Opting for a voluntary deductible
In order to determine the premiums in year t, we need to know which insured opt for which deductible option. In other words, for the ex-ante differentiation, we need to know for year t which group of insured did not opt for a voluntary deductible and which groups of insured opted for a voluntary deductible with either a 1-, 2-, 3-, 4-, or 5-year contract period. For the ex-post differentiation, we need to know for year t which group of insured did not opt for a voluntary deductible, which group opted for a voluntary deductible in year t, but not in year t − 1, which group opted for a voluntary deductible in year t and t − 1, but not in year t − 2, etc.
Following the theory of rational consumer behavior, the distributions of insured over the deductible options would ideally be determined by comparing the insured’s expected benefits with his/her expected costs of opting for a voluntary deductible, implying that only insured for whom their expected healthcare expenses under the deductible are smaller than the premium rebate would opt for a voluntary deductible. However, whether insured opt for a voluntary deductible in a certain year depends on the premium, but at the same time the premium depends on the distribution of insured over the deductible options. This makes the premium, which is also our variable of interest, an endogenous variable. This means that we cannot use the premium as the input variable to determine who opts for a deductible. Therefore, to get an estimate of these premiums, we make assumptions about the distribution of insured over the deductible options for both the ex-ante and ex-post differentiation. We assume that insured with the lowest predicted healthcare expenses would opt for a deductible. Several models, which can be found in “Appendix 1”, to determine the rank of insured based upon their predicted healthcare expenses in year t have been tested. The most accurate model, based upon the Spearman’s correlation coefficient, is an OLS model with a log transformation of healthcare expenses and we use this model for our empirical simulations. The dependent variable regards the total healthcare expenses under basic insurance in year t. The independent variables indicate several background characteristics that are in the dataset: an age and gender interaction, classification into a PCG and/or DCG in year t (based upon information from year t − 1), degree of urbanization in the residential area, ethnicity and past total healthcare expenses in year t − 1 classified into vigintiles. A detailed description of the independent variables can be found in “Appendix 2”. After the healthcare expenses are predicted, insured are ranked accordingly. Furthermore, we determine the rank of insured in years t − 1, t − 2, t − 3, and t − 4 based upon their predicted healthcare expenses in those years. In order to do so, we use the same model specification as for year t, but the variables are based upon data from earlier years.Footnote 8 Note that for the ex-ante differentiation, insured have to decide on the duration of their contract period in year t (i.e., 2007) and that we use information from the years t + 1, t + 2, t + 3 and t + 4 (i.e., 2008, 2009, 2010, 2011) to determine the rank of insured in these years. However, one might question whether insured in year t have (all) information concerning the upcoming years. An alternative approach would be to use only the information from year t and t − 1 to determine the rank of insured in future years. With the first approach, we would overestimate adverse selection, while with the second approach we would underestimate adverse selection into multiple-year contracts. After all, research shows that substantial consumer information surplus exists also for multiple-year contracts [32], meaning that insured do have some information regarding their future healthcare expenses that may not be picked up by administrative information from year t − 1. Therefore, and for reasons of simplicity, we determine the rank of insured for all years using the first mentioned approach for both the ex-ante and ex-post differentiation. In “Appendix 3” we will show that the possible overestimation of adverse selection under this approach has no impact on the main conclusions of this paper.
The ex-ante differentiation
For the ex-ante differentiation, we simulate a distribution of insured over the different contract periods. We assume that an insurer wants to determine the premiums in year t (i.e., 2007 for the ex-ante differentiation) in case he would offer six different insurance policies: a policy without a voluntary deductible and five policies with different contract periods for the voluntary deductible, i.e., 1, 2, 3, 4 or 5 years. Remember that for all years we have ranked insured according to their predicted expenses in that year. We assume that the half of the sample with the lowest predicted expenses in year t opts for an insurance policy with a deductible. To then determine who will opt for which multi-year contract, we sum the rank of the insured over the different contract periods. In other words, for a 2-year contract, we sum the rank of insured in year t and t + 1, and for a 3-year contract, we sum the rank of insured in year t, t + 1 and t + 2, etc. From the half of the sample that is assumed to opt for a policy with a deductible, the quintile with the lowest sum-rank for a 5-year contract is assumed to opt for that policy. From the remaining 40 % of insured opting for a deductible, the quarter with the lowest sum-rank for a 4-year contract is assumed to opt for that policy. From the remaining 30 % of insured opting for a deductible, the third with the lowest sum-rank for a 3-year contract is assumed to opt for that policy. From the remaining 20 % of insured opting for a deductible, the half of insured with the lowest sum-rank for a 2-year contract is assumed to opt for that policy and the other half is assumed to opt for a 1-year contract with a deductible. Note that this process does not include the simulation of a behavioral effect where insured would also opt for a long contract period even if they incidentally expect high healthcare expenses in 1 year during the contract period. In the end, this process provides us with a distribution of insured in year t where a group of 50 % of the insured does not opt for a deductible and five groups of 10 % do opt for a deductible with respectively a 1-, 2-, 3-, 4- or 5-year contract period. For this distribution of insured, we subsequently determine the premiums per insurance policy.
The ex-post differentiation
For the ex-post differentiation, we simulate a distribution of insured in year t (i.e., 2011 for the ex-post differentiation) based upon the number of previous consecutive years insured have opted for a voluntary deductible. For this differentiation, we assume that an insurer decreases the premium with each additional consecutive year an insured has opted for a voluntary deductible since year t − 4 (i.e., 2007 for this differentiation). Two scenarios are simulated depending on the potential behavioral effect of this differentiation.
In scenario I, we assume that the differentiation of the premium has no effect on the decision to opt for a voluntary deductible, which is contrary to what would be expected (and was expected by the Dutch government). Insured only opt for a deductible if they belong to the half of the sample with the lowest predicted expenses. Looking back from year t, we determine for insured who are assumed to opt for a deductible in year t the number of previous consecutive years they are assumed to opt for a voluntary deductible as well.
In scenario II, we assume a moderate behavioral effect of the differentiation of the premium. We assume that insured are willing to keep the voluntary deductible for 1 year they expect (high) healthcare expenses (i.e., belong to the half of the sample with the highest predicted healthcare expenses). This means for instance that if an insured is assumed to opt for a voluntary deductible in year t − 4, he will also opt for a deductible in year t − 3, irrespective of his rank in that year. The insured is thereafter assumed to opt out of the voluntary deductible in year t − 2 only if he belongs to the half of the sample with the highest predicted healthcare expenses in both year t − 3 and t − 2, etc. In the end, this process provides us with a scenario where some retention of the voluntary deductible results from the differentiation of the premium, but where insured also opt out of the voluntary deductible if they for instance incur a chronic disease. The simulation process for these scenarios results in a distribution of insured in year t over six groups: insured without a voluntary deductible, insured with a voluntary deductible with different numbers of previous consecutive years they have opted for deductible (i.e., 0, 1, 2, 3, or 4 previous consecutive years).
Composition of the premium
After the distribution of insured over the deductible options for both the ex-ante and ex-post differentiation in year t are simulated, we calculate the premium for each of the six aforementioned groups per distribution. For the analyses, we assume a voluntary deductible of €1000. The average healthcare expenses per individual (\(\mathop {\overline{\text{HCE}} }\limits^{{}}\)) in the dataset are €1894Footnote 9 in all years. The premium is determined using Eqs. (1a) and (1b) for respectively insured without and with a voluntary deductible:
$$P_{\text{NVD}} = \mathop {\overline{\text{IC}}_{\text{NVD}} } \limits^{{}} + \mathop {\overline{\text{REP}}_{\text{NVD}} }\limits^{{}}$$
(1a)
$$P_{\text{VD}} = \mathop {\overline{\text{IC}}_{\text{VD}} }\limits^{{}} + \mathop {\overline{\text{REP}}_{\text{VD}} }\limits^{{}}$$
(1b)
where P is the premium, NVD indicates insured without a voluntary deductible, VD indicates insured with a voluntary deductible (with either different contract periods or different numbers of previous years they have opted for a deductible), \(\mathop {\overline{\text{IC}} }\limits^{{}}\) are the average insurance claims and \(\mathop {\overline{\text{REP}} }\limits^{{}}\) represents the average risk equalization payment. Without any risk equalization, the equations show that the premium equals the average insurance claims in the group. With risk equalization, however, the premium is affected by the risk equalization payment, which is determined for insured without a voluntary deductible using Eq. (2a)Footnote 10:
$$\mathop {\overline{\text{REP}}_{\text{NVD}} }\limits^{{}} = \frac{x}{100}\left[ {\mathop {\overline{\text{HCE}} }\limits^{{}} - \mathop {\overline{\text{IC}}_{\text{NVD}} }\limits^{{}} } \right]$$
(2a)
where x indicates the quality of the risk equalization modelFootnote 11 and \(\mathop {\overline{\text{HCE}} }\limits^{{}}\) indicates the average healthcare expenses in the data without any cost-sharing arrangements. Due to the voluntary deductible, the risk equalization payment for insured with a voluntary deductible is different to that of insured without a voluntary deductible and determined using Eq. (2b):
$$\mathop {\overline{\text{REP}}_{\text{VD}} }\limits^{{}} = \frac{x}{100}\left[ {\mathop {\overline{\text{HCE}} }\limits^{{}} - \left( {\mathop {\overline{\text{IC}}_{\text{VD}} }\limits^{{}} { + }\mathop {\overline{\text{MHR}}_{\text{VD}} }\limits^{{}} { + }\mathop {\overline{\text{OOP}}_{\text{VD}} }\limits^{{}} } \right)} \right]$$
(2b)
where \(\mathop {\overline{\text{MHR}} }\limits^{{}}\) and \(\mathop {\overline{\text{OOP}} }\limits^{{}}\) respectively indicate the average moral hazard reduction and the average out-of-pocket expenses for the group of insured with a voluntary deductible (for different contract periods or in multiple consecutive years) resulting from the deductible. After the risk equalization payment for the different groups of insured is determined, the premiums can be calculated using Eqs. (1a) or (1b) depending on whether the insured has a deductible or not.
In order to determine the differentiated premiums that can be offered by insurers, we need to know (1) the average healthcare expenses in the data, (2) the average insurance claims, the average moral hazard reduction and the average out-of-pocket expenses for the different groups of insured, and (3) the quality of the risk equalization model. Firstly, the average healthcare expenses in the data are already mentioned and equal €1894. Secondly, for the average insurance claims for insured who are not assumed to opt for a deductible, we use the healthcare expenses in the data. Since no cost-sharing arrangements are in place in our data, the healthcare expenses in the data for insured who are assumed to opt for a deductible include a moral hazard reduction and out-of-pocket expenses they would have in case of a voluntary deductible. Many researchers have studied the reduction of healthcare expenses resulting from voluntary deductibles [e.g., 2, 3, 13, 18, 30]. For our simulations, we use the reduction as determined in the study by Trottmann et al. [30] since the researchers of this recent study corrected for the selection effect that arises when taking out voluntary deductibles. Consequently, the healthcare expenses in the data of insured with a voluntary deductible are reduced by 22.6 % due to the voluntary deductible. The size of the out-of-pocket expenses is determined as the healthcare expenses after the moral hazard reduction in the interval [0:1000]. The insurance claims for insured with a voluntary deductible are then determined as the healthcare expenses in the data minus the moral hazard reduction and minus the out-of-pocket expenses. For instance, an insured with healthcare expenses of “€1250 in the data” and a voluntary deductible of €1000 will have a moral hazard reduction of €283 (€1250 × 0.226), out-of-pocket expenses of €967 (€1250 − €283) and no insurance claims (€1250 − €283 − €967). However, if an insured who opts for a voluntary deductible of €1000 has healthcare expenses of “€2500 in the data”, the moral hazard reduction will be €566 (€2500 × 0.226), the out-of-pocket expenses will be €1000 (€2500 − €566 = €1934) and the insurance claims equal €934 (€2500 − €566 − €1000). Thirdly, to determine the effect of risk equalization on the premium, Van Kleef et al. [35] show that equalization based upon region, age and gender, and equalization based upon demographic factors, PCGs and DCGs respectively reduce the adverse selection component of the premium rebate for the highest Swiss voluntary deductibles with respectively 47 and 74 % in 2006. For our simulations, we therefore study the effect of no risk equalization, perfect risk equalization and the two models used in the research by Van Kleef et al. [35]. Note that due to extensive research, risk equalization schemes have become more sophisticated and that the Dutch scheme of 2015 is already more sophisticated than the 74 % model studied by Van Kleef et al. [35].