2006 Life Satisfaction and Satisfaction in Domains of Life

8/13/2019 2006 Life Satisfaction and Satisfaction in Domains of Life

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MARIANO ROJAS

LIFE SATISFACTION AND SATISFACTION IN DOMAINS

OF LIFE: IS IT A SIMPLE RELATIONSHIP?

(Received 18 August 2005; Accepted 14 April 2006)

ABSTRACT. This paper studies the nature of the relationship between lifesatisfaction and satisfaction in domains of life. The domains-of-life literature

assumes that a persons overall satisfaction with his or her life depends on his

or her satisfaction in many concrete areas of life, which are classified into a

few main domains of life. This paper addresses the issue of what character-

istics the relationship between life satisfaction and satisfaction in domains of

life has by focusing on its specification. The domains-of-life literature has

commonly assumed that an additive relationship between domains satisfac-

tion and life satisfaction does exist. This paper argues that the use of an

additive relationship has substantially restricted our comprehension of therelationship; since it makes impossible to empirically address questions such

as: Is life satisfaction just a weighted average of domain satisfactions? How

easy is it to substitute satisfaction in one domain by satisfaction in another?

Is it reasonable to expect similar additional benefits when we continuously

improve satisfaction in one domain? What happens with our life satisfaction

when we manage to continuously improve satisfaction in all domains? What

happens with the importance of one domain when satisfaction in another

domain declines? The paper argues that there could be substantial gains in

the understanding of the relationship by assuming alternative specifications.

At an empirical level the investigation works with four different specifica-tions: an additive relationship, a semi-logarithm relationship, a loga-

rithmlogarithm relationship, and a constant elasticity of substitution (CES)

relationship. Using a database from Mexico, the investigation finds out that

an additive specification provides at least for Mexico a goodness of fit

similar to those of alternative specifications. However, there are some rele-

vant issues in the relationship between domains satisfaction and overall life

satisfaction that cannot be studied with an additive specification; hence,

the use of an alternative specification in particular a CES specification is

preferable if the objective is to understand rather than to predict lifesatisfaction.

KEY WORDS: domains of life, life satisfaction, Mexico, specification,

subjective well-being

Journal of Happiness Studies (2006) 7:467497 Springer 2006DOI 10.1007/s10902-006-9009-2


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INTRODUCTION

This investigation studies the relationship between overall life

satisfaction and satisfaction in domains of life. There is a gen-

eral consensus on the existence of a relationship between a per-

sons life satisfaction and his or her satisfaction in different

areas of life, which are classified into a few main domains oflife.

This paper studies the nature of the relationship between life

satisfaction and satisfaction in domains of life. The direction

of causality in the relationship has been a subject of debate inthe relevant literature1; however, the nature of the relationship

has not been studied yet. This paper addresses the issue of

what characteristics the relationship has. It is argued that thestudy of the relationship is fundamental for the understanding

of life satisfaction; and it is shown that different specifications

do imply different assumptions on how the relationship works.Researchers have commonly used an additive specification

to study the relationship between life satisfaction and domainssatisfaction. The use of an additive specification could imply asimplification of what is really a complex and rich phenome-

non. With respects to the relationship between life satisfaction

and satisfaction in domains of life it could be that there arenot simple things, only simplified ones, as Bachelard used to

say. It is surprising that such an important issue as the nature

of the relationship between domain satisfaction and life satis-

faction has been completely neglected by the relevant litera-ture. The presumption of an additive relationship needs to be

further studied, and it should be contrasted against richer

specifications. This investigation does not hope to exhaust theissue; on the contrary, it expects to motivate a theoretical dis-

cussion about the nature of the relationship between life satis-

faction and domains satisfaction; it also expects to initiate asequence of empirical research to substantiate this theoretical

discussion.This paper studies the convenience and limitations of using

an additive specification by contrasting it theoretically and

empirically to three different and more flexible specifications:

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A semi-logarithm specification, a logarithmlogarithm (loglog)specification, and a constant elasticity of substitution (CES)

specification.Using a database from Mexico, the investigation finds out

that an additive specification provides at least for Mexico a

goodness of fit similar to those of alternative specifications.

However, there are some relevant issues in the relationship be-

tween domains satisfaction and life satisfaction that cannot bestudied with an additive specification; hence, the use of an alter-

native specification in particular a CES specification is pref-

erable if the objective is to understand rather than to predictlife satisfaction.

THE LITERATURE ON DOMAINS OF LIFE SATISFACTION

The domains-of-life literature states that life can be approached

as a general construct of many specific domains, and that lifesatisfaction can be understood as the result of satisfaction in thedomains of life (Cummins, 1996, 1998, 2003; Headey and Wear-

ing, 1992; Headey et al., 1984; Meadow et al., 1992; Rampichini

and DAndrea, 1998; Salvatore and Mun oz Sastre, 2001; Saris

and Ferligoj, 1996; Sirgy et al., 1995; Veenhoven, 1996) Conse-quently, a relationship between life satisfaction and satisfaction

in domains of life is assumed.

The enumeration and demarcation of the domains of life isarbitrary; it can range from a small number to an almost infinite

recount of all imaginable human activities and spheres of being2.

Thus, there are many possible partitions of a human life, andthe selected partition depends on the researchers objectives.

Nevertheless, any partition must value parsimony the number

of domains must be manageable and domains should refer toclearly separable information3, meaning the domains of life,

as delimited by the researcher, must relate to the way people

think about their lives , and usefulness the delimitation mustcontribute to the understanding of the subject.

On the basis of a meta-study of the literature Cummins (1996)

has argued for a seven-domain partition: material well-being,

LIFE SATISFACTION AND SATISFACTION IN DOMAINS OF LIFE 469


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health, productivity, intimacy, safety, community, and emo-tional well-being. Argyle (2001) mentions domains such as

money, health, work and employment, social relationships, lei-sure, housing, and education. Day (1987) considers 13 areas,among them: family life, working activity, social activity, recre-

ation, personal health, consumption, ownership of durable

commodities and properties, self, spiritual life, and countrys

situation. Flanagan (1978) mentions 15 components, amongthem: economic, physical, and health well-being, having and

raising children, relations with spouse, with relatives and with

friends, community and social activities, political activities, pas-sive and active recreational activities, personal development

activities, and work. Headey and Wearing (1992) use leisure,

marriage, work, standard of living, friendships, sex life, andhealth.

A few investigations have studied satisfaction in all domains

of life (Andrews and Withey, 1976; Campbell, 1981; Campbellet al., 1976; Haavio-Mannila, 1971; Zapf and Glatzer, 1987)

However, most researchers have focused on the study of satis-faction in a few or just one domain of life; for example, job-sat-isfaction studies. The relationship between subjective well-being

and a persons condition in a few domains is also the main re-

search topic of many studies; for example, employment and

happiness (Clark and Oswald, 1994; Di Tella et al., 2001)van Praag et al. (2003) study the relationship of satisfaction

in different domains of life (health, financial situation, job,

housing, leisure, and environment) and satisfaction with life asa whole. They state that satisfaction with life as a whole can

be seen as an aggregate concept, which can be unfolded into its

domain components (p. 3).Most studies have assumed that the relationship between life

satisfaction and domains-of-life satisfaction is additive4. For

example, when Mller and Saris (2001, p. 106) explain theirmethodology to study the relationship between domains of life

and subjective well-being they state that The analyses havebeen done with Lisrel 8 assuming the above-specified relationships

were linear and additive as is normally assumed. In their book,

van Praag and Ferrer-i-Carbonell (2004) also work with an

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additive specification to study the relationship between lifesatisfaction and satisfaction in domains of life. There is little

discussion and less empirical research on the validity of thelinear and additive assumption; as well as on this assumptionsimplications for the nature of the relationship between life satis-

faction and domains-of-life satisfaction5. This paper studies the

implications of using an additive specification to model the rela-

tionship between life satisfaction and domains-of-life satisfac-tion. The implications of the additive specification are

compared to alternative specifications such as a semi-logarithm

specification, a logarithmlogarithm specification, and a con-stant elasticity of substitution specification.

RELATIONSHIP BETWEEN LIFE SATISFACTION

AND DOMAINS-OF-LIFE SATISFACTION

Relevant Features in a Relationship

In general terms, the existence of a relationship between life sat-isfaction and domains-of-life satisfaction can be expressed as:

LS f DSk :k 1; . . .; n 1

where LS refers to life satisfaction, DSk refers to satisfaction in

domain k; k = 1,, n, f refers to the specification used; itdescribes the nature relevant features of the relationship.

This sub-section studies the relevant features in a relationship

between life satisfaction and satisfaction in domains of life,which are implicitly described by specification f. Five features

are considered:

a. Marginal Returns to Domain Satisfaction

This feature describes how a persons life satisfaction changes

when his or her satisfaction in domain i changes. Marginal

returns could be positive, negative, or nil. In the positivecase, life satisfaction increases when domain satisfaction i in-

creases; while in the negative case life satisfaction decreaseswhen domain satisfaction increases. Using Eq. (1), this feature

can be expressed in mathematical terms as the first derivative



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of life satisfaction with respects to domain satisfaction i: fi;where

f 0

i @LS

@DSi

@fDSk :k 1; ::::; n

@DSi

>0 positive

0 null0 increasing

0 constant


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c. Synergy

This feature refers to whether marginal returns to domain satis-

faction i do depend on another domain js current satisfactionlevel. It is of interest to know whether marginal returns to do-main satisfaction i do increase, decrease or remain the same as

satisfaction in domain j increases. It is possible to distinguish

three different kinds of synergies:

Positive synergy: marginal returns to domain i increase as

satisfaction in domain jraises.

Negative synergy: marginal returns to domain i increase assatisfaction in domain jraises.

No synergy: marginal returns to domain i remain constantas satisfaction in domain jraises.

This feature can be expressed in mathematical terms as the

cross-derivative of life satisfaction (equation 1) with respects to

domain satisfaction iand domain satisfaction j: f 00

ij; where:

f 00

ij @2LS

@DSi@DSj

@2fDSk :k 1; ::::; n

@DSi@DSj

>0 positive

0 nosynergy


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Constant global returns to domains satisfaction: life satisfac-tion doubles as satisfaction in all domains of life doubles.

Decreasing global returns to domains satisfaction: life satis-faction less than doubles as satisfaction in all domains of lifedoubles.

This feature can be expressed in mathematical terms as the de-gree of homogeneity of Eq. (1) with respects to satisfaction in

all domains of life: h; where

h @lnfkDSk :

k 1; ::::; n@lnk

>1 increasing

1 constant


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it is impossible to substitute satisfaction in one domain by satis-faction in another; it is then said that there is no substitutability

between domains satisfaction.The MRSij has the disadvantage of being dependant on the

scale used to measure satisfaction. Hence, most researchers opt

for a scale-neutral measure of substitutability, which in the liter-

ature is called as the elasticity of substitution: es; where

es

@ln DSiDSj

@ln MRSij 7

If es is equal to zero then there is no substitution in domains

satisfaction at all. If es is positive then there is an increasingMRSij; while if es is negative then there is a decreasing MRSij.

As es approaches plus or minus infinity then it is said that there

is perfect substitution in domain satisfaction, and the MRSijbe-

comes constant. In general, the degree of substitution is mea-sured by the value of es; the larger its value (in absolute terms),

the easier it is to substitute domains satisfaction.

Alternative Specifications for the Relationship

This investigation considers four alternative specifications for

the relationship between satisfaction in domains of life andlife satisfaction. On the basis of Eq. (1), the four specifications

are

The additive specification:

LS a0Xni1

aiDSi 8

wherea0 and ai(i= 1, . . .;n) are parameters. The semi-logarithm specification:

eLS AYni1

DSaii 9

whereA and ai (i= 1, . . .;n) are parameters. The logarithmlogarithm (loglog) specification:

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LS AYn

i1

DSaii 10

whereA and ai (i= 1, . . .;n) are parameters. The constant elasticity of substitution (CES) specification:

LSXni1

aiDSri

!e=r11

whereai (i= 1, . . .;n),, and r are parameters.

Implications of Alternative Specifications

There are important differences for the nature of the relation-

ship between life satisfaction and satisfaction in domains of lifeamong the four specifications under consideration6.

The Additive Specification

This specification implies:

Constant returns to domain satisfaction. No synergy in domains satisfaction.

Constant global returns to domains satisfaction.

A constant marginal rate of substitution (it is always thesame and independent of domain satisfaction levels).

Perfect substitution between satisfactions in domains of life

(elasticity of substitution approaches infinity).

It is clear that the additive specification is a very restrictive one,

and that it implicitly makes strong assumptions about the rela-tionship between life satisfaction and satisfactions in domains of

life. These assumptions could be correct or not, but the issuecan not be studied with the additive specification. More flexible

specifications are needed.

The Semi-logarithm Specification


Diminishing returns to domain satisfaction. No synergy in domains satisfaction.

Decreasing global returns to domains satisfaction.

An increasing marginal rate of substitution.



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A rigid degree of substitution between domains satisfaction;which is in between no substitution at all and perfect sub-

stitution. The elasticity of substitution is equal to one.

It is observed that the semi-logarithm specification modifies some

assumptions on the relationship between life satisfaction and sat-

isfaction in domains of life with respects to the additive specifica-tion. It could either be a better specification if it really captures

the main features of the relationship or a worse specification.

The LogarithmLogarithm Specification


Flexible returns to domain satisfaction. Returns could beincreasing, diminishing, or constant depending on the value

of the estimated parameters.

Flexible synergy in domains satisfaction. Synergy could be

positive, negative, or nil depending on the value of the esti-mated parameters.

Flexible global returns to domains satisfaction. Globalreturns could be increasing, decreasing, or constant depend-ing on the value of the estimated parameters.

An increasing marginal rate of substitution.

A rigid degree of substitution between domains satisfaction;which is in between no substitution at all and perfect sub-

stitution. Elasticity of substitution is equal to one.

It is observed that the loglog specification is quite flexible with

respects to the behaviour of marginal returns, of synergy be-tween domains, and of global returns. However, it is restrictive

with respects to modelling domains satisfaction substitutability.

The Constant Elasticity of Substitution Specification


Flexible returns to domain satisfaction. Returns could be

increasing, diminishing, or constant depending on the valueof the estimated parameters. Flexible synergy in domains satisfaction. Synergy could be

positive, negative, or nil depending on the value of the esti-

mated parameters.

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Flexible global returns to domains satisfaction. Globalreturns could be increasing, decreasing, or constant depend-

ing on the value of the estimated parameters. Flexible marginal rate of substitution. It could be increasing,

constant or decreasing depending on the value of the esti-

mated parameters.

Flexible degree of substitution between domains satisfaction.

It could range from no substitution at all to perfect substitu-tion, and it depends on the value of the estimated parameters.

It is clear that the CES specification is very flexible and itallows for the study of all features under consideration in this

investigation. Thus, from a theoretical perspective, the CESspecification is preferable because of its capability to capture all

kind of imaginable situations in the relationship between life

satisfaction and satisfaction in domains of life.

THE DATA BASE

Survey and Information

A survey was conducted in five states of central and south Mex-

ico7 as well as in the Federal District (Mexico City) during

October and November of 2001. A stratified-random samplewas balanced by household income, gender and urbanrural

areas; 1535 questionnaires were properly completed. However,

only 579 observations are used in this investigation because of

the need to work with persons who can report a satisfaction inall domains of life, as it will be explained ahead.

The survey gathered information regarding the following

variables:Life Satisfaction: the following question was asked: Taking

everything in your life into consideration, how satisfied with

your life are you? A 7-option answering scale was used. A7-option answering scale was used. The scales answering

options are: extremely unsatisfied, very unsatisfied, unsatisfied,neither satisfied nor unsatisfied, satisfied, very satisfied, extremely

satisfied. Life Satisfaction was handled as a cardinal variable,

with values between 1 and 7; where 1 was assigned to the

lowest level of satisfaction and 7 to the highest8.



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Satisfaction with Concrete Areas of Life: Twenty-four ques-tions were asked to inquire about satisfaction in many aspects

of life, such as: housing conditions, job conditions, job responsi-bilities, working shifts, health, health services, financial sol-vency, income, neighbourhood relations, neighbourhood safety,

trash collection in the neighbourhood, public transport, family

relations, and so on. A 7-option answering scale similar to the

life-satisfaction scale was used.

The Construction of Domains of Life and Domains-of-Life

Satisfaction VariablesThe following methodology was used to construct the domains

of life:

First, most people in the survey could not assess a satisfactionlevel in some concrete areas of life. All these people were short of

information in one or more aspects of life, not because they did

not want to provide an answer, but because they did not functionin those aspects of life. For example, some people could not as-

sess their satisfaction with their job nor with their workingresponsibilities because they were not employed. A similar situa-tion applies to those persons who do not have children, or who

are not married. Because it is convenient to work with compara-

ble people, only those persons who function in all aspects of life

are considered in the investigation9. Thus, the study uses only 579

persons out of the original 1535 who answered the questionnaire.

Second, some aspects of life refer to a similar life-functioning

domain; thus, satisfaction in these facets is highly correlated.Hence, factor analysis was used to reduce the number of dimen-

sions and to demarcate the domains of life. This technique permits

to keep as much information as possible while it avoids the prob-lem of duplication in the use of information. Seven main domains

of life were distinguished on the basis of the factorial analyses:

health: satisfaction with current health and with the avail-

ability and quality of medical services.

economic: satisfaction with housing and living conditions,with incomes purchasing power, and with financial solvency.

job: satisfaction with jobs activity, with jobs responsibilities,with working shifts, and with hierarchical working relationships.

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family: satisfaction with spouse or stable-partner relation-ship, with children relationship, and with rest-of-family rela-

tionship. friendship: satisfaction with friends and with availability of

time to spend with them.

personal: satisfaction with availability of time to pursue per-

sonal hobbies and interests, with recreational activities, and

with personal development; as well as satisfaction with edu-cation and training.

community environment: satisfaction with community services

such as trash collection, public transport, road conditions,public lights, neighbourhood safety and trust in local

authorities; as well as satisfaction with neighbours.

It is obvious that the demarcation of the domains of life is

somewhat determined by the original set of 24 questions.However, given the set of original questions, the factorial analy-

sis allows not only for a reduction of the dimensions, but also

for a good demarcation of the domains on the basis of cluster-ing together those questions with similar information and set-

ting apart those questions with different information10. Hence,

the technique permits to identify groups of questions that pro-vide related information about a persons life; and it allows for

a non-arbitrary demarcation of the domains of life.

Third, once the domains of life were defined, it was practicalto construct a single variable for each domain on the basis of

the group of questions in the domain. A principal-components

technique was used to create the new variable for satisfaction in

each domain, and a regression method was used to calculate thefactor score11. The factor score was rescaled to a 1100 basis to

facilitate its manipulation and interpretation.

SOME DESCRIPTIVE STATISTICS

Correlations Across Domains of LifeTable I shows Pearsons correlations across satisfaction in theseven domains of life. All correlations are positive and some are

relatively high12: economic and job satisfaction show a 0.52

correlation coefficient; economic and personalsatisfaction have a



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0.51 coefficient; while economic and health satisfaction have a0.48 coefficient. Correlations are relatively low for the relation-

ship between the community domain and all the other domains;

as well as for the friendship domain and all the other domains.Positive correlations indicate that satisfactions tend to come

together in all domains. In general, if a person is satisfied in

some domains she is also satisfied in the others; and if she isnot satisfied in some domains she is also not satisfied in the

other domains. However, a positive correlation in domains

satisfaction does not apply to everybody in the survey; it ispossible to find people who are highly satisfied in some domains

and lowly satisfied in others13.

Correlation Between Life Satisfaction and Domains Satisfaction

Table II shows Pearsons correlations for overall life satisfaction

and satisfaction in each domain of life. Life satisfaction is posi-

tively correlated to satisfaction in all domains; however, not allcorrelations are equally important. It is observed that the higher

correlation is between life satisfaction and family satisfaction,

with a coefficient of 0.45. The correlation between life satisfac-

tion and health satisfaction is also very high. Correlationsbetween life satisfaction and economic, job, and personal satis-

faction are also relatively high. The lowest correlation isbetween life satisfaction and community satisfaction, with a

coefficient of only 0.12.

TABLE I

Satisfaction in domains of life

Health Economic Job Family Friendship Personal Community

Pearsons correlations across domains

Health 1.00

Economic 0.408 1.00

Job 0.40 0.52 1.00

Family 0.42 0.38 0.36 1.00

Friendship 0.28 0.26 0.25 0.34 1.00

Personal 0.45 0.51 0.39 0.35 0.35 1.00

Community 0.23 0.27 0.12 0.06 0.17 0.20 1.00

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ESTIMATION OF ALTERNATIVE SPECIFICATIONS

Estimated Coefficients

Equations (8)(11) were estimated using either linear ornon-linear least squares techniques and assuming a random,independently, and identically distributed error. The general

specification is given by Eq. (12):

LSfHea; Eco; Job; Fam; Fri; Per; Com; l 12

where LS is Life satisfaction in a 17 scale, Hea is Health satis-faction in a 1100 scale, Eco is Economic satisfaction in a 1100

scale, Job is Job satisfaction in a 1100 scale, Fam is Family sat-isfaction in a 1100 scale. Fri is Friendship satisfaction in a

1100 scale. Per is Personalsatisfaction in a 1100 scale, Com isCommunity services satisfaction in a 1100 scale, l is error term.

Table III shows the estimated coefficients and their t-tests for

each specification, as well as the goodness of fit coefficient for

each regression (R-squared coefficient).It is observed in Table III that all specifications show a simi-

lar tendency with respects to the importance and statistical sig-nificance of each domains-of-life coefficient. Family satisfactionalways has the highest coefficient; while friendship and commu-nity satisfaction have very low and non-statistically different

than zero coefficients. Coefficients for health, job, family, and

TABLE II

Life satisfaction and domains satisfaction

Domain Correlation

Pearsons correlations

Health 0.44

Economic 0.41

Job 0.40

Family 0.45

Friendship 0.20

Personal 0.40

Community 0.12



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personal satisfaction are always statistically significant at a 10%

degree of significance. Economic satisfaction is statistically sig-nificant in all but the CES specification; in the CES specifica-

tion it is weakly significant (12% degree of significance).

Comparison of Regressions

There are two main considerations when comparing different

specifications. First, a specification is preferred if it fits the ob-served data much better than alternative specifications. In other

words, the specification is superior if it explains much of the vari-

ability in the dependent variable with respects to alternative spec-

ifications. Hence, this consideration focuses on the value of theR-squared coefficient. However, as it is stated by Gujarati (1995,

p. 211) Sometimes researchers play the game of maximizing R2,

that is, choosing the model that gives the highest R2. But thismay be dangerous, for in regression analysis our objective is not

to obtain a high R2 per se... the researcher should be more

TABLE III

Life satisfaction and domains of life satisfaction: alternative specifications*

Additive Semi-loga-

rithm

Loglog CES

Coeff. Prob

> t

Coeff. Prob

> t

Coeff. Prob

> t

Coeff. Asymp.

Prob > t

Constant 2.4430 0.00 )3.664 0.00 )0.280 0.05

a-Health 0.0097 0.00 0.276 0.00 0.061 0.01 0.074 0.07

a-Economic 0.0058 0.03 0.517 0.00 0.102 0.00 0.044 0.12

a-Job 0.0079 0.00 0.243 0.00 0.053 0.01 0.059 0.07

a-Family 0.0151 0.00 0.776 0.00 0.161 0.00 0.107 0.09

a-Friendship )0.0023 0.31 )0.066 0.34 )0.011 0.51 )0.014 0.25

a-Personal 0.0080 0.00 0.449 0.00 0.104 0.00 0.067 0.07

a-Community )0.0002 0.95 )0.022 0.80 )0.002 0.91 0.000 0.50

0.525 0.00r 1.108 0.01

R-squared 0.334 0.308 0.313** 0.334

*The specifications used correspond to Eqs. (8)(11) in the text.

**Because the dependent variable in the loglog specification is not the same as

the dependent variable in the other regressions, the R-squared has been

recalculated in order to make it comparable. See Gujarati (1995), chapter 7.

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concerned about the logical or theoretical relevance of theexplanatory variables to the dependent variable and their statisti-

cal significance. Thus, a second consideration when comparingdifferent specifications says that a specification is preferred if ithas better theoretical support and allows for a richer analysis of

the phenomena, even if there is a minor loss in goodness of fit.

It is observed in Table III that the R-squared coefficient of

the four specifications under consideration is relatively similar.The CES and the additive specifications show slightly higherR-squared coefficients; hence, on the basis of their goodness

of fit it is not possible to assert that there is a superior specifica-tion. In consequence, the comparison among the four specifica-

tions must take into consideration their theoretical support and

capability for potential analyses. In this respect it is clear thatthe CES specification is superior to the additive specification be-

cause of its flexibility and potential to study complex satisfac-

tion issues such as decreasing or increasing returns to domainsatisfaction, satisfaction synergies across domains, non-constant

global returns to domain satisfaction, and domain satisfactionsubstitutability14.

Characteristics of the Relationship

Table IV shows the characteristics of the relationship betweenlife satisfaction and satisfaction in domains of life. These char-

acteristics are assessed for each specification on the basis of the

estimated parameters, which are shown in Table III.

It is important to state that some specifications such as theadditive and the semi-logarithm specifications are very rigid;

and most of their observed characteristics are the result of the

specification itself, rather than of the nature of the relationship.In other words, because of their functional form, the estimated

parameters in an additive and a semi-logarithm specification

can not generate any other characteristic for the relationship be-tween life satisfaction and satisfaction in domains of life. Thus,

it is not worth to comment on the characteristics of the additiveand semi-logarithm specifications except by contrasting them tothe assessed characteristics found in more flexible specifications,

such as the loglog and the CES specifications.



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TABLEIV

Characteristicsoftherelationshipbetweenlifesatisfactionandsatisfactionin

domainsoflife*:

onthebasisofalternativ

especifications**

Characteristics

Additive

Semi-logarithm

Loglog

CES

Returnsto

domain

satisfaction

Positiveor

nilDepending

onthedomain

under

consideration

Positiveornil

Depending

onthedomain

under

consideration

Positiveornil

Dependingonth

e

domainunder

consideration

Positiveornil

Dependingon

thedomainunder

consideration

Marginal

returnsto

domain

satisfaction

[Constant]

[Diminishing]

DiminishingIna

ll

thosedomains

withpositive

returnsConstant

inallother

domains

VaryingInall

thosedomains

withpositive

returnsConstant

inallotherdomains

Synergyin

satisfaction

[None]

[None]

Positiveornil

Dependingonth

e

domainsunder

consideration

Negativeorn

il

Depending

onthedomains

underconside

ration

Global

returnsto

domain

satisfaction

[Constant]

[Decreasing]

Decreasing(0.47)

Decreasing(0.53)

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Marginalrate

ofsubstitutio

n

[Constant]Its

specificvalue

dependsonthe

domainsunder

consideration

[Increasing]Itsvalue

dependsonthe

domainsunder

consideration

[Increasing]Itsspecific

valuedependsonth

e

domainsunder

consideration

DecreasingInallthose

domainswithpo

sitive

returns,itsspeci

fic

valuedependsonthe

domainsunder

consideration

Constantandnil

inallotherdom

ains

Elasticityof

substitution

[Infinity]

[1]

[1]

)9.24***

*Whenthech

aracteristicisinbracketsitmeansthatthespecificationisnotflexibleenoughtoprovideadifferentresult;thus,

thischaracter

isticistheresultofthespecificationitselfandnotoftheobservedbehaviorof

thedata.

**Thesecharacteristicsareassessedon

thebasisoftheestimated

valuesoftheparametersineachspecification,which

are

showninTab

leIII.

***Theelasticityofsubstitutionis)4.2

7whentheCESspecificationisestimatedwithoutth

efriendshipandcommunity

domains;whichshowcoefficientsstatist

icallynondifferentthanzero.Theexclusionofthefriendshipandcommunitydomains

donotaffect

othercharacteristicsoftherelationship.



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Returns to Domain Satisfaction

All specifications show positive or nil returns to domain satis-

faction. Results are consistent along all specifications. Familysatisfaction has the larger coefficient; the coefficients for health,economic, job, and personal satisfaction are also positive; whilecommunity and friendship satisfaction show a nil impact on life

satisfaction.

Behaviour of Marginal Returns to Domain Satisfaction

The loglog specification shows decreasing returns; while the

behavior of returns in the CES specification is more complex,they vary along domain satisfaction levels and they also depend

on satisfaction levels in the other domains of life. It is common

for domains to show increasing returns at low satisfaction levelsand decreasing returns at high domain satisfaction levels15.

The semi-logarithm specification is not flexible enough to

model different marginal returns do domain satisfaction. How-ever, it is clear that the semi-logarithm specification is able to

capture this characteristic of the relationship because it alwaysimplies decreasing marginal returns. On the other hand, theadditive specification leads to an incorrect assessment of the

behaviour of marginal returns to domain satisfaction, since it

always implies constant returns.

Synergy in Domains Satisfaction

The CES specification is the most flexible one with respects to

the study of synergy between domains. The estimated parame-ters for this specification imply that there is negative synergybetween all domains of life; with the exception of those cases

where friendship and community satisfaction are considered

(there is no synergy in these cases). In other words, as satisfac-tion in one domain increases, the marginal impact on life satis-

faction of satisfaction in another domain tends to decline. This

issue is of consequence because it implies that the relative

importance of a domain in increasing life satisfaction is contin-gent on satisfaction levels in other domains. For example, an

increase in economic satisfaction leads to a higher rise in life

satisfaction if a person is unsatisfied in his or her family domainthan if he or she is very satisfied. In other words, attaining

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more economic satisfaction is not as important for a person whois very satisfied in his or her family domain as for a person who

is very unsatisfied in that domain.The finding of negative synergy in domains satisfaction can

be partially explained by the fact that life satisfaction is boun-

ded. If satisfaction in domain i rises then life satisfaction is

approaching its upper limit and it becomes more difficult to ob-

tain additional increases in life satisfaction; thus, the marginalimpact of any increase in domain js satisfaction declines.

The other specifications under consideration are not flexible

enough to model different marginal returns to domain satisfac-tion. The loglog specification shows positive synergy; however,

this specification could imply negative synergy only if some mar-

ginal returns to domain satisfaction are negative. In other words,the loglog specification cannot generate negative synergy and

positive marginal returns simultaneously. The semi-logarithm

and the additive specifications lead to an incorrect assessment ofthe behaviour of synergies in domains satisfaction, since they

implicitly presume the existence of no synergy at all.

Global Returns to Domain Satisfaction

Both the loglog and the CES specifications show relatively

similar decreasing returns to scale. An increase of 10% in

satisfaction in all domains leads to a rise of about 5% in lifesatisfaction. This result is reasonable because life satisfaction is

a bounded variable; it should be more difficult to obtain

additional increases in life satisfaction as it goes up. Thesemi-logarithm specification is able to capture this decreasing-

returns-to-scale feature; however, the additive specification

cannot model this feature of the relationship between life satis-faction and satisfaction in domains of life.

Substitutability in Domains Satisfaction

The CES specification is the only one of the specifications under

consideration that can be used to study the issue of substitut-ability in domains satisfaction. It is found that the marginal

rate of substitution between any two domains of life is decreas-

ing; with the exception of those cases where friendship and com-munity satisfaction are considered (marginal rate of substitution



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is constant in these cases)16. In other words, the relationship be-tween life satisfaction and satisfaction in domains of life is, in

mathematical terms, convex. For example, the required increasein economic satisfaction to compensate for a given decline in job

satisfaction becomes smaller as economic satisfaction rises andjob satisfaction declines. This is a surprising finding, in special

because domains have varying marginal returns. Hence, the

finding emerges because of the existence of negative synergy;which off-sets the impact of varying marginal returns.

None of the other specifications under consideration are flex-

ible enough to study domains satisfaction substitutability. Boththe semi-logarithm and the loglog specifications imply non-

decreasing marginal rates of substitution; with an elasticity of

substitution equal to one. These specifications presume the exis-tence of a concave relationship between life satisfaction and sat-

isfaction in domains of life; this presumption is shown wrong

by the finding of a convex. Also, the additive specifications pre-sumption of an elasticity of substitution equal to infinity is also

shown wrong by the empirical finding.

FINAL CONSIDERATIONS

Because of its flexibility the CES specification can be used to

contrast and to validate the assumptions implicit in other speci-fications, such as the additive, semi-logarithm, and loga-

rithmlogarithm specification. In addition, the CES specification

shows a goodness of fit which is as good as that of the otherspecifications.

On the basis of the estimated parameters from the CES spec-

ification it is possible to conclude that, at least for the database

from Mexico, the relationship between life satisfaction and sat-isfaction in domains of life shows positive and varying marginal

returns to domain satisfaction, negative synergy between do-

mains satisfaction, a decreasing marginal rate of substitution,

and substitutability that leads to a convex relationship.In simple words, the main findings for Mexico imply that:

a. Life satisfaction is not just a weighted average of domain

satisfactions, the relationship happens to be complex. There

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are some domains that in general are much more important

for life satisfaction than others. For working people with

close family (partner and children) satisfaction in the familydomain is crucial for life satisfaction; while satisfaction in

the health, personal and job domains is important. Satisfac-

tion in the economic domain is just relevant. Satisfaction inthe friendship and community domains seems to be irrele-

vant for these people. However, the relative importance of

each domain of life is not independent of what is happeningin the other domains.

b. It is possible but not as easy as the additive specificationpresumes to substitute satisfaction in one domain by satis-

faction in another domain in order to keep life satisfactionconstant. This implies that a person can have a fair life sat-

isfaction if she manages to have high satisfaction levels in

some relevant domains, even if she is very unsatisfied inother domains of life.

c. The additional life satisfaction benefits from increasing sat-

isfaction in all domains tend to decay rapidly. Thus, personswho are very unsatisfied with their life do attain greater in-

creases in life satisfaction than persons who are fairly satis-fied when satisfaction in all domains increases. This is a

reasonable and expected finding because life satisfaction is

bounded.d. The additional life satisfaction benefits from increasing

satisfaction in one domain also tend to decay as domain

satisfaction goes up; however, for low satisfaction levelsthey may show an increasing behavior. This result is also

reasonable because life satisfaction is bounded.

e. The attractiveness of any domain as a source of additionallife satisfaction declines as satisfaction in other domains

increases. Thus, with respects to a person who is very unsat-

isfied in some domains of life, a person who is highly satis-fied in those domains gets less additional life satisfaction

from improvements in the remaining domains.Hence, the additive specification, which is commonly used by

researchers, is a very restrictive. It does provide a simplified

but not a simple analysis of the relationship between life



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satisfaction and satisfaction in domains of life; many features ofthe relationship are lost because of its simplification. It has been

found that if the objective is to predict life satisfaction, theadditive specification performs as good as more flexible ones;however, if the objective is to understand life satisfaction then a

more flexible specification is needed.

The theoretical foundation and empirical implications of

subjective well-being variables being bounded is a theoreticalissue that needs further study. Diminishing marginal returns to

domain satisfaction, negative synergy in domains satisfaction,

and decreasing global returns are more likely to emerge whenthe explained variable is bounded than when it is not.

The paper has not directly addressed the issue of causality. A

topdown versus bottomup discussion is well-placed in the lit-erature. However, the paper raises new challenges for research-

ers in favor of a topdown argument, since they must now

address the issues of why the impact of greater life satisfactionon domains satisfaction is not uniform across domains and why

it works in such an intricate way. It seems more reasonablebut it is definitively not the unique possibility to assume thata bottomup impact exists, that not all domains are equally

important, and that their relationship is complex.

The study of the relationship between life satisfaction and

satisfaction in domains of life has many implications for humanbehaviour that need further research. It is reasonable to assume

that within his or her cognitive and informational limitations a

person is interest in pursuing greater life satisfaction. It is alsosound to believe that a person has some control over resources

that generate domain satisfaction17. Thus, a persons portfolio

of satisfaction in domains of life is partially endogenousthrough his or her allocation of personal resources. In conse-

quence, every person must decide how to allocate his or her

personal resources to attain domain satisfactions that lead togreater life satisfaction. Under these assumptions, a persons

behavior depends on his or her endowment of resources, on themalleability of these resources to generate satisfaction indomains of life, and on the nature of the relationship between

satisfaction in domains of life and life satisfaction. This paper

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has addressed the later issue; further research is needed on theformer issues.

ACKNOWLEDGMENT

The author expresses his gratitude to CONACYT, Mexico for agrant that partially financed this investigation.

NOTES1 There has been some discussion on the causality of the relationship

between satisfaction in domains of life and life satisfaction. Even though

most researchers accept that satisfaction in domains of life contributes to the

explanation of life satisfaction, some researchers have raised questions about

the nature of the causality. They argue for the possibility of a reversed

causality; this is: it could be that satisfaction in domains of life explains life

satisfaction, but it could also be that overall life satisfaction explains a

persons satisfaction in the domains of life. See Argyle (2001) and Diener

(1984). For a discussion on topdown versus bottomup theories of life satis-faction see Headey et al. (1991); Lance et al. (1989); and Scherpenzeel and

Saris (1996). Leonardi et al. (1999) and Fox and Kahneman (1992) propose

a constructionist approach to the issue of causality. The issue of causality

has not yet been settled, and it is unlikely that it can be settled on the basis

of empirical research; since empirical research can only aspire to provide

antecedence tests, but not causality ones.2 As it is stated by Cummins The possible number of domains is large. If

each term describing some aspect of the human condition is regarded as

separate, then their number is very large indeed. (Cummins, 1996, p. 304).3 Cummins (1996) argues that many terms describing some aspects of the

human condition share a great deal of their variance.4 Other studies have approached life satisfaction as an ordinal variable; see

for example van Praag et al. (2003) The use of ordinal techniques such as

ordered-probit techniques is useful because it recognizes the ordinality of life

satisfaction; however, these techniques do not allow for an in depth study of

the characteristics between life satisfaction and satisfaction in domains of

life.5 Campbell et al (1976), in their pioneer study about the quality of life in

the United States, explored the issue of non-additive effects on the relation-ship between domain satisfactions and life satisfaction.6 The following statements will not be proven here. See Beattie and Taylor

(1985) for an in depth study of the relationships characteristics implicit in

each specification.



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7 The states are Oaxaca, Veracruz, Puebla, Tlaxcala and the State of

Mexico. The survey was applied in both rural and urban areas.8

Ferrer-i-Carbonell and Frijters (2004) show that there are no substantialdifferences when satisfaction is treated either as a cardinal or as an ordinal

variable. They state in their conclusions that: We found that assuming

cardinality or ordinality of the answers to general satisfaction questions is

relatively unimportant to results.9 The relationship between subjective well-being and satisfaction in

domains of life is different for people who function in all the domains of life

under consideration and people who are domain-absentee. See Rojas (2005).10 This classification is close to Cummins (1996). The health domain is

considered by Cummins; while the family, job and economic domains closely

resemble Cumminss intimacy, productivity and material domains. The com-

munity environment domain encompasses Cummins safety and community

domains. The friendship domain is not considered by Cummins as a separate

domain.11 The factor score provides a cardinal score that permits to order people

according to their satisfaction in the constituent aspects of any domain of

life.12 Even though correlations are statistically significant, they are not so high

as to state that each domain of life does not provide additional useful

information.13 See Cohen (2000) for an in-depth study of the domains of life correlations

on the basis of Facet Theory and Multiple Discrepancy Theory.14 The simplicity of estimation of the additive specification should not be an

advantage in this age of friendly and powerful statistical software packages.15 Marginal returns are constant in those domains which show nil returns

on life satisfaction.16 The elasticity of substitution is )4.27 when the CES specification is

estimated without the friendship and community domains; which show coeffi-

cients statistically non different than zero. The exclusion of the friendship

and community domains do not affect other characteristics of the relation-ship.17 Diener and Fujita (1995) discuss the existence of personal resources that

can be used to attain greater subjective well-being.

REFERENCES

Andrews, F.M. and S.B. Withey: 1976, Social Indicators of Well-Being

Americans Perceptions of Life Quality (Plenum Press, New York).

Argyle, M.: 2001, The Psychology of Happiness (Routledge).

Beattie, B. and R. Taylor: 1985, The Economics of Production (John Wiley &

Sons).

MARIANO ROJAS494


29/31

Campbell, A.: 1981, The Sense of Well-Being in America (McGraw-Hill, New

York).

Campbell, A., P.E. Converse and W.L. Rogers: 1976, The Quality of AmericanLife: Perceptions, Evaluations, and Satisfactions (Russell Sage Foundation,

New York).

Clark, A.E. and A.J Oswald: 1994, Unhappiness and unemployment, The

Economic Journal 104, pp. 648659.

Cohen, E.H: 2000, A facet theory approach to examining overall and life facet

satisfaction relationships, Social Indicators Research 51, pp. 223237.

Cummins, R.A: 1996, The domains of life satisfaction: An attempt to order

chaos, Social Indicators Research 38, pp. 303332.

Cummins, R.A.: 1998, Directory of Instruments to Measure Quality of Life and

Cognate Areas 4 (School of Psychology, Deakin University, Melbourne).

Cummins, R.A.: 2003, A Model for the Measurement of Subjective Well-Being

through Domains, draft (School of Psychology, Deakin University,

Melbourne).

Day, R.L.: 1987, Relationships between life satisfaction and consumer satis-

faction, in A. Coskun Samli (ed.), Marketing and the Quality of Life

Interface (Quorum Books, New York), .

Di Tella, R., R. MacCulloch and A.J Oswald: 2001, Preferences over inflation

and unemployment: Evidence from surveys of happiness, American Eco-

nomic Review 91, pp. 335341.Diener, E: 1984, Subjective well-Being, Psychological Bulletin 95, pp.

542575.

Diener, E. and F Fujita: 1995, Resources, personal strivings, and subjective

well-being: A nomothetic and idiographic approach, Journal of Personality

and Social Psychology 68(5), pp. 926935.

Ferrer-i-Carbonell, A. and P. Frijters: 2004, How important is methodology

for the estimates of determinants of happiness? The Economic Journal

114(July), pp. 641659.

Flanagan, J: 1978, A research approach to improving our quality of life,

American Psychologist 33, pp. 138147.

Fox, C.R. and D Kahneman: 1992, Correlation, causes and heuristics in

survey of life satisfaction, Social Indicator Research 27, pp. 221234.

Gujarati, D.: 1995, Basic Econometrics (McGraw-Hill).

Haavio-Mannila, E: 1971, Satisfaction with family, work, leisure and life

among men and women, Human Relations 24, pp. 585601.

Headey, B., E. Holmstro m and A.J Wearing: 1984, The impact of life events

and changes in domain satisfactions on well-being, Social Indicators

Research 15, pp. 203227.

Headey, B., R. Veenhoven and A.J Wearing: 1991, Topdown versus bot-tomup theories of subjective well-being, Social Indicators Research 24,

pp. 81100.



30/31

Headey, B. and A. Wearing: 1992, Understanding happiness: A theory of

subjective well-being (Longman Cheshire, Melbourne, Australia).

Lance, C.E., G.J. Lautenschlager, C.E. Sloan and P.E Varca: 1989, A Com-parison between bottomup, topdown, and bidirectional models of rela-

tionships between global and life facet satisfaction, Journal of Personality

57, pp. 601624.

Leonardi, F., C. Gagliardi, F. Marcellini and L Spazzafumo: 1999, The

topdown/bottomup controversy from a constructionist approach: A

method for measuring top-down effects applied to sample of older people,

Social Indicators Research 48, pp. 187216.

Meadow, H.L., J.T. Mentzer, D.R. Rahtz and M.J Sirgy: 1992, A life satis-

faction measure based on judgment theory, Social Indicators Research 26,

pp. 2359.

Mller, V. and W.E Saris: 2001, The relationship between subjective well-

being and domain satisfactions in South Africa, Social Indicators Research

55, pp. 97114.

Praag, B., P. Frijtersvan and A Ferrer-i-Carbonell: 2003, The anatomy

of subjective well-being, Journal of Economic Behavior & Organization 51,

pp. 2949.

Praag, B. and A. Ferrer-i-Carbonell: 2004, Happiness quantified: A satisfaction

calculus approach (xford University Press).

Rampichini, C. and S.S DAndrea: 1998, A hierarchical ordinal probit modelfor the analysis of life satisfaction in Italy, Social Indicators Research 44(1),

pp. 4169.

Rojas, M (2005) Domain-absentee persons and the relationship between life

satisfaction and satisfaction in domains of life, Working paper.

Salvatore, N. and M.T Mun oz Sastre: 2001, Appraisal of ife: Area versus

Dimension conceptualizations, Social Indicators Research 53, pp.

229255.

Saris, W.E. and A. Ferligoj: 1996, Life satisfaction and domain satisfaction in

10 european countries: correlation at the individual level, in W.E. Saris

(ed.), A Comparative Study of Satisfaction with Life in Europe (Eo tvo s

University Press, Hungary), pp. 275280.

Scherpenzeel, A.C. and W.E Saris: 1996, Causal direction in a model of life-

satisfaction: the Top-down/bottom-up controversy, Social Indicators


Sirgy, M.J., D. Cole, R. Kosenko, H.L. Meadow, D. Rahtz, M. Cicic, G. Xi

Jin, D. Yarsuvat, D.L. Blenkhorn and N Nagpal: 1995, A life satisfaction

measure: Additional validational data for the congruity life satisfaction

measure, Social Indicators Research 34, pp. 237259.

Veenhoven, R: 1996, Developments in satisfaction research, Social Indicators


MARIANO ROJAS496


31/31

Zapf, W. and W Glatzer: 1987, German social report: living conditions and

subjective well-being, (19781984), Social Indicators Research 19, pp. 117.

Address for correspondence:

MARIANO ROJAS

Departmento De Economia

Universidad de las Americas

Apdo. 480-UDLA, Santa Catarina Martir

Puebla, 72820

Mexico

E-mail: [email protected]


2006 Life Satisfaction and Satisfaction in Domains of Life

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2006 Life Satisfaction and Satisfaction in Domains of Life