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

-50

5

Re

sid

ua

ls

5 6 7 8 9Fitted values

-10

-50

5

Resid

ua

ls

0 .2 .4 .6 .8 1incomeQ2

-10

-50

5

Resid

ua

ls

0 .2 .4 .6 .8 1incomeQ3

-10

-50

5

Resid

ua

ls

0 .2 .4 .6 .8 1incomeQ5

-10

-50

5

Resid

ua

ls

0 .2 .4 .6 .8 1incomeQ6

-10

-50

5

Resid

ua

ls

0 .2 .4 .6 .8 1Marriage

-10

-50

5

Resid

ua

ls

0 2 4 6 8Children

-10

-50

5

Resid

ua

ls

20 40 60 80 100Age

-10

-50

5

Resid

ua

ls

0 2000 4000 6000 8000Age²

-10

-50

5

Resid

ua

ls

1 2 3 4 5rhealth

-10

-50

5

Resid

ua

ls

0 .2 .4 .6 .8 1Job satisfaction

-10

-50

5

Resid

ua

ls

0 .2 .4 .6 .8 1Social

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

77.5

8

Life

sa

tisfa

ctio

n

1 2 3 4 5Income Quintiles

Life

sa

tisfa

ction

66.5

77.5

8

0 .5 1 1.5 2 2.5Log(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