Effect of the Dutch compulsory deductible on GP visits

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Effect of the Dutch

Compulsory Deductible on

GP Visits

Vivianne Vluggen

Master’s Thesis

Student number: 6304672 / 10005110 Date of final version: October 7, 2015 Master’s Programme: Econometrics

Specialisation: Econometrics Supervisor: prof. dr. J.F. Kiviet Second Reader: dr. J.C.M. van Ophem

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Statement of Originality

This document is written by Student Vivianne Vluggen who declares to take full responsibility for the contents of this document. I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and

its references have been used in creating it.

The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

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Abstract

In this thesis the effect of the introduction and rise of the compulsory deductible from 2007 until 2013 on yearly General Practitioner (GP) visits in the Netherlands is investigated. From 2006 the Dutch health care insurance system was reformed. Part of the reformation was the introduction of the compulsory deductible in 2008. In this empirical investigation different model specifications for the number of GP visits are proposed as well as different estimation methods. Of these methods the Arellano-Bond difference GMM estimation method provides the more reliable results. Using this method the endogeneity and predeterminedness of health status indicators and choices for insurance are taken into account. The results point out that no clear significant effect of the compulsory deductible on the number of yearly GP visits can be concluded. This is remarkable, since the phenomenon of moral hazard predicts a decrease in health care demand when the financial burden to make use of health care increases. A possible explanation for the weak significance of the estimated effect is that the exclusion of GP services from the compulsory deductible cancels out this negative effect of moral hazard. The results of this study should be handled with caution when desiring to draw generic conclusions about the effect of the compulsory deductible. During this investigation a number of areas for improvement have surfaced, which lead to the encouragement to extend this research.

Keywords: panel data, compulsory deductible, moral hazard, GP visits, negative binomial count model, Arellano-Bond difference GMM, Dutch insurance system

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List of Tables and Figures

Table 1. Premiums for basic health insurance at some insurance companies from 2009 – 2015.

(Homefinance B.V., n.d.) ... 52

Table 2. Number of participants in each year of the panel, before and after merging the waves and leaving out observations. ... 52

Table 3. Descriptive sample statistics. ... 53

Table 4. Dependent and explanatory variables... 54

Table 5. Descriptive statistics of explanatory variables. ... 57

Table 6. Descriptive statistics of GP visits. ... 59

Table 7. Number of individuals choosing for voluntary deductibles from 2007 until 2013. ... 59

Table 8. Mean values for some variables conditional on chosen voluntary deductible. ... 60

Table 9. Mean values for some variables conditional on chosen complementary insurance. ... 60

Table 10. Average GP visit counts for some subsamples. ... 60

Table 11. Initial (weak) assumptions regarding endogenous, predetermined or exogenous nature of included variables. ... 61

Table 12. Autocorrelation tests under initial (weak) assumptions. ... 61

Table 13. Hansen and Difference-in-Hansen tests on validity of instruments for initial (weak) assumptions. ... 62

Table 14. Hansen and Difference-in-Hansen tests on validity of instruments for final (stronger) assumptions. ... 63

Table 15. Autocorrelation tests under final (stronger) assumptions. ... 64

Table 16. Instrument matrices. ... 64

Table 17. Arellano-Bond difference GMM estimation results. ... 65

Table 18. Negative binomial count model estimation results. ... 67

Figure 1. Health care expenditures as percentage of GDP in 2006 and 2010 in different countries. (Schnabel, 2014) ... 68

Figure 2. Total health care expenditures as a share of GDP. (Rapport Taskforce Beheersing Zorguitgaven, 2012). ... 68

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1. Introduction

Health care expenditures make up a substantial portion of total Gross Domestic Product (GDP) in all OECD (Organisation for Economic Co-operation and Development) countries. For most of these countries, health care expenditures as a share of total GDP have trended upward over the last years and decades. In the Netherlands the share increased from 8% in 1972 to more than 12% in 2010 (Van der Horst, 2011). Figure 1 shows health care expenditures as a percentage of GDP for some (OECD) countries. From the figure it becomes clear that the expenditures have grown strongly for most of the countries. Yet, there is something remarkable: in the Netherlands this health care expenditures growth is relatively high. The most commonly cited reasons for this increase are the expanding technological possibilities in the health services sector as well as the ageing of the population, coupled in many countries with a large public health sector where the incentive structures may not promote efficient use of resources. The Netherlands is one such country with a large publicly funded health sector.

The real health care expenditures in the Netherlands have risen since the beginning of this century by more than 4.5% per year. This growth rate is almost three times as high as the structural economic growth rate. In addition to this long-term growth, there is the problem of the difficult manageability of health care expenditures. In the past decades the Dutch government has failed to control these growing health care expenditures within the set limits. Over the past 15 years the expenditures remained only just once within the Health Care Budget (HCB, Budgettair Kader Zorg). This is despite the increase in annual growth of the HCB from 1.3% in 1994 to 4.3% in 2010.

The Bureau for Economic Policy Analysis Netherlands (Centraal Planbureau) shows that health care expenditures as a share of GDP have been rising for decennia, but since the beginning of the 21st century the costs of health care increased much more than the long-term trend since 1972 predicted. Figure 2 makes this visible.

Internationally the Netherlands spends comparatively much more money on health care than other countries, both per capita and as a percentage of GDP. The Netherlands even spends more on prolonged health care than almost any other country. In the Netherlands about €5000 is spent per person annually on health care. For a two-income household with a total income of 1.5 times the average income, the payments on health care premiums are nearly a quarter of gross income. Next to the high level of public health care expenditures it is

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striking that these expenditures also have an above average growth rate. (Rapport Taskforce Beheersing Zorguitgaven, 2012).

The main reason for the rising expenditures is the growing consumption of health care. As stated before, three developments contribute to this growth in health care consumption. The first development that is a major factor in the growth of health care consumption is the persistent growth of technological innovation in medical care. Okunade and Murthy (2002) show that there is a significant and stable long-run relationship among per capita real health care expenditures, per capita real income and broad-based R&D expenditures. A second development attributing to the growth of health care consumption is the significant change in the age composition of the population in developed countries during the last 30 years. The relative number of people above the age of 80 has steadily increased and in general elderly consume more health care then youngsters. The age composition is expected to shift even more towards the geriatric age groups in the future, because of growing life expectancy and diminishing birth rate (Zweifel et al., 1999). In EU countries, for example, life expectancy at birth has increased by six years since 1980 (OECD, 2010). A third development is that the existence of large scale insurance schemes results in a separation between the amount of health care consumed by individuals and the costs that this health care consumption actually invokes (Chiappori, et al., 1998). There are two reasons for this separation between consumed health care and the actual costs when individuals are insured. (i) The first reason is that individuals have an incentive to overconsume health care, because they no longer bear all the costs for the medical services. The use of unnecessary health care is a consequence of moral hazard. (ii) A second reason is that individuals may know more about their risk types than insurers. Less healthy individuals, of whom the health status is known to the specific individual but not to the insurer, tend to buy more insurance than healthier individuals. The insurers are not able to correct for this in the price of the insurance (Cardon and Hendel, 2001). Less healthy individuals consume more health care, which is relatively less costly for them than for healthier individuals. This is the so-called adverse selection (Frank et al., 2000).

The first two developments listed above do not offer fairly good opportunities to restrain the costs of health care in the (near) future. However, the last development does. In view of the ever-rising health care expenditures the Dutch government systematically tries to adjust the health care insurance system with the aim to slacken the growth of health care expenditures. The Dutch government aims to diminish the moral hazard and adverse selection

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effects by law and regulations. One of its policies is the introduction of compulsory deductibles (Holly et al., 1998; Van Kleef et al., 2009). A system of compulsory deductibles invokes public awareness about health usage and strengthens the rational use of health care. Moreover, it attempts to provide an incentive for individuals to reduce the overconsumption of health care that was initially encouraged by the basic health care insurance.

For these reasons, among others, the Dutch government set a health care reform into force in 2006, with the implementation of a real compulsory deductible in 2008. This deductible replaced the no-claim rule that prevailed in 2006 and 2007. The introduction of the compulsory deductible was accompanied by the possibility to raise the amount of the deductible voluntarily in return of lower insurance premiums. The deductible is a measure to shift the risks and costs of health care from the government and insurers to the insureds (Gechert, 2010; Van Kleef et al., 2009).

Nevertheless, the introduction of the deductible also came with some detrimental effects. Namely, five years after the introduction the National Association of GP’s (Landelijke Vereniging van Huisartsen) reported in 2013 that patients now, more often than ever before, ignore a referral to see a specialist given by their GP because of financial reasons. Even 94 percent of the GP’s said to experience the fact that a patient does not act upon a referral for financial reasons every now and then (Joosten, 2015). Also in 2013 it became clear that two percent of the Dutch insureds sometimes refused to make use of health care because of its costs, whereas they presumed they actually earnestly needed the care. This emerged from a study mandated by the Minister of Health in the Netherlands. Moreover, this study pointed out that there are a lot of misconceptions about the deductible. For example, nineteen percent of the insured assume wrongly that the costs of a GP visit have to be paid from the deductible. In addition, 41 percent assumes wrongly that the costs of a visit to a medical specialist do not have to be paid from the deductible (NRC, 2013).

This study aims to investigate the effect of the introduction of the real compulsory deductible in the Netherlands in 2008 on the number of GP visits by the insured. Since the amount of the compulsory deductible more than doubled in the years after its introduction, this investigation takes the increase of the deductible over time into account and examines whether a significant trend in the number of GP visits from 2007 until 2013 can be traced, which is due to this increasing deductible, ceteris paribus. If such a trend can be established, the question arises whether this is the effect that the Dutch government desired when introducing the compulsory deductible in 2008. Until this moment in time there is still a lack

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of research on the effects of the introduction of the compulsory deductible. Van Ophem and Berkhout (2009) analysed the decision to accept a deductible or not in the case of health insurance in the Netherlands. Their results indicate that the main argument of the Dutch government for the introduction of a deductible (making people more aware of the costs of health care), appeared not to be relevant. Now that the compulsory deductible is already in operation for some years, data on related variables have been gathered over the period since the introduction. With these longitudinal data the aimed investigation can be performed, whereas in recent history effects of the Dutch deductible are only estimated with cross-section analyses, among others by Van Ophem (2013). Furthermore, whereas Van Ophem (2013) and Stroosnier and Van Ophem (2013) investigated the effects of moral hazard and adverse selection on the choice of different insurance schemes, this investigation on the other hand will concentrate on the effect of the compulsory deductible imposed by the government on the demand for health care.

This study is organized as follows. Previous research on this topic is reviewed in Section 2. In Section 3 the data will be discussed and it will be explained what changes are made to the data set in order to be able to use it. In Section 4 the models that will be used to explain the yearly number of GP visits are introduced, after which the results of the estimations are presented in Section 5. Section 6 concludes and Section 7 discusses possible pitfalls in drawing conclusions and discusses possibilities for future research.

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2. Economic Considerations and Previous Research

On January 1st 2006 the Dutch health care insurance system was reformed. The reform shifted the health care insurance system from a publicly provided to a more libertarian one (Maarse and Ter Meulen, 2006; Van Kleef et al., 2008). As before the reform, Dutch residents are still obliged to obtain at least basic health insurance. However, this is from this date on only offered by private insurance companies. The government sets the rules and the insurance companies have to make the best out of it within the set framework. Insurance companies are obliged to accept any individual and offer them at least a basic coverage as determined by the government. On top of that a compulsory deductible was introduced. In 2006 and 2007 this compulsory deductible had the form of a no claim arrangement of €255. Those insured that claimed less than this amount received the difference between €255 and their claim in cash at the end of the year. After 2007 this no claim was reformed to a real compulsory deductible of initially €150 in 2008. This real compulsory deductible needs to be paid out of pocket before insured can claim a refund of the incurred costs of health care. In later years the amount increased substantially. Furthermore, individuals have the option to accept an additional voluntary deductible at the benefit of a lower monthly insurance premium. The voluntary deductible offers individuals a trade-off between a lower premium of their insurance and higher financial risk (Van Ophem, 2013). On top of that, individuals can voluntarily take out complementary health care insurance. Both complementary insurance and deductibles are manners to shift health risks and costs from the government and insurers to the insured. (Gechert, 2010; Van Kleef et al., 2009). Before 2006 the focus of the health care insurance system was on the supply of services. With the introduction of the new system, focus shifted towards the demand (Stroosnier and Van Ophem, 2013).

2.1 Moral Hazard

The government’s purpose of the introduction of the deductible was to make people more aware of the costs of health care and to diminish unnecessary health care demand. The relation between the deductible in health care insurance and the demand for health care is clear-cut, at least in theory. If health care utilization is free, or at least perceived to be free, the demand will be higher. This is the moral hazard phenomenon (Van Ophem, 2013). This phenomenon suggests that some of the demand is not strictly necessary and that people can directly manipulate their demand if that is advantageous to them. The problem with moral

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hazard is that people make more use of health care than is strictly necessary, since they do not bear any costs for this ‘unnecessary’ use of health care. After the reform, people experiencing the deductible will not make use of the health care system for every itch or other bagatelle anymore, but are encouraged to think consciously about their health care utilization choices. The reason for this is that when a deductible is in force, using more health care does involve direct financial repercussions. Policy makers assume that individuals can make a conscious choice about their health care demand and that some health care can be avoided. Therefore, deductibles will diminish the perception that health care is ‘for free’, and thereby diminish the effect of moral hazard. Recent investigations on the effect of health care insurance choices on the demand for health care can be found in Cameron and Trivedi (1991), Hurd and McGarry (1997), Cardon and Hendel (2001), Godfried et al. (2001), Beaulieu (2002), Riphahn et al. (2003), Deb et al. (2006), Finkelstein and McGarry (2006), Fang et al. (2008), Cutler et al. (2008), Barros et al. (2008) and Resende and Zeidan (2010). These studies investigate the effects of moral hazard on health care demand. Most of them use a model based on cross-sectional data. Riphahn et al. (2003) use longitudinal data. They estimate a bivariate count process for the individual demand for GP and hospital visits, for which they specify a Poisson estimator with lognormally distributed random effects in the following way. They assume that every person 𝑖 has 𝑔 different outcome observations 𝑦 (i.e. doctor and hospital visits) in any period 𝑡, and that

𝑦_𝑖𝑡𝑔 ~ 𝑃𝑜𝑖(𝜆_𝑖𝑡𝑔), 𝑔 = 1,2 ln(𝜆𝑖𝑡1) = 𝛽1′𝑥𝑖𝑡1+ 𝑢𝑖1+ 𝜖𝑖𝑡1 ln(𝜆_𝑖𝑡2) = 𝛽₂′_𝑥 𝑖𝑡2+ 𝑢𝑖2+ 𝜖𝑖𝑡2 (𝜖_𝑖𝑡1, 𝜖_𝑖𝑡2) ~ 𝑁₂(0, 0, 𝜎_𝜖12 _{, 𝜎} 𝜖22, 𝜌) 𝑢_𝑖1 ~ 𝑁(0, 𝜎_𝑢12 ₎ 𝑢_𝑖2 ~ 𝑁(0, 𝜎_𝑢22 ₎ 𝐸[𝜖_𝑖𝑡𝑔𝑢_𝑗ℎ] = 0 ∀ 𝑖, 𝑡, 𝑔, 𝑗, ℎ 𝐸[𝜖𝑖𝑡𝑔𝜖𝑗𝑠ℎ] = 0 𝑖𝑓 𝑡 ≠ 𝑠 ∨ 𝑖 ≠ 𝑗 ∨ 𝑔 ≠ ℎ 𝐸[𝑢_𝑖𝑔𝑢_𝑗ℎ] = 0 𝑖𝑓 𝑖 ≠ 𝑗 ∨ 𝑔 ≠ ℎ

where 𝑥𝑖𝑡1 and 𝑥𝑖𝑡2 contain, among others, exogenous covariates that represent characteristics

of the choices individuals make regarding the different types of health care insurance, and do not contain 𝜆𝑖𝑡𝑔 for 𝑔 = 1,2. By using this bivariate system, they take the possible correlation

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insurance type does not yield a statistically significant influence on the demand for health care, thereby not supporting the presence of moral hazard effects. Although their results are not supportive of the existence of moral hazard effects, they still cannot fully exclude them in their conclusion.

2.2 Adverse Selection

Another important phenomenon that needs to be considered when investigating effects of insurance choices on health care demand is adverse selection. Adverse selection comes into discussion because less healthy people are more likely to opt for complementary insurance. Furthermore, less healthy people are less likely to opt for an extra voluntary deductible on top of the compulsory deductible. They expect to use an amount of health care that is worth more than, or at least as much as the amount that needs to be paid for under the scheme of the compulsory deductible. With respect to the effect of adverse selection the evidence is mixed. According to Cutler et al. (2008, p.161) most studies appear to find some effect of adverse selection that corresponds with microeconomic theory. Cutler et al. (2008) offer an explanation for the apparently limited (or even contradicting) effects of adverse selection that relies on behavioural differences towards risk. Thus, they state that estimating the effect of adverse selection is only possible if these kinds of behavioural differences are taken into account. They propose the following equations:

Ι(𝑖𝑛𝑠𝑢𝑟𝑎𝑛𝑐𝑒)_𝑖 = 𝛽₀+ 𝛽₁𝐵𝑒ℎ𝑎𝑣𝑖𝑜𝑟_𝑖+ 𝑋_𝑖Γ + 𝜀_𝑖 𝑅𝑖𝑠𝑘𝑜𝑐𝑐𝑢𝑟𝑒𝑛𝑐𝑒𝑖 = 𝛼0+ 𝛼1𝐵𝑒ℎ𝑎𝑣𝑖𝑜𝑟𝑖 + 𝑋𝑖Π + 𝜂𝑖

where Ι(𝑖𝑛𝑠𝑢𝑟𝑎𝑛𝑐𝑒)_𝑖 is an indicator variable for whether the individual has a particular type of insurance, 𝑅𝑖𝑠𝑘𝑜𝑐𝑐𝑢𝑟𝑒𝑛𝑐𝑒_𝑖 is a measure of the occurrence of the risk the insurance in question would cover, 𝐵𝑒ℎ𝑎𝑣𝑖𝑜𝑟_𝑖 is one of their measures of risk tolerance, and 𝑋 represents other covariates.

Riphahn et al. (2003) also aim to provide an empirical test for the existence of adverse selection in the demand for health care. Like Cameron et al. (1988) they test whether insurance choice is correlated with, and endogenous to subsequent health care demand. Cameron et al. (1988) do this by predicting dichotomous insurance indicators using an instrumental variables procedure. Riphahn et al. (2003) apply a binary logit estimator to predict whether an individual purchases complementary insurance. The predicted values are then considered in a least squares regression of health care demand. Based on these values, a

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Hausman test is applied. While their results cannot be interpreted as unambiguous proof of adverse selection, they consider them as suggestive evidence in that direction. They state that their evidence is in line with the results presented by Holly et al. (1998), who use Swiss cross-sectional data, and strongly reject the exogeneity of insurance purchase to subsequent demand for health care. Another study that confirms that individuals with a high demand for health care choose insurance plans with complementary coverage is Ellis (1989).

Furthermore, there is a group of researchers that took both the effect of adverse selection and moral hazard intro account. The overall conclusion about both phenomena is that moral hazard and adverse selection exist, but that they are interrelated and hard or even impossible to distinguish (Van Ophem, 2013). Chiappori et al. (1998) state that it is not clear whether an increase in health care consumption is a reaction of individuals to the particular incentives provided by the insurance contracts or, on the contrary, whether individuals decide to buy a particular insurance contract because they know they will need the health care in the near future. Schellhorn (2001) allows for the endogeneity of deductible choice in health care consumption. However, he only considers a constant effect of the deductible on health care demand, whereas, in a related paper, Sapelli and Vial (2003) allow for the more general specification where all variables in health care demand are allowed to differ across insurance choice. As a consequence of the mixed evidence of adverse selection, it is aimed in this paper to take the possible effect of adverse selection into account.

2.3 Visits to a General Practitioner

Another governmental measure to reduce unnecessary health care demand is that GPs function as gatekeepers in the Dutch health care system. Contact with a GP is always the first step that has to be taken to get access to other services of the health care system. The case of a real emergency when individuals go, or usually will be brought, to a hospital directly is excepted from this measure. Although seeing a GP brings about almost negligible costs for a patient, its consequences usually do not. GPs will often prescribe drugs or will refer to medical specialists or therapists. The costs involved will be charged to the patient. Therefore, we expect that individuals will take this fact into account when considering visiting a GP. Seeing a GP is an independent choice made by the individual. Decisions on the options resulting from this choice, e.g. using drugs or seeing a medical specialist, will have to be made in accordance with the GP, which makes these decisions no longer purely individual

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decisions. What is more, the opinion of the GP will, almost always, be decisive (Van Ophem, 2013). For these reasons mentioned, the choice has been made to model the number of GP visits, and not the number of visits to medical specialists. In this way the effect of the introduction and increase of the compulsory deductible on the independent choice of the individual to go to a GP can be investigated, and will not be biased by decisions of other physicians or medical specialists. “Many other investigations on health care utilization concentrate mainly on GP visits, among others Chiappori et al. (1998), Schellhorn (2001), Cockx and Brasseur (2003), Sapelli and Vial (2003), and Winkelmann (2004).” (Van Ophem, 2013).

More about how the Dutch health care insurance system exactly works in practice is explained in the following subsection.

2.4 The Dutch Health Care System

Since the late 90’s, the central supply- and demand-regulation in the health care insurance system in the Netherlands made way for regulated competition. In this regulated competition health insurers are stimulated to act as cost-conscious buyers of health care on behalf of their policy holders. An important milestone in this development was the introduction of the Health Insurance Act (HIA, Zorgverzekeringswet) in 2006. With the introduction of the HIA, the Health Care Market Act (Wet Marktordening Gezondheidszorg) and the Care Institutions Admission Act (Wet Toelating Zorginstellingen) in 2006 steps have been put towards a health care system based on regulated competition. This competition is aimed to create permanent incentives for efficiency improvements and to generate opportunities to provide quality care at the lowest possible price. The regulation aims to ensure solidarity and accessibility, and to prevent market failure (Van Kleef et al., 2009).

The HIA regulates the basic health care insurance for every Dutch citizen. Taking out a basic insurance under the HIA is mandatory for anyone who is insured under the Exceptional Medical Expenses Act (EMEA, Algemene Wet Bijzondere Ziektekosten). An individual is insured under the EMEA if the individual is a Dutch resident, or is not a resident but pays income tax in the Netherlands. There are some exceptions to this rule, which can be found precisely in the Dutch Royal Decree 746 (Koninklijk Besluit 746). An individual that is required to take out a basic health care insurance, can take out this insurance from a preferred insurance company. The obligation to have a basic health care insurance also entails

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an obligation for the insurer, which is the obligation of acceptance: an insurer may not refuse to insure anyone who desires an insurance policy, irrespective of gender, age or health status. This obligation of acceptance does not apply to additional (complementary) insurance.

When someone wants to take out basic health care insurance, there is no need to compare the compensations the different insurers provide, since the basic insurance covers all costs for services that are mentioned in the basic package determined by the government. This package provides the same in terms of coverage for each insured. However, the costs of an insurance policy can vary significantly across insurers. In some cases there may even be a €10 to €20 difference between the heights of the monthly premiums. It may therefore be wise to compare the insurers’ premiums with each other to prevent oneself from paying too much. The price differences are due to differences in policy-types and choices of care that come with it. In Table 1 policy-prices for different health care insurers in the Netherlands are presented.

The Dutch basic health care insurance is compulsory whereby the insured is entitled to coverage of services that are in the basic package. The basic package slightly changes every year. If this basic package does not offer sufficient coverage, it is possible to take out additional health care insurance with different and/or extended care-compensations. A list of what is included in the basic package in 2013 is given here (2013 is the last year of the panel used in this research):

 Medical care by GP’s, medical specialists and midwives

 Hospitalization

 Dyslexia care

 Medication

 Mental health care (Geestelijke Gezondheids Zorg (GGZ))

 Maternity care

 Medical aids

 (Limited) physiotherapy and exercise therapy, from the 21st treatment on

 Speech therapy and occupational therapy

 Pelvic physiotherapy for urinary incontinence until the 9th treatment

 Dental care (control and treatment) until the age of 18

 Dental care such as dentures and dental surgeon

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 Quit Smoking Programs

 Up to three hours of treatment for dietary advice (Zorgverzekering Basispakket 2013, n.d.)

As stated, one has to deal with the compulsory deductible when using health care since 2008. The height of the compulsory deductible from 2008 until 2015 is presented in Figure 3. A visit to a GP is always covered by the basic health insurance package, without the need to pay the amount of the deductible first. This regulation holds not only for the services provided by a GP. There are more services for which there is no need to firstly pay the deductible to receive coverage from the insurer. All services for which this regulation holds are:

 Services of a GP (Prescribed drugs and blood tests are not excluded from the deductible.)

 Obstetric care and maternity care (Note that there needs to be paid a personal contribution in this case.)

 Medical aids on loan

 Care for young people under the age of 18

 Care for which a compensation is provided by an additional insurance

 Care for which a compensation is provided by the Long Term Care Act (Wet langdurige zorg) or Social Support Act (Wet maatschappelijke ondersteuning)

 Some national population screenings and vaccinations

As mentioned earlier, there is a possibility to voluntarily increase the deductible by an amount up to €500. When one chooses to do so, a discount on the health insurance premium can be received. The size of this discount depends on the insurer, but can reach up to €25 monthly. The downside is that one has to pay more out of pocket before one is entitled to receive the ‘free’ care under the basic insurance package. Therefore this method is especially popular among young healthy people.

2.5 Factors Affecting GP Visits

A considerable amount of previous research has examined the factors that influence the number of GP visits. For the obvious there are the factors describing an individual’s

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health status. Hurd and McGarry (1997) separately estimate the probability of a service use, and conditionally on a service use, the number of visits. They use the self-reported health status of people born in 1923 or earlier that participated in the Asset and Health Dynamics Survey. They find the anticipated effects for the probability of a visit: those in better (self-reported) health have lower probabilities of visiting a GP than those in worse health. They include 16 specific health conditions for which they find an increase of the probability. Smoking decreases the probability as well as lower income and wealth. Furthermore, they also find no monotonic increase in the probability of a doctor visit with age. They state that apparently an increase in disease conditions and a deterioration in health, which happens to go hand in hand with aging, cause more use of health care, not age per se. When estimating the number of visits they find that (self-reported) health status and the disease conditions influence this number significantly, though slightly differently than how they influence the probability. The effect of smoking on the number of visits is negative and significant. Wealth and income effects are small and not significant. The number of visits seems to decline with age. They propose that this could be caused by the fact that travelling to and from a doctor’s office is more burdensome at higher ages, and that if a higher use of services is observed with higher age, this is a result of deteriorating health, not age per se.

Riphahn et al. (2003) used explanatory variables like a degree of health-satisfaction, handicap and its degree, marriage, schooling, household income, number of children in household and information on employment. In their bivariate estimation of doctor and hospital visits, presented in Section 2.1, they only find significant effects for the following variables that are treated as exogenous: age, square of age, health satisfaction, degree of handicap, schooling, and self-employment.

Schellhorn (2001) aims to explain the number of physician visits for men and women. In his analysis only the choice of the voluntary deductible is treated as endogenous. He uses next to health-, education- and employment-related explanatory variables, also characteristics of the residence, like dummies for small and large towns and metropolitan areas. Though, only for the metropolitan areas he finds significant results. Furthermore, he finds that having overweight as well as being a drinker significantly affects physician visits for men and women. He also uses age categories, which have a significant positive effect on the number of visits. Moreover he uses a dummy for being a foreigner, and one for being a retiree, for both of which he finds differences in significance for men and women.

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Based on the explanatory variables used in the discussed previous researches, the available data in the LISS-panel used for this research, and common knowledge about factors that most probably have some influence on GP visits, the explanatory variables in this study are deliberately chosen. The exact choice of the variables and their descriptive statistics, will be presented in Section 3.

2.6 Approach of this Thesis

In this study the number of GP visits is investigated, which is a count variable. A natural way to start the estimations is by exploiting a model that takes this count nature into account. Cameron & Trivedi (2005) propose two types of count models that can be used with panel data, namely the Poisson individual-specific effects model and the negative binomial individual-specific effects model.

However, as stated, Schellhorn (2001) and Riphahn et al. (2003) already gave rise to possible predeterminedness and/or endogeneity of regressors that should be considered in models for health care consumption. To test for exogeneity of the included regressors, and if exogeneity is rejected, to account for it, a different approach is necessary. Arellano and Bond (1991) propose to use their difference GMM estimation method, which is a general estimator designed for situations with “small T, large N” panels, independent variables that are not strictly exogenous, fixed effects, and heteroscedasticity and autocorrelation within individuals.

The exploitation of the models as well as the suspected predeterminedness and endogeneity of the included regressors will be elaborated on in more detail in Section 4.

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3. Data

In the Netherlands there is unfortunately still little detailed data from health insurers or health care institutions available and/or accessible for research. Nevertheless, with the data that are available at this moment some research can be done that is of decisive importance for health insurers and the Dutch government. The data used in this investigation come from the LISS-panel (Longitudinal Internet Studies for the Social Sciences). The panel is based on a probability sample of households drawn from the population register by Statistics Netherlands (Centraal Bureau voor de Statistiek). A probability sample is a sample in which every unit in the population has a chance (greater than zero) of being selected in the sample, and this probability can be accurately determined. Households that could not otherwise participate are provided with a computer and internet connection. Panel members complete online questionnaires every month of about 15 to 30 minutes in total. They are paid for each completed questionnaire. One member in the household provides the household data and updates this information at regular time intervals.

Part of the interview time available in the LISS panel is reserved for the LISS Core Study. This longitudinal study is repeated yearly and is designed to follow changes in the life course and living conditions of the panel members. In addition to the LISS Core Study there is ample room to collect data for different research purposes. Many disciplines, from linguistics to medical sciences, have taken up the opportunity to use the research infrastructure. The LISS panel has been in full operation since October 2007, and all data are made available through the LISS data archive.

The LISS panel is intended for scientific, policy or socially relevant research. The quality and the coverage of the sample is of prime concern. To establish the LISS panel, a traditional random sample was drawn from the population registers, in collaboration with Statistics Netherlands. All people in the sample were approached in traditional ways (by letter, followed by telephone call and/or house visit) with an invitation to participate in the panel. Individuals not included in the original sample cannot participate, so there can be no self-selection.

The recruitment of a first refreshment sample was carried out between June and December 2009. In cooperation with Statistics Netherlands, a stratified sample was drawn, intended to improve the representativeness of the panel by oversampling the difficult to reach

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groups which had a below-average response in the main recruitment. The refreshment sample in 2009 was stratified on three variables: household type, age and ethnicity.

Between October 2011 and May 2012 a second refreshment sample for the LISS panel was recruited. This sample was randomly drawn from the population registers by Statistics Netherlands, in the same way as the original sample of 2007. Between November 2013 and June 2014 a third refreshment sample, stratified as in 2009, was recruited. About 80% of the eligible persons living in the registered panel households participate in the panel. The monthly response of these participants varies between about 50% and 80%, depending on the questionnaire and month. Between October 2007 and February 2010 the monthly response gradually decreased. From March 2010 onwards, it slightly increased again, as a result of special efforts to contact inactive panel members.

In this investigation data relating to the years 2007 until 2013 will be used, originating from two separate questionnaires:

 Background variables LISS Panel

 Health – LISS Core Study – Wave 1 to 71

For every year in this time span between 5000 and 7000 participants filled out the Health questionnaire. However, these participants were not the same for each year by definition. When merging the datasets from the different waves an unbalanced panel was established. For this investigation the panel has been reshaped into a balanced panel. This is momentous because of the following reason. In the early years of the panel the compulsory deductible was introduced, whereas in the later years this deductible increased significantly. To capture the yearly changes concerning consumption-behaviour on an individual’s level due to the yearly changes in the compulsory deductible a balanced panel is beneficial. To reshape the unbalanced panel into a balanced one the following procedure has been followed. Firstly, the first and the second wave were merged. Next, the participants that did not fill out the survey in both merged parts were left out of the sample. Thereafter, this merged sample

1_{Data collection periods are the following:}

Wave 1: 2007-11-05 to 2007-11-28. Wave 2: 2008-11-03 to 2008-11-26. Wave 3: 2009-11-02 to 2009-11-25. Wave 4: 2010-11-01 to 2010-11-30. Wave 5: 2011-11-07 to 2011-11-30. Wave 6: 2012-11-05 to 2012-11-27. Wave 7: 2013-11-04 to 2013-11-26.

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was merged again with the third wave, and so on. By leaving out the participants that did not fill out the questionnaire for all seven consecutive years, 2495 individuals remained that did fill out the questionnaire for all seven years. Leaving out the participants that not participated in all seven years led to a loss of many observations. However, the sample that remained seemed to stay representative for conducting this research, because it still possessed the main characteristics of the initial probability sample. After also having left out the children and adolescents under the age of 18 in 2007 (the first year of the sample), 2411 individuals remained in the sample. Minors could be left out of the investigation, because the introduction of the deductible does not affect their use of healthcare, since the deductible does not apply to health care for minors. An overview of the total number of participants in each year of the panel, as well as the number of observations that remain after leaving out the discussed observations can be found in Table 2.

After the merging, the sample of 2411 individuals still contained some missing observations on variables that are likely important when investigating their influence on the number of GP visits. When these observations would have been left missing, they would not have been taken into account in regressions with panel data. To prevent the sample from further reductions, possibly going hand in hand with a declining representativeness of the sample, the greater number of those missing observations were manually generated. This was done by using the value of the variables of concern in the preceding or following year. The value in one of these surrounding years was then pasted over the missing observation. This procedure was carried out for the variables that represent weight, contact with a medical specialist, regularly suffering from some specific complaints, wearing glasses, wearing a hearing aid, the extent to which physical health or emotional problems hinder daily, social, and working activities, net income, and position within the household. Nevertheless, after this procedure, there were still some missing observations left within the income variables. This was due to the fact that for some of the individuals no information was available in any of the years. This means there was no starting point for the indication of their incomes. Because for these individuals a complete variable would have become unusable, they were left out of the sample when performing a regression with panel data. This left 2331 individuals in the sample for regression analyses. Assuming these individuals did not omit to provide information on their income because of a common systematic reason, we continued with the sample of 2331 individuals.

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Furthermore, some missing observations actually represent a zero count for some variables, so they were replaced by zero’s. This kind of replacements were done for the missing observations for the variables that represent the number of GP visits, having a chronical illness, having complementary insurance, height voluntary deductible, drinking habits and the amount of days that the individual was unable to go to work, school or perform housekeeping due to disease. After generating values for the missing observations of the listed variables above, still some missing values were left in the sample. These were missing observations that could not conveniently be replaced by some value generated by one of the two methods discussed.

Some individuals have a zero count of the number of GP visits for every year from 2007 to 2013. When performing regressions with panel data, these individuals are not taken into account in the analysis due to this zero variation in the dependent variable. This is the case for 73 individuals. They were left out of the sample as well, since their observations did not provide any extra information for the investigation of the effect of the compulsory deductible on the number of GP visits. This left 2258 individuals in the sample for regression analyses. Furthermore, the reported values for the number of visits to a GP can be subject to some reporting errors. There are small peaks at the counts of 10, 15, 20, 50, or even 100. These errors could be caused by individuals just reporting rounded counts, because they did not keep track perfectly of their real count. However, the total number of individuals reporting those rounded numbers is only a small fraction of the total sample, so this problem was considered negligible. What is more, is that two observations of a count higher than 500 were observed. These counts were manually mutated into counts of 100. A count of 100 is the next highest count observed at a somewhat larger group of individuals (4 times). Besides, a count of higher than 300 seemed unrealistic, since such a high count implies the individual visited a GP about six times a week, all year round.

The observations on the 2258 individuals that remained after adjusting the missing observations still seemed to constitute a representative sample for conducting this research. This representativeness can be derived from the descriptive statistics that are provided in Table 3. From this table no extraordinary outliers or patterns can be detected.

The dependent variable in this empirical analysis is the number of times the individual made use of the services of a GP. The explanatory variables that are used, as well as the meanings of their reported values are presented in Table 4. Descriptive statistics of the explanatory variables can be found in Table 5 and of the dependent variable in Table 6.

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From Table 5 it is observable that the age does not increase with unity each year. This is due to the fact that the survey is not filled in at exact the same date each year, however, it is filled in every year in November. For this reason it can happen that for individuals whose birthdays are in the month November, but who fill in the survey at different dates in November every year, the same age is reported for two consecutive years. If these individuals fill out the survey the next year at some date in November after their birthdays, the ages make a jump of two in the data file. Because inclusion of the age-variable, it is unnecessary to also include time-dummies. After all, the values of both variables make a yearly jump of one unit. Reporting the same age in two consecutive years is thereby assumed to be relatively uncommon, so that this does not substantially affect the estimation of the particular coefficient.

Table 6 shows that the average number of GP-visits is between 2.09 and 2.36 yearly, and that this average is declining from 2007 until 2013. The number of 0 GP visits in the sample ranges from about ¼ to ⅓ of the total sample and is increasing from 2007 until 2013. In all of the seven years of the panel more than 85% of the respondents did not see a GP more than four times. Counts above 20 are rarely observed. The yearly standard deviations of the count of GP visits are up to almost two times as high as their means.

Table 7 represents counts of people choosing for a particular height of the voluntary deductible. On average, each year 78% of the respondents in the sample did not opt for a voluntary deductible. From the data in Table 7 it becomes clear that in the year 2008 something extraordinary was going on concerning this insurance variable. Namely in 2008 the percentage of people not opting for a voluntary deductible is substantially lower than in the other years. This could possibly be due to the fact that in 2008 the compulsory deductible had its introduction, which tangled a lot of Dutch citizens about the health care insurance system and the choices they could make regarding the deductibles.

When looking in more detail at data about the voluntary deductible in Table 8, it becomes clear that the people without a voluntary deductible are on average more than 4.5 years older than the ones with the highest possible voluntary deductible, and that they visit a GP considerably more often. In this sample, men have higher voluntary deductibles than women. The individuals reporting a relatively better health status opt for a higher voluntary deductible than people reporting a relatively worse health status. Chronically ill opt for a rather low voluntary deductible.

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Considering Table 9, a similar analysis can be carried out for having complementary insurance. Individuals with some form of complementary insurance tend to visit a GP more often, and are feeling less healthy than individuals without complementary insurance. Among the people with complementary insurance are more chronically ill people and more women.

In Table 10 the average counts of visits to a GP are given for some subsamples. Remarkable in this table are the lower average counts for drinkers and smokers compared to non-drinkers and non-smokers respectively. The lower counts for drinkers and smokers could likely be due to some living standards and other characteristics that smokers and drinkers have in common, that makes them less eager to see a GP for certain health issues.

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4. Model

As stated, the aim of this study is to estimate a model for the number of GP visits using panel data from 2007 until 2013. As already mentioned in Section 2, it is natural to start the estimations by employing a count model for panel data as proposed by Cameron & Trivedi (2005), thereby assuming that all regressors are strictly exogenous. However, this assumption of strict exogeneity of the regressors is very difficult to substantiate in reality. The suspected ways in which endogeneity or predeterminedness among the included regressors can be present are therefore elaborated on, after which a different method for model estimation is proposed. This is the Arellano-Bond difference GMM estimation method.

This section begins with discussing the advantages of using panel data. Thereafter, possibilities in which to model count data are set out and the choice for a specific count model is explained under the assumption that all included regressors are exogenous. What follows is discussion on individual-specific effects. Next, a discussion on the suspected predeterminedness and endogeneity of the included regressors is set forth, after which the Arellano-Bond difference GMM estimation method is presented that takes this possible predeterminedness and endogeneity into account. Next, it is set forth how the results should be interpreted.

4.1 Panel Data

This study will exploit the advantages of panel data to investigate the effect of the compulsory deductible on the number of GP visits in the Netherlands. A major advantage of panel data is increased precision in estimation. This is the result of an increase in the number of observations owing to combining several time periods of data for each individual.

A second attraction of panel data is the possibility of consistent estimation of the fixed effects model, which allows for unobserved heterogeneity that may be correlated with regressors. If unobserved heterogeneity is present, this will lead in a cross-section analysis to omitted variable bias that could in principle be corrected by instrumental variables methods. In practice however, it can be very difficult to obtain valid instruments. Therefore, the exploitation of panel data is beneficial in the presence of unobserved heterogeneity

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4.2 Models for Count Data

In modelling the demand for GP visits it should be taken into account that the number of GP visits by an individual is a count variable. Various econometric models for count data have been applied in a number of studies on demand for health care. As stated Cameron & Trivedi (2005) propose two count models that can be used with panel data, which are the Poisson individual-specific effects model and the negative binomial individual-specific effects model.

Their proposition is based on the following. Hausman et al. (1984) assume that the dependent variable 𝑦_𝑖𝑡 is independent and identically distributed negative binomial 1 (NB1) with scalar distribution-parameters (that constitute the mean and variance) 𝛼_𝑖𝜆_𝑖𝑡 and 𝜙_𝑖, where 𝜆𝑖𝑡 = exp (𝒙𝑖𝑡′ 𝛽) with 𝑥𝑖𝑡 a vector of explanatory variables, so that 𝑦𝑖𝑡 has mean

𝛼𝑖𝜆𝑖𝑡/𝜙𝑖 and variance (𝛼𝑖𝜆𝑖𝑡/𝜙𝑖) × (1 + 𝛼𝑖/𝜙𝑖). The parameters 𝜙𝑖 and 𝛼𝑖 can only be

identified up to their ratio. Nevertheless, this ratio drops out of the conditional density for the 𝑖th observation, such that the 𝛽′s can be consistently estimated. Cameron and Trivedi (2005) state that consistent estimation of 𝛽 in the presence of individual-specific fixed effects is, besides for the Poisson model, also possible for a particular parametrization of the negative binomial model. Their proposed conditional maximum likelihood (ML) negative binomial fixed effects estimator of 𝛽 maximizes the log-likelihood function based on the conditional joint probability of the counts for each group, conditioned on the sum of the counts for the group (i.e., the observed ∑𝑛𝑖 𝑦_𝑖𝑡

𝑡=1 ). However, the Poisson fixed effects model is more

commonly used in practice since it is consistent under much weaker distributional assumptions. (Cameron and Trivedi, 2005).

Though, the negative binomial model also has some advantages compared to the Poisson model. Winkelmann (2004) states that a criticism for the use of the Poisson count regression model is its single index structure. This single index structure implies that once the mean is given, all other aspects of the distribution, like the variance and its skewness, are determined as well. The Poisson model could therefore be less appropriate to model the number of GP visits in this investigation. The negative binomial distribution does not have such a single index structure, and is therefore beneficial. Furthermore, in an early stage of this research, values of the estimated log likelihoods were obtained for regressions performed with the Poisson count model, as well as for regressions performed with the negative binomial count model, both with the same data. The log likelihoods were compared with each

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other and it turned out that the negative binomial model performed better than the Poisson model in terms of their likelihoods. Taking the considerations just mentioned into account the negative binomial count model is chosen to be exploited for the first estimations in which it is assumed that all included regressors are strictly exogenous.

4.3 The Negative Binomial Count Model for Panel Data

2

Let 𝑦_𝑖𝑡 denote the dependent count variable of which the conditional mean is specified as 𝐸[𝑦_𝑖𝑡|𝑥_𝑖𝑡] = 𝜇_𝑖𝑡 = exp (𝑥_𝑖𝑡′_{𝛽), where 𝑥}

𝑖𝑡 is a vector of parameters for individual 𝑖 at time

𝑡. If a probability density function like the Poisson or a negative binomial distribution is assumed, the coefficients can be estimated by maximum likelihood.

Following Schellhorn (2001) it is omitted in modelling to distinguish having visited a GP or not from the actual number of the visits. The model used in this investigation treats users and non-users identically and assumes they do not differ systematically from each other in making decisions about whether or not to visit a GP.

Riphahn et al. (2003) take the approach from Cameron et al. (1988) as a basis for their research. Cameron et al. (1988) obtain that, unconditional of the insurance choice, the demand (𝑒) for the 𝑘th type of medical service can be written as

𝐸[𝑒𝑘(𝑠)] = exp (𝑍′𝛽𝑘+ ∑ 𝜂𝑗𝑘𝐷𝑗 𝐽

𝑗=1

+ 𝜖𝑘)

where Z is a vector of covariates, 𝐷_𝑗 are dummy variables for the 𝑗th insurance form and 𝑠 denotes the state of the world.

As is substantiated in the previous subsection, the negative binomial model with its extensions for panel data is exploited for the first estimations of the number of GP visits. This model is explained in more detail in the following. First, the basic framework for using the Poisson count model for panel data is considered, following Riphahn et al. (2003), from which the negative binomial count model for panel data is naturally derived. In a Poisson model it is assumed that the dependent variable is Poisson distributed. The distribution only has one parameter 𝜆_𝑖𝑡. This is called the intensity. Covariates are introduced using an

2_{Individual-specific effects are not incorporated in the expressions in this subsection. This incorporation of}

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exponential parameterization of 𝜆_𝑖𝑡 such that the expected value of the dependent variable is a function of the covariates and their respective coefficients in the following way:

𝑦_𝑖𝑡~ 𝑃𝑜𝑖(𝜆_𝑖𝑡) 𝑝(𝑦_𝑖𝑡 = 𝑚) = 𝑒−𝜆𝑖𝑡𝜆𝑖𝑡𝑚 𝑚! . 𝐸[𝑦𝑖𝑡] = 𝑉[𝑦𝑖𝑡] = 𝜆𝑖𝑡 = 𝑒𝑥𝑖𝑡 ′_𝛽 .

The problem of the single index structure of the Poisson model has led to a large number of new models of which the most popular is the negative binomial model with its extensions for panel data. (Cameron and Trivedi, 1998). The negative binomial model is introduced into econometrics by Hausman et al. (1984) and Cameron and Trivedi (1986). In this model the deterministic nature of the link between intensity 𝜆𝑖𝑡 and covariates 𝑥𝑖𝑡 is

relaxed by consideration of a Gamma distributed random error. Conditional on this error the count 𝑦_𝑖𝑡 is again Poisson distributed. Since this error is not observable, it has to be integrated out in order to obtain an unconditional expressions for the maximum likelihood estimation. The important and renown characteristics of the negative binomial model are overdispersion, i.e. conditional on the covariates the variance exceeds the mean, and a likelihood function which is easy to implement (Riphahn et al., 2003).

In the negative binomial panel model used every individual 𝑖 has an outcome observation 𝑦 for every period 𝑡. Then 𝑦_𝑖𝑡~ 𝑁𝐵(𝑟_𝑖𝑡, 𝑝_𝑖𝑡), where 𝑟_𝑖𝑡 is the number of failures until the experiment is stopped, and 𝑝𝑖𝑡 is the probability of success in each experiment. The

mean and variance are defined as

𝐸[𝑦𝑖𝑡] = 𝑝𝑖𝑡𝑟𝑖𝑡/(1 − 𝑝𝑖𝑡)

𝑉[𝑦_𝑖𝑡] = 𝑝𝑖𝑡𝑟𝑖𝑡 (1 − 𝑝_𝑖𝑡)2

The expectation is modelled conditional on the covariates as 𝐸[𝑦_𝑖𝑡|𝑥_𝑖𝑡, 𝜀_𝑖𝑡] = exp(𝑥_𝑖𝑡′_{𝛽 + 𝜀}

𝑖𝑡) = ℎ𝑖𝑡𝜆𝑖𝑡 (𝟏)

where 𝜆_𝑖𝑡 is the parameter of a Poisson distribution, and where ℎ_𝑖𝑡 = exp(𝜀_𝑖𝑡) is assumed to have a one-parameter Gamma distribution with mean 1 and variance 1 𝜃⁄ = 𝜅. After integrating out ℎ𝑖𝑡 of the joint distribution, the marginal negative binomial distribution is

obtained:

𝑃[𝑌 = 𝑦_𝑖𝑡|𝑥𝑖𝑡] =

Γ(𝜃 + 𝑦𝑖𝑡)𝑟𝑖𝑡𝜃(1 − 𝑟𝑖𝑡)𝑦𝑖𝑡

Γ(1 + 𝑦_𝑖𝑡)Γ(𝜃) where 𝑦 = 0,1, … , 𝜃 > 0 and 𝑟_𝑖𝑡 = 𝜃 (𝜃 + 𝜆⁄ _𝑖𝑡).

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The latent heterogeneity induces overdispersion while preserving the conditional mean and variance:

𝐸[𝑦_𝑖𝑡|𝑥_𝑖𝑡] = 𝜆_𝑖𝑡

𝑉[𝑦𝑖𝑡|𝑥𝑖𝑡] = 𝜆𝑖𝑡 [1 + (1 𝜃⁄ )𝜆𝑖𝑡] = 𝜆𝑖𝑡[1 + 𝜅𝜆𝑖𝑡]

where 𝜅 = V[ℎ_𝑖𝑡]. Maximum likelihood estimation of the parameters of this negative binomial model is then straightforward (Greene, 2008).

4.4 Individual-Specific Fixed Effects

As stated in Section 4.1, one of the attractions of using panel data is the possibility of consistent estimation of the fixed effects model that allows for unobserved heterogeneity. Fixed effects are a particular type of individual-specific effects. An individual-specific effects model allows each cross-sectional unit to have a different intercept term, though all slopes are the same, so that for the linear case 𝑦𝑖𝑡 = 𝑎𝑖+ 𝑥𝑖𝑡′𝛽 + 𝜀𝑖𝑡, where 𝜀𝑖𝑡 is iid over 𝑖 and 𝑡. The

𝑎_𝑖 are random variables that capture the unobserved heterogeneity. One variant of the model treats 𝑎_𝑖 as unobserved random variable that is potentially correlated with the observed regressors 𝑥𝑖𝑡. This variant is called the fixed effects (FE) model. The other variant of the

model assumes that the unobservable individual effects 𝑎_𝑖 are random variables that are distributed independently of the regressors. This model is called the random effects (RE) model. However, it should be clear that 𝑎_𝑖 is a random variable in both fixed and random effects models.

For the linear case, both models assume that 𝐸[𝑦_𝑖𝑡|𝑐_𝑖, 𝑥_𝑖𝑡] = 𝑐_𝑖+ 𝑥_𝑖𝑡′_{𝛽 where 𝑐}

𝑖 is the

individual-specific effect that is unknown and cannot be consistently estimated when T is fixed and finite, but N may grow to infinity. Instead 𝑐𝑖 can be eliminated by taking the

expectation with respect to 𝑐𝑖, leading to 𝐸[𝑦𝑖𝑡|𝑥𝑖𝑡] = 𝐸[𝑐𝑖|𝑥𝑖𝑡] + 𝑥𝑖𝑡′ 𝛽. For the RE model it is

assumed that 𝐸[𝑐𝑖|𝑥𝑖𝑡] = 𝑎𝑖, so 𝐸[𝑦𝑖𝑡|𝑥𝑖𝑡] = 𝑎𝑖 + 𝑥𝑖𝑡′𝛽 and hence it is possible to identify

𝐸[𝑦𝑖𝑡|𝑥𝑖𝑡]. In the FE model, however, 𝐸[𝑐𝑖|𝑥𝑖𝑡] varies with 𝑥𝑖𝑡 and it is not known how it

varies, so it is not possible to identify 𝐸[𝑦_𝑖𝑡|𝑥_𝑖𝑡]. It is nonetheless possible to consistently estimate 𝛽 in the FE model. Thus, it is possible in the FE model to identify the marginal effect 𝛽 = 𝜕𝐸[𝑦𝑖𝑡|𝑐𝑖, 𝑥𝑖𝑡]/𝜕𝑥𝑖𝑡, even though the conditional mean is not identified. Modern

econometrics literature emphasizes fixed effects.

The FE model has the attraction of allowing the exploitation of panel data to establish causation under weaker assumptions than those needed to establish causation with

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section data or with panel data models without fixed effects, such as pooled models and RE models. In some studies random effects may be appropriate when causation is clear. In other cases it may be sufficient to use a random effects analysis to measure the extent of correlation, with determination of causation left to further research taking other approaches. Economists are unusual in preferring a fixed effects approach however, because of a desire to measure causation in spite of reliance on observational data.

The FE model also has several practical weaknesses. Estimation of the coefficient of any time-invariant regressor is not possible as it is absorbed into the individual-specific effect. Coefficients of time-varying regressors are estimable, but these estimates may be very imprecise if most of the variation in a regressor is cross sectional rather than over time. Changes in the conditional mean caused by changes in time-varying regressors can be predicted. However, even coefficients of time-varying regressors may be difficult to identify in nonlinear models with fixed effects (Cameron and Trivedi, 2005).

One can test whether fixed or random effects are preferred using a Hausman test. The Hausman test verifies whether there is a statistically significant difference between the FE and RE estimators. A large value of the Hausman test statistic leads to rejection of the null hypothesis that the individual-specific effects are uncorrelated with the regressors, which leads to the conclusion that fixed effects are present (Cameron and Trivedi, 2005).

The suspected presence of fixed effects in our data is supported by the intuition that the individual-specific effects are correlated with the regressors used. It is likely that the chosen variables do not completely describe the entire health status of an individual. There are without doubt time-invariant factors that do describe someone’s health status or that define personal habits, but that are omitted in the estimations, because no data on these factors are available. It is likely that these omitted factors are correlated with time-varying factors that are included in the regressions.

Taking the above mentioned arguments and results of the Hausman tests into account, it is deliberately chosen to estimate a negative binomial count model with fixed effects for panel data.

4.5 Suspected Endogeneity

As is explained in Section 2 some of the regressors included in the estimations are potentially endogenous or predetermined with respect to the number of GP visits. Verifying

Effect of the Dutch compulsory deductible on GP visits