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Distributional dynamics of life satisfaction in Europe (1990-2013)

Vanesa Jordá, Borja López-Noval, José María Sarabia

Department of Economics, University of Cantabria, Spain

Abstract

The main purpose of this paper is to study the distributional dynamics of life satisfaction in Europe since 1990. To deal with the ordinal nature of subjective well-being variables, we use scale independent inequality measures based on the ordering proposed by Allison and Foster (2004). We also compute polarization measures to investigate patterns of convergence clubs in Europe. Our results show the different evolutions of inequality and polarization in life satisfaction, thus pointing out that both concepts differ also on the empirical basis. The analysis suggests that the current dynamics of the life satisfaction distribution, associated to the Great Recession, differs from the dynamics observed during the early 90’s economic crisis. During both crises the proportion of citizens with low levels of life satisfaction rose, but only in the current crisis, the proportion of the population at the top category remained unchanged, thus increasing inequality and polarization.

Keywords: life satisfaction, financial crisis, ordinal variables, inequality, polarization.

1. Introduction

It seems we are witnessing a period especially concerned about which should be the goals of public policy. It is well known that economic performance, measured mainly through GDP per capita, has had a central place in public policy evaluation in the past (at least this is said one million times a day). No need to say that the traditional economic approach has been especially prevalent in economics. One of the reasons is that GDP can be viewed as summarizing, under some assumptions, a set of generally-desired outcomes (Benjamin et al., 2012). Well-being is ordinarily included among those generally-desired outcomes both in public policy evaluation and economics1. Nonetheless, there is an emerging consensus as regards the limitations of traditional economic approach to well-being and the benefit of using other indicators, such as subjective well-being measures2 (Diener and Seligman, 2004; Kahneman and Krueger, 2006; Stiglitz et al., 2009).

1 Although well-being does not comprehend all possible goals of public policy (as would be discussed

briefly below) and actually the prevalent acceptation of the economic concept of “utility”, which in its origins was tightly linked to well-being, refers nowadays to a preference ranking which relationship with well-being is less stringent. 2 This concern is not new. Pigou (1932), one of the main contributors to the economic approach to well-being, already pointed out that economic well-being is just one component of total well-being, which could eventually even come into conflict with others. Pigou also anticipated the possible moderator role of one psychological mechanism: adaptation, in the relationship between economic and total well-being.

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The most appealing feature of those subjective well-being measures, which we would discuss in the following section, is that they reflect a wide range of experiences, including those unrelated to market exchange (Benjamin et al., 2012). From a more critical point of view, many authors claim that a crucial assumption of the revealed preferences (economic) approach to well-being, that individuals have sufficient information when making decisions, is not fulfilled. Thus they advocate the adoption of the realized preferences (subjective well-being) approach to well-being. Besides, subjective well-being measures avoid any arbitrary selection of objective indicators, and the functional form that relates them to well-being. Additionally, they would be interesting because subjective well-being (SWB) has positive spillovers—it is associated with other desire outcomes (Lyubomirsky et al. 2005, in Ed Diener 2006).

Nonetheless, there is some controversy with respect to the usage of SWB indicators in public policy evaluation. On the one hand, there is some dispute about (which should be) the role of subjective well-being in public policy. Sen ([1999] 2000) considers that subjective well-being is only one component, among others, of the things that people

have reasons to value3. In a similar vein, Benjamin et al. (2012) point out that SWB measures may not capture all factors that enter into preferences or utility (although Sen, [1999] 2000, argues that information beyond individual utilities may be needed to avoid unjust policy evaluations given that preferences might be affected by the psychological mechanism of adaptation). In any case, as a component of the things that people have

reasons to value SWB measures are very relevant. Besides, many authors give a special status to SWB among the things that people have reasons to value: firstly, all the things that people have reasons to value are supposed to be associated to subjective well-being; and secondly, as was mentioned previously, SWB is associated with other desire outcomes (Lyubomirsky et al. 2005, in Ed Diener 2006).

On the other hand, two opposite hypothesis question the real possibility of establishing SWB as a policy goal. Firstly, it is the hypothesis that SWB is unstable, sensible to many factors, and thus difficult to control. As none public policy encompasses all the determinants of SWB other goals should be targeted. Nevertheless, there is some evidence regarding the stability of SWB self-assessments at the population level (Robinson and Shaver, 1969, in Easterlin, 1974). And that is precisely the point of the second hypothesis, which states that SWB is a personal trait independent (in the long term) of social, institutional and even personal conditions. Easterlin (2003) explicitly addresses this issue and provides extensive evidence against the set point theory.

Thus, additional economic growth would eventually have no impact in terms of total well-being once basic needs are covered and the psychological mechanism of adaptation prevails and cancels out that effect. Easterlin (1974) pioneered the use of survey questions about one's own happiness or life satisfaction as proxies of total well-being. 3 Other component of the things that people have reasons to value, independently of their actual impact on individuals' subjective well-being, are rights and freedom.

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Literature that addresses social determinants of mental health provides also evidence regarding the impact of social and institutional conditions on SWB.

In economics SWB measures are gaining importance, firstly recovering some of the original acceptation of utility4, and then using them to test several assumptions of standard economic theory (Easterlin, 1974; Benjamin et al., 2011; Benjamin et al., 2012). Economic research is connected to other fields' well established theory and evidence, mainly health related quality of life research and psychological well-being studies, and to recent quality of life initiatives lead by important international institutions such as the European Union and the OECD.

Notwithstanding the expansion of well-being levels is one of the main policy goals, its distribution is also relevant. Distributional patterns of SWB have received an increasing attention in recent years, but the bulk of this literature relies on the cardinalization of the categorical variables to compute conventional inequality measures (see e.g, Ott, 2005; Kalmijn and Veenhoven, 2005; Veenhoven, 2005). However, these inequality measures are heavily dependent on the scales assigned, which may vary among individuals. Recently there have been some attempts to develop scale independent inequality measures for ordinal variables. The ordering proposed by Allison and Foster (2004) lays the foundations of this class of indicators which measure the spread of the distribution from the median.

Median-based inequality measures were developed in the context of health inequalities and consequently they have been widely applied to measure disparities in self assessed levels of health (Madden, 2010; Jones et al., 2011). Some studies have also considered this methodology to evaluate disparities in SWB. The work by Madden (2010) investigates the evolution of happiness inequality in Ireland for the period 1994-2001. Dutta and Foster (2013) also studied inequality in happiness in the US for a longer period from 1972 to 2010, proposing a new indicator which can be decomposed by population subgroups. More recently, Balestra and Ruiz (2014) investigated inequality in life satisfaction for the OECD countries in 2010.

Using a radically different approach, Apergis and Georgellis (2014) pointed out a pattern of convergence clubs in Europe. The standard inequality measures are not able to reveal these distributional dynamics, which are related with the concept of polarization. Apouey (2007) developed a measure of polarization for ordinal data which also relies on the Allison and Foster (AF) ordering. Median-based inequality measures only satisfy the AF ordering which states that if there is a spread way from the median inequality increases. Polarization indices, instead, must verify also the property of increased bipolarity (Apouey, 2007). This property states that polarization cannot decrease when the distribution concentrates more in each part of the mode. Then, the

4 Economics abandoned long time ago any aspiration to give a cardinal interpretation to utility, and thereafter takes it as a preference indicator which maximization is independent of any underlying physiological and/or psychological phenomenon.

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distribution becomes more homogeneous at each side of the mode and hence inequality decreases, but polarization arguably increases.

The aim of this study is to investigate the evolution of distributional patterns of life satisfaction in Europe over the period 1990-2013. As a previous step, we justify the use of SWB variables as valid indicators of well-being. Thereafter, we describe main theoretical differences between polarization and inequality in ordinal variables. To study distributional patterns of life satisfaction in Europe, we perform a sensitivity analysis of inequality and polarization. To our knowledge, this is the first piece of research that studies polarization and inequality in life satisfaction for a long time period, making a clear distinction between this phenomenon and inequality, both theoretically and empirically. Our data come from Eurobarometer surveys, which monitor the European integration project. Thus, it allows studying the distributional characteristics (e.g., inequality and polarization) of SWB and their evolution along time for such geographical and political entity, which seems particularly interesting given that European Union main purpose is to increase well-being across its member states. The study period is especially relevant since it is characterized by (i) an important economic expansion from the mid-90's until 2007 driven by the increase in international trade and the integration of financial markets; and (ii) the Great Recession or global economic downturn started in 2007.

In this study, we compute the Abul Naga and Yalcin (2008) inequality measure, which allows us to ascribe different weights for the probability mass points placed at both sides of the median. This property turns out to be of great interest in order to interpret our findings. Thus, the evolution of inequality in each side of the distribution shows the forces that underlie the evolution of inequality when equal weights are given to both sides of the distribution. On the other hand, we use the polarization measure proposed by Apouey (2007) to shed additional light on the life satisfaction distribution dynamics regarding the definition of clubs. The analysis suggests that the current dynamics of the life satisfaction distribution, associated to the Great Recession, differs from the dynamics observed during the early 90’s economic crisis. During both crises the proportion of citizens with low levels of life satisfaction rose, but only in the current crisis the proportion of the population at top category remained unchanged, thus increasing inequality and polarization.

In the next section we discuss the concepts of SWB and life satisfaction and several issues regarding their measurement. In section 2 we also explain methodological issues involved in the measurement of inequality and polarization of ordinal variables. In section 3 we present and discuss main empirical findings. The paper ends with the conclusions.

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2. Measuring inequality and polarization in subjective well-being

2.1. Concepts of subjective well-being and life satisfaction

In social sciences “subjective well-being refers to all of the various types of evaluations, both positive and negative, that people make of their lives [...], events happening to them, their bodies and minds, and the circumstances in which they live” (Diener, 2006 p. 153). Thus, subjective well-being is a mental state only observed by the individual herself and consequently it can be hardly distinguished from its measurement method: self-assessments. Of course, there are physiological processes involved in those evaluations that can be directly observed by scientists through brain wave; or inferred widely from verbal and non-verbal behaviour and expressions, actions, attention, and memory (Darwin, [1872] 2009; Frey and Stutzer, 2002; Diener, 2006).

Subjective well-being has two main dimensions: on the one hand, the hedonic or affective SWB which refers to emotional reactions (that are unconscious) to life events, such as joy and sadness; and on the other hand, the reflective or cognitive dimension, which entails a cognitive process in which individuals might take into account, apart from current feelings, 1) other persons' conditions, 2) own past experience and 3) expectations of the future (Frey and Stutzer, 2002). Within the reflective or cognitive dimension there can be distinguished several sub-dimensions: (i) satisfaction (e.g., “overall, how satisfied are you with your life nowadays?”), (ii) meaning and engagement (e.g., “how often do you feel that your life has meaning?”), and (iii) overall evaluations (e.g., “how much you like your life?”). Finally, reflective or cognitive subjective well-being may refer to life-as-a-whole evaluations, mayor life domains evaluations (e.g. health, work, leisure, social relationships and family), or satisfaction with specific life aspects (e.g. specific activities, public or private services, consumption goods, etc.)

Subjective well-being and ill-being are the product of evolution. Humans share with other animals the hedonic or affective subjective well-being (although their affective systems have different levels of complexity). Affective feelings are signals that allow sensitive living beings to adapt behaviour and thus enlarge survival probabilities. In humans, reasoning capacity enables to improve the quality of that survival in the form of well-being (Damasio [2010] 2012; Heylighen y Bernheim, 2000; Veenhoven 2005).

Life satisfaction, as was seen previously, is a sub-dimension of the cognitive subjective well-being; and it is one of those evaluations that assess individual's life as a whole. It is suppose to reflect how comfortable the individual feels, no matter if she would choose another kind of life (overall evaluation) or even she things that her life could be more meaningful (meaning and engagement). Thus, it could be understood as a summary or integrative measure of the affective subjective well-being in which the individual herself gives weights to each instant feeling (or affective balance) based on her preferences, life circumstances, expectations of the future, own past experience and social comparisons. Although preferences involved in life satisfaction evaluations

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would be somehow diluted as opposed to preferences involved in overall life evaluations.

Actually, the scope of life satisfaction assessments may be larger. Baumeister et al. (2012) suggest that life meaning and engagement might be so important for life satisfaction that both phenomena could be hardly distinguished. And other authors propose to use life satisfaction assessments as the primary source of information about (non-diluted) preferences (Fleurbaey et al., 2009, in Benjamin et al., 2012).

Some additional issues regarding the idea of SWBwould be discussed in the next section when talking about its measurement. Thus, we would say a word about the universality of the phenomenon and the issue of the personal rating scales (associated, the latter, to the link between SWBitself and its assessment).

2.2 Measurement issues of life satisfaction

In international analyses, the variety of countries (cultures) included in the sample may shed doubts regarding between countries comparability of life satisfaction measures. Thus, on the one hand, we must assume that life satisfaction is a common feeling with an appropriate translation into each language/culture. There is some evidence supporting this assumption (Inkeles, 1960, in Easterlin, 1974). It seems to be even the case that happiness determinants are very similar worldwide: mainly economic, health and family circumstances (Cantril, 1965, in Easterlin, 1974). Additionally, Europe is a quite homogeneous cultural entity.

On the other hand, the fact that social norms and reference groups (key social and psychological mechanisms determining subjective well-being5) might be determined at country level could be considered an issue for our analysis. Actually the issue of non-universal (and/or constant) rating scales affects also national samples, either at a given point in time between different population segments, or at two different times (for example, social norms and reference groups may be changing from national to European standards as the European integration process develops). Easterlin (1974) states that in any case meaningful comparisons can be carried out between different individuals' life satisfaction self-assessments. He compares life satisfaction self-reports to other opinion surveys, which are based by definition on personal rating scales, such as presidential aspirants’ evaluations, which are of interest due to their implications for prospective behaviour of the respondents. It could be argued that apart from that, life satisfaction self-assessments do actually measure an objective and interesting by itself phenomenon (which happens to be affected by social norms6, social comparison and other psychological mechanisms, such as adaptation).

5 Easterlin (1974) already considered the importance of social norms and reference groups determining subjective well-being. Social norms are shaped at a general social level, whereas social comparisons are carried out with respect to each individual's specific reference group. 6 It must be noted that social norms as determinants of subjective well-being are not a problem for our analysis, whereas social norms as possible determinants of subjective well-being self-assessments would be. We discuss this issue below.

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Besides the comparability issues discussed above (associated to the sample and the wording of the question) there are others that have to do with the reliability of self-reports on subjective well-being.

First, we may have doubts as regards the capacity of the respondents to assess their subjective well-being. Those doubts are somehow mitigated by tests of consistency of self-assessments with (1) evaluations by outside judges—such as peers and professional psychologists (Wilson, 1967, in Easterlin, 1974), and (2) objective measures presumed to be indicative of subjective well-being—such as physical health indicators, and other psychological states such as depression and self-esteem (Bradburn, 1969, and Robinson and Shaver, 1969, in Easterlin, 1974).

A second concern has to do with the honesty of the respondents. Actually, some researchers point out respondents could eventually exhibit a strategic behaviour once SWB surveys are perceived as policy or political instruments. Nevertheless, those surveys are not probably perceived that way yet and, in any case, overall SWB assessments seem less inclined to such behaviour.

And third, responses to an anonymous interviewer might be adjusted by social norms or desirability. Thus, if it is believed that being well is the proper or socially desirable state, there would be an upward bias in the replies of those individuals with lower SWB than that perceived as socially desirable. Some tests have been performed about the possible correlation between SWB self-assessments and tendency toward social conformity, as measured by standard psychological tests. The evidence is not conclusive (Bradburn, 1969, and Wilson, 1967, in Easterlin, 1974).

Finally, there is one technical issue that have to do with the stability of replies and consequently, again, with their comparability. Thus, the ordering of the survey questions might affect life satisfaction self-assessments. The point is that the weighting of the different aspects considered when making life satisfaction self-assessments may change depending on previous survey questions. Or the individual may answer the way he thinks a person with such previously detail characteristics or circumstances “ought” to answer (Easterlin, 1974). Most of the Eurobarometer surveys formulate the life satisfaction question at the beginning of the interview to avoid this problem.

2.3. Inequality and polarization in ordinal variables

Data on SWB normally presents a categorical structure. The participants of the survey are asked to answer questions about their perception of how good is their quality of life. Answers are categorized in a number of different states of life satisfaction, ranging from very satisfied to not at all satisfied, for instance. Responses have then an ordinal structure, but their qualitative essence makes impossible to compute conventional inequality measures. An intuitive solution is to define a scale, i.e. to assign a number to each category in order to transform the categorical variable into cardinal. The definition of a scale is completely arbitrary and the sole restriction is that the scales must respect the ordinal nature of the data. In this sense, a sequence of equally spaced integer

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numbers starting from 1 is typically considered. In fact, some surveys provide a numerical scale to answer the question about life satisfaction, where the higher the number, the higher the level of SWB. However, even when we can establish an ordinal ranking across individuals’ responses, we do not know by how much one person that gives a response of 10 is happier than a person who answers 9, and such amount can be different across individuals.

Several studies followed this approach of transforming categorical data into a cardinal variable. Classical inequality measures such as the standard deviation or Gini index were then computed (Ott, 2005; Venhoven, 2005). Note, however, that most inequality measures take the mean as a reference point to measure the dispersion of the distribution. The problem is that the ranking of countries according to mean life satisfaction is heavily dependent of the scale (Allison and Foster, 2004). To see this, consider the following example. Let x = [0.2, 0.2, 0.2, 0.2, 0.2] and y = [0.4, 0.1, 0.1, 0.1, 0.3] be two frequency distributions of subjective well-being. Applying a typical scale c = [1, 2, 3, 4, 5], we have µx (c) = 3 > µy (c) = 2.8. If we use instead the alternative scale c’ = [1, 2, 3, 4, 50], µx (c’) = 12 and µy (c’) = 16.3. This simple example points out the sensitivity of the mean-based orderings of distributions, and consequently, the robustness and validity of inequality assessment using inequality measures that depend on the mean, which might be also affected by rescaling. Consider, for instance, the coefficient of variation of both distributions using the different scales. CVx (c) = 0.47 < CVy (c) = 0.61, while applying the alternative scale leads CVx (c’) = 1.58 > CVy (c’) = 1.35.

Taking the mean as a reference point for the assessment of disparities in ordinal variables alters not only the amount of inequality, but also the ranking of distributions. A priori, there is no reason to restrict ourselves to the use of one scale or another. The consideration inequality measures based on order statistics should be usefull in this context since they are invariant to scale. Within this class we find the interquartile range, which measures the difference between the value of the bottom and the upper 25 percent of the population. The value of this indicator is scale dependent, but since it is based on the ranking of individuals, it is order preserving. The main problem of this measure is that it ignores a large amount of information contained between the two quartiles, and then it is completely insensitive to changes in the middle of the distribution7.

The limitations of conventional measures to assess inequality in categorical variables make room for alternative approaches based on order statistics. In particular, the use of the median as a reference point seems to provide an adequate framework. Blair and Lacy (2000) measure was one of the first attempts to obtain a median-based inequality index for ordinal variables. Thereafter, Allison and Foster (2004) developed a measure

7 Another shortcoming of this kind of measures is that they seem to perform poorly in extreme distributions, but it does not might be a characteristic of happiness distributions (Kalmijn and Veenhoven, 2005).

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of inequality based on the so-called AF-ordering, which ranks distribution according to their spread to the median.

Let F(x) = (F1, …, FC-1, 1) be the cumulative distribution of the categorical variable x and f(x) = (f1, …, fC-1, fC) the probability distribution function, where fc is the proportion of population for the category c. Let m denote the median category such that Fm-1< 1/2 and Fm ≥ 1/2.

The partial ordering defined by Allison and Foster (2004) ranks distributions which satisfy three conditions.

Definition 1. AF-ordering (Allison and Foster, 2004). Given two cumulative distribution functions F1 and F2, F2 has greater spread from the median than F1, that is

21 FF AFp

if the following conditions are satisfied:

(1) F1 and F2 have the same median category, m(F1) = m(F2) = m.

(2) .21 mcFF cc <∀≤

(3) .21 mcFF cc ≥∀≥

1F has a greater proportion of population concentrated around the median and consequently, F1 is less spread away from the median. In this context, F1 is associated with lower levels of inequality for all possible scales.

Figure 1. Increased spread from the median of a life satisfaction distribution

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The distinction between the concepts bipolarization and inequality in ordinal variables seems to be unclear. According to Zheng (2008), median-based inequality measures are indeed polarization measures, since they measure how concentrated the data is around the lower and the upper category. Bipolarization is seen as a measure of the size of the middle class since it focuses on the concentration of the population around two poles8. To clarify the difference between these two phenomena, we shall first focus on the two basic properties of bipolarization measures.

Property 1 (Increased spread). A regressive transfer in the Pigou-Dalton sense from someone below the median to an individual above the median would increase bipolarization.

For categorical variables, the transfer is characterized as a Median Preserving Spread and hence this property is represented by the AF-partial ordering given in Definition 1. To see this graphically, in Figure 1 we present the distribution of a life satisfaction variable with five possible categories: “not at all satisfied”, “not very satisfied”, “neither satisfied nor dissatisfied”, “fairly satisfied”, “very satisfied”. For convenience we assume that individuals are clustered in two categories “not very satisfied” and “fairly satisfied”, above and below the median category: “neither satisfied nor dissatisfied”. Now assume the there is a relocation of the groups. Individuals that were “not very satisfied” become “not at all satisfied” and the group of population that was “fairly satisfied”, becomes “very satisfied”. Note that these movements increase the spread of the distribution from the median. As a result, both bipolarization and inequality would increase.

Property 2. Increased bipolarity (IB). A progressive Pigou-Dalton transfer on either side of the median would increase polarization. The transfer decreases the dispersion within the group of population below/above the median, thus fostering the levels of polarization.

Figure 2 exemplifies graphically an increase of bipolarity. Below the median all individuals are “not very satisfied” with their life, while at the median and above, there is an equal proportion of individuals that are “satisfied” and “very satisfied”. Suppose that these two groups cluster at the category “fairly satisfied” as indicated in Figure 2. This new situation would clearly present lower levels of inequality since the distribution above the median is more homogeneous, however polarization would increase. This is because the new situation is reached through two movements of the probability mass: an increased spread from the median (from “satisfied” to “fairly satisfied”) and a decreased spread (from “very satisfied” to “fairly satisfied”). Consequently, the first movement of population must receive more weight than the second one when measuring polarization.

8 The concept of bipolarization is associated with the population in two poles, while polarization considers a clustering of population around an arbitrary number of poles. While being pretty close definitions both phenomena can present contrasting evolutions (see Duclos and Taptué, 2014).

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Figure 2. Increased bipolarity of a life satisfaction distribution

Definition 2. Increased bipolarity (IB) transfer. We say the there is an increased bipolarity transfer of a proportion ζ > 0, from the category ci to ci+ 1 and from cj to cj-1 if fi, fj > ζ , ci+ 1 ≤ cj-1 and ci ≥ m or cj < m.

Definition 3. Increased bipolarity ordering (Apouey, 2007). Let IBf define the

partial ordering, for any two distributions F1, F2, such that m(F1) = m(F2) = m, we say

that 21 FF IBf if F2 is obtained from F1 by a finite sequence of IB transfers.

The inequality measures developed in the literature (Blair and Lacy, 2000; Allison and Foster, 2004, Abul Naga and Yalcin, 2008) focused on the AF partial ordering, but polarization measures verify also IB (Apouey, 2007). Indeed, IB property distinguishes bipolarization from inequality, since a progressive transfer between individuals that are both above or below the median would decrease inequality while increasing polarization (Foster and Wolfson, 2010).

Abul Naga and Yalcin (2008) relied on the partial AF-ordering to construct a family of inequality indices which are invariant to scale.

Let )(FΦ be an order-preserving function of the AFf relation. Let F̂ denote the most

egalitarian distribution, which has all the probability mass concentrated at the median

category.F~

is the most unequal distribution, where half of the distribution is situated at the lowest category and the other half of the population is characterized by the best

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possible state9. In fact, F~

is not only the least egalitarian distribution, it also corresponds to the most bipolarized one (Abul Naga and Yalcin, 2008).

The family proposed by Abul Naga and Yalcin (Thereafter ANY measure) is

constructed by normalizing )(FΦ by )ˆ(FΦ and )~

(FΦ , as:

.)ˆ()

~(

)ˆ()()(

FF

FFFI

Φ−ΦΦ−Φ=

(1)

A function of the form ∑∑ ≥<−=Φ

mcmcFgFgF )()()( 21 was chosen, which satisfies the

AF-ordering when g1 and g2 are strictly increasing on F (see Lemma 4, Abul Naga and

Yalcin (2008)). In particular, ( )αcFFg =)(1

and ( )β

cFFg =)(2 . Replacing this functions

in Eq. (1) the inequality the ANY index can be written as,

,)1())2/1)((1()2/1)(1(

)1()()(

)(,mnmnk

mnFF

FI kic

kic

−++−+−−

−++−=

∑∑><

βα

βα

βα

where α and β are parameters to represent the value judgments of the society for inequalities below and above the median. Iα,β satisfies the AF-ordering for any positive value of parameters α and β (see Lemma 4 in Abul Naga and Yalcin (2008)). However, the measure was originally defined for parameter values higher or equal to 1. In this sense, the measure becomes more sensitive to the bottom part of the distribution α→1 for a given value of β and it becomes insensitive to this part of the distribution for α→∞. Likewise, for a fixed value of α, we neglect inequalities above the median as β→∞.

To analyze the emergence of clusters in either side of the median the measures used must be consistent with the IB ordering. The measure developed by Apouey (2007) verifies both the AF-ordering and the IB ordering and hence it is able to represent an increase of polarization. The index is given by the following expression,

,2

1

1

1

2

1)(

1

122

−

−−

= ∑−

=

C

ccF

CKFP

αα

where K2 is a strictly positive constant which can be set to 2α for normalization purposes, thus ensuring that P2 is ranged from 0 to 1. C is the number of categories, Fc denotes the cumulative distribution function and α is a parameter that reflects the importance given to the median category. This index satisfies the AF-ordering when

α2/1−cF is strictly increasing (Proposition 1, Apouey (2007)), that is for any positive

9 The most equal distribution has all the probability mass in one category and then we have:

]1,..1,...,0,0[ˆ =F .Note that F̂ is not unique. The probability mass can cluster around any category, so

there are C different most equal distributions. The most unequal distribution concentrates the probability

mass around the two ends: ].1,...,5.0,5.0[~ =F

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value of the α parameter. P2 is strictly increasing in IB when α is ranged between 0 and 1 (see Apouey (2007), Proposition 4). As the α parameter approaches to 1 the index become more sensitive to the categories far away from the median. When α→0, more importance is given to the relative contribution of the median in overall polarization.

3. Distributional dynamics of happiness in Europe

In this section we analyze the evolution of the distribution of SWB in 12 countries of the European Union10 over the period 1990-2013. We consider the nations that were involved in the EU-12, which was founded at the beginning of the nineties. We investigate whether the conformation of the European Union brought also convergence in the levels of life satisfaction, or instead, this pattern was restricted to the macroeconomic performance as has been repeatedly pointed out in the literature (see e.g. Badinger et al. (2004)).

3.1 Data

Life satisfaction is measured in Eurobarometer surveys since 1975 through a 4-point scale variable that corresponds to the question: “on the whole, are you very satisfied, fairly satisfied, not very satisfied or not at all satisfied with the life you lead?”, whose wording has remained unchanged during the whole period (1975-2013), which is essential to make the measure perfectly comparable on this respect11. Diener (2006) distinguishes two possible meanings regarding life in the life satisfaction question: on the one hand it could refer to current life-as-a-whole; and on the other hand it could refer to life since birth. The wording of the question in Eurobarometer surveys (“[...] the life you lead […]”) points, although not explicitly, to the former meaning.

Nine countries (Belgium, West Germany, Denmark, France, Great Britain, Ireland, Italy, Luxembourg and The Netherlands) have participated in all Eurobarometer surveys. Greece joint the survey in 1980; Spain and Portugal in 1985; East Germany in 1990; Finland in 1993; Austria and Sweden in 1994; and Bulgaria, Cyprus, Czech Republic, Estonia, Hungary, Lithuania, Latvia, Malta, Poland, Romania, Slovenia and Slovakia in 200412. We limit our sample to the nine original countries and those that entered into the survey up to 1990 in order to study the evolution of the distributional characteristics for a sufficiently long period of time.

10 We consider 12 countries in this analysis, but we work with 13 territorial areas in practice, since Germany is divided into East and West Germany. 11 Actually, since 2012 the survey distinguishes among individuals who do not answer the question and those that answer “I do not know”, but given that only very few people choose this reply category it does not seem a problem to simply omit them. 12 Czech Republic, Hungary, and Poland had already participated in a Eurobarometer survey in 2002, but they participate regularly since 2004. Besides, there are several countries that participate sporadically in the Eurobarometer surveys (since): Norway (1990), Turkey (2004), Turkish Republic of Northern Cyprus (2004), Croatia (2004, and regularly since 2012), Switzerland (2005), Island (2005), Macedonia (2007), Montenegro (2011), and Serbia (2012).

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Figure 3. Abul Naga-Yalcin inequality index for selected values of the parameters.

Table A1.1 shows the sample size by year and country. Eurobarometer surveys usually targets 1,000 persons per country13, and the actual number of observations for a given country-year depends on the number of surveys (in which the life satisfaction question is formulated) carried out that year. That number ranges from around 1,000 observations (1988, 1995-1998, 2003, and 2005) to around 4,000 observations (1989, 1992, 2009, and 2013) for a given country-year. Table A1.2 shows the life satisfaction question response rate by year and country. As it is observed in most of the surveys that collect data on life satisfaction the response rate is remarkably high: always over 98%.

3.2. Results

Before going any further, it is worth mentioning that the distribution of SWB has the same median category, “fairly satisfied”, over the whole period (see Table A2 in Appendix 1). This fact allows us to use the median-based inequality measures that preserve the AF-ordering.

Let us start with the index proposed by Abul-Naga and Yalcin (2008). Figure 3 presents the evolution of this indicator over the period 1990-2013 in the EU-12 for the three limiting cases. The absolute value index I1,1 is very sensitive to the top and the bottom

categories, while β,∞I and ∞,αI only pay attention to the upper and the bottom part of the

distribution respectively. These two last indices can be used to map inequality levels of

all possible combinations of the β and α parameters, since the index βα ,I can be

decomposed as a function of these two terms (Abul Naga and Yalcin, 2008). Then, the

13 With the exception of Luxembourg that usually collects data of 300 individuals; and Great Britain that interview 1,000 individuals in England, Wales and Scotland and 300 additional ones in Northern Ireland.

1990 1995 2000 2005 20100.30

0.35

0.40

0.45

0.50

0.55

0.60

0.65

Α=1

Β=1

Α=1

Β=¥

Α=¥

Β=1

15

trends of inequality levels would be a combination of the evolution of the spread of the

distribution above and below the median represented respectively by β,∞I and ∞,αI .

The evolution of inequality in life satisfaction presents different evolutions depending on the importance given to the categories above and below the median. Overall, three different stages can be roughly distinguished. During the nineties, the limiting case

,,∞αI that ignores the distribution of life satisfaction above the median, presents an

upward trend of inequality. This result is driven by the increase of dissatisfied citizens during the first ten years of the study period. In contrast, if we focus only on the top categories, a convergence pattern is observed due to the move of probability mass from the top category to the median. Since the absolute value index is a weighted sum of these two measures, the previous trends offset each other, thus resulting in the

stagnation of inequality levels in life satisfaction when measured using 1,1I .

The period around 1999 to 2003 is characterized by several ups and downs when we only look at the top of the distribution. This evolution reflects the numerous changes experienced by this part of the distribution. The peaks are driven by the increase of the probability mass at the top category very satisfied. Overall, the evolution of the spread of this part of the distribution during these years shows a J-pattern that results in a substantial rise of inequality levels, coinciding with the economic boom before the crisis. At the other extreme, inequality at the bottom part of the distribution also exhibits an irregular pattern, but disparities remain constant on average. The evolution of the absolute value index presents a U-pattern that comes from the combination of the previous two trends.

Figure 4. Growth rate of the Abul Naga and Yalcin measure for different combinations of β and α parameters.

alpha

beta

11.

251.

51.

752

1 2 3 4 5 6

0.04

0.06

0.08

0.10

0.12

0.14

0.16

16

Figure 5. Apouey index of polarization for selected values of the sensitivity parameter.

The last years of the study period are characterized by an increase in inequality levels when focusing on the distribution below the median, while a stagnation phase is observed if only the spread of the top of the distribution is considered. This pattern underlines the deep effect of the financial crisis on the bottom part of the distribution of life satisfaction. The proportions of responses not at all satisfied and not very satisfied increased over the last years at expense of the median category, while the upper category remained constant over this period. This evolution suggests that the consequences of the crisis focused on the lower part of the distribution, rising the probability mass of the bottom categories and increasing its spread from the median.

To analyze how the value judgments regarding the importance given to the categories above and below the median affect our conclusions about the evolution of inequality, the growth rate of the ANY measure is computed for several combinations of the parameters14 (Figure 4). For given values of β, the greater the α parameter, that is, the lower the weight given to the bottom of the distribution, the lower the growth rate of inequality. Similarly, as less importance is given to categories above the median, the divergence rate is higher for a given α.

The Apouey measure is able to capture IB movements that increase the concentration in either side of the median. We present the evolution of polarization in the EU-12 over the last three decades in Figure 5. The Apouey measure has been computed for different values of the α parameter. In particular, we consider α = 0.25, 0.5, 0.75 and (ln(4)-ln(3))/ln(2). The last value is the parameter that calibrates the polarization measure such that it gives a value of 0.5 for the uniform distribution (see Apouey, 2007). As the

14 We define a sequence for the β parameter that varies from 1 to 2 by increments of 0.01 and for the α parameter ranging from 1to 6 by 0.01.

1990 1995 2000 2005 2010

0.10

0.15

0.20

0.25

0.30

Α=0.75

Α=0.5

Α=0.4150

Α=0.25

17

sensitivity parameter decreases the index becomes more sensitive to the center of the distribution.

Polarization in life satisfaction presents a smoother trend than those observed for inequality. Whatever the value of the sensitivity parameter to the center of the distribution, the first decade of the study period is characterized by the stagnation of polarization levels. This result is driven by the fact that again the two opposite trends observed for the top and the bottom categories offset each other. The irregular trend observed for inequality from 1999 to 2004 is not as rough as in the case of inequality, although the ups and downs are still appreciable. The raise of the spread above the median is counterbalanced by the stable pattern of the bottom categories. Moreover, the U-pattern is also observed for the case of polarization. After 2008, a positive trend is observed independently of the value of the sensitivity parameter. This trend is due to the negative effect of the crisis on the European citizens, which increased the proportion of responses in the bottom category, while leaving the probability mass at the top unchanged. As a result both inequality and polarization increase during the last years.

Conclusions

The European integration project has as one of its founding principles the promotion of well-being among its member states. Nowadays it is widely accepted that the GDP per capita is a limited indicator of well-being, and that other aspects should be taken into account to truly capture that policy goal. In this spirit, SWB measures reflect a wide range of experiences that go beyond the economic sphere (Benjamin et al., 2012). In this paper we investigate the distributional patterns of life satisfaction in the EU-12 for the period 1990-2013 using data from the Eurobarometer surveys.

The ordinal nature of the life satisfaction variable makes the usage of conventional measures of inequality, which are generally scale dependent, misleading. A complementary framework has been developed in the literature which studies median-based inequality measures which are suitable for ordinal variables. Abul Naga and Yalcin (2008) inequality measure allows us to ascribe different weights for the probability mass points placed at both sides of the median. This property turns out to be of great interest in order to interpret our findings as regards both inequality and polarization. Thus, focusing on the two limiting cases: first, giving all the weight to the lower part of the distribution, and then, all the weight to the upper part; we observe two markedly different patterns in the evolution of estimated inequality along the period. On the one hand, if we focus in the lower part of the distribution, inequality increases slightly during the 90's; it comes back to its initial level in the first 2000's; and finally it rises again from 2008. On the other hand, if we focus in the upper part of the distribution, inequality decreases steadily along the 90's and keep below its initial level until 2003; since 2004 inequality remains rather stable around its initial level.

18

Overlapping both evolution curves, and at the light of socio-economic trends, we observe the underling forces driving the estimated evolution of inequality (giving equal weight to both sides of the distribution), and polarization. Thus, the constant life satisfaction inequality level observed in the period 1990-1998, characterized by a socio-economic crisis, is the product of two opposite and equal forces: a higher life satisfaction inequality in the lower part of the distribution; and a lower inequality level in the upper part. Polarization also remains constant during this period. We may argue that due to the socio-economic crisis, people at the top category tended to the median, while individuals at the median or below departed from the median towards categories at the bottom, keeping both the spread and bipolarity rather constant. In the period 1999-2003 we observe the lowest levels of inequality and polarization of the whole series. The fact that inequality in the lower part of the distribution is back to its initial level while it remains under that level in the upper part of the distribution explains both the lower inequality and polarization levels. (individuals in the lower part of the distribution moved towards the median while individuals in the upper part of the distribution kept especially—with respect to other periods—concentrated around the median). In the period 2004-2007 inequality remains rather stable around its initial level (up from its level in the previous period) as inequality in both sides of the median rose back to their initial levels as well. Polarization also remains constant (up from its level in the previous period) from 2004 to 2007. Finally, during the current socio-economic crisis (2008-2013) both inequality and polarization are increasing steadily driven by the rising inequality in the lower part of the distribution. Interestingly, the inequality level in the upper part of the distribution is remaining rather constant during the current crisis, due to the fact that the probability mass associated to the top category has not changed significantly.

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Appendix 1 Table A1.1. Sample size by year and country

COUNTRY (ISO 3166)

year BE DE-E DE-W DK ES FR GB GR IE IT LU NL PT Total

1990 2,961 1,983 3,092 3,000 3,001 3,031 4,068 3,007 3,038 3,138 899 3,162 3,000 37,380

1991 2,067 2,161 2,073 2,000 2,001 2,007 2,729 2,001 2,020 2,083 939 2,044 2,000 26,125

1992 4,136 4,199 4,104 4,000 4,025 4,021 5,421 4,009 4,009 4,162 1,994 4,029 4,000 52,109

1993 2,025 2,186 2,083 2,000 2,022 2,043 2,740 2,005 2,008 2,051 1,015 2,004 2,000 26,182

1994 2,130 2,092 2,082 2,006 2,009 2,041 2,724 2,012 2,070 2,113 1,125 2,062 1,999 26,465

1995 1,056 1,049 1,055 1,000 1,000 1,002 1,371 1,006 1,000 1,057 499 1,010 1,000 13,105

1997 1,005 1,031 1,038 1,001 1,000 1,006 1,379 1,010 1,003 997 597 1,020 1,000 13,087

1998 1,007 1,007 1,005 1,000 1,000 1,045 1,366 1,013 1,000 1,000 606 1,031 1,000 13,080

1999 2,045 2,048 2,043 2,001 2,000 2,007 2,680 2,014 2,002 2,015 1,215 2,013 2,002 26,085

2000 2,111 2,048 2,028 2,000 2,000 2,005 2,741 2,006 2,001 1,987 1,209 1,979 2,000 26,115

2001 3,086 3,066 3,036 3,003 3,000 3,011 3,962 3,011 2,967 2,987 1,813 3,045 3,002 38,989

2002 2,082 2,067 2,018 2,000 2,000 2,014 2,625 2,005 2,000 2,043 1,202 1,997 2,000 26,053

2003 1,022 1,023 1,016 1,000 1,000 1,015 1,362 1,001 1,014 1,008 587 1,006 1,000 13,054

2004 1,985 1,040 2,038 2,039 2,068 2,024 2,676 2,000 2,000 2,025 1,012 2,025 2,000 24,932

2005 1,000 505 1,015 1,051 1,024 1,012 1,347 1,000 1,006 1,004 504 1,006 1,005 12,479

2006 2,023 1,018 2,033 2,011 2,008 2,027 2,620 2,000 2,003 2,006 1,003 2,027 1,997 24,776

2007 2,033 1,016 2,006 2,001 2,000 2,049 2,659 2,000 2,007 2,055 1,013 2,014 2,011 24,864

2008 2,005 1,017 2,043 2,034 2,033 2,067 2,614 2,000 2,004 2,083 1,001 2,082 2,001 24,984

2009 4,007 1,976 4,105 4,035 4,032 4,156 5,305 4,000 4,024 4,180 2,040 4,127 4,055 50,042

2010 3,016 1,592 3,078 3,096 3,013 3,059 3,934 3,000 3,029 3,083 1,518 3,074 3,050 37,542

2011 3,073 1,624 3,021 3,028 3,018 3,121 3,963 3,000 3,046 3,114 1,506 3,022 3,098 37,634

2012 3,166 1,563 3,006 3,016 3,023 3,042 3,910 3,002 2,997 3,094 1,512 3,031 3,026 37,388

2013 4,159 2,125 4,077 4,026 4,044 4,121 5,276 4,009 4,014 4,055 2,025 4,090 4,113 50,134

Total 64,299 39,436 64,603 63,422 62,373 63,988 83,978 63,126 63,249 64,941 30,126 64,003 62,359 789,903

22

Table A1.2. Life satisfaction question response rate by year and country

COUNTRY (ISO 3166) Year BE DE-E DE-W DK ES FR GB GR IE IT LU NL PT Total

1990 99.02 99.5 99.55 99.4 99.5 98.68 99.53 99.67 99.51 99.65 99.67 98.99 98.97 99.34

1991 99.47 99.35 99.28 99.7 99.85 98.95 99.38 99.45 99.06 99.66 99.15 99.41 99.55 99.41

1992 99.06 99.43 99.49 99.7 99.35 99.33 99.45 99.43 99.65 99.52 99.45 99.53 99.63 99.46

1993 99.26 99.5 99.42 99.65 99.46 99.76 99.56 99.6 98.9 99.66 99.31 99.55 99.45 99.48

1994 98.59 99.43 99.38 99.7 99.6 99.71 99.56 99.7 98.65 98.91 99.38 99.42 99.6 99.35

1995 99.62 98.38 98.48 99.8 99.2 98.9 99.56 99.9 99.3 99.53 99.8 100 99.7 99.38

1997 99 98.35 98.36 100 99.7 99.2 99.42 99.9 99.4 99.3 99.5 99.8 99.4 99.33

1998 99.11 99.3 98.81 99.7 100 97.61 98.83 99.61 98.4 99.4 99.01 100 99.4 99.16

1999 99.32 98.93 99.36 99.8 99.35 99.25 99.03 99.6 98.35 99.45 99.67 99.75 99.55 99.32

2000 99.34 98.83 98.62 98.8 99.75 99.05 99.42 99.85 98.45 99.65 98.76 99.7 99.2 99.2

2001 99.13 99.15 99.31 99.8 99.23 98.8 99.57 99.8 98.45 99.36 99.28 99.77 99.7 99.34

2002 100 100 100 100 100 100 100 100 100 100 100 100 100 100

2003 100 100 100 100 100 100 100 100 100 100 100 100 100 100

2004 99.75 100 100 99.9 99.23 99.9 99.74 100 100 99.7 100 100 99.7 99.82

2005 100 100 100 100 100 100 100 100 100 100 100 100 100 100

2006 100 100 100 100 100 100 100 100 100 100 100 100 100 100

2007 100 100 100 100 100 100 100 100 100 100 100 100 100 100

2008 100 100 100 100 100 100 100 100 100 100 100 100 100 100

2009 100 100 100 100 100 100 100 100 100 100 100 100 100 100

2010 100 100 100 100 100 100 100 100 100 100 100 100 100 100

2011 100 100 100 100 100 100 100 100 100 100 100 100 100 100

2012 99.91 99.81 99.7 99.9 99.83 99.51 99.74 99.83 99.07 99.29 99.8 100 99.8 99.7

2013 99.93 99.76 99.85 99.95 99.9 99.85 99.83 99.8 99.63 99.48 100 99.9 99.93 99.83

Total 99.41 99.51 99.49 99.71 99.59 99.45 99.65 99.76 99.44 99.66 99.6 99.66 99.63 99.59

23

Appendix 2

Table A2. Cumulative distribution frequencies of Life Satisfaction in EU-12

Not at all satisfied

Not very satisfied

Fairly satisfied

Very satisfied

1990 0.0417 0.1204 0.5597 0.2782

1991 0.0395 0.1402 0.5437 0.2766

1992 0.0438 0.1462 0.5496 0.2604

1993 0.0487 0.1573 0.5481 0.2459

1994 0.0436 0.1506 0.5556 0.2501

1995 0.0478 0.1453 0.5602 0.2467

1997 0.0435 0.1652 0.5479 0.2433

1998 0.0471 0.1683 0.5496 0.2350

1999 0.0245 0.1212 0.5863 0.2680

2000 0.0386 0.1522 0.5791 0.2301

2001 0.0293 0.1301 0.5645 0.2762

2002 0.0367 0.1483 0.5863 0.2287

2003 0.0393 0.1658 0.5611 0.2337

2004 0.0328 0.1056 0.5401 0.3215

2005 0.0363 0.1313 0.5543 0.2781

2006 0.0368 0.1272 0.5563 0.2797

2007 0.0360 0.1301 0.5562 0.2776

2008 0.0434 0.1554 0.5401 0.2611

2009 0.0438 0.1505 0.5322 0.2734

2010 0.0518 0.1440 0.5278 0.2764

2011 0.0508 0.1424 0.5195 0.2873

2012 0.0686 0.1592 0.5049 0.2673

2013 0.0651 0.1543 0.5038 0.2769