Exploring the predictive power of interaction terms in a sophisticated risk equalization model using regression trees.

This study explores the predictive power of interaction terms between the risk adjusters in the Dutch risk equalization (RE) model of 2014. Due to the sophistication of this RE-model and the complexity of the associations in the dataset (N = ~16.7 million), there are theoretically more than a million interaction terms. We used regression tree modelling, which has been applied rarely within the field of RE, to identify interaction terms that statistically significantly explain variation in observed expenses that is not already explained by the risk adjusters in this RE-model. The interaction terms identified were used as additional risk adjusters in the RE-model. We found evidence that interaction terms can improve the prediction of expenses overall and for specific groups in the population. However, the prediction of expenses for some other selective groups may deteriorate. Thus, interactions can reduce financial incentives for risk selection for some groups but may increase them for others. Furthermore, because regression trees are not robust, additional criteria are needed to decide which interaction terms should be used in practice. These criteria could be the right incentive structure for risk selection and efficiency or the opinion of medical experts.

Shifted deductibles for high risks: more effective in reducing moral hazard than traditional deductibles.

In health insurance, a traditional deductible (i.e. with a deductible range [0,d]) is in theory not effective in reducing moral hazard for individuals who know (ex-ante) that their expenditures will exceed the deductible amount d, e.g. those with a chronic disease. To increase the effectiveness, this paper proposes to shift the deductible range to [s(i),s(i)+d], with starting point s(i) depending on relevant risk characteristics of individual i. In an empirical illustration we assume the optimal shift to be such that the variance in out-of-pocket expenditures is maximized. Results indicate that for the 10-percent highest risks in our data the optimal starting point of a euro1000-deductible is to be found (far) beyond euro1200, which corresponds with a deductible range of [1200,2200] or further. We conclude that, compared to traditional deductibles, shifted deductibles with a risk-adjusted starting point lower out-of-pocket expenditures and may further reduce moral hazard.

Risk equalization and voluntary deductibles: a complex interaction.

The presence of voluntary deductibles in the Swiss and Dutch mandatory health insurance has important implications for the respective risk equalization systems. In a theoretical analysis, we discuss the consequences of equalizing three types of expenditures: the net claims that are reimbursed by the insurer, the out-of-pocket expenditures and the expenditure savings due to moral hazard reduction. Equalizing only the net claims, as done in Switzerland, creates incentives for cream skimming and prevents insurers from incorporating out-of-pocket expenditures and moral hazard reductions into their premium structure. In an empirical analysis, we examine the effect of self-selection and conclude that the Swiss and Dutch risk equalization systems do not fully adjust for differences in health status between those who choose a deductible and those who do not. We discuss how this may lead to incentives for cream skimming and to a reduction of cross-subsidies from healthy to unhealthy individuals compared to a situation without voluntary deductibles.

Can premium differentiation counteract adverse selection in the Dutch supplementary health insurance? A simulation study.

Most health insurers in the Netherlands apply community-rating and open enrolment for supplementary health insurance, although it is offered at a free market. Theoretically, this should result in adverse selection. There are four indications that adverse selection indeed has started to occur on the Dutch supplementary insurance market. The goal of this paper is to analyze whether premium differentiation would be able to counteract adverse selection. We do this by simulating the uptake and premium development of supplementary insurance over 25 years using data on healthcare expenses and background characteristics from 110,261 insured. For the simulation of adverse selection, it is assumed that only insured for whom supplementary insurance is expected not to be beneficial will consider opting out of the insurance. Therefore, we calculate for each insured the financial profitability (by making assumptions about the consumer's expected claims and the premium set by the insurer), the individual's risk attitude and the probability to opt out or opt in. The simulation results show that adverse selection might result in a substantial decline in insurance uptake. Additionally, the simulations show that if insurers were to differentiate their premium to 28 age and gender groups, adverse selection could be modestly counteracted. Finally, this paper shows that if insurers would apply highly refined risk-rating, adverse selection for this type of supplementary insurance could be counteracted completely.

A voluntary deductible in health insurance: the more years you opt for it, the lower your premium?

Adverse selection regarding a voluntary deductible (VD) in health insurance implies that insured only opt for a VD if they expect no (or few) healthcare expenses. This paper investigates two potential strategies to reduce adverse selection: (1) differentiating the premium to the duration of the contract for which the VD holds (ex-ante approach) and (2) differentiating the premium to the number of years for which insured have opted for a VD (ex-post approach). It can be hypothesized that premiums will decrease with the duration of the contract or the number of years for which insured have opted for a VD, providing an incentive to insured to opt for a deductible also in (incidental) years they expect relatively high expenses. To test this hypothesis, we examine which premium patterns would occur under these strategies using data on healthcare expenses and risk characteristics of over 750,000 insured from 6 years. Our results show that, under the assumptions made, only without risk equalization the premiums could decrease with the duration of the contract or the number of years for which insured have opted for a VD. With (sophisticated) risk equalization, decreasing premiums seem unfeasible, both under the ex-ante and ex-post approach. Given these findings, we are sceptical about the feasibility of these strategies to counteract adverse selection.

Overpaying morbidity adjusters in risk equalization models.

Most competitive social health insurance markets include risk equalization to compensate insurers for predictable variation in healthcare expenses. Empirical literature shows that even the most sophisticated risk equalization models-with advanced morbidity adjusters-substantially undercompensate insurers for selected groups of high-risk individuals. In the presence of premium regulation, these undercompensations confront consumers and insurers with incentives for risk selection. An important reason for the undercompensations is that not all information with predictive value regarding healthcare expenses is appropriate for use as a morbidity adjuster. To reduce incentives for selection regarding specific groups we propose overpaying morbidity adjusters that are already included in the risk equalization model. This paper illustrates the idea of overpaying by merging data on morbidity adjusters and healthcare expenses with health survey information, and derives three preconditions for meaningful application. Given these preconditions, we think overpaying may be particularly useful for pharmacy-based cost groups.

Potential determinants of deductible uptake in health insurance: How to increase uptake in The Netherlands?

In health insurance, voluntary deductibles are offered to the insured in return for a premium rebate. Previous research has shown that 11 % of the Dutch insured opted for a voluntary deductible (VD) in health insurance in 2014, while the highest VD level was financially profitable for almost 50 % of the population in retrospect. To explain this discrepancy, this paper identifies and discusses six potential determinants of the decision to opt for a VD from the behavioral economic literature: loss aversion, risk attitude, ambiguity aversion, debt aversion, omission bias, and liquidity constraints. Based on these determinants, five potential strategies are proposed to increase the number of insured opting for a VD. Presenting the VD as the default option and providing transparent information regarding the VD are the two most promising strategies. If, as a result of these strategies, more insured would opt for a VD, moral hazard would be reduced.

How profitable is a voluntary deductible in health insurance for the consumer?

To counteract moral hazard in health insurance, insured can be offered a voluntary deductible (VD) in return for a premium rebate. In the Dutch mandatory basic health insurance however, only 11 per cent of the insured opted for a VD in 2014. Several determinants could affect the decision to opt for a VD. This paper examines one of these determinants: the financial profitability. A VD is profitable for the consumer if the out-of-pocket expenses do not exceed the offered premium rebate. The empirical analyses, based upon individual-level data on costs and characteristics of over 800,000 Dutch insured, show that a VD of €500 on top of the mandatory deductible of €360 would have been financially profitable for 48 per cent of the Dutch insured given the average premium rebate of € 240 in 2014. If the whole population had a VD, most insured would obtain either the maximum loss (44 per cent) or the maximum gain (41 per cent). A VD is profitable for males, young insured, healthy insured and insured with few healthcare expenses in the past. To further reduce moral hazard, the following strategies can be used to increase the number of insured opting for a VD: provide insured with information regarding the VD and introduce a shifted deductible.

Is there one measure-of-fit that fits all? A taxonomy and review of measures-of-fit for risk-equalization models.

This study provides a taxonomy of measures-of-fit that have been used for evaluating risk-equalization models since 2000 and discusses important properties of these measures, including variations in analytic method. It is important to consider the properties of measures-of-fit and variations in analytic method, because they influence the outcomes of evaluations that eventually serve as a basis for policymaking. Analysis of 81 eligible studies resulted in the identification of 71 unique measures that were divided into 3 categories based on treatment of the prediction error: measured based on squared errors, untransformed errors, and absolute errors. We conclude that no single measure-of-fit is best across situations. The choice of a measure depends on preferences about the treatment of the prediction error and the analytic method. If the objective is measuring financial incentives for risk selection, the only adequate evaluation method is to assess the predictive performance for non-random groups.

Improving the prediction model used in risk equalization: cost and diagnostic information from multiple prior years.

Currently-used risk-equalization models do not adequately compensate insurers for predictable differences in individuals' health care expenses. Consequently, insurers face incentives for risk rating and risk selection, both of which jeopardize affordability of coverage, accessibility to health care, and quality of care. This study explores to what extent the predictive performance of the prediction model used in risk equalization can be improved by using additional administrative information on costs and diagnoses from three prior years. We analyze data from 13.8 million individuals in the Netherlands in the period 2006-2009. First, we show that there is potential for improving models' predictive performance at both the population and subgroup level by extending them with risk adjusters based on cost and/or diagnostic information from multiple prior years. Second, we show that even these extended models do not adequately compensate insurers. By using these extended models incentives for risk rating and risk selection can be reduced substantially but not removed completely. The extent to which risk-equalization models can be improved in practice may differ across countries, depending on the availability of data, the method chosen to calculate risk-adjusted payments, the value judgment by the regulator about risk factors for which the model should and should not compensate insurers, and the trade-off between risk selection and efficiency.

Does risk equalization reduce the viability of voluntary deductibles?

Theoretically, a risk avers consumer takes a deductible if the premium rebate (far) exceeds his/her expected out-of-pocket expenditures. In the absence of risk equalization, insurers are able to offer high rebates because those who select into a deductible plan have below-average expenses. This paper shows that, for high deductibles, such rebates cannot be offered if risk equalization would "perfectly" adjust for the effect of self selection. Since the main goal of user charges is to reduce moral hazard, some effect of self selection on the premium rebate can be justified to increase the viability of voluntary deductibles.