The Strength of the Causal Relationship Between Living Conditions and Satisfaction

8/14/2019 The Strength of the Causal Relationship Between Living Conditions and Satisfaction

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The strengthOfThe causal

relationshipbetween living

conditionsAnd

satisfactionBy

Willem E. SarisUniversity of Amsterdam


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Abstract

This paper attempts to explicate the subjective variable satisfaction with life in

general by means of the objective variable income. The reason for this study

is that so far the objective living conditions have been found to have little effect on

the subjective feelings of people. Several different approaches have been used to

estimate the strength of this relationship. First of all, correction for measurement

errors was tried, then an alternative formulation of the relationship was tested

using difference scores instead of the original variables. Next nonlinear

relationships between these variables were introduced. None of these methods led

to any substantial strengthening of the relationship. Finally, a model was tested

controlling for lagged variables and correcting for measurement errors in a panel

design. The combination of these changes led to a considerable effect of the

objective variable on satisfaction all these tests have been conducted on the basis

of a Russian panel study where it was possible to use lagged variables as

suppresser variables and to correct for measurement errors in the different

variables. This paper shows how biased estimates of relationships can be. Only a

specific combination of approaches led to a fundamentally different result.


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The table shows clearly how little the different variables representing aspects ofthe living conditions explain satisfaction with respect to life in general,

satisfaction with their house, satisfaction with the finances and the satisfaction

with social contacts. Only in one case is an explained variance of 20% obtained,

viz. for satisfaction with income in Germany. In all other cases the explained

variance is most of the time considerably lower.

Although there is a very large amount of evidence supporting the hypothesis that

the satisfaction of the individuals is not very strongly affected by the living

conditions, we will nevertheless try once more to proof the opposite.

Table 1 the explained variance obtained for different satisfaction variables using

gender, age, education and income as explanatory variables, in 13 different

language areas (Veenhoven and Saris 1996).________________________________________________________________________________________

Population Life in general House Finances Contact________________________________________________________________________________________

Flanders .02 .04 .06 04

Walonia .03 .03 .06 .03

Brussels .03 .08 .13 .03

Netherlands .01 .03 .10 .00

Germany .09 .05 .20 .15

Norway .05 .03 .10 .03

Sweden .01 .01 .06 .03

Italy .08 .03 .13 .03

Spain .05 .06 .04 .00

Tartars .01 .06 .09 .01

Russia .02 .09 .13 .01

Slovenia .02 .03 .04 .02Hungary .12 .12 .09 .05_______________________________________________________________________________________

Possible reasons for finding a weak relationship could include (Saris and

Stronkhorst (1984) :


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1. Measurement errors. It is possible that the variables contain so much error that

the estimates of the strength of the relationships are considerably attenuated.2. Misspecification of the form of the relationships. We are thinking of two

possibilities. The first is that the relationships are nonlinear rather than linear,

as assumed in equation (1). The second possibility is that a difference equation

should be used instead of the equation with the variables in equation 1.

3. Omitted suppresser variables. The last possibility is that variables are omitted

in the equation which suppresses the relationship. The idea is that the strength

of the relationship should increase if such suppresser variables are included

into the model.

In the next sections we will explore each of these possibilities for the

relationship between income and satisfaction with life in general1. These two

variables have been chosen because it seems rather obvious that a relationship

should exist between them if living conditions do indeed affect the satisfaction of

the people.

The different possibilities will be explored on the basis of a panel study

conducted in Russia. The data have been collected by the Russian research

company CESSI from a multistage probability sample of the Russian population.

The study was begun in 1993 with 4000 households. The second wave was in

1994 and the third in 1995. The panel study still continues but we shall use the

data from the first three waves. Due to wave no response, partial no response andattrition, only 1371 households provided data for all relevant questions for this

study. We will use these 1371 households to estimate the models discussed in this

paper. With respect to the background variables the 1371 households for which

complete data are available do not deviate greatly from the population. The means,

standard deviations and correlation matrices on which the analyses are based are

presented in appendix 1.

1. Correction for measurement error

It is well known that measurement error can considerably attenuate the

relationships between variables (Andrews 1984, Bollen 1989, Saris and Mnnich1995). Therefore the IRMCS group has conducted a study in several European

countries to determine the size of the random and systematic measurement error in

responses to satisfaction questions and to see whether the relationships between

satisfaction and living conditions would be stronger if measurement error were

corrected for. There are two different approaches to correct for measurement error.

1In fact the same analyses could have been performed for satisfaction with finances. We have done

these analyses and the results were comparable with those reported in this paper.


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The first is to use a model with a latent variable for satisfaction and at least two

observed variables for this latent variable. The second approach is to use existingestimates of the measurement error variance to correct for these errors in the

study.

In the first approach two observations of the variable of interest are needed to

estimate the model. The third wave in the Russian panel study fulfilled this

requirement. Therefore we will illustrate this approach using the data of the third

wave.

In this case the first equation remains the same as indicated above but we assume

that the dependent variable is not directly observed. There are, however, two

observed variables which can be seen as indicators for the satisfaction variable of

interest. The relationships between these variables are specified in equation 1a and

1b:

si1 = qi1Si + ei1 (1a)

si2 = qi2Si + ei2 (1b)

Where sij is the jth indicator for the ith satisfaction variable and

eij is the error variable jth indicator for the ith satisfaction variable and

qij is the a measure of the quality of the indicator sij for the variable Si .

In these models the errors are assumed to be mutually uncorrelated and alsouncorrelated with any explanatory variables in the model. If these assumptions are

realistic, an estimate of the effects, corrected for measurement error, of the

independent variables in (1) on the dependent variable Si can be obtained using

programs for structural equation modeling.

On the basis of the Russian data in appendix 1, the procedure was used for the

variable satisfaction with life in general. The result of the analysis was that the

variance explained by the three variables used increase to 4% where previously it

was 2% without correction for measurement error. Although in this case the

correction led to minimal improvement of the explained variance, this is not

necessarily so. It depends on the quality of the indicators (q ij) and, of course, onthe size of the original correlation as well. If the quality is very good the correction

will be very small; if the effect is very small the quality of the measure must be

very bad to have an effect. In this case the quality was .85 which is rather good

and the relationship was rather weak. Therefore the correction was only very

small.

Using the second approach, the correction is very simple because it has been

shown (Saris and Scherpenzeel, 1995) that the R2

could be corrected for random

measurement error (e) as follows:


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Corrected R2 = R2/ qij2 (2)

The quality of the measure (qij) can be obtained from a separate

methodological study using the Multitrait multimethod approach. For details of

this approach we refer to Saris and Mnnich (1995). Table 2 presents the

estimates of the reliability and validity for the same regions mentioned above. The

quality of the measure (qij) can be obtained from this table if one has information

about the exact question , the position of the questions in the questionnaire and the

way the data have been collected. In the Russian panel study, the following

procedure has been used for the satisfaction with life in general: A 5 points scale

was used in face to face research. The position in the questionnaire was between

the 6th

and the 45th

question. The interval between the two measures was more than 5 minutes and

less

than 20 minutes. Using this information the reliability and validity of the measure

can be estimated in the following way:

validity reliability

Mean .940 .911

domain: life in general -.006 -.038

response scale: 5 points -.022 -.026

data collection; face to face +.011 +.012

position: 6-45 +.017 -.001

time between:5-20 +.017 +.063order: first -.015 -.025

country: Russians +.043 +.004

Total .985 .900


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Table 2.

Meta-analysis of life satisfaction data across countries.

Validity Coefficient Reliability Coefficient

Mean = .940 Mean = .911

N Multivariate Multivariate

measures Deviations Deviations

SATISFACTION DOMAIN

Life in general 54 -.006 -.038

House 54 .005 .029

Finances 54 .003 .020

Social contacts 54 . -.001 -.011

RESPONSE SCALE

100 p. number scale 64 -.021 -.027

10 p. number scale 72 .011 .051

5/4 p. category cale 72 -.022 -.026

graphical line scale 8 .058 -.007

DATACOLLECTION

Face-to-face interview 96 .011 .012

Telephone interview 52 .002 -.051

Mail questionnaire 40 -.014 -.011

Tele-interview 28 -.022 .067

POSITION

1 - 5 48 .011 .026

6 - 45 68 .017 -.001

50+ 100 -.017 -.012

TIME BETWEEN REPETITIONS

alone in interview 32 .010 -.071

first/last 5-20 minutes 64 .017 .063

first/last 30- 60 minutes 80 -.021 -.023

middle, 5-20 minutes 16 .043 .028middle, 30-60 minutes 24 -.017 -.016

ORDER OF PRESENTATION

first measurement 60 -.015 -.025

repetition 156 .006 .010

COUNTRY

Slovenia 12 .020 -.013

Germany 16 .007 .028

Catalonia (Spain) 12 -.039 -.022

Italy 12 .013 .043

Flanders (Belg)+ Netherlands 64 -.028 -.039

Wallonia (Belgium) 12 -.026 -.028

Brussels (Belgium) 12 .006 .000

Sweden 12 .023 .099

Hungary 12 .050 .046

Norway 16 -.018 .031

Russians (Russia) 12 .043 .004Tatarians (Russia) 12 .033 .003

Other nationalities in Russia 12 .039 .000


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On the basis of this observation one can calculate as estimated value for the

validity of .985 and for the reliability of .90 for the measure used in this study. Thequality indicator can be shown to be identical to the product of these two

coefficients (Saris and Andrews 1981). Using this approach, we derive that q ij =

.886 which is somewhat higher than the estimate given before. If this estimate is

used to correct for measurement error using equation (2) approximately the same

result will be found as given before.

If such a table as Table 2 is available, the estimates of effects and of explained

variances can be corrected for measurement error. Table 3 presents the explained

variance with and without correction for measurement error using this approach.

Table 3. Explained variance in individual satisfaction by Age, Sex, Education and Income.

Uncorrected- and corrected for measurement error.__________________________________________________________________________________________

Population Life in general House Finances Contact

uncorr corr uncorr corr uncorr corr uncorr corr__________________________________________________________________________________________

Flanders .02 .03 .04 .06 .06 .09 .04 .04

Walonia .03 .05 .03 .04 .06 .09 .03 .03

Brussels .03 .04 .08 .09 .13 .17 .03 .03

Netherlands .01 .02 .03 .05 .10 .14 .00 .00

Germany .09 .10 .05 .05 .20 .21 .15 .15

Norway .05 .07 .03 .04 .10 .13 .03 .04

Sweden .01 .02 .01 .02 .06 .07 .03 .05

Italy .08 .10 .03 .04 .13 .14 .03 .04

Spain .05 .08 .06 .07 .04 .06 .00 .00

Tartars .01 .01 .06 .07 .09 .11 .01 .01

Russia .02 .02 .09 .10 .13 .14 .01 .01

Slovenia .02 .03 .03 .06 .04 .06 .02 .05

Hungary .12 .19 .12 .16 .09 .13 .05 .08__________________________________________________________________________________________

Table 3 shows that for the other regions too the results were not changed greatly

by correcting for measurement error due to the extremely weak relationships and

the relative good quality of the measures of satisfaction with life in general. .

This suggests that measurement error alone cannot be the reason for the weak

relationship. Therefore we have looked for other approaches to strengthen the

relationship between these variables.


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2. Correction for misspecification of the model

As mentioned earlier we have considered two possibilities. The first possibilitywas the specification of nonlinear relationships rather than the linear relationship

in equation (1).

2.1. Nonlinear relationships

There is considerable evidence to suggest that the income satisfaction model (1)

assuming linear and additive effects are too simple. First of all, it has been

suggested by several studies that the satisfaction level depends not only on the

income of the person but rather on deviation of income from peoples income

aspirations (Michalos, 1985). This point has been made most recently by Saris

(1996) who tried to explain why strong relationships between these variables have

been found at the aggregate level and very weak relationships at the micro level.

Secondly, the effect of an increase of income cannot be expected to be the same

for all values of income. The effect of an identical rise in income might be

expected to diminish with higher levels of income is higher (Hamblin 1971). We

suggest therefore that the relationship between income and satisfaction is

nonlinear and not additive. If this relationship is indeed nonlinear, this may be

one of the reasons why the relationship normally found between these two

variables is much weaker than one would otherwise expect.

Therefore we propose that the satisfaction is greater if the ratio between real

income and aspiration level is greater than 1 and less if the ratio is smaller than 1.

In order again to understand how the effect can become smaller for larger valuesof the ratio we adopt the psychophysical model of a power function. We can then

formulate the following relationship:

S = a2(I/As)g

3a

where As is the aspiration level of a person while a2 and g are parameters of the

model..

Further we propose for income that

I = a.Eg11

.Ag12

3b

This relationship suggests that income varies as a multiplicative power function of

education and age. This form of a relationship has been found for several topics

(Hamblin, 1971). This means that the increase in income due to age is greater

depending on ones education level. The coefficients g11 and g12 have been added

in order to allow for unequal effects for different values of the causal variables.


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Further, we expect a persons level of aspiration to be determined by age andeducation in the same way as the income variable itself, thus:

As= a Eg11

.Ag12

3c

Substituting of this equation (3c) in (3a) gives

S = a2(I/ (a. Eg11

.Ag12

))g

3d

All these equations are nonlinear and no additive. However, if we take the log of

both sides of the equations 3b and 3d we get:

y1 = 1 + 11x1 + 12x2 + 1 4a

y2 = 2 + 21y1 - 21x1 - 22x2 + 2 4b

where y1= ln(I); y2 = ln(S); x1 = ln(E) ; x2 = ln(A)

in 4a/b 1 =ln(a1), 11 = g11, 12 = g 2 = ln(a2) 21= g 21=g.g11 22= g.g12

The model specified in 4a and 4b can be estimated using standard estimation

procedures (regression or structural equation modeling). We have used LISREL8

to estimate the parameters of the model. The results are presented in table 4

Table 4 the estimated values of the parameters using model

___________________________________________________________________

Ln(A) Ln(E) Ln(I) R2

Ln (I) -.22 .29 - .18

Ln(S) -.12 -.03 .15 .04

___________________________________________________________________

The 4% explained variance is indeed greater than the explained variance in

the case of a linear additive model which explains only 2% of the variance in life

satisfaction. However the improvement is still very small.There is one rather obvious possible reason for this weak relationship, viz.

measurement error in the measurement of satisfaction. As we have mentioned

above, in the Russian study, satisfaction is asked twice - once at the beginning of

the interview and once at the end. Therefore a model can be specified with a latent

variable and two observed variables. This has been done in this case and the


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parameters of this model which corrects for measurement error are presented in

table 5. The parameters have been estimated with the LISREL procedure2.

Table 5 The parameter estimates for the model specified in equations 4a and 4b,

taking into account correction for measurement error.

______________________________________________________________________________________

Ln(A) Ln(E) Ln(I) Ln(S) R2

y1= Ln (I) -.22 .29 - - .18

y2= Ln(S) -.12 -.02 .20 - .07

y3= Ln(S1) - - - .85

y4= Ln(S2) - - - .85

This result shows that the correction of measurement error enhances the effect of

income on satisfaction as expected. Without correction the effect was .15 whereas

after correction for measurement error the coefficient is .20. The explained

variance is also increased from 4% to 7%. Nevertheless, the change is again not a

dramatic one because the measurement error is relatively small for this satisfaction

variable. This has also been found in previous research (Saris et al. 1996)

2.2.The use of a difference equation

Let us now look at another possibility. In most survey research the hypothesis

is made that a change in one variable will cause a change in another variable. But

in the testing phase this hypothesis is transformed into a hypothesis, where change

in the cause variables is substituted by difference between units on the causal

variable and the change in the dependent variable is substituted by differences

between units on the dependent variable. In the analysis of satisfaction data within

a country, differences in income between individuals substitute for the increase of

income, and differences in satisfaction substitute for changes in satisfaction. It

should be clear that these differences are not the same as the changes in which one

is really interested. For this reason, there is the possibility of reaching a wrongconclusion about the relationship between income and satisfaction at the

individual level for this reason. Normally change data are not available, but the

Russian panel study provides the opportunity to study the effects of change. The

2 In this analysis the correlations of the second table in appendix 1 have been used. The ML

estimator has been used for estimation. The model has 2 degrees of freedom and a chi2 value of .9.

The model thus fits very well. With 21=0 chi2

with df=3 is 228 which means that 21 is really

needed to get an acceptable fit of the model


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next test is then whether the causal relationship between income and satisfaction

is stronger when difference scores are used. This means that we now use theequation:

S = a + b I + u (5)

Where S = St - St-1 and I = It - It-1

For simplicity, we have omitted the variables age and education because these

variables have hardly any effect anyway. If the scores for the two variables inequation (5) are determined on the basis of the Russian panel data in the way

indicated above, we can estimate the effect of the change in income on the change

in satisfaction. It then turns out that the relationship is very weak. The explained

variance is .04. This means only 4% of the variance in the change in satisfaction

can be explained by the change in income.

One of the reasons why this relationship is so weak is again measurement error. In

this case there are good reasons to consider this possibility because the

measurement error of a difference variable is equal to the sum of the error

variance of the original variables. The error variance will therefore normally

increase by a factor 2. However, even taking this fact into account we cannot

expect a strong increase in the strength of the relationship because the relationshipitself is so weak. Therefore we shall not discuss this possibility further.

3. Omitted suppresser variables

There remains only one last possibility for improving the relationship; that is, the

detection of some suppresser variables. Such variables suppress the existing

relationship in the bivariate relationship. This is, for example, the case if the direct

effect between two variables is positive while the suppresser variable causes a

negative spurious relationship between the same variables. In the context of the

relationship between income and satisfaction one can think of suppresser effectsof lagged variables. In this section we shall explore this possibility. Headey and

Wearing (1991) suggested the following equation as the basic model of their

dynamic equilibrium model:

satt = bssM(sat


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events that occur between time t-1 and time t. The model suggests that the

satisfaction level of a person is determined by his /her stock of normalsatisfaction and the flow of recent, new events with which the person is

confronted. Applying this idea in the income domain, we suggest the following

model for the satisfaction with life in general:

St = bssSt-1 + bsi It + st (7)

Where It is, as before, the change in income from t-1 to t or It - It-1 and

st is the disturbance term for the variable S at time t..The idea of this formulation is that satisfaction is strongly determined by

satisfaction at the previous point in time as a result of earlier events and also by

the most important new event of the last year with respect to income, i.e. a change

in income.

Note that this model is equivalent to the previous model (5) using the difference

equation if bss were 1. In that case bringing St-1 to the other side would give

equation (5). In this section we try to avoid the difference score because of the

large measurement errors. This can be done by rewriting equation (7) as follows:

satt = bsssatt-1 + bsi (It - It-1) + st (8)

and consequently

satt = bsssatt-1 + bsi It - bsi It-1 + st (9a)

With respect to income we expect an effect of age and education and also of

income at the previous point in time besides disturbances which can be

considerable in Russia due to the changing political and economic situation. These

ideas lead to equation (9b):

It =bii It-1 + gia A + gie E + It (9b)

Where A stands for Age and E for Education and it is the disturbance in the

income variable at time t.

This very simple theory is represented by the path diagram 1


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A E

i1 I1 I2 I3

+ i2 i3

+ - + - +

s1 S1 S2 S3+ +

s2 s3

Path diagram 1. A simple model for the effect of income on satisfaction in a panel

study for a three wave panel. A + indicates a positive effect and a - a negative

one.

This diagram shows that I1 produces a spurious relationship between income at

time 2 and satisfaction at time 2. A direct, spurious effect is negative and an

indirect (through S1) spurious effect is positive. This suggests the possibility thatthe effect of I2 on S2 could be much larger than the observed correlation which is

normally rather low when the negative spurious relationship is stronger than the

positive relationship. This means that the size of the effect of It on St will depends

on the size of the different coefficients. It is this possibility which will be explored

on the basis of the Russian panel study.

This model can be estimated using standard procedures, but we know already that

the estimates will be attenuated if we are not correcting for measurement error3.

Therefore we would like to introduce this correction immediately into the model.

There are two ways to make these corrections. The first approach is to use the

estimates of data quality obtained above for the measure of satisfaction which was

approximately .85. Using this approach to correct for measurement error only a

minimal improvement in the explained variance is obtained. Furthermore, the

model did not fit the data and several other effects had to be introduced. Because

this did not seem an attractive option a second approach has been used.

3In this case the estimation of the model without correction for measurement error led to a very

bad fit as well, requiring the introduction of many more parameters which are not necessary if the

data are corrected for measurement error.


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3.1 Correction for measurement error in income and satisfaction

In the second approach, a distinction is made between the latent income variables

and observed answers to questions concerning this variable. The difference

between the latent variables and the observed variables is measurement error

again.

With respect to satisfaction there are actually two reasons to expect differences

between the variable of interest and the observed variable. One is again

measurement error and the other is the varying moods of the respondents. When

respondents answer the questions they can be in different moods which may be

short-lived and therefore have no permanent effect on the respondents

satisfaction. This is not the case for specific event such as a marriage, a school

degree etc.

Given these arguments the I and S variables mentioned in the model will be

treated as latent variables while the responses to the questions are used as

observed indicators of these variables. This is done by adding the equations (9c)

and (9d):

st = qstSt + est (9c)

it = qitIt + eIt (9d)

where s and i are the observed variables , est and eIt represent the measurementerrors and qjt are parameters indicating the strength of the relationship between the

latent and the observed variables. The assumption is made that the error terms are

not correlated with each other. This assumption seems reasonable because there is

more than a year between the waves of the panel.

Using the ML estimator of LISREL (Jreskog and Srbom, 1989), the

correlations between these variables could be corrected for measurement error

which generally leads to higher estimates of the correlations ( Bollen 1989, Saris

et al 1996). This correction for measurement error can be carried out separately

from the estimation of the model using the quasi simplex model (Heise, 1971,

Wiley and Wiley 1971) but it is most often done simultaneously with theestimation of the parameters of the structural model. The estimates of the quality

of the measures were respectively qit=.8 for the income variables and qst=.64 for

the life satisfaction variables. In the estimation it was assumed that the

measurement error variances were the same over time.

This result indicates that there is a considerable difference in the strength of the

relationship between the latent and observed life satisfaction variables estimated at

any single point in time (.85) and estimated using panel data over time (.64). The

difference between the two is that, in the latter, the effect of fluctuation of moods


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through time is also included in the error variance, weakening the the relationship

between the latent and the observed variable, whereas in the former case the moodvariables are included in the latent variable. This difference is in itself already

sufficient to produce considerable differences in the substantive results. But in this

case it is also assumed that the income variable contains errors. So far, we have

assumed that these variables are without errors. The combination of these two

changes in the approach has a considerable effect on the correlations between the

variables if we compare the uncorrected and corrected correlations between these

variables. These differences are shown in table 6.

This table shows clearly that all correlations are considerably enhanced by

correction for measurement error in the variables income and satisfaction. Now

the correlation between income and satisfaction at time 1 is .36 while it was .19 at

time 2 it is .32 where it was .18 and at time 3 it is .25 in stead of .12. This

means that the direct effect could be approximately double what it would be

without correcting for errors.

The estimation of the parameters has not been performed in two steps,

estimating first a disattenuated correlation matrix like the one in table 6, and after

that the model of pathdiagram 1. The model was extended with measurement

equation 9c and 9d and estimated in one step using the ML estimator available in

LISREL. We use LISREL for this purpose because we want to take into account

the fact that the income data as well as the satisfaction data contain measurement

error and that the ML estimator has been shown to be robust in the case of non-normal data (Anderson and Amemiya 1988 Satorra 1990)

In the estimation, we assume that all effects of the income variables on the

satisfaction variables are the same except for the sign, as assumed in equation 9a

but we also assume that these effects are the same at different points in time.

Furthermore, more we have assumed that the error variances for the income

variables are the same through time and the same is assumed for the satisfaction

variables. In this way a model with 20 parameters has to be estimated which is

identified. This model fits the data quite well. The chi2 statistic is 14.1 with 13

degrees of freedom. The results of the estimation ar summarized in path diagram2.

In this model, all coefficients are significant at the .05 level except for the effects

of Age and Education on Income at the third point in time.

The most important result is that the direct effect of income on satisfaction at any

point in time is .57. This is a much stronger effect than has ever been reported for

the effect of a living condition variable on a satisfaction variable. This


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standardized effect is also much greater than the correlation between the two

variables, which was around.18.

Table 6 The correlations between the variables corrected (in bold) and uncorrected

for measurement error

I1 I2 I3 S1 S2 S3 A E

I1 1.0

I2 .57 1.0

.88 1.0

I3 .53 .60 1.0

.82 .93 1.0

S1 .19 .18 .14 1.0

.36 .33 .31 1.0

S2 .10 .18 .12 .31 1.0

.21 .32 .29 .75 1.0

S3 .08 .11 .12 .21 .29 1.0

.11 .19 .25 .52 .70 1.0

A -.24 -.32 -.29 -.10 -.10 -.13 1.0

-.30 -.39 -.38 -.17 -.18 -.12 1.0

E .24 ,32 .29 .10 .13 .06 -.39 1.0

.29 .41 .36 .17 .19 .11 -.39 1.0

________________________________________________________________

-.39

A E

-. 21 -.09 -.03 .21 .13 -.03

I1 I2 I3(.88) .82 .93

(.19) (.13)-.20 .57 -.57 .57 -.57 .57

S1 S2 S3(.92) .77 .72

(.36) (.46)

Path diagram 2. The standardized coefficients of the model estimated on the basis

of the data in table 1.The measurement error variance for the income v

variables is .35 and for the satisfaction variables .58.

This result has been obtained as a result of two departures from the commonly

used approaches. The first is that the variables have been corrected for

measurement error and the second is that lagged variables are introduced as


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suppresser variables. They produce a negative, spurious relationship between

income and satisfaction at the same point in time.The effect of the correction for measurement error was shown in table 5. We

will now show the effect of the negative spurious relationship. Path analysis

suggests that the correlation is equal to the sum of the direct effects, indirect

effects, spurious relationship and joint effects. For the correlation between I2 and

S2, ignoring the effect of the exogenous variables Age and education since these

have very small effects, we can write:

effects

direct .57

indirect .00

spurious .82x.57x.77-.82x.57 =- .11

joint effect -.20x.82x.77 = -.12___________________________________ +

correlation .33

This calculation gives a result which is very close to the estimated value of the

correlation between these two variables corrected for measurement error (.32)

For the correlation between the variables I3 and S3 in the same way we get:

effects

direct .57

indirect .00

spurious .93x.57x.72-.93x.57=-.146

joint effects -.23x.93x.72 = -.154

__________________________________ +

correlation .26

This result also agrees closely with the result obtained after correcting for

measurement error, which was .25. These results show that the relatively low

correlation between the income and satisfaction is the sum of a relatively strong,

direct effect of income at the same time and a quite large negative, spurious

relationship of income at the previous point in time, and also the negative joint

effects of income and satisfaction at the previous point in time. This result shows

how strong in this case is the effect of the suppresser variables on the relationship

between income and satisfaction: without introducing this suppresser variable inthe model one cannot detect the strength of this effect.

Given the importance of the Income variable at the previous point in time as

suppresser variable, one might ask whether these variables are really necessary for

the fit of the model to the data. If they were, the obtained result would not be very

important. This is, however, not the case. Omitting I1 and I2 from the explanation

for S2 and S3 increases the chi2 fit statistic with more than 50 points, while one

does not gain any degree of freedom, because in the restricted model these


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parameters were assumed to be equal to other parameters except for the sign. This

result clearly indicates that the model specified is much better than the modelwithout the lagged variables in the equations.

The last results to be presented are the total effects of the different variables on the

satisfaction variables. Table 7 summarizes these results. In this table only the

explanation of the satisfaction variables at time 2 and 3 is discussed because the

explanation at time 1 is not complete due to missing variables.

This table shows that satisfaction at a previous point in time has the greatest effect

on both variables. On the other hand, we also see that the effect of the income

variables is also considerable. The effect of the income variable at the same point

in time is equal to the direct effect (.57) while the income variable at a previous

point in time still has a total effect (direct +indirect effect) of approximately .30,

even though the direct effect is a considerable negative one (-.57). But the indirect

effects are positive and so large that the end result is still a quite strong, positive

total effect. The background variables have only minor effects compared with the

income variables.

Table 3 The total effects of the different variables on satisfaction at time 2

and time 3

Satisfaction Satisfaction

at time 2 at time 3

total effect of

age -.12 -.09

education .14 .07

income at time 1 .33 .20

income at time 2 .57 .36

income at time 3 - .57

satisfaction at time 1 .74 .55

satisfaction at time 2 - .72

________________________________________________

All these results indicate that a living condition (income) has much more effect

than expected on the basis of the results reported so far.

Conclusions

In this paper, the strength of the relationship between variables characterizing the

living condition of people and their life satisfaction has been evaluated. Some

authors predict a strong relationship whereas others predict a weak or no

relationship at all.

We have used a Russian panel study as our basic data source and concentrated

mainly on the impact of income changes on satisfaction with life in general. In the


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original data, the bivariate relationship between income and life satisfaction is just

as weak as in many other countries.We have tried to improve the estimates of the relationship by:

1. correcting for measurement error;

2. introducing of a nonlinear formulation of the relationship;

3. using difference scores instead of the original values; and

4. the introduction suppresser variables into the equation

None of these approaches alone had a substantial effect on the estimates of the

strength of the relationship. However, the combination of lagged income variables

as suppressers and correction for measurement error in both variables using a

simplex design increased the estimates of the effects considerably. If these two

improvements are introduced in the analysis, the formulation of nonlinear

relationships no longer has any effect and has been omitted from the presentation

for that reason.

Normally, the standardized effect of income on satisfaction is at most .2 . In the

model with a suppresser variable and correction for errors in the simplex design,

the standardized effect is increased to .57 with additionally an effect of the lagged

income variable of .30 while the direct effect is -.57. This suggests that income

has much more effect on satisfaction than can be detected in the bivariate

relationships.

Besides the introduction of suppresser variables, correction for measurement

error is very important. In the panel approach, corrections for measurement errorshave been made in both variables ; the income variables as well as the satisfaction

variables. Starting with the income variables, it is normally assumed that these

variables are measured without error. This is not necessarily the case. People do

not always have access to exact information. In our panel study, the strength of the

relationship between the latent and observed income variable turned out to be .8.

This is reasonably high but it still means that 36% of the variance of the observed

variable is measurement error. Correction for these errors had a considerable

effect on the correlations between the variables (see table 6) and therefore also on

the estimates of the strength of the relationship between income and satisfaction..

The difference in the estimation of the error variance at a single time point ,using parallel measures and the error variance obtained in a simplex model, was

also very important. The last error variance is more than twice as much as the first

causing the relationship between the latent and the observed satisfaction variable

in the simplex model to be much weaker (.64) than in the measures at a single

time point (.85). The explanation for this phenomenon is the effect which

fluctuating variables like moods have on the satisfaction measures over time

(Ehrhardt, Saris and Veenhoven 1998). These fluctuating variables are included in

the error term in the panel design analysis whereas they are part of the latent


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variable in the analysis at a single time point. This means that the latent

satisfaction variable in the panel study is not the same as that in the study at asingle time point. In the latter the satisfaction variable includes the mood of a

person while this is not the case in the former. Because of this difference, the

errors also differ and the strength of the effect on income on latent satisfaction

variable can increase. The results show that income has much more effect on the

more stable satisfaction variable than on the satisfaction variable which also takes

into account the fluctuating moods.

Another interesting technical point is that the final model is essentially the

same as the model specifying the difference equation (5). The reason that the same

results were not found with that model is that in that formulation of the model the

errors in the variables ( being differences) are so large that the relationship is

underestimated. In the final model the errors are corrected efficiently and therefore

the strength of the disattenuated relationship could be estimated.

These results bring us to the interesting conclusion that there is more truth in the

idea of the liveability theory. The living conditions turned out to have more effect

on the satisfaction of the people than expected on the basis of the reported studies

on individual data previously quoted. Our analyses clearly show a strong effect of

the income variables on the satisfaction variables.

On the other hand, we have found that in the best fitting model the effects of

income at time t and t-1 are the same except for the sign. This means that the

model is in agreement with equation (5) which suggests that satisfaction at time tis affected by satisfaction at time t-1 and the difference in income between time t-

1 and time t. The best interpretation of the income effect is thus that it is an effect

of the change in income rather than the level of the income. Such an interpretation

accords closely with the dynamic equilibrium model of Heady and Wearing who

suggest that a stock of satisfaction produced by past events cause stability in

satisfaction whereas new events (change in income) cause changes in the

satisfaction. This is indeed exactly the result we have found here.


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Appendix 1 The descriptive statistics form the Russian panel data on which the

analyses are based

1. Descriptive statistics of the original dataVariable Mean Std Dev Min Max N

EDUCW1 3.55 1.68 0 8 3727

T4W1M1 5.02 2.51 1 10 3618

T4W3M1 5.10 2.35 1 10 2253

T4W2M1 5.14 2.33 1 10 2774

T4W3M2 5.20 2 .27 1 10 2261

AGEW1 45.31 16.27 18 93 3727

FAMINCW1 77883.26 87839.79 0 1700000 3208

FAMINCW2 43704.87 224535.95 0 3500000 2398

FAMINCW3 577520.02 516676.18 0 6000000 1948

Correlations:

AGEW1 1.0000

EDUCW1 -.3959 1.0000

FAMINCW1 -.2355 .2354 1.0000

FAMINCW2 -.3124 .3202 .5686 1.0000

FAMINCW3 -.2875 .2882 .5302 .5986 1.0000

T4W1M1 -.1051 .1062 .1896 .1778 .1346 1.0000

T4W2M1 -.0965 .1323 .1014 .1750 .1221 .3111 1.000

T4W3M1 -.1302 .0597 .0739 .1069 .1169 .2116 .2903 1.000

T4W3M2 -.1248 .0841 .1172 .1278 .1696 .2393 .3126 .7488 1.000

2. Descriptive statistics of the log transformed data

Variable Mean Std Dev Min Max N

LNEDUC 1.12 .60 .00 2.08 3722

LNS1 1.43 .67 .00 2.30 3618

LNS3 1.49 .59 .00 2.30 2253

LNS2 1.49 .60 .00 2.30 2774

LNS32 1.52 .55 .00 2.30 2261

LNAGE 3.75 .38 2.89 4.53 3727

LNFI1 10.88 .88 6.86 14.35 3193

LNFI2 12.08 .84 9.08 15.07 2384

LNFI3 12.99 .75 10.24 15.61 1940

Correlation matrix


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LNAGE 1.0000

LNEDUC -.4452 1.0000

LNFI1 -.3181 .3576 1.0000

LNFI2 -.3706 .4090 .6683 1.0000

LNFI3 -.3425 .3820 .5803 .6806 1.0000

LNS1 -.1256 .1231 .2900 .2375 .2109 1.0000

LNS2 -.1218 .1414 .1849 .2405 .1950 .3153 1.000

LNS3 -.1600 .0849 .1095 .1556 .1830 .2224 .2764 1.0000

LNS32 -.1402 .0981 .1532 .1664 .2146 .2552 .3074 .7208 1.0000

Documents

The Strength of the Causal Relationship Between Living Conditions and Satisfaction