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: l.spierdijk@rug.nl.
†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: gijsbert.van.lomwel@achmea.nl.
‡Achmea, Occupational Health Division, P.O. Box 700, NL-7300 HC, Apeldoorn. Email:
wilco.peppelman@achmea.nl. 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.
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 neurologpsycholog-ical 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
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
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
(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. SecSec-tion 3 describes the data, while SecSec-tion 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.
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
(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. Fr¨olich 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
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.
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
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.2For 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
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
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).
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→0IP(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(z0β)λ0(x), (2)
wherezis aK-dimensional vector of covariates,βa vector of coefficients of the same dimension, andλ0(·) 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
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 ann-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
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
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
that we include in the CPH model. The functionI(r ≤t ≤s) takes the value 1 if
r≤t≤sand 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 respectivep-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 duradura-tions 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.
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 insurinsur-ance 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-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.
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 thesurvivallibrary 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
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Table 1:Estimation results
This table gives the abbreviations of the explanatory variables used with their description.
name description
contract features
brand2 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 class
advisor dummy for advisor
architect dummy for architect
director dummy for director
hairdresser dummy for hairdresser
shop owner dummy for shop owner
farmer dummy for farmer
type of illness
cardiovascular dummy for cardiovascular disease
pregnancy dummy for pregnancy
locomotor dummy for locomotor disease
neurological dummy for neurological disease psychological dummy for psychological disease
digestive dummy for digestive disease
urogenous dummy for urogenous disease
individual characteristic
age claimant’s age
woman dummy for female claimants
trend
start disability quarter in which the disability started (counted as of January 2000)
case management
CM dum dummy for the period after mid-2003 (after the introduction of case management)
business cycle
GDP growth growth rate of the Dutch economy (quarterly level, in %) unempl rate unemployment rate (quarterly level, as % of total labor force)
Table 2:Sample statistics
% single claim 72
median duration benefit payment 141
range benefit payment durations 1 to 2,126 days
median duration sick leave 192
range sick leave durations 15 to 2,185 days
% right censored sick leave durations 36
% males 75
% females 25
average age men 48 years
average age women 40 years
range age 21-65 years
% brand 1 75
% brand 2 13
% brand 3 12
% deferment period 30 days 71
% deferment period 90 days 13
average compensation benefit level first year 26,000 euro
average compensation benefit level second year 20,000 euro
occupational class % advisors 14 % architects 3 % directors 24 % hairdressers 5 % shop owners 4 % farmers 8 % others 42 illness % cardiovascular 7 % pregnancy 8 % locomotive 40 % neurological 4 % psychological 16 % digestive 5 % urogenous 4 % others 14 business cycle
% average quarterly growth of GDP (2000-2005) 0.4
Table 3:Estimation results
This table displays the estimation results for the Cox proportional hazards (CPH) models with gamma frailty.
standard CPH CPH (TVC)
variables coef exp(coef) p-value coef exp(coef) p-value
brand2 0.296 1.344 0.073 0.286 1.331 0.083 brand3 0.184 1.201 0.120 0.171 1.187 0.140 advisor 0.055 1.057 0.620 0.051 1.052 0.650 architect 0.005 1.005 0.980 0.017 1.017 0.940 director 0.020 1.020 0.840 0.021 1.021 0.830 hairdresser -0.465 0.628 0.011 -0.458 0.633 0.012 shop owner -0.122 0.885 0.560 -0.122 0.885 0.560 farmer 0.251 1.285 0.190 0.246 1.278 0.200 cardio vascular -0.253 0.777 0.180 -0.265 0.768 0.170 pregnancy 0.959 2.610 0.000 0.959 2.610 0.000 locomotor 0.015 1.015 0.920 0.010 1.010 0.940 neurological -0.976 0.377 0.001 -0.976 0.377 0.001 psychological -0.516 0.597 0.001 -0.520 0.594 0.001 digestive -0.042 0.959 0.840 -0.046 0.955 0.820 urogenous 0.071 1.073 0.740 0.055 1.056 0.790
diff comp benefit 0.010 1.010 0.008 0.010 1.010 0.008
age -0.023 0.977 0.000 -0.023 0.977 0.000 woman -0.136 0.872 0.230 -0.137 0.872 0.220 start disability 0.371 1.449 0.005 0.384 1.468 0.004 start disability2 -0.025 0.975 0.034 -0.028 0.973 0.030 start disability3 0.001 1.001 0.060 0.001 1.001 0.050 CM dum 0.075 1.078 0.710 0.119 1.126 0.560 real GDP growth -0.184 0.832 0.036 unempl rate 0.026 1.026 0.770
Figure 1: Unemployment rate and GDP growth over time -1 0 1 2 3 4 5 6 7 8 3 /1 /2 0 0 0 7 /1 /2 0 0 0 1 1 /1 /2 0 0 0 3 /1 /2 0 0 1 7 /1 /2 0 0 1 1 1 /1 /2 0 0 1 3 /1 /2 0 0 2 7 /1 /2 0 0 2 1 1 /1 /2 0 0 2 3 /1 /2 0 0 3 7 /1 /2 0 0 3 1 1 /1 /2 0 0 3 3 /1 /2 0 0 4 7 /1 /2 0 0 4 1 1 /1 /2 0 0 4 3 /1 /2 0 0 5 7 /1 /2 0 0 5 1 1 /1 /2 0 0 5 3 /1 /2 0 0 6
Figure 2: Fraction of ongoing claims (0-5 years)
This figure displays the Kaplan-Meier estimator of the fraction of ongoing claims as 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
Figure 3: Fraction of ongoing claims (0-600 days)
This figure displays the Kaplan-Meier estimator of the fraction of ongoing claims as a function of time (measured in days), zooming in on the first 600 days of the benefit payment duration. The dashed lines constitute a 95% asymptotic
confidence interval. 0 100 200 300 400 500 600 0.0 0.2 0.4 0.6 0.8 1.0 days
Figure 4: Fraction of ongoing claims for different deferment periods This figure displays the Kaplan-Meier estimator of the fraction of ongoing claims as 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
fraction of ongoing claims
deferment period 365 deferment period 90 deferment period 30
Figure 5: Fraction of ongoing claims before and after mid-2003 This figure displays the Kaplan-Meier estimator of the fraction of ongoing claims as a function of time (measured in days), before and after mid-2003.
50 100 150 200 0.0 0.2 0.4 0.6 0.8 1.0 days
fraction of ongoing claims
after mid−2003 before mid−2003
