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Can money buy
“happiness” for Belgians?
Graduate Seminar in Economics: Research Paper
Emily Van de Walle
Master Economic Policy
Graduate seminar in economics
J. Bouckaert, J. Vanneste, E. Vanhaecht , P. Vanpachtenbeke
Faculty of Applied Economic Sciences
Academic year 2015-2016
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Abstract
This paper explores the relationship between subjective well-being and income for Belgian
inhabitants. Explicitly, the impact of income on subjective well-being shall be analyzed as well as
the existence of a satiation point, which in accordance to theory claims that the marginal effect of
income on subjective well-being is positive but decreasing to zero. The analysis is accomplished by
applying a cross-sectional study within the country of Belgium, using data from the year 2010
provided by the European Social Survey. Overall, the results suggest the following three findings.
First, there is a positive relationship between subjective well-being and income. Second, the
marginal effect of income on subjective well-being is positive but conclusions on whether the
marginal effect increases or decreases seem to depend on the method. Third, there is no evidence
that confirms the existence of a satiation point.
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Contents
Abstract.....................................................................................................................................................................2
1. Introduction...................................................................................................................................................4
2. Review of the literature ............................................................................................................................5
3. Data...................................................................................................................................................................6
4. List of relevant variables ..........................................................................................................................6
4.1 The dependent variable..........................................................................................................................7
4.2 The independent variables....................................................................................................................9
4.3 Data description and summary statistics..................................................................................... 10
5. The econometric model and inference procedures .................................................................... 10
5.1 The starting point .................................................................................................................................. 10
5.2 Inference procedures ........................................................................................................................... 11
6. The results................................................................................................................................................... 15
6.1 Relationship between income and subjective well-being...................................................... 15
6.2 Marginal effect of income on subjective well-being................................................................. 17
6.3 The satiation point................................................................................................................................. 18
7. Conclusion................................................................................................................................................... 18
References ............................................................................................................................................................ 19
Appendix
A.1 Description of the independent variables.................................................................................... 22
A.2 Figures ....................................................................................................................................................... 24
A.3 Tables......................................................................................................................................................... 27
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1. Introduction
Can happiness be bought? Are the rich (always) happier than the poor? These questions concerning
the relationship between income and subjective well-being may be described as tricky in the sense
that a straightforward answer is lacking due to the difficulties in measuring subjective well-being.
However, these questions are definitely compelling to ponder upon and are effectively analyzed in
the field of happiness economics. (Happiness economics, 2016)
This paper confronts these questions of interest with respect to the country of Belgium and allows
for a comprehensive analysis by distinguishing and addressing the following two aspects.
The first aspect concerns the relationship between subjective well-being and income. An illustrative
question may be the following: If I were to give you a sum of money, would you be better off (or
read as happier) than in your initial position had you not received that sum of money? Typically,
you would feel better off ex-post. This illustrates the expected positive correlation between income
and subjective well-being. However, does this positive correlation always apply? Is the relationship
between subjective well-being and income irrespective of the amount of wealth you own? Thinking
a step further leads to these new questions, which are discussed in the next aspect. (Stevenson &
Wolfers, 2013)
The second aspect concerns the marginal effect of income on subjective well-being and the satiation
point. A satiation point implies that money can buy you happiness, but only to a certain degree thus,
money cannot buy you unlimited happiness. For example, as a poor person, receiving an additional
sum of money allows you to cover your basic necessities, leading to an increase in your life
satisfaction (or read as subjective well-being). However, as you receive more money, the
contribution of receiving that amount of money to your happiness would still be positive but will
become marginally less (according to the theory). Furthermore, at a certain point which is known
as the satiation point, you are sufficiently wealthy that receiving more money no longer contributes
to your happiness, which implies a marginal effect of zero. A graphical illustration of the
transformation of the marginal effect and the satiation point may be found in figure 1 of the
appendix. This occurrence is identified as the modified version of Easterlin’s hypothesis by
Stevenson & Wolfers (2013) and its existence is argued by a number of researchers due to its
logical plausibility. (Stevenson & Wolfers, 2013)
These two aspects shall be analyzed by constructing an econometric model in Stata13 using data
from the year 2010 for the country of Belgium provided by the European Social Survey (ESS, n.d. a).
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2. Review of the literature
Whether happiness can be bought or not is one of the fundamental questions of happiness
economics as the individual income of inhabitants and the gross domestic product of the nation are
considered as important determinants of subjective well-being. In light of this, there has been
considerable research concerning this subject. Results found in existing academic literature
concerning the two aforementioned aspects shall be discussed in this section and a review of the
literature concerning the relevant variables of the happiness-income relationship shall be discussed
in section 4. (Happiness economics, 2016)
First, the majority of studies typically find a “positive relationship between subjective well-being
and income across countries and over time” (Stevenson & Wolfers, 2013). However, this is only the
case when this relationship is effectively acknowledged by the researchers of a certain study. For
clarification, this implies that a number of researchers argue that at a certain point, the satiation
point, the relationship disappears between subjective well-being and income. (Happiness
economics, 2016; Stevenson & Wolfers, 2013)
Second, the existence of the satiation point or rather the modified version of the Easterlin’s
hypothesis is acknowledged by a number of researchers due to its logical plausibility rather than on
evidence. When based on evidence, however, this hypothesis has been rejected by a number of
researchers such as Sacks, Stevenson, Wolfers and Deaton. These authors found a “robust positive
relationship between subjective well-being and income across countries over time” (Stevenson &
Wolfers, 2013). Nevertheless, despite the existence of a satiation point being debunked, the positive
relationship between subjective well-being and income still implies that “increasing income yields
diminishing marginal gains in subjective well-being” (Stevenson & Wolfers, 2013).
Third, the relationship between income and subjective well-being depends on the exact definition
of subjective well-being. An interesting paper by Kahneman & Deaton (2010) highlights this
importance by “distinguishing two aspects of subjective well-being: emotional well-being [which]
refers to the emotional quality of an individual’s everyday experience and life evaluation [which in
turn] refers to the thoughts that people have about their life when they think about it”. By making
this distinction, Kahneman & Deaton (2010) conclude that while high income may be robust
positively correlated with life satisfaction, this is not the case with emotional well-being. In this
research paper, the focus is limited to life evaluation. This shall be further elaborated in section 4,
but first, it is essential to be informed of the dataset. (Deaton & Kahneman, 2010).
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3. Data
The European Social Survey (ESS) is organized by academics that collect cross-sectional data for
several countries across Europe. The data applied in this analysis is collected from the fifth round of
this survey, which is for the year 2010, for the country of Belgium. (ESS, n.d. a; ESS, n.d. b)
The fifth round of the European Social Survey is not arbitrarily chosen but is rather chosen based
on the following three considerations. (ESS, n.d. a)
First, the survey round was chosen based on the rotating section of the questionnaire that
highlights different themes every round. The specific theme of family work and well-being was
chosen due to a focus on life evaluation, which is one of the elements of subjective well-being. (ESS,
n.d. d; ESS, n.d. e; OECD, 2013)
Second, rounds with the same theme may still differ in the questions effectively asked in the survey,
making it necessary to compare the questionnaires to one another. (ESS, n.d. d; ESS, n.d. e)
Third, the measurement of the household income has changed since the fourth ESS round. Namely,
the income categories are “based on deciles of the actual household income range in the given
country” (ESS, n.d. f, p. 2). This translates to a slight preference towards round four and above as
household income is better represented with respect to the actual income distribution in the given
country. (ESS, n.d. d; ESS, n.d. e; ESS, n.d. f)
Taking all of this into account, the fifth round (the year 2010) of the ESS was chosen based on the
OECD guidelines for measuring subjective well-being. (ESS, n.d. a; OECD, 2013)
4. List of relevant variables
As a starting point for constructing the economic model, the ESS dataset, as well as the ESS
questionnaire, are analyzed, using two complementary approaches in order to construct a list of
relevant variables. This list functions as a guide of which variables should be included in the initial
economic model. This list, however, does not imply that these variables are statistically significant.
Tests of statistical significance have yet to follow and they shall be carried out within the context of
the econometric model. (ESS, n.d. a; ESS, n.d. c)
First, the analysis necessary to construct the list of relevant variables is conducted by asking two
questions: “Which variable is the best representative of the subjective well-being of an individual?”
and “Which variables are likely to have an impact on the subjective well-being of an individual?”
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The former question concerns the dependent variable, the subjective well-being while the latter
question concerns the independent variables. Note that these questions are inquired on the
individual level as a within-country analysis of Belgium will be applied in this paper.
Second, a complete list of relevant variables within the borders of the ESS dataset is ensured by
answering these questions while relying on two criteria: intuition and insights of the academic
literature.
The list of relevant variables is composed of a dependent variable (subjective well-being, life
evaluation), the main independent variable (income) and other control variables. This shall be
further expanded in the next two sub-sections.
4.1 The dependent variable
It is of great importance to first develop an understanding of subjective well-being before
considering the concrete variables for the economic model. This will allow a better grasp on the
variables which best represent this concept and the chosen explanatory variables. (OECD, 2013)
Understanding subjective well-being
Contrary to popular belief, subjective well-being constitutes more than just happiness. The
definition of subjective well-being put forward by the OECD is that largely of Diener et al. (2006):
“Good mental states, including all of the various evaluations, positive and negative, that people
make of their lives and the affective reactions of people to their experiences” (OECD, 2013, p. 12).
This is a rather complete definition as it describes the three elements of subjective well-being: life
evaluation, affect, and eudaimonia. (OECD, 2013)
The first element, life evaluation (life satisfaction), is defined as “a reflective assessment of a
person’s life or some aspect of it” (OECD, 2013, p. 12).
The second element, affect, is defined as “a person’s feelings or emotional states” (OECD, 2013,
p.12) and may be divided into “two hedonic dimensions: positive affect and negative affect” (OECD,
2013, p. 33).
The third element, eudaimonia (psychological “flourishing”), is defined as “a sense of meaning and
purpose in life, or good psychological functioning” (OECD, 2013, p. 12).
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Focusing on life evaluation
The focus of this paper lies on the first element of subjective well-being, life evaluation, and this
selection is based on two reasons.
A first reason is due to the fact that the chosen dependent variable (stflife) best represents this
element of subjective well-being as will be seen shortly. (ESS, n.d. c)
A second reason is simply due to practical considerations. Only accounting for one element of
subjective well-being limits the number of explanatory variables which need to be taken into
account as each element implies a handful of explanatory variables. Specifically, variables relating
to personal feelings, which refer to affect, and variables relating to a sense of meaning and purpose
of life, which refer to eudaimonia, shall be omitted from the economic model. This limitation of
variables is in line with parsimony, which is one of the properties indicating a good economic
model. Nevertheless, the two elements, affect, and eudaimonia, are also of importance and even
more so in the field of psychology. However, as a studying economist, I believe it is more
straightforward and transparent to have a grasp on life evaluation. (OECD, 2013; Gabaix & Laibson,
2008)
Variables representing subjective well-being
When evaluating the ESS questionnaire, there are two variables which may represent subjective
well-being with a focus on life evaluation: stflife and happy. Both variables represent single-item
measures of subjective well-being and are quite explicitly expressed by the OECD to be a measure of
life evaluation (life satisfaction). (ESS, n.d. c; International Wellbeing Group, 2013; OECD, 2013)
Life satisfaction/life evaluation (stflife)
The variable stflife is constructed by asking respondents: “All things considered, how satisfied are
you with your life as a whole nowadays” on a scale of 0 to 10 (ESS, n.d. c, p. 37)? It is considered as
“a primary measure of subjective well-being [of which] the intent is to obtain a cognitive evaluation
on their level of life satisfaction” (OECD, 2013, p. 253, p. 255).
Happiness (happy)
The variable happy is constructed by asking respondents: “Taking all things together, how happy
would you say you are” on a scale of 0 to 10 (ESS, n.d. c, p. 40)? This is described by the OECD
(2013, p. 255) as “an alternative of measuring the same underlying concept as the primary measure
of life evaluation”, stflife. (ESS, n.d. c)
These insights reveal that the variables stflife or happy are approximately equivalent to one
another. Though this may the case, the variable stflife shall be chosen as the dependent variable as it
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is considered as a primary measure of subjective well-being. On these grounds, every mention of
subjective well-being in this paper actually refers to the aspect life evaluation of subjective well-
being. (ESS, n.d. c; OECD, 2013)
On a side note, it may be an interesting extension of this paper to apply the same analysis but using
happy as the dependent variable.
4.2 The independent variables
The relationship between subjective well-being and its explanatory variables are on the level of the
individual, as a within-country analysis will be applied in this paper. This translates to the following
set of explanatory variables which is widely agreed upon in the literature: household income,
marital status, number of children, gender, age, health, employment status, job satisfaction,
education, and social life. Other variables such as handicap, religion, and discrimination are also
included in the analysis as they are potentially relevant variables. The household income shall be
elaborated upon and a description of the other independent variables can be found in A1 of the
appendix. (Bandura & Conceição, 2008; Binder & Coad, 2014; ESS, n.d. c; Helliwell, 2002; OECD,
2013)
Household income (income, incomeD1,...,incomeD10, incomeQ1,...,incomeQ5)
Our main independent variable is the household’s total net income originating from all possible
sources. Income is not represented as a cardinal quantitative variable but as a group of indicator
variables in order to correctly incorporate the ordinal information. These indicator variables
(incomeD1,…,incomeD10, incomeQ1,…,incomeQ5) indicate the income category (decile/quintile) in
which the respondents’ household belongs to. These income categories are “based on deciles of the
actual household income range in [Belgium]” (ESS, n.d. f, p. 2), which can be seen in table 1 of the
appendix. (ESS, n.d. c; OECD, 2013).
Note that household income, not individual income, is relevant for our analysis, as it is “household
income that drives living standards and consumption possibilities” (OECD, 2013, p. 149). Rather
than individual income, it is consumption (which is driven and proxied by household income) that
influences subjective well-being. Furthermore, by using household income instead of individual
income, there is less uncertainty if there were to be a possible endogeneity problem between
individual income and subjective well-being. (ESS, n.d. c; OECD, 2013)
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First econometric model
𝑠𝑡𝑓𝑙𝑖𝑓𝑒 = 𝛽0 + 𝛽1 𝑖𝑛𝑐𝑜𝑚𝑒𝐷2 + 𝛽2 𝑖𝑛𝑐𝑜𝑚𝑒𝐷3 + 𝛽3 𝑖𝑛𝑐𝑜𝑚𝑒𝐷4 + 𝛽4 𝑖𝑛𝑐𝑜𝑚𝑒𝐷5 + 𝛽5 𝑖𝑛𝑐𝑜𝑚𝑒𝐷6
+ 𝛽6 𝑖𝑛𝑐𝑜𝑚𝑒𝐷7 + 𝛽7 𝑖𝑛𝑐𝑜𝑚𝑒𝐷8 + 𝛽8 𝑖𝑛𝑐𝑜𝑚𝑒𝐷9 + 𝛽9 𝑖𝑛𝑐𝑜𝑚𝑒𝐷10
+ 𝛽10 𝑚𝑎𝑟𝑟𝑖𝑒𝑑 + 𝛽11 𝑐ℎ𝑖𝑙𝑑𝑟𝑒𝑛 + 𝛽12 𝑚𝑎𝑙𝑒 + 𝛽13 𝑎𝑔𝑒 + 𝛽14 ℎ𝑒𝑎𝑙𝑡ℎ𝑦
+ 𝛽15 ℎ𝑎𝑛𝑑𝑖𝑐𝑎𝑝 + 𝛽16 𝑤𝑜𝑟𝑘(𝑗𝑜𝑏𝑠𝑎𝑡) + 𝛽17 𝑒𝑑𝑢𝑦𝑟𝑠 + 𝛽18 𝑠𝑜𝑐𝑖𝑎𝑙 + 𝛽19 𝑖𝑛𝑚𝑑𝑖𝑠𝑐
+ 𝛽20 𝑟𝑒𝑙𝑖𝑔𝑖𝑜𝑢𝑠 + 𝛽21 𝑑𝑖𝑠𝑐𝑟𝑖 + 𝑢
4.3 Data description and summary statistics
The data description and summary statistics of the relevant variables can be found in table 2 and 3
of the appendix. While the data description gives an overview of the variables names and their
labels, the summary statistics illustrate how the sample is composed of and inspect for data flaws,
such as errors-in-variables.
5. The econometric model and inference procedures
5.1 The starting point
The starting point of the multiple linear regression model is the following. This model was created
in order to address the research questions concerning the relationship between subjective well-
being and income; and the marginal effect of income on subjective well-being. The variables
specified in section 4 are included in the model. Note that this is only a temporary model as it shall
go through a number of adjustments in the following subsections for further improvement.
The ordinary least squares (OLS) estimation procedure was applied. Regarding the estimation
technique, it is important to note that despite life evaluation being an ordinal variable (ranked on a
scale from 1 to 10), it shall be treated as if it is cardinal in OLS. According to conventional
econometrics, an ordered choice model is more appropriate due to the ordinal dependent variable.
However, this is not as problematic as it may seem. A paper by Ferrer-i-Carbonell and Frijters
(2004) shows that “that the difference in results between using cardinal OLS versus the
econometrically more appropriate ordered choice model is negligible” when explaining happiness
(Binder & Coad, 2014, p. 8). (Griffiths et al., 2012)
Design weights provided by ESS shall be applied as recommended. These weights “correct for [a
potential sample] bias that is introduced by the sampling design” (ESS, 2014, p. 1).
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5.2 Inference procedures
Selection between jobsat or work
Note that the variable jobsat between parentheses indicates that either work or jobsat can be
included in the regression but not both as they are highly collinear. After all, a value for the variable
jobsat is only present when the respondent has a job. Running a regression alternating the inclusion
of work and jobsat points out that jobsat is highly significant and work is insignificant. This can be
seen using income deciles and income quintiles in table 4 and 5 in the appendix. This implies that
instead of being employed or not, it is job satisfaction which is an important driver for life
satisfaction. Therefore, the variable jobsat (and not work) shall be included in the upcoming
regressions. (Griffiths et al., 2012; OECD, 2013)
Selection between income deciles or income quintiles
Running a first regression using the income deciles, as is shown in table 5.1 of the appendix,
indicates the vast majority of the income deciles variables to be insignificant (at a significance level
of 10%) due to an abundant amount of categories. To solve this problem, income quintiles will be
used instead. This is illustrated in table 5.2 of the appendix. In this second regression, only one
variable (incomeQ2) of the income indicator variables remains insignificant.
Testing for statistically significant variables
Running the regression using income quintiles delivers output shown in table 5.2 of the appendix.
The output suggests that next to incomeQ2, the variables discri, male, religious, age, healthy, eduyrs,
inmdisc, and handicap are insignificant as the individual t-tests fail to reject the null hypothesis of a
coefficient with value zero at a significance level of 10%. (Griffiths et al., 2012)
In addition to these individual t-tests, a joint hypothesis test (F-test) was executed in order to verify
whether at least one of these coefficients is nonzero. The F-test, which can be found in table 6 of the
appendix, confirms that the nine variables are not only individually insignificant but also jointly
insignificant. (Griffiths et al., 2012)
Exclusion of insignificant variables
Instead of simply excluding all nine insignificant variables from the model, it is vital to think
whether some of these variables should still be included despite being insignificant. In light of this,
it is important to evaluate the insignificant variables highly recommended by academic literature
before omission. (Griffiths et al., 2012)
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The variable incomeQ2 shall be kept retained in the model as it is an important variable relevant for
our research question, belonging to the group of indicator variables of the income quintiles.
The variables discri, religious and handicap were initially included due to their potential relevance
based on intuition. But as they have deemed to be insignificant and they are not highly
recommended by academic literature, these three variables shall be omitted from the regression.
The variable inmdisc shall also be omitted from the regression as there is another variable (social)
which is significant and also represents social life. A regression excluding these four variables can
be found in table 7 of the appendix.
The remaining insignificant variables male, age, healthy, and eduyrs are highly endorsed by
academic literature and thus verge more attention.
Health
The importance of health on subjective well-being has been proven in several studies. “Health and
subjective well-being are [positively] significantly associated” with one another (Lamu & Olsen,
2016, p.2). For this reason, health will be retained in the regression. However, health will not be
retained as the indicator variable healthy due to its insignificance but as the ordinally ranked
variable rhealth. The paper by Helliwell (2002) also includes health as an ordinally ranked variable.
The variable rhealth is statistically significant as can be seen in table 8 of the appendix. However, its
nature of ordinality heeds caution during interpretation. (Griffiths et al., 2012; OECD, 2013)
Age
The relationship between age and life satisfaction is notorious for its U-shape relationship. This “U-
bend of life” (2010) can partially be witnessed in the ESS 2010 data set for Belgium in figure 2 of
the appendix. There seems to be a U-shape relationship between life satisfaction and age up until
the age of 75, after which life satisfaction goes downhill. As the relationship is evidently non-linear,
a polynomial term age2, age to the power of two, is added to the regression. By cause of the
inclusion of age2, table 9 of the appendix shows age and age2 to now be significant at a significance
level of 10%. (Griffiths et al., 2012; OECD, 2013; “The U-bend of life”, 2010)
Gender
The majority of studies dedicated to answering the question of whether “men are happier than
women, found only minimal gender-related differences in subjective well-being”(Inglehart, 2002,
p. 1). However, a paper by Inglehart (2002) shows that gender-related differences in subjective
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Second econometric model
𝑠𝑡𝑓𝑙𝑖𝑓𝑒 = 𝛽0 + 𝛽1 𝑖𝑛𝑐𝑜𝑚𝑒𝑄2 + 𝛽2 𝑖𝑛𝑐𝑜𝑚𝑒𝑄3 + 𝛽3 𝑖𝑛𝑐𝑜𝑚𝑒𝑄4 + 𝛽4 𝑖𝑛𝑐𝑜𝑚𝑒𝑄5 + 𝛽5 𝑚𝑎𝑟𝑟𝑖𝑒𝑑
+ 𝛽6 𝑐ℎ𝑖𝑙𝑑𝑟𝑒𝑛 + 𝛽7 𝑎𝑔𝑒 + 𝛽8 𝑎𝑔𝑒² + 𝛽9 𝑟ℎ𝑒𝑎𝑙𝑡ℎ + 𝛽10 𝑗𝑜𝑏𝑠𝑎𝑡 + 𝛽11 𝑠𝑜𝑐𝑖𝑎𝑙 + 𝑢
well-being are present but they are hidden in an “interaction effect between age, gender and well-
being” (Inglehart, 2002, p. 1). This implies that the effect of age on stflife may differ between males
and females. Due to this finding, an interaction term of male and age, age_male, was constructed
and included in the regression. Unfortunately, statistical tests of significance, shown in table 10 of
the appendix, point out that male and age_male are individually and jointly insignificant. The results
of this regression and sample seem to be in line with the majority of the studies and not with
Inglehart (2002) as an insignificant relationship was found. As a consequence, the variables male
and age_male were omitted. (Inglehart, 2002; OECD, 2013)
Education
According to the paper by Michalos (2007), finding whether education has a significant influence on
subjective well-being or not depends on the definitions of the variables representing these two
concepts. If education is defined as “the highest level of formal education attained” and subjective
well-being is represented as a single-item measure such as life satisfaction, then “education has
very little influence on happiness” (Michalos, 2007, p.2). As our variables eduyrs and stflife are
indeed limited to these definitions, it is unsurprising why the relationship is found to be
insignificant. In fact, even if eduyrs is transformed into a polynomial term, an indicator variable for
highly educated people or an interaction term, it remains insignificant and shall thus be omitted
from the regression (results not included).
Statistical tests and scrutiny considering the significance of variables have led to the creation of the
following econometric model of which its results can be found in table 11 of the appendix.
A comparison of the first and the second econometric model in table 12 of the appendix shows that
the model has improved considerably: R² and adjusted R² have increased while the Akaike and
Bayesian information criteria have decreased.
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Testing the functional form
A next step is detect whether the second model is misspecified or has overlooked some non-
linearities. Preforming the Ramsey RESET test in table 13 of the appendix shows that there was
initially a problem of functional form misspecification in the first econometric model. Fortunately,
the corrections imposed on the regression during the statistical tests of significance have solved
this problem as the second econometric model does not have a functional form misspecification.
(Griffiths et al., 2012)
Testing for multicollinearity
To determine whether multicollinearity is present in the model, the variance inflation factor (VIF)
was constructed for the second econometric model in table 14 of the appendix. With the mean VIF
higher than 5, the model is characterized by high multicollinearity. However, this does not come as
a surprise as the mean VIF has been inflated due to a high VIF of the variables age, age2 and to a
smaller extent due to incomeQ3, incomeQ4, and incomeQ5. The high multicollinearity is less
problematic as it may seem as it is only natural that they are collinear: age2 is the square of age and
incomeQ3, incomeQ4 and incomeQ5 belong to the same group of indicator variables.
Multicollinearity can be tolerated to some extent, however during interpretation, it is vital to
remember that a high multicollinearity may stand in the way of measuring the precise individual
effects. (Griffiths et al., 2012)
Testing for heteroskedasticity
As a final step, an informal approach, as well as a formal test, was applied to detect the presence of
heteroskedasticity.
First, the residuals were plotted against the fitted values and the residuals were plotted against
each explanatory variable as can be seen in figure 3 of the appendix. Unfortunately, it is quite
difficult to identify the presence of heteroskedasticity in these figures as there is no clear pattern of
panning out. (Griffiths et al., 2012)
Second, a White test was executed in table 15 of the appendix. Although it was unclear in the
informal approach whether there was heteroskedasticity or not, the White test confirms that the
model is indeed characterized by heteroskedasticity. (Griffiths et al., 2012)
In order to alleviate the problem of heteroskedasticity, robust standard errors may be used in large
samples and appropriate weights should be applied. As was mentioned earlier in subsection 5.1,
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design weights provided by the ESS were continuously implemented throughout all of the
regressions and robust standard errors have already been automatically applied due to the design
weights. (ESS, 2014; Griffiths et al., 2012)
As all of the robustness checks have been covered, it is now appropriate to interpret the results of
the model.
6. The results
The final model estimated by ordinary least squares (OLS), using ESS design weights and robust
standard errors is shown in table 11 of the appendix. This model was created in order to analyze
the relationship between subjective well-being and income; and the marginal effect of income on
subjective well-being.
The goodness-of-fit measure R² implies that 14% of the variation in the dependent variable, life
satisfaction (stflife), is explained by the included independent variables. The value of R² is rather
low thus, in this regard the model requires improvement. The model, however, does include
important explanatory variables as instructed by academic literature. (Griffiths et al., 2012; OECD,
2013)
Ten out of the eleven independent variables (incomeQ3, incomeQ4, incomeQ5, married, children, age,
age2, rhealth, jobsat and social) are individually statistically significant at a significance level of
10%. The variable incomeQ2, on the other hand, is insignificant at a significance level of 10%.
IncomeQ2 is kept in the regression due to it is relevance to our research question concerning the
relationship between subjective well-being and income. (Griffiths et al., 2012)
6.1 Relationship between income and subjective well-being
The first and main research question concerns the relationship between subjective well-being and
income in Belgium. The results from table 11 of the appendix confirm the general finding of a
positive relationship between subjective well-being and income. The significance of the
relationship, however, depends on the reference group and on the income quintile. (Stevenson &
Wolfers, 2013)
Income is represented as a group of indicator variables which indicate the income quintile the
respondent belongs to. The income quintiles are shown in table 1 of the appendix. The omitted
indicator variable, incomeQ1, is the reference group. The coefficients of the included income
16 | P a g e
quintiles (incomeQ2, incomeQ3, incomeQ4 and incomeQ5) are interpreted with respect to the
reference group, incomeQ1. (Griffiths et al., 2012)
The interpretation of the sign and the significance of the income variables is relatively
straightforward.
Respondents belonging to the second income quintile have a higher life satisfaction (+0.1115) than
respondents belonging to the first income quintile while holding other explanatory variables
constant. This effect, however, is insignificant. A similar interpretation holds for the other income
quintiles. Respondents belonging to the third income quintile (+0.6364), the fourth income quintile
(+0.7023), and the fifth income quintile (+0.8627) have a higher life satisfaction than respondents
belonging to the first income quintile while holding other explanatory variables constant. All three
effects are significant. Note that the numbers between brackets are the magnitudes of the effects,
which will be discussed next.
It is of great importance to be cautious when interpreting the coefficients in terms of magnitude as
the dependent variable, stflife, is an ordinal variable but is implemented in the model as if it were
cardinal. (Griffiths et al., 2012)
For example, the coefficient of 0.1115 belonging to incomeQ2 technically implies that moving from
the first income quintile to the second with a notion of ceteris paribus, increases life satisfaction by
0.1115 in terms of the life satisfaction scale. However, as life satisfaction is ordinally ranked on a
scale from 1 to 10, you should not make statements such as “a life satisfaction of 5 is twice as better
than a life satisfaction of 10” or ‘”life satisfaction has increased by 0.1115 units” as these “units” do
not make much sense. Strictly speaking, you can only make statements of whether life satisfaction
has increased or decreased but not by how much. Statements such as the following, however, are
allowed and useful “the increase in life satisfaction by being in the fifth income quintile is higher
than being in the fourth quintile, as +0.8627 is bigger than +0.7023, with respect to the first income
quintile”.
Thus, the magnitude does give an idea of the size of the effect (especially in comparison to another
effect) but there is no clear-cut interpretation in terms of units. (ESS, n.d. f; Griffiths et al., 2012)
17 | P a g e
+0.122
1st
income
quintile
+0.525
Significant
2nd
income
quintile
+0.066
3rd
income
quintile
+0.160
4th
income
quintile
5th
income
quintile
6.2 Marginal effect of income on subjective well-being
The second research question concerns the marginal effect of income on subjective well-being.
Previous results have shown that there is a positive relationship, but does the effect of income on
subjective-wellbeing decrease as respondents become richer? Is the marginal effect decreasing?
Different conclusions about the marginal effect are made depending on the method.
This question is answered by assessing the effect of upward movements in the income categories
on life satisfaction. In order to make such an assessment possible, different models were generated
by applying the second econometric model while alternating the reference group concerning the
income quintiles. An overview of these models can be found in table 16 of the appendix.
The effect on life satisfaction by moving from the first income quintile to the second income quintile
is positive but insignificant (+0.112). The effect on life satisfaction by moving from the second
income quintile to the third income quintile is positive and highly significant (+0.525). The effect on
life satisfaction by moving from the third income quintile to the fourth income quintile is positive
but insignificant (+0.066). The effect on life satisfaction by moving from the fourth income quintile
to the fifth income quintile is positive but insignificant (+0.160). Note that a ceteris paribus notion
holds for all of the previous statements. A schematic illustrating this can be found below.
Increasing Decreasing Increasing
Remarkably, the only significant effect of an upward movement in the income categories is from the
second to the third income quintile. Furthermore, the size of the coefficients, as is given in between
brackets, seems to suggest that the marginal effect is not strictly decreasing. The marginal effect of
movements up until the second income quintile seems to be increasing, after which the marginal
effect decreases when moving to the third income quintile and proceeds to increase again. This
peculiar conclusion may be due to the use of indicator variables.
Another conclusion on the marginal effect is reached when simply plotting the income quintiles on
the scale of life satisfaction (figure 4 in the appendix). The marginal effect is strictly decreasing as
the slope of a higher income quintile is consistently flatter than the previous income quintile.
18 | P a g e
6.3 The satiation point
The third research question concerns the existence of a satiation point. As previously pointed out,
figure 4 suggests a positive, but decreasing marginal effect of income on subjective well-being. But
does this imply that there exists a satiation point, a point after which the relationship between
income and subjective well-being disappears? The graph in figure 5 suggests that no such satiation
point exists.
In order to assess the possible existence of a satiation point, the graph in figure 5 of the appendix
was created. This graph plots life satisfaction on the log of income by using a linear fit and a lowess
fit. Notice that the log of income was taken in order to allow a flattening out of the relationship
between income and subjective well-being. The interpretation of the graph is as follows.
The existence of a possible satiation point is verified when “the non-parametric fit flattens out once
basic needs were met” (Stevenson & Wolfers, 2013, p. 2). In figure 5, there is no flattening out in the
lowess fit. This implies that there is presumably no satiation point given the income categories.
While plotting such a graph is a valid method to confirm the possible existence of a satiation point,
especially given the limitations of the data set, it remains to be an informal method. A possible
improvement would be to set up a formal econometric model and use hypothesis tests to verify
whether a satiation point exists. However, this is only possible when data is available on the
quantitative income of the respondents, which is unfortunately not the case for the ESS dataset.
(ESS, n.d. c; Stevenson & Wolfers, 2013)
7. Conclusion
In this paper, we set out to explore the relationship between subjective well-being and income for
Belgian inhabitants. The results of the cross-sectional model confirm this relationship, just as the
marginal effect of income on subjective well-being, to be positive. Conclusions on how the marginal
effect unfolds as people become richer depend on the applied method. While the model using
indicator variables of income, suggests that the marginal effect increases, decreases and then
proceeds to increase; a graph plotting the income quintiles against life satisfaction suggests this
effect to be strictly decreasing. In turn, a strictly decreasing marginal effect suggests the existence
of a possible satiation point, after which the relationship between subjective well-being and income
disappears. No concrete evidence for such a satiation point was found. The positive relationship
between subjective well-being and income persists through the different income categories.
Ultimately, the paper boils down to one question: “Can money buy happiness for Belgians? The
results suggest yes, overall richer people tend to be happier.
19 | P a g e
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22 | P a g e
Appendix
A.1 Description of the independent variables
Marital status (married)
This variable indicates whether the respondent is married (or in a legally registered civil union) or
not. (ESS, n.d. c)
Number of children (children)
This variable indicates the number of children living in the household. (ESS, n.d. c)
Gender (male)
This variable indicates the gender of the respondent. (ESS, n.d. c)
Age (age)
This variable indicates the age of the respondent. (ESS, n.d. c)
Health (healthy, rhealth)
The variable healthy indicates whether the subjective general health of the respondent is
considered to be good or bad. The variable rhealth indicates the health ranking (on a scale from 1 to
5) in which the respondent places himself or herself. (ESS, n.d. c)
Handicap (handicap)
This variable indicates whether the respondent is “hampered by any sort of handicap (longstanding
illness, or disability, infirmity or mental health problem) in their daily activities” or not (ESS, n.d. c,
p. 42).
Employment status (work)
This variable indicates whether the respondent is in paid work (employed) or not. (ESS, n.d. c)
23 | P a g e
Job satisfaction (jobsat)
This variable indicates whether the employed respondents are satisfied with their job or not. (ESS,
n.d. c)
Education (eduyrs)
This variable indicates the number of “years of full-time education completed” (ESS, n.d. c, p. 95).
Social life (social, inmdisc)
The variables social and inmdisc are associated with the social life of the respondent. (ESS, n.d. c)
The variable social indicates “how often the respondent meets up with friends, relatives or
colleagues” (ESS, n.d. c, p. 41). The respondent is considered to be relatively more social when they
have social meetings ranging from several times a month to several times a week. Alternatively, the
respondent is considered to be relative less social when they have social meetings ranging from
(almost) never to once a month. (ESS, n.d. c)
The variable inmdisc indicates whether the respondent has a confidant, “anyone to discuss intimate
and personal matters with” (ESS, n.d. c, p. 41), or not.
Religion (religious)
This variable indicates whether the respondent “belongs to a particular religion or denomination”
or not (ESS, n.d. c, p. 43).
Discrimination (discri)
This variable indicates whether the respondent describes themselves as a “member of a group that
is discriminated in [Belgium]” or not (ESS, n.d. c, p. 60).
24 | P a g e
A.2 Figures
Figure 1: The modified –Easterlin hypothesis
Source: Stevenson & Wolfers, 2013
Figure 2: U-shape relationship between age and life satisfaction
This graph is constructed using the lowess technique (locally weighted scatterplot smoothing).
25 | P a g e
Figure 3: Detecting heteroskedasticity
-10
-5
05
Residuals
5 6 7 8 9
Fitted values
-10
-5
05
Residuals
0 .2 .4 .6 .8 1
incomeQ2
-10
-5
05
Residuals
0 .2 .4 .6 .8 1
incomeQ3
-10
-5
05
Residuals
0 .2 .4 .6 .8 1
incomeQ5
-10
-5
05
Residuals
0 .2 .4 .6 .8 1
incomeQ6
-10
-5
05
Residuals
0 .2 .4 .6 .8 1
Marriage
-10
-5
05
Residuals
0 2 4 6 8
Children
-10
-5
05
Residuals
20 40 60 80 100
Age
-10
-5
05
Residuals
0 2000 4000 6000 8000
Age²
-10
-5
05
Residuals
1 2 3 4 5
rhealth
-10
-5
05
Residuals
0 .2 .4 .6 .8 1
Job satisfaction
-10
-5
05
Residuals
0 .2 .4 .6 .8 1
Social
26 | P a g e
Figure 4: Plotting income on life satisfaction using the lowess technique
Figure 5: Satiation point - Plotting log(income) on life satisfaction
6.5
7
7.5
8
1 2 3 4 5
Income Quintiles
Lifesatisfaction
6
6.5
7
7.5
8
0 .5 1 1.5 2 2.5
Log(income)
Lowess Linear fit
27 | P a g e
A.3 Tables
Table 1: Income deciles and quintiles for Belgium
Income deciles
1 < €11 040
2 € 11 040 – € 14 160
3 € 14 160 – € 17 640
4 € 17 640 – € 21 360
5 € 21 360 – € 25 560
6 € 25 560 – € 30 600
7 € 30 600 – € 37 440
8 € 37 440 – € 44 880
9 € 44 880 – € 56 760
10 > € 56 760
Source: ESS, n.d. f, p.4
Table 2: Data description
Dependent variables
Variable name Variable label
stflife How satisfied with life as a whole – Scale of 0 to 10
happy How happy are you – Scale of 0 to 10
Independent variables
Variable name Variable label
income Household's total net income, all sources (deciles)
incomeQ1,…,incomeQ5 Household's total net income - 1st quintile,…,5th quintile
incomeD1,…,incomeD10 Household's total net income - 1st decile,…10th decile
married 1 Married / 0 Not married
children Number of children
male 1 Male / 0 Female
age Age of respondent
healthy 1 Healthy / 0 Not healthy
rhealth Subjective general health – Scale of 1 to 5
handicap 1 Handicap/ 0 No handicap
work 1 Employed / 0 Unemployed
jobsat 1 Job satisfaction/ 0 No job satisfaction
eduyrs Years of full-time education completed
social 1 Social / 0 Not social
inmdisc Confidant / 0 No confidant
religious 1 Religious / 0 Not religious
discri 1 Discriminated / 0 Not discriminated
Income quintiles
1 < € 14 160
2 € 14 160 – € 21 360
3 € 21 360 – € 30 600
4 € 30 600 – € 44 880
5 > € 44 880
28 | P a g e
Table 3: Summary statistics
Dependent variables
Variable Obs Mean Std. Dev. Min Max
stflife 1424 7.497893 1.648269 0 10
happy 1424 7.835674 1.407127 0 10
Independent variables
Variable Obs Mean Std. Dev. Min Max
income 1424 5.95014 2.424613 1 10
incomeQ1 1424 .0919944 .2891196 0 1
incomeQ2 1424 .2191011 .4137826 0 1
incomeQ3 1424 .2380618 .4260468 0 1
incomeQ4 1424 .2745787 4464585 0 1
incomeQ5 1424 .176264 .3811785 0 1
incomeD1 1424 .0245787 .1548915 0 1
incomeD2 1424 .0674157 .2508287 0 1
incomeD3 1424 .0969101 .2959393 0 1
incomeD4 1424 .122191 .3276213 0 1
incomeD5 1424 .1116573 .315055 0 1
incomeD6 1424 .1264045 .3324214 0 1
incomeD7 1424 .1615169 .3681363 0 1
incomeD8 1424 .1130618 .3167796 0 1
incomeD9 1424 .1032303 .3043664 0 1
incomeD10 1424 .0730337 2602832 0 1
married 1424 .5351124 .4989408 0 1
children 1424 .7549157 1.122023 0 7
male 1424 .4803371 .4997887 0 1
age 1424 47.7802 7.96378 15 94
healthy 1424 .9578652 .2009673 0 1
rhealth 1424 2.060393 .7947501 1 5
handicap 1424 .2345506 .4238664 0 1
work 1424 .5351124 .4989408 0 1
jobsat 730 .9164384 .276919 0 1
eduyrs 1424 12.69874 3.628744 1 27
social 1424 .8953652 .3061898 0 1
inmdisc 1424 .8876404 .3159192 0 1
religious 1424 .4234551 .4942797 0 1
discri 1424 .0491573 .2162723 0 1
29 | P a g e
Note that only the relevant aspects are highlighted in the following tables, implying that there are
more (in)significant variables than the ones highlighted.
Table 4: Regression of the first econometric model using work
Table 4.1 Income deciles
Linear regression Number of obs = 1424
F( 21, 1402) = 7.97
Prob > F = 0.0000
R-squared = 0.1371
Root MSE = 1.5426
------------------------------------------------------------------------------
| Robust
stflife | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
incomeD2 | .0383124 .3472944 0.11 0.912 -.6429602 .719585
incomeD3 | .3921308 .3245277 1.21 0.227 -.2444814 1.028743
incomeD4 | .3420934 .3145772 1.09 0.277 -.2749993 .9591862
incomeD5 | .6438971 .3136798 2.05 0.040 .0285648 1.259229
incomeD6 | .7685312 .3027232 2.54 0.011 .174692 1.36237
incomeD7 | .7357802 .3079323 2.39 0.017 .1317225 1.339838
incomeD8 | 1.066969 .3074412 3.47 0.001 .4638749 1.670064
incomeD9 | 1.045569 .3114351 3.36 0.001 .43464 1.656498
incomeD10 | .9410447 .3251922 2.89 0.004 .3031289 1.57896
married | .3281534 .1032586 3.18 0.002 .1255955 .5307114
children | -.1741508 .0462813 -3.76 0.000 -.2649388 -.0833628
male | .1145105 .0836686 1.37 0.171 -.0496186 .2786397
age | .000728 .0029193 0.25 0.803 -.0049986 .0064546
healthy | .9547749 .2972692 3.21 0.001 .3716346 1.537915
handicap | -.4638559 .1150009 -4.03 0.000 -.6894483 -.2382635
work | .0663897 .0994239 0.67 0.504 -.1286459 .2614253
eduyrs | -.0254463 .0133356 -1.91 0.057 -.0516061 .0007135
social | .6279197 .1662838 3.78 0.000 .3017279 .9541115
inmdisc | .4020903 .1533945 2.62 0.009 .1011829 .7029977
religious | .1288917 .0855055 1.51 0.132 -.0388407 .2966242
discri | -.5484973 .2340076 -2.34 0.019 -1.00754 -.0894546
_cons | 5.23153 .5026337 10.41 0.000 4.245534 6.217525
------------------------------------------------------------------------------
Table 4.2 Income quintiles
Linear regression Number of obs = 1424
F( 16, 1407) = 9.58
Prob > F = 0.0000
R-squared = 0.1338
Root MSE = 1.5427
------------------------------------------------------------------------------
| Robust
stflife | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
incomeQ2 | .3327523 .1993628 1.67 0.095 -.058328 .7238326
incomeQ3 | .6767538 .1915895 3.53 0.000 .300922 1.052586
incomeQ4 | .8362169 .1965822 4.25 0.000 .4505911 1.221843
incomeQ5 | .9651059 .2051636 4.70 0.000 .5626464 1.367565
married | .3293819 .1019277 3.23 0.001 .1294352 .5293285
children | -.1779147 .0458519 -3.88 0.000 -.2678602 -.0879692
male | .1105063 .0838854 1.32 0.188 -.0540476 .2750603
age | .0006676 .0028863 0.23 0.817 -.0049942 .0063294
healthy | .9560698 .2977074 3.21 0.001 .3720718 1.540068
handicap | -.4746559 .1151355 -4.12 0.000 -.7005115 -.2488003
work | .0756469 .0986565 0.77 0.443 -.1178828 .2691766
eduyrs | -.0252168 .0132784 -1.90 0.058 -.0512644 .0008309
social | .64777 .1661267 3.90 0.000 .3218874 .9736526
inmdisc | .41127 .1536191 2.68 0.008 .109923 .7126171
religious | .1215717 .08547 1.42 0.155 -.0460905 .289234
discri | -.5426634 .2322401 -2.34 0.020 -.9982374 -.0870893
_cons | 5.242665 .4390709 11.94 0.000 4.38136 6.103969
------------------------------------------------------------------------------
Work is statistically insignificant on a significance level of 10%.
Legend
 Insignificant variables
At a significance level of 10%
30 | P a g e
Table 5: Regression of the first econometric model using jobsat
Table 5.1 Income deciles
Linear regression Number of obs = 730
F( 21, 708) = 4.08
Prob > F = 0.0000
R-squared = 0.1240
Root MSE = 1.3641
------------------------------------------------------------------------------
| Robust
stflife | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
incomeD2 | .086196 .7281809 0.12 0.906 -1.343456 1.515848
incomeD3 | .4202934 .7126108 0.59 0.556 -.9787898 1.819377
incomeD4 | .2436483 .6658778 0.37 0.715 -1.063683 1.55098
incomeD5 | .7024271 .6564792 1.07 0.285 -.5864519 1.991306
incomeD6 | .8334468 .6565641 1.27 0.205 -.4555988 2.122492
incomeD7 | .7759848 .6516952 1.19 0.234 -.5035017 2.055471
incomeD8 | 1.087773 .6469581 1.68 0.093 -.1824129 2.357959
incomeD9 | 1.099949 .6521661 1.69 0.092 -.1804623 2.38036
incomeD10 | 1.068144 .6553251 1.63 0.104 -.2184689 2.354757
married | .268877 .1234711 2.18 0.030 .0264637 .5112902
children | -.1370221 .0515801 -2.66 0.008 -.2382903 -.0357539
male | -.0175619 .1016473 -0.17 0.863 -.2171281 .1820043
age | -.0025749 .0055666 -0.46 0.644 -.013504 .0083541
healthy | -.5702315 .9726968 -0.59 0.558 -2.479947 1.339484
handicap | -.2750421 .1725407 -1.59 0.111 -.6137948 .0637106
jobsat | .9560621 .2190361 4.36 0.000 .5260242 1.3861
eduyrs | -.0152691 .0167077 -0.91 0.361 -.0480718 .0175335
social | .5089216 .1935471 2.63 0.009 .1289266 .8889165
inmdisc | .334244 .2216629 1.51 0.132 -.1009514 .7694393
religious | -.0162215 .104886 -0.15 0.877 -.2221463 .1897033
discri | -.0798791 .2634945 -0.30 0.762 -.5972032 .437445
_cons | 6.126796 1.227709 4.99 0.000 3.716409 8.537182
------------------------------------------------------------------------------
Table 5.2 Income quintiles
Linear regression Number of obs = 730
F( 16, 713) = 4.89
Prob > F = 0.0000
R-squared = 0.1190
Root MSE = 1.3632
------------------------------------------------------------------------------
| Robust
stflife | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
incomeQ2 | .2248806 .3542428 0.63 0.526 -.470603 .9203642
incomeQ3 | .7006381 .3351216 2.09 0.037 .0426949 1.358581
incomeQ4 | .8392231 .3303806 2.54 0.011 .190588 1.487858
incomeQ5 | 1.008037 .3356162 3.00 0.003 .3491232 1.666951
married | .2868382 .1235237 2.32 0.021 .0443245 .529352
children | -.1412504 .0513935 -2.75 0.006 -.242151 -.0403498
male | -.020102 .1024242 -0.20 0.844 -.2211912 .1809872
age | -.0031764 .0056075 -0.57 0.571 -.0141856 .0078328
healthy | -.618309 .9574875 -0.65 0.519 -2.498141 1.261523
handicap | -.2872884 .1742246 -1.65 0.100 -.629343 .0547661
jobsat | .9695932 .2155557 4.50 0.000 .5463933 1.392793
eduyrs | -.0142122 .0166929 -0.85 0.395 -.0469854 .0185609
social | .5391867 .1945524 2.77 0.006 .1572227 .9211508
inmdisc | .3420861 .2230536 1.53 0.126 -.0958342 .7800065
religious | -.0249486 .1042907 -0.24 0.811 -.2297021 .179805
discri | -.0524371 .2581833 -0.20 0.839 -.5593275 .4544533
_cons | 6.214764 1.066258 5.83 0.000 4.121383 8.308146
------------------------------------------------------------------------------
Jobsat is statistically significant on a significance level of 1%.
Legend
 Insignificant variables
 Significant variables
At a significance level of 10%
31 | P a g e
Table 6: Joint hypothesis test
An F-test, which includes all nine individually statistically insignificant variables, fails to reject the null
hypothesis that all of the coefficients are zero at a significance level of 10%. This implies that all nine
variables are jointly statistically insignificant and individually statistically insignificant. (Griffiths et al.,
2012)
( 1) discri = 0
( 2) male = 0
( 3) religious = 0
( 4) age = 0
( 5) healthy = 0
( 6) eduyrs = 0
( 7) inmdisc = 0
( 8) handicap = 0
( 9) incomeQ2 = 0
F( 9, 713) = 0.76
Prob > F = 0.6527
Table 7: Regression excluding insignificant variables discri, religious,
handicap, and inmdisc
(sum of wgt is 7.3000e+02)
Linear regression Number of obs = 730
F( 12, 717) = 6.17
Prob > F = 0.0000
R-squared = 0.1105
Root MSE = 1.366
------------------------------------------------------------------------------
| Robust
stflife | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
incomeQ2 | .244316 .3562422 0.69 0.493 -.4550866 .9437185
incomeQ3 | .6968752 .3390904 2.06 0.040 .0311465 1.362604
incomeQ4 | .8426035 .3348062 2.52 0.012 .1852858 1.499921
incomeQ5 | 1.028983 .3418543 3.01 0.003 .3578282 1.700138
married | .3054176 .1223734 2.50 0.013 .0651646 .5456705
children | -.1436692 .0518477 -2.77 0.006 -.2454606 -.0418777
male | -.0330698 .1019519 -0.32 0.746 -.2332296 .1670901
age | -.0046121 .0056715 -0.81 0.416 -.0157469 .0065226
healthy | -.3844807 .9263368 -0.42 0.678 -2.203137 1.434176
jobsat | 1.017689 .2206994 4.61 0.000 .5843946 1.450983
eduyrs | -.0118488 .0165444 -0.72 0.474 -.0443301 .0206325
social | .5832671 .1926915 3.03 0.003 .2049601 .9615741
_cons | 6.180312 1.033384 5.98 0.000 4.151492 8.209132
------------------------------------------------------------------------------
32 | P a g e
Table 8: Regression retaining health as rhealth instead of healthy
(sum of wgt is 7.3000e+02)
Linear regression Number of obs = 730
F( 12, 717) = 7.32
Prob > F = 0.0000
R-squared = 0.1393
Root MSE = 1.3436
------------------------------------------------------------------------------
| Robust
stflife | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
incomeQ2 | .1994126 .3518145 0.57 0.571 -.4912972 .8901223
incomeQ3 | .6942943 .3332789 2.08 0.038 .0399751 1.348614
incomeQ4 | .7819775 .3278825 2.38 0.017 .1382531 1.425702
incomeQ5 | .9601196 .3333698 2.88 0.004 .3056219 1.614617
married | .3040201 .1199518 2.53 0.011 .0685213 .5395189
children | -.1349578 .0507661 -2.66 0.008 -.2346257 -.0352898
male | -.0394691 .1005005 -0.39 0.695 -.2367796 .1578413
age | .0003164 .0055498 0.06 0.955 -.0105794 .0112122
rhealth | -.3934461 .0900234 -4.37 0.000 -.570187 -.2167051
jobsat | .8940039 .2326333 3.84 0.000 .4372801 1.350728
eduyrs | -.018303 .0164183 -1.11 0.265 -.0505367 .0139307
social | .5230677 .1876254 2.79 0.005 .1547069 .8914285
_cons | 6.61704 .5312949 12.45 0.000 5.573961 7.66012
------------------------------------------------------------------------------
Table 9: Regression including the polynomial term age2
(sum of wgt is 7.3000e+02)
Linear regression Number of obs = 730
F( 13, 716) = 6.97
Prob > F = 0.0000
R-squared = 0.1459
Root MSE = 1.3394
------------------------------------------------------------------------------
| Robust
stflife | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
incomeQ2 | .1320555 .3541913 0.37 0.709 -.5633221 .8274331
incomeQ3 | .6556891 .3348226 1.96 0.051 -.0016624 1.31304
incomeQ4 | .7385725 .3290176 2.24 0.025 .0926179 1.384527
incomeQ5 | .9160769 .3352024 2.73 0.006 .2579799 1.574174
married | .303908 .119105 2.55 0.011 .0700711 .5377449
children | -.0905175 .0542329 -1.67 0.096 -.196992 .015957
male | -.0386483 .1004088 -0.38 0.700 -.2357792 .1584826
age | -.0869104 .0399506 -2.18 0.030 -.1653447 -.0084762
age2 | .0010423 .0004742 2.20 0.028 .0001112 .0019733
rhealth | -.3830084 .0910184 -4.21 0.000 -.5617033 -.2043135
jobsat | .8660684 .2313582 3.74 0.000 .4118468 1.32029
eduyrs | -.0153524 .0164932 -0.93 0.352 -.0477333 .0170284
social | .5272051 .1870814 2.82 0.005 .1599115 .8944987
_cons | 8.279273 .8889059 9.31 0.000 6.534099 10.02445
------------------------------------------------------------------------------
33 | P a g e
Table 10: Tests of significance of the interaction term age_male
Both the individual t-tests and the joint F-test fail to reject their corresponding null hypothesis,
implying that the variables age and age_male are statistically insignificant on the individual level and
on the collective level. (Griffiths et al., 2012)
Table 10.1 t-tests
( 1) male = 0
F( 1, 715) = 1.04
Prob > F = 0.3084
( 1) age_male = 0
F( 1, 715) = 0.93
Prob > F = 0.3361
Table 10.2 F-test
( 1) male = 0
( 2) age_male = 0
F( 2, 715) = 0.52
Prob > F = 0.5920
Table 11: Second (and final) econometric model
(sum of wgt is 7.3000e+02)
Linear regression Number of obs = 730
F( 11, 718) = 8.05
Prob > F = 0.0000
R-squared = 0.1445
Root MSE = 1.3386
------------------------------------------------------------------------------
| Robust
stflife | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
incomeQ2 | .1115113 .3531017 0.32 0.752 -.5817239 .8047464
incomeQ3 | .6364453 .3349621 1.90 0.058 -.0211768 1.294067
incomeQ4 | .7023397 .3308095 2.12 0.034 .0528702 1.351809
incomeQ5 | .8626895 .3319481 2.60 0.010 .2109846 1.514394
married | .3114766 .1191606 2.61 0.009 .0775318 .5454215
children | -.0897844 .0544247 -1.65 0.099 -.196635 .0170663
age | -.0894775 .0400256 -2.24 0.026 -.1680587 -.0108963
age2 | .0010809 .0004739 2.28 0.023 .0001506 .0020112
rhealth | -.375493 .0898125 -4.18 0.000 -.5518195 -.1991665
jobsat | .8687183 .2320963 3.74 0.000 .4130497 1.324387
social | .5251169 .1878954 2.79 0.005 .1562269 .8940069
_cons | 8.098052 .8720042 9.29 0.000 6.386069 9.810035
------------------------------------------------------------------------------
34 | P a g e
Table 12: Comparison of the first and the second econometric model
First Econometric Model Second Econometric Model
R² .1240 .1445
Adjusted R² .0980 .1314
AIC 2 546.6563 2 509.3758
BIC 2 647.7033 2 564.4923
Table 13: Testing the functional form – Ramsey RESET test
Performing the Ramsey RESET test allows the detection of a possible functional form
misspecification. The null hypothesis of non-misspecification is rejected using the first econometric
model: the first econometric model is misspecified. Fortunately, the corrections imposed during the
statistical tests of significance have seemed to solve this problem as we fail to reject the null
hypothesis for the second econometric model. The second econometric model does not have a
problem of functional form misspecification. (Griffiths et al., 2012)
Table 13.1 Ramsey RESET test of the first econometric model
Ramsey RESET test using powers of the fitted values of stflife
Ho: model has no omitted variables
F(3, 705) = 11.96
Prob > F = 0.0000
Table 13.2 Ramsey RESET test of the second econometric model
Ramsey RESET test using powers of the fitted values of stflife
Ho: model has no omitted variables
F(3, 715) = 1.81
Prob > F = 0.1445
Table 14: Testing for multicollinearity
A variance inflation factor (VIF) higher than 5 implies that multicollinearity is high. (Griffiths et al.,
2012)
Variable | VIF 1/VIF
-------------+--------------------
age | 65.53 0.015
age2 | 64.92 0.015
incomeQ4 | 6.89 0.145
incomeQ5 | 6.09 0.164
incomeQ3 | 5.28 0.189
incomeQ2 | 3.88 0.257
children | 1.44 0.695
married | 1.41 0.707
rhealth | 1.08 0.922
social | 1.04 0.963
jobsat | 1.03 0.968
-------------+--------------------
Mean VIF | 14.42
35 | P a g e
Table 15: Testing for heteroskedasticity
The White test has detected the presence of heteroskedasticity: the null hypothesis of constant
variance (homoscedasticity) was rejected at a significance level of 5%. (Griffiths et al., 2012)
White's general test statistic : 91.790 Chi-sq(63) P-value = .0104
Note: The Breusch-Pagan test was not executed as it is inappropriate in combination with the
design weights.
Table 16: Second econometric model with alternating reference group
The name of the model indicates the reference group (=the omitted indicator variable), the
coefficients of the income quintiles are interpreted with respect to the reference group. (Griffiths et
al., 2012)
--------------------------------------------------------------------------
Variable | IncomeQ1 IncomeQ2 IncomeQ3 IncomeQ4
-------------+------------------------------------------------------------
incomeQ1 | -0.112 -0.636* -0.702**
incomeQ2 | 0.112 -0.525*** -0.591***
incomeQ3 | 0.636* 0.525*** -0.066
incomeQ4 | 0.702** 0.591*** 0.066
incomeQ5 | 0.863*** 0.751*** 0.226 0.160
married | 0.311*** 0.311*** 0.311*** 0.311***
children | -0.090* -0.090* -0.090* -0.090*
age | -0.089** -0.089** -0.089** -0.089**
age2 | 0.001** 0.001** 0.001** 0.001**
rhealth | -0.375*** -0.375*** -0.375*** -0.375***
jobsat | 0.869*** 0.869*** 0.869*** 0.869***
social | 0.525*** 0.525*** 0.525*** 0.525***
_cons | 8.098*** 8.210*** 8.734*** 8.800***
--------------------------------------------------------------------------
legend: * p<.1; ** p<.05; *** p<.01

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Paper: Can money buy happiness for Belgians?

  • 1. Can money buy “happiness” for Belgians? Graduate Seminar in Economics: Research Paper Emily Van de Walle Master Economic Policy Graduate seminar in economics J. Bouckaert, J. Vanneste, E. Vanhaecht , P. Vanpachtenbeke Faculty of Applied Economic Sciences Academic year 2015-2016
  • 2. 2 | P a g e Abstract This paper explores the relationship between subjective well-being and income for Belgian inhabitants. Explicitly, the impact of income on subjective well-being shall be analyzed as well as the existence of a satiation point, which in accordance to theory claims that the marginal effect of income on subjective well-being is positive but decreasing to zero. The analysis is accomplished by applying a cross-sectional study within the country of Belgium, using data from the year 2010 provided by the European Social Survey. Overall, the results suggest the following three findings. First, there is a positive relationship between subjective well-being and income. Second, the marginal effect of income on subjective well-being is positive but conclusions on whether the marginal effect increases or decreases seem to depend on the method. Third, there is no evidence that confirms the existence of a satiation point.
  • 3. 3 | P a g e Contents Abstract.....................................................................................................................................................................2 1. Introduction...................................................................................................................................................4 2. Review of the literature ............................................................................................................................5 3. Data...................................................................................................................................................................6 4. List of relevant variables ..........................................................................................................................6 4.1 The dependent variable..........................................................................................................................7 4.2 The independent variables....................................................................................................................9 4.3 Data description and summary statistics..................................................................................... 10 5. The econometric model and inference procedures .................................................................... 10 5.1 The starting point .................................................................................................................................. 10 5.2 Inference procedures ........................................................................................................................... 11 6. The results................................................................................................................................................... 15 6.1 Relationship between income and subjective well-being...................................................... 15 6.2 Marginal effect of income on subjective well-being................................................................. 17 6.3 The satiation point................................................................................................................................. 18 7. Conclusion................................................................................................................................................... 18 References ............................................................................................................................................................ 19 Appendix A.1 Description of the independent variables.................................................................................... 22 A.2 Figures ....................................................................................................................................................... 24 A.3 Tables......................................................................................................................................................... 27
  • 4. 4 | P a g e 1. Introduction Can happiness be bought? Are the rich (always) happier than the poor? These questions concerning the relationship between income and subjective well-being may be described as tricky in the sense that a straightforward answer is lacking due to the difficulties in measuring subjective well-being. However, these questions are definitely compelling to ponder upon and are effectively analyzed in the field of happiness economics. (Happiness economics, 2016) This paper confronts these questions of interest with respect to the country of Belgium and allows for a comprehensive analysis by distinguishing and addressing the following two aspects. The first aspect concerns the relationship between subjective well-being and income. An illustrative question may be the following: If I were to give you a sum of money, would you be better off (or read as happier) than in your initial position had you not received that sum of money? Typically, you would feel better off ex-post. This illustrates the expected positive correlation between income and subjective well-being. However, does this positive correlation always apply? Is the relationship between subjective well-being and income irrespective of the amount of wealth you own? Thinking a step further leads to these new questions, which are discussed in the next aspect. (Stevenson & Wolfers, 2013) The second aspect concerns the marginal effect of income on subjective well-being and the satiation point. A satiation point implies that money can buy you happiness, but only to a certain degree thus, money cannot buy you unlimited happiness. For example, as a poor person, receiving an additional sum of money allows you to cover your basic necessities, leading to an increase in your life satisfaction (or read as subjective well-being). However, as you receive more money, the contribution of receiving that amount of money to your happiness would still be positive but will become marginally less (according to the theory). Furthermore, at a certain point which is known as the satiation point, you are sufficiently wealthy that receiving more money no longer contributes to your happiness, which implies a marginal effect of zero. A graphical illustration of the transformation of the marginal effect and the satiation point may be found in figure 1 of the appendix. This occurrence is identified as the modified version of Easterlin’s hypothesis by Stevenson & Wolfers (2013) and its existence is argued by a number of researchers due to its logical plausibility. (Stevenson & Wolfers, 2013) These two aspects shall be analyzed by constructing an econometric model in Stata13 using data from the year 2010 for the country of Belgium provided by the European Social Survey (ESS, n.d. a).
  • 5. 5 | P a g e 2. Review of the literature Whether happiness can be bought or not is one of the fundamental questions of happiness economics as the individual income of inhabitants and the gross domestic product of the nation are considered as important determinants of subjective well-being. In light of this, there has been considerable research concerning this subject. Results found in existing academic literature concerning the two aforementioned aspects shall be discussed in this section and a review of the literature concerning the relevant variables of the happiness-income relationship shall be discussed in section 4. (Happiness economics, 2016) First, the majority of studies typically find a “positive relationship between subjective well-being and income across countries and over time” (Stevenson & Wolfers, 2013). However, this is only the case when this relationship is effectively acknowledged by the researchers of a certain study. For clarification, this implies that a number of researchers argue that at a certain point, the satiation point, the relationship disappears between subjective well-being and income. (Happiness economics, 2016; Stevenson & Wolfers, 2013) Second, the existence of the satiation point or rather the modified version of the Easterlin’s hypothesis is acknowledged by a number of researchers due to its logical plausibility rather than on evidence. When based on evidence, however, this hypothesis has been rejected by a number of researchers such as Sacks, Stevenson, Wolfers and Deaton. These authors found a “robust positive relationship between subjective well-being and income across countries over time” (Stevenson & Wolfers, 2013). Nevertheless, despite the existence of a satiation point being debunked, the positive relationship between subjective well-being and income still implies that “increasing income yields diminishing marginal gains in subjective well-being” (Stevenson & Wolfers, 2013). Third, the relationship between income and subjective well-being depends on the exact definition of subjective well-being. An interesting paper by Kahneman & Deaton (2010) highlights this importance by “distinguishing two aspects of subjective well-being: emotional well-being [which] refers to the emotional quality of an individual’s everyday experience and life evaluation [which in turn] refers to the thoughts that people have about their life when they think about it”. By making this distinction, Kahneman & Deaton (2010) conclude that while high income may be robust positively correlated with life satisfaction, this is not the case with emotional well-being. In this research paper, the focus is limited to life evaluation. This shall be further elaborated in section 4, but first, it is essential to be informed of the dataset. (Deaton & Kahneman, 2010).
  • 6. 6 | P a g e 3. Data The European Social Survey (ESS) is organized by academics that collect cross-sectional data for several countries across Europe. The data applied in this analysis is collected from the fifth round of this survey, which is for the year 2010, for the country of Belgium. (ESS, n.d. a; ESS, n.d. b) The fifth round of the European Social Survey is not arbitrarily chosen but is rather chosen based on the following three considerations. (ESS, n.d. a) First, the survey round was chosen based on the rotating section of the questionnaire that highlights different themes every round. The specific theme of family work and well-being was chosen due to a focus on life evaluation, which is one of the elements of subjective well-being. (ESS, n.d. d; ESS, n.d. e; OECD, 2013) Second, rounds with the same theme may still differ in the questions effectively asked in the survey, making it necessary to compare the questionnaires to one another. (ESS, n.d. d; ESS, n.d. e) Third, the measurement of the household income has changed since the fourth ESS round. Namely, the income categories are “based on deciles of the actual household income range in the given country” (ESS, n.d. f, p. 2). This translates to a slight preference towards round four and above as household income is better represented with respect to the actual income distribution in the given country. (ESS, n.d. d; ESS, n.d. e; ESS, n.d. f) Taking all of this into account, the fifth round (the year 2010) of the ESS was chosen based on the OECD guidelines for measuring subjective well-being. (ESS, n.d. a; OECD, 2013) 4. List of relevant variables As a starting point for constructing the economic model, the ESS dataset, as well as the ESS questionnaire, are analyzed, using two complementary approaches in order to construct a list of relevant variables. This list functions as a guide of which variables should be included in the initial economic model. This list, however, does not imply that these variables are statistically significant. Tests of statistical significance have yet to follow and they shall be carried out within the context of the econometric model. (ESS, n.d. a; ESS, n.d. c) First, the analysis necessary to construct the list of relevant variables is conducted by asking two questions: “Which variable is the best representative of the subjective well-being of an individual?” and “Which variables are likely to have an impact on the subjective well-being of an individual?”
  • 7. 7 | P a g e The former question concerns the dependent variable, the subjective well-being while the latter question concerns the independent variables. Note that these questions are inquired on the individual level as a within-country analysis of Belgium will be applied in this paper. Second, a complete list of relevant variables within the borders of the ESS dataset is ensured by answering these questions while relying on two criteria: intuition and insights of the academic literature. The list of relevant variables is composed of a dependent variable (subjective well-being, life evaluation), the main independent variable (income) and other control variables. This shall be further expanded in the next two sub-sections. 4.1 The dependent variable It is of great importance to first develop an understanding of subjective well-being before considering the concrete variables for the economic model. This will allow a better grasp on the variables which best represent this concept and the chosen explanatory variables. (OECD, 2013) Understanding subjective well-being Contrary to popular belief, subjective well-being constitutes more than just happiness. The definition of subjective well-being put forward by the OECD is that largely of Diener et al. (2006): “Good mental states, including all of the various evaluations, positive and negative, that people make of their lives and the affective reactions of people to their experiences” (OECD, 2013, p. 12). This is a rather complete definition as it describes the three elements of subjective well-being: life evaluation, affect, and eudaimonia. (OECD, 2013) The first element, life evaluation (life satisfaction), is defined as “a reflective assessment of a person’s life or some aspect of it” (OECD, 2013, p. 12). The second element, affect, is defined as “a person’s feelings or emotional states” (OECD, 2013, p.12) and may be divided into “two hedonic dimensions: positive affect and negative affect” (OECD, 2013, p. 33). The third element, eudaimonia (psychological “flourishing”), is defined as “a sense of meaning and purpose in life, or good psychological functioning” (OECD, 2013, p. 12).
  • 8. 8 | P a g e Focusing on life evaluation The focus of this paper lies on the first element of subjective well-being, life evaluation, and this selection is based on two reasons. A first reason is due to the fact that the chosen dependent variable (stflife) best represents this element of subjective well-being as will be seen shortly. (ESS, n.d. c) A second reason is simply due to practical considerations. Only accounting for one element of subjective well-being limits the number of explanatory variables which need to be taken into account as each element implies a handful of explanatory variables. Specifically, variables relating to personal feelings, which refer to affect, and variables relating to a sense of meaning and purpose of life, which refer to eudaimonia, shall be omitted from the economic model. This limitation of variables is in line with parsimony, which is one of the properties indicating a good economic model. Nevertheless, the two elements, affect, and eudaimonia, are also of importance and even more so in the field of psychology. However, as a studying economist, I believe it is more straightforward and transparent to have a grasp on life evaluation. (OECD, 2013; Gabaix & Laibson, 2008) Variables representing subjective well-being When evaluating the ESS questionnaire, there are two variables which may represent subjective well-being with a focus on life evaluation: stflife and happy. Both variables represent single-item measures of subjective well-being and are quite explicitly expressed by the OECD to be a measure of life evaluation (life satisfaction). (ESS, n.d. c; International Wellbeing Group, 2013; OECD, 2013) Life satisfaction/life evaluation (stflife) The variable stflife is constructed by asking respondents: “All things considered, how satisfied are you with your life as a whole nowadays” on a scale of 0 to 10 (ESS, n.d. c, p. 37)? It is considered as “a primary measure of subjective well-being [of which] the intent is to obtain a cognitive evaluation on their level of life satisfaction” (OECD, 2013, p. 253, p. 255). Happiness (happy) The variable happy is constructed by asking respondents: “Taking all things together, how happy would you say you are” on a scale of 0 to 10 (ESS, n.d. c, p. 40)? This is described by the OECD (2013, p. 255) as “an alternative of measuring the same underlying concept as the primary measure of life evaluation”, stflife. (ESS, n.d. c) These insights reveal that the variables stflife or happy are approximately equivalent to one another. Though this may the case, the variable stflife shall be chosen as the dependent variable as it
  • 9. 9 | P a g e is considered as a primary measure of subjective well-being. On these grounds, every mention of subjective well-being in this paper actually refers to the aspect life evaluation of subjective well- being. (ESS, n.d. c; OECD, 2013) On a side note, it may be an interesting extension of this paper to apply the same analysis but using happy as the dependent variable. 4.2 The independent variables The relationship between subjective well-being and its explanatory variables are on the level of the individual, as a within-country analysis will be applied in this paper. This translates to the following set of explanatory variables which is widely agreed upon in the literature: household income, marital status, number of children, gender, age, health, employment status, job satisfaction, education, and social life. Other variables such as handicap, religion, and discrimination are also included in the analysis as they are potentially relevant variables. The household income shall be elaborated upon and a description of the other independent variables can be found in A1 of the appendix. (Bandura & Conceição, 2008; Binder & Coad, 2014; ESS, n.d. c; Helliwell, 2002; OECD, 2013) Household income (income, incomeD1,...,incomeD10, incomeQ1,...,incomeQ5) Our main independent variable is the household’s total net income originating from all possible sources. Income is not represented as a cardinal quantitative variable but as a group of indicator variables in order to correctly incorporate the ordinal information. These indicator variables (incomeD1,…,incomeD10, incomeQ1,…,incomeQ5) indicate the income category (decile/quintile) in which the respondents’ household belongs to. These income categories are “based on deciles of the actual household income range in [Belgium]” (ESS, n.d. f, p. 2), which can be seen in table 1 of the appendix. (ESS, n.d. c; OECD, 2013). Note that household income, not individual income, is relevant for our analysis, as it is “household income that drives living standards and consumption possibilities” (OECD, 2013, p. 149). Rather than individual income, it is consumption (which is driven and proxied by household income) that influences subjective well-being. Furthermore, by using household income instead of individual income, there is less uncertainty if there were to be a possible endogeneity problem between individual income and subjective well-being. (ESS, n.d. c; OECD, 2013)
  • 10. 10 | P a g e First econometric model 𝑠𝑡𝑓𝑙𝑖𝑓𝑒 = 𝛽0 + 𝛽1 𝑖𝑛𝑐𝑜𝑚𝑒𝐷2 + 𝛽2 𝑖𝑛𝑐𝑜𝑚𝑒𝐷3 + 𝛽3 𝑖𝑛𝑐𝑜𝑚𝑒𝐷4 + 𝛽4 𝑖𝑛𝑐𝑜𝑚𝑒𝐷5 + 𝛽5 𝑖𝑛𝑐𝑜𝑚𝑒𝐷6 + 𝛽6 𝑖𝑛𝑐𝑜𝑚𝑒𝐷7 + 𝛽7 𝑖𝑛𝑐𝑜𝑚𝑒𝐷8 + 𝛽8 𝑖𝑛𝑐𝑜𝑚𝑒𝐷9 + 𝛽9 𝑖𝑛𝑐𝑜𝑚𝑒𝐷10 + 𝛽10 𝑚𝑎𝑟𝑟𝑖𝑒𝑑 + 𝛽11 𝑐ℎ𝑖𝑙𝑑𝑟𝑒𝑛 + 𝛽12 𝑚𝑎𝑙𝑒 + 𝛽13 𝑎𝑔𝑒 + 𝛽14 ℎ𝑒𝑎𝑙𝑡ℎ𝑦 + 𝛽15 ℎ𝑎𝑛𝑑𝑖𝑐𝑎𝑝 + 𝛽16 𝑤𝑜𝑟𝑘(𝑗𝑜𝑏𝑠𝑎𝑡) + 𝛽17 𝑒𝑑𝑢𝑦𝑟𝑠 + 𝛽18 𝑠𝑜𝑐𝑖𝑎𝑙 + 𝛽19 𝑖𝑛𝑚𝑑𝑖𝑠𝑐 + 𝛽20 𝑟𝑒𝑙𝑖𝑔𝑖𝑜𝑢𝑠 + 𝛽21 𝑑𝑖𝑠𝑐𝑟𝑖 + 𝑢 4.3 Data description and summary statistics The data description and summary statistics of the relevant variables can be found in table 2 and 3 of the appendix. While the data description gives an overview of the variables names and their labels, the summary statistics illustrate how the sample is composed of and inspect for data flaws, such as errors-in-variables. 5. The econometric model and inference procedures 5.1 The starting point The starting point of the multiple linear regression model is the following. This model was created in order to address the research questions concerning the relationship between subjective well- being and income; and the marginal effect of income on subjective well-being. The variables specified in section 4 are included in the model. Note that this is only a temporary model as it shall go through a number of adjustments in the following subsections for further improvement. The ordinary least squares (OLS) estimation procedure was applied. Regarding the estimation technique, it is important to note that despite life evaluation being an ordinal variable (ranked on a scale from 1 to 10), it shall be treated as if it is cardinal in OLS. According to conventional econometrics, an ordered choice model is more appropriate due to the ordinal dependent variable. However, this is not as problematic as it may seem. A paper by Ferrer-i-Carbonell and Frijters (2004) shows that “that the difference in results between using cardinal OLS versus the econometrically more appropriate ordered choice model is negligible” when explaining happiness (Binder & Coad, 2014, p. 8). (Griffiths et al., 2012) Design weights provided by ESS shall be applied as recommended. These weights “correct for [a potential sample] bias that is introduced by the sampling design” (ESS, 2014, p. 1).
  • 11. 11 | P a g e 5.2 Inference procedures Selection between jobsat or work Note that the variable jobsat between parentheses indicates that either work or jobsat can be included in the regression but not both as they are highly collinear. After all, a value for the variable jobsat is only present when the respondent has a job. Running a regression alternating the inclusion of work and jobsat points out that jobsat is highly significant and work is insignificant. This can be seen using income deciles and income quintiles in table 4 and 5 in the appendix. This implies that instead of being employed or not, it is job satisfaction which is an important driver for life satisfaction. Therefore, the variable jobsat (and not work) shall be included in the upcoming regressions. (Griffiths et al., 2012; OECD, 2013) Selection between income deciles or income quintiles Running a first regression using the income deciles, as is shown in table 5.1 of the appendix, indicates the vast majority of the income deciles variables to be insignificant (at a significance level of 10%) due to an abundant amount of categories. To solve this problem, income quintiles will be used instead. This is illustrated in table 5.2 of the appendix. In this second regression, only one variable (incomeQ2) of the income indicator variables remains insignificant. Testing for statistically significant variables Running the regression using income quintiles delivers output shown in table 5.2 of the appendix. The output suggests that next to incomeQ2, the variables discri, male, religious, age, healthy, eduyrs, inmdisc, and handicap are insignificant as the individual t-tests fail to reject the null hypothesis of a coefficient with value zero at a significance level of 10%. (Griffiths et al., 2012) In addition to these individual t-tests, a joint hypothesis test (F-test) was executed in order to verify whether at least one of these coefficients is nonzero. The F-test, which can be found in table 6 of the appendix, confirms that the nine variables are not only individually insignificant but also jointly insignificant. (Griffiths et al., 2012) Exclusion of insignificant variables Instead of simply excluding all nine insignificant variables from the model, it is vital to think whether some of these variables should still be included despite being insignificant. In light of this, it is important to evaluate the insignificant variables highly recommended by academic literature before omission. (Griffiths et al., 2012)
  • 12. 12 | P a g e The variable incomeQ2 shall be kept retained in the model as it is an important variable relevant for our research question, belonging to the group of indicator variables of the income quintiles. The variables discri, religious and handicap were initially included due to their potential relevance based on intuition. But as they have deemed to be insignificant and they are not highly recommended by academic literature, these three variables shall be omitted from the regression. The variable inmdisc shall also be omitted from the regression as there is another variable (social) which is significant and also represents social life. A regression excluding these four variables can be found in table 7 of the appendix. The remaining insignificant variables male, age, healthy, and eduyrs are highly endorsed by academic literature and thus verge more attention. Health The importance of health on subjective well-being has been proven in several studies. “Health and subjective well-being are [positively] significantly associated” with one another (Lamu & Olsen, 2016, p.2). For this reason, health will be retained in the regression. However, health will not be retained as the indicator variable healthy due to its insignificance but as the ordinally ranked variable rhealth. The paper by Helliwell (2002) also includes health as an ordinally ranked variable. The variable rhealth is statistically significant as can be seen in table 8 of the appendix. However, its nature of ordinality heeds caution during interpretation. (Griffiths et al., 2012; OECD, 2013) Age The relationship between age and life satisfaction is notorious for its U-shape relationship. This “U- bend of life” (2010) can partially be witnessed in the ESS 2010 data set for Belgium in figure 2 of the appendix. There seems to be a U-shape relationship between life satisfaction and age up until the age of 75, after which life satisfaction goes downhill. As the relationship is evidently non-linear, a polynomial term age2, age to the power of two, is added to the regression. By cause of the inclusion of age2, table 9 of the appendix shows age and age2 to now be significant at a significance level of 10%. (Griffiths et al., 2012; OECD, 2013; “The U-bend of life”, 2010) Gender The majority of studies dedicated to answering the question of whether “men are happier than women, found only minimal gender-related differences in subjective well-being”(Inglehart, 2002, p. 1). However, a paper by Inglehart (2002) shows that gender-related differences in subjective
  • 13. 13 | P a g e Second econometric model 𝑠𝑡𝑓𝑙𝑖𝑓𝑒 = 𝛽0 + 𝛽1 𝑖𝑛𝑐𝑜𝑚𝑒𝑄2 + 𝛽2 𝑖𝑛𝑐𝑜𝑚𝑒𝑄3 + 𝛽3 𝑖𝑛𝑐𝑜𝑚𝑒𝑄4 + 𝛽4 𝑖𝑛𝑐𝑜𝑚𝑒𝑄5 + 𝛽5 𝑚𝑎𝑟𝑟𝑖𝑒𝑑 + 𝛽6 𝑐ℎ𝑖𝑙𝑑𝑟𝑒𝑛 + 𝛽7 𝑎𝑔𝑒 + 𝛽8 𝑎𝑔𝑒² + 𝛽9 𝑟ℎ𝑒𝑎𝑙𝑡ℎ + 𝛽10 𝑗𝑜𝑏𝑠𝑎𝑡 + 𝛽11 𝑠𝑜𝑐𝑖𝑎𝑙 + 𝑢 well-being are present but they are hidden in an “interaction effect between age, gender and well- being” (Inglehart, 2002, p. 1). This implies that the effect of age on stflife may differ between males and females. Due to this finding, an interaction term of male and age, age_male, was constructed and included in the regression. Unfortunately, statistical tests of significance, shown in table 10 of the appendix, point out that male and age_male are individually and jointly insignificant. The results of this regression and sample seem to be in line with the majority of the studies and not with Inglehart (2002) as an insignificant relationship was found. As a consequence, the variables male and age_male were omitted. (Inglehart, 2002; OECD, 2013) Education According to the paper by Michalos (2007), finding whether education has a significant influence on subjective well-being or not depends on the definitions of the variables representing these two concepts. If education is defined as “the highest level of formal education attained” and subjective well-being is represented as a single-item measure such as life satisfaction, then “education has very little influence on happiness” (Michalos, 2007, p.2). As our variables eduyrs and stflife are indeed limited to these definitions, it is unsurprising why the relationship is found to be insignificant. In fact, even if eduyrs is transformed into a polynomial term, an indicator variable for highly educated people or an interaction term, it remains insignificant and shall thus be omitted from the regression (results not included). Statistical tests and scrutiny considering the significance of variables have led to the creation of the following econometric model of which its results can be found in table 11 of the appendix. A comparison of the first and the second econometric model in table 12 of the appendix shows that the model has improved considerably: R² and adjusted R² have increased while the Akaike and Bayesian information criteria have decreased.
  • 14. 14 | P a g e Testing the functional form A next step is detect whether the second model is misspecified or has overlooked some non- linearities. Preforming the Ramsey RESET test in table 13 of the appendix shows that there was initially a problem of functional form misspecification in the first econometric model. Fortunately, the corrections imposed on the regression during the statistical tests of significance have solved this problem as the second econometric model does not have a functional form misspecification. (Griffiths et al., 2012) Testing for multicollinearity To determine whether multicollinearity is present in the model, the variance inflation factor (VIF) was constructed for the second econometric model in table 14 of the appendix. With the mean VIF higher than 5, the model is characterized by high multicollinearity. However, this does not come as a surprise as the mean VIF has been inflated due to a high VIF of the variables age, age2 and to a smaller extent due to incomeQ3, incomeQ4, and incomeQ5. The high multicollinearity is less problematic as it may seem as it is only natural that they are collinear: age2 is the square of age and incomeQ3, incomeQ4 and incomeQ5 belong to the same group of indicator variables. Multicollinearity can be tolerated to some extent, however during interpretation, it is vital to remember that a high multicollinearity may stand in the way of measuring the precise individual effects. (Griffiths et al., 2012) Testing for heteroskedasticity As a final step, an informal approach, as well as a formal test, was applied to detect the presence of heteroskedasticity. First, the residuals were plotted against the fitted values and the residuals were plotted against each explanatory variable as can be seen in figure 3 of the appendix. Unfortunately, it is quite difficult to identify the presence of heteroskedasticity in these figures as there is no clear pattern of panning out. (Griffiths et al., 2012) Second, a White test was executed in table 15 of the appendix. Although it was unclear in the informal approach whether there was heteroskedasticity or not, the White test confirms that the model is indeed characterized by heteroskedasticity. (Griffiths et al., 2012) In order to alleviate the problem of heteroskedasticity, robust standard errors may be used in large samples and appropriate weights should be applied. As was mentioned earlier in subsection 5.1,
  • 15. 15 | P a g e design weights provided by the ESS were continuously implemented throughout all of the regressions and robust standard errors have already been automatically applied due to the design weights. (ESS, 2014; Griffiths et al., 2012) As all of the robustness checks have been covered, it is now appropriate to interpret the results of the model. 6. The results The final model estimated by ordinary least squares (OLS), using ESS design weights and robust standard errors is shown in table 11 of the appendix. This model was created in order to analyze the relationship between subjective well-being and income; and the marginal effect of income on subjective well-being. The goodness-of-fit measure R² implies that 14% of the variation in the dependent variable, life satisfaction (stflife), is explained by the included independent variables. The value of R² is rather low thus, in this regard the model requires improvement. The model, however, does include important explanatory variables as instructed by academic literature. (Griffiths et al., 2012; OECD, 2013) Ten out of the eleven independent variables (incomeQ3, incomeQ4, incomeQ5, married, children, age, age2, rhealth, jobsat and social) are individually statistically significant at a significance level of 10%. The variable incomeQ2, on the other hand, is insignificant at a significance level of 10%. IncomeQ2 is kept in the regression due to it is relevance to our research question concerning the relationship between subjective well-being and income. (Griffiths et al., 2012) 6.1 Relationship between income and subjective well-being The first and main research question concerns the relationship between subjective well-being and income in Belgium. The results from table 11 of the appendix confirm the general finding of a positive relationship between subjective well-being and income. The significance of the relationship, however, depends on the reference group and on the income quintile. (Stevenson & Wolfers, 2013) Income is represented as a group of indicator variables which indicate the income quintile the respondent belongs to. The income quintiles are shown in table 1 of the appendix. The omitted indicator variable, incomeQ1, is the reference group. The coefficients of the included income
  • 16. 16 | P a g e quintiles (incomeQ2, incomeQ3, incomeQ4 and incomeQ5) are interpreted with respect to the reference group, incomeQ1. (Griffiths et al., 2012) The interpretation of the sign and the significance of the income variables is relatively straightforward. Respondents belonging to the second income quintile have a higher life satisfaction (+0.1115) than respondents belonging to the first income quintile while holding other explanatory variables constant. This effect, however, is insignificant. A similar interpretation holds for the other income quintiles. Respondents belonging to the third income quintile (+0.6364), the fourth income quintile (+0.7023), and the fifth income quintile (+0.8627) have a higher life satisfaction than respondents belonging to the first income quintile while holding other explanatory variables constant. All three effects are significant. Note that the numbers between brackets are the magnitudes of the effects, which will be discussed next. It is of great importance to be cautious when interpreting the coefficients in terms of magnitude as the dependent variable, stflife, is an ordinal variable but is implemented in the model as if it were cardinal. (Griffiths et al., 2012) For example, the coefficient of 0.1115 belonging to incomeQ2 technically implies that moving from the first income quintile to the second with a notion of ceteris paribus, increases life satisfaction by 0.1115 in terms of the life satisfaction scale. However, as life satisfaction is ordinally ranked on a scale from 1 to 10, you should not make statements such as “a life satisfaction of 5 is twice as better than a life satisfaction of 10” or ‘”life satisfaction has increased by 0.1115 units” as these “units” do not make much sense. Strictly speaking, you can only make statements of whether life satisfaction has increased or decreased but not by how much. Statements such as the following, however, are allowed and useful “the increase in life satisfaction by being in the fifth income quintile is higher than being in the fourth quintile, as +0.8627 is bigger than +0.7023, with respect to the first income quintile”. Thus, the magnitude does give an idea of the size of the effect (especially in comparison to another effect) but there is no clear-cut interpretation in terms of units. (ESS, n.d. f; Griffiths et al., 2012)
  • 17. 17 | P a g e +0.122 1st income quintile +0.525 Significant 2nd income quintile +0.066 3rd income quintile +0.160 4th income quintile 5th income quintile 6.2 Marginal effect of income on subjective well-being The second research question concerns the marginal effect of income on subjective well-being. Previous results have shown that there is a positive relationship, but does the effect of income on subjective-wellbeing decrease as respondents become richer? Is the marginal effect decreasing? Different conclusions about the marginal effect are made depending on the method. This question is answered by assessing the effect of upward movements in the income categories on life satisfaction. In order to make such an assessment possible, different models were generated by applying the second econometric model while alternating the reference group concerning the income quintiles. An overview of these models can be found in table 16 of the appendix. The effect on life satisfaction by moving from the first income quintile to the second income quintile is positive but insignificant (+0.112). The effect on life satisfaction by moving from the second income quintile to the third income quintile is positive and highly significant (+0.525). The effect on life satisfaction by moving from the third income quintile to the fourth income quintile is positive but insignificant (+0.066). The effect on life satisfaction by moving from the fourth income quintile to the fifth income quintile is positive but insignificant (+0.160). Note that a ceteris paribus notion holds for all of the previous statements. A schematic illustrating this can be found below. Increasing Decreasing Increasing Remarkably, the only significant effect of an upward movement in the income categories is from the second to the third income quintile. Furthermore, the size of the coefficients, as is given in between brackets, seems to suggest that the marginal effect is not strictly decreasing. The marginal effect of movements up until the second income quintile seems to be increasing, after which the marginal effect decreases when moving to the third income quintile and proceeds to increase again. This peculiar conclusion may be due to the use of indicator variables. Another conclusion on the marginal effect is reached when simply plotting the income quintiles on the scale of life satisfaction (figure 4 in the appendix). The marginal effect is strictly decreasing as the slope of a higher income quintile is consistently flatter than the previous income quintile.
  • 18. 18 | P a g e 6.3 The satiation point The third research question concerns the existence of a satiation point. As previously pointed out, figure 4 suggests a positive, but decreasing marginal effect of income on subjective well-being. But does this imply that there exists a satiation point, a point after which the relationship between income and subjective well-being disappears? The graph in figure 5 suggests that no such satiation point exists. In order to assess the possible existence of a satiation point, the graph in figure 5 of the appendix was created. This graph plots life satisfaction on the log of income by using a linear fit and a lowess fit. Notice that the log of income was taken in order to allow a flattening out of the relationship between income and subjective well-being. The interpretation of the graph is as follows. The existence of a possible satiation point is verified when “the non-parametric fit flattens out once basic needs were met” (Stevenson & Wolfers, 2013, p. 2). In figure 5, there is no flattening out in the lowess fit. This implies that there is presumably no satiation point given the income categories. While plotting such a graph is a valid method to confirm the possible existence of a satiation point, especially given the limitations of the data set, it remains to be an informal method. A possible improvement would be to set up a formal econometric model and use hypothesis tests to verify whether a satiation point exists. However, this is only possible when data is available on the quantitative income of the respondents, which is unfortunately not the case for the ESS dataset. (ESS, n.d. c; Stevenson & Wolfers, 2013) 7. Conclusion In this paper, we set out to explore the relationship between subjective well-being and income for Belgian inhabitants. The results of the cross-sectional model confirm this relationship, just as the marginal effect of income on subjective well-being, to be positive. Conclusions on how the marginal effect unfolds as people become richer depend on the applied method. While the model using indicator variables of income, suggests that the marginal effect increases, decreases and then proceeds to increase; a graph plotting the income quintiles against life satisfaction suggests this effect to be strictly decreasing. In turn, a strictly decreasing marginal effect suggests the existence of a possible satiation point, after which the relationship between subjective well-being and income disappears. No concrete evidence for such a satiation point was found. The positive relationship between subjective well-being and income persists through the different income categories. Ultimately, the paper boils down to one question: “Can money buy happiness for Belgians? The results suggest yes, overall richer people tend to be happier.
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  • 21. 21 | P a g e Lamu, A.N., & Olsen, J. A. (2016). The relative importance of health, income and social relations for subjective well-being: An integrative analysis. Social Science & Medicine, 152, 176-185. doi: 10.1016/j.socscimed.2016.01.046 Michalos, A.C. (2007). Education, happiness and wellbeing. OECD, 2nd World Forum, Istanbul 2007. Retrieved on 24/04/2016 from http://www.oecd.org/site/worldforum06/38303200.pdf OECD. (2013). OECD Guidelines on Measuring Subjective Well-being. OECD Publishing. doi: 10.1787/9789264191655-en Stevenson, B.,& Wolfers, J. (2013). Subjective well-being and income: Is there any evidence of satiation. American Economic Review, 103(5), 598-604. doi:http://dx.doi.org/10.1257/aer.103.3.598 The U-bend of life. (2010, December 16). The Economist. Retrieved on 24/04/2016 from www.economist.com Van Praag, B.M.S., Frijters, P., & Ferrer-i-Carbonell, A. (2003). The anatomy of subjective well-being. Journal of Economic Behaviour and Organisation, 51, 29-49.
  • 22. 22 | P a g e Appendix A.1 Description of the independent variables Marital status (married) This variable indicates whether the respondent is married (or in a legally registered civil union) or not. (ESS, n.d. c) Number of children (children) This variable indicates the number of children living in the household. (ESS, n.d. c) Gender (male) This variable indicates the gender of the respondent. (ESS, n.d. c) Age (age) This variable indicates the age of the respondent. (ESS, n.d. c) Health (healthy, rhealth) The variable healthy indicates whether the subjective general health of the respondent is considered to be good or bad. The variable rhealth indicates the health ranking (on a scale from 1 to 5) in which the respondent places himself or herself. (ESS, n.d. c) Handicap (handicap) This variable indicates whether the respondent is “hampered by any sort of handicap (longstanding illness, or disability, infirmity or mental health problem) in their daily activities” or not (ESS, n.d. c, p. 42). Employment status (work) This variable indicates whether the respondent is in paid work (employed) or not. (ESS, n.d. c)
  • 23. 23 | P a g e Job satisfaction (jobsat) This variable indicates whether the employed respondents are satisfied with their job or not. (ESS, n.d. c) Education (eduyrs) This variable indicates the number of “years of full-time education completed” (ESS, n.d. c, p. 95). Social life (social, inmdisc) The variables social and inmdisc are associated with the social life of the respondent. (ESS, n.d. c) The variable social indicates “how often the respondent meets up with friends, relatives or colleagues” (ESS, n.d. c, p. 41). The respondent is considered to be relatively more social when they have social meetings ranging from several times a month to several times a week. Alternatively, the respondent is considered to be relative less social when they have social meetings ranging from (almost) never to once a month. (ESS, n.d. c) The variable inmdisc indicates whether the respondent has a confidant, “anyone to discuss intimate and personal matters with” (ESS, n.d. c, p. 41), or not. Religion (religious) This variable indicates whether the respondent “belongs to a particular religion or denomination” or not (ESS, n.d. c, p. 43). Discrimination (discri) This variable indicates whether the respondent describes themselves as a “member of a group that is discriminated in [Belgium]” or not (ESS, n.d. c, p. 60).
  • 24. 24 | P a g e A.2 Figures Figure 1: The modified –Easterlin hypothesis Source: Stevenson & Wolfers, 2013 Figure 2: U-shape relationship between age and life satisfaction This graph is constructed using the lowess technique (locally weighted scatterplot smoothing).
  • 25. 25 | P a g e Figure 3: Detecting heteroskedasticity -10 -5 05 Residuals 5 6 7 8 9 Fitted values -10 -5 05 Residuals 0 .2 .4 .6 .8 1 incomeQ2 -10 -5 05 Residuals 0 .2 .4 .6 .8 1 incomeQ3 -10 -5 05 Residuals 0 .2 .4 .6 .8 1 incomeQ5 -10 -5 05 Residuals 0 .2 .4 .6 .8 1 incomeQ6 -10 -5 05 Residuals 0 .2 .4 .6 .8 1 Marriage -10 -5 05 Residuals 0 2 4 6 8 Children -10 -5 05 Residuals 20 40 60 80 100 Age -10 -5 05 Residuals 0 2000 4000 6000 8000 Age² -10 -5 05 Residuals 1 2 3 4 5 rhealth -10 -5 05 Residuals 0 .2 .4 .6 .8 1 Job satisfaction -10 -5 05 Residuals 0 .2 .4 .6 .8 1 Social
  • 26. 26 | P a g e Figure 4: Plotting income on life satisfaction using the lowess technique Figure 5: Satiation point - Plotting log(income) on life satisfaction 6.5 7 7.5 8 1 2 3 4 5 Income Quintiles Lifesatisfaction 6 6.5 7 7.5 8 0 .5 1 1.5 2 2.5 Log(income) Lowess Linear fit
  • 27. 27 | P a g e A.3 Tables Table 1: Income deciles and quintiles for Belgium Income deciles 1 < €11 040 2 € 11 040 – € 14 160 3 € 14 160 – € 17 640 4 € 17 640 – € 21 360 5 € 21 360 – € 25 560 6 € 25 560 – € 30 600 7 € 30 600 – € 37 440 8 € 37 440 – € 44 880 9 € 44 880 – € 56 760 10 > € 56 760 Source: ESS, n.d. f, p.4 Table 2: Data description Dependent variables Variable name Variable label stflife How satisfied with life as a whole – Scale of 0 to 10 happy How happy are you – Scale of 0 to 10 Independent variables Variable name Variable label income Household's total net income, all sources (deciles) incomeQ1,…,incomeQ5 Household's total net income - 1st quintile,…,5th quintile incomeD1,…,incomeD10 Household's total net income - 1st decile,…10th decile married 1 Married / 0 Not married children Number of children male 1 Male / 0 Female age Age of respondent healthy 1 Healthy / 0 Not healthy rhealth Subjective general health – Scale of 1 to 5 handicap 1 Handicap/ 0 No handicap work 1 Employed / 0 Unemployed jobsat 1 Job satisfaction/ 0 No job satisfaction eduyrs Years of full-time education completed social 1 Social / 0 Not social inmdisc Confidant / 0 No confidant religious 1 Religious / 0 Not religious discri 1 Discriminated / 0 Not discriminated Income quintiles 1 < € 14 160 2 € 14 160 – € 21 360 3 € 21 360 – € 30 600 4 € 30 600 – € 44 880 5 > € 44 880
  • 28. 28 | P a g e Table 3: Summary statistics Dependent variables Variable Obs Mean Std. Dev. Min Max stflife 1424 7.497893 1.648269 0 10 happy 1424 7.835674 1.407127 0 10 Independent variables Variable Obs Mean Std. Dev. Min Max income 1424 5.95014 2.424613 1 10 incomeQ1 1424 .0919944 .2891196 0 1 incomeQ2 1424 .2191011 .4137826 0 1 incomeQ3 1424 .2380618 .4260468 0 1 incomeQ4 1424 .2745787 4464585 0 1 incomeQ5 1424 .176264 .3811785 0 1 incomeD1 1424 .0245787 .1548915 0 1 incomeD2 1424 .0674157 .2508287 0 1 incomeD3 1424 .0969101 .2959393 0 1 incomeD4 1424 .122191 .3276213 0 1 incomeD5 1424 .1116573 .315055 0 1 incomeD6 1424 .1264045 .3324214 0 1 incomeD7 1424 .1615169 .3681363 0 1 incomeD8 1424 .1130618 .3167796 0 1 incomeD9 1424 .1032303 .3043664 0 1 incomeD10 1424 .0730337 2602832 0 1 married 1424 .5351124 .4989408 0 1 children 1424 .7549157 1.122023 0 7 male 1424 .4803371 .4997887 0 1 age 1424 47.7802 7.96378 15 94 healthy 1424 .9578652 .2009673 0 1 rhealth 1424 2.060393 .7947501 1 5 handicap 1424 .2345506 .4238664 0 1 work 1424 .5351124 .4989408 0 1 jobsat 730 .9164384 .276919 0 1 eduyrs 1424 12.69874 3.628744 1 27 social 1424 .8953652 .3061898 0 1 inmdisc 1424 .8876404 .3159192 0 1 religious 1424 .4234551 .4942797 0 1 discri 1424 .0491573 .2162723 0 1
  • 29. 29 | P a g e Note that only the relevant aspects are highlighted in the following tables, implying that there are more (in)significant variables than the ones highlighted. Table 4: Regression of the first econometric model using work Table 4.1 Income deciles Linear regression Number of obs = 1424 F( 21, 1402) = 7.97 Prob > F = 0.0000 R-squared = 0.1371 Root MSE = 1.5426 ------------------------------------------------------------------------------ | Robust stflife | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- incomeD2 | .0383124 .3472944 0.11 0.912 -.6429602 .719585 incomeD3 | .3921308 .3245277 1.21 0.227 -.2444814 1.028743 incomeD4 | .3420934 .3145772 1.09 0.277 -.2749993 .9591862 incomeD5 | .6438971 .3136798 2.05 0.040 .0285648 1.259229 incomeD6 | .7685312 .3027232 2.54 0.011 .174692 1.36237 incomeD7 | .7357802 .3079323 2.39 0.017 .1317225 1.339838 incomeD8 | 1.066969 .3074412 3.47 0.001 .4638749 1.670064 incomeD9 | 1.045569 .3114351 3.36 0.001 .43464 1.656498 incomeD10 | .9410447 .3251922 2.89 0.004 .3031289 1.57896 married | .3281534 .1032586 3.18 0.002 .1255955 .5307114 children | -.1741508 .0462813 -3.76 0.000 -.2649388 -.0833628 male | .1145105 .0836686 1.37 0.171 -.0496186 .2786397 age | .000728 .0029193 0.25 0.803 -.0049986 .0064546 healthy | .9547749 .2972692 3.21 0.001 .3716346 1.537915 handicap | -.4638559 .1150009 -4.03 0.000 -.6894483 -.2382635 work | .0663897 .0994239 0.67 0.504 -.1286459 .2614253 eduyrs | -.0254463 .0133356 -1.91 0.057 -.0516061 .0007135 social | .6279197 .1662838 3.78 0.000 .3017279 .9541115 inmdisc | .4020903 .1533945 2.62 0.009 .1011829 .7029977 religious | .1288917 .0855055 1.51 0.132 -.0388407 .2966242 discri | -.5484973 .2340076 -2.34 0.019 -1.00754 -.0894546 _cons | 5.23153 .5026337 10.41 0.000 4.245534 6.217525 ------------------------------------------------------------------------------ Table 4.2 Income quintiles Linear regression Number of obs = 1424 F( 16, 1407) = 9.58 Prob > F = 0.0000 R-squared = 0.1338 Root MSE = 1.5427 ------------------------------------------------------------------------------ | Robust stflife | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- incomeQ2 | .3327523 .1993628 1.67 0.095 -.058328 .7238326 incomeQ3 | .6767538 .1915895 3.53 0.000 .300922 1.052586 incomeQ4 | .8362169 .1965822 4.25 0.000 .4505911 1.221843 incomeQ5 | .9651059 .2051636 4.70 0.000 .5626464 1.367565 married | .3293819 .1019277 3.23 0.001 .1294352 .5293285 children | -.1779147 .0458519 -3.88 0.000 -.2678602 -.0879692 male | .1105063 .0838854 1.32 0.188 -.0540476 .2750603 age | .0006676 .0028863 0.23 0.817 -.0049942 .0063294 healthy | .9560698 .2977074 3.21 0.001 .3720718 1.540068 handicap | -.4746559 .1151355 -4.12 0.000 -.7005115 -.2488003 work | .0756469 .0986565 0.77 0.443 -.1178828 .2691766 eduyrs | -.0252168 .0132784 -1.90 0.058 -.0512644 .0008309 social | .64777 .1661267 3.90 0.000 .3218874 .9736526 inmdisc | .41127 .1536191 2.68 0.008 .109923 .7126171 religious | .1215717 .08547 1.42 0.155 -.0460905 .289234 discri | -.5426634 .2322401 -2.34 0.020 -.9982374 -.0870893 _cons | 5.242665 .4390709 11.94 0.000 4.38136 6.103969 ------------------------------------------------------------------------------ Work is statistically insignificant on a significance level of 10%. Legend  Insignificant variables At a significance level of 10%
  • 30. 30 | P a g e Table 5: Regression of the first econometric model using jobsat Table 5.1 Income deciles Linear regression Number of obs = 730 F( 21, 708) = 4.08 Prob > F = 0.0000 R-squared = 0.1240 Root MSE = 1.3641 ------------------------------------------------------------------------------ | Robust stflife | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- incomeD2 | .086196 .7281809 0.12 0.906 -1.343456 1.515848 incomeD3 | .4202934 .7126108 0.59 0.556 -.9787898 1.819377 incomeD4 | .2436483 .6658778 0.37 0.715 -1.063683 1.55098 incomeD5 | .7024271 .6564792 1.07 0.285 -.5864519 1.991306 incomeD6 | .8334468 .6565641 1.27 0.205 -.4555988 2.122492 incomeD7 | .7759848 .6516952 1.19 0.234 -.5035017 2.055471 incomeD8 | 1.087773 .6469581 1.68 0.093 -.1824129 2.357959 incomeD9 | 1.099949 .6521661 1.69 0.092 -.1804623 2.38036 incomeD10 | 1.068144 .6553251 1.63 0.104 -.2184689 2.354757 married | .268877 .1234711 2.18 0.030 .0264637 .5112902 children | -.1370221 .0515801 -2.66 0.008 -.2382903 -.0357539 male | -.0175619 .1016473 -0.17 0.863 -.2171281 .1820043 age | -.0025749 .0055666 -0.46 0.644 -.013504 .0083541 healthy | -.5702315 .9726968 -0.59 0.558 -2.479947 1.339484 handicap | -.2750421 .1725407 -1.59 0.111 -.6137948 .0637106 jobsat | .9560621 .2190361 4.36 0.000 .5260242 1.3861 eduyrs | -.0152691 .0167077 -0.91 0.361 -.0480718 .0175335 social | .5089216 .1935471 2.63 0.009 .1289266 .8889165 inmdisc | .334244 .2216629 1.51 0.132 -.1009514 .7694393 religious | -.0162215 .104886 -0.15 0.877 -.2221463 .1897033 discri | -.0798791 .2634945 -0.30 0.762 -.5972032 .437445 _cons | 6.126796 1.227709 4.99 0.000 3.716409 8.537182 ------------------------------------------------------------------------------ Table 5.2 Income quintiles Linear regression Number of obs = 730 F( 16, 713) = 4.89 Prob > F = 0.0000 R-squared = 0.1190 Root MSE = 1.3632 ------------------------------------------------------------------------------ | Robust stflife | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- incomeQ2 | .2248806 .3542428 0.63 0.526 -.470603 .9203642 incomeQ3 | .7006381 .3351216 2.09 0.037 .0426949 1.358581 incomeQ4 | .8392231 .3303806 2.54 0.011 .190588 1.487858 incomeQ5 | 1.008037 .3356162 3.00 0.003 .3491232 1.666951 married | .2868382 .1235237 2.32 0.021 .0443245 .529352 children | -.1412504 .0513935 -2.75 0.006 -.242151 -.0403498 male | -.020102 .1024242 -0.20 0.844 -.2211912 .1809872 age | -.0031764 .0056075 -0.57 0.571 -.0141856 .0078328 healthy | -.618309 .9574875 -0.65 0.519 -2.498141 1.261523 handicap | -.2872884 .1742246 -1.65 0.100 -.629343 .0547661 jobsat | .9695932 .2155557 4.50 0.000 .5463933 1.392793 eduyrs | -.0142122 .0166929 -0.85 0.395 -.0469854 .0185609 social | .5391867 .1945524 2.77 0.006 .1572227 .9211508 inmdisc | .3420861 .2230536 1.53 0.126 -.0958342 .7800065 religious | -.0249486 .1042907 -0.24 0.811 -.2297021 .179805 discri | -.0524371 .2581833 -0.20 0.839 -.5593275 .4544533 _cons | 6.214764 1.066258 5.83 0.000 4.121383 8.308146 ------------------------------------------------------------------------------ Jobsat is statistically significant on a significance level of 1%. Legend  Insignificant variables  Significant variables At a significance level of 10%
  • 31. 31 | P a g e Table 6: Joint hypothesis test An F-test, which includes all nine individually statistically insignificant variables, fails to reject the null hypothesis that all of the coefficients are zero at a significance level of 10%. This implies that all nine variables are jointly statistically insignificant and individually statistically insignificant. (Griffiths et al., 2012) ( 1) discri = 0 ( 2) male = 0 ( 3) religious = 0 ( 4) age = 0 ( 5) healthy = 0 ( 6) eduyrs = 0 ( 7) inmdisc = 0 ( 8) handicap = 0 ( 9) incomeQ2 = 0 F( 9, 713) = 0.76 Prob > F = 0.6527 Table 7: Regression excluding insignificant variables discri, religious, handicap, and inmdisc (sum of wgt is 7.3000e+02) Linear regression Number of obs = 730 F( 12, 717) = 6.17 Prob > F = 0.0000 R-squared = 0.1105 Root MSE = 1.366 ------------------------------------------------------------------------------ | Robust stflife | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- incomeQ2 | .244316 .3562422 0.69 0.493 -.4550866 .9437185 incomeQ3 | .6968752 .3390904 2.06 0.040 .0311465 1.362604 incomeQ4 | .8426035 .3348062 2.52 0.012 .1852858 1.499921 incomeQ5 | 1.028983 .3418543 3.01 0.003 .3578282 1.700138 married | .3054176 .1223734 2.50 0.013 .0651646 .5456705 children | -.1436692 .0518477 -2.77 0.006 -.2454606 -.0418777 male | -.0330698 .1019519 -0.32 0.746 -.2332296 .1670901 age | -.0046121 .0056715 -0.81 0.416 -.0157469 .0065226 healthy | -.3844807 .9263368 -0.42 0.678 -2.203137 1.434176 jobsat | 1.017689 .2206994 4.61 0.000 .5843946 1.450983 eduyrs | -.0118488 .0165444 -0.72 0.474 -.0443301 .0206325 social | .5832671 .1926915 3.03 0.003 .2049601 .9615741 _cons | 6.180312 1.033384 5.98 0.000 4.151492 8.209132 ------------------------------------------------------------------------------
  • 32. 32 | P a g e Table 8: Regression retaining health as rhealth instead of healthy (sum of wgt is 7.3000e+02) Linear regression Number of obs = 730 F( 12, 717) = 7.32 Prob > F = 0.0000 R-squared = 0.1393 Root MSE = 1.3436 ------------------------------------------------------------------------------ | Robust stflife | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- incomeQ2 | .1994126 .3518145 0.57 0.571 -.4912972 .8901223 incomeQ3 | .6942943 .3332789 2.08 0.038 .0399751 1.348614 incomeQ4 | .7819775 .3278825 2.38 0.017 .1382531 1.425702 incomeQ5 | .9601196 .3333698 2.88 0.004 .3056219 1.614617 married | .3040201 .1199518 2.53 0.011 .0685213 .5395189 children | -.1349578 .0507661 -2.66 0.008 -.2346257 -.0352898 male | -.0394691 .1005005 -0.39 0.695 -.2367796 .1578413 age | .0003164 .0055498 0.06 0.955 -.0105794 .0112122 rhealth | -.3934461 .0900234 -4.37 0.000 -.570187 -.2167051 jobsat | .8940039 .2326333 3.84 0.000 .4372801 1.350728 eduyrs | -.018303 .0164183 -1.11 0.265 -.0505367 .0139307 social | .5230677 .1876254 2.79 0.005 .1547069 .8914285 _cons | 6.61704 .5312949 12.45 0.000 5.573961 7.66012 ------------------------------------------------------------------------------ Table 9: Regression including the polynomial term age2 (sum of wgt is 7.3000e+02) Linear regression Number of obs = 730 F( 13, 716) = 6.97 Prob > F = 0.0000 R-squared = 0.1459 Root MSE = 1.3394 ------------------------------------------------------------------------------ | Robust stflife | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- incomeQ2 | .1320555 .3541913 0.37 0.709 -.5633221 .8274331 incomeQ3 | .6556891 .3348226 1.96 0.051 -.0016624 1.31304 incomeQ4 | .7385725 .3290176 2.24 0.025 .0926179 1.384527 incomeQ5 | .9160769 .3352024 2.73 0.006 .2579799 1.574174 married | .303908 .119105 2.55 0.011 .0700711 .5377449 children | -.0905175 .0542329 -1.67 0.096 -.196992 .015957 male | -.0386483 .1004088 -0.38 0.700 -.2357792 .1584826 age | -.0869104 .0399506 -2.18 0.030 -.1653447 -.0084762 age2 | .0010423 .0004742 2.20 0.028 .0001112 .0019733 rhealth | -.3830084 .0910184 -4.21 0.000 -.5617033 -.2043135 jobsat | .8660684 .2313582 3.74 0.000 .4118468 1.32029 eduyrs | -.0153524 .0164932 -0.93 0.352 -.0477333 .0170284 social | .5272051 .1870814 2.82 0.005 .1599115 .8944987 _cons | 8.279273 .8889059 9.31 0.000 6.534099 10.02445 ------------------------------------------------------------------------------
  • 33. 33 | P a g e Table 10: Tests of significance of the interaction term age_male Both the individual t-tests and the joint F-test fail to reject their corresponding null hypothesis, implying that the variables age and age_male are statistically insignificant on the individual level and on the collective level. (Griffiths et al., 2012) Table 10.1 t-tests ( 1) male = 0 F( 1, 715) = 1.04 Prob > F = 0.3084 ( 1) age_male = 0 F( 1, 715) = 0.93 Prob > F = 0.3361 Table 10.2 F-test ( 1) male = 0 ( 2) age_male = 0 F( 2, 715) = 0.52 Prob > F = 0.5920 Table 11: Second (and final) econometric model (sum of wgt is 7.3000e+02) Linear regression Number of obs = 730 F( 11, 718) = 8.05 Prob > F = 0.0000 R-squared = 0.1445 Root MSE = 1.3386 ------------------------------------------------------------------------------ | Robust stflife | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- incomeQ2 | .1115113 .3531017 0.32 0.752 -.5817239 .8047464 incomeQ3 | .6364453 .3349621 1.90 0.058 -.0211768 1.294067 incomeQ4 | .7023397 .3308095 2.12 0.034 .0528702 1.351809 incomeQ5 | .8626895 .3319481 2.60 0.010 .2109846 1.514394 married | .3114766 .1191606 2.61 0.009 .0775318 .5454215 children | -.0897844 .0544247 -1.65 0.099 -.196635 .0170663 age | -.0894775 .0400256 -2.24 0.026 -.1680587 -.0108963 age2 | .0010809 .0004739 2.28 0.023 .0001506 .0020112 rhealth | -.375493 .0898125 -4.18 0.000 -.5518195 -.1991665 jobsat | .8687183 .2320963 3.74 0.000 .4130497 1.324387 social | .5251169 .1878954 2.79 0.005 .1562269 .8940069 _cons | 8.098052 .8720042 9.29 0.000 6.386069 9.810035 ------------------------------------------------------------------------------
  • 34. 34 | P a g e Table 12: Comparison of the first and the second econometric model First Econometric Model Second Econometric Model R² .1240 .1445 Adjusted R² .0980 .1314 AIC 2 546.6563 2 509.3758 BIC 2 647.7033 2 564.4923 Table 13: Testing the functional form – Ramsey RESET test Performing the Ramsey RESET test allows the detection of a possible functional form misspecification. The null hypothesis of non-misspecification is rejected using the first econometric model: the first econometric model is misspecified. Fortunately, the corrections imposed during the statistical tests of significance have seemed to solve this problem as we fail to reject the null hypothesis for the second econometric model. The second econometric model does not have a problem of functional form misspecification. (Griffiths et al., 2012) Table 13.1 Ramsey RESET test of the first econometric model Ramsey RESET test using powers of the fitted values of stflife Ho: model has no omitted variables F(3, 705) = 11.96 Prob > F = 0.0000 Table 13.2 Ramsey RESET test of the second econometric model Ramsey RESET test using powers of the fitted values of stflife Ho: model has no omitted variables F(3, 715) = 1.81 Prob > F = 0.1445 Table 14: Testing for multicollinearity A variance inflation factor (VIF) higher than 5 implies that multicollinearity is high. (Griffiths et al., 2012) Variable | VIF 1/VIF -------------+-------------------- age | 65.53 0.015 age2 | 64.92 0.015 incomeQ4 | 6.89 0.145 incomeQ5 | 6.09 0.164 incomeQ3 | 5.28 0.189 incomeQ2 | 3.88 0.257 children | 1.44 0.695 married | 1.41 0.707 rhealth | 1.08 0.922 social | 1.04 0.963 jobsat | 1.03 0.968 -------------+-------------------- Mean VIF | 14.42
  • 35. 35 | P a g e Table 15: Testing for heteroskedasticity The White test has detected the presence of heteroskedasticity: the null hypothesis of constant variance (homoscedasticity) was rejected at a significance level of 5%. (Griffiths et al., 2012) White's general test statistic : 91.790 Chi-sq(63) P-value = .0104 Note: The Breusch-Pagan test was not executed as it is inappropriate in combination with the design weights. Table 16: Second econometric model with alternating reference group The name of the model indicates the reference group (=the omitted indicator variable), the coefficients of the income quintiles are interpreted with respect to the reference group. (Griffiths et al., 2012) -------------------------------------------------------------------------- Variable | IncomeQ1 IncomeQ2 IncomeQ3 IncomeQ4 -------------+------------------------------------------------------------ incomeQ1 | -0.112 -0.636* -0.702** incomeQ2 | 0.112 -0.525*** -0.591*** incomeQ3 | 0.636* 0.525*** -0.066 incomeQ4 | 0.702** 0.591*** 0.066 incomeQ5 | 0.863*** 0.751*** 0.226 0.160 married | 0.311*** 0.311*** 0.311*** 0.311*** children | -0.090* -0.090* -0.090* -0.090* age | -0.089** -0.089** -0.089** -0.089** age2 | 0.001** 0.001** 0.001** 0.001** rhealth | -0.375*** -0.375*** -0.375*** -0.375*** jobsat | 0.869*** 0.869*** 0.869*** 0.869*** social | 0.525*** 0.525*** 0.525*** 0.525*** _cons | 8.098*** 8.210*** 8.734*** 8.800*** -------------------------------------------------------------------------- legend: * p<.1; ** p<.05; *** p<.01