subjective well-being equation

Correlations between the individual effects of romantic partners in a

subjective well-being equation

Sanne Jonker BSc

October 6, 2015

Masters Thesis Econometrics, Operations Research and Actuarial Studies

Supervisor: J. de Bresser

Correlations between the individual effects of romantic partners in a subjective well-being equation

Sanne Jonker, Rijksuniversiteit Groningen.

November 9, 2015

Abstract

This thesis contributes to the literature on random effects ordered response models and subjective well-being by introducing a refinement of the standard random effects ordered probit model on panel data. An extra parameter representing the correlation between the individual effects of romantic partners has been added. Models have been estimated with and without covariates for general satisfaction as well as for six different domain levels of satisfaction. Significant correlations up to 0.949 have been found as well as a systematical efficiency gains op to 41.4 %, indicating that the adjustment is a valuable refinement of the standard model. The liss panel has been used to estimate the different equations.

1 Introduction

The popularity of research on subjective well-being (swb), the satisfaction of an individual with the quality of his or her life, has increased significantly over the last two decades (Kahneman and Krueger, 2006, Krueger and Schkade, 2008). This is not surprising since knowledge on the mechanisms behind swb has many applications. Policymakers can use the resulting knowledge to customize their policies to the needs of different groups of inhabitants. Employers are interested in these mechanisms as well, since more satisfied employees are expected to be more positive about the organisation. They will perform better and are expected to be more loyal to the company (Freeman, 1978, Akerlof et al., 1988, Clark, 2001, Bontis et al., 2011). More applications can be found in for example the field of spatial science, see the literature overview of section 2.

Brown (2000) concludes that the levels of satisfaction between married individuals and unmarried individuals who are in a stable relationship are comparable. This thesis will therefore only distinguish between individuals who are in a stable relationship, romantic partners, and individuals who are not, singles.

It is found in the literature that swb follows a U-shaped relationship with age, where the lowest

levels occur at midlife. A similar relation has been found for specific domains of satisfaction such as

leisure and financial satisfaction. The effects of other variables like the number of children living in

the household differ much between domains. Education is for example not always found to have a

positive relation with levels of satisfaction. One might expect a positive relation since more educated

people are expected to have better jobs. But aspirations rise with the level of education, which

might result in expectations that cannot be met. This emphasises the subjective nature of this type of data.

Most research on swb has been done using cross-sectional data, where each participant is observed only once. It is not possible to include individual effects when using this type of data. But the mechanisms behind the levels of satisfaction are expected to be highly subjective. Levels of subjective well-being often differ from what would be expected based on one’s objective situation. That is why improvements can be made using panel data, which consists of individuals that are observed for several time periods. These repeated observations can be used to add unobserved hetrogeneity caused by individual effects to the model. These individual effects are for example the result of the personality of an individual

Based on the literature review performed for this thesis, papers on subjective well-being that use panel data are found to use standard models, mostly ordered random effects probit models, that implicitly assume that the individual effects related to subjective well-being are uncorrelated between individuals. This might be an incorrect assumption when it comes to romantic partners.

The methodological addition of this thesis to the literature will be to test whether this assumption can be made or not for the Dutch population. A standard random effects ordered probit model will be extended in order to allow for correlations between romantic partners. Following van Praag et al. (2003), eight different scales of satisfaction will be used: subjective well-being or general satisfactions and six domain levels of satisfaction, of which one is defined by two different notions.

The domain levels are: job, financial, house, environment, health and leisure satisfaction. The last domain will be divided in satisfaction with the amount of leisure time and satisfaction with the way this leisure time is spent. The main question will therefore be: Are the individual effects that predict subjective well-being and its six different domains correlated among romantic partners?

Large correlations have been found between the individual effects of romantic partners for the levels of swb (0.849) and levels of financial (0.949) and leisure satisfaction (0.744 and 0.759). Smaller correlations have been found for health and job satisfaction. Part of the correlations can be explained by demographical variables such as household income and household size. The correlations become smaller for most domains when these variables are added to the model but none become insignificant.

Notwithstanding the fact that the estimate for house satisfaction is insignificant, it is concluded that evidence has been found that the assumption of complete independence between the individual effects of Dutch inhabitants cannot be made.

Estimated parameters of the covariates used to model the different equations do not differ much between the standard model and the adjusted model used in this thesis. This means that the economic results found in the existing literature and future literature that used or will use a standard model will be close to the results found when correlations between the individual effects of romantic partners are taken into account. But the adjusted model has been found to be more efficient. The standard errors of the parameters estimated using the adjusted model are almost always smaller than those of the standard ordered probit model, with decrements up to 41.4%. The adjusted model could therefore be seen as a valuable refinement of the standard model.

The most important economic result is that financial satisfaction is the most important predictor of

swb, followed by job satisfaction and satisfaction with the way leisure time is spend. An individual

must have the feeling that he or she has the resources to buy the goods and services that meet his

or her expectations. Satisfaction with the activities performed during the day turn out to be the

second and third most important factors.

Household income has a significant and mostly positive relation with all levels of satisfaction, where the relation is only negative for leisure satisfaction. Being in a stable relationship is expected to have a positive relation with most satisfaction levels as well. Women generally react more positively to the number of children in the household and men to the complete size of the household. Results on other variables as education differ between domains.

This thesis is structured as follows. Section 2 gives an overview of the most important literature on subjective well-being and its domains. Section 3 gives a description of the data used in this thesis, followed by section 4, which presents the adapted random effects ordered probit model. Chapter 5 gives an overview of the most important results, which are discussed in section 6. Section 7 concludes this thesis.

2 Literature

As an economist one tries to predict the choices people make based on revealed preferences, observations of a person’s actual choices and decisions. It is assumed that each individual makes rational decisions in order to maximize his or her individual utility. Unfortunately, individuals fail to make rational choices. The choices they make are inconsistent when compared to these revealed preferences and seem to be dependent on the situations of their peers (Kahneman and Krueger, 2006). It therefore seems to be necessary to look at subjective preferences based on subjective reports of their likes and dislikes as well.

It should come as no surprise that research on subjective well-being (swb) has become popular.

Both Kahneman and Krueger (2006) and Krueger and Schkade (2008) conclude that the amount of literature on swb has exploded with more than 100 papers on this subject being published in the period 2001 to 2005, while only 4 such papers have been published from 1991 to 1995.

Swb is defined as the amount of satisfaction one feels with his or her life as a whole. It can be seen as the weighted sum of satisfaction with different domains in life. Following van Praag et al.

(2003) we use six different domains: job satisfaction, financial satisfaction, house satisfaction, health satisfaction, leisure satisfaction and environment satisfaction. This thesis will mainly focus on swb and the first five domains.

A first question could be on the reliability of self-reported levels of swb. Krueger and Schkade (2008) found sufficiently high correlations between the responses over a period of two weeks on different questions related to swb. They therefore conclude that the measurements yield useful information for the type of research that will be performed in this paper.

In addition, van Praag et al. (2003) conclude that measurements on swb are comparable between individuals within a given language community. First Diener and Lucas (1999) conclude that people are able to observe and foresee the satisfaction levels of other individuals. Secondly, van Praag (1991) found that people within a language community translate internal feelings in a similar manner into a numerical scale. Last, van Praag et al. (2003) bring as an argument that Diener and Lucas (1991) have found a stable relationship between levels of satisfaction and objective variables. We will continue discussing the main variables predicting swb, assuming that the measurements are reliable enough for the type of research that has been done so far.

Several studies found that not only the income of an individual but the difference with one’s

reference income, the level of income to which an individual compares his own income, is an

important predictor as well, see for example Clark and Oswald (1996), Ferrer-i-Carbonell (2005) and Luttmer (2005). This reference income can be seen as the income one expects to earn for the type of job he or she does and the number of hours one works per week. Individuals compare their income to their expectations. That is why income itself will not always perform well in predicting the level of satisfaction, as expectations rise with income. As an example, Easterlin (1995) found that the levels of self-reported happiness of residents of Japan did not increase between 1958 and 1987, despite the fact that their income increased fivefold. This emphasizes the difficulty of predicting swb based on objective variables such as income.

In line with this, a lot of research has been done on how people adapt to positive and negative events in their lives. Paraplegics do not respond to be extremely unhappy and lottery winners do not respond to be the happiest people on earth, they adapt to their situation, see Brickman et al. (1978). Oswald and Powdthavee (2006) found that life satisfaction drops after the onset of a disability, but fully recovers after two years for a modest disability. People with severe disabilities adapt as well, but will not reach their original levels. Smith et al. (2005) found that the drop is more severe for those with lower wealth, which suggests a buffering effect for those with a higher wealth. Marriage and bereavement have an effect on swb, but adaption takes place quickly. Clark et al. (2006) for example found that the happiness of 235 German women increased in the year prior to marriage and in the first year of marriage, but fully adapted to the previous levels afterwards.

Most researchers find a U-shaped relationship between age and swb, with the highest levels of satisfaction for the youngest and oldest and the lowest levels at middle age. See for example Blanchflower and Oswald (2004a) and Ferrer-i-Carbonell and Gowdy (2007). The literature on the influence of education on swb is less clear. Blanchflower and Oswald (2004b) found a positive relation between education and swb, while Stutzer (2004) found an inverse U-shaped relationship.

The influence of education on swb can be very interesting for policy makers, since it is important for them to know on which level of education they should focus in their policy.

The effect of being in a relationship is quite interesting. It is agreed that being married results in the highest levels of satisfaction and being separated with the lowest, see for example Helliwell (2003). The interesting part is that Brown (2000) concludes that unmarried people who are in a stable relationship have levels of satisfaction similar to those who are married. Satisfaction levels therefore are not so much influenced by the official status of his or her relationship but by how an individual experiences it.

Having children seems to have a positive effect on swb when financial aspects are being controlled for, see for example Haller and Hadler (2006), Lelkes (2006) and Schwarze and H¨ arpfer (2003).

Children have a negative effect on a family’s financial situation but it is agreed on that they play an important part in the overall well-being of an individual.

Van Praag et al. (2003) found financial, health and job satisfaction to be the most important predictors of subjective well-being. Next in line is leisure satisfaction and both house and environment satisfaction turn out to be of less importance.

Job satisfaction

The field determining which variables determine the levels of job satisfaction is mainly interesting

for employers. Freeman (1978), Akerlof et al. (1988) and Clark (2001) found that job satisfaction

can be used to predict future quits and Bontis et al. (2011) conclude that more satisfied employees

are expected to be more positive about the organisation and therefore perform better.

Clark and Oswald (1996) found that education is negatively correlated with job satisfaction.

Aspirations rise with education and will be harder to meet, which will result in lower levels of job satisfaction. Van Praag et al. (2003) found that household income has a positive influence on job satisfaction. More household income will give an individual more freedom when choosing a job.

Men generally report themselves to be less satisfied (Clark et al., 1996, van Praag et al., 2003), which is surprising since women’s jobs generally are worse than those of men. Women mostly fulfil jobs that are more demanding and pay less such as home care and education while men dominate the financial institutions. This might be the result of a difference in aspirations, which can be underpinned by the observation that the differences in satisfaction disappear for those who are younger, higher educated, professionals and those who work in male dominated places (Clark, 1997;

Mora and Ferrer-i-Carbonell, 2009). The difference in expectations between men and women is expected to be much smaller for these groups of employees.

As expected, the number of hours one works per week have a negative effect on job satisfaction (Clark et al., 1996; Clark, 1997). The number of adults in the household also has a negative effect.

Van Praag et al. (2003) found a U-shaped relation for age with a minimum around 50. Wheatly (2014) found that commuting time has a negative relation. This is in line with our expectations as travel-to-work is experienced as one of the least satisfying activities of the day (Kahneman et al., 2004; Wheatley, 2013).

Financial satisfaction

The research on financial satisfaction is important for private decision making as well as for policy.

The link between personal income, perceived income and financial satisfaction can for example be important in different policy domains such as employment discrimination (DePianto, 2011).

The number of children and adults in West-German households have, as expected, a negative effect on financial satisfaction according to the study of van Praag et al. (2003). But they did find a positive effect of having a partner. This should be no surprise, since a partner can increase household income.

Generally, men tend to be less satisfied than women, following the study of van Praag et al. (2003).

DePianto (2011) found that in the U.S. white males have higher returns to personal income than females and black males, indicating that white males are more sensitive to changes in personal income. An explanation could be that women and minorities tend to have jobs with lower payments (Macpherson and Hirsch, 1995; Blau and Kahn, 2000) and therefore are less accustomed to big increases in their personal income. Another explanation might be that the drivers of financial satisfaction differ between men and women (Brown et al., 2014).

But the precise influence of income is more complex and dependent on age. Plagnol (2011) found

that financial satisfaction follows an inverted U-shape with age, being highest at middle age while

several other studies found that financial satisfaction increases with age (see for example Plagnol

and Easterlin, 2008). Brown et al. (2014) suggest that this might be due to different financial

situations in different steps of the life cycle. Older people are for example expected to have lower

debts and more assets, while younger people just bought their first house which leads to a high

mortgage debt. He indeed found that the influence of job income is restricted to the early life stages

and that income from investments and housing equity play a larger role later on in life. This finding

can be very important for policy makers as different policies are needed for different groups in the

population in order to positively influence their financial satisfaction.

House satisfaction

Age has a U-shaped effect on house satisfaction, according to the findings of van Praag et al. (2003), reaching a minimum at 29. The mean of the household income over several years has a positive effect, while the number of children and adults in the household both have a negative effect. For the East Germans they found a significant negative effect of education, indicating that more educated people have a tendency to be more critical on their housing or have higher aspirations which cannot be met.

The research on house satisfaction is important in order to build houses that satisfy the needs of different people in different stages of their lives. The birth of a child might for instance lead to the need for a bigger house and the move out of a child might lead to the need for a smaller and less expensive house and a new job might even lead to a need for a different location. This research will not go enough into detail to obtain any direct conclusions on this but might be used as a handle for further more detailed research.

Health satisfaction

Van Praag et al. (2003) found that health satisfaction has a negative relationship with age and a positive relationship with income for Western Germans. The shock effect of income, the difference in income between the current and previous year, turned out to be insignificant. They also found a positive relationship between education and health satisfaction. This indicates that more educated people have a healthier life style. For working individuals they found a significant difference between men and women, with males being more satisfied with their health than females. The difference is insignificant for non-working individuals.

Leisure satisfaction

The age effect again is U-shaped with a minimum between an age of 30 and 35, following the results of Van Praag et al. (2003). The effects of household income are positive but small and more educated people are less satisfied with their leisure.

Van Praag et al. (2003) concluded that people seem to enjoy their leisure time more when they live alone, as both the presence of children and adults have a negative effect on leisure satisfaction. This might be due to the constraints these extra household members put on an individual, especially when it comes to children. Gronau and Hamermesh (2003) indeed found a negative relationship between household responsibilities and leisure satisfaction.

Estimation on the Dutch population

Based on the literature and availability, different sets of variables will be used. The subjective well- being equations will be estimated using the discussed domain levels of satisfaction as independent variables. In addition, all levels of satisfaction apart from environment satisfaction will be estimated using a set of demographical variables, namely ‘age’, ‘age squared’, ‘having a partner’, ‘number of children in a household’, ‘number of members in a household’, ‘log of household income’ and

‘education level’.

The variables ‘work hours’ and ‘commuting time’ have been added to the set of demographical variables for job satisfaction, while only the variable ‘work hours’ has been added to the model of financial satisfaction. The variables ‘working’ and ‘practicing sports’ have been added to the models of leisure satisfaction.

Correlations between partners

A large part of the studies discussed above use cross-sectional data and the studies that did use panel data in order to control for individual effects implicitly assume these effects to be uncorrelated between individuals, even between romantic partners. This thesis will test whether this assumption can be made. One can imagine that the unobserved individual characteristics of romantic partners are highly correlated and therefore will influence the unobserved effects that predict the levels of swb and the underlying domains of their partner.

3 Data

The empirical analysis is based on the Longitudinal Internet Studies for the Social Sciences (LISS panel), a longitudinal household panel in the Netherlands. The panel is a good representation of the Dutch population since participants are a true probability sample of Dutch households drawn from the population register by Statistics Netherlands (Centraal Bureau voor de Statistiek). Only households that were selected are able to participate and participants that could not participate any other way were provided with a special computer and an Internet connection.

The sample includes 13, 319 individuals who were observed 47, 536 times in the period 2008 to 2014, see table 1. In each wave around 8, 000 individuals were observed. There are 8, 179 households of which 4, 969 consist of a so-called couple household, a household where the household head lives with his or her romantic partner in the same household. Only the household head and his or her partner were included in the dataset used for this thesis.

Men and women are equally represented with 48.3% being male. Participants age from 16 to 96 years old with men being a little bit older on average than women, 51.4 versus 49.9 years old, respectively. Almost 62% of the men is working versus 57% of the women and men work more hours per week than women, 35.4 versus 24.8 hours on average. Immigrants are a little bit under represented with 11.8% of the men and 13.1% of the women being non-Dutch, while these numbers should be between 17 and 21 percent according to Statistics Netherlands, see table 1. Most variables do not differ much between genders apart from those related to income and the amount of time spend on work related activities. Men generally earn more, work more hours per week and spend more time on commuting.

The question asked to measure an individual’s subjective well-being is given by ‘How satisfied are you with the life you lead at the moment?’ and similar questions follow for the other domains.

Only the question on the domain health is not specifically about satisfaction, but comes as close

as possible to health satisfaction in the LISS panel questionnaires. The question is given by ‘How

would you describe your health, generally speaking?’

All levels are measured on a 0 to 10 scale, except for health satisfaction which has values from 1 to 5. The answers 0, 1 and 2 were combined for all levels apart from health satisfaction because of the relatively low number of individuals that gave these answers. Combing these categories will not significantly affect the final results since the number of responses to this new category were small (mostly below 1% of the total responses). A complete description of all variables being used can be

found in appendix A.

Table 2 gives a summary of all satisfaction levels for men and women. Differences between genders are small with the largest differences for leisure satisfaction and men always being more satisfied than women.

Men Women

Mean Obs. Ind. Mean Obs. Ind.

Age 51.436 (14.829) 23035 6430 49.856 (15.031) 24501 6889

Children 0.826 (1.125) 23035 6430 0.822 (1.110) 24501 6889 Household size 2.667 (1.296) 23035 6430 2.606 (1.288) 24501 6889 Household income 3076.491 (5076.768) 21080 5954 3043.784 (6315.33) 22400 6391 Workhours 35.396 (14.661) 9622 3255 24.754 (12.893) 10617 3686 Commuting time 27.662 (20.889) 8552 2892 22.074 (17.348) 9311 3178

Partner 81.00% 23035 6430 76.16% 24501 6889

Low education 33.54% 13836 4104 38.86% 16188 4954

Medium education 30.72% 13836 4104 31.81% 16188 4954

High education 35.75% 13836 4104 29.33% 16188 4954

Non-Dutch origin 11.81% 16916 3857 13.06% 19448 4541

Working 61.60% 14244 4198 57.02% 16667 5058

Sport 50.77% 14612 4219 52.06% 16975 5026

Table 1: Descriptives and (S.E.) of explanatory variables in the LISS sample.

Men Women

Mean Obs. Ind. Mean Obs. Ind.

Subjective well-being 7.472 (1.358) 13670 3969 7.474 (1.353) 15861 4800 Job satisfaction 7.438 (1.503) 8587 2899 7.466 (1.506) 9265 3168 Financial satisfaction 6.821 ( 1.654) 12884 3774 6.712 (1.755) 14641 4497 Housing satisfaction 7.943 (1.422) 8669 2594 7.968 (1.501) 10940 3460 Health satisfaction (1-5 scale) 3.107 (0.752) 13679 3646 3.059 (0.736) 15783 4336 Leisure satisfaction (amount of) 7.295 (2.105) 14454 4204 7.269 (2.028) 16729 5002 Leisure satisfaction (spending) 7.210 (1.660) 14486 4208 7.081 ( 1.725) 16834 5013 Environment satisfaction 7.741 (1.441) 8683 2594 7.794 (1.518) 11001 3473

Table 2: Average and (S.E.) of satisfaction levels in the LISS sample.

4 Methodology

In this thesis, seven different satisfaction levels are analysed. First, general satisfaction, or subjective well-being, will be explained based on the six different domain satisfaction scales, namely job, financial, house, health, leisure and environment satisfaction. The satisfaction levels of leisure are given by a level of satisfaction with the amount of leisure time and the level of satisfaction with the way this leisure time is being spend. The levels of health satisfaction are scaled for this part of the model, in order to make the resulting slope comparable to those of the other satisfaction levels.

Secondly, the levels of general, job, financial, house and health satisfaction and the two levels of leisure satisfaction are estimated without covariates and are estimated with demographical and other related variables.

The models used in this thesis are based on a standard random effects ordered probit. An additional parameter indicating the covariance between the individual effects of partners is added to this standard model in order to be able to test whether the unobserved individual effects of romantic partners are correlated. The resulting model will be discussed in general in the next section.

General model

It is assumed that a latent variable y ^∗ _it is determined by

y _it ^∗ = x ⁰ _it β + c i +  it ,  it ∼ N (0, 1),

where  _it , x _it and c _i are independent of each other, x _i is a (K × 1)-vector of independent variables and c _i represents an individual effect. This model does not contain a constant term because of identifiability. The related observed variable y it is an ordered response variable taking on the values {M ₁ , . . . , M ₂ } defined by the following observation rule:

y it = M 1 if y _it ^∗ ≤ a _M

,

y _it = m if a _m−1 < y _it ^∗ ≤ a _m , m = M ₁ + 1, . . . , M ₂ − 1, y _it = M ₂ if a _M

−1 < y ^∗ _it ,

with a M

< a M

+1 < · · · < a M

−1 being unknown thresholds.

The density function for the observed dependent variable is a function of the probability of being in each of the M ₂ − M ₁ + 1 categories. These probabilities are given by

P (y it = M 1 |x _it , c i ) = P (y _it ^∗ ≤ a _M

|x _it , c i )

= P (β 0 + x ⁰ β + c i +  it < a M

|x _it , c i ) = Φ(a M

− β ₀ − x ⁰ β − c i )

P (y _it = m|x _it , c _i ) = P (a _m−1 < y ^∗ _it ≤ a _m |x _it , c _i ) = Φ(a _m − β ₀ − x ⁰ β − c _i ) − Φ(a _m−1 − β ₀ − x ⁰ β − c _i ) P (y _it = M ₂ |x _it , c _i ) = P (y _it ^∗ > a _M

−1 |x _it , c _i ) = 1 − Φ(a _M

−1 − β ₀ − x ⁰ β − c _i ),

for m = M 1 + 1, . . . , M 2 − 1.

The resulting density function conditional on the individual effect c _i is given by

f (y it |x _it , c i , β) =P (y it = M 1 |x _it , c i , β) ^I(y

^=M

⁾ · P (y _it = M 1 + 1|x it , c i , β) ^I(y

^=M

⁺¹⁾ · . . . ·

P (y it = M 2 − 1|x _it , c i , β) ^I(y

^=M

⁻¹⁾ · P (y _it = M 2 |x _it , c i , β) ^I(y

^=M

⁾ .

Single men and women

First we focus on households where the household head does not share the household with a romantic partner. The model distinguishes between men, indicated by an m, and women, indicated by an f , where it is typically assumed that the distribution of the individual effects of single men is given by c ^m _i ∼ N (0, σ _c,m ² ). A similar distribution is given for the individual effects of women.

The contribution to the log likelihood of each male i that is not in a romantic relationship is given by the logarithm of

f (y _i ^m |x ^m _i , c ^m _i , β ^m ) =

T

Y

t=1

f (y ^m _it |x ^m _it , c ^m _i , β ^m )

= Z ∞

−∞





T

Y

t=1

f (y ^m _it |x ^m _it , σ _c,m z, β ^m )



 φ(z)dz,

where t indicates the time period of the observation with T _i ^m time periods in total. A similar formulation is given for females.

Romantic partners

Next step is the addition of a parameter indicating the correlation between the individual effects of romantic partners. It is assumed that, given the assumption that a couple consists of a man and a woman in order to simplify the estimation, the individual effects of couples are distributed as (c ^m _i , c ^f _j ) ⁰ ∼ N (0, Σ), where

Σ = σ ² _c,m σ _s σ s σ _c,f ²

!

and where c ^m _i and c ^f _j are independent of x ^m _i , x ^f _i ,  ^m _it and  ^f _it . The correlation between the individual effects of partners is given by σ s . The individual effects can be simulated as Az, with

A = α ₁ 0 α 3 α 4

! ,

a Cholesky decomposition of the covariance matrix of the individual effects satisfying AA ⁰ = Σ

and with z = (z ₁ , z ₂ ) ⁰ having uncorrelated standard normally distributed elements z _i . As a result

we find σ ² _c,m = α ² ₁ , σ _c,f ² = α ² ₃ + α ² ₄ and σ s = α 1 α 3 .

Finally, the contribution to the log likelihood of each couple i is given by the log of f (y _i ^m , y ^f _j |x ^m _i , x ^f _j , c ^m _i , c ^f _j , β ^m , β ^f )

=

T

Y

t=1

f (y ^m _it |x ^m _it , c ^m _i , β ^m ) ·

T

Y

t=1

f (y ^f _jt |x ^f _jt , c ^f _j , β ^f )

= Z ∞

−∞

Z ∞

−∞





T

Y

t=1

f (y _it ^m |x ^m _it , (1 0)Az, β ^m ) ·

T

Y

t=1

f (y _it ^f |x ^f _it , (0 1)Az, β ^f )



 φ(z ₁ )φ(z ₂ )dz ₁ dz ₂

= Z ∞

−∞

Z ∞

−∞





T

Y

t=1

f (y _it ^m |x ^m _it , α ₁ z ₁ , β ^m ) ·

T

Y

t=1

f (y _it ^f |x ^f _it , α ₃ z ₁ + α ₄ z ₂ , β ^f )



 φ(z ₁ )φ(z ₂ )dz ₁ dz ₂ .

Estimation

The corresponding numerical approximations per household i are given by the log of 1

R

R

X

j=1

( _T

Y

t=1

f (y _it ^m |x ^m _it , α ₁ z ₁ ^j , β ^m ) · f (y ^f _it |x ^f _it , α ₃ z ₁ ^j + α ₄ z ₂ ^j , β ^f ) )

,

where z ₁ ^j and z ₂ ^j are pseudo random draws from a standard normal distribution, T _i corresponds to the number of waves observed for household i and R corresponds to the number of simulations.

The function f (·) is replaced by 1 if there were no observations for that individual for the given time period. The individual either does not exist in the given household (single male or female household) or there was no observation for that individual in the given time period.

Finally, the resulting log likelihood of the model is given by the sum of each of these contributions.

All variables are estimated using the ml function in stata for the models that did not have any covariates. The thresholds a M

< a M

+1 < · · · < a M

−1 are not estimated based on the ml function for the models with covariates. The threshold of these functions are estimated using two different standard ordered probit models of the models with covariates, one for men and one for women.

This has been done in order to shorten the computation time.

5 Results

This chapter contains the results of the estimations of the swb equation and of the domain equations.

The variables are chosen based on the literature and on availability.

5.1 Estimation without covariates

All equations have been estimated without covariates in order to compare the correlations between

the individual effects of partners, see table 3. Table 8 in the appendix presents the number of

observations and households used for these estimations.

SWB Job Financial House

Men Women Men Women Men Women Men Women

Variance c

2.398*** 1.662*** 1.494*** 1.292*** 3.0924*** 2.505*** 2.156*** 2.094***

(0.0766) (0.0547) (0.0684) (0.0603) (0.0970) (0.0761) (0.104) (0.0824)

Correlation c

0.849*** 0.135*** 0.949*** 0.00214

(0.0118) (0.0257) (0.00728) (0.0188)

Log likelihood -41,379.248 -27,992.702 -42,929.483 -29,081.764

Health Leisure (amount of) Leisure (spending)

Men Women Men Women Men Women

Variance c

2.413*** 2.0029*** 2.440*** 1.616*** 1.919*** 1.316***

(0.0947) (0.0683) (0.0831) (0.0499) (0.0617) (0.0412)

Correlation c

0.373*** 0.744*** 0.759***

(0.0221) (0.0133) (0.0153)

Log likelihood -26,522.362 -54,837.212 -52,149.451

Standard errors in parentheses

*** p < 0.01, ** p < 0.05, * p < 0.1

Table 3: Estimation results without covariates.

The variances of the individual effects differ significantly between men and women for subjective well-being, financial, job, health and both scales of leisure satisfaction at a 5% significance level.

The differences are even significant at a 1% significance level for subjective well-being, financial, health and leisure satisfaction. The difference is insignificant for house satisfaction. The variances are larger for males than for females for all scales. This indicates that the satisfaction levels are more persistent for men and therefore vary less over time.

Correlations between the individual effects of romantic partners are extremely high for financial satisfaction and swb. The correlations are still high for both scales of leisure satisfaction and medium high for health satisfaction. The correlations are low for job satisfaction and the individual effects are uncorrelated for house satisfaction.

5.2 Estimation with covariates

In addition all equations have been estimated with covariates in order to observe how this influences the correlations found in the previous section and to be able to give an economic interpretation on the mechanisms behind the satisfaction levels.

Subjective well-being

First, the estimation results of two standard random effects ordered probit models for men and

women separately are compared to those of the adjusted model, which includes a correlation between

the individual effects of romantic partners and where the estimates for men and women were

obtained simultaneously, see table 4. The estimations are based on 7, 632 observations on 2, 693

households of which 1, 773 were a so called couple household, a household where the household head

lives together with a romantic partner.

The estimations of the parameters β ^m and β ^f do not differ much between the standard and adjusted model and the variances of the individual effects turn out to be a little underestimated by the standard model. A small negative correlation between the individual effects of romantic partners is found, which is weakly significant.

For both men and women, the most important predictor of swb is financial satisfaction, followed by the satisfaction with the spending of his or her leisure time. The third most important predictor is job satisfaction. Next in line are health, environment and house satisfaction. Environment satisfaction is more important than house satisfaction for men and visa versa for women. The satisfaction with the amount of leisure time is insignificant. Only the estimates related to the variables job an environment satisfaction differ significantly between men and women at a 5% and 10% significance level, respectively. Men value their job and environment more than women.

Secondly, it has been tried to predict swb and the six other satisfaction levels based on several demographic variables, see tables 5, 6 and 7. The number of observations on which these models and the standard random effects ordered probit models, see tables 10, 11 and 12, are estimated are given in the appendix in table 9. The differences between the estimates based on the standard and adjusted models are small. Important is the observation that all variances of individual effects have been underestimated for the standard models, which is in line with the observation concerning the variances of the individual effects of the previous model. The variances are larger for men than for women, apart from those found for house and health satisfaction for which the results are reversed.

Looking at the results of swb, a significant difference, at a 1% significance level, is found between the age effect for men and women. Both effects follow in inversed U-shape, where women reach their minimum around age 34 while men do around 8 year later. Having a partner has a positive influence on the level of swb of both men and women and the gender difference in the size of this effect is insignificant. Having children has a negative effect for men, while the household size has a positive effect. The results are insignificant for women. The income effect is positive and does not differ significantly between men and women. Education follows an inverse U-shape.

Job satisfaction

The differences between the linear age effects of men and women are small but the difference for the quadratic effect is still significant at a 10% significance level. An inverse U-shape is found with a minimum around 30 years old. The effect of having a partner is positive for men, while the effect is negative for women. This difference is significant at a 1% level. The effects of the number of children in the household and the size of the household are insignificant.

Household income has a positive effect, which is the largest for women. The estimates differ between men and women at a 1% significance level. The effect of education is very small. The number of workhours have a small positive effect and the time spend on commuting a small negative effect.

These effects differ between men and women at a 5% significance level.

Subjective well-being Standard model Adjusted model

Men Women Men Women

Financial 0.257*** 0.250*** 0.247*** 0.245***

(0.0200) (0.0165) (0.0191) (0.0154)

Health 0.145*** 0.155*** 0.140*** 0.150***

(0.0201) (0.0170) (0.0180) (0.0152)

Job 0.208*** 0.157*** 0.204*** 0.153***

(0.0190) (0.0159) (0.0173) (0.0146)

Leisure (amount of) 0.0139 0.00439 0.0186 0.00981

(0.0160) (0.0140) (0.0157) (0.0137)

Leisure (spending) 0.207*** 0.174*** 0.214*** 0.174***

(0.0204) (0.0171) (0.0194) (0.0167)

House 0.159*** 0.113*** 0.161*** 0.120***

(0.0248) (0.0212) (0.0239) (0.0200)

Environment 0.123*** 0.0746*** 0.130*** 0.0751***

(0.0246) (0.0200) (0.0235) (0.0192)

2010 0.0618 -0.0901 0.0624 -0.0909

(0.0670) (0.0582) (0.0660) (0.0570)

2011 0.0152 -0.131** 0.00689 -0.129**

(0.0683) (0.0589) (0.0671) (0.0578)

2012 -0.0217 -0.177*** -0.0430 -0.179***

(0.0727) (0.0641) (0.0713) (0.0630)

2013 -0.0248 -0.0691 -0.0385 -0.0682

(0.0710) (0.0634) (0.0696) (0.0623)

2014 -0.0708 -0.211*** -0.0912 -0.206***

(0.0714) (0.0642) (0.0703) (0.0628)

Variance c

0.895*** 0.682*** 1.000*** 0.694***

(0.0814) (0.0592) (0.0660) (0.0444)

Correlation c

- -0.192*

- (0.0741)

Log likelihood -4059.0471 -5178.3739 -9289.8031

Standard errors in parentheses

*** p < 0.01, ** p < 0.05, * p < 0.1

Table 4: Estimation results of a standard random effects ordered probit and the adjusted version.

Financial satisfaction

The inverse U-shaped effects of age differ between men and women at a 5% significance level with a minimum around 34 and 37 years old, respectively. The effect of having a partner is positive but small and even insignificant for women. The effect of the number of children is insignificant and the effect of the household size is negative but small and even insignificant for women. The effect of education is clearly positive, a higher level of education is expected to result in higher levels of financial satisfaction. The effect of the number of workhours per week is insignificant.

House satisfaction

The age effect is small. Only a small positive linear affect can be found for women. Having a partner has a positive effect which does not differ significantly between men and women. Having children has a positive effect and the household size has a negative effect for women. These effects are insignificant for men. Household income has a positive effect and education follows an inverse U-shape, where the estimates differ at a 10% level between men and women for high levels of education.

Health satisfaction

The age effect is small but similar between men and women and follows an inverse U-shape with a minimum at retirement. The effect of having a partner is insignificant for men but has a significant positive effect for women. The number of children in the household and household size have no significant effect for men but have, respectively, a significant positive and negative effect for women.

The income effect is positive as well as the that of the level of education. The effect of having a high level of education differs significantly between men and women at a 1% significance level.

Leisure satisfaction

A lot of differences have been found between men and women for the predictors of satisfaction with the amount of leisure time. The effect of age is positive for both men and women but differs significantly at a 1% level. The effect of having a partner is positive as well and does not differ between men and women. The effect of the number of children in the household is negative for men and insignificant for women and visa versa for the number of household members.

The effect of household income is small and negative for men and insignificant for women. The effect of education is insignificant for men but significantly negative for women. Having a job has a clear negative effect. This effect is larger for men and differs significantly from the estimate for women at a 1 % significance level. Practicing sports has a positive effect which does not differ between men and women.

The estimates for the predictors of the level of satisfaction with the way leisure time has been spend

is similar between men and women. The age effect is very small. Having a partner has a positive

effect for men and this effect is insignificant for women. The number of children and other members

in the house have no significant effect. There is a relatively small positive effect of household income

and education has a negative effect. Having a job has a negative effect while practicing sports has a

clear significant positive effect on the level of satisfaction with how leisure time has been spend.

Efficiency gains

An effecieny gain is found when the standard errors of the standard random effects ordered probit models are compared to those of the adjusted model, see table 13. All estimates of the adjusted model have smaller standard errors, apart from those of the estimations of the parameters of women of the variables concerning the number of children and household size for the model of financial satisfaction.

The standard errors are on average 13.2 % smaller, with a maximum efficiency gain of 41.4%.

Noteworthy is that the average gains do not differ much between the models but the sizes of the gains can be divided into three groups of variables. The smallest gains have been found for the time dummies (1.8% on average), followed by the satisfaction levels (5.6% on average) and the variables ‘workhours’, ‘commuting time’, ‘working’ and ‘practicing sport’ (9.3% on average), which have been used for a number of functions. The largest gains have been found for the demographic variables that have been used for all domains and for general satisfaction: ‘age’, ‘age squared’,

‘having a partner’, ‘number of children’, ‘household size’, ‘log of household income’ and ‘education level’ (22.1% on average).

6 Discussion

The most important result is the efficiency gain of the adjusted model in comparison to a standard random effect ordered probit model. The estimated parameters do not differ much between both models, but the adjusted model is expected to obtain estimates that are closer to the real values.

Another important observation is that the standard model systematically underestimates the variances of the individual effects and therefore underestimates the persistence of the satisfaction levels. The variances found are larger for men than for women in five of the seven models, which shows that the persistence of these levels is larger for men for these levels and visa versa for the other two levels, namely house and health satisfaction.

It is found that the mechanisms resulting in the levels of subjective well-being differ little between men and women. Only the importance of job and environment satisfaction differ between men and women for the model that used domain satisfactions as covariates. Men value satisfaction with their job more than women, as expected based on traditional roles within a household (Centraal Bureau voor de Statistiek, 2014). Men add more value to the level of satisfaction with their environment as well.

For the model of swb that used demographic covariates, it is found that only the estimated parameters related to age, number of children and the size of the household differ significantly between men and women. Women are expected to be the least satisfied at 34 years old and men eight years later at age 42. Men tend to become less satisfied with their live when more children are added to the household but become more satisfied as the household size itself increases. This might be because men will be put in second place after a child has been born.

Financial satisfaction is the most important predictor of swb for both men and women. This may

be the most important factor since a better financial situation gives an individual more freedom with

respect to choices that influence the satisfaction levels of the other domains. The second and third

most important domains are job satisfaction and satisfaction with the way an individual spends his

or her leisure time. People either sleep, work or have leisure time, that is why it is not surprising

Depend. var. SWB Job Financial

Men Women Men Women Men Women

Age -0.0451*** -0.0161** -0.0336*** -0.0572*** -0.0364*** -0.0683***

(0.00788) (0.00686) (0.0126) (0.0123) (0.0117) (0.0125) Age2 0.000542*** 0.000238*** 0.000568*** 0.000907*** 0.000541*** 0.000957***

(7.26e-05) (6.72e-05) (0.000136) (0.000140) (0.000125) (0.000141)

Minimum age

41.605 33.824 29.578 31.533 33.641 35.684

Partner 0.487*** 0.485*** 0.204* -0.274** 0.157* 0.0504

(0.0975) (0.0995) (0.117) (0.136) (0.0943) (0.116)

Children -0.207** 0.0794 -0.0250 -0.0210 0.00566 0.0229

(0.0949) (0.0989) (0.110) (0.133) (0.0815) (0.117)

Household size 0.159* -0.0715 -0.0628 0.0433 -0.165** -0.149

(0.0922) (0.0987) (0.110) (0.133) (0.0791) (0.114)

ln(household inc.) 0.365*** 0.313*** 0.218*** 0.404*** 0.985*** 1.049***

(0.0307) (0.0265) (0.0412) (0.0394) (0.0376) (0.0407)

Medium educ -0.104** -0.114*** -0.0618 -0.0193 0.176*** 0.187***

(0.0489) (0.0407) (0.0638) (0.0542) (0.0561) (0.0555)

High educ -0.0714 -0.0496 -0.111* -0.108* 0.545*** 0.503***

(0.0503) (0.0457) (0.0671) (0.0584) (0.0579) (0.0612)

Work hours 0.00293** 0.00721*** -0.00189 0.00154

(0.00117) (0.00142) (0.00118) (0.00149)

Commuting time -0.000795 -0.00419***

(0.00100) (0.00114)

2010 -0.0590 -0.0677** -0.198*** -0.236*** -0.167*** -0.148***

(0.0371) (0.0342) (0.0436) (0.0418) (0.0445) (0.0441)

2011 -0.125*** -0.130*** -0.214*** -0.166*** -0.116** -0.0782*

(0.0387) (0.0356) (0.0465) (0.0443) (0.0465) (0.0456)

2012 -0.180*** -0.170*** -0.132*** -0.217*** -0.195*** -0.158***

(0.0383) (0.0354) (0.0464) (0.0442) (0.0467) (0.0466)

2013 -0.191*** -0.151*** -0.178*** -0.274*** -0.177*** -0.199***

(0.0399) (0.0370) (0.0480) (0.0459) (0.0496) (0.0496)

2014 -0.369*** -0.320*** -0.370*** -0.297*** -0.303*** -0.279***

(0.0393) (0.0363) (0.0476) (0.0459) (0.0487) (0.0485)

Variance c

2.941*** 2.125*** 1.811*** 1.544*** 2.090*** 2.055***

(0.0824) (0.0534) (0.0674) (0.0508) (0.0671) (0.0644)

Correlation c

0.844*** 0.198*** 0.869***

(0.0105) (0.0344) (0.0183)

Log likelihood -34,689.217 -24,602.388 -22,522.335

a

The age at wihich the minimum of the quadratic form in age in reached.

Standard errors in parentheses

*** p < 0.01, ** p < 0.05, * p < 0.1

Table 5: Estimation results of the adjusted random effects ordered probit, part 1.

Depend. var. House Health

Men Women Men Women

Age 0.00989 0.0271*** -0.0734*** -0.0743***

(0.00999) (0.00874) (0.00972) (0.00817)

Age2 0.000183* -1.64e-05 0.000440*** 0.000579***

(9.40e-05) (8.78e-05) (9.26e-05) (7.99e-05)

Minimum age

- - 83.409 64.162

Partner 0.311** 0.336*** 0.145 0.403***

(0.130) (0.119) (0.109) (0.120)

Children -0.145 0.284** 0.0942 0.600***

(0.131) (0.114) (0.102) (0.116) Household size 0.107 -0.293*** -0.159 -0.471***

(0.128) (0.113) (0.100) (0.114) ln(household income) 0.346*** 0.315*** 0.422*** 0.416***

(0.0389) (0.0322) (0.0361) (0.0305) Medium educ -0.153** -0.161*** 0.211*** 0.136**

(0.0652) (0.0612) (0.0605) (0.0576)

High educ -0.0274 -0.204*** 0.540*** 0.294***

(0.0696) (0.0656) (0.0590) (0.0592)

2010 -0.198*** -0.165*** -0.0837* -0.154***

(0.0464) (0.0421) (0.0439) (0.0419)

2011 -0.0744 -0.162*** -0.254*** -0.195***

(0.0478) (0.0437) (0.0453) (0.0432)

2012 -0.257*** -0.197*** -0.242*** -0.225***

(0.0487) (0.0450) (0.0465) (0.0447)

2013 -0.209*** -0.183*** -0.205*** -0.225***

(0.0491) (0.0458) (0.0460) (0.0445)

2014 -0.215*** -0.259*** -0.259*** -0.354***

(0.0484) (0.0453) (0.0475) (0.0460)

Variance c

1.949*** 1.977*** 3.098*** 3.339***

(0.0732) (0.0667) (0.0813) (0.0776)

Correlation c

-0.0183 0.130***

(0.0193) (0.0146)

Log likelihood -23,784.491 -21,043.459

a

The age at wihich the minimum of the quadratic form in age in reached.

Standard errors in parentheses

*** p < 0.01, ** p < 0.05, * p < 0.1

Table 6: Estimation results of the adjusted random effects ordered probit, part 2.

Depend. var. Leisure (amount of) Leisure (spending)

Men Women Men Women

Age 0.0459*** 0.0157*** 0.00324 0.0100*

(0.00749) (0.00606) (0.00715) (0.00589)

Age2 -0.000105 0.000123** 0.000199*** 0.000133**

(7.17e-05) (6.12e-05) (6.74e-05) (5.85e-05)

Minimum age

- - - -

Partner 0.269*** 0.349*** 0.417*** 0.0613

(0.0802) (0.0933) (0.0830) (0.0884)

Children -0.180** 0.0702 -0.129 -0.0938

(0.0751) (0.0938) (0.0797) (0.0873) Household size -0.0510 -0.240** -0.0910 -0.0281

(0.0726) (0.0931) (0.0776) (0.0864) ln(household income) -0.0826*** -0.0182 0.125*** 0.0822***

(0.0286) (0.0244) (0.0283) (0.0232) Medium educ -0.0507 -0.130*** -0.131*** -0.182***

(0.0459) (0.0409) (0.0454) (0.0405)

High educ 0.0684 -0.175*** -0.155*** -0.175***

(0.0495) (0.0439) (0.0485) (0.0439) Working -0.998*** -0.606*** -0.255*** -0.194***

(0.0427) (0.0344) (0.0415) (0.0340)

Sport 0.130*** 0.123*** 0.262*** 0.236***

(0.0311) (0.0273) (0.0310) (0.0262)

2010 -0.0363 0.0277 -0.0818** -0.0171

(0.0357) (0.0330) (0.0353) (0.0325)

2011 -0.127*** -0.0574* -0.170*** -0.0869**

(0.0371) (0.0343) (0.0367) (0.0339)

2012 -0.0776** -0.00978 -0.133*** -0.0803**

(0.0373) (0.0344) (0.0367) (0.0339)

2013 -0.116*** -0.0101 -0.243*** -0.166***

(0.0379) (0.0352) (0.0373) (0.0347)

2014 -0.0889** -0.0459 -0.172*** -0.163***

(0.0379) (0.0354) (0.0373) (0.0347)

Variance c

1.589*** 1.331*** 1.684*** 1.348***

(0.0499) (0.0379) (0.0459) (0.0358)

Correlation c

0.426*** 0.453***

(0.0270) (0.0209)

Log likelihood -42,439.95 -41,395.321

a

The age at wihich the minimum of the quadratic form in age in reached.

Standard errors in parentheses

*** p < 0.01, ** p < 0.05, * p < 0.1

Table 7: Estimation results of the adjusted random effects ordered probit, part 3.

that the satisfaction with activities performed at work and in one’s leisure time are second most important for subjective well-being.

Health satisfaction is the fourth most important predictor. A better (subjective) health gives an individual more freedom to do what he or she wants while the opposite will limit an individual in his or her activities. Next are house and environment satisfaction. The Dutch apparently attach more value to the activities they perform than to the place they live.

The large correlation between the individual effects of romantic partners for financial satisfaction can be explained by the fact that the probably most important predictor of financial satisfaction, household income, is the same between partners.

The second highest correlations within the domains are for the levels of leisure satisfaction. This might indicate that couples have a similar idea on how leisure time could be spend best and will spend it similarly as well. For example, an individual that travels a lot to different countries might influence the probability of his or her partner traveling a lot as well, since partners might influence each other’s valuation of the importance of exploring different cultures and environments.

In addition, the fact that more women start working and men take care of the household as well (Centraal Bureau voor de Statistiek, 2014), might result in more equally divided amounts of leisure time between partners and might give them an opportunity to spend more of their leisure time together.

The correlation found for health satisfaction indicates that couples have some similar perception of how good health is defined and of how it can be achieved. But the correlation is not large, probably because of gender differences in life style. The low correlation found for job satisfaction is as expected, since couples generally do not work at the same company. In addition, men and women generally have different types of jobs, where men fulfil more influential positions (Centraal Bureau voor de Statistiek, 2014). The correlation found for house satisfaction is insignificant, which might be the result of different requirements that men and women have related to their residence.

Looking more closely to the models on general satisfaction, it is observed that the correlation between the individual effects of romantic partners is approximately equal for the models without covariates and with demographical variables, while the correlation becomes really small for the model with domain satisfaction levels as covariates. A lot of the correlation between the individual effects related to swb can apparently be explained by the correlations between the levels of satisfaction of partners within different domains, while it is more difficult to explain these correlations based on demographical variables.

Part of the correlation found for financial satisfaction can be explained by demographical variables.

This is as expected since a lot of these variables (children, household size and household income) are the same within a couple. The same arguments hold for the decrements found for health and leisure satisfaction.

It is interesting to see that household income almost always has a positive relation with the different levels of satisfaction. Money does seem to increase the happiness of an individual. The negative relation of household income with satisfaction with the amount of leisure time is obvious since more income generally means more working hours and less leisure time.

The levels of satisfaction are positively related to the number of children in the household for women

and a similar realtionship is found for men for the total number of members in the household. This

rhymes with the assumption that women generally play a larger role in raising the children than

men (Centraal Bureau voor de Statistiek, 2014).

Having a partner generally increases the levels of satisfaction for both men and women, apart from job satisfaction where women are less satisfied when they are involved in a romantic relationship. It might be the case that women tend to take a job they are less satisfied about when their husband could bring in money as well, which is a more traditional setting.

The effects of education differ per domain. For example, the medium educated individuals score the lowest for general and job satisfaction. The highest educated individuals score the best for financial and health satisfaction, which could be expected since they are assumed to have the highest income and have the best knowledge on how to live healthy.

7 Conclusion

This thesis tried to improve the estimation of random effects ordered response models. A standard random effects ordered probit model has been extended in order to allow for correlations between the individual effects of partners. Models with and without covariates have been estimated for the levels of subjective well-being and the domains job, financial, house, health and leisure satisfaction.

The main results of this thesis are: First, correlations between the individual effects of partners have been found. The correlations are large for financial, overall and leisure satisfaction. The correlations are smaller for health and job satisfaction and zero for house satisfaction. The correlations become smaller when demographical variables are added but the essence of the estimations maintains.

Secondly, it is observed that the standard errors of the estimated parameters of the adjusted model are almost everywhere smaller than those of a standard random effects ordered probit model.

Efficiency gains up to 41.4% have been found. It can therefore be concluded that the adjusted model is more efficient than the standard model.

Last, it has been found that financial satisfaction is the most important predictor of subjective well-being. Followed by satisfaction with the way leisure time has been spend and job satisfaction.

Satisfaction with the amount of money one has access to and with the activities performed during the day turn out to be more important than satisfaction with health and home.

The conclusions found in this thesis have different policy implications. Financial satisfaction should be one of the most important targets in new policies. Important factors for financial satisfaction are household income and education level, which should be as large as possible.

In addition, firms should be stimulated to offer jobs that meet the requirements of the Dutch citizens and these citizens should be stimulated to spend their leisure time in the best possible way. Age, household income and workhours are the most important predictors of job satisfaction, while household income, education level, having a job and practicing sports are the most important predictors of satisfaction with the spending of leisure time. Policy goals could be accomplished when a good balance can be found between income levels, workhours, education levels and physical activities.

The research has been done based on a representative sample of the Dutch population. Further research could use data of another country and could even try to compare between different countries.

Another improvement could be made by including more relations into the model. This research only

observed the household head and his or her partner. It might be interesting to look at relations

between parents and their children, between siblings and so on.

8 Acknowledgements

Ik would like to thank J. de Bresser for supervising my thesis. I like to thank CentERdata for making the data available for this thesis.

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