

1.885

JO

Jordan

2.868

0.238

0.683

1.105

3.170

JP

Japan

1.809

0.235

0.426

1.092

1.976

KR

Korea

1.942

0.226

0.439

1.045

2.028

MA

Morocco

1.803

0.222

0.401

1.025

1.849

MD

Moldova

2.261

0.222

0.502

1.023

2.314

ML

Mali

2.592

0.224

0.581

1.033

2.678

MX

Mexico

2.053

0.279

0.573

1.298

2.665

MY

Malaysia

1.789

0.233

0.416

1.078

1.928

NL

Netherlands

1.328

0.257

0.341

1.196

1.588

NO

Norway

1.506

0.265

0.399

1.235

1.860

NZ

New Zealand

1.860

0.262

0.488

1.222

2.274

PE

Peru

2.231

0.236

0.527

1.097

2.447

PL

Poland

2.082

0.236

0.491

1.095

2.280

RO

Romania

2.385

0.223

0.531

1.025

2.444

RS

Serbia

2.087

0.224

0.467

1.031

2.151

RU

Russia

2.436

0.224

0.546

1.033

2.518

RW

Rwanda

2.112

0.224

0.473

1.032

2.180

SE

Sweden

1.605

0.256

0.411

1.193

1.916

SI

Slovenia

1.951

0.241

0.470

1.120

2.184

TH

Thailand

1.806

0.240

0.434

1.116

2.016

TR

Turkey

2.228

0.247

0.550

1.148

2.559

TT

Trinidad

2.225

0.241

0.537

1.122

2.496

TW

Taiwan

2.064

0.229

0.472

1.058

2.184

UA

Ukraine

2.360

0.222

0.525

1.024

2.417

US

United States

1.717

0.243

0.417

1.130

1.940

UY

Uruguay

1.873

0.247

0.462

1.148

2.151

VN

Viet Nam

1.891

0.238

0.449

1.103

2.085

ZA

South Africa

2.402

0.236

0.567

1.096

2.632

ZM

Zambia

2.497

0.224

0.559

1.032

2.577

Appendix B

Country. characteristics used in the analysis

All indicators are taken from Teorell, J., Charron, N., Samanni, M., Holmberg, S., Rothstein, B., 2010. The Quality of Govern- ment Dataset, version May27, 2010. University of Gothenburg, The Quality of Government Institute, http:// www.qog.pol.gu.se.

Gender equality scale: Based on Word Value Survey. Original source: Inglehart, R., Norris, P., 2003. Rising Tide, Gender Equality and Cultural Change around the World. Cambridge University Press, Cambridge.

Social security (% GDP): Government expenditure on social security and welfare (% of GDP). Original source: Easterly, W.R., 2001. The lost decades: Developing countries’ stagnation in spite of policy reform 1980–1998. Journal of Economic Growth, 6 (2), 135–157.

Government effectiveness, Control of corruption, Rule of law, Regulatory quality, Voice and accountability, Political stability: Original source: World Bank – Governance Indicators (http://www.govindicators.org). Kaufmann, D., Kraay, A., Mastruzzi, M., 2009. Governance Matters VIII: Aggregate and Individual Governance Indicators for 1996–2008. World Bank Policy, Re- search Paper No. 4978.

Economic freedom (Heritage): Economic Freedom Index, Heritage Foundation (http://www.heritage.org/ index/).

Economic freedom (Fraser), Size of government: Fraser Institute – Economic Freedom of the World (http://www.freethe- world.com/); Original source: Gwartney, J., Lawson, R., 2006. Economic Freedom of the World: 2006 Annual Report. Vancou- ver, The Fraser Institute.

J. Delhey, U. Kohler / Social Science Research 40 (2011) 742–756 755

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