Complementary Insurance and Deductibles in the Dutch Health Care System

Transcription

1 Complementary Insurance Deductibles in the Dutch Health Care System by: Daan Stroosnier In 2006 the Netherls experienced a health care reform that shifted part of the health care risk from the insurer public system to the insured thus shifted some of the financial burden more towards the public. This shift was an attempt to reduce the steady increase of health costs during the last decades. Two of the changes were the introduction of a voluntary additional deductible the possibility to opt for a complementary voluntary health insurance (VHI), in order to enable a rational use of health care thereby diminishing the effects of moral hazard adverse selection. This article addresses the choice for having a complementary voluntary health insurance a voluntary additional deductible in the Netherls. Introduction In theory, complementary health insurance deductibles are methods to influence the unnecessary dem for health care induced by moral hazard (Barros, Machado, & Sanz-de-Galdeano, ; Schellhorn, ). If the difference between the expected use of health care with without complementary insurance is large, then individuals are less likely to take a complementary insurance because it might bring them financial gain by means of lower insurance premiums. This means the complementary insurance ensures that, at least a part of, the unnecessary use of health care disappears. In case of the additional deductible the difference between expected health care usage under having no deductible having one should also be large to ensure that the unnecessary use of health care disappears. This is because individuals are more likely to accept an additional deductible because it might bring them financial gain by means of reduction of insurance premiums. In both cases unnecessary health care usage partly disappears, because the problem of moral hazard is tackled, one of the reasons the new health care system in the Netherls has been introduced (Schäfer et al., ; van Ophem & Berkhout, ). Daan Stroosnier Daan Stroosnier finished his Master s degree in Econometrics last March. He wrote his thesis, under supervision of Dr. Hans van Ophem, about the choice for having a complementary voluntary health insurance a voluntary additional deductible in the Netherls. The thesis was nominated for the UvA Thesis Prize As from 1 September, Daan will be Analyst at the Quantitative Analysis division of PwC. On the other h individuals will also consider their health status when having to choose for a complementary insurance a deductible or not (Godfried, Oosterbeek, & Tulder, ; van Ophem & Berkhout, ). The consideration of health status reflects adverse selection. The aim of this article is to examine what the determinants for the choice of taking a complementary insurance accepting an additional deductible are how health care dem influences these choices. On top of that the relation with moral hazard adverse selection is modeled. To achieve this, the simultaneity between the choice for having a complementary health insurance, having a deductible health care dem has to be modeled. Therefore possible dependence between health care dem these choices has to be taken into account as well as dependence between the choices themselves. In the remainder of this article, an econometric model which reflects the choice for a voluntary additional deductible a complementary VHI is developed. The general model was split up into three separate estimable models (Stroosnier, ). Only the first model is presented in this article, because it is the most important model for the research less known in literature. Furthermore, the main emperical results, following from the estimations of the first model, their implications are presented. Econometric model The health status especially health care dem, approximated by the expected number of physician visits, are expected to be considered by an individual in the decision to take an additional voluntary 2 AENORM vol. 19 (75) May 2012

2 deductible a complementary VHI. Individuals opt for a deductible if they believe that the expected utility of this insurance option is higher than the alternative of no deductible. In similar fashion, individuals opt for a complementary insurance if they believe that the expected utility is higher than if they take no complementary insurance. Taking the possible dependence between the choice for a deductible the choice for a complementary insurance into account, an econometric model for these choices is specified in eq. (1) eq. (2) under the assumption that the utility functions can be approximated by a linear function: (1) variables, indicated by X i. Second, is made dependent on the difference in expected number of physician visits with without a complementary insurance. The expected number of physician visits with a complementary insurance consists of which are the expected number of physician visits with a deductible without. The expected number of physician visits without a complementary insurance is composed by the expected number of physician visits with a deductible without, denoted by. The probability of occurrence of the deductible is indicated by. The error terms in eq. (1) eq. (2) are reflected in they are distributed as follows: (3) The tendency to accept a deductible, denoted by, is made dependent on health indicators, collected in H i, other explanatory variables, indicated by X i. Furthermore, depends on the difference in expected number of physician visits with without a deductible. The expected number of physician visits with a deductible is composed by the expected number of physician visits with a complementary insurance without, denoted by. The same holds for the expected number of physician visits without a deductible where denote the expected number of physician visits with a complementary insurance without. The probability of occurrence of complementary insurance is reflected in. Because in both equations the difference in expected number of physician visits is decomposed into four regimes, possible dependence between the choice for a deductible the choice for a complementary insurance has to be considered in estimating the model. Unfortunately, estimating this general model in eq. (1) eq. (2) appeared not to be feasible if endogeneity of expected health care dem is taken into account. Monte Carlo simulations showed that under different assumptions this model cannot be estimated properly with the estimation techniques at h. Therefore the above discussed model was split up into three separate models. The first model, which is presented in this article, does take endogeneity of expected health care dem into account, but does not consider dependence between the two insurance choices. The model is a switching count model (van Ophem & Berkhout, ). (2) Switching count model Eq. (2) reveals three aspects. First, the tendency to choose for a complementary insurance,, depends on health indicators, collected in H i, other explanatory Applying the switching count model leads to the following simplification of the general model described in the previous section. 1 P.P. Barros, M.P. Machado A. Sanz-de-Galdeano: Moral harzard the dem for health services: a matching estimator approach, Journal of health economics, 27 (4) (2008): M. Schellhorn: The effect of variable health insurance dedutibles on the dem for physican visits, Health economics, 10(5) (2001) : W. Schäfer, M. Kroneman, W. Boerma, M.V.D. Berg, G. Westert, W. Devillé E.V. Ginneken: The Netherls: Health system review, Health Systems in Transition, 12 (1) (2010): H. van Ophem P. Berkhout: The deductible in healt insurance: do the insured make a choice based on the arguments as intended by the polici makers? Working paper QE 2010/07 University of Amsterdam 5 M. Godfried, H. Oosterbeek F.V.A.N. Tulder: Adverse selection the dem for supplementary dental insurance, De Economist, 2 (2001): D.M. Stroosnier: Complementary insurance deductibles in the Dutch health care system MSc-thesis, University of Amsterdam 2012 AENORM vol. 19 (75) May

3 The inclination to accept a deductible does not depend on the choice for a complementary insurance anymore vice versa. This means the difference in the expected number of physician visits (y i ) with without a deductible is simplified to. The difference in the expected number of physician visits with without a complementary insurance is given by. Furthermore, are, contrary to the general model, not dependent have zero mean constant variances. Other possible factors influencing the choice for a deductible a complementary insurance i.e. health indicators (H i ), socio-economic explanatory variables (X i ) are still present. The unknown parameters need to be estimated. To complete the model presented above one more aspect has to be noted. In eq. (4) eq. (5) are not observed. Only under one of the regimes the number of physician visits is observed. The latent variable determines under which regime the number of physician visits is observed viz. or. The number of physician visits observed under or is determined by : where are the cumulative distributions of the counts with expectations under regime j. Say, health care dem, approximated by physician count, depends on a variety of explanatory variables. Suppose these explanatory variables are collected in a vector Z i, then the model is completed by assuming. This model can be estimated by employing the copula estimation technique. This method takes full account of the possible dependences between the rom variables, in eq. (4) eq. (6) between the rom variables, in eq. (5) eq. (7) 7. The copula estimation technique can be employed if the exact marginal distributions are specified. This article assumes Poisson or Negative Binomial (NB2) distributed (4) (5) (6) (7) counts normally distributed error terms. The variance of the error terms can only be estimated up to a scaling factor will therefore be put equal to 1. Results In the empirical research a number of different specifications of the switching count model are employed for both the deductible complementary VHI choice. On top of that two different copulas are used in estimating this model i.e. the Frank copula the Gaussian copula. It was shown that the specification with Negative Binomial 2 distributed physician counts, which treats the groups of individuals with without a deductible completely separate, should be preferred compared to the other specifications. Whether the estimates using the Frank copula should be preferred to the ones using the Gaussian copula is ambiguous. Both copulas produce very similar estimation results across the specifications. These findings are the same for the complementary VHI choice. Table 1 shows the estimation results of the aforementioned specification using the Gaussian copula. The only significant adverse selection found is that individuals who have had a flu vaccination are less likely to opt for a deductible. The results do not exhibit effects of moral hazard. Further determinants are being a breadwinner the number of children in the household. For the factors influencing health care dem, considerable differences are distinguished between the group of individuals with a deductible without. This indicates that the underlying process governing the amount of health care used is different for these groups. Finally, significant negative dependence between the choice for a deductible health care dem is found. This suggests that individuals take account of their (expected) health care dem in their decision to take a deductible or not, although the relevant explanatory variables are not observed. Table 1 also shows the results of the switching count model relating to the complementary VHI choice. It shows significant adverse selection in terms of a negative effect of self-assessed health. Self-assessed healthier individuals are less likely to opt for a complementary insurance. Moral hazard is found to play a role in the choice for having a complementary VHI. Other determinants are age, being a breadwinner, income, the number of children in the household having a partner. The effect of age has an inverted U-shape. For the factors influencing health care dem, some differences are distinguished between the group of individuals with a complementary VHI without, although these differences are small compared to the deductible case. This indicates that the underlying process governing the amount of health care used is to some extent different for these groups. Finally, 7 Since y d1i y d0i are not observed simultaneously, the dependence between thesecounts is not identifiable. The same holds for y c1i y c0i. 4 AENORM vol. 19 (75) May 2012

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5 dependence between the probability of choosing for a complementary insurance health care dem under having a complementary insurance is found positive significant. This suggests that individuals take account of their (expected) health care dem under having a complementary insurance in their decision to take a complementary insurance or not, although the relevant explanatory variables are not observed. Conclusion The results indicate that the choice for a complementary health insurance depends on the health status of individuals the difference between expected health care dem with without having a complementary insurance. Consequently, adverse selection moral hazard appear to be relevant in the choice for a complementary insurance. Other determinants are age, being a breadwinner, income, number of children having a partner. In the choice for a deductible moral hazard does not appear to be relevant the effect of adverse selection is limited. Determinants are being a breadwinner number of children. Finally, the underlying process governing the amount of health care used is different for different insurance schemes. Subsequent research can focus on a number of issues. First, the switching count model distinguishes only two regimes, but there are many more possible choices in the deductible complementary insurance choice. A research taking more choices into account could prove interesting results. Second, investigating the behavior of the switching count model under different specifications, misspecification or under estimation using a two-step method might show useful results. Third, further research may use other marginal distributions or copulas for estimation. For example, zero-inflated Poisson distributed counts might lead to better estimations. Another option is semi- or nonparametric estimation of the marginal distributions. Finally, only the number of physician visits is used as a measure of health care dem, leaving other measures unexplored. deductibles on the dem for physician visits, Health Economics, 10 (5) (2010): W. Schäfer, M. Kronema, W. Boerma, M.V.D. Berg, G. Westert, W. Devillé E.V. Ginneken: The Netherls: Health system review, Health Systems in Transition, 12(1) (2010):1-229 D.M. Stroosnier: Complementary insurance deductibles in the Dutch health care system MScthesis Econometrics, University of Amsterdam (2012) H. van Ophem P. Berkhout: The deductible in health insurance: do the insured make a choice based on the arguments as intended by the policy makers? Working papar QE 2010/07, University of Amsterdam References P.P. Barros, M.P. Machado A. Sanz-de-Galdeano: Moral hazard the dem for health services: a matching estimator approach, Journal of health economics, 27(4) (2008): M. Godfried, H. Oosterbeek F.V. Tulder: Adverse selection the dem for supplementary dental insurance, De Economist, (2) (2001): M. Schellhorn: The effect of variable health insurance 6 AENORM vol. 19 (75) May 2012