This document summarizes a study examining the relationship between income and subjective well-being in Belgium using data from the 2010 European Social Survey. It describes the dependent variable of life satisfaction, key independent variables like household income and employment, and the econometric models used to analyze the data. Regression analysis found a significant positive relationship between income and life satisfaction up to the 4th income quintile, but not at higher income levels, providing partial evidence that money can buy happiness in Belgium up to a point.

1. Can money buy “happiness”
for Belgians?
Graduate Seminar in Economics
Emily Van de Walle

2. Overview
1. Introduction & Literature Review
2.Data
3.List of Relevant Variables
4.The Econometric Model & Inference Procedures
5.The Results
6.Conclusion

3. Introduction
& Literature Review
The starting point: Can happiness be bought?
Research Questions
1

4. Can happiness be bought?

6. Belgium
2010

7. Can money buy “happiness”?
3 aspects
(1) Relationship between income & subjective well-being
(2) Marginal effect of income on subjective well-being
(3) The Satiation Point

8. (1) Relationship between income & subjective well-being
Can money buy “happiness”?
Positive relationship across countries and over time
HOWEVER....

9. (2) The marginal effect of income on subjective well-being
(3) The satiation point
Can money buy “happiness”?
Level of GDP per capita
Happiness Satiation point
“The modified version
of Easterlin’s
hypothesis”
(Stevenson & Wolfers, 2013)
Source: Stevenson & Wolfers, 2013

10. Understanding subjective well-being
 2 different aspects
→ (1) Emotional well-being
→ (2) Life evaluation
→ Robust positive relationship for life evaluation!
(Kahneman & Deaton)

11. Data
Exploring the European Social Survey
2

12.  European Social Survey (ESS)
 5th round (2010) – Belgium
European Social Survey
Source: http://www.europeansocialsurvey.org/

13. List of Relevant
Variables
An overview of the dependent &
independent variables
3

14. Dependent variable: Subjective well-being
Definition
“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)
Affect
Life evaluation
Eudaimonia

15. Dependent variable: Subjective well-being
Affect Eudaimonia
Life
Evaluation
Definition – Life evaluation (life satisfaction)
“A reflective assessment of a person’s life or some aspect of it”
(OECD, 2013, p. 12)

16. Subjective well-being: Life evaluation
Life satisfaction/Life evaluation (stflife)
“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)?
Happiness (happy)
“Taking all things together, how happy would you say you are ”
on a scale of 0 to 10 (ESS, n.d. c, p. 40)?
→ Primary measure
→ Alternative measure

17. Independent variables
Marital
status
Number of
children
Gender
Age
Health
Employment
status
Social life
Education Discrimin
-ation
Handicap Religion
Job
satisfaction
Household
income

18. Main independent variable: Household income
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
 = Household’s total net income originating
from all possible sources
 Cardinal variable
→ Indicator variables (ordinal information)
 incomeD1,...,incomeD10,incomeQ1,...,incomeQ5
→ Income deciles, income quintiles
 “Based on deciles of the actual household
income range in Belgium” (ESS,n.d.f.,pg.2)
ESS,n.d.f.,p.4

19. The Econometric Model
& Inference Procedures
The Methodology
4

20. 4.1 The starting point
𝒔𝒕𝒇𝒍𝒊𝒇𝒆 = 𝜷 𝟎 + 𝜷 𝟏 𝒊𝒏𝒄𝒐𝒎𝒆𝑫𝟐 + 𝜷 𝟐 𝒊𝒏𝒄𝒐𝒎𝒆𝑫𝟑 + 𝜷 𝟑 𝒊𝒏𝒄𝒐𝒎𝒆𝑫𝟒
+ 𝜷 𝟒 𝒊𝒏𝒄𝒐𝒎𝒆𝑫𝟓 + 𝜷 𝟓 𝒊𝒏𝒄𝒐𝒎𝒆𝑫𝟔 + 𝜷 𝟔 𝒊𝒏𝒄𝒐𝒎𝒆𝑫𝟕 + 𝜷 𝟕 𝒊𝒏𝒄𝒐𝒎𝒆𝑫𝟖
+ 𝜷 𝟖 𝒊𝒏𝒄𝒐𝒎𝒆𝑫𝟗 + 𝜷 𝟗 𝒊𝒏𝒄𝒐𝒎𝒆𝑫𝟏𝟎 + 𝜷 𝟏𝟎 𝒎𝒂𝒓𝒓𝒊𝒆𝒅 + 𝜷 𝟏𝟏 𝒄𝒉𝒊𝒍𝒅𝒓𝒆𝒏
+ 𝜷 𝟏𝟐 𝒎𝒂𝒍𝒆 + 𝜷 𝟏𝟑 𝒂𝒈𝒆 + 𝜷 𝟏𝟒 𝒉𝒆𝒂𝒍𝒕𝒉𝒚 + 𝜷 𝟏𝟓 𝒉𝒂𝒏𝒅𝒊𝒄𝒂𝒑
+ 𝜷 𝟏𝟔 𝒘𝒐𝒓𝒌(𝒋𝒐𝒃𝒔𝒂𝒕) + 𝜷 𝟏𝟕 𝒆𝒅𝒖𝒚𝒓𝒔 + 𝜷 𝟏𝟖 𝒔𝒐𝒄𝒊𝒂𝒍 + 𝜷 𝟏𝟗 𝒊𝒏𝒎𝒅𝒊𝒔𝒄
+ 𝜷 𝟐𝟎 𝒓𝒆𝒍𝒊𝒈𝒊𝒐𝒖𝒔 + 𝜷 𝟐𝟏 𝒅𝒊𝒔𝒄𝒓𝒊 + 𝒖
First Econometric Model

21. 4.1 The starting point
 Ordinary Least Squares (OLS) Estimation Procedure
→ BUT: Life evaluation = Ordinal variable
→ Ordered choice model is more appropriate!!
→ Ferrer-i-Carbonell & Frijters (2004):
Cardinal OLS ↔ Ordered choice model
“Differences between the models are negligible”
 Design Weights
→ “Correct for a [potential sample] bias that is introduced by
e the sampling design” (ESS, 2014, p.1)

22. 4.2 Inference procedures
 Jobsat (job satisfaction) v.s. Work (employed/unemployed)
→ Jobsat = Significant ↔ Work = Insignificant
→ Jobsat → Sample limited to employed people
P>|t| for work P>|t| for jobsat
Econometric model using
income deciles
0.50 0.00***
Econometric model using
income quintiles 0.44 0.00***

23. 4.2 Inference procedures
Income deciles
Income deciles P>|t|
incomeD2 0.906
incomeD3 0.556
incomeD4 0.715
incomeD5 0.285
incomeD6 0.205
incomeD7 0.234
incomeD8 0.093*
incomeD9 0.092*
incomeD10 0.104
Income quintiles P>|t|
incomeQ2 0.526
incomeQ3 0.037**
incomeQ4 0.011**
incomeQ5 0.003***
Econometric models using jobsat - Significance level = 10%
v.s. Income quintiles

24. 4.2 Inference procedures
 Tests of statistical significance
P>|t|
incomeQ2 0.526
incomeQ3 0.037**
incomeQ4 0.011**
incomeQ5 0.003***
married 0.021**
children 0.006***
male 0.844
Age 0.571
P>|t|
healthy 0.519
handicap 0.100
jobsat 0.000***
eduyrs 0.395
social 0.006***
inmdisc 0.126
religious 0.811
discri 0.839
Econometric models using jobsat, income quintiles - Significance level = 10%
(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
Individual t-tests Joint F-test

25. 4.2 Inference procedures
 Insignificant variables
→ discri
→ religious
→ handicap
→ inmdisc
→ incomeQ2
→ age
→ healthy
→ eduyrs
→ male
Not recommended by academic literature → Omit!
Another (significant) variable which proxies social life → Omit!
Relevant to our research question → Retain!
Highly
recommended
by the literature
→ Omit!
age, age² (significant) → Retain!
rhealth (significant) → Retain!

26. The Econometric Models
𝒔𝒕𝒇𝒍𝒊𝒇𝒆 = 𝜷 𝟎 + 𝜷 𝟏 𝒊𝒏𝒄𝒐𝒎𝒆𝑸𝟐 + 𝜷 𝟐 𝒊𝒏𝒄𝒐𝒎𝒆𝑸𝟑 + 𝜷 𝟑 𝒊𝒏𝒄𝒐𝒎𝒆𝑸𝟒
+ 𝜷 𝟒 𝒊𝒏𝒄𝒐𝒎𝒆𝑸𝟓 + 𝜷 𝟓 𝒎𝒂𝒓𝒓𝒊𝒆𝒅 + 𝜷 𝟔 𝒄𝒉𝒊𝒍𝒅𝒓𝒆𝒏 + 𝜷 𝟕 𝒂𝒈𝒆 + 𝜷 𝟖 𝒂𝒈𝒆²
+ 𝜷 𝟗 𝒓𝒉𝒆𝒂𝒍𝒕𝒉 + 𝜷 𝟏𝟎 𝒋𝒐𝒃𝒔𝒂𝒕 + 𝜷 𝟏𝟏 𝒔𝒐𝒄𝒊𝒂𝒍 + 𝒖
SecondEconometric Model
𝒔𝒕𝒇𝒍𝒊𝒇𝒆 = 𝜷 𝟎 + 𝜷 𝟏 𝒊𝒏𝒄𝒐𝒎𝒆𝑫𝟐 + 𝜷 𝟐 𝒊𝒏𝒄𝒐𝒎𝒆𝑫𝟑 + 𝜷 𝟑 𝒊𝒏𝒄𝒐𝒎𝒆𝑫𝟒
+ 𝜷 𝟒 𝒊𝒏𝒄𝒐𝒎𝒆𝑫𝟓 + 𝜷 𝟓 𝒊𝒏𝒄𝒐𝒎𝒆𝑫𝟔 + 𝜷 𝟔 𝒊𝒏𝒄𝒐𝒎𝒆𝑫𝟕 + 𝜷 𝟕 𝒊𝒏𝒄𝒐𝒎𝒆𝑫𝟖
+ 𝜷 𝟖 𝒊𝒏𝒄𝒐𝒎𝒆𝑫𝟗 + 𝜷 𝟗 𝒊𝒏𝒄𝒐𝒎𝒆𝑫𝟏𝟎 + 𝜷 𝟏𝟎 𝒎𝒂𝒓𝒓𝒊𝒆𝒅 + 𝜷 𝟏𝟏 𝒄𝒉𝒊𝒍𝒅𝒓𝒆𝒏
+ 𝜷 𝟏𝟐 𝒎𝒂𝒍𝒆 + 𝜷 𝟏𝟑 𝒂𝒈𝒆 + 𝜷 𝟏𝟒 𝒉𝒆𝒂𝒍𝒕𝒉𝒚 + 𝜷 𝟏𝟓 𝒉𝒂𝒏𝒅𝒊𝒄𝒂𝒑
+ 𝜷 𝟏𝟔 𝒘𝒐𝒓𝒌(𝒋𝒐𝒃𝒔𝒂𝒕) + 𝜷 𝟏𝟕 𝒆𝒅𝒖𝒚𝒓𝒔 + 𝜷 𝟏𝟖 𝒔𝒐𝒄𝒊𝒂𝒍 + 𝜷 𝟏𝟗 𝒊𝒏𝒎𝒅𝒊𝒔𝒄
+ 𝜷 𝟐𝟎 𝒓𝒆𝒍𝒊𝒈𝒊𝒐𝒖𝒔 + 𝜷 𝟐𝟏 𝒅𝒊𝒔𝒄𝒓𝒊 + 𝒖
First Econometric Model

27. The Econometric Models
First Econometric Model Second Econometric Model
R² 0.1240 0.1445
Adjusted R² 0.0980 0.1314
AIC 2 546.656 2 509.376
BIC 2 647.703 2 564.492
Comparisonofthefirstandsecondeconometricmodel

28. 4.2 Inference procedures
 Testing the functional form (FF)
→ Ramsey RESET test
→ 1st econometric model: FF misspecification
→ 2nd econometric model: no FF misspecification
First Econometric Model Second Econometric Model
Prob > F 0.000 0.1445
RamseyRESETtest
Ramsey RESET test using powers of the fitted values of stflife
H0: Model has no omitted variables

29. 4.2 Inference procedures
 Multicollinearity
→ Variance inflation factor (VIF)
→ Mean VIF > 5 → High multicollinearity!
→ Multicollinearity can be tolerated
Variable VIF
age 65.53
age2 64.92
incomeQ4 6.89
incomeQ5 6.09
incomeQ3 5.28
incomeQ2 3.88
children 1.44
married 1.41
rhealth 1.08
social 1.04
jobsat 1.03
MEAN VIF 14.42

30. 4.2 Inference procedures
 Testing for heteroscedasticity
→ White test: Heteroscedasticity!
→ Solution: Robust standard errors + Weights
Second Econometric Model
P-value 0.104
WhiteTest
H0: Constant variance (Homoscedasticity)
White’s general test statistic: 91.790
Chi-sq(63) P-value = 0.0104

31. Results
Can money buy “happiness” for Belgians?
5

32. Second Econometric Model

33. 5.1 Relationship between income & subjective well-being
 Sign?
→ Positive relationship
 Significance?
→ Depends on…
- the reference group (here: incomeQ1)
- the income quintile
 Interpretation: Sign + Significance
Variable Coef. P>|t|
incomeQ2 .1115 0.752
incomeQ3 .6364 0.058*
incomeQ4 .7023 0.034**
incomeQ5 .8626 0.010*
Secondeconometricmodel

34. 5.1 Relationship between income & subjective well-being
 Magnitude?
→ Caution: stflife = ordinal variable
→ Interpretation in terms of units
→ Statements: ↓,↑, comparisons
Variable Coef. P>|t|
incomeQ2 .1115 0.752
incomeQ3 .6364 0.058*
incomeQ4 .7023 0.034**
incomeQ5 .8626 0.010*
Secondeconometricmodel
0.8626 > 0.7023

35. 5.2 Marginal effect of income on subjective well-being
 Decreasing marginal effect?
 Different conclusions depending on the
method
→ 1) Second econometric model
→ 2) Plotting income quintiles on
the scale of life satisfaction Level of GDP per capita
Happiness
Satiation point
Source: Stevenson & Wolfers, 2013

36. 5.2.1 Assessing the marginal effect via the econometric model
 Second econometric model with alternating reference groups (incomeQ)

37. 5.2.1 Assessing the marginal effect via the econometric model
 Only significant upward movement: 2nd income quintile → 3rd income quintile
 Marginal effect: ↑ ↓ ↑

38. 5.2.2 Assessing the marginal effect via a plot of income
quintiles on the scale of life satisfaction
 Plot:
→ X-axis: Income Quintiles (1-5)
→ Y-axis: Life Satisfaction (1-10)
 Decreasing marginal effect
 Satiation point?
6.5
7
7.5
8
Lifesatisfaction
1 2 3 4 5
Income Quintiles
Satiation point?

39. 5.3 The Satiation Point
Lifesatisfaction
6
6.5
7
7.5
8
0 .5 1 1.5 2 2.5
Log(income)
Lowess Linear fit
 Plot:
→ X-axis: Log(income)
→ Y-axis: Life Satisfaction (1-10)
→ Lowess & Linear fit
 Stevenson & Wolfers (2013, p.2)
→ Satiation point:
“The non-parametric fit flattens
out once basic needs were met”
→ No satiation point

40. Conclusion
The finishing line
6

41. Conclusion
 Relationship between income and subjective well-being for Belgians
(1) Relationship between income and subjective well-being
→ Robust positive relationship
(2) Marginal effect of income on subjective well-being
→ Depends on the method: Model (↑,↓,↑) ↔ Plot (↓)
(3) Satiation point
→ No evidence

42. Can money buy
“happiness” for Belgians?

43. References
References of the paper: Can money buy “happiness” for Belgians?
◈Adkins, L. C., & Carter Hill, R. (2011). Using Stata for Principles of Econometrics (4th ed.). John
Wiley & Sons
◈Bandura, R., & Conceição, P. (2008). Measuring Subjective Wellbeing : A Summary Review of the
Literature. United Nations Development Programme: research papers. Retrieved on 12/03/2016
from
http://web.undp.org/developmentstudies/docs/subjective_wellbeing_conceicao_bandura.pdf
◈Binder, M., & Coad, A. (2014). Heterogeneity in the Relationship between Unemployment and
Subjective Well-Being: A Quantile Approach (Working paper No. 808). Retrieved from the Levy
Economics Institute of Bard College website:
http://www.levyinstitute.org/publications/heterogeneity-in-the-relationship-between-
unemployment-and-subjective-well-being-a-quantile-approach
◈Deaton, Q., & Kahneman, D. (2010). High income improves evaluation of life but not emotional
well-being. PNAS, 107(38), 16489–16493. doi:10.1073/pnas.1011492107
◈Diener, E., Lucas, R.E., & Scollon, C.N. (2006). Beyond the hedonic treadmill: Revising the
adaptation theory of well-being”. American Psychologist, 61(4), 305-314.
◈ESS. (n.d. a). ESS5 – 2010 Data Download. Retrieved on 08/02/2016 from
http://www.europeansocialsurvey.org/data/download.html?r=5
◈ESS. (n.d. b). About ESS. Retrieved on 10/03/2016 from

44. 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.
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45. Thanks!
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Feel free to ask!
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