The Determinants of Sick Leave Durations of Dutch Self-Employed Laura Spierdijk * Gijsbert van Lomwel † Wilko Peppelman ‡ September 24, 2008 * Corresponding author. Department of Economics & Econometrics, Faculty of Economics and Business, University of Groningen, P.O. Box 800, NL-9700 AV Groningen, The Netherlands. Phone: +31 50 363 5929. Fax: +31 50 363 3720. E-mail: [email protected]. † Achmea, Occupational Health Division, P.O. Box 700, NL-7300 HC, Apeldoorn. Phone: +31 55 579 20 45. Fax: +31 55 579 49 83. Email: [email protected]. ‡ Achmea, Occupational Health Division, P.O. Box 700, NL-7300 HC, Apeldoorn. Email: [email protected]. The authors are grateful to the seminar participants at Stockholm School of Economics. We also thank Roel Bakker, Jan van Ours, Lou Spoor and Gerard van den Berg for useful comments. The usual disclaimer applies. 1
Transcript
The Determinants of Sick Leave Durations of
Dutch Self-Employed
Laura Spierdijk∗ Gijsbert van Lomwel† Wilko Peppelman‡
September 24, 2008
∗Corresponding author. Department of Economics & Econometrics, Faculty of Economics andBusiness, University of Groningen, P.O. Box 800, NL-9700 AV Groningen, The Netherlands. Phone:+31 50 363 5929. Fax: +31 50 363 3720. E-mail: [email protected].
‡Achmea, Occupational Health Division, P.O. Box 700, NL-7300 HC, Apeldoorn. Email:[email protected]. The authors are grateful to the seminar participants at StockholmSchool of Economics. We also thank Roel Bakker, Jan van Ours, Lou Spoor and Gerard van denBerg for useful comments. The usual disclaimer applies.
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Abstract
This paper analyzes sickness absenteeism among self-employed in the Nether-
lands. Using a unique data set provided by a large Dutch private insurance
company, we assess the determinants of sick leave durations. Age and the type
of illness are among the most significant determinants of the disability spell.
The recovery rate decreases with age and claimants suffering from psycholog-
ical and neurological diseases have a substantially lower recovery rate relative
to claimants with other disorders. Contract-specific factors such as insurance
brand, deferment period and compensation benefit level are typical characteris-
tics of insurance contracts for self-employed and play an important role. If the
benefit compensation level in the second and later years is lower than in the
first year, recovery is significantly faster. The introduction of insurer-based case
management as of mid-2003 significantly increased the recovery rate of claims
with an ongoing spell up to one year. By contrast, case management did not
succeed in improving the recovery rate for claimants trapped in long-term dis-
ability. We do not establish any significant gender differences in the sick leave
durations of self-employed.
Keywords: sick leave duration, disability duration, case manage-
ment
JEL classification: I19, C41, G22
1 Introduction
Since August 2004, disability insurance for self-employed workers in the Netherlands
has only been available from private insurance companies. Before, self-employed fell
under the ‘Wet Arbeidsongeschiktheid Zelfstandigen’ (Law on Disability of Self-
Employed), which obliged them to participate in a collective disability insurance
scheme. With the new legislation, private disability insurance has gained importance.
For the insurance companies involved it is crucial to understand which factors affect
the duration of sick leave. These risk factors can be used to determine evidence-based
underwriting criteria for disability insurance. Another relevant issue for insurance
companies is how to design the service process in order to improve the recovery
probability of sick workers, thus shortening the duration of benefit payments. In
other words, can the speed of recovery be influenced by the way sickness absenteeism
is monitored and managed and, if so, how?
There exists an extensive body of literature on the risk factors for disability
among employees. Sociodemographic characteristics, disease category and severe-
ness, economic incentives, mental and physical health of the employee, job and com-
pany characteristics, employer or insurer-based disability management and macro-
economic factors have been shown to affect the return to work process (see the survey
article by Krause et al., 2001). Due to a lack of data, studies focusing on disability
among self-employed workers are extremely scarce. Bakker et al. (2006), who review
over 350 articles on disability, point out that the disability risk factors identified for
employees do not necessarily apply to the self-employed. The two populations may
have different characteristics. Moreover, their working conditions and benefits, as
well as their remuneration methods, generally differ. For example, a variable that is
often related to sick leave is the business cycle. During recessions, the prevalence of
sick leave among employees is likely to be lower as a result of e.g. decreased work
load or the threat of job losses. However, sick leave among the self-employed may
increase in an economic downturn, owing to a ‘secondary gain’. That is, disability
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insurance does not only protect self-employed against income loss due to disability,
but also against income loss due to adverse economic conditions and income loss in
general (Bakker et al., 2006). Other differences may arise due to the specific nature
of private insurance, in which risk assessment generally plays a more important role
than in private insurance. Indeed, Yelin et al. (1980) and Krause et al. (1997) docu-
ment, respectively, shorter and longer disability durations for self-employed relative
to employees. Also among the few empirical studies on disability of self-employed
is Hartman et al. (2003). The authors use data on sick leave claims provided by a
private Dutch insurance company to analyze the frequency and duration of disabil-
ity among (self-employed) Dutch farmers. The authors find that both the claimant’s
age and type of illness affect the duration of the incapacity.
Our study assesses the determinants of sick leave durations among self-employed,
thus contributing to the scarce literature on sickness absenteeism in this group. We
use a unique data set of sick leave claims by self-employed working in various pro-
fessions, provided by a private Dutch insurance company. A wide range of survival
models is applied to assess the determinants of the disability duration. We explic-
itly take into account various sociodemographic, contract-specific, and business-cycle
variables. In particular, we investigate how a fundamental change in the way the in-
surance company monitored claimants affected the duration of benefit claims. More
specifically, until mid-2003 this insurance company focused primarily on assessing
the legitimacy of the claims and on determining the proper benefit payment accord-
ing to the terms of the claimant’s insurance contract. From mid-2003 onwards, the
insurance company shifted its focus to trying to shorten benefit payment durations
by active case management. To this end, dedicated case managers now perform the
intake interview and monitor the recovery process, while opportunities for alterna-
tive employment and the usefulness of interventions are also considered as part of the
standard procedure. To our best knowledge, the existing literature on case manage-
ment and vocational interventions all focus on employees and not on self-employed
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(see e.g. Donceel, 1999; Høgelund and Holm, 2006). Therefore, the present paper is
also an initial attempt to assess the impact of insurer-based case management on
the self-employed. Furthermore, we consider the role of economic incentives on the
return-to-work process of self-employed by assessing the impact of the compensation
benefit level on the duration of the incapacity.
Based on a wide range of models, specifications and estimation methods, our
case study shows that various sociodemographic, contract-specific and business-cycle
specific factors significantly affect disability durations for the self-employed. Age and
the type of illness are among the most significant determinants of the disability spell.
The recovery rate decreases with age and claimants suffering from psychological and
neurological diseases have a substantially lower recovery rate relative to claimants
with other disorders. Disability durations are longer in periods of high economic
growth. Hence, we do not find any evidence for a secondary-gain effect. Contract-
specific factors such as insurance brand, deferment period and compensation benefit
level are typical characteristics of insurance contracts for self-employed and play an
important role. For example, if the income replacement benefit in the second and
later years is lower than in the first year, recovery is significantly faster. Hence,
loss of income in the second and later years relative to the first year provides an
incentive for faster recovery. The introduction of insurer-based case management
significantly increased the recovery rate of claims with a spell up to one year. By
contrast, case management did not succeed in improving the recovery rate for the
longer lasting claims. We do not establish any significant gender differences in the
sick leave durations of self-employed.
The paper is structured as follows. A brief literature review is presented in Sec-
tion 2. Section 3 describes the data, while Section 4 provides an explorative analysis
of the claims in our sample. Next, Section 5 describes the survival models used
and Section 6 discusses the corresponding empirical results and robustness checks.
Lastly, we present our conclusions in Section 7.
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2 Literature review: determinants of disability dura-
tions
There exists a vast literature on sick leave durations. Where the medical-statistical
literature generally focuses on the determinants of disability spells, the economic lit-
erature often puts emphasis on the role of economic incentives in the return-to-work
process. Furthermore, the medical-statistical literature is characterized by an abun-
dance of studies focusing on work absence related to low back pain; see Krause et al.
(2001). The latter article also provides an extensive overview of the various determi-
nants of disability durations found in the literature. Another important difference
between the various studies on disability durations is that some distinguish between
work-related and non-work-related injuries, whereas others do not. Other studies
distinguish explicitly between short-term and long-term sick leave and disability.1
Also the type of data analyzed differs across studies, e.g. individual insurance claim
data, sample survey data, insurance claim data for individual firms, aggregate data,
microeconomic data. A common feature of virtually all studies in the field is their
focus on work absenteeism among employees. Research on disability durations of
self-employed is extremely scarce (Bakker et al. 2006).
The goal of this section is not to provide a complete overview of the factors the
literature has identified to affect disability durations, but to review some previous
work that is relevant in the context of this paper. In the abundant literature assessing
the determinants of disability durations among employees it is often not hard to find
two studies with opposite empirical results regarding certain risk factors. However,
for most determinants there is a predominant effect, reflecting the general outcome
of the majority of studies in this field. Sociodemographic factors that are generally
found to prolonge disability durations are e.g. female gender, old age, low education,
and limited previous labor market experience. Also the impact of economic incentives
on disability durations has been analyzed extensively. See e.g. Johansson and Palme
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(1996, 2002, 2005), who find that workers adapt their work absenteeism behavior to
the generosity of the sickness insurance scheme. Fenn (1981), Doherty (1979), Meyer
et al. (1995) and Galizzi and Boden (2003) find that higher wage replacement ben-
efits prolonge sick leave durations. By contrast, Butler and Worrall (1985) do not
find any significant impact of the wage replacement benefit on the return-to-work
process. Several studies analyze the influence of macro-economic factors and busi-
ness cycle variables on sick leave durations. According to Shapiro and Stiglitz (1984)
unemployment may act as a worker discipline device. Empirical evidence supports
this theory, see e.g. Henrekson and Persson (2004) and Johansson and Palme (2005)
who find that disability durations are shorter in periods of high unemployment. Also
economic growth has been shown to affect sickness absenteeism. During recessions,
the frequency or duration of sick leave among employees is generally lower as a re-
sult of e.g. decreased work load or the threat of job losses (Bakker et al., 2006).
Another strand of literature evaluates the impact of vocational interventions on the
return-to-work process. Several types of interventions have been considered, such
as educational measures, adjustment of working conditions, and case management.
There is no evidence that educational measures reduce sick leave durations (see e.g.
Frolich et al.; 2004), but adjustment of working conditions has been shown to signif-
icantly shorten disability spells (Fitzler and Berger, 1982, 1983). Case management
can either be medically or socially oriented and can be initiated by the employer or
insurer. Donceel et al. (1999) find that insurance-based case management improves
the return-to-work process. Høgeland and Holm (2006) show that case management
performed by social workers (focusing on vocational rather than medical aspects)
increases the probability of returning to work for the pre pre sick leave employer.
However, it does not significantly affect the probability of resuming work at a new
employer. Indahl et al. (1995) evaluate a specific type of medically oriented case
management applied to low back pain patients and document a faster recovery rate.
For some variables it is not obvious that they will affect sick leave durations of
5
self-employed in the same way as they influence disability spells of employees. For
example, self-employed are their own employer and therefore not exposed to the risk
of getting fired. Hence, the argument that unemployment acts as a worker disci-
pline device (Shapiro and Stiglitz, 1984) seems less relevant for the self-employed.
Our study will shed more light on the potential differences in sick leave behavior
between employees and self-employed. Moreover, our study differs from the existing
literature in three major ways. First, we analyze sick leave durations corresponding
to self-employed instead of employees. We use individual claim data provided by
a major Dutch insurance company. The claims in our data set correspond to both
short-term and long-term sick leave and disability. Second, we evaluate the impact
of insurer-based case management on the return-to-work process. To our best knowl-
edge, only one paper (Donceel et al., 1999) has assessed the impact of this type of
case management on work absenteeism. Third, we also consider the role of economic
incentives on the return-to-work process of self-employed by assessing the impact of
the compensation benefit level on the duration of the incapacity.
3 Data
This section gives a detailed description of our data sample and motivates the choice
of explanatory variables. Moreover, it also provides sample statistics.
3.1 Description of data
Until 2004, state-provided social insurance for self-employed workers in the Nether-
lands only included compensation for loss of income after one year of sickness and for
a maximum of 70% of the statutory minimum wage. In addition, private insurance
companies provided additional insurance for self-employed workers wanting extra or
earlier compensation in the event of disability. The collective state disability insur-
ance scheme for self-employed workers was abolished in August 2004. Since then,
this type of insurance has only been available from private insurance companies.
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Private insurance policies differ with respect to the deferment period (i.e. the time
between falling ill and the start of the benefit payment, which is meant to determine
the insured’s state of health more exactly and to prevent him or her from using
disability benefits for relatively minor health problems), the employment criterion
used (i.e. a return to the same job or alternative employment) and the maximum
duration of benefit payments. Individuals opt for the contract and conditions that
suit best their personal preferences and situation, in relation to the premium.
This paper uses information on disability benefit claims provided by a private
Dutch insurance company. In our analysis we focus on the duration of each claimant’s
disability, which we obtain as the sum of the deferment period and the duration of the
benefit payment. This results in an inflow sample, consisting of left-truncated (and
right-censored) spells. Unfortunately, the information available from the insurance
company does not permit a detailed analysis of the incidence of claims over the
years. We therefore focus solely on the disability duration. The data set of claims
contains personal characteristics (such as date of birth and occupational class), type
of illness, characteristics of the insurance product (such as the deferment period),
characteristics of the claim (such as the starting and ending dates of payments),
and variables related to the business cycle. We exclude claims with incomplete or
inconsistent information. Claims, for example, for which benefit payments started
before the end of the deferment period are regarded as inconsistent. The final sample
consists of 1,368 claims, of which 125 started in 2000, 130 in 2001, 168 in 2002, 189
in 2003, 414 in 2004 and 342 in 2005. Since some individuals were still ill at the
end of our sample period (end 2005), the corresponding payment durations are right
censored.
3.2 Choice of explanatory variables
Our sample contains claims initiated before August 2004, when self-employed still
fell under the Wet Arbeidsongeschiktheid Zelfstandigen (WAZ). This law obliged
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them to participate in a collective state disability insurance. Consequently, the claims
during that period only apply to additional insurance. As of August 2004, the claims
apply to full disability insurance, although the terms and conditions of the insurance
vary across clients and depend on the type of insurance. Each claim in the sample
corresponds to an insurance contract of a particular brand. There are three brands
(which we simply refer to as brand 1, 2 and 3), but brand 2 and 3 are not present in
the sample before the year 2004. Brand 1 has national coverage, whereas brand 2 and
brand 3 have a regional scope in, respectively, the East and West of the Netherlands.
All insurance contracts have a deferment period of either 7, 14, 30, 60, 90, 180 or 365
days. Insured individuals only start receiving benefit payments after the deferment
period. We attribute a specific compensation benefit level to each insurance contract,
where we distinguish between the first year and the second and later years. The
compensation benefit level represents the maximum amount of money available each
year in the event of illness.2 For 1,255 claims we also record the type of illness causing
the disability. Table 1 describes the explanatory variables in our data set. The choice
of these variables is motivated by previous studies that qualify these factors as
determinants of disability durations of employees (see Section 2) in combination
with availability in our data set. In particular, we consider several factors specific to
private disability insurance, for example insurance brand and compensation benefit
level. With respect to the latter variable, we include the difference between the
compensation benefit levels in the first and later years. This is a measure of the
generosity of the disability insurance in the second year relative to the first year.
To distinguish the impact of case management as of mid-2003 from any trend in
the recovery rate, we use the approach of Johansson and Palme (2005) who write
(at page 1883) ‘(. . . ) behavioral changes that can be referred to trends, or gradual
changes in society, cannot be recorded as jumps or discontinuous changes in the
data, as opposed to the effect of policy interventions implemented at a particular
date’. This is exactly the reason why we include both a trend (based on the starting
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time of the benefit claims) and a dummy in the CPH model. The former captures
any gradual changes in the recovery rate over time, whereas the latter picks up the
difference in the hazard rate before and after the introduction of case management.
Since we will later extend the model with time-varying business cycle variables
measured on a quarterly level, we measure time in units of a quarter.
4 Preliminary duration analysis
To obtain an initial impression of relevant sample properties of the data at hand,
this section provides an explorative data analysis. From Table 2 we see that the
duration of benefit payments ranges from 1 to 2,126 days (almost six years), whereas
the disability durations range from 15 to 2,185 days. The censoring rate is 36%.
Table 2 also reports sample statistics for the sick leave durations and the explanatory
variables available in our data set. This table also contains summary statistics for
two business cycle variables (GDP growth rate and unemployment rate), which are
observed at a quarterly level.3 Later we will use these variables to assess the impact
of the business cycle on the recovery rate of self-employed workers. Figure 1 displays
unemployment and GDP growth over time.
To gain more insight into the disability duration, we obtain a Kaplan-Meier sur-
vival curve (see Figure 2). This curve shows the duration of the disability duration
(measured in years) on the horizontal axis and the percentage of ongoing claims
on the vertical axis. The curve becomes almost flat after 2.5 years, although ap-
proximately 25% of the disability spells are still continuing at that point. In short,
individuals either recover within two or three years or are trapped in long-term ill-
ness. Figure 3 focuses on the first 600 days of the disability duration to give a more
detailed picture. In 50% of cases, the disability lasts less than 192 days. A relatively
high number of claims also end within about 110 days, as the small hump at this
point on the survival curve shows. This is mainly attributable to pregnancies, which
generally have a fixed payment duration of 16 weeks.4 There is another small hump
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around 366 days, caused by the relatively many durations that end after one year.
Since individuals have different deferment periods, the periods during which
people have been ill before starting to receive benefit payments also vary. If we
distinguish between deferment periods of 30, 90 and 365 days, we can construct
different survival curves based on claim duration (see Figure 4). Individuals who
have been ill for a year recover relatively slowly compared with people who have
been ill for only 30 or 90 days. Claims with longer deferment period may correspond
to the more severe cases in terms of illness, which could explain the lower recovery
rate.
Next, we construct two distinct survival curves to get an initial idea of the impact
of case management, which became effective as of mid-2003. By then the insurance
company had decided to monitor ill individuals more closely and to shift its focus
to trying to shorten benefit payment durations by active case management.5 We
emphasize that the new policy was only applied to new cases of sick leave as of
the second half of 2003. The first survival curve corresponds to disability durations
starting before mid-2003, while the second reflects the claims initiated thereafter.
Figure 5 makes clear that the survival curve for claims lodged before mid-2003 is
above the one for claims lodged in the second half of 2003 and later, thus at first sight
reflecting a faster recovery process in the period since the start of case management.
5 Modeling approach
This section briefly discusses the survival model that we will later use to assess the
determinants of the recovery rate. A useful tool in survival analysis is the hazard rate,
which reflects the instantaneous probability that a duration will end within the next
instant of time. In practice, the hazard rate will often depend on certain covariates.
For instance, the survival time of a patient will be affected by characteristics such
as age and gender. The most frequently used semiparametric method to estimate
conditional hazard rates is Cox Proportional Hazards (CPH) model (Cox, 1972).
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The CPH model is formulated in terms of the hazard rate, conditional on certain
covariates. The conditional hazard rate of a duration X given covariates Z = z is
defined as
λ(x | z) = lim∆x→0
IP(X ≤ x + ∆x | X > x,Z = z)/∆x [x > 0]. (1)
We emphasize that the hazard rate is not a true probability in the sense that it can
be larger than 1. According to the CPH model the hazard rate is of the form
λ(x | z) = exp(z′β)λ0(x), (2)
where z is a K-dimensional vector of covariates, β a vector of coefficients of the same
dimension, and λ0(·) the baseline hazard. To deal with individual-specific unobserved
heterogeneity (such as risk aversion, motivation to recover, willingness to take pre-
scribed medication), we include gamma frailty in the model. For some claimants we
have more than one claim in our data set. More precisely, 11% of the total number
of claims origins from individuals who issued two or more claims. By including a
frailty term in our model, we also deal with these multiple claims (we assume a
shared frailty term for different claims by the same individuals). The choice for the
gamma distribution is motivated by Abbring and Van den Berg (2006), who focus
on a broad class of hazard models with proportional unobserved heterogeneity. In
this class of models the distribution of the heterogeneity among survivors converges
to a gamma distribution.
We include the explanatory variables listed in Table 1 as covariates in the CPH
models. The time trend related to the starting time of the incapacity is taken to be
a third-order polynomial and is included to pick up any deterministic patterns in
the recovery rate. Its order length has been determined on the basis of the Akaike
criterion.
6 Empirical results
This section formalizes the preliminary data analysis of Section 4.
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6.1 Determinants of disability durations
Since we only know the type of illness for a subset of the data, we confine the es-
timation of the model to the subsample of 1,255 complete observations. We start
with the CPH model and estimate two versions: one without the business cycle vari-
ables and one including them. Both GDP growth and unemployment are measured
on a quarterly level. They act as time-varying covariates and need to be treated
accordingly in the CPH. We follow the usual approach and apply episode-splitting
to estimate the CPH model with gamma frailty by means of penalized likelihood
(Klein and Moeschberger, 2004) including the two business cycle variables.6
The estimation results for the standard CPH model (without business cycle
variables) in Table 3 shows that various factors have a significant impact on the
disability duration, including the occupational class of the insured, the type of illness,
the insurance brand, the compensation benefit level and the claimant’s age. The
exponentiated coefficients of the dummy variables in Table 3 (see the ‘standard
CPH model’ and the column captioned ‘exp(coef)’) reflect the impact of a variable
on the hazard rate. For instance, the exponentiated coefficient of age is 0.98, which
means that the recovery rate of an n-year old is 2% higher than of an (n + 1)-year
old. This implies that the probability that a 60-year-old individual will recover is
only 63% of the recovery rate of a 40-year-old. The occupational class of the insured
plays only a modest role in explaining the duration of absence from work, with
the only significant effect being found for hairdressers, who have a relatively slow
recovery process. By contrast, the type of illness plays a very important role. Benefit
payments to individuals with neurological or psychological disorders continue for
relatively long periods, whereas − as expected − women recover relatively quickly
from a pregnancy. After correction for individual, time and contract-specific factors,
gender does not significantly affect the length of the disability duration. If we do
not include the professional class of the claimant in the CPH model, then women
recover significantly more slowly than men. On the other hand, when we omit the
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type of illness, women recover significantly faster than men. Apparently, in our data
sample, the typical jobs that women have lead to slower recovery, whereas their
type of illness is less severe. The role of professional class and type of illness also
emphasizes the importance of taking into account these variables. Claimants with a
disability insurance of brand 2 recover significantly faster than those with a contract
of brand 1. Brand 2 was sold in the East of the Netherlands (which is a more rural
area), whereas brand 1 has national coverage and brand 3 was predominantly sold
in the West (industrialized area). Hence, the differences among the brands may
reflect regional differences. Furthermore, if the income replacement benefit in the
second year is lower than in the first year, recovery is significantly faster. If the
compensation benefit in the second and later years relative to the first year drops
with 1,000 euro, the hazard rate increases with 1%. Hence, loss of income in the
second and later years relative to the first year provides an incentive for faster
recovery. This finding supports the results of e.g. Meyer et al. (1995) and Galizzi
and Boden (2003), who find that higher wage replacement benefits prolonge sick
leave durations. Although our measure of income replacement benefits is differently
defined than in the aforementioned studies, ours is also related to the generosity
of the disability insurance. Hence, we conclude that the generosity of the disability
insurance affects the recovery rate. Finally, we note that the frailty parameter related
to the gamma distribution turns out insignificant in the CPH model.
The CPH including the two business cycle variables does not differ much from the
model excluding these factors. The estimation results for this model are displayed
in Table 3 in the columns with the caption ‘CPH (TVC)’. As expected, the un-
employment rate does not significantly affect the disability duration. GDP growth
has a negative effect on the recovery rate, which is significant at the 10% level.
Hence, in periods of economic downturn the self-employed workers in our sample
recovered relatively quickly, whereas their benefit dependence lasted relatively long
in the periods that the economy was booming. Thus, we do not find any evidence
13
for a secondary gain. Instead, self-employed respond similarly to economic growth
as employees according to the literature.7
To assess the impact of the deferment period on the claim duration, we estimate
the above CPH models in terms of the benefit payment duration instead of the total
disability spell. We then also include dummy variables for the different deferment
periods in the model. The estimation results show that the longer the deferment
period, the lower the recovery rate. This finding confirms the result of the preliminary
data analysis of Section 6. Claims with a longer deferment period may correspond
to the more severe cases in terms of illness, which could explain the lower recovery
rate. The remaining model coefficients are very similar to the ones established in the
CPH models for the total disability spell.8
6.2 The impact of case management on the recovery rate
The dummy variable for the period prior to mid-2003 is insignificant, which means
that there are no significant differences in the recovery rate before and after the
introduction of case management by the insurance company. At first sight, this
seems to contradict Figure 5, according to which the recovery probability is higher
after the insurer-based case management became effective. However, the estimates
in Figure 5 have not been corrected for the wide range of covariates included in
the CPH model. All in all, the Kaplan-Meier estimates incorrectly suggest that
case management has succeeded to increase the recovery probability. However, the
insignificant case management dummy in the CPH model is only informative about
the ‘average’impact of case management on the recovery rate. The standard CPH
does not distinguish between the impact of case management on the hazard rate
coming from shorter and longer spells. To get a better understanding of the influence
of insurer-based case management on the hazard rate, we estimate an extended CPH
model that allows case management to affect the hazard rate coming from short and
long durations in a different way. For this purpose we create several new variables
14
that we include in the CPH model. The function I(r ≤ t ≤ s) takes the value 1 if
r ≤ t ≤ s and 0 otherwise. We add four new (time-varying) variables to the standard
CPH model, namely (1) I(t ≤ 90)× CM dum, (2) I(90 < t ≤ 365)× CM dum, (3)
I(365 < t ≤ 2 × 365) × CM dum and (4) I(t > 2 × 365) × CM dum. From the
estimation results it follows that the hazard from spells up to one year significantly
increased after the introduction of case management. More precisely, the first two
of the above variables have estimated coefficients equal to 0.435 and 0.408, with
respective p-values 0.049 and 0.046. However, case management did not significantly
affect the hazard coming from the longer spells; the third and fourth variables have
respective coefficient −0.192 (p-value 0.394) and −0.081 (p-value 0.880). Hence, case
management significantly increased the recovery rate for claimants with an ongoing
sick leave duration up to one year. The increase in the hazard rate is about 50%.
By contrast, case management did not succeed in improving the recovery rate for
claimants trapped in long-term disability. This is to some extent to be expected,
since the longer lasting claims are likely to be the most difficult cases with the most
severe disorders.9
6.3 Robustness checks
To further assess the robustness of the CPH models used in our analysis, we estimate
several alternative models and specifications.
We re-estimate all models excluding claims due to pregnancy, as pregnancy dura-
tions are likely to be much more predictable than the claim durations corresponding
to other diseases. Also, we run all estimations confining the claims to those of brand
1 only (bearing in mind that brand 2 and brand 3 were not present before the year
2004 and may thus distort the results). These modifications do not at all affect the
outcomes of our previous investigations, emphasizing once more the robustness of
our findings.
The CPH model imposes proportionality on the hazard rate; in other words, the
15
hazard ratio between two sets of covariates is assumed constant over time. Misspec-
ification of the conditional hazard rate may have serious consequences for statistical
inference; see e.g. Lagakos and Schoenfeld (1984), Schemper (1992) and Spierdijk
(2008). The accelerated failure time (AFT) model is another widely used survival
model, but does not impose proportionality on the hazard rate. We re-estimate all
prior specifications using a Weibull AFT model with gamma frailty. Throughout,
the CPH and AFT models produce very similar results.10
7 Conclusions
This paper contributes to the scarce literature on disability among self-employed
workers. It analyzes the disability durations of self-employed with disability insur-
ance from a major Dutch insurance company. Our case study focuses on the duration
of claims and assesses the determinants of these spells.
Our analysis reveals that several disability risk factors for employees also affect
the claim durations of self-employed. Age and the type of illness are among the
most significant determinants of the disability duration. The recovery rate decreases
with age and claimants suffering from psychological and neurological diseases have
a lower recovery rate relative to claimants with other disorders. Disability durations
are longer in periods of high economic growth. Hence, we do not find any evidence
for a secondary-gain effect. Contract-specific factors such as insurance brand, defer-
ment period and compensation benefit level are typical characteristics of insurance
contracts for self-employed and play an important role. For example, if the com-
pensation benefit level in the second year is lower than in the first year, recovery
is significantly faster. Hence, loss of income in the second year relative to the first
year provides an incentive for faster recovery. This leads to the important conclu-
sion that the generosity of the disability insurance affects the return-to-work process
of self-employed. The introduction of insurer-based case management significantly
increased the recovery rate of claimants with an ongoing spell up to one year. By con-
16
trast, case management did not succeed in improving the recovery rate for claimants
trapped in long-term disability. We do not establish any significant gender differences
in the sick leave durations of self-employed.
Our study suggests that the risk factors considered in our analysis affect disabil-
ity spells of self-employed in a similar way as they influence sick leave durations of
employees according to the literature. This conclusion could have important con-
sequences for insurers who want to determine appropriate underwriting criteria for
disability insurance for self-employed. However, given that our study is based on
claim data for a single insurance company and does not consider all risk factors
that are potentially relevant for the self-employed, further research is needed to get
a more complete picture of the determinants of the return-to-work process in this
group.
17
Endnotes
1In this paper we use the terminology ‘sick leave’ and ‘disability’ interchangeably.
2The maximum benefit payment is received if an individual has a disability factor of 100%.
3These variables have been obtained from the ‘Centraal Bureau voor de Statistiek’ (Statistics
Netherlands), see www.statline.cbs.nl (visited February 2008). Both GDP growth and unemploy-
ment rates are measured relative to the previous quarter.
4The data include sick leave attributable to pregnancy. Dutch self-employed women can take
private insurance against loss of income during pregnancy, usually for a period of 16 weeks, under
certain terms and conditions.
5We underline that the introduction of case management was not announced in advance, exclud-
ing any anticipation effects.
6All estimations in the paper have been done in R version 2.7.1 using the survival library version
2.34.
7We note that the use of detrended business cycle variables provides very similar outcomes.
8To save space we do not report these estimation results. They are available from the authors
upon request.
9The results are robust to alternative specifications. The hazard from shorter spells increases
significantly for various choices of the time dummies. The remaining model coefficients are similar
to those in the standard CPH model. In the CPH model with business cycle variables we also find
similar results. The estimation results for the extension of the CPH model are available from the
authors upon request.
10To save space we do not report the estimation results for the Weibull AFT model. They are
available from the authors upon request.
18
References
Abbring, J.H. and Van den Berg, G.J. (2007). The unobserved heterogeneity distri-
bution in duration analysis, Biometrika 94, 87-99.
Determinants of duration of disability and return-to-work after work-related injury
and illness: Challenges for future research. American Journal of Industrial Medicine
40, 464-484.
Lagakos, S.W. and Schoenfeld, D.A. (1984). Properties of proportional hazards score
tests under misspecified regression models. Biometrics 40, 1037-1048.
Meyer, B.D., Viscusi, K.W., and Durbin, D.L. (1995). Workers’compensation and
20
injury duration: Evidence form a natural experiment. American Economic Review
85, 322-340.
Schemper, M. (1992). Cox analysis of survival data with non-proportional hazard
functions. The Statistician 41, 455-465.
Shapiro, C. and Stiglitz, J.E. (1984). Equilibrium unemployment as a worker disci-
pline device. American Economic Review 74, 433-444.
Spierdijk, L. (2008). Nonparametric conditional hazard rate estimation: A local lin-
ear approach. Computational Statistics and Data Analysis 52, 2419-2434.
Yelin, E., Meenan, R., Nevitt, M., Epstein, W. (1980). Work disability in rheumatoid
arthritis: Effects of disease, social, and work factors. Annals of Internal Medicine 93,
551-556.
21
Table 1: Estimation results
This table gives the abbreviations of the explanatory variables used with theirdescription.
name description
contract featuresbrand2 dummy for brand 2 (region: East of the Netherlands)brand3 dummy for brand 3 (region: West of the Netherlands)diff comp benefit difference in compensation benefit
level between the first and later years (in units of 1,000 euro)occupational classadvisor dummy for advisorarchitect dummy for architectdirector dummy for directorhairdresser dummy for hairdressershop owner dummy for shop ownerfarmer dummy for farmer
type of illnesscardiovascular dummy for cardiovascular diseasepregnancy dummy for pregnancylocomotor dummy for locomotor diseaseneurological dummy for neurological diseasepsychological dummy for psychological diseasedigestive dummy for digestive diseaseurogenous dummy for urogenous disease
individual characteristicage claimant’s agewoman dummy for female claimants
trendstart disability quarter in which the disability started (counted as of January 2000)
case managementCM dum dummy for the period after mid-2003 (after the introduction of case management)
business cycleGDP growth growth rate of the Dutch economy (quarterly level, in %)unempl rate unemployment rate (quarterly level, as % of total labor force)
22
Table 2: Sample statistics
% single claim 72median duration benefit payment 141range benefit payment durations 1 to 2,126 daysmedian duration sick leave 192range sick leave durations 15 to 2,185 days% right censored sick leave durations 36% males 75% females 25average age men 48 yearsaverage age women 40 yearsrange age 21-65 years% brand 1 75% brand 2 13% brand 3 12% deferment period 30 days 71% deferment period 90 days 13average compensation benefit level first year 26,000 euroaverage compensation benefit level second year 20,000 euro
Figure 1: Unemployment rate and GDP growth over time
-1
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�������� ����� ������unemployment rate (%) GDP growth rate (%)
25
Figure 2: Fraction of ongoing claims (0-5 years)
This figure displays the Kaplan-Meier estimator of the fraction of ongoing claimsas a function of time (measured years). The dashed lines constitute a 95%asymptotic confidence interval.
0 1 2 3 4 5
0.0
0.2
0.4
0.6
0.8
1.0
years
frac
tion
of o
ngoi
ng c
laim
s
26
Figure 3: Fraction of ongoing claims (0-600 days)
This figure displays the Kaplan-Meier estimator of the fraction of ongoing claimsas a function of time (measured in days), zooming in on the first 600 days of thebenefit payment duration. The dashed lines constitute a 95% asymptoticconfidence interval.
0 100 200 300 400 500 600
0.0
0.2
0.4
0.6
0.8
1.0
days
frac
tion
of o
ngoi
ng c
laim
s
27
Figure 4: Fraction of ongoing claims for different deferment periods
This figure displays the Kaplan-Meier estimator of the fraction of ongoing claimsas a function of time (measured in days), for different deferment periods.
100 200 300 400 500
0.0
0.2
0.4
0.6
0.8
1.0
days
frac
tion
of o
ngoi
ng c
laim
s
deferment period 365deferment period 90deferment period 30
28
Figure 5: Fraction of ongoing claims before and after mid-2003
This figure displays the Kaplan-Meier estimator of the fraction of ongoing claimsas a function of time (measured in days), before and after mid-2003.
