## Bernard van Praag and Ada Ferrer-i-Carbonell

Print publication date: 2004

Print ISBN-13: 9780198286547

Published to Oxford Scholarship Online: January 2005

DOI: 10.1093/0198286546.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2019. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use.  Subscriber: null; date: 09 December 2019

# The Aggregation Of Satisfactions: General Satisfaction As An Aggregate

Chapter:
(p.77) 4 The Aggregation Of Satisfactions: General Satisfaction As An Aggregate
Source:
Happiness Quantified
Publisher:
Oxford University Press
DOI:10.1093/0198286546.003.0004

# Abstract and Keywords

This chapter focuses on the development of the satisfaction aggregation model. Satisfaction with life as a whole or general satisfaction is analysed as a weighted aggregate of the domain satisfactions. It is shown that various domain levels can be distinguished, leading to a two- or three-layer model. The model is applied to job satisfaction for the British data set; the job is broken down into sub-domains such as salary, safety, permanence, etc. The employee then evaluates his/her job based on these. It is argued that various satisfactions can be dealt with as observed numerical variables, which can be used in econometric one- and multiple-equation(s) models.

This chapter is partly based on Van Praag, Frijters, and Ferrer‐i‐Carbonell (2003).

# 4.1. INTRODUCTION

As we pointed out in Chapter 1 we can distinguish various life domains and, on top of that, ‘life as a whole’. We can evaluate our satisfaction with respect to these separate domains in numerical terms; similarly, we can evaluate our satisfaction with ‘life as a whole’. We call the latter concept ‘general satisfaction’, or GS for short. We are aware of the fact that some people will express their doubts as to whether it is possible to evaluate the quality of their ‘life as a whole’. And even if it is thought possible, some may have reservations about the validity of such answers. However, we observe that thousands of respondents apparently have no difficulty in answering such a question, and that those responses seem to be comparable. Hence, we will accept this as empirical evidence that respondents are able to evaluate their life and that those responses lend themselves to scientific analysis.

General satisfaction can be analyzed as a domain satisfaction (DS), as we did in the previous chapter. We shall start by doing that. A second approach is to consider GS as an aggregate of all the DS. If our satisfaction with respect to one domain increases, this should imply that our GS increases as well under ceteris paribus conditions. That means that not only our variable to be explained is a satisfaction but that our explanatory variables are (domain) satisfactions as well. We do not know of this approach in the existing literature. Hence, we are interested not only in the estimated relationship but in the methodology as well.

Moreover, in the British data set there is not only a question on job satisfaction (JS) as such but there are also questions posed with respect to several aspects of the job values; job sub‐domains, so to speak. We may then consider JS itself as an aggregate of satisfaction with respect to those separate sub‐domains. Hence, in this chapter we apply the aggregating approach to JS as an aggregate of various job sub‐domain satisfactions.

(p.78) General satisfaction is obtained from respondents in a similar way to the domain questions. The only difference is that we ask about satisfaction with ‘life as a whole’. The fact that respondents are able to respond to such questions, and that they can evaluate their life on a numerical scale, is evidence for the thesis that such questions may be posed and can be answered by normal individuals. It is obvious that ‘life as a whole’ is a rather vague concept. The longer you think about its meaning, the vaguer it becomes. Respondents may think of their life today, or during the last year, or even their whole life from birth. Unfortunately, this was not made precise in the questionnaires we are studying, and perhaps it is a question which induces ‘too much thinking’, resulting in confusion because respondents are likely to have difficulties in responding.

We shall assume that all respondents understand the same thing by the vague term ‘quality of life’, while acknowledging that this is only true to a certain extent. However, if we are able to explain GS by specific variables, then it is indirect but positive evidence that our assumption is acceptable. If we cannot find a good explanation for GS—however hard we might try—then this still does not mean that respondents give different meanings to the blanket term ‘quality of life’. It would only mean that the phenomenon is not explicable by means of the variables we expected would do this. Then, we are in the same position as for any ordinary regression equation, where the dependent variable y is measurable and interpretable in an unambiguous way, but nevertheless not explicable by the independent variables provided. We shall see that GS is explicable, and hence we will utilize the GS question assuming that it is understood in a similar way by all respondents; for in so far as this is not true, the error term will account for that. If we were to reject this assumption in favor of complete agnosticism, we could not analyze the question at all.

When we look at the GS equation it is again possible to deal with it by means of the four methods which we described in Chapter 2 above. We take the POLS road again for reasons which will soon become clear. The other methods yield almost the same results, except for a multiplication factor. Therefore, we will not vex the reader with multiple presentations that are approximately the same.

# 4.2. THE PREDICTIVE (ORTHODOX) APPROACH

First, we consider an explanation of GS in an orthodox way, where selecting a number of directly and objectively measurable variables which might have explanatory value. It has to be understood that many selections have been tried and that we produce only that choice which seems to be intuitively clear, and statistically significant. However, we also include some variables which are non‐significant, just to let the reader know that they really were non‐significant against our, and probably the reader's, expectations. Moreover, for (p.79) some variables we include average values over the observation period, which enables us to distinguish between level and shock effects. The estimated equation is presented in Tables 4.1 and 4.2, for Germany and the UK respectively. It is in the same spirit as DiTella, MacCulloch, and Oswald (2001), Clark and Oswald (1994), etc.

The time dummies show a remarkable pattern. West German well‐being appears to decline over the period, while East German well‐being appears to rise over the same period. This points to a certain convergence of the two parts of the reunited country. It is seen that household income is an important determinant of GS. The effect of children is ambiguous. The introduction of the interaction term with household income makes the children effect income‐dependent. It follows that the total effect of children is negative for low incomes but positive for high incomes. A possible exception is found for West German workers, where all the children effects do not differ significantly from 0.

The age effect is very pronounced. The individual's satisfaction with life decreases until rather late in life. Although we are no psychologists, it is tempting to interpret the phenomenon. We assume that most people start early in life with a set of expectations which set a norm for a happy life. If those satisfactions are fulfilled one feels happy, and if not one feels disappointed. At the beginning of life, when the horizon widens those expectations will even increase. For most people expectations will define a too high aspiration level and this generates disappointment, but it triggers an adaptation process as well. This yields the behavior in which life satisfaction reaches a minimal level in the fifties and increases from then onwards. The effect of savings is small but significant.

For the UK we find a similar but much stronger age effect. The minimum age is reached much earlier than for Germans; that is, in the early thirties. Surprisingly, the effect of income on life satisfaction is negligible in the UK. The other British results are in line with the German ones. The most striking finding is, however, that most of the variables have a small effect compared to similar effects we found for the domain satisfactions. This may be explained by the fact that although variables may have a sizeable effect on various separate domains, this does not automatically imply a strong effect on the aggregate general satisfaction, because the effects on the domains may be contradictory. It may also be that a variable has a strong effect on only one of the domains and not on any other. Then, the overall effect is weakened because the specific domain is only one of the channels through which general satisfaction is determined. A final point is that some variables which are intuitively important are not included in this specification; for example, individual health. It is difficult to define one variable which characterizes the health of the individual. Some variables like age and income are predictors of health but their predictive value, as we already saw in the previous chapter, is very low. We need a more comprehensive approach, which takes account of the information collected with respect to the domain satisfactions. (p.80)

Table 4.1. Predictive explanation of general satisfaction Germany, 1992–1997, POLS individual random effects

West workers

East workers

West non‐workers

East non‐workers

Estimate

t‐ratio

Estimate

t‐ratio

Estimate

t‐ratio

Estimate

t‐ratio

Constant

3.234

3.750

3.542

2.650

7.579

9.750

13.620

11.150

Dummy for 1992

0.137

9.830

−0.094

−4.240

0.176

9.440

−0.135

−4.250

Dummy for 1993

0.077

5.380

−0.046

−2.090

0.155

8.090

−0.103

−3.490

Dummy for 1994

0.056

3.770

−0.044

−1.940

0.070

3.560

−0.119

−4.050

Dummy for 1995

0.035

2.550

0.011

0.540

0.058

3.140

−0.066

−2.330

Dummy for 1996

0.009

0.550

0.003

0.130

−0.012

−0.540

−0.045

−1.430

Ln(age)

−2.414

−4.930

−2.921

−3.840

−5.179

−12.100

−8.357

−12.580

(Ln(age))2

0.298

4.310

0.363

3.360

0.670

11.390

1.123

12.330

Minimum Age

57.643

56.185

47.724

41.294

Ln(household income)

0.069

3.680

0.172

5.460

0.017

0.670

0.061

1.380

Ln(years education)

−0.034

−0.800

−0.046

−0.670

0.038

0.650

−0.170

−2.070

Ln(children + 1)

−0.100

−0.540

−0.716

−2.360

−0.434

−1.920

−0.718

−1.630

−0.036

−2.000

−0.049

−1.560

−0.031

−1.140

−0.025

−0.490

Ln(working hours)

−0.021

−1.500

−0.062

−2.420

Ln(family income)* Ln (children + 1)

0.012

0.540

0.080

2.150

0.051

1.850

0.103

1.870

Ln(savings)

0.010

4.750

0.021

6.200

0.018

5.990

0.019

3.850

Second earner

−0.028

−1.740

−0.097

−3.520

Gender

0.009

0.530

0.002

0.090

−0.144

−6.280

−0.081

−2.630

Living together

0.101

5.630

0.176

4.880

0.163

8.550

0.101

2.760

Ln(leisure time)

0.005

3.740

0.002

0.760

0.001

0.800

0.000

−0.080

Mean (ln(family income))

0.142

4.580

0.119

2.360

0.239

6.140

0.159

2.460

Mean (ln(ch + 1))

−0.027

−1.010

0.046

1.080

−0.106

−2.740

−0.129

−1.920

0.008

0.260

−0.177

−3.430

−0.116

−2.740

−0.276

−3.760

Mean (ln(savings))

0.037

8.670

0.023

3.450

0.034

6.030

0.037

4.340

Mean (ln(working hours))

−0.019

−2.100

0.008

0.630

Standard deviation of individual random effect ɛn

0.643

0.549

0.735

0.620

% variance due to ɛn

0.510

0.458

0.530

0.450

Number of observations

30,625

12,354

20,909

8,540

Number of individuals

8,150

32,38

6,427

2,695

R2:

Within

0.011

0.021

0.015

0.014

Between

0.060

0.096

0.105

0.169

Overall

0.046

0.067

0.086

0.1157

(p.81) (p.82)

Table 4.2. Predictive explanation of general satisfaction, UK, 1996–1997, POLS individual random effects

Workers

Non‐Workers

Estimate

t‐ratio

Estimate

t‐ratio

Constant

7.740

11.371

6.739

9.784

Dummy for 1996

−0.014

−1.522

0.005

0.373

Dummy for 1997

−0.015

−1.771

−0.018

−1.332

Ln(age)

−4.851

−12.557

−4.409

−12.692

(Ln(age))2

0.685

12.561

0.641

13.481

Minimum Age

34.457

31.210

Ln(household income)

−0.001

−0.096

0.012

0.838

Ln(years education)

−0.071

−4.496

−0.076

−3.243

Ln(children + 1)

−0.111

−2.251

0.060

0.694

Ln(children+1)2

0.017

0.494

0.041

0.853

−0.046

−1.595

−0.081

−1.656

Ln(working hours)

−0.030

−2.597

Ln(family income)* Ln(children + 1)

0.050

1.649

−0.089

−2.322

Ln(savings)

0.010

3.718

0.004

0.664

Second earner

0.012

0.656

Gender

−0.019

−1.403

−0.076

−3.952

Living together

0.140

6.309

0.149

6.142

Ln(leisure time)

−0.014

−0.680

−0.059

−1.272

Mean (ln(household income)

−0.005

−0.259

−0.023

−1.098

Mean (ln(children + 1))

0.030

0.886

−0.092

−1.353

0.044

1.220

0.157

2.775

Mean (ln(savings))

0.012

2.638

0.029

3.387

Mean (ln(working hours))

0.007

0.756

Standard Deviation of individual random effect ɛn

0.471

0.526

% variance due to ɛn

0.507

0.454

Number of observations

17,921

11,985

Number of individuals

7,774

5,784

R2:

Within

0.003

0.001

Between

0.045

0.092

Overall

0.034

0.073

# 4.3. THE AGGREGATING APPROACH

Now we turn to the second approach, which we call the aggregating approach.

As argued in an intuitive manner in the first chapter, we may view life as an aggregate of various life domains. One may evaluate each domain separately and the results are Domain Satisfactions $D S 1 , … , D S k$.

(p.83) Hence, we may assume a model equation of the type:

$Display mathematics$
4.1
.

For instance, we might think of a linear aggregate:

$Display mathematics$
4.2
.

This is precisely what we will do where we operationalize the $D S j$ variables $( j = 1 , … , k )$ by their conditional expectations, as we did for the POLS estimation in Chapter 3. We define:

$Display mathematics$
4.3

We see here the enormous advantage of choosing the POLS approach. We can deal (again) with satisfactions as ordinary variables. If we had stuck with the ordered‐probit approach, it would have been quite problematic as to how to operationalize the explanatory variables in this model. It would involve ($k + 1$)‐dimensional normal orthant probabilities, which do not lend themselves to large‐scale statistical computations as a matter of routine. Another econometric approach would be via ‘simulated‐moments’ methods (see Hajivassiliou and Ruud 1994; Gourieroux and Monfort 1995; Eggink, Hop, and Van Praag, 1994), which are, in practice, also unfeasible at the scale at which we would need them.

Hence, our basic model will be of the type:

$Display mathematics$
4.4

In this equation we explain GS by the domain satisfactions and by a mysterious variable Z, which we shall describe in a moment. We leave the possibility open of including some other variables X. Moreover, we add the averages over the observation periods in order to distinguish between level and shock effects, and we do likewise for the error term by introducing individual random effects.

Let us now explain the Z‐variable. When we considered the DS equations in the previous chapter we observed that the DS could not be fully explained by the observed variables. There may be some psychological traits (e.g. optimism vs. pessimism) that codetermine satisfactions but that cannot be, or at least are not, observed in the present samples. Those omitted variables are part of the regression error term. More specifically, if we assume them to be stable traits over time, they will be part of the individual random effect $ɛ j , n$ (see equation 3.5).

When we consider all DS together, we may assume that they are all influenced by the same psychological traits, albeit to varying extents. But if that is assumed it follows, almost as a matter of course, that the $ɛ j , n$ for different domains, say for j and j, will be correlated. Indeed, after the six German (or the eight British) (p.84) domain equations have been estimated, it is possible to calculate the residuals on the basis of the estimated structural equations. We consider the British case, where we have eight domain equations which are estimated by:

$Display mathematics$
4.5
.

The $γ ̂ j$ stands for the vector of estimated parameters in the jth domain equation, and the vector $X j$ for the selection of explanatory variables for the jth domain. Then, we find the calculated residuals $ɛ ̂ j n t = ɛ ̂ j n + η ̂ j n t ( j = 1 , … , 6 ) .$. Averaging those calculated residuals per individual over time, for individual n and domain j, we find an estimate of the individual effect $ɛ ̂ j n$, because the average of the second term over time tends to 0 per individual. Then, it is possible to estimate the covariance of the fixed effects for two domains as:

$Display mathematics$
4.6
.

We present the $( 8 * 8 )$ variance/correlation matrix for the British married workers. The diagonal cells present the variances and the off‐diagonal cells the correlation coefficients. It is evident that the correlations between the fixed effects are considerable.

If there is a common psychological trait in these fixed effects, this must show up in a common variable that is responsible for the sizeable correlation between the fixed effects.

This component is isolated by application of a principal‐components1 analysis on the fixed‐effect covariance matrix. We do indeed find that the first principal component explains more than 50 percent of the total variance in the error/covariance matrix. Consider for individual n that his individual effect vector $ɛ n = ( ɛ 1 n . , … , ɛ 8 n . )$. Introducing a new coordinate system with the principal components as coordinate axes, we may rewrite each individual effect vector in terms of the new coordinate system as $ɛ n = ( υ 1 n . , … , υ 8 n . )$. Here the number $υ 1 n .$ is the loading with respect to the first principal component, which we identify with the latent psychological trait. This number is denoted as $Z n$. In this way we have succeeded in isolating (part of) the latent psychological trait.

Considering Equation (4.4), we now see that it is very likely that the common psychological trait which codetermines the domain satisfactions DS will affect GS, the evaluation of ‘life as a whole’, as well. For GS too this common trait will be included in the error term. Naive estimation by regression of Equation (4.4) will lead to biased results in this case. We have the situation that econometricians call an endogeneity bias (see Greene 2000).

We speak of an ‘endogeneity bias’ if the error term in the regression equation is correlated with one or more of the explanatory variables in that equation.

(p.85)

Table 4.3. Domain error variance/correlation matrix, British individuals with job and married

Job satisfaction

Housing satisfaction

Financial satisfaction

Health satisfaction

Leisure‐use satisfaction

Leisure‐satisfaction

Social‐life satisfaction

Marriage satisfaction

Job satisfaction

0.625

Financial satisfaction

0.395

0.655

Housing satisfaction

0.279

0.355

0.667

Health satisfaction

0.292

0.357

0.251

0.858

Leisure‐use satisfaction

0.335

0.345

0.290

0.335

0.719

Leisure Amount satisfaction

0.351

0.335

0.263

0.290

0.676

0.742

Social‐Life satisfaction

0.411

0.370

0.313

0.341

0.681

0.609

0.663

Marriage satisfaction

0.226

0.208

0.243

0.200

0.287

0.263

0.328

0.797

(p.86) The fundamental OLS assumption is that there is no correlation and in that case the estimates of the regression coefficients are unbiased. That is, the only reason why the estimate for a specific sample may differ from the population parameter is that the specific sample is not completely representative for the underlying population distribution. This is because the sample is a random selection out of the population. If the sample size tends to infinity, the estimated value will tend to the population value. In the case of endogeneity bias this will not be the case. However, we have now isolated and assessed this common trait as the variable Z. It follows that if we add Z as an additional explanatory variable to the equation we make the omitted variable visible. It is no longer included in the error term and the endogeneity bias is discarded.

In Tables 4.4 and 4.5 we present our estimates of Equation (4.4) for the four German sub‐samples and the two British sub‐samples respectively. For the British, the selection of the various DS differs from the German selection. It is obvious that respondents who are unmarried or do not live with a partner cannot answer the question about marital satisfaction. Therefore, we include a dummy variable for non‐married, which is 0 when the respondent is married or living with a partner, and which equals 1 for a single respondent.

The estimation results are most fascinating. We see that GS can indeed be regarded as an aggregate of all the separate DS. Each domain makes its specific contribution to the aggregate. It is very interesting to see that almost all domain effects are significant. The Z‐variable, which stands for the common omitted trait, is significant only for a few cases. The correlation coefficients are surprisingly high, especially when compared with the traditional explanation, as presented in Table 4.3. Intuitively, this can be explained as follows. There is a two‐layer model, which can be sketched as:

Figure 4.1. The two‐layer model

and is summarized as:

Objective variables $→$ Domain satisfactions $→$ General satisfaction

It is obvious, therefore, that we get a more detailed and more accurate description when we concentrate on the second arrow in the sequence than when we try to cover the two stages in one equation.

(p.87)

Table 4.4. German general satisfaction explained, 1992–1997, POLS individual random effects

West workers

East workers

West non‐workers

East non‐workers

Estimate

t‐ratio

Estimate

t‐ratio

Estimate

t‐ratio

Estimate

t‐ratio

Constant

0.051

4.697

−0.036

−1.950

0.021

1.369

−0.111

−4.798

Dummy for 1992

0.065

5.382

−0.092

−4.991

0.093

5.552

−0.153

−5.810

Dummy for 1993

0.037

3.079

−0.071

−3.841

0.077

4.626

−0.115

−4.443

Dummy for 1994

0.001

0.120

−0.013

−0.709

−0.027

−1.592

−0.138

−5.369

Dummy for 1995

0.015

1.247

0.019

1.028

−0.002

−0.131

−0.071

−2.769

Dummy for 1996

0.002

0.171

−0.004

−0.227

−0.015

−0.959

−0.049

−1.955

Job satisfaction

0.138

23.452

0.145

17.701

Financial satisfaction

0.128

22.669

0.154

18.166

0.125

17.008

0.142

12.681

Housing satisfaction

0.072

11.677

0.077

8.497

0.083

8.994

0.099

7.615

Health satisfaction

0.169

25.419

0.108

10.175

0.245

28.066

0.190

13.441

Leisure satisfaction

0.061

9.937

0.036

3.905

0.076

8.730

0.074

5.909

Environment satisfaction

0.044

7.453

0.044

4.798

0.056

7.074

0.028

2.307

Mean (job satisfaction)

0.063

3.835

0.047

2.167

Mean (financial satisfaction)

0.235

15.593

0.243

10.142

0.380

18.251

0.341

11.499

Mean (house satisfaction)

−0.012

−0.919

−0.042

−2.271

0.003

0.212

−0.032

−1.524

Mean (health satisfaction)

0.088

7.276

0.087

4.789

0.113

8.654

0.057

2.753

Mean (leisure satisfaction)

0.021

0.967

0.036

1.389

−0.017

−1.115

0.112

4.662

Mean (environment satisfaction)

−0.010

−0.706

0.037

1.632

−0.146

−4.463

−0.029

−0.567

First component

−0.070

−1.630

−0.063

−1.038

−0.193

−3.384

−0.076

−0.798

Standard Deviation of individual random effect ɛn

0.362

0.342

0.446

0.430

% variance due to ɛn

0.284

0.279

0.324

0.307

Number of observations

29,636

11,941

20,427

8,335

Number of individuals

7,995

3,157

6,353

2,651

R2:

Within

0.170

0.153

0.137

0.116

Between

0.567

0.519

0.536

0.470

Overall

0.464

0.413

0.464

0.405

(p.88)

Table 4.5. British general satisfaction explained, 1996–1998, POLS individual random effects

Workers

Non‐Workers

Estimate

t‐ratio

Estimate

t‐ratio

Constant

−0.887

−126.015

−0.908

−85.739

Dummy for 1996

−0.001

−0.139

−0.018

−1.498

Dummy for 1997

−0.009

−1.137

−0.012

−1.021

Job Satisfaction

0.067

11.899

Financial Satisfaction

0.075

11.810

0.037

3.864

Housing Satisfaction

0.019

3.447

0.055

6.458

Health Satisfaction

0.066

12.085

0.096

10.132

Leisure‐use Satisfaction

0.103

15.057

0.134

12.589

Leisure‐amount Satisfaction

0.032

4.729

0.057

5.842

Marriage satisfaction

0.054

9.524

0.046

4.141

Social‐life satisfaction

0.086

12.779

0.143

14.135

Mean (job satisfaction)

0.046

3.700

Mean (financial satisfaction)

−0.011

−0.919

0.050

4.013

Mean (housing satisfaction)

0.022

2.621

0.002

0.166

Mean (health satisfaction)

0.035

2.300

0.071

5.603

Mean (leisure‐use satisfaction)

0.007

0.389

0.103

5.698

Mean (leisure‐amount satisfaction)

0.003

0.166

−0.082

−5.225

Mean (marriage satisfaction)

0.017

2.212

0.022

1.600

Mean (social‐life satisfaction)

0.030

2.897

0.044

3.126

First component

−0.019

−0.437

−0.149

−4.917

Dummy for non‐married

−0.024

−2.567

−0.047

−3.955

Standard Deviation of  individual random effect ɛn

0.254

0.254

% variance due to ɛn

0.279

0.203

Number of observations

17,310

11,578

Number of individuals

7,580

5,717

R2:

Within

0.206

0.230

Between

0.555

0.588

Overall

0.478

0.531

It is explicitly observed that it also emerges from these tables that general satisfaction (GS) should not be treated as identical to financial satisfaction (FS). Although this observation looks rather trivial in the present context, we should not forget that in the economic literature as a rule no sharp distinction is made between the two concepts. But now it appears that maximization of FS must lead to different results than maximization of GS.

(p.89) The estimated effects are seemingly much smaller for the British samples than for the German samples. However, we have to realize that the number of explanatory variables is different and that the number of distinct response categories is 11 in the German data set and 7 in that of the UK. Given that we find similar results for each of the six different sub‐samples distinguished, it follows that we have ample evidence that this method can be used and will lead to approximately the same results for any western data sets. Although we do not have evidence for non‐western countries, we conjecture that we will also find the same kinds of results for other populations.

Again, we may distinguish between the shock and the level effects. For instance, for West German workers the shock effect of FS is 0.128, while the level effect is 0.363 (0.128 + 0.235). We present the corresponding level effects in Tables 4.6. and 4.7.

The fact that we find a shock and a level effect indicates that there is a dynamic adaptation process working over time. Hence, the immediate impact of a change in $x t$ is the shock effect and 1/6 of the impact of a change of the average. The ratio $0.128 / 0.363 + 0.235 / ( 6 * 0.363 ) = 0.35 + 0.11 = 0.46$ may be interpreted as the fraction of a change which is immediately absorbed. If the change in $x t$ is permanent, the remaining fraction of 54 percent is absorbed over the remaining five years of the adaptation period. If the change was

Table 4.6. Level effects for the German data set

West German workers

East German workers

West German non‐workers

East German non‐workers

Job Satisfaction

0.202

0.191

Financial Satisfaction

0.363

0.397

0.505

0.483

Housing Satisfaction

0.060

0.035

0.086

0.067

Health Satisfaction

0.257

0.194

0.357

0.246

Leisure Satisfaction

0.082

0.072

0.059

0.186

Environment Satisfaction

0.035

0.081

−0.091

−0.001

Table 4.7. Level effects for the British data set

Workers

Non‐workers

Job Satisfaction

0.112

Financial Satisfaction

0.064

0.087

Housing Satisfaction

0.041

0.057

Health Satisfaction

0.102

0.166

Leisure‐use Satisfaction

0.109

0.237

Leisure‐amount Satisfaction

0.036

−0.025

Marriage satisfaction

0.071

0.068

Social‐life satisfaction

0.116

0.187

(p.90) incidental, in the next five years the effect will be only 11 percent, after which the effect suddenly drops to 0. Similar estimates of the adaptation process can be made for the temporal impact of other variables. We notice that there is not one adaptation process but that the process differs per variable. It is obvious that this modelling of the adaptation process is rather crude. This is because we assumed the Mundlak model, in which unweighted averages over time are used. It would be fascinating to estimate the weights, but this is outside the scope of this chapter. We shall describe a more modest attempt to estimate these ‘memory weights’ in Chapter 7.

From the same tables we can derive the trade‐offs between domains. For, just as we can calculate trade‐off coefficients between objective variables, we can also calculate trade‐off ratios between domains from the estimated GS equation. For example, if we assume that job satisfaction (JS) is reduced by $Δ J S$, by what amount do we have to increase FS in order that GS remains at the same level? For the West German workers this boils down to solving the equation:

$Display mathematics$
4.7
.

This yields:

$Display mathematics$
4.8
.

The trade‐off ratio is (0.202/0.363), which is about 0.55. At first sight we may consider this calculation of trade‐offs between satisfactions as rather esoteric. However, if we realize that FS in its turn depends on income and that an increase in FS may be generated by a specific increase in income, we see that a decrease (or increase ) in JS may be translated into a monetary equivalent. We will make extensive use of those trade‐offs in some of the chapters that follow. In fact, the GS equation makes the various DS that figure in that equation comparable with each other. We see, for example, that we may construct a hierarchy of domains. For West German workers financial satisfaction scores highest, followed by health satisfaction. Then we get job, leisure, and housing satisfaction, in that order. Environment satisfaction scores lowest.

We also see that this hierarchy and even the numerical order of those ratios is rather similar over the German subgroups. For the UK, satisfaction with health scores higher than satisfaction with finance; while satisfaction with social life scores the highest of all for British workers. We remind the reader that a question on satisfaction with social life and one on marriage were not asked in the German survey.

In order to evaluate the status of ‘non‐married’ against the status of being ‘married’2 we compare the addition of non‐married with the addition of a marriage. The level effect of a marriage is 0.071 (see Table 4.7). As the non‐ (p.91) married effect equals $− 0.024$ (see Table 4.5) it follows that the non‐married‐status is equivalent to a marriage that yields a marriage satisfaction of $− ( 0.024 / 0.071 ) = − 0.34$. This is, so to speak, the threshold value for divorce.

# 4.4. A BREAKDOWN OF JOB SATISFACTION

It is evident that the use of the aggregation model discussed above is one example of the breakdown of a satisfaction (in this case general satisfaction) into its constituent satisfaction components. Thus, it creates the possibility of a ‘calculus of satisfactions’.

The same methodology can also be used to break down each of the domain satisfactions. For we can distinguish various aspects of a domain, and we are able to express our satisfaction with respect to those aspects separately. We might call those aspects or sub‐domains.

In the UK data set we find the opportunity to apply the technique to the domain of job satisfaction (JS). The questionnaire contains a question with respect to ‘job satisfaction as a whole’, but alongside it there are satisfaction questions posed with respect to several aspects of the job.3 Again there are 7 satisfaction levels specified. The aspects are: promotion prospects, total pay, relations with supervisor, job security, opportunity to take initiative, satisfaction with the work itself and with the hours worked. We now re‐estimate the regression for JS, where we now specify the equation as an aggregate of those sub‐domain satisfactions as follows:

$Display mathematics$
4.9

We then specify JS sub‐domains analogously to the procedure in Chapter 3. We do the same for self‐employed individuals, where we add a dummy variable for ‘self‐employed’. Note that for a self‐employed worker the relations with the boss and promotion prospects are irrelevant. They are replaced by one dummy variable, which equals 1 when the respondent is self‐employed and is 0 otherwise.

The sub‐domain questions in Table 4.8 are very interesting. We see that the higher the income, the less satisfied workers are with their supervision and with their job security. Age presents the now familiar log‐parabolic pattern. Males are less satisfied than females, and the self‐employed are more satisfied with their situation than employed workers.

The second equation, presented in Table 4.9, shows that it is possible to break down JS in terms of satisfaction levels with respect to its various sub‐domains. The level effects are given in Table 4.10.

We see that the content of the work itself has the greatest weight, followed by pay. The quality of supervision also appears to be quite important. (p.92)

Table 4.8. The seven Job sub‐domain equations, UK, 1996–1997, POLS individual random effects

Satisfaction with promotion

Satisfaction with pay

Satisfaction with supervisor

Satisfaction with job security

Satisfaction with Initiative

Satisfaction with work itself

Satisfaction with hours worked

Estimate

t‐ratio

Estimate

t‐ratio

Estimate

t‐ratio

Estimate

t‐ratio

Estimate

t‐ratio

Estimate

t‐ratio

Estimate

t‐ratio

Constant

7.941

6.296

3.880

3.840

6.559

6.013

6.915

6.670

0.252

0.250

1.949

1.925

3.677

3.707

Dummy for 1996

0.017

1.098

−0.006

−0.413

0.002

0.100

−0.001

−0.066

0.006

0.412

0.016

1.159

0.013

0.981

Ln(working income)

0.060

2.105

0.089

6.530

−0.145

−5.510

−0.032

−2.388

−0.018

−1.340

0.001

0.067

−0.004

−0.310

Ln(age)

−4.524

−6.056

−2.339

−3.946

−3.275

−5.060

−3.651

−6.004

−0.360

−0.609

−1.388

−2.338

−1.630

−2.802

(Ln(age))2

0.660

6.200

0.345

4.104

0.481

5.232

0.512

5.942

0.085

1.012

0.245

2.906

0.249

3.019

Minimum age

30.765

29.730

30.093

35.277

8.369

17.089

26.429

Ln(working hours)

−0.035

−1.043

−0.071

−2.842

−0.073

−2.372

−0.007

−0.287

0.001

0.025

−0.038

−1.515

−0.099

−4.000

Ln(extra hours)

0.035

2.394

0.040

2.976

0.048

3.246

0.016

1.221

0.054

3.998

0.024

1.760

−0.059

−4.386

Work at night

−0.161

−2.165

−0.025

−0.368

−0.091

−1.305

−0.220

−3.239

−0.050

−0.751

−0.237

−3.511

0.003

0.039

Gender (male)

−0.131

−4.801

−0.117

−4.924

−0.045

−1.787

−0.150

−6.198

−0.064

−2.706

−0.124

−5.197

−0.088

−3.792

Self‐employed

0.404

4.758

−0.134

−1.579

0.254

3.002

0.080

0.945

−0.003

−0.037

Ln(years education)

−0.114

−3.403

−0.034

−1.147

−0.042

−1.327

−0.075

−2.473

−0.023

−0.780

−0.003

−0.100

−0.112

−3.816

Mean(Ln work income)

0.006

0.233

0.076

4.645

0.043

1.853

0.018

1.088

0.022

1.369

0.001

0.056

0.011

0.676

Mean(working hours)

−0.093

−2.281

−0.214

−7.318

0.003

0.091

−0.034

−1.142

−0.033

−1.116

−0.007

−0.229

−0.085

−2.921

Mean(overtime)

0.036

1.735

−0.048

−2.575

−0.040

−2.007

0.028

1.486

Standard Deviation of individual random effect ɛn

0.744

0.714

0.647

0.741

0.007

0.397

0.022

1.179

−0.111

−5.944

% variance due to ɛn

0.555

0.521

0.426

0.546

0.706

0.717

0.690

Number of observations

8,784

11,615

10,095

11,522

0.509

0.521

0.501

Number of individuals

5,547

6,972

6,154

6,923

11,629

11,659

11,656

R2:

6,972

6,986

6,985

Within

0.004

0.010

0.002

0.001

0.007

0.006

0.002

Between

0.020

0.048

0.036

0.023

0.042

0.033

0.073

Overall

0.019

0.042

0.028

0.019

0.037

0.028

0.062

(p.93) (p.94)

Table 4.9. Job satisfaction explained by Job sub‐domain satisfactions, UK, 1996–1997, POLS with individual random effects

Estimate

T‐ratio

Constant

−0.201

−17.150

Dummy for 1996

−0.042

−3.142

Satisfaction with promotion

0.128

6.995

Satisfaction with pay

0.098

6.073

Satisfaction with supervisor

0.164

10.389

Satisfaction with job security

0.124

7.557

Satisfaction with initiative

0.017

0.987

Satisfaction with work itself

0.224

13.231

Satisfaction with hours worked

0.119

7.436

Mean(satisfaction with promotion)

0.020

0.638

Mean(satisfaction with pay)

0.081

3.982

Mean(satisfaction with supervisor)

0.007

0.259

Mean(satisfaction with job security)

−0.006

−0.246

Mean(satisfaction with initiative)

0.029

0.930

Mean(satisfaction with work itself)

0.052

1.259

Mean(satisfaction with hours worked)

0.024

1.150

First component

−0.166

−1.902

Self‐employed

0.192

6.029

Standard Deviation of individual  random effect ɛn

0.493

% variance due to ɛn

0.374

Number of observations

9,842

Number of individuals

6,172

R2:

Within

0.242

Between

0.507

Overall

0.482

Table 4.10. Level effects of various job aspects on job satisfaction

Satisfaction with promotion

0.148

Satisfaction with pay

0.179

Satisfaction with supervisor

0.171

Satisfaction with job security

0.118

Satisfaction with initiative

0.046

Satisfaction with work itself

0.276

Satisfaction with hours worked

0.143

# (p.95) 4.5. CONCLUSION

In this chapter we have developed the satisfaction aggregation model. We have shown that we can distinguish various domain levels, which lead to a two‐ or three‐layer model. First, we looked at the level of general satisfaction with ‘life as a whole’. It was shown that we could explain it by the satisfaction levels with respect to the separate domains. In the second half of the chapter we applied the same method to job satisfaction, and were able to explain satisfaction by various sub‐domains or aspects of the job domain. It follows that we could combine the two models, and hence get a three‐layer model.

The most important point of this chapter is that we can deal with the various satisfactions as if they were observed numerical variables, which can be used in econometric one‐ and multiple‐equation(s) models. This opens up new avenues for the ‘econometrics of feelings’.

Clearly, we have to see the present attempt as a first endeavor. There is certainly considerable room for improvement. For instance, the model structure could be further refined with respect to causality. Also, this type of research very much depends on the available data and, because of cautiousness on the part of mainstream economics towards satisfaction issues, there is no rich source of data available yet.

In the following chapters we will use the developed model rather selectively. We will concentrate on specific aspects and equations, basing our material partly on older work.

## Notes:

(1) Unfortunately, it is beyond the scope of this study to explain principal‐components analysis to the reader. For an elementary explanation see Dhrymes (1970).

(2) We do not distinguish between the status of being legally married and any other status of permanent partnership.

(3) Some of the sub‐domain job‐satisfaction questions were not posed after 1997.