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RISK PREFERENCE AND HEALTH
INSURANCE VOLUNTARY
DEDUCTIBLE CHOICE IN THE
NETHERLANDS
Mirjam Geerts
s2713527
Supervisor:
dr. C. Laureti
June 2020
University of Groningen
Abstract This thesis explores the role of risk preference on the voluntary deductible choice in
the Dutch health insurance market. I make use of the data from LISS from the years 2009-2018. The results suggest that highly risk-averse individuals are less likely to opt for a non-zero voluntary deductible than risk-neutral and risk-seeking individuals. The impact of risk preference on voluntary deductible choice is lower compared to the impact of health risk in both magnitude and statistical significance. The proposed strategy to introduce the maximum voluntary deductible as the default option in the insurance contract potentially increases the take-up of voluntary deductibles and reduces moral hazard in the Dutch health insurance market.
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1. Introduction
Insurance choices are important for individuals for managing their financial risks (i.e. the risk of losing money). However, some individuals do not make optimal insurance decisions from a rational perspective. Several studies show that people tend to be overinsured (Kunreuther, Pauly, and McMorrow, 2012; Lee, 2017), while other individuals are likely to be underinsured (Cox and Zwinkels, 2019; Laury, McInnes, and Swarthout, 2009) compared to what is assumed to be the optimal insurance choice. Therefore, the assumption in classical economic models about the rational decision making of agents does not seem to hold in many insurance markets.
Behavioral economists are trying to explain the deviations from the optimal insurance decisions with several behavioral phenomena. Concerning insurance, the literature has considered several behavioral factors affecting take-up, such as framing effects (Johnson, Hershey, Meszaros, and Kunreuther, 1993), affection effect (Hsee and Kunreuther, 2000) and more recently, financial literacy (Lin, Bruhn, and William, 2019). Framing effects are decision biases that occur when presenting information in different ways to consumers. The concept of framing effects shows the importance of the design of a policy and the information framework that is available for the consumer for decision-making. Regarding the design of insurance policies, Johnson et al. (1993) wonder if changing the frame in which an insurance policy is communicated to the consumer affects the insurance decision. From survey data, they observe that households prefer a more expensive policy with a rebate over an initially less expensive insurance policy with a deductible, while the last one is financially more profitable considering the time value of money.
Although Johnson et al. (1993) find that consumers appear to dislike deductibles, governments in several countries (e.g. Switzerland, United States, and the Netherlands) have decided to implement deductibles in the insurance market to reduce the problem of moral hazard. 1 A deductible implies that an insured individual pays a fixed amount of the loss out-of-pocket and the insurer covers the remaining loss. Next to the existence of compulsory deductibles, insurers offer their insured the option to choose for a voluntary deductible in exchange for a premium discount. The literature shows that the individual choices on insurance voluntary deductibles are not optimal. In the Dutch health insurance market, Van Winssen, Van Kleef, and Van de Ven (2015) find that in 2014 only 11 percent of the insurance takers opted for a voluntary deductible, while it would have been financially profitable for at least 48 percent of the insurance takers to opt for such a deductible. This implies that financial
1 Moral hazard in the domain of health insurance refers to the influence of health insurance on
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profitability is not the only driver for the voluntary deductible choice. In a follow-up study, Van Winssen, Van Kleef, and Van de Ven (2016) identify possible behavioral determinants of the uptake of deductibles. The six potential determinants Van Winssen et al. (2016) mention from a behavioral economic perspective are loss aversion, risk attitude, ambiguity aversion, debt aversion, omission bias, and liquidity constraints. Van Winssen et al. (2016) explain these determinants in a theoretical framework. Regarding risk attitude, they argue that the effect of risk preference on the take-up voluntary deductible is not completely clear, since risk preference is dependent on the reference point for the insured’s decision.
The purpose of this paper is to explore the role of risk preference on household decisions to take up insurance deductibles. I empirically analyze the effect of risk preference on the deductible uptake in the Dutch health insurance market by using panel data from the Longitudinal Internet Studies for the Social Sciences (LISS) from the years 2009-2018. This thesis adds to the existing literature by using multiple and different elicitation methods for risk preference. Besides, the relationship between risk preference and voluntary deductible choice is established over a longer time period. Dependent on the outcome of the effect, I discuss the implications for the design of the deductible policy.
This thesis finds that highly risk-averse individuals are less likely to choose for a non-zero voluntary deductible than risk-neutral and risk-seeking individuals. From the two types of private information affecting insurance decisions (Finkelstein and McGarry, 2006), the impact of health risk outweighs the impact of risk preference. The result is robust over time, but is different across elicitation methods for risk preference.
The remainder of this paper is structured as follows. Section 2 reviews the relevant literature and gives a short overview of the organization of the Dutch health insurance market. Section 3 explains the data collection process and methodology thoroughly. Section 4 provides and discusses the regression results and elaborates on the relative impact of risk preference on the voluntary deductible choice. The final section of this thesis contains a conclusion and presents some policy recommendations and suggestions for further research.
2. Literature review
This section, first, provides an overview of the most important theories on individual risk preference and the measurement methods. Thereafter, I discuss the influence of risk preference on decision-making in different insurance markets, among which the health insurance market. Finally, the paper discusses the organization of the Dutch health insurance market and focus on the role of risk preference on health insurance and deductible choices in the Netherlands.
2.1. Theories on risk preference
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of expected utility; based on this principle, Tversky (1975) formulated the expected utility theory. The principle of expected utility theory in the context of decision-making means that an individual should choose the action that gives her the greatest expected utility. Weighting the possible outcomes of different actions and their occurring probabilities determine the expected utility. Furthermore, Bernoulli assumed the utility function to be concave; in other words, people are expected to be risk-averse.Mathematicians Van Neumann and Morgenstern build on Tversky (1975) expected utility theory. Instead of assuming risk-averse attitude, they add two other risk attitudes (e.g. risk–loving attitude and risk-neutral attitude), making a total of three categories of risk attitudes. The risk attitudes form the basis for the shape of the utility functions, which plot utility against total wealth. If an individual is risk loving (i.e. risk-seeking), risk-neutral, or risk-averse, the utility function is respectively convex, linear, or concave.
Kahneman and Tversky (1979) are having critique on the earlier developed expected utility theory. They show that this theory is not consistent with the actual observed behavior of individuals and they develop a different theory, called the prospect theory. This theory emphasizes the importance of a reference point in decision-making and a value function over gains and losses replaces the utility function from expected utility theory. The value function is steeper for losses than gains and reflects the principle of loss aversion, as Kahneman and Tversky (1979) explain by stating that “losses loom larger than gains”. Based on the actual observed individual behavior, they argue that individuals tend to behave risk-averse in the domain of gains and risk-seeking in the domains of losses. This means that people are likely to choose for sure wins (risk-averse) and try to avoid losses by engaging in risk-seeking behavior. As a numerical illustration, concerning gains, most people prefer the option to get $40 with certainty over the option of having a chance of 90% to get $50. As opposed to gains, regarding losses, most people prefer the option of having a 90% chance to lose $50 over the option of losing $40 with certainty.
Another contribution of Kahneman and Tversky is their observation that individuals tend to overweight low-probability events and underweight medium to high-probability events. This implies that most people rather lose a small amount with certainty than having a small risk to lose a huge amount (Kahneman and Tversky, 1979). This observation, together with the developed value function, has led to the theory of the fourfold pattern of risk attitudes (Tversky and Kahneman, 1992). The fourfold pattern of risk attitudes states that individuals are risk-averse for small probability losses and medium to large probability gains; in contrast, individuals are risk-seeking for small probability gains and medium to large probability losses.
2.2. Measurements of risk preference
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with complete certainty over a gamble with the same expected amount. They develop measures for absolute risk aversion and relative risk aversion. Absolute risk aversion considers the absolute amount of wealth invested in risky assets, while relative risk aversion considers the relative amount of wealth invested in risky assets. Equation 1 shows the Arrow-Pratt absolute risk aversion measure, while Equation 2 shows the Arrow-Pratt relative risk aversion measure in which w represents the individual’s wealth.
𝑅𝐴(𝑤) = −𝑢′′(𝑤)
𝑢′(𝑤) (1) 𝑅𝑅(𝑤) = 𝑤 ∗ 𝑅𝐴(𝑤) =
−𝑤𝑢′′(𝑤)
𝑢′(𝑤) (2)
Guiso and Sodini (2013) give two possible approaches to measure attitudes of individuals towards risk. First, a way to measure the degree of risk aversion is by means of the Arrow-Pratt measures of risk aversion as shown in Equation (1) or Equation (2). However, these measures are hard or even impossible to calculate directly as it requires estimations of individual utility functions. An option to obtain this measure is to rewrite models in which the Arrow degree of risk aversion is an independent variable. An example of a model which could be rewritten is Merton’s portfolio choice model (Merton, 1969), in which the optimal risky share (𝜔𝑖) is dependent on the expected risk premium (𝐸𝑟𝑖𝑒(𝑤)), volatility of risky assets (𝜎𝑖2) and the Arrow-Pratt degree of relative risk aversion (𝛾𝑖 ):
𝜔𝑖 = 𝐸𝑟𝑖 𝑒(𝑤)
𝛾𝑖 𝜎𝑖2 (3)
The second approach in determining risk preference is by means of experiments or surveys. The method from Holt and Laury (2002) is one of the most popular methods in determining risk preference. This method is popular as the method is easy to use, the exercise in the experiment is easy to understand and the incentives are clear for the subjects (Anderson and Mellor, 2009). For the interested reader, Table B.1 (Appendix) shows the Holt and Laury (2002) lottery experiment method to elicit risk preference. Next to the Holt and Laury (2002) method, several other lottery experiments and survey questions involving hypothetical gambles or self-reported measures have been used to elicit an individual’s risk preference (see, e.g., Barsky, Kimball, Juster, and Shapiro, 1997; Coppola, 2014; Anderson and Mellor, 2008).
2.3 Risk preference & insurance decisions
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markets, people can insure themselves against losses varying both in size and occurring probabilities. Below, I shortly discuss some empirical studies on insurance decisions in several insurance markets with different characteristics.
As an illustration, one of the insurance decisions that has been investigated is the decision whether to hold flood insurance (see, e.g., Attanasi and Karlinger, 1979; Petrolia, Landry, and Coble, 2013; Collier, Schwartz, Kunreuther, and Michel-Kerjan, 2017). The probability that flood and damage of the flood occurs, is generally believed to be relatively low. However, if damage occurs, the financial consequences for a household are dramatic. According to prospect theory, people tend to be risk-averse in the loss domain with small probabilities. Hence, we would expect that most people are taking up flood insurance to protect themselves against the small probability and high stake loss of a flood.
In accordance with both prospect theory, Petrolia et al. (2013) find the degree of individual risk aversion is positively related to uptake of flood insurance in the United States (U.S.). Collier et al. (2017) draw the same conclusion, looking at two aspects of the flood insurance contract: coverage limit and the deductible. The coverage limit is the large stake decision of the contract, while the choice for the level of the deductible is the small stake decision. In their analysis of flood insurance decisions of over 100,000 households in the U.S., they find that 77 percent of the households fully insure and that 94 percent of households decide to agree to one of the two lowest deductibles in the contract. The low deductible uptake is in line with the finding of Johnsson et al. (1993) that consumers appear to dislike deductibles in general.
In health insurance markets, risk preference is one of the two types of private information affecting the demand for different health insurance products (Finkelstein and McGarry, 2006; Cutler, Finkelstein, and McGarry, 2008). To avoid the negative financial consequences from uncertain severe health shocks, risk-averse people are expected to take-up more insurance than risk-neutral or risk-seeking individuals (Barsky et al., 1997). Chatterjee and Nielsen (2010) find that the degree of risk aversion is indeed positively related to the uptake of health insurance by examining nationally representative data from young U.S. citizens in 2006. Also, Cutler et al. (2008) find that risk aversion is related to higher health insurance coverage in the U.S in 1992 and 1995.
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2.4. Risk preference & health insurance market in the Netherlands
In the Netherlands, the Health Insurance Act came into effect on 1 January 2006 and mandated by law that every individual is obliged to have health insurance and that every insurer must accept every individual who applies for the mandatory health insurance. The insurance premium is community-rated; an insurer cannot charge different premiums based on an individual’s health risk. An insurer receives a compensation from the Health Insurance Fund if any financial disadvantage occurs from having to accept every individual. Next to the mandatory basic insurance, individuals can voluntarily choose for different kinds of supplementary health insurance to insure themselves for usage of types of health care not covered by the basic insurance. Dental care and physiotherapy are examples of health care only insured for via supplementary health insurance.
In 2008, the government introduced the compulsory deductible within the basic health insurance system. This law required each insured to pay the first incurred health cost out-of-pocket. Some health care costs are not subject to out-of-pocket payments, such as general practitioner visits. At the time of implementation, the compulsory deductible amount was 150 euro. In the years after, the level of the deductible has increased and now, in 2020, the amount is 385 euro per year.
Besides the compulsory deductible, Dutch insurance companies give the option to their insured to choose for an extra voluntary deductible (e.g. €100, €200, €300, €400, or €500) in exchange for a lower health insurance premium. People have to actively opt in for a non-zero voluntary deductible (VD); a zero VD is the default option. Table 1 shows the average yearly premium discounts for the different categories of voluntary deductible. The table shows that the offered premium discount is slightly less than half of the chosen voluntary deductible and has increased over time. Relatively, the offered discount is most beneficial for the maximum voluntary deductible of €500. In general, opting for a higher deductible implies that an individual is willing to voluntarily expose herself to more financial risk.
In an optimal world with rational agents, agents choose to opt for a voluntary deductible if it is financially profitable. A VD is financially profitable for an individual if the monthly discount on the health insurance premium exceeds the out-of-pocket health care costs under the voluntary deductible. The voluntary deductible would be most beneficial for individuals with low health risk, because their probability of getting sick and having to pay the out-of-pocket payments under the voluntary deductible are low. However, Van Winssen et al. (2015) find that in 2014 only 11 percent of the insurance takers opted for a voluntary deductible, while it would have been financially profitable for at least 48 percent of the insurance takers to opt for a VD.
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following prospect theory, the individual’s reference point is very important. Based on different scenarios, Van Winssen et al. (2016) infer the individual’s risk attitude and its effect on the individual’s voluntary deductible choice. The reference point for the decision is most likely the full insurance option, implying a zero voluntary deductible, since it is the default option in insurance contracts. One of the scenarios regarding the choice for the maximum VD is one in which the insured’s perceptions of the decision is a mixed prospect of probability p (probability of not getting sick) to gain the discount on the premium (e.g. see Table 1: €232) and a probability of 1-p to lose the difference between the premium discount and the out-of-pocket payments under the maximum voluntary deductible (e.g. see Table 1: €500-€232=€268)2. For the group of low health risk individuals for whom the VD is profitable (i.e. individuals who are part of the observed gap between optimal (48%) and actual take-up (11%) of voluntary deductibles (Van Winssen et al., 2015)), the probability of losing money under the voluntary deductible is low. Based on prospect theory, risk-averse behavior is expected for those individuals, as people tend to behave risk-averse for small probability losses.
The only empirical paper I am aware of is Gorter and Schilp (2012), who investigate the impact of risk preference on the voluntary deductible choice in the Netherlands in 2008. They use data from the Dutch Household Survey (DHS). Risk preference is determined by a combination of multiple proxies for risky behavior and financial risk tolerance. The financial risk tolerance is based on the response to the following survey statement on a 7 point Likert-scale: ‘I am willing to run the risk of losing money if there is also a chance that I will make money’. They find that risk preference significantly affects the decision-making on deductibles. Also, separately, a higher degree of financial risk tolerance positively affects the take-up of deductible. Interestingly, the effect of risk preference on taking up a voluntary deductible
2 In the scenario, the assumption is made that out-of-pocket payments do not occur at all or it covers the complete amount of the VD (Van Winssen et al., 2016). In reality, an individual can face out-of-pocket payments that only partially cover the amount of voluntary deductible.
Table 1. Average yearly premium discounts per voluntary deductible category in the period 2009-2018. Voluntary deductible (€) 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 100 42 44 44 45 45 46 45 44 46 46 200 84 86 86 87 88 90 89 86 87 88 300 121 126 127 129 131 133 132 126 129 129 400 162 166 168 174 175 178 176 169 173 172 500 205 210 219 229 230 236 236 228 232 232
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choice is higher than the effect of health risk, which is measured by self-assessed health status and general practitioner visits.
This thesis distinguishes itself from the study from Gorter and Schilp (2012) in two ways. Firstly, Gorter and Schilp (2012) use one self-reported measure for financial risk tolerance, while I use multiple elicitation methods for risk preference. Besides, all my elicitation methods are not self-reported and hence they are less subjective than the method used in Gorter and Schilp (2012). Secondly, this thesis explores the effect of risk preference on voluntary deductible choice over a longer time period, from 2009-2018. Gorter and Schilp (2012) only establish the relationship between risk preference and voluntary deductible choice in 2008. As 2008 is the implementation year of the voluntary deductible system, people probably have limited knowledge and are not able to make an informed choice on the voluntary deductible at that moment in time. Therefore, it is valuable to investigate the relationship over more recent years and a longer time period.
2.5. Hypothesis
Following the empirical evidence on insurance decisions, the scenario of Van Winssen et al. (2016) and the empirical finding of Gorter and Schilp (2012), I hypothesize that risk preference, measured by an individual’s financial risk attitude, is related to voluntary deductible choice as follows: People who are more risk-averse are less likely to opt for a voluntary deductible than people who are less risk-averse.
3. Data & Methodology
This section discusses the data source and how the data set for this research is constructed. Furthermore, I will discuss the econometric model and the statistical hypothesis and give a description of the variables. Finally, I provide the summary statistics of all the variables and provide separate summary statistics on the distribution of the voluntary deductible choice over the time period.
3.1 Data source
In this thesis I make use of data of the LISS panel administered by CentERdata (Tilburg University, The Netherlands). The LISS panel consists of Dutch individuals who participate in monthly Internet surveys. The panel is based on a true probability sample of households drawn from the population register. Households that could not otherwise participate are provided with a computer and internet connection.3 They are paid for each completed questionnaire.
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On average, the LISS online questionnaires are sent to 7,000 LISS panel members within more than 4,500 households every year. The selection of households is different every year. The LISS panel members have been receiving questionnaires since October 2007 and the LISS Data Archive consists of data from the years 2007-2020. The panel members receive a questionnaire every month to update the information on their background characteristics, such as age and income. At the end of every year, the panel members receive a questionnaire with questions from different domains. These longitudinal surveys, referred to as the LISS Core Study, include surveys in 10 different domains4. I use data from the Health Core Study, which includes 11 waves covering the period from 2007 to 20185. The Health surveys were sent to all LISS panel members aged 16 years and older and the average yearly response rate is about 80%, which corresponds to approximately 5,500 yearly responses.
Besides the LISS Core Studies, researchers can use the opportunity to collect data from the research infrastructure of LISS for their own studies. The assembled studies are studies in various domains and are published in the LISS online data archive. The data collection of an assembled study is only taking place once. One of the assembled studies is called ‘True Risk Preferences’, conducted on the LISS panel in 2012. 1,647 randomly selected panel members received the survey with the title ‘Testing Mechanisms for Identifying True Risk Preferences’ and 1,153 panel members completed the survey. The data from this assembled study is the basis for measuring risk preference in this study. Another assembled study is ‘Measuring Higher Order Risk Attitudes of the General Population’, conducted on the LISS panel in 2009. 3,425 randomly selected LISS panel members completed the survey, from which questions will be used to elicit risk preference for a robustness check.
3.2 Data set construction
The background characteristics and the data from the different core- and assembled studies are provided in separate data sets. I merge the data from the different data sets into one based on a unique individual indicator. Subsequently, the variables from the core- and assembled studies are linked to the observations based on the year in which they are observed. The resulting unbalanced panel data set consists of data on 24,130 unique individuals with a total of 124,677 observations. Thus, the data set consists of 5.17 observations on average per individual from 11 different years in the period 2007-2018.
Since young people do not face the voluntary deductible choice within the Dutch health insurance system, I drop the 25,363 observations, relative to the 4,653 individuals below 18 years old. All the remaining observations with missing values regarding deductible choice (49,379 observations, relative to 8,669 individuals) and observations of respondents who do
4 The 10 different domains from the LISS core study are the following: Health, Religion and Ethnicity,
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not know their deductible choice are dropped as well (6,958 observations, relative to 833 individuals), leaving us with 42,977 observations on 9,975 individuals.
Table A.1 in the Appendix show the distribution of the voluntary deductible choice over the different years and the year 2008 clearly diverges from the other years with almost 70 percent choosing a voluntary deductible in 2008 and about 20 percent in the 2009-2019 period. This might have to do with the way the voluntary deductible is interrogated in the survey in 2008. In 2009, the question changed from “What is your own risk?” to “In 2009 you have an obliged own risk of 155 euro. Besides a voluntary own risk is possible. What is your own voluntary risk?”. The line of questioning in 2008 clearly led to a measurement error as people possibly included the amount of the obliged deductible (in 2008: €150) in their answer. Therefore, I decide to exclude the year 2008 from the analysis and data set, which meant dropping 3,798 observations relative to 693 individuals. Subsequently, 32,753 observations relative to 8,195 individuals with missing values for the main independent variable of interest (i.e. risk preference elicited from the assembled study True Risk Preferences) are dropped from the data set. Observations with only missing values for any of the other independent variables are kept in the data set.
Testing for possible outliers, Figure A.1 (Appendix) shows the distribution of the constructed variable log of net household income. Figure A.1 does not illustrate significant outliers, which led to keeping all the observations. The final constructed unbalanced panel data set now consists of 6,426 observations relative to 1,087 individuals over the observation period 2009-2018.
3.3 Econometric Model
The dependent variable is whether an individual chooses to have a voluntary deductible or not. This variable is a binary variable and can take either value 0 (zero voluntary deductible) or value 1 (non-zero voluntary deductible). Econometric textbooks discuss a few models dealing with binary dependent variables (see, e.g., Verbeek, 2012; Brooks, 2014). The linear probability model (LPM) is the simplest model dealing with binary dependent variables. The LPM is easy to estimate (by OLS) and the estimation results are the easiest to interpret. However, one of the major flaws of the LPM is that the estimation probabilities do not always lie between 0 and 1.
12 The specification of the logit model is as follows:
Pr(𝑉𝑖𝑡 = 1) = 𝐹(𝛼 + 𝛽𝑅𝑖,𝑡−1+ 𝜃𝐵𝑖,𝑡−1+ 𝛿𝐻𝑖,𝑡−1+ 𝛾𝑋𝑖,𝑡−1+ 𝜆𝑡+ 𝑢𝑖𝑡) (4) 𝑢𝑖𝑡 = 𝑐𝑖 + 𝑣𝑖𝑡 (5)
where Vit is the voluntary deductible choice of individual i in time t. F indicates the cumulative distribution function of the logistic distribution. Ri,t-1 is the main independent variable of interest indicating risk preference; Bi,t-1 are indicators for risky behavior; Hi,t-1 are health risk indicators; Xi,t-1 are several individual background characteristics used as control variables; 𝜆𝑡 is the time fixed effect; and 𝑢𝑖𝑡 is the error term. The inclusion of 𝜆𝑡 in the model controls for time-specific effects affecting individuals in the same way. Time fixed effects are included in the model as pretesting the model including the time dummies has led to the conclusion that the time dummies are not redundant6. The independent variables are taken from the last month in the previous calendar year, since insurance decisions in the Netherlands are made ex-ante. The voluntary deductible choice made at the end of the previous year (t-1) is reported in the LISS data in the current year (t).
As mentioned in Section 3.1, the study on risk preference within the LISS panel is only performed once in 2012. This means that only the observations on the risk preference of the LISS panel at the end of 2012 are present and without making any assumptions only the deductible choice in 2013 can be analyzed. To use the risk preference measure for all the years in our sample, I must assume that risk preference is stable over time. In economic models and theory, preferences are assumed to be stable. However, there is a debate in the empirical literature on whether the assumption of risk preference being constant over time does hold or not. Schildberg-Hörisch (2018) and Zeisberger, Vrecko, and Langer (2012) find that risk preference changes over the life cycle, while Harrison, Johnson, McInnes, and Rutström (2005) find that measured risk preference is stable within individuals over time. Following these contradictory findings, the model is estimated for all the years in the data set (2009-2018) and for the year 2013 only.
Estimating the model for all the years means that we should run a logit regression for panel data. By default, when running a logit model for panel data, Stata estimates the random effects logit model. However, a major drawback of the random effects model is that it requires the error term and the explanatory variables to be uncorrelated. Most importantly, it requires that the individual component of the error term, 𝑐𝑖 in Equation 5, is uncorrelated with the explanatory variables in Equation 4. This is a very strong assumption, as unobserved individual effects are rarely uncorrelated with explanatory variables. The fixed effect model allows for
6 Based on the Wald-test with value of chi-square test statistic of 20.58 and corresponding p-value of
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correlation between the individual component of the error term and the explanatory variables as it controls for the time-invariant heterogeneity between individuals. For that reason, a fixed effects model is in general mostly preferred over a random effects model. However, in a fixed effects model, estimates of the time-invariant variables are omitted. Using a fixed effects model for the model estimation would therefore be problematic, since risk preference is time-invariant. I perform a formal test on whether the random effects or fixed effects is preferred. The value of the chi-square test statistic (12.87) and the corresponding p-value (0.68) of the Hausman test shows that the null-hypothesis that the random effect model is consistent cannot be rejected.
Furthermore, the random effects logit model is estimated with clustered robust errors at the individual level to deal with heteroskedasticity. As the magnitude of the effect is not directly interpretable from the logit model regression coefficients, average marginal effects are computed to determine the size of the effect.
3.4 Variables
In this subsection, the construction of the dependent variable, independent variables, and a set of control variables are further elaborated on.
3.4.1 Dependent variable: voluntary deductible choice
The dependent variable is whether a respondent chose for a non-zero voluntary deductible. A score of 1 has been allocated to respondents who chose a non-zero voluntary deductible. A score of 0 indicates that individuals chose the zero-voluntary deductible.
3.4.2 Main explanatory variable: risk preference
The LISS database makes it possible to elicit risk preference in multiple ways. Three measurement methods are considered in this study. The first one very strongly resembles the Holt and Laury (2002) lottery method; the second one is a new measurement method in an insurance-related context; the third one is a lottery method introduced in Noussair, Trautmann, and van de Kuilen (2014). In this study I use the second and the third measure. The first measure of Holt and Laury (2002) is the one of the most popular methods in the literature as the method is easy to use, the exercise in the experiment is easy to understand and the incentives are clear for the subjects (Anderson and Mellor, 2009). However, because of the low number of observations, the results from the model estimations might not be reliable and the method is therefore not appropriate to use in this study .7
7 Only 216 out of the 1,166 respondents from the survey ‘Testing Mechanisms for Identifying True
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A more detailed explanation of the two measurement methods used in this study follow below and in Table B.3 and Table B.4 in the Appendix.
The first measure of risk preference is a method from the LISS assembled study ‘True Risk Preferences’, in which the survey question is framed in an insurance context.
In this survey question, presented in an insurance context, individuals have to choose whether to insure themselves against a possible loss of €10 and by how much. The participants have the choice between five options, from which the lower extreme option entails no insurance, while the higher extreme option implies full insurance. The other three options offer the chance to the individuals to choose for partial insurance. The higher the take-up of insurance, the lower the expected earnings (Table B.3 in Appendix).
I construct the variable risk preference as a categorical variable with 5 categories ranging from 0 (i.e. choosing no insurance) to 4 (i.e. choosing full insurance); 0 is not risk- averse (i.e. risk-neutral and risk-seeking) and 4 is highly risk-averse.
As a higher value of the variable risk preference indicates a higher level of risk aversion, the coefficients are expected to be negative.
The second measure of risk preference is an alternative to the Holt and Laury (2002) lottery method and is based on the method of Noussair, Trautmann, and van de Kuilen (2014), in which the number of safe choices in a lottery decision task determine an individual’s risk preference. For this measure, I use data from the LISS assembled study ‘Measuring Higher Order Risk Attitudes’.
In this gamble, participants are faced with a five decision lottery task, in which they have to make a choice between a sure payoff and a risky lottery. The sure payoff is different in every decision task and ranges from 20 to 40 euro (Table B.4 in the Appendix). The risky lottery implies having an equal chance of winning either 65 euro or 5 euro. A safe choice corresponds to choosing for the sure payoff.
Based on the number of safe choices and following the classification of Noussair et al. (2014), Table B.4 in the Appendix shows the risk attitudes allocated to the groups of individuals ranging from risk-seeking (=0) to highly risk-averse (=5).
3.4.3 Indicators of risky behavior
Another way to observe individual risk preference is to use alcohol use and smoking behavior as a proxy for the degree of risk taking of individuals (see, e.g., Cutler, Finkelstein, and McGarry, 2008; Doiron, Jones, and Savage, 2008). This proxy will be used as an addition to the risk preference measure from section 3.4.2, which is measured in a financial context.
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2008). Because the LISS survey does not include this information, I use the number of days on which alcohol is consumed in the last seven days. I construct a dummy variable which has value 1 if the respondent is a daily drinker (i.e. respondent answered with seven). All the other respondents received a score of zero.
Regarding smoking, following Doiron et al. (2008) and Cutler et al. (2008), daily smoking is used as a proxy for a risky attitude. The smoking dummy variable has a value of 1 if the respondent is a daily smoker, while a zero represents all the other respondents who do not smoke daily.
As choosing for a voluntary deductible can be perceived as taking more (financial) risk, smoking and drinking behavior is expected to be positively related to the up-take of a voluntary deductible. However, one could argue that smoking and drinking could lead to more health care usage and smokers and drinkers might therefore choose for a lower voluntary deductible. Accordingly, the sign of the coefficients of smoking and drinking behavior can be either positive or negative, depending on which effect dominates. Both Doiron et al. (2008) and Cutler et al. (2008) find that people who take part in in risky behavior (i.e. daily smoking or excessive drinking) buy health insurance less frequently. Based on these empirical findings, it is expected that the coefficients for smoking and drinking are positive.
3.4.4 Health risk
Risk preference and health risk type are the two types of private information influencing an individual’s demand for health insurance (Finkelstein and McGarry, 2006). Therefore, it is important to account for health risk in the model. Following Gorter and Schilp (2012), the number of general practitioner (GP) visits and self-assessed health status (SAHS) are used to predict health risk and next year’s health care expenses. In addition to the number of GP visits, medical specialist visits are included to capture health risk.
GP visits are not directly leading to higher out-of-pocket expenses, but GP visits might increase the likelihood that a person consumes other healthcare in the future. As an illustration, people need a referral from their GP to visit a medical specialist. Subsequently, visits to a medical specialist have to be paid out-of–pocket. Concerning GP visits, I construct a continuous variable covering the number of GP visits in the year of the survey. Regarding medical specialist visits, I construct a dummy variable, which has value 1 if the respondent visited a medical specialist in the year of the survey and value 0 if not. Hence, the number of GP visits and medical specialist visits are expected to be negatively related to the uptake of a non-zero VD and the coefficient sign is expected to be negative.
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information about her own health condition (Finkelstein and McGarry, 2006). The SAHS is determined by asking the respondents the following question: “How would you describe your health, generally speaking?”. Respondents could answer this question on a scale from 1 to 5; from poor to excellent health. A dummy variable is created, for which a value of 1 is allocated to the individuals with a very good or excellent self-assessed health status. The respondents with a good, moderate, or poor SAHS receive a score of zero. The sign of the SAHS coefficient is expected to be positive, as it is for other financial decisions (Rosen and Wu, 2004).
3.4.5 Control variables
The control variables added to the model are several individual background characteristics and socio-economic variables such as gender (1=male), age, marital status (1=married), children (1=having children), owning a home (1=homeowner), living environment (1= extremely or very urban), type of occupation (1=self-employed), net household income, and education. In addition, a measure of numeracy is included.
Men are less risk-averse than women (see, e.g., Eckel and Grossman, 2003; Borghans, Heckman, Golsteyn, and Meijers, 2009) and are expected to be more likely to opt for a non-zero deductible. From the population data (Vektis, 2016), it follows that the take-up of voluntary deductibles continuously decreases with age. Also, it is found in other literature that risk-taking decreases with age (Dohmen, Falk, Huffman, Sunde, Schupp, and Wagner, 2011). Therefore, an age variable is included in the model. A dummy variable indicating whether an individual is married is included, because single investors are found to be more risk tolerant (see, e.g., Grable, 2000). Regarding the type of occupation, self-employed individuals are exposed to more financial risk (Brown, Dietrich, Ortiz-Nuñez, and Taylor, 2011) Income has a positive relation with risk tolerance (see, e.g., Grable and Lytton, 1998). Household income is used instead of individual income, because the income of the household members is important in absence of individual income. As mentioned in Section 3.2, the log of net household income is calculated to remove potential outliers and make the distribution of income look more normal (Figure A.1 in Appendix A).
A higher level of education is associated with higher financial risk tolerance (Grable, 2000). Education is included as a categorical variable with the following levels: low education, medium education and high education. The reference category is the low education level. Following the standard of the CBS8 and the International Standard Classification of Education (ISCED), the low education, medium education and high education labels are allocated to the individuals with ISCED level 0-2, 3-4, and 5-6, respectively.
8 CBS is the Central Agency for Statistics in the Netherlands (‘Centraal Bureau voor de Statistiek’).
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A measure for numeracy is included as it is proved to be a determinant in health insurance decisions and deductible choice (Dillingh, Kooreman, and Potters, 2016) and could possibly affect both the dependent and main independent variable. Control questions from the survey ‘Measuring True Risk Preferences’ are used to determine an individuals’ degree of numeracy and are displayed in Table B.5 in the Appendix. A score of 1 has been allocated to the respondents who answered one of the three questions correctly, a score of 2 to those who gave two correct answers, and a score of 3 to respondents who answered all the three questions correctly. The fact that these cognitive abilities are only measured once would not give rise to a problem, because cognitive abilities are stable over time (Dillingh et al., 2016).
3.5 Descriptive Statistics
Table 2 gives an overview of the summary statistics of all the variables over the years 2009-2018. Columns 1 – 3 present the summary statistics for the full sample. Columns 4 – 6 and Columns 7 – 9 present the summary statistics separately for the subsamples for which the choice for the deductible is respectively zero and non-zero. Column 10 shows the significance of the difference in the subsample means by using a t-test.
Column 2 shows all variable means of the full sample. On average, 19% of the people choose for a positive voluntary deductible and individuals are 54.2 years old. This is older than the average population age in the Netherlands in the period 2009-2017, which is between 39.9 and 41.6 years9. An explanation for this difference is that the individuals below 18 years are dropped from the data set as they do not make deductible choices. From our full sample, 48% is male and this is in line with the key figures from the CBS. Regarding our main explanatory variable, column 2 shows that on average the score for the insurance risk preference variable is 1.71 and 3.33 for the risk preference measure using the lottery method from Noussair et al. (2014). According to these measures, the values suggest that people are on average slightly risk-averse to risk-averse.
Next to the full sample characteristics, it is interesting to point out some of the differences between the two subsamples. Comparing column 5 and column 8, we observe that 56% of the people choosing a non-zero voluntary deductible are men, while the share of men in the subsample of people with a zero-voluntary deductible is only 46%. This implies that men are more likely to choose a positive voluntary deductible than women. This observation is in line with the widespread view that men are less risk-averse than women (see, e.g., Eckel and Grossman, 2003; Borghans, et al., 2009; Hartog, Ferrer-i-Carbonell, and Jonker, 2002).
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Table 2. Summary Statistics (Full sample: 2009-2018)
N Mean St.Dev N (VD=1) Mean (VD=1) St. Dev (VD=1) N (VD=0) Mean (VD=0) St. Dev. (VD=0) T-test diff. means VD=1 & VD=0 Variables (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
VD choice (=1 if voluntary deductible >0) 6,426 0.19 0.39 1,226 1 0 5,200 0 0
Risk preference (insurance) (0-4; 4=highly risk-averse) 6,426 1.71 1.65 1,226 1.51 1.57 5,200 1.76 1.67 ***
Risk preference (lottery) (0-5; 5=highly risk-averse) 3,139 3.33 1.73 577 3.16 1.73 2,562 3.37 1.72 **
Smoking behavior (=1 if daily smoker) 6,426 0.22 0.42 1,226 0.25 0.43 5,200 0.22 0.41 **
Drinking behavior (=1 if daily drinker) 4,697 0.15 0.36 893 0.14 0.35 3,804 0.15 0.36
GP visits (number) 5,318 2.36 5.00 1,001 1.79 4.58 4,317 2.50 5.09 ***
Medical specialist visits (=1 if number of visits > 0) 5,318 0.40 0.49 1,001 0.26 0.44 4,317 0.43 0.50 ***
Self-assed health status (=1 if very good/excellent) 5,329 0.23 0.42 1,003 0.32 0.47 4,326 0.20 0.40 ***
Gender (=1 if male) 6,426 0.48 0.50 1,226 0.56 0.50 5,200 0.46 0.50 ***
Age (years) 6,426 54.21 15.45 1,226 49.25 15.87 5,200 55.38 15.11 ***
Married (=1 if married) 6,426 0.64 0.48 1,226 0.56 0.50 5,200 0.65 0.48 ***
Children (=1 if having children) 6,426 0.34 0.47 1,226 0.40 0.49 5,200 0.32 0.47 ***
Medium education (=1 if medium education level) 6,420 0.32 0.47 1,226 0.30 0.46 5,194 0.33 0.47 *
High education (=1 if high education level) 6,420 0.32 0.47 1,226 0.43 0.49 5,194 0.29 0.45 ***
Homeowner (=1 if homeowner) 6,426 0.75 0.43 1,226 0.77 0.42 5,200 0.74 0.44 *
Urban (=1 if very/extremely urban) 6,403 0.38 0.48 1,211 0.38 0.49 5,192 0.37 0.48
Log of net household income (€) 5,910 7.85 0.51 1,140 7.91 0.54 4,770 7.83 0.49 ***
Numeracy (0-3; 3=excellent) 6,394 1.01 1.09 1,217 1.06 1.13 5,177 1.00 1.08 *
Self-employed (=1 if self-employed) 6,425 0.04 0.20 1,225 0.06 0.23 5,200 0.04 0.18 ***
*/**/*** represents the significance of the difference between group means VD=1 and VD=0 at the 10%/5%/1% level (t-test). Notes: N indicates number of observations.
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Furthermore, Column 5 and Column 8 illustrate that individuals who chose a nonzero voluntary deductible are on average more than five years younger, more often reported having children, have a higher income, and are on average more likely to have a high education level. Also, individuals choosing a non-zero deductible are more likely to be self-employed and score on average slightly higher on the test concerning numeracy.
Regarding the indicators of risky behavior, a point worth noticing is that the group who chose a non-zero voluntary deductible consists of more smokers than the group that chose the zero deductible. This observation validates the use of smoking behavior as a proxy for risk-taking behavior. This, however, does not hold for drinking behavior, as the difference in means is not statistically significant at any level.
Besides, looking at the health risk, it seems that the number of GP visits, medical specialist visits, and self-assessed health status are quite important in deciding on whether to opt for a non-zero voluntary deductible. The individuals choosing for a non-zero deductible had on average less GP visits in a year, were less likely to visit a medical specialist, and assessed their health to be better than the group of individuals choosing a zero VD.
One last observation, but an important one, is the descriptive evidence of the effect of both the risk preference measure on deductible choice, since the differences between the subsample means are statistically significant at the 1% and 5% level. Regarding both risk preference measures, the expectation that individuals choosing a VD are less risk-averse seems to hold.
As the model is also estimated for the year 2013 only, Table B.6 in the Appendix provides the summary statistics for the observations in 2013 only.
3.5.1. Distribution of the independent variable: voluntary deductible choice
This subsection elaborates on the distribution of the voluntary deductible choice in the survey data. It discusses the implications of the sample selection and the difference in distribution between the survey data and the population data. Thereafter, summary statistics on the voluntary deductible choice within individuals over time are provided to show the stability of voluntary deductible choice.
Table 3 shows the distribution of the voluntary deductible choice among our selected samples, all respondents to the voluntary deductible question and the population (Vektis, 2013)10. Table 3 illustrates that the selection of our sample does not significantly affect the distribution of the deductible choice.
10 Vektis publishes a report every year, called ‘Zorgthermometer: Verzekerden in Beeld’, with data
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Comparing the distribution of our selected sample to the population distribution, we observe that our selected samples have a lower percentage of individuals opting for a zero VD (80.02% and 80.92%) than the population (90.3%). A possible explanation for a part of this difference are the individuals who do not know the height of their chosen deductible. As mentioned before, those individuals have been dropped from the data set. If we would assume that these individuals have a zero-voluntary deductible, which is the default option, the percentage of opting for a zero deductible in our sample comes closer to the population distribution. However, this does not account for the complete observed difference as it would only increase the percentage of people choosing for a zero VD to 82.06% for the selection sample in 2013 and to 82.9% for the selected respondents within the full sample. The population and selected sample both show that out of the group of people choosing for a deductible, most of the individuals choose for the highest deductible (i.e. €500). Overall, the survey data is a reasonable representation of the population data, although there is an observed difference in the uptake of voluntary deductibles.
Since the LISS panel members are followed over time, one could have a look at the distribution of the voluntary deductible choice between and within individuals over time. Table B.7 and Table B.8 in the Appendix show the overall, between, and within variation and the transition probabilities on voluntary deductible choice. Both tables show that the voluntary deductible choice is quite stable over time within individuals. The voluntary deductible choice of zero is more stable, meaning that people with a zero VD tend to switch less than people with a non-zero VD.
Table 3. Voluntary deductible choice: comparison between selected respondents, all respondents and the population.
Voluntary deductible (€) Selection (2013) (%) All respondents (2013) (%) Selection (2009-2013, 2015-2018) (%) All respondents (2009-2013, 2015-2018) (%) Population 2013 (%) 0 80.02 80.19 80.92 80.15 90.30 100 1.40 2.12 2.89 3.00 1.46 200 2.34 2.62 5.37 5.05 * 300 7.59 7.03 3.39 3.82 * 400 0.82 1.04 1.20 1.32 * 200-400* 10.75 10.69 9.96 10.19 2.04 500 7.83 7.01 6.22 6.65 6.21 No. observations 856 4,537 6,426 39,179
* The data in the report ‘Verzekerden in Beeld’ from Vektis only reports the share of the population
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Table B.7 shows that conditional on an individual ever having a zero VD, 84.41% of her observations have a zero VD. For non-zero VD, this percentage is significantly lower with only 49.74%. Table B.8 confirms this observation by showing the transition probabilities from the voluntary deductible choice. Each year, about 90% of the individuals with a zero VD kept their zero VD in the next year. From the individuals with a non-zero VD, only 63% of those chose for a non-zero VD again in the next year. This observation can be considered as prima facie evidence of the presence of status quo bias or inertia. Also, this could be an indicator of an individual’s ability of planning their health expenditures.
4. Results
This section provides the results of the model estimations. First, the regression results for the full sample with the insurance related risk preference measure are discussed. Predicted probabilities are shown for the average individual to compare the impact of the two types of private information (i.e. health risk and risk preference) with each other and to the other determinants of voluntary deductible choice. Thereafter, I discuss three alternative estimation models used as a robustness check.
4.1 Results full sample
Table 4 shows the coefficient estimates and the estimated average marginal effects of the random effects logit model estimation for the full sample of 2009-2018, in which risk preference is elicited with the insurance related method. The p-value of the Wald test (0.000) indicates that we can reject the null-hypothesis that all the coefficients together are not statistically different from zero. Column 1 shows the coefficient estimates and Column 2 shows the average marginal effects. Most of the signs of the coefficients are as expected beforehand and the statistically significant variables are discussed below.
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Concerning the indicators of risky behavior, the smoking and drinking coefficient have a positive sign, but only the coefficient for smoking is statistically significant. This is in line with the findings of Cutler et al. (2006) who also find only daily smoking to significantly affect the take-up of health insurance. More precisely, daily smokers 2.4% more likely to take-up a VD than not daily smokers.
Regarding health risk, the coefficients for medical specialist visits and self-assessed health status are significant at the 5% and 1% level, respectively.
Medical specialist visits are negatively related to the uptake of a non-zero VD. People who visited a medical specialist in the last year are 3.2% less likely to opt for a non-zero VD in the next year than people who did not visit a medical specialist. The result is in line with the expectations that medical specialist visits imply higher out-of-pocket payments and result in a decrease in the likelihood of taking-up a non-zero VD.
Self-assessed health status has a positive relationship with the take-up of a non-zero VD. It implies that people who report better health are more likely to select a non-zero VD. More specifically, an individual with a very good or excellent health is 6.1% more likely to take-up a VD than an individual with a good, moderate, or poor health. The positive association intuitively makes sense as better health results in lower health care expenditures and lower out-of-pocket payments.
Most of the coefficients of the control variables are not statistically different from zero, except for gender, age, high education, and numeracy.
The sign for the coefficient gender is negative and is significant at the 1% significance level, indicating that men are on average 6.7% more likely to opt for a non-zero voluntary deductible than women. It is a widespread view that males are less risk-averse than females and are taking more financial risk (Eckel and Grossman, 2003; Borghans et al., 2009). Therefore, the negative coefficient confirms the expectations based on the other literature and the descriptive evidence in Section 3.5.
The coefficient for age is negative, implying that younger people are more likely to opt for a positive VD than older people are. An increase in age with one year leads on average to a decrease in the probability of choosing a non-zero VD by 0.31%. This result is in line with the intuition that health care costs increase with age and older people therefore tend to have more insurance and, thus, a lower deductible. In line with our finding, the population data shows that the choice for a zero VD seems logical for older people as they are often topping up the deductible (Vektis Zorgthermometer, 2019). Besides, it is found in other literature that financial risk taking decreases with age (Jianakoplos and Bernasek, 2006; Dohmen et al., 2011; Schildberg-Hörisch 2018).
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Table 4: Voluntary Deductible Choice: Regression Results Full Sample (2009-2018)
Coefficients Marginal Effects
Variables (1) (2) Risk preference (1) – Slightly risk-averse 0.390 0.0359 (0.320) (0.0302) (2) – Risk-averse 0.293 0.0266 (0.340) (0.0314) (3) – Very risk-averse 0.487 0.0454 (0.401) (0.0388) (4) – Highly risk-averse -0.499* -0.0405* (0.289) (0.0230)
Indicators risky behavior
Smoking 0.268* 0.0238* (0.163) (0.0147) Drinking 0.158 0.0140 (0.217) (0.0196) Health risk GP visits -0.008 -0.0007 (0.015) (0.0013)
Medical specialist visits -0.370** -0.0320**
(0.158) (0.0136)
Self-assessed health status 0.667*** 0.0614***
(0.177) (0.0171) Control variables Gender 0.768*** 0.0670*** (0.222) (0.0191) Age -0.036*** -0.0031*** (0.008) (0.0007) Married -0.325 -0.0287 (0.220) (0.0196) Children -0.159 -0.0138 (0.263) (0.0225) Medium education -0.232 -0.0201 (0.254) (0.0216) High education 0.655** 0.0591** (0.259) (0.0242) Homeowner 0.269 0.0230 (0.261) (0.0218) Urban -0.051 -0.0045 (0.220) (0.0191)
Log of net household income -0.027 -0.0023
(0.191) (0.0166) Numeracy -0.226** -0.0197** (0.111) (0.0096) Self-employed 0.231 0.0207 (0.447) (0.0413) Constant -1.137 (1.500)
Time fixed effects YES YES
P-value Wald test 0.0000
Number of observations / individuals 4,322 / 902 4,322 / 902
Robust standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1.
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The coefficient and marginal effect for high education level is positive, indicating that the likelihood to take-up of a non-zero VD is increased by 5.9% for people with a high
education level compared to individuals with a low education level. The reasoning behind this result could be that people who followed high level education (i.e. higher vocational
education and university) are more financially literate. This possibly results in choosing a VD more often.
The sign of the numeracy variable is negative, which indicates that people with better numeracy skills are less likely to choose for a non-zero VD compared to people with lower numeracy skills. Dillingh et al. (2016) find the same negative relationship between (probability) numeracy and voluntary deductible uptake. However, this result seems rather odd. One of the possible reasons Dillingh et al. (2016) gives for this result is that a very innumerate individual will buy as little insurance as possible as insurance is costly and the individual is not aware of the advantage insuring gives to him personally. An alternative explanation provided by Dillingh et al. (2016) is that less numerate individuals could have indicated the height of their chosen deductible incorrectly.
From the regression results and the marginal effects estimations, it can be concluded that risk preference affects voluntary deductible choice as follows: highly risk-averse individuals are less likely to opt for a non-zero VD than risk-neutral and risk-seeking individuals. Among the health risk- and control variables, gender, age, self-assessed health status, and medical specialist visits have a significant impact on the take-up of a non-zero VD. Gender seems to have the highest impact in terms of the size of the marginal effect and is closely followed by self-assessed health status. The results on the control variables are conforming to the findings of Van Winssen et al. (2015) that a voluntary deductible is the most beneficial for males, young individuals, and individuals with low health risk.
4.1.1 Comparing the impact of risk preference to other determinants
As we are specifically interested in the effect of risk preference on deductible choice, it is interesting to dive further into the relative impact of risk preference on the VD choice for the average individual compared to the other determinants from the model estimation. A convenient way to present the comparison of impact between determinants is by means of predicted probabilities of non-zero deductible choice (Long, 1997).
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self-assessed health status, smoking- and drinking behavior) and the variables with a negative coefficient to its maximum (i.e. risk preference, number of GP visits, and medical specialist visits). The opposite strategy holds for determining the higher extreme.
From Table 5, it can be observed that, for the average individual, health risk can explain more of the deviation in VD choice (0.099) than risk preference can (0.040). Even when combining the impact of the risk preference measure with the indicators of risky behavior (0.077), the impact of health risk is higher. For the average individual, health risk can explain the upward deviation better, while risk preference explains the downward deviation better. Overall, health risk is the type of private information (Finkelstein and McGarry, 2006) with the highest impact on the deductible choice. This finding is in contrast with the empirical findings of Gorter and Schilp (2012), who find that financialrisk tolerance and risky behavior are explaining more variation than health risk. One possible explanation for this difference is that they did not include any information on medical specialist visits in their study and included more proxies for risky behavior.
Table 5. Predicted probabilities non-zero voluntary deductible choice for average individual and subgroups based on health risk and risk preference
Variables Lower extreme
VD choice Higher extreme VD choice Range of 𝑃𝑟̂ Average individual* 0.181 Health risk
Self-assessed health status (D) 0.169 0.231 0.062
Number of GP visits1 0.180 0.183 0.003
Medical specialist visits (D) 0.163 0.195 0.032
Combined health risk variables 0.149 0.248 0.099
Risk preference
Risk aversion 0.141 0.181 0.040
Indicators of risky behavior
Smoking (D) 0.175 0.199 0.024
Drinking (D) 0.179 0.193 0.014
Combined risk preference and risky behavior variables
0.134 0.211 0.077
Notes: (D) indicates a dummy variable. Number of observations is 4,322.
1For determining the lower extreme VD choice, chosen number of GP visits is 5 (90th percentile). This
is to avoid misleading outcomes from an individual with an extreme number of GP visits. *The average individual implies all variables at the mean values.
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when comparing at the average age of about 54 years, seems to explain much variation in the VD choice. Therefore, gender and age are determinants that can explain more of the variation in VD choice than risk preference.
As an overall conclusion, for the average individual, the other determinants (i.e. gender, health risk, and age) have a higher impact on deductible choice than risk preference. Although the relative impact of the other determinants is found to be higher, ceteris paribus, risk preference can still explain a substantial difference in the take-up of non-zero voluntary deductibles between individuals.
4.2 Alternative estimation models: robustness checks
This subsection discusses three alternative model estimations used as a robustness check. First, the results of the ordered logit model estimation are discussed and compared to the ordinary logit model estimation. Secondly, I provide and discuss the regression results using the subsample consisting of the year 2013 only. The model is estimated to see whether the results are robust over time considering the stable risk preference assumption. Besides, the goodness of fit of the model is determined using two different tests. Thirdly, the logit model for the full sample is estimated with another measure of risk preference to determine whether the results are consistent across elicitation methods.
Over all the three robustness checks, I conclude that the model adequately fits the data and that the results are robust over time, but the results are not consistent across elicitation methods of risk preference.
4.2.1. Ordered logit model
As data is available on the exact amount of the chosen deductible (e.g. €0, €100, €200, €300, €400, or €500) and the different voluntary deductible options have a meaningful order, an ordered logit model is estimated. One important assumption underlying the ordered logit model is the proportional odds assumption, which implies that the relationship between all pairs of outcome groups is the same. For panel data models, there are no formal tests available in the statistical software program to test whether this assumption is not violated. Therefore, I assume here that the proportional odds assumption holds.
The marginal effects for the ordered logit model estimation are provided in Table C.1 in the Appendix. The coefficient results for the choice for a zero VD in Column 1 in Table C.1 are of the opposite sign compared to the results from the ordinary logit regression in Table 4 and they are nearly identical in size.
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size of the effect is lower for the choice for a €500 VD than for choosing any non-zero VD in the logit model estimation.
4.2.2 Subsample analysis: year 2013
The ordinary logit model is also estimated for the subsample consisting of observations in the year 2013 only. Table C.2 in the Appendix shows that the results for the subsample are quite similar to the results for the complete sample in terms of signs and significance11. Therefore, it seems that the results are robust over time.
The proportion of people choosing for a non-zero VD is quite small, which makes it harder to fit a good model as the distribution of the of zero voluntary deductibles and non-zero voluntary deductibles is not evenly balanced. As an illustration, from the regression sample of the years 2009-2018 and its 4,322 observations, 19.0% of the individuals chose for a non-zero voluntary deductible. From the regression sample from 2013 only, 20.8% of the 663 individuals chose for a positive voluntary deductible. Therefore, it is important to determine the goodness of fit of the model.
Several tests can be performed on the one-year analysis to determine the goodness of fit. First, the Hosmer-Lemeshow test indicates whether a model is a poor fit. As the p-value of the test-statistic is higher than 0.05 (0.2959), the model is considered to adequately fit the data. Second, as an alternative, Table C.3 in the Appendix shows the classification table. Overall, the table shows that the model predicts about 66.5% of the observations correctly. Following the criterion of Brooks (2014), it can be concluded that the model gives a reasonable set of predictions.
4.2.3 Different elicitation method for risk preference (Noussair et al., 2014)
For robustness check, I wanted to use a similar method to the Holt and Laury (2002) lottery method, which is one of the most widely used method in the literature to elicit risk preference. Unfortunately, due to the low number of observations, this lottery method is not appropriate to use as a robustness check here12. As an alternative, I use the elicitation method for risk preference used in Noussair et al. (2014) for robustness check. This method is similar to the Holt and Laury (2002) in the way that the number of safe choices in a lottery task determine an individual’s risk preference. The method deviates from Holt and Laury (2002) as the method used in Noussair et al. (2014) only consists of five choices instead of ten and the distinction between the five decision tasks is based on a change in the amount of money instead of a change in the probabilities.
11 The difference is that the variable for drinking behavior is significant for the subsample and that the medical specialist visits-, high education-, numeracy-, and smoking variable are not significant anymore
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Table C.4 in the Appendix shows the regression results and the average marginal effect estimations for the model in which risk preference are elicited following the method in Noussair et al. (2014). The analysis is performed on a subsample of 2,233 observations, which is about half of the observations from the original full sample analysis. Column 1 in Table C.4 shows that the coefficients for the different categories of risk attitudes are negative, implying that risk-neutral and risk-averse individuals are less likely to opt for a VD than risk-seeking individuals. However, the coefficients are not statistically significant at any conventional level, meaning that the conclusion that risk preference has a significant effect on voluntary deductible decisions cannot be drawn. Hence, the results are different when adopting different methods to elicit risk preference.
