**1. Introduction**

Health insurers try to foster healthy lifestyles among their insureds by promoting exercise, supporting fitness center memberships, and more recently, the use of wearable connected devices. The data collected from the latter permit insurance companies to track the individual's physical activity, diet, or sleep patterns for instance. Subsequently, insureds carrying on a healthy lifestyle benefit from premium discounts or other kinds of monetary rewards. Why health insurers promote a healthy lifestyle is not unfounded. There is a strand of medical literature assessing the effect of the lifestyle on health documenting that a healthier lifestyle leads to better health, relating to lower medical costs (Johansson and Sundquist 1999; Andersen et al. 2000; Lee and Skerrett 2001; Joshipura et al. 2001; Penedo and Dahn 2005; Dauchet et al. 2006; Inyang and Okey-Orji 2015; Miller et al. 2017). However, the relationship between health and health insurance decisions has been sparsely investigated. While there is a clearly demonstrated link between lifestyle and health in the medical literature, this relation has not been used in actuarial science, leaving the field with little or no evidence of the effect of lifestyle on health insurance decisions.

In our study, using data from the Swiss Health Survey (SHS), we aim to seize the indirect effect of lifestyle—encompassed by the body mass index (BMI), diet, physical activity and commuting mode—on health insurance decisions, i.e., the choice of the plan and the level of deductible. We consider that the decisions are mediated through latent variables linked to health and health care consumption. We set up a structural equation modeling (SEM) framework that allows capturing such indirect effects. We define health as a latent variable embodied by the self-assessed health, as well as chronic and limiting daily activities health conditions. Thereby, the latter offer an objective measure. Further, health directly impacts health care consumption, our second latent variable captured by the number of doctor visits and hospital stays. Additionally, the model is able to account for the bidirectional relationship between health care consumption and the choice of the insurance plan and the deductible level.

The results from our model provide empirical support for the correlation between health insurance choice and lifestyle via health and health care consumption. Using 9301 observations obtained from the SHS dataset, we control the choice of deductible and insurance plan for socio-economic characteristics (gender, nationality, education, income, number of children in the household, importance of freedom of choice of the specialist doctor, linguistic region, and urbanization) and allow for the two endogenous variables to correlate. We show that an increase in age and BMI correlates with a decrease in health, whereas an increase in the number of portions of fruits and vegetables eaten per day, the number of physical activities performed in a week, and the usage of a bike to commute correlates with an increase in health. Further results display a negative correlation between health and health care consumption, where the latter variable is positively associated with the choice of a standard, i.e., non-restricting, health insurance plan. Similarly, an increase in health care consumption correlates positively with a low level of deductible. Linking our results, we obtain the indirect effect of lifestyle on insurance decisions. Thereby, an increase in age and BMI is associated with having a low deductible and opting for a standard insurance plan whereas, having a "healthy" lifestyle (good diet and physical activity) correlates with having a high deductible and preferring a more restrictive insurance plan at lower cost.

The remainder of this paper is organized as follows: In Section 2, we briefly review the Swiss health insurance system, as well as the literature related to the development of our research hypotheses. In Section 3, we pursue the setup of the model. Results are displayed along with a discussion in Section 4. Finally, we conclude in Section 5.

#### **2. Background Information and Research Hypotheses**

#### *2.1. Insurance Plans and Deductibles in the Swiss Health System*

Before developing our research, we expose some basic features of the Swiss health insurance system that are relevant for the matter of this study. Basic health insurance in Switzerland is mandatory and regulated by Federal law, which sets up the reimbursement policies. Under Federal law, basic health insurance coverage is compulsory for all residents and organized through private insurance companies. All insurance companies proposing basic health insurance are obliged to accept any individual independently of the health status. Premiums are calculated by the insurers, are determined by regions along cantons and urbanicity, and are validated by the Swiss government. Note that prices are the same for all individuals within the three age classes: up to 18 years, 19 to 25 years, and 26 years or more. Thus, insurers are not allowed to take into account other variables like gender, exact age, or health status. Beyond the basic plan, individuals can subscribe to private complementary health insurance. Regarding the catalog of reimbursements, on the one hand, the basic plan covers basic health risks, but does not extend to dental treatments, to alternative medicine techniques, nor to glasses or lens purchases, with exceptions made for some specific medical conditions. On the other hand, complementary health policies cover the costs that go beyond the basic insurance scheme. In this study, we focus on the decisions on basic health insurance by individuals aged 18 years and older. These individuals face several choices for their insurance plan and deductible level.

#### 2.1.1. Insurance Plans

The insurance policies currently offered in Switzerland can be grouped into four families. The first plan is the "standard" plan, and it is chosen by most individuals. This policy offers the freedom of choice to visit any doctor or specialist and presents no specific restriction. This plan has the highest premium. The second most popular plan is the so-called "family doctor" model. Its peculiarity lies in the importance of the general practitioner (GP) that acts as a gatekeeper and centralizes information of the individual. Indeed, holders of this type of policy commit to always consulting the same GP in case of any health issues. They have to chose their doctor in advance from a list of recognized GPs provided by their health insurer. As a gatekeeper, the GP transfers the patient to a specialist if necessary. This plan typically displays premiums that are 15 to 20% lower than those of standard plans. The third most common plan is known as "CallMed". As its name suggests, this model brings the constraint of calling a medical hotline prior to physically seeking advice from a doctor. Depending on the specific policy rules, there may be an unrestricted choice of the doctor after the phone consultation. Policyholders from this scheme profit from premium reductions of up to 20%. Finally, there is the "HMO" model where the acronym stands for health maintenance organization. Under this model, the insureds commit to always pass through a doctor affiliated with the selected HMO group for a first consultation. Like in the CallMed model, if necessary, the following consultation may take place outside of the HMO medical team, depending on the health insurer. This last type of plan can come with premiums up to 25% below the standard plan.

#### 2.1.2. Deductible Levels

In all insurance plans and on a yearly basis, policyholders chose a deductible. Here, the decision environment is less complex. With amounts regulated by the health insurance law, there exist six levels of deductibles, namely CHF 300, 500, 1000, 1500, 2000, and 2500. Once medical costs up to the chosen level are paid out-of-pocket, there only remains a co-paymen<sup>t</sup> of 10% up to CHF 700 on the additional costs, whereafter the health insurer entirely reimburses the spending.

#### *2.2. Literature Review and Development of the Hypothesis*

While partial insights into our research can be gained by studying descriptive statistics, we propose to structure our analyses around selected conjectures and embed the latter in the body of existing literature. A recent study conducted by Li et al. (2018) identified five health risk-reducing lifestyle factors. Among them, three characteristics are of particular interest for our study. Indeed, three lifestyle indicators are found to play a role in mortality. More specifically, life expectancy increases with a BMI ranging between 18.5 and 24.9, 30 min or more per day of exercising, and a healthy diet. In addition to these measures, we considered in our research another factor: the commuting mode. This variable has been found to be a relevant factor for health conditions in the literature (Oja et al. 1991; Pucher et al. 2010 and Riiser et al. 2018). Since these factors are relatively easily trackable and modifiable, as opposed to, for example, alcohol or tobacco consumption, we used them as determinants for lifestyle.
