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JOURNAL OF APPLIED ECONOMETRICS
J. Appl. Econ. 26: 549– 579 (2011)
Published online 14 December 2009 in Wiley Online Library
(wileyonlinelibrary.com) DOI: 10.1002/jae.1134
HOW DOES HETEROGENEITY SHAPE THE SOCIOECONOMIC
GRADIENT IN HEALTH SATISFACTION?
ANDREW M. JONESa AND STEFANIE SCHURERb *
a
b
Department of Economics and Related Studies, University of York, York, UK
Melbourne Institute of Applied Economic and Social Research, University of Melbourne, Parkville, Victoria, Australia
SUMMARY
Individual heterogeneity plays a key role in explaining variation in self-reported health and its socioeconomic
gradient. It is hypothesised that the influence of this heterogeneity varies over levels of health and increases
over the life cycle. These hypotheses are tested by applying a threshold-specific alternative to the conditional
fixed-effects logit and longitudinal data from Germany. Our results suggest that income influences health at
the lower end, but not at the higher end of the health distribution, once unobservable factors are controlled
for. The underlying assumptions of the statistical model matter for this conclusion, in particular for the older
age groups. Copyright  2009 John Wiley & Sons, Ltd.
Received 8 October 2007; Revised 19 February 2009
1. INTRODUCTION
We use data of the German Socio-Economic Panel (GSOEP) to explore the socioeconomic gradient
in self-reported health satisfaction. The main focus is on the appropriate choice of an econometric
specification that accommodates omitted variable bias, nonlinearities in the income effect, and
changes in heterogeneity over the life cycle. Three hypotheses are tested: (1) whether the choice
of the statistical model, and its underlying assumptions on the relationship between unobserved
factors and income, matters for the conclusions on the effect of income on health; (2) whether there
are nonlinearities in the effect of income on health, i.e. a stronger effect of income on individuals
in lower health states than on individuals in higher health states; and (3) whether the influence of
unobserved heterogeneity on both income and health increases over the life cycle and, therefore,
whether the potential bias due to omitted variables increases for older age groups.
A controversial question in economic policy is whether it makes sense to redistribute income to
improve population health (Deaton, 2002). The question is strongly disputed, because the direction
of the causal link may run both ways: from childhood health to socioeconomic status (Almond,
2006; Bleakley, 2007; Currie and Stabile, 2006; Behrman and Rosenzweig, 2004; Black et al.,
2007), but also from low socioeconomic status to health (Grossman, 1972; Frijters et al., 2005a;
Duflo, 2000; Lindahl, 2005; Lleras-Muney, 2005).
Judgements about the health–income nexus are further complicated by methodological limitations induced by the data available for assessing the link. Usually, health outcomes are approximated by subjective, i.e. self-assessed, health measures. Even though self-assessed health has
Ł Correspondence to: Stefanie Schurer, Melbourne Institute of Applied Economic and Social Research, The University of
Melbourne, 161 Barry St, Alan Gilbert Building Level 7, Melbourne 3010, VIC, Australia.
E-mail: [email protected]
Copyright  2009 John Wiley & Sons, Ltd.
550
A. M. JONES AND S. SCHURER
been widely accepted as a reliable predictor of morbidity and mortality (Mossey and Shapiro,
1982; Idler and Benyamini, 1997; Mackenbach et al., 2002), the measure is strongly influenced
by individual-specific, and usually unobserved, heterogeneity. On the one hand, individuals with
the same level of objective health may perceive, and thus report, their health differently (Juerges,
2007; Lindeboom and Van Doorslaer, 2004; Maurer et al., 2007). On the other hand, health status,
no matter whether it is measured objectively or subjectively, is largely driven by genetic factors
or personality traits, which are also highly correlated with socioeconomic status. For instance,
Auld and Sidhu (2005) show that both schooling and cognitive ability are strongly associated with
lower health status and that intelligence accounts for about one quarter of the association between
schooling and health. Singh-Manoux et al. (2005) conclude that up to 40% of the relationship
between socioeconomic status and self-rated health can be explained by cognitive ability. Children’s IQ strongly predicts adult socioeconomic outcomes (Jencks et al., 1972, 1979) and 20–40%
of total observed variation in education, occupation, and earnings can be linked to genetic differences in cognitive ability (Gottfredson, 2004). There is also evidence that IQ is generally a very
good predictor of health outcomes (Gottfredson, 1997, 2002; Gottfredson and Deary, 2004) and,
specifically, children’s IQ predicts survival rates in older age (Whalley and Deary, 2001; Betty
and Deary, 2004).
The problem of confounding and the necessity to control for cognitive ability has been widely
acknowledged in the labour economics literature (Blackburn and Neumark, 1995; Card, 1995).
The strong influence of individual-specific and unobserved factors is also widely debated in the
happiness literature (Lykken and Tellegen, 1996), which render the identification of a causal effect
of important micro- and macroeconomic variables on life satisfaction difficult (see Clark et al.,
2008, for an overview of the literature).
Reporting and omitted variable bias suggests the use of panel data methods that allow for a
correlation between unobserved heterogeneity and the regressors of the model. In general, these
are not readily available for nonlinear models, such as binary and ordered-choice models, due
to the incidental parameter problem (Neyman and Scott, 1948). The conditional fixed effects
logit (Chamberlain, 1980) provides consistent parameter estimates, but it incurs a great loss of
information, a reduction in sample size, and marginal effects cannot be easily calculated due to the
lack of information on the distribution of the individual heterogeneity (Wooldridge, 2002). A recent
extension of Chamberlain’s model, the conditional ordered fixed effects logit (Ferrer-i-Carbonell
and Frijters, 2004; Frijters et al., 2004a,b, 2005a), suggests a method to reduce the drastic loss
in the number of observations. Its original formulation, however, is highly computation-intensive
and it cannot identify changes in health and well-being across the full distribution.
Other approaches relax the orthogonality assumption to apply pooled ordered, generalised
ordered (Terza, 1985) or random effects ordered models and their extensions based on the
‘correlated effects’ approach of Mundlak (1978) and Chamberlain (1980). Generalised ordered
probit models relax the single index assumption to control for reporting bias and have been
widely applied in the literature (Kerkhofs and Lindeboom, 1995; Groot, 2000; Sadana et al., 2000;
Shmueli, 2002; Van Doorslaer and Jones, 2003; Hernandez-Quevedo et al., 2008; Contoyannis
et al., 2004; Etilé and Milcent, 2006; Jones et al., 2006; Gannon, 2005; Pudney and Shields,
2000; Boes and Winkelmann, 2006).
Despite their wide application, the threshold-specific parameter estimates obtained from generalised ordered response models are theoretically not identified, without making additional assumptions about parameter values to ensure that the thresholds are ordered consistently (Cunha et al.,
Copyright  2009 John Wiley & Sons, Ltd.
J. Appl. Econ. 26: 549–579 (2011)
DOI: 10.1002/jae
HETEROGENEITY AND HEALTH SATISFACTION
551
2007; Ronning, 1990). In addition, parameter estimates may be biased due to the presence of confounding factors as discussed above. The magnitude of the bias is a matter of empirical evidence,
but it is likely that it is larger for older age groups, assuming that the influence of unobservable factors on both health and socioeconomic outcomes increases over the life cycle. There are
convincing arguments for this assumption.
Health status naturally worsens over the life cycle due to idiosyncratically accumulated health
shocks, either due to accidents or genetic factors (Liang et al., 2005; Frijters et al., 2005b). Scarr
and McCartney (1983) argue that genetic factors become more influential in determining choices,
e.g. those determining socioeconomic status (tertiary schooling, professional training, on-the-job
training) and health behaviours (diet, smoking, exercise) in older age. This has to do with the
fact that, once they leave the nurturing environment of the family and compulsory schooling,
individuals engage in niche-building activities that correlate with their talents, interests, and
personality characteristics. It has also been shown that the influence of genetic factors on variations
in cognitive ability increases over the life cycle (McGue et al., 1993; Plomin, 1986; Plomin and
Petrill, 1997; Bouchard, 1998).
In light of these theoretical and statistical caveats, we take a pragmatic approach to identifying
the effect of income on health. We rely on a large sample drawn from the GSOEP, and proxy
health status with an ordered categorical measure of health satisfaction. For each possible threshold
value, for which health satisfaction can be dichotomised, we estimate a conditional fixed-effects
logit model. This formulation allows for nonlinearities in the effect of income on the underlying
health status. Whether or not nonlinearities are present is then tested by comparing the estimated
coefficients against those obtained from the conditional ordered fixed effects logit (Ferrer-iCarbonell and Frijters, 2004). Whether or not the underlying assumptions of the econometric
model matter for assessing the link between income and health is tested by comparing the marginal
effects against those obtained from pooled ordered and random-effects logits. Finally, whether the
omitted variable bias increases over the life cycle is tested by interacting the effect of income on
health with age-group dummy variables.
The results reveal that income influences health at the lower end of the health distribution, but
not at the higher end, once unobservable factors are controlled for. The underlying assumptions
of the statistical model matter for this conclusion. The income gradient for older age groups is
more sensitive to omitted variable bias than the income gradient for younger ones.
The remainder of the paper is structured as follows. Section 2 outlines the econometric models,
discusses their underlying assumptions and explains the methods to calculate marginal effects.
Section 3 describes the data. Section 4 presents the estimation results and the tests for heterogeneity
in the age-specific income coefficients, the differences in the marginal effects of income across
model assumptions, and the robustness of the marginal effects with respect to their calculation
method. Section 5 discusses the implications of the results.
2. ECONOMETRIC METHODOLOGY
2.1. Model
We specify a reduced-form model for latent health HSŁit , which is the outcome of health-related
choices and individual circumstances:
HSŁit D ˛i C ˇ0 Xit C uit
Copyright  2009 John Wiley & Sons, Ltd.
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J. Appl. Econ. 26: 549–579 (2011)
DOI: 10.1002/jae
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A. M. JONES AND S. SCHURER
where i D 1, . . . , N and t D 1, . . . , Ti (unbalanced panel). ˛i is an intercept term that varies across
individuals and represents in this context cognitive ability, Xit is a vector of exogenous variables
that influence health,
and
uit is an idiosyncratic error term, assumed to be distributed as standard
2
logistic uit ¾  0, 3 . is a monotonically increasing function of the linear index.
Reported health status HSit D j for j 2 f1, . . . , Jg is observed if latent health lies within an
interval between ij1 and ij :
HSit D j if ij1 < HSŁit ij
2
We allow the individual thresholds to differ across individual-specific, but time-invariant
characteristics:
3
ij D ij1 C Qij
where the Qij are individual- and threshold-specific effects and where Qij > 0 8 i.1 The individualspecific threshold values are interpreted as differences in reporting behaviour that are a function of
personality characteristics that influence the perception and assessment of health (e.g. optimism).
These individual effects are assumed to be increasing in categories, which ensures that
ij1 < ij 8 i, j
4
Condition (4) states that our specification respects stochastic monotonicity and is coherent with
the ordering of the categorical outcomes (Cunha et al., 2007, pp. 1290–1291). In contrast to
our formulation, generalised ordered-response models (Terza, 1985; Maddala, 1983), which allow
the thresholds to be a function of observable time-varying characteristics, do not guarantee
that each individual has a coherent ordering of thresholds. Cunha et al. (2007) and Ronning
(1990) have demonstrated that threshold-specific parameter estimates are not identified without
making additional assumptions about parameter values to ensure that the thresholds are ordered
consistently.2
Plugging equation (3) into equation (2) and replacing HSŁit by the linear index of equation (1),
then HSit D j if
ij1 < ˛i C ˇ0 Xit C uit ij
5
By rearrangement, we obtain
ij1 ˛i C ˇ0 Xit < uit ij ˛i C ˇ0 Xit 0
0
6
˛i ij1 ˇ Xit < uit ˛i ij ˇ Xit 7
˛ij1 ˇ0 Xit < uit ˛ij ˇ0 Xit 8
Equation (8) results naturally by rearranging, using equation (3) and defining ˛ij D ˛i ij .
The latter makes clear that we cannot separately identify the individual-specific threshold ij ,
1 As
an example, assume Qij D exp˛ij .
the generalised model is estimated by FIML failure of the identification restrictions will manifest itself as failure to
compute the log-likelihood, as contributions to the log-likelihood involve the log of a negative number (see equation (10)).
In practice, the generalised model is often estimated as separate binary-choice models, in which case the estimated
parameters may not satisfy the coherency conditions.
2 When
Copyright  2009 John Wiley & Sons, Ltd.
J. Appl. Econ. 26: 549–579 (2011)
DOI: 10.1002/jae
HETEROGENEITY AND HEALTH SATISFACTION
553
which is a function of personality traits affecting perception, Qij , from ˛i , which we assumed to
be cognitive ability.
The probability that an individual reports health status HSit D j is
Pitj D PHSit D jj˛ij , Xit D F˛ij ˇ0 Xit F˛ij1 ˇ0 Xit 9
where F D . is the logistic distribution function. The sample log-likelihood function to be
maximised is
ln Lˇ D
Ti N J
ditj ln[˛ij ˇ0 Xit ˛ij1 ˇ0 Xit ]
10
iD1 tD1 jD1
Equation (10) presents a generalisation of ordered response models with individual effects Qij in
the cut-points , but which differ by time-invariant factors only. Each individual shares the same
ordering of health states, i.e. very bad < bad < fair < good < very good, but for each individual
the position of each threshold varies by a person-specific factor Qij . For instance, for optimists,
the threshold may systematically shift to the left, i.e. for a given level of the latent health index
they will tend to report a better level of health satisfaction than less optimistic individuals.
In practice, we estimate this model with a conditional fixed-effects logit (Chamberlain, 1980) for
each of the J 1 threshold values into which the ordered categorical dependent variable of health
satisfaction can be dichotomised. In doing so, we condition out the threshold-specific individual
unobserved heterogeneity (˛ij ).
Applying Chamberlain’s (1980) approach to all possible threshold values yields heterogeneous
parameter vectors for our variables of interest. Evidence of variation in the coefficients over the
categories may be interpreted as evidence of nonlinearity in the latent health index that is not
captured by including logarithmic or polynomial transformation of the regressors X within the
linear index. For instance, with concavity of . in the latent health index, variables such as
income may play a greater role at the bottom of the health distribution than at the top.3
We test for the presence of nonlinearities by comparing our results with those obtained from the
conditional ordered fixed-effects logit (Ferrer-i-Carbonell and Frijters, 2004). The latter assumes
homogeneous coefficients across categories and threshold-independent unobserved heterogeneity
(ˇj D ˇ) and (˛ij D ˛i ).
For estimation of the conditional fixed-effects approach each dependent variable is recoded to
B,j
equal 1 (HSit D 1) if health satisfaction remains below or equal to the threshold j:
B,j
HSit D 1 if HSit j
B,j
HSit D 0 if HSit > j
where j 2 f1, . . . , J 1g and B stands for binary variable.
To eliminate the individual fixed effect from the log-likelihood function, this method takes
advantage of a set of sufficient statistics. We have to find J 1 sufficient statistics j for ˛ij , for
which the distribution of the sample, given j , does not depend on ˛ij :
B,j
B,j
fHSit jXit , ˛ij , j D fHSit jXit , j 3 Our
11
estimation approximates the nonlinearity of . by a step function, with steps at the boundaries of the categories.
Copyright  2009 John Wiley & Sons, Ltd.
J. Appl. Econ. 26: 549–579 (2011)
DOI: 10.1002/jae
554
A. M. JONES AND S. SCHURER
i
B,j
In the case of the logistic regression, Andersen (1970, 1971) shows that TtD1
HSit is a sufficient
statistic for ˛ij and that conditional ML estimates are consistent. We use this result for the J 1
Ti
Ti
B,j
binary equations. Conditioning on
tD1 HSit D
tD1 ditj , i D 1, . . . , Nj , and t D 1, . . . , Ti ,
B,j
where ditj D 1 if HSit D 1 and 0 otherwise, the log-likelihood is in our case
ln L D
J1
ln Lj IHSi1 > j, . . . , IHSiTi > jj
jD1
Nj
J1 jD1 iD1
exp
ln
Ti
B,j
HSit X0it
exp
d2Bij
T
i
IHSit > j D cj D
tD1
ˇj
tD1
Ti
12
ditj X0it ˇj
tD1
where
Bij D
dj D di1j , . . . , diTi j jditj 2 f0, 1g and
Ti
tD1
ditj D
Ti
D
B,j
HSit
D cj
.
tD1
Bij is the set of all possible sequences of 0s and 1s for which the sum of Ti binary outcomes
i
i
B,j
equals TtD1
ditj D cj . Those individuals for whom 0 < TtD1
HSit < Ti does not hold true do
not contribute to the log-likelihood and, therefore, will be dropped from the sample. Hence sample
sizes Nj across the J 1 categories will differ, i.e. NjD1 6D . . . 6D NjDJ1 . In total, there will be
Ti 1 alternative sets Bij . This methods yields J 1 estimated coefficient vectors ˇj .
In contrast, Ferrer-i-Carbonell and Frijters (2004) estimate the coefficient vector ˇ assuming
linearity in the effect of income on true health. Their method collapses the ordered categorical
variable into a binary format using an individual specific threshold ji , rather than one threshold j
applied to the entire sample. To find this individual threshold, the authors maximise a weighted sum
of J 1 log-likelihood functions, similar to Das and Van Soest (1999), subject to the constraint
that the sum of squared weights across all possible threshold values across all individuals must
be equal to the number of individuals in the sample. This constraint means that one can use
only weights wij 2 f0, 1g, and so only one of J 1 log-likelihood functions for each individual
contributes to the total log-likelihood, and all the others will drop out. This log-likelihood function
is the one for which the analytical expected Hessian is minimised.
B,j
In practice, the authors dichotomise their dependent variable into HSit for each possible
threshold value j. In a second step, Chamberlain’s estimator is used choosing one arbitrary
threshold value that equally applies to all individuals: let us say j D 3. The predetermined
B,j
parameter vector Ǒ jD3 along with the realisations of HSit and Xitj for all j 2 1, . . . , J is
used to calculate analytically for each individual, which surpasses the corresponding threshold
j, the expected Hessian. In a third step, the log-likelihood function Lij for which the analytical
expected Hessian is minimised receives the weight wij D 1 and the corresponding threshold value
ji is earmarked. In a last and fourth step the parameter vector of interest is estimated with the
Chamberlain approach, dichotomising the ordered variable according to the individual-specific
threshold ji . As an approximation one can simply use the within-individual mean values of the
Copyright  2009 John Wiley & Sons, Ltd.
J. Appl. Econ. 26: 549–579 (2011)
DOI: 10.1002/jae
HETEROGENEITY AND HEALTH SATISFACTION
555
health status score as the threshold. Using the mean values as cut-off values one loses only those
individuals who never change their health status over time.4
Our model could also be estimated with J 1 random effects logit specifications, but we have
to assume that the threshold-specific unobserved heterogeneity ˛ij is independent of Xit . Whether
this assumption is tenable depends on the context. As argued in the Introduction, there are good
reasons to expect that unobserved factors influence strongly both socioeconomic status and health.
Hence, imposing orthogonality most likely will yield inconsistent parameter estimates. Comparing,
therefore, marginal effects from such a model with marginal effects from the conditional fixedeffects logit is a test for the potential cost of the inappropriate assumption of uncorrelated effects.
A similar case holds for applying a pooled ordered logit model which, besides the orthogonality
assumption, imposes ˇj D ˇ.
2.2. Test for Heterogeneity in Income Coefficients
We test whether nonlinearities in the effect of income on health, which we understand as an
additional form of heterogeneity, can be observed in the data. To do this we test the null hypothesis
that the estimated coefficient vectors across four different models that result from equation (12)
are not statistically different from each other. For the testing, we stack the four datasets and
interact the regressors of the model with each of three dummy variables that take the value 1 if
the observation belongs to sample j 1, and 0 otherwise.
B,j
dj D 1 if HSit D 1 if 0 <
Ti
1 B
HSitj < 1
Ti tD1
13
Then we re-estimate a conditional fixed effect logit model of any change in health satisfaction
(over one particular threshold value j) on the set of interacted regressors for the stacked sample:
0
0
0
0
HSBŁ
it D ˛i C ˇ Xit , ˇ2 d2 Xit , ˇ3 d3 Xit , ˇ4 d4 Xit C uit
14
The null hypothesis is that the coefficient vectors on the interaction terms ˇ2 , ˇ3 , and ˇ4 equal
zero:
15
H 0 : ˇ2 D ˇ 3 D ˇ 4 D 0
For the case the null hypothesis cannot be rejected, we conclude that using a conditional ordered
fixed-effects logit proposed by Ferrer-i-Carbonell and Frijters (2004) is sufficient to account for
heterogeneity in the data.
2.3. Marginal Effects
Marginal effects for the logarithm of net monthly household equivalent income are evaluated for
each age-specific group at the mean value of the independent variables for each group. Computing
4 Many thanks to Paul Frijters for valuable comments, parts of the GAUSS syntax and making us aware of this
simplification that can be implemented easily in STATA. We estimated our models by both the full computation method
in GAUSS and its simplification in STATA. Since results are very similar, we conducted the entire analysis with the
simplified approach.
Copyright  2009 John Wiley & Sons, Ltd.
J. Appl. Econ. 26: 549–579 (2011)
DOI: 10.1002/jae
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A. M. JONES AND S. SCHURER
the marginal effect for the ordered logit is fairly standard (Cameron and Trivedi, 2005, p. 522).
For calculating the marginal effects for the conditional fixed and random effects logits we need
to make an additional assumption on the distribution of the unobserved effect ˛ij . One common
solution is to set its estimate ˛O ij D 0. In this case the marginal effect is calculated by the logit
density function multiplied by the coefficient of interest:
MEj D Ǒ j Xit Ǒ j C ˛O ij 1 Xit Ǒ j C ˛O ij D Ǒ j Xit Ǒ j 1 Xit Ǒ j 16
where j stands for the particular threshold value.
Another solution is to find a valid approximation for ˛O ij . Analytically, the individual fixed effect
is the mean difference between the latent health status and the linear index, evaluated at the mean
value of all regressors. It can be approximated by
B,j
˛O ij ' 1 HSi Xi Ǒ j
17
B,j
where HSi is the sample average of the observed health status variable that results from
dichotomising the ordinal variable at threshold j, Xi is the individual-specific sample average
of each exogenous variable in the model, and 1 is the inverse of the logistic function. Ǒ j is
obtained from a conditional fixed-effects logit estimated for threshold j. Since all individuals for
B,j
whom HSi D 0, 1 do not contribute to the log-likelihood, possible values for 1 . are strictly
bounded.
In light of the hypothesis that there should be an increasing variability in the individual fixed
effect over the life span of an individual, we calculate the average of the individual fixed effect
for each age group k:
N
1 ˛O k D
˛O ij Dk
18
Nk iD1
where Dk is an indicator variable that takes the value 1 if the individual belongs to the particular
age group k, and 0 otherwise. The total number of individuals in each age group is indicated by
Nk , where N is the total sample.
To make the marginal effects calculated from a random-effects logit comparable to those of a
pooled ordered logit, we have to multiply the coefficients ˇ by 1 O (Arulampalam, 1999),
O ˛2j
where O D
.
1 C O ˛2j
3. DATA
We use 22 waves of the GSOEP running from 1984 to 2005.5 As a measure of self-reported health
we use satisfaction with health, as it is available for all years of the sample. Satisfaction with health
5 The data used in this paper were extracted from the SOEP database provided by the DIW Berlin (http://www.diw.de/soep)
using the add-on package PanelWhiz v1.0 (October 2006) for Stata. PanelWhiz was written by Dr John P. HaiskenDeNew ([email protected]). The PanelWhiz generated DO file to retrieve the SOEP data used here and any Panelwhiz
plug-ins are available upon request. Any data or computational errors in this paper are our own. Haisken-DeNew and
Hahn (2006) describe PanelWhiz in detail.
Copyright  2009 John Wiley & Sons, Ltd.
J. Appl. Econ. 26: 549–579 (2011)
DOI: 10.1002/jae
557
HETEROGENEITY AND HEALTH SATISFACTION
Density
.25
0
0
.05
.1
.15
Density
.1
.05
.15
.2
(b)
.2
(a)
.25
is coded from 0 to 10, where 0 means the lowest possible level of self-reported health and 10
means the highest possible level. This measure has been used in the literature to proxy the more
commonly applied measure self-assessed health (e.g. Frijters et al., 2005a). This latter measure
is coded from 1 to 5, where 1 represents bad self-reported health and 5 very good self-reported
health.
Figure 1 displays the distribution of satisfaction with health for both men and women in the
sample. The two distributions are almost identical; they are both skewed to the left, and the most
commonly reported values are 7 and 8.
Figure 2 illustrates the distribution of self-assessed health for both men and women. Again,
both distributions are similar for men and women, skewed to the left, and the most commonly
reported values are 3 and 4 (satisfactory and good health).
To make satisfaction with health (SWH) comparable to self-assessed health (SAH) and our
results manageable, we collapse SWH into a five-point scale. The mapping is undertaken according
to overlaps in the cumulative distribution functions, the cross-tabulations of each category and the
0
1
2
3
4
5
6
7
8
9
10
0
1
Satisfaction with health
2
3
4
5
6
7
8
9
10
Satisfaction with health
Women
Men
(a)
.1
.2
Density
.2
0
0
.1
Density
.3
.3
.4
(b)
.4
Figure 1. Distribution of health measure: satisfaction with health (SWH)
1
2
3
4
5
1
2
3
Selfassessed health
Selfassessed health
Men
Women
4
5
Figure 2. Distribution of health measure: self-assessed health (SAH)
Copyright  2009 John Wiley & Sons, Ltd.
J. Appl. Econ. 26: 549–579 (2011)
DOI: 10.1002/jae
558
A. M. JONES AND S. SCHURER
correlation structure between each sub-category of the two measures. A detailed description of the
recoding is provided upon request. We choose the following recoding:
ž SWH
ž SWH
ž SWH
ž SWH
ž SWH
D 0,
D 3,
D 5,
D 7,
D 9,
1, 2 into SAH D 1 (bad health)
4 into SAH D 2 (poor health)
6 into SAH D 3 (satisfactory health)
8 into SAH D 4 (good health)
10 into SAH D 5 (very good health)
The main focus of this paper is the impact of socioeconomic status on health satisfaction and,
in particular, the role of household income. Another proxy for socioeconomic status is education;
however, this measure shows little variation over the years. The chosen econometric framework
of conditional fixed-effects logits requires variables that vary over time. Equivalent income is
constructed by dividing net monthly household income by the square root of the number of
household members.6
We refrain from using relative income, which has been emphasised in the happiness literature.
Recent evidence has shown that relative income has little effect on self-reported health (Jones
and Wildman, 2008; Gravelle and Sutton, 2003, 2009; Lorgelly and Lindley, 2008; Miller and
Paxson, 2006). Some of the arguments against relative income are that it may have a delayed
effect of 15 years or more (Subramanian and Kawachi, 2004) and the difficulties in identifying
the appropriate peer group.
The income variable is interacted with six age-group dummy variables to obtain a vector of six
different income coefficients. Age groups are defined from 16 to 30, 31 to 40, 41 to 50, 51 to
60, 61 to 70 and 71 and older. These age groups are also required to test the hypothesis that the
omitted variable bias should become more prominent for older individuals.
In addition, we control for the total number of years of schooling, immigrant and marital status,
the number of household members, geographical location (East versus West Germany, and the
Bundeslaender), employment status, working disabilities, the number of hours overworked during
the week, and time effects. We separate our sample into men and women to account for the
gender-specific difference in the relationship between socioeconomic status and health.
In total, our sample contains 134,626 person-year observations for men and 145,030 person-year
observations for women. Detailed summary statistics are provided in Table III, separately for men
and women, in the Appendix.
4. ESTIMATION RESULTS
4.1. Interpretation of Coefficients
The next two subsections show the estimation results for men and women for three different
models. The models comprise the pooled ordered logit (POL), the random-effects logit (REL),
and the conditional fixed-effects logit (CFEL) specifications. The latter two models both assume
6 This is a simplification applied in OECD studies to adjust household income for needs. It is an approximation of the
OECD modified equivalence scale (Hagenaars et al., 1994), which assigns to the household head a value of 1, each
additional member of the household a value of 0.5, and each child below the age of 16 a value of 0.3. We tested both
methods. Since the results do not differ, we opted for the simplified version.
Copyright  2009 John Wiley & Sons, Ltd.
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HETEROGENEITY AND HEALTH SATISFACTION
559
the presence of threshold-specific time-invariant heterogeneity, but differ in their assumption on
the relationship between this heterogeneity and the regressors of the model.
The first column of Table IV in the Appendix report the estimated coefficients of the POL model
for men and women, respectively (estimated coefficients for time dummy variables are omitted and
will be provided upon request). The results suggest that East Germans are generally less likely to
report a high level of health satisfaction, all age groups are less likely to report high levels of health
satisfaction than the youngest group aged between 16 to 30, and that the diminishing probability is
increasing with age. Extra household income is associated with higher levels of health satisfaction
and this effect is also increasing with age. Whereas the number of years of education are associated
with greater levels of health satisfaction, unemployment, work disabilities, and hours of overwork
are associated with lower levels. Singles report on average higher levels of health satisfaction, an
association which may be mainly driven by the age of singles. Last, individuals living in larger
households are associated to report greater levels of health satisfaction. These results are similar
for women and, overall, they reflect the trends in the empirical literature.
The results on the estimated coefficients obtained from various random-effects logits specifications are reported in columns 2–7 of the same tables, whereas the estimated coefficients obtained
from various conditional fixed effects logits are reported in Table V in the Appendix.
4.2. Tests for Heterogeneity in Coefficients
Tables I and II show the p-values of the null hypothesis for each possible pairwise test of equality
of the coefficients, obtained from different CFEL specifications for men and women, respectively.
Coefficient and full results are reported in columns 1–6 in Table V in the Appendix.7
Overall, the test results suggest that the heterogeneity in the effect of income on health
satisfaction is present especially for the middle-aged groups, but conclusions differ across the
pairwise comparisons.
For men, we cannot reject the null hypothesis for pairwise comparisons between ˇ1 D ˇ2 and
ˇ2 D ˇ3 for almost all age groups. However, we reject for all age groups the null hypothesis that
ˇ3 D ˇ4 , ˇ2 D ˇ4 , and ˇ1 D ˇ4 , except for the youngest and oldest age groups. Individuals in age
groups 41–50 and 51–60 are those for whom equality of the coefficients is rejected most often
(four out of six cases). The oldest and the youngest age groups (16–30, 71 and older) are the
two groups for whom heterogeneity in the effect of income on health satisfaction plays the least
important role.
For women, heterogeneity also plays the most important role for individuals in the middle-aged
groups. Heterogeneity is rejected for the two oldest age groups, though. For these two age groups,
it would be sufficient to apply a conditional ordered fixed-effects logit specification.
These results are interpreted as follows: income affects individuals differently, depending on
whether they perceive their own health as bad/poor or as good/very good. Differential effects of
income also play a role for individuals who perceive their health as good or very good. Income
has, however, the same effect on perceived health when the individual perceives health as poor
or bad.
7 In Table V columns 1–4 show the results when using the threshold values j D 1 to j D 4 to dichotomise the dependent
variable (assuming heterogeneity), whereas columns 5 and 6 show the results when using the mean and the median
(assuming homogeneity), respectively, to dichotomise the dependent variable. The model using the median of health
satisfaction as cut-off value to dichotomise the ordered dependent variable avoids problems associated with the arbitrary
scaling of the ordered variable.
Copyright  2009 John Wiley & Sons, Ltd.
J. Appl. Econ. 26: 549–579 (2011)
DOI: 10.1002/jae
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A. M. JONES AND S. SCHURER
Table I. Test for heterogeneity in income coefficients for sample of men
Pairwise tests of age-specific income coefficients that result from different threshold js
ˇ1 D ˇ2
ˇ2 D ˇ3
ˇ3 D ˇ4
ˇ1 D ˇ4
ˇ2 D ˇ4
ˇ1 D ˇ3
Income age group 16–30
0.44
2 1
0.5056
Prob. >
2
Income age group 31–40
1.34
0.2477
1.44
0.2300
4.05
0.0443
4.39
0.0361
2.08
0.1490
0.03
2 1
Prob. >
2
0.8564
Income age group 41–50
0.45
0.5036
9.20
0.0024
5.74
0.0166
10.16
0.0014
0.42
0.5154
3.40
2 1
0.0650
Prob. >
2
Income age group 51–60
3.50
0.1689
3.50
0.0615
16.45
0.0000
8.65
0.0033
8.61
0.0033
2.29
2 1
0.1302
Prob. >
2
Income age group 61–70
2.83
0.0927
3.59
0.0582
16.14
0.0001
10.11
0.0015
8.24
0.0041
0.14
2 1
0.7051
Prob. >
2
Income age group 71 and older
0.01
0.9057
8.37
0.0038
7.58
0.0059
8.26
0.0040
0.23
0.6287
2 1
Prob. >
2
2.26
0.1323
0.11
0.7416
1.94
0.1632
0.67
0.4148
4.34
0.0372
0.64
0.4249
Note: Columns 1–6 report the 2 statistic and the p-value of the hypothesis that coefficients of income across different
thresholds of satisfaction with health are pairwise the same for men. Column 7 reports the same statistic for the
hypothesis that all four income coefficients are equal. The null hypothesis of homogeneity is not rejected if the p-value
>0.10. The method used for testing equality of two coefficients is taken from Allen McDowell, Stata Corp, July 2005.
http://www.stata.com/support/faqs/stat/testing.html.
4.3. Marginal Effects of Income
In this section the marginal effects and their confidence intervals for the logarithm of net monthly
household equivalent income are reported for each age-specific subgroup. The main hypothesis is
that the correlation between the individual fixed effect and socioeconomic status increases over
the life cycle since the magnitude of the individual fixed effect grows over time. Therefore, the
parameter bias is expected to be greater for older age groups; the difference in the marginal effects
calculated for the POL and the CFEL should be no smaller for the older age groups than for the
younger ones.
In a first step, we look at reports of very good health satisfaction; i.e. in the case of the POL,
the probability of reporting very good health satisfaction, and in the case of the REL and CFEL
the probability of reporting at least once a health satisfaction level greater than 4. These results
are contrasted with the probability of reporting a health satisfaction level beyond bad or poor to
assess whether there are asymmetries in the effect of income on health satisfaction.
Figure 3 shows the box-plots of the marginal effects of log-income on the probability of reporting
very good health satisfaction and their confidence intervals for each age group (Figure 3(a)–(f)).
The dot in the figure represents the magnitude of the marginal effect, while the vertical, capped
lines represent the upper and the lower bound of a 95% confidence interval. The marginal effects
Copyright  2009 John Wiley & Sons, Ltd.
J. Appl. Econ. 26: 549–579 (2011)
DOI: 10.1002/jae
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HETEROGENEITY AND HEALTH SATISFACTION
Table II. Test for heterogeneity in income coefficients for sample of women
Pairwise test of equality of age-specific income coefficients
ˇ1 D ˇ2 D
ˇ1 D ˇ2
ˇ2 D ˇ3
ˇ3 D ˇ4
ˇ1 D ˇ4
ˇ2 D ˇ4
ˇ1 D ˇ3
ˇ3 D ˇ4
Income age group 16–30
2.36
2 1
0.1246
Prob. >
2
Income age group 31–40
0.66
0.4163
9.20
0.0024
13.60
0.0002
10.21
0.0014
4.71
0.0299
22.30
0.0001
3.72
2 1
Prob. >
2
0.0537
Income age group 41–50
0.23
0.6295
0.05
0.8208
4.84
0.0278
0.07
0.7862
5.62
0.0178
5.80
0.1217
6.75
2 1
0.0094
Prob. >
2
Income age group 51–60
4.29
0.0383
5.06
0.0245
30.77
0.0000
14.98
0.0001
18.17
0.0000
35.54
0.0000
3.39
2 1
0.0655
Prob. >
2
Income age group 61–70
8.31
0.0039
0.01
0.9308
13.43
0.0002
5.75
0.0165
17.22
0.0000
23.19
0.0000
0.04
0.38
2 1
0.8325
0.5370
Prob. >
2
Income age group 71 and older
0.17
0.6825
0.01
0.9109
0.01
0.9321
0.07
0.7899
0.42
0.9356
2 1
Prob. >
2
0.06
0.8002
0.93
0.3339
0.01
0.9331
0.92
0.3380
1.96
0.5814
1.83
0.1765
0.22
0.6399
Note: Columns 1–6 report the 2 statistic and the p-value of the hypothesis that coefficients of income across different
thresholds of satisfaction with health are pairwise the same for women. Column 7 reports the same statistic for the
hypothesis that all four income coefficients are equal. The null hypothesis of homogeneity is not rejected if the p-value
>0.10. The method used for testing equality of two coefficients is taken from Allen McDowell, Stata Corp, July 2005.
http://www.stata.com/support/faqs/stat/testing.html.
for men (women) are indicated by an M (W) on the horizontal axis. From left to right, each chart
reports the box-plot resulting from the POL, the REL, and the CFEL model.
The marginal effect is greatest using the estimated coefficients from the POL models for both
men and women alike, but the effect tends to be slightly greater for women among the younger
age groups and smaller for the older age groups than for men. For both men and women in the
middle-aged groups (31–40, 41–50, and 51–60) each additional unit of the logarithm of income
translates into a greater probability of reporting very good health satisfaction by 4–6 percentage
points. For instance, all things being equal, a doubling of log-income per month will increase
the probability to report very good health by about 6 percentage points for the male age group
51–60.8 The effect is smallest for the youngest (0.015, Figure 3(a)) and the oldest age group
(0.03, Figure 3(f)).
In contrast, the marginal effect of log-income obtained from the CFEL differs more strongly
between men and women and generally converges to zero. For men, it is either zero (age groups
16–30, 41–50, 51–60, and 71 and older) or negative (age groups 31–40 and 61–70). For women,
the marginal effect is also either zero (age groups 41–50, 61–70, and 71 and older), positive (age
8A
1% increase in log-income increases the probability of reporting very good health by 0.06.
Copyright  2009 John Wiley & Sons, Ltd.
J. Appl. Econ. 26: 549–579 (2011)
DOI: 10.1002/jae
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A. M. JONES AND S. SCHURER
(a)
REL
CFEL
(b)
POL
REL
CFEL
.05
P(SWH>4)
–.05
0
0
–.06 –.04 –.02
P(SWH>4)
.02
.1
.04
POL
M
F
M
F
M
F
M
F
Age group 16–30
CFEL
(d)
POL
REL
CFEL
–.05
F
M
F
M
F
M
F
Age group 41–50
F
M
F
CFEL
(f)
POL
REL
CFEL
.05
0
–.1
–.1
–.05
0
P(SWH>4)
.05
.1
REL
.1
POL
M
Age group 51–60
–.05
P(SWH>4)
F
.05
P(SWH>4)
.05
0
–.05
P(SWH>4)
M
(e)
M
.1
REL
.1
POL
F
0
(c)
M
Age group 31–40
M
F
M
F
Age group 61–70
M
F
M
F
M
F
M
F
Age group 71
Figure 3. Marginal effects of income on the probability of reporting the highest value of satisfaction with
health for both men (M) and women (W) obtained from three different models: pooled ordered logit (POL),
random-effects logit (REL), and conditional fixed-effects logit (CFEL)
groups 31–40 and 51–60), or negative (age group 16–30). The magnitude of the marginal effects
obtained from the REL lies between those obtained from the POL and the CFEL.
The fewer restrictions we impose on the model concerning unobserved heterogeneity, the smaller
the effect of a marginal increase of income on the probability of reporting very good health. This
Copyright  2009 John Wiley & Sons, Ltd.
J. Appl. Econ. 26: 549–579 (2011)
DOI: 10.1002/jae
HETEROGENEITY AND HEALTH SATISFACTION
563
last result highlights one important finding in favour of choosing methodology prudently: once the
individual fixed effect is controlled for and allowed to correlate with regressors in the model, the
influence of observable socioeconomic status on very good self-reported health disappears. This
decrease is the largest for the middle-aged and older groups (41–50, 51–60, and 61–70). For these
groups the difference between the marginal effects of income between the POL and CFEL model
lies between 6 and 10 percentage points for men. For women, the difference is slightly smaller.
The effect is less marked for the youngest age group of 16–30 years old (and for women also for
31–40 years old). This result strengthens our hypothesis that the influence of the individual fixed
effect plays a greater role in mediating the relationship between income and health status in older
age.
It is notable that the marginal effects of log-income on the probability of reporting health satisfaction levels beyond bad or poor do not disappear once controlling for unobserved heterogeneity.
As illustrated in Figure 4, for men the marginal effect obtained from the CFEL takes values
between 2.5 and 5 percentage points for all age groups except for the oldest group. For women,
the effect is slightly smaller and becomes zero for the two oldest age groups.
Also, for the two youngest age groups, the estimated difference in the marginal effects between
the POL and the CFEL is relatively small (less than 2 percentage points, and no difference for
women in age group 31–40), whereas this difference grows in the older age group (up to 12
percentage points). These results provide additional evidence in favour of the hypothesis that the
omitted variable bias increases with age.
4.4. Predicted Probabilities
A similar picture emerges when studying the predicted probabilities of reporting very good health
satisfaction for the three models in Figure 5. In these figures we graph the change in reporting
probabilities over a range of potential net monthly household incomes from ¤500 to ¤5500.
The predicted probabilities for both men and women make it clear that the overall effect of
income on very good health is relatively small. At maximum, giving an extra ¤5000 per month
to a poor person in any middle-aged group raises the probability to report very good health by
20 percentage points in the POL (Figure 5(a) and (b)), and by 10 percentage points in the REL
(Figure 5(c) and (d)). For the youngest and the oldest groups these effects are even less.
Once individual-specific heterogeneity is controlled for, as illustrated in Figure 5(e) and (f),
income does not have any effect on the probability of reporting very good health satisfaction. A
sole exception are women aged 31–40 and 51–60, who still experience an increase of 8 percentage
points.
In contrast, additional income increases quite substantially the probability of reporting a health
satisfaction level beyond bad or poor for almost all age groups in all models (Figure 6). In the
POL, an additional ¤5000 in household income increases the probability of reporting better than
the lowest levels of health satisfaction by more than 22 percentage points, even for the oldest
age group. The two youngest age groups remain unaffected, though. Similar effects of half the
magnitude are obtained from the REL models for both men and women.
Once controlling for unobserved heterogeneity in the CFEL, an additional ¤5000 increases the
probability of reporting better health satisfaction levels than bad or poor by almost 10 percentage
points for both men and women, except for the oldest age group. These results suggest that despite
individual-specific differences in reporting behaviour increased levels of income for middle-aged
individuals raise levels of perceived health.
Copyright  2009 John Wiley & Sons, Ltd.
J. Appl. Econ. 26: 549–579 (2011)
DOI: 10.1002/jae
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A. M. JONES AND S. SCHURER
(a)
CFEL
(b)
POL
REL
CFEL
.04
P(SWH>2)
.02
.03
.02
0
0
.01
P(SWH>2)
.04
.06
REL
.05
POL
M
F
M
F
M
F
M
F
Age group 16 to 30
CFEL
(d)
F
POL
REL
CFEL
.08
P(SWH>2)
.1
.06
.05
.04
.02
.02
.04
.03
P(SWH>2)
M
F
M
F
M
F
M
F
F
M
F
CFEL
(f)
POL
REL
CFEL
.05
0
.05
P(SWH>2)
.1
.05
0
P(SWH>2)
.1
.15
REL
.15
POL
M
Age group 51–60
Age group 41–50
(e)
M
.12
REL
.07
POL
F
.06
(c)
M
Age group 31–40
M
F
M
F
M
F
Age group 61–70
M
F
M
F
M
F
Age group 71
Figure 4. Marginal effects of income on the probability to report satisfaction with health greater than two for
both men (M) and women (W) obtained from three different models: pooled ordered logit (POL), randomeffects logit (REL), and conditional fixed-effects logit (CFEL)
4.5. Robustness Checks of Marginal Effects
Figures 7 and 8 display the distribution of the approximated individual fixed effect, which we
calculated according to equation (17) and averaged for each age group according to equation (18).
The different figures illustrate to what degree the arbitrary assumption of scaling the individual
Copyright  2009 John Wiley & Sons, Ltd.
J. Appl. Econ. 26: 549–579 (2011)
DOI: 10.1002/jae
565
.2
.1
.2
Pr(SWH = 5)
.3
.3
.4
(b)
0
0
.1
Pr(SWH = 5)
(a)
.4
HETEROGENEITY AND HEALTH SATISFACTION
500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500
500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500
Monthly Income (in Euro)
Monthly Income (in Euro)
16 to 30
51 to 60
31 to 40
61 to 70
41 to 50
71 and older
16 to 30
51 to 60
41 to 50
71 and older
Pol (women)
.3
0
.2
.1
.2
Pr(SWH = 5)
.4
.3
Pr(SWH = 5)
.4
(e)
.5
.5
Pol (men)
(d)
31 to 40
61 to 70
500
1500
2500
3500
4500
5500
500
1500
Monthly Income (in Euro)
16 to 30
51 to 60
31 to 40
61 to 70
2500
16 to 30
51 to 60
41 to 50
71 and older
4500
5500
31 to 40
61 to 70
41 to 50
71 and older
REL (women)
.35
.5
.4
.45
Pr(SWH = 5)
.6
.55
Pr(SWH = 5)
.5
(f)
.55
.65
REL (men)
(e)
3500
Monthly Income (in Euro)
500
1500
2500
3500
4500
5500
Monthly Income (in Euro)
16 to 30
51 to 60
31 to 40
61 to 70
CFEL (men)
500
1500
2500
3500
4500
5500
Monthly Income (in Euro)
41 to 50
71 and older
16 to 30
51 to 60
31 to 40
61 to 70
41 to 50
71 and older
CFEL (women)
Figure 5. Simulation of the probability of reporting the highest level of satisfaction with health for changes
in income from ¤500 to ¤5500 for three different models: pooled ordered logit (POL), random-effects logit
(REL), and conditional fixed-effects logit (CFEL) for both men and women. This figure is available in color
online at wileyonlinelibrary.com/journal/jae
Copyright  2009 John Wiley & Sons, Ltd.
J. Appl. Econ. 26: 549–579 (2011)
DOI: 10.1002/jae
566
.9
.8
Pr(SWH > 2)
.6
.7
.8
.6
.7
Pr(SWH > 2)
1
1
(b)
.9
(a)
A. M. JONES AND S. SCHURER
500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500
500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500
Monthly Income (in Euro)
16 to 30
51 to 60
31 to 40
61 to 70
Monthly Income (in Euro)
41 to 50
71 and older
16 to 30
51 to 60
31 to 40
61 to 70
41 to 50
71 and older
POL (women)
(d)
.2
.4
.4
.6
Pr(SWH > 2)
.6
.5
Pr(SWH > 2)
.8
.7
(c)
1
POL (men)
500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500
500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500
Monthly Income (in Euro)
Monthly Income (in Euro)
16 to 30
51 to 60
31 to 40
61 to 70
41 to 50
71 and older
16 to 30
51 to 60
41 to 50
71 and older
REL (women)
.88
.82
.75
.84
.86
Pr(SWH > 2)
.85
.8
Pr(SWH > 2)
.9
.9
(f)
.92
REL (men)
(e)
31 to 40
61 to 70
500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500
Monthly Income (in Euro)
16 to 30
51 to 60
31 to 40
61 to 70
CFEL (men)
500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500
Monthly Income (in Euro)
41 to 50
71 and older
16 to 30
51 to 60
31 to 40
61 to 70
41 to 50
71 and older
CFEL (women)
Figure 6. Simulation of the probability of reporting satisfaction with health better than bad and poor for
changes in income from ¤500 to ¤5500 for three different models: pooled ordered logit (POL), random
effects logit (REL), and conditional fixed-effects logit (CFEL) for both men and women. This figure is
available in color online at wileyonlinelibrary.com/journal/jae
Copyright  2009 John Wiley & Sons, Ltd.
J. Appl. Econ. 26: 549–579 (2011)
DOI: 10.1002/jae
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HETEROGENEITY AND HEALTH SATISFACTION
.3
(b)
.2
Density
.1
.2
0
0
.1
Density
.3
(a)
.4
fixed effect to zero for calculating the marginal effects of income is sensible for varying threshold
values j and the different age groups (here we depict only the distributions for threshold values
j D 2 and j D 4).
For both men and women the distribution of the individual fixed effect is centred around zero
for the three younger age groups and slightly tilted to the left of zero for the three older age groups.
The degree of skewness depends on the threshold value j: the smaller the threshold value, the
more the distribution is moved to the left of zero for the three older age groups. For these cases,
we would expect the zero value assumption to bias the calculation of the marginal effects the most.
Figures 9 and 10 confirm the suggestion that only the effects of income on the probability of
reporting satisfaction with health beyond bad and poor (SWH > 2) for the older age groups
should be different. The first column of the box-plot depicts the original marginal effect obtained
from a conditional fixed-effects model that assumes the individual fixed effect to be zero. The
second column depicts the marginal effects obtained from the same model, except for using the
approximated value of the individual fixed effect.
–6
–4
–2
0
2
4
–5
0
x
x
16 to 30
41 to 50
61 to 70
31 to 40
51 to 60
71 and older
5
16 to 30
41 to 50
61 to 70
Threshold value j = 2
31 to 40
51 to 60
71 and older
Threshold value j = 4
.3
(b)
.2
Density
.1
.2
0
0
.1
Density
.3
(a)
.4
Figure 7. Probability distribution of individual fixed effect obtained from the conditional fixed-effects logit
(CFEL), when the threshold values are j D 2 and j D 4 for the sample of men
–6
–4
–2
0
2
4
–5
0
x
x
16 to 30
41 to 50
61 to 70
31 to 40
51 to 60
71 and older
Threshold value j = 2
16 to 30
41 to 50
61 to 70
5
31 to 40
51 to 60
71 and older
Threshold value j = 4
Figure 8. Probability distribution of individual fixed effect obtained from the conditional fixed effects logit
(CFEL), when the threshold values are j D 2 and j D 4 for the sample of women
Copyright  2009 John Wiley & Sons, Ltd.
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A. M. JONES AND S. SCHURER
(b)
.04
–.04 –.02
–.06
M
F
M
F
M
ALT ME
(d)
F
ORIGINAL
ALT ME
.04
.02
–.04 –.02
0
P(SWH>4)
.02
0
P(SWH>4)
–.02
–.04
M
F
M
F
M
Age group 41–50
(e)
M
.06
.04
ORIGINAL
F
Age group 31–40
Age group 16–30
(c)
ALT ME
.02
P(SWH>4)
0
–.02
–.04
P(SWH>4)
ORIGINAL
.06
ALT ME
.02
ORIGINAL
0
(a)
M
F
ALT ME
(f)
ORIGINAL
ALT ME
–.1
–.05
0
P(SWH>4)
0
–.05
–.1
P(SWH>4)
.05
.05
.1
ORIGINAL
F
Age group 51–60
M
F
M
Age group 61–70
F
M
F
M
F
Age group 71
Figure 9. Robustness checks of marginal effects of income obtained from the conditional fixed effects logit
(CFEL) on the probability of reporting the highest value of satisfaction with health
For instance, for men aged between 51 and 60 the marginal effect of income on the probability
of reporting health better than bad and poor is almost 2 percentage points greater in the alternative
calculation than when assuming a zero individual fixed effect (Figure 10(d)). Similar differences
are obtained for men in the 61–70 age group. For women these differences are also present for
the same age groups, but smaller in magnitude (1 percentage point difference).
Copyright  2009 John Wiley & Sons, Ltd.
J. Appl. Econ. 26: 549–579 (2011)
DOI: 10.1002/jae
569
HETEROGENEITY AND HEALTH SATISFACTION
(a)
ALT ME
(b)
ORIGINAL
ALT ME
.04
P(SWH>2)
.02
.03
.02
0
0
.01
P(SWH>2)
.04
.06
.05
ORIGINAL
M
F
M
F
M
Age group 16–30
ALT ME
(d)
.04
F
M
F
M
Age group 41–50
M
F
ALT ME
(f)
ORIGINAL
ALT ME
0
P(SWH>2)
.04
.02
–.05
.06
.08
.05
ORIGINAL
F
Age group 51–60
–.02
–.1
0
P(SWH>2)
ALT ME
.1
ORIGINAL
.02
M
(e)
F
.08
P(SWH>2)
.06
.04
.02
P(SWH>2)
.08
ORIGINAL
M
.06
(c)
F
Age group 31–40
M
F
M
F
M
F
Age group 61–70
M
F
Age group 71
Figure 10. Robustness checks of marginal effects of income obtained from the conditional fixed effects logit
(CFEL) on the probability of reporting satisfaction with health better than bad or poor
5. SUMMARY AND CONCLUSION
Choosing the right econometric model for accurately testing the socioeconomic gradient of health
is quite a challenging task for the applied researcher, given that unobserved factors play such a
dominant role in influencing both socioeconomic status and health outcomes. The literature so far
has concentrated on controlling for time-invariant unobserved heterogeneity in nonlinear models,
Copyright  2009 John Wiley & Sons, Ltd.
J. Appl. Econ. 26: 549–579 (2011)
DOI: 10.1002/jae
570
A. M. JONES AND S. SCHURER
which reduces the options either to conditional fixed effects estimation by dichotomising the
categorical dependent variable or to impose orthogonality between the unobserved heterogeneity
and regressors of the model. Some papers applied threshold-specific models, but failed to treat
the difficulty of identification, as emphasised by Cunha et al. (2007) and Ronning (1990). Little
attention has been paid in the literature to these identification problems while controlling for
omitted variable and reporting bias.
We applied a conditional fixed-effects logit model to estimate the socioeconomic gradient
in health satisfaction while allowing for threshold-specific, time-invariant heterogeneity. Such
a formulation complies with the stochastic monotonicity requirement and allows us to test three
hypotheses: first, whether income influences health satisfaction in a heterogeneous fashion; second,
whether this impact differs across age groups, and third, whether assumptions imposed on the
relationship between unobserved heterogeneity and socioeconomic status in assessing health
satisfaction make a larger practical difference for older age groups. To illustrate our point, we
estimate a model of health satisfaction using 22 waves of the GSOEP.
On the one hand, we find that imposing a homogeneous relationship between income and health
satisfaction, independent of whether time-invariant individual heterogeneity is controlled for or not,
is too restrictive. That is to say, that the pooled ordered logit and the conditional ordered fixedeffects logit (Ferrer-i-Carbonell and Frijters, 2004) do not sufficiently account for the heterogeneity
in the data, and thus conclusions about the potential effects of income on health can be misleading.
On the other hand, ignoring individual- and threshold-specific heterogeneity, which may
represent cognitive ability that determines perception and judgement of one’s own health, leads to
an overestimation of the effect of income on health, especially for the effect of income on reports
of very good health. Once controlling for individual-specific effects, income does not exert an
independent effect. However, income helps to increase reports of health satisfaction for changes
at the lower end of the health distribution.
The overstatement of the income effect is stronger for the older age groups, supporting the
hypothesis that individual-specific factors such as perception and cognitive ability play a greater
role in determining health in older age.
Our robustness checks indicate that the zero value assumption on the individual fixed effects
used for calculating the marginal effects of income does not matter substantially. If at all, it matters
for older age groups when calculating the marginal effect for the probability of reporting health
satisfaction greater than bad or poor. We suggest that marginal effects in conditional fixed-effects
logits are reliable under the zero value assumption, especially if marginal effects are averaged
across several age groups.
ACKNOWLEDGEMENTS
The results reported in this paper were generated using STATA SE 10.2. The programs are available
from the authors upon request. Grant sponsor was the Thyssen Krupp von Halbach Foundation.
We thank two anonymous referees and Steven N. Durlauf for very helpful comments. We also
thank Nigel Rice, Jan Brenner, Paul Frijters, Pilar Garcı́a Gomez, John Haisken-DeNew, Michael
Shields, and participants of the Health, Econometrics, and Data Group at the University of York,
UK, the Brown Bag Seminar at the RWI Essen, Essen, Germany, the First Doctoral Conference
of the RGS in Economics, University of Dortmund, Germany, the International Association of
Copyright  2009 John Wiley & Sons, Ltd.
J. Appl. Econ. 26: 549–579 (2011)
DOI: 10.1002/jae
HETEROGENEITY AND HEALTH SATISFACTION
571
Health Economics (IHEA), Copenhagen, Denmark, and the Chair of Empirical Economics and
Statistics, University of Zurich, Switzerland. All errors are our own.
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APPENDIX
Table III. Summary statistics for men and women
Variable
Men
East Germany
Age group 31–40
Age group 41–50
Age group 51–60
Age group 61–70
Age group 71 and older
Income age group 1630
Income age group 3140
Income age group 4150
Income age group 5160
Income age group 6170
Income age group 71
No. years of education
Registered unemployed
Hours worked overtime
Work disability
Divorced, separated, or widowed
Single, never married
Number of person in household
Women
East Germany
Age group 31–40
Age group 41–50
Age group 51–60
Age group 61–70
Age group 71 and older
Income age group 1630
Income age group 3140
Income age group 4150
Income age group 5160
Income age group 6170
Income age group 71
No. years of education
Registered unemployed
Hours worked overtime
Work disability
Divorced, separated, or widowed
Single, never married
Number of person in household
Mean
SD
Min.
Max.
N
0.219
0.199
0.182
0.158
0.122
0.072
1.858
1.398
1.295
1.127
0.866
0.512
11.4
0.072
1.572
0.033
0.075
0.272
3.049
0.413
0.399
0.386
0.365
0.327
0.259
3.097
2.811
2.749
2.612
2.328
1.836
2.993
0.258
3.454
0.178
0.264
0.445
1.368
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
10.366
9.782
10.366
10.801
11.082
10.473
18
1
56.1
1
1
1
17
134,626
134,626
134,626
134,626
134,626
134,626
134,626
134,626
134,626
134,626
134,626
134,626
134,626
134,626
134,626
134,626
134,626
134,626
134,626
0.223
0.2
0.18
0.148
0.125
0.102
1.701
1.398
1.28
1.049
0.877
0.709
10.946
0.064
0.59
0.024
0.173
0.206
2.903
0.416
0.4
0.384
0.355
0.331
0.303
2.995
2.806
2.743
2.529
2.325
2.103
2.789
0.245
1.926
0.153
0.378
0.405
1.397
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
10.801
10.254
10.366
11.166
10.656
10.473
18
1
68
1
1
1
17
149,030
149,030
149,030
149,030
149,030
149,030
149,030
149,030
149,030
149,030
149,030
149,030
149,030
149,030
149,030
149,030
149,030
149,030
149,030
Note: Summary statistics for year dummy variables are omitted.
Copyright  2009 John Wiley & Sons, Ltd.
J. Appl. Econ. 26: 549–579 (2011)
DOI: 10.1002/jae
Copyright  2009 John Wiley & Sons, Ltd.
Income age group 71
Income age group 6170
Income age group 5160
Income age group 4150
Income age group 3140
Income age group 1630
Age group 71 and older
Age group 61–70
Age group 51–60
Age group 41–50
Age group 31–40
Men
East Germany
0.150
(0.026)ŁŁŁ
1.786
(0.330)ŁŁŁ
3.624
(0.360)ŁŁŁ
5.386
(0.362)ŁŁŁ
5.483
(0.390)ŁŁŁ
4.665
(0.582)ŁŁŁ
0.062
(0.031)ŁŁ
0.235
(0.042)ŁŁŁ
0.430
(0.043)ŁŁŁ
0.616
(0.043)ŁŁŁ
0.610
(0.048)ŁŁŁ
0.451
(0.078)ŁŁŁ
Ordered logit
Estimated
thresholds
0.073
(0.070)
2.863
(0.981)ŁŁŁ
5.178
(0.938)ŁŁŁ
5.662
(0.881)ŁŁŁ
4.906
(0.951)ŁŁŁ
2.368
(1.025)ŁŁ
0.306
(0.103)ŁŁŁ
0.626
(0.107)ŁŁŁ
0.863
(0.095)ŁŁŁ
0.838
(0.081)ŁŁŁ
0.695
(0.095)ŁŁŁ
0.201
(0.109)Ł
jD1
0.043
(0.048)
1.565
(0.592)ŁŁŁ
3.221
(0.578)ŁŁŁ
4.548
(0.559)ŁŁŁ
4.632
(0.614)ŁŁŁ
2.935
(0.724)ŁŁŁ
0.230
(0.062)ŁŁŁ
0.385
(0.066)ŁŁŁ
0.517
(0.060)ŁŁŁ
0.614
(0.055)ŁŁŁ
0.603
(0.065)ŁŁŁ
0.273
(0.085)ŁŁŁ
jD2
0.268
(0.040)ŁŁŁ
2.070
(0.413)ŁŁŁ
3.283
(0.427)ŁŁŁ
5.204
(0.434)ŁŁŁ
5.849
(0.489)ŁŁŁ
4.328
(0.630)ŁŁŁ
0.139
(0.042)ŁŁŁ
0.361
(0.048)ŁŁŁ
0.434
(0.048)ŁŁŁ
0.603
(0.048)ŁŁŁ
0.662
(0.057)ŁŁŁ
0.367
(0.080)ŁŁŁ
jD3
0.373
(0.044)ŁŁŁ
1.360
(0.401)ŁŁŁ
3.602
(0.454)ŁŁŁ
6.122
(0.506)ŁŁŁ
6.656
(0.622)ŁŁŁ
5.495
(0.865)ŁŁŁ
0.058
(0.037)
0.048
(0.050)
0.277
(0.057)ŁŁŁ
0.539
(0.063)ŁŁŁ
0.558
(0.081)ŁŁŁ
0.340
(0.118)ŁŁŁ
jD4
0.141
(0.023)ŁŁŁ
0.051
(0.295)
0.603
(0.306)ŁŁ
1.553
(0.307)ŁŁŁ
1.377
(0.349)ŁŁŁ
1.610
(0.442)ŁŁŁ
0.042
(0.028)
0.037
(0.035)
0.032
(0.036)
0.143
(0.036)ŁŁŁ
0.146
(0.042)ŁŁŁ
0.151
(0.057)ŁŁŁ
j D mean
Random effects logits Threshold j used to dichotomise SWH
Table IV. Ordered and random effects logits
0.257
(0.028)ŁŁŁ
0.385
(0.354)
0.265
(0.365)
1.364
(0.366)ŁŁŁ
1.534
(0.414)ŁŁŁ
1.474
(0.527)ŁŁŁ
0.098
(0.033)ŁŁŁ
0.158
(0.043)ŁŁŁ
0.063
(0.043)
0.083
(0.043)Ł
0.132
(0.050)ŁŁŁ
0.106
(0.069)
j D median
HETEROGENEITY AND HEALTH SATISFACTION
575
J. Appl. Econ. 26: 549–579 (2011)
DOI: 10.1002/jae
Copyright  2009 John Wiley & Sons, Ltd.
Income age group 1630
Age group 71 and older
Age group 61–70
Age group 51–60
Age group 41 to 50
Age group 31–40
Observations
Women
East Germany
Constant
Work disability
Hours worked overtime
Registered unemployed
No. years of education
0.117
(0.043)ŁŁŁ
1.619
(0.508)ŁŁŁ
3.248
(0.507)ŁŁŁ
4.957
(0.499)ŁŁŁ
3.115
(0.536)ŁŁŁ
2.427
(0.555)ŁŁŁ
0.179
(0.054)ŁŁŁ
0.021
(0.061)
1.137
(0.856)
4.128
(0.811)ŁŁŁ
4.873
(0.782)ŁŁŁ
2.610
(0.824)ŁŁŁ
0.928
(0.802)
0.387
(0.090)ŁŁŁ
0.150
(0.025)ŁŁŁ
2.302
(0.300)ŁŁŁ
3.466
(0.338)ŁŁŁ
4.934
(0.333)ŁŁŁ
4.343
(0.368)ŁŁŁ
3.199
(0.444)ŁŁŁ
0.088
(0.030)ŁŁŁ
134 626
0.026
(0.006)ŁŁŁ
0.337
(0.042)ŁŁŁ
0.017
(0.004)ŁŁŁ
1.192
(0.046)ŁŁŁ
1.906
(0.440)ŁŁŁ
134 626
jD2
0.063
(0.010)ŁŁŁ
0.398
(0.062)ŁŁŁ
0.031
(0.007)ŁŁŁ
1.468
(0.063)ŁŁŁ
3.142
(0.730)ŁŁŁ
134 626
jD1
0.288
(0.037)ŁŁŁ
1.799
(0.368)ŁŁŁ
3.127
(0.385)ŁŁŁ
4.475
(0.397)ŁŁŁ
4.562
(0.440)ŁŁŁ
2.374
(0.494)ŁŁŁ
0.155
(0.038)ŁŁŁ
0.029
(0.005)ŁŁŁ
0.263
(0.035)ŁŁŁ
0.003
(0.003)
1.065
(0.044)ŁŁŁ
0.484
(0.302)
134 626
jD3
0.348
(0.042)ŁŁŁ
3.107
(0.374)ŁŁŁ
3.666
(0.433)ŁŁŁ
6.554
(0.487)ŁŁŁ
6.512
(0.571)ŁŁŁ
3.375
(0.697)ŁŁŁ
0.067
(0.036)Ł
0.030
(0.005)ŁŁŁ
0.101
(0.041)ŁŁ
0.003
(0.003)
0.832
(0.064)ŁŁŁ
0.498
(0.268)Ł
134 626
jD4
0.114
(0.021)ŁŁŁ
0.506
(0.267)Ł
0.551
(0.279)ŁŁ
1.377
(0.284)ŁŁŁ
0.736
(0.313)ŁŁ
1.272
(0.339)ŁŁŁ
0.036
(0.026)
0.004
(0.003)
0.079
(0.027)ŁŁŁ
0.006
(0.002)ŁŁŁ
0.670
(0.037)ŁŁŁ
0.146
(0.202)
134 915
j D mean
Random effects logits Threshold j used to dichotomise SWH
0.011
(0.004)ŁŁŁ
0.269
(0.032)ŁŁŁ
0.000
(0.002)
1.165
(0.033)ŁŁŁ
Ordered logit
Estimated
thresholds
Table IV. (Continued )
0.131
(0.025)ŁŁŁ
0.253
(0.318)
0.880
(0.331)ŁŁŁ
1.382
(0.339)ŁŁŁ
0.764
(0.368)ŁŁ
0.713
(0.396)Ł
0.104
(0.031)ŁŁŁ
0.024
(0.004)ŁŁŁ
0.063
(0.033)Ł
0.005
(0.002)ŁŁ
0.486
(0.046)ŁŁŁ
0.990
(0.241)ŁŁŁ
134 915
j D median
576
A. M. JONES AND S. SCHURER
J. Appl. Econ. 26: 549–579 (2011)
DOI: 10.1002/jae
Copyright  2009 John Wiley & Sons, Ltd.
149,030
0.341
(0.036)ŁŁŁ
0.438
(0.039)ŁŁŁ
0.587
(0.038)ŁŁŁ
0.489
(0.045)ŁŁŁ
0.255
(0.057)ŁŁŁ
0.029
(0.004)ŁŁŁ
0.258
(0.029)ŁŁŁ
0.009
(0.004)ŁŁ
1.167
(0.036)ŁŁŁ
0.476
(0.094)ŁŁŁ
0.811
(0.080)ŁŁŁ
0.827
(0.074)ŁŁŁ
0.478
(0.083)ŁŁŁ
0.091
(0.078)
0.062
(0.009)ŁŁŁ
0.241
(0.063)ŁŁŁ
0.035
(0.011)ŁŁŁ
1.402
(0.067)ŁŁŁ
2.402
(0.634)ŁŁŁ
149,030
jD1
0.338
(0.056)ŁŁŁ
0.496
(0.053)ŁŁŁ
0.654
(0.051)ŁŁŁ
0.371
(0.058)ŁŁŁ
0.163
(0.062)ŁŁŁ
0.043
(0.006)ŁŁŁ
0.228
(0.040)ŁŁŁ
0.005
(0.006)
1.121
(0.049)ŁŁŁ
1.853
(0.383)ŁŁŁ
149,030
jD2
0.333
(0.043)ŁŁŁ
0.430
(0.043)ŁŁŁ
0.524
(0.044)ŁŁŁ
0.498
(0.052)ŁŁŁ
0.090
(0.061)
0.050
(0.005)ŁŁŁ
0.192
(0.033)ŁŁŁ
0.005
(0.004)
0.936
(0.048)ŁŁŁ
0.003
(0.274)
149,030
jD3
0.285
(0.046)ŁŁŁ
0.266
(0.053)ŁŁŁ
0.565
(0.061)ŁŁŁ
0.529
(0.074)ŁŁŁ
0.004
(0.095)
0.002
(0.005)
0.118
(0.041)ŁŁŁ
0.014
(0.005)ŁŁŁ
0.762
(0.073)ŁŁŁ
0.814
(0.261)ŁŁŁ
149,030
jD4
0.025
(0.031)
0.025
(0.032)
0.122
(0.032)ŁŁŁ
0.059
(0.038)
0.101
(0.042)ŁŁ
0.017
(0.003)ŁŁŁ
0.049
(0.026)Ł
0.003
(0.003)
0.535
(0.039)ŁŁŁ
0.258
(0.189)
149,374
j D mean
Random effects logits Threshold j used to dichotomise SWH
0.071
(0.037)Ł
0.015
(0.038)
0.073
(0.039)Ł
0.015
(0.044)
0.003
(0.050)
0.009
(0.004)ŁŁ
0.020
(0.031)
0.004
(0.004)
0.382
(0.050)ŁŁŁ
0.998
(0.224)ŁŁŁ
149,374
j D median
Note: Column 1 reports the coefficients obtained from a pooled ordered logit model, regressing the categorical variable health satisfaction on the full set of control
variables. Columns 2–5 report the coefficients obtained from a random effects logit when dichotomising the dependent variable health satisfaction with threshold
values j D 1, 2, 3, 4. Columns 6 and 7 report the estimated coefficients of a model that uses the mean and the median as threshold values. Coefficients for time
dummy variables, marital status, and persons in household are omitted. Asterisks indicate significance at Ł 10% level, ŁŁ 5% level, and ŁŁŁ 1% level.
Observations
Constant
Work disability
Hours worked overtime
Registered unemployed
No. years of education
Income age group 71
Income age group 6170
Income age group 5160
Income age group 4150
Income age group 3140
Ordered logit
Estimated
thresholds
Table IV. (Continued )
HETEROGENEITY AND HEALTH SATISFACTION
577
J. Appl. Econ. 26: 549–579 (2011)
DOI: 10.1002/jae
Copyright  2009 John Wiley & Sons, Ltd.
Observations
Work disability
Hours worked overtime
Registered unemployed
No. years of eduction
Income age group 71
Income age group 6170
Income age group 5160
Income age group 4150
Income age group 3140
Income age group 1630
Age group 71 and older
Age group 61–70
Age group 51–60
Age group 41–50
Age group 31–40
Men
East Germany
0.218
(0.389)
0.380
(1.193)
1.075
(1.195)
0.757
(1.157)
0.980
(1.247)
5.592
(1.438)ŁŁŁ
0.254
(0.138)Ł
0.266
(0.124)ŁŁ
0.507
(0.112)ŁŁŁ
0.483
(0.098)ŁŁŁ
0.297
(0.116)ŁŁ
0.388
(0.155)ŁŁ
0.012
(0.023)
0.278
(0.066)ŁŁŁ
0.026
(0.008)ŁŁŁ
1.102
(0.064)ŁŁŁ
29,058
jD1
0.038
(0.211)
0.355
(0.689)
0.636
(0.706)
1.006
(0.702)
0.218
(0.769)
3.084
(0.979)ŁŁŁ
0.148
(0.077)Ł
0.240
(0.075)ŁŁŁ
0.263
(0.070)ŁŁŁ
0.304
(0.066)ŁŁŁ
0.244
(0.078)ŁŁŁ
0.234
(0.116)ŁŁ
0.024
(0.013)Ł
0.216
(0.044)ŁŁŁ
0.014
(0.004)ŁŁŁ
0.908
(0.047)ŁŁŁ
61,511
jD2
0.052
(0.135)
0.826
(0.466)Ł
0.609
(0.510)
0.879
(0.528)Ł
1.048
(0.603)Ł
0.544
(0.845)
0.042
(0.050)
0.178
(0.054)ŁŁŁ
0.139
(0.057)ŁŁ
0.158
(0.057)ŁŁŁ
0.231
(0.069)ŁŁŁ
0.006
(0.109)
0.009
(0.008)
0.150
(0.036)ŁŁŁ
0.003
(0.003)
0.843
(0.045)ŁŁŁ
91,177
jD3
Thresholds j from 1 to 4
0.166
(0.133)
0.186
(0.457)
0.015
(0.568)
0.021
(0.662)
0.995
(0.844)
0.565
(1.297)
0.037
(0.043)
0.062
(0.058)
0.031
(0.071)
0.032
(0.083)
0.142
(0.109)
0.062
(0.175)
0.023
(0.007)ŁŁŁ
0.022
(0.044)
0.001
(0.003)
0.580
(0.065)ŁŁŁ
76,910
jD4
Table V. Estimated coefficients for various conditional fixed effects logits
0.131
(0.106)
0.610
(0.366)Ł
0.763
(0.407)Ł
1.445
(0.420)ŁŁŁ
1.071
(0.483)ŁŁ
0.274
(0.674)
0.041
(0.037)
0.058
(0.044)
0.079
(0.047)Ł
0.167
(0.047)ŁŁŁ
0.173
(0.057)ŁŁŁ
0.012
(0.088)
0.022
(0.006)ŁŁŁ
0.107
(0.030)ŁŁŁ
0.004
(0.002)Ł
0.720
(0.038)ŁŁŁ
121,664
j D mean
0.230
(0.127)Ł
0.802
(0.445)Ł
1.270
(0.488)ŁŁŁ
1.694
(0.502)ŁŁŁ
1.555
(0.571)ŁŁŁ
0.166
(0.796)
0.116
(0.045)ŁŁŁ
0.000
(0.053)
0.065
(0.056)
0.124
(0.056)ŁŁ
0.165
(0.067)ŁŁ
0.005
(0.103)
0.027
(0.007)ŁŁŁ
0.106
(0.036)ŁŁŁ
0.004
(0.003)
0.615
(0.047)ŁŁŁ
92,802
j D median
Thresholds j mean or median
578
A. M. JONES AND S. SCHURER
J. Appl. Econ. 26: 549–579 (2011)
DOI: 10.1002/jae
Copyright  2009 John Wiley & Sons, Ltd.
0.328
(0.274)
0.304
(1.012)
1.631
(1.011)
0.930
(0.993)
2.985
(1.064)ŁŁŁ
4.860
(1.072)ŁŁŁ
0.311
(0.116)ŁŁŁ
0.411
(0.112)ŁŁŁ
0.620
(0.096)ŁŁŁ
0.534
(0.087)ŁŁŁ
0.046
(0.102)
0.243
(0.104)ŁŁ
0.038
(0.021)Ł
0.133
(0.067)ŁŁ
0.028
(0.012)ŁŁ
0.980
(0.068)ŁŁŁ
37,583
0.323
(0.160)ŁŁ
0.228
(0.584)
1.215
(0.610)ŁŁ
1.330
(0.614)ŁŁ
1.374
(0.672)ŁŁ
1.944
(0.725)ŁŁŁ
0.106
(0.066)
0.160
(0.065)ŁŁ
0.322
(0.062)ŁŁŁ
0.339
(0.059)ŁŁŁ
0.019
(0.070)
0.065
(0.081)
0.034
(0.011)ŁŁŁ
0.115
(0.042)ŁŁŁ
0.005
(0.006)
0.804
(0.050)ŁŁŁ
75,817
jD2
0.264
(0.118)ŁŁ
0.542
(0.413)
0.848
(0.449)Ł
0.603
(0.482)
0.076
(0.541)
1.253
(0.639)ŁŁ
0.041
(0.045)
0.121
(0.048)ŁŁ
0.159
(0.049)ŁŁŁ
0.110
(0.052)ŁŁ
0.078
(0.063)
0.118
(0.079)
0.024
(0.008)ŁŁŁ
0.064
(0.035)Ł
0.002
(0.005)
0.666
(0.048)ŁŁŁ
104,862
jD3
0.006
(0.124)
1.987
(0.426)ŁŁŁ
0.850
(0.529)
1.891
(0.638)ŁŁŁ
0.969
(0.770)
0.110
(1.005)
0.145
(0.042)ŁŁŁ
0.138
(0.053)ŁŁ
0.024
(0.065)
0.102
(0.079)
0.030
(0.099)
0.078
(0.135)
0.003
(0.007)
0.016
(0.044)
0.005
(0.005)
0.491
(0.076)ŁŁŁ
81,994
jD4
0.198
(0.095)ŁŁ
1.323
(0.335)ŁŁŁ
1.531
(0.368)ŁŁŁ
1.532
(0.389)ŁŁŁ
0.234
(0.436)
0.581
(0.507)
0.068
(0.035)Ł
0.119
(0.040)ŁŁŁ
0.150
(0.041)ŁŁŁ
0.148
(0.043)ŁŁŁ
0.021
(0.051)
0.095
(0.063)
0.013
(0.006)ŁŁ
0.058
(0.029)ŁŁ
0.003
(0.004)
0.589
(0.041)ŁŁŁ
136,738
j D mean
0.252
(0.112)ŁŁ
1.571
(0.399)ŁŁŁ
1.834
(0.436)ŁŁŁ
1.709
(0.461)ŁŁŁ
0.308
(0.511)
0.717
(0.590)
0.112
(0.041)ŁŁŁ
0.108
(0.048)ŁŁ
0.136
(0.049)ŁŁŁ
0.115
(0.051)ŁŁ
0.025
(0.060)
0.149
(0.073)ŁŁ
0.003
(0.007)
0.079
(0.035)ŁŁ
0.011
(0.005)ŁŁ
0.513
(0.051)ŁŁŁ
107,089
j D median
Thresholds j mean or median
Note: Columns 1–4 report the coefficients obtained from a conditional fixed-effects logit when dichotomising the dependent variable health satisfaction with
threshold values j D 1, 2, 3, 4. Columns 5 and 6 report the estimated coefficients of a model that uses the mean and the median as threshold values. Coefficients
for time dummy variables, marital status and persons in household are omitted. Asterisks indicate significance at Ł 10% level, ŁŁ 5% level, and ŁŁŁ 1% level.
Observations
Work disability
Hours worked overtime
Registered unemployed
No. years of education
Income age group 71
Income age group 6170
Income age group 5160
Income age group 4150
Income age group 3140
Income age group 1630
Age group 71 and older
Age group 61–70
Age group 51–60
Age group 41–50
Age group 31–40
Women
East Germany
jD1
Thresholds j from 1 to 4
Table V. (Continued )
HETEROGENEITY AND HEALTH SATISFACTION
579
J. Appl. Econ. 26: 549–579 (2011)
DOI: 10.1002/jae