Financial planning decisions under changing long term carefinancing

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Financial planning decisions under

changing long term care financing

Tom Wijnhorst

Master’s Thesis to obtain the degree in Actuarial Science and Mathematical Finance University of Amsterdam

Faculty of Economics and Business Amsterdam School of Economics Author: Tom Wijnhorst Student number: 6180108

Email: tom wijnhorst@hotmail.com Date: July 30, 2015

Supervisor UvA: dr. Tim Boonen

Second reader: dr. Leendert van Gastel Supervisors EY: Lars van den Berg MSc. AAG

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Abstract:

The goal of this research is to calculate optimal retirement decisions, for a number of future old age care financing scenarios that should ensure sustainable collective spending. The main choice is what percentage of retire-ment capital should be invested in efficient annuities, and what percentage should be kept liquid to create a buffer for possible out-of-pocket care costs. A life cycle model can express this choice into one value of expected utility, thereby providing a powerful tool for comparing retirement choices. It turns out that for every scenario full annuitization is optimal as a result of the mortality premium.

With a growing number of elderly, continuing the current pay-as-you-go old age care financing system unaltered will lead to unacceptable taxes. Among the considered alternative scenarios are a lifetime maximum, separation of living and care costs and a mandatory insurance scenario. Since the division of old age care costs is very skew and costs are high, linking out-of-pocket costs to realised care use cannot reduce collective spending by a large fraction. However, mandatory insurance does work, and using a premium of 10% of retirement capital could reduce collective spending by as much as 48%. This result can be used to create a funded system of old age care financing that reduces sensitivity to demographic shocks. Because such a system is vulner-able to interest and inflation shocks, a pay-as-you-go system should coexist to offer steady social security on a more basic level.

Keywords: Intertemporal choice, Life-cycle finance, Pensions, Annuitisation, Retirement phase, Old age care, Nursing home, Government spending, Health care financing.

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Introduction

The Dutch pension system, historically considered to be one of the best in the world1, is currently under a lot of discussion. Subsequent economic challenges have hit the system, leaving pension funds with low coverage ratios and participants who have received no in-dexation or even a discount on their pension with low confidence. In recent years stock markets have been recovering and economic growth appears to have slowed down some-what. Interest rates have been at an all-time low and the health expectancy is increasing rapidly. Since sponsors of pension plans are not keen on bearing such risks, a trend of risk transfer from the sponsor to the participant has been visible over the recent years. This shift from Defined Benefit (DB) pension plans to Defined Contribution (DC) pension plans has however given new opportunities of flexibility. Since every participant is entitled to his own accrued individual pension capital in such a plan, choices like the asset mix of investments or the way the benefits phase is structured could be offered to participants. The Dutch system comprises three ‘pillars’. The first pillar is a Pay-As-You-Go (PAYG) system. It offers social security to every Dutch citizen. From the retirement age, a fixed benefit is paid to every citizen, providing the minimum income for a decent quality of life. For 2015 this amount is close toe14,000 a year for an unmarried person, and almost e10,000 for a married person. On top of this, everyone working for an employer or in a sector that has a collective pension plan is obligated to save a part of his or her salary for retirement. This system of personal claims forms the second pillar. On top of these two systems, additional pension and life insurance products are offered. This is mostly on a commercial basis and is referred to as the third pillar. The retirement age is currently gradually increasing from 65 to 67 in 2021 in order to keep this social security affordable. From 2020 on, the retirement age will be directly linked to the life expectancy.

To approve for tax benefits when saving for a pension product in the second and third pil-lar, a strict demand from the Dutch government is the complete, lifelong annuitisation of pension savings2. This rule should prevent people from overspending after retirement and possibly outliving their pension savings. In addition, making lifelong annuities mandatory ensures an effective hedge of longevity risk and protects the system against the effects of adverse selection. However, the combination of mandatory participation in a pension plan and the obligation to fully annuitise can be considered as too much. A person facing only longevity risk upon retirement should optimally invest all of his wealth in lifelong annuities. Introducing other risks and motives however, can change this optimal strategy. Chapter 2 focuses more on the drivers for full or partial annuitisation. The need for liq-uidity to account for unexpected large expenses is one of these drivers. Since the largest risk faced by the elderly, besides longevity risk, is that of long term health care expenses, this topic will be investigated on a deeper level.

In other countries such strict annuitisation regulations do not exist, or to a smaller extent. Australia has incorporated a new system over 25 years ago, giving complete freedom to pensioners on how they spend their pension savings. Even though annuitisation in the sec-ond pillar yields tax benefits, most pension payments are lump-sum on the retirement date. The pension system in the United States is similar; second pillar schemes can be provided by the employer, but the option to annuitise pension savings is rarely offered. Average replacement rates of the first pillar systems for these two countries are only around 40%.

1

According to the Melbourne Mercer Global Pension Index (third place in 2014).

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Whereas these two countries struggle to increase annuitisation levels, the United Kingdom is moving in the opposite direction. From April 2015 on, members of DC pension funds are allowed to take their entire pension as a lump-sum payment from the age of 55. Since this is a relatively recent regulation change, the effects on average annuitisation are unclear for the time being. Other countries do have an obligation to annuitise at least to some extent, but ambitions will generally be lower than the 70% of the average pre-retirement income the Dutch system aspires to.

Old age care costs are mainly financed collectively in the Netherlands, causing out-of-pocket payments to be very low compared to other countries. However, an increasing elderly population relative to the working population puts this collective system under pressure. With the additional effect of quickly rising health care prices, old age care costs will soon be impossible to pay if the financing system remains the same. The design of a new, more sustainable financing system should is currently a hot topic of debate. A number of possible scenarios is put to the test, to see if they can turn the tide. Both the effect of these scenarios on collective spending and on average pensioners’ consumption levels are investigated, to find a reasonable solution to this growing problem.

The goal of this research is to determine what the optimal financial planning decisions are for pensioners, and to what extent different, more sustainable scenarios of old age care financing will affect pensioners and decrease collective spending. In order to compare the effects of different choices, a life-cycle model is defined in Chapter 3. Such a model can show how pension choices, like the fraction of annuitisation, or the way wealth is invested can affect the expected utility of a pensioner. In order to use such a complicated model, assumptions will have to be made and observed data is used to estimate parameters. The distribution of health expenditure is examined in Chapter 4, resulting in a model for health care costs. Future scenarios of health care financing are also defined here. Chapter 5 fo-cuses on the results that arise from testing the different scenarios and provides insights into the consequences of a changing system. Using these new insights, Chapter 6 gives an exploration of opportunities, in the form of new ways of handling pensions and long term care insurance. Finally, Chapter 7 contains a short summary of all relevant findings and provides a conclusion and discussion to this research.

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2.

Drivers to and away from full

annuitisation

2.1 Literature review

A lot of research on the financial planning decisions of individuals upon retirement has been done in the past. Being the first to incorporate an uncertain time of death into the life-cycle framework, Yaari (1965) shows that converting all wealth into lifelong annuities is optimal for an individual without a bequest motive who faces only longevity risk. The strong efficiency in annuities is caused by the addition of a mortality credit on the rate of return as the probability of not surviving to the next period is discounted in the price of an annuity. Milevsky (2005) studies this topic into more detail.

Even though full annuitisation of wealth clearly has its advantages, only a limited num-ber of people buy additional life insurance products alongside their mandatory pension benefits. According to Statistics Netherlands (2010) in 2007 the first pillar and second pillar took up 95% of pension savings, leaving only 5% for the third pillar. This while almost 70% of people upon retirement have a capital of more than e20,000. This dis-crepancy is called the annuity puzzle, and numerous researchers have tried to solve this puzzle. Among the proposed motives for keeping a portion of liquid wealth are the desire to leave a bequest, see Lockwood (2012), inefficiency in the market for life insurance, see Bikker and Van Leuvensteijn (2008), the influences of adverse selection, see Finkelstein and Poterba (2004), the lack of protection a lifelong annuity provides from inflation risk, see Kuin (2014), behavioural motives, see Brown (2007), and the fear of not being able to cope with large, unexpected expenses. Especially the last motive will be the main topic of this research. The other large risk an older individual faces besides longevity risk is the risk of high health care costs. Long-term health care and old age care can prove to be very costly. Peijnenburg et al. (2011) investigate this effect for the United States, and find that especially high costs early in retirement influence the optimality of full annuitisation.

2.2 Financing of health care costs

Currently out-of-pocket health care costs (the part to be financed privately) only account for a small part of Dutch household spending. This is because of the way the health care costs are financed. The Netherlands has a very solidary and collective financing system; this system, however, is currently under great pressure from increasing health care costs. In the current system, curative health care is financed through mandatory participation in a basic health insurance fund. The composition of this basic insurance is regulated and participants cannot be declined by the insurer. To decrease high medical spending as a result of moral hazard, this basic insurance has a compulsory deductible. To keep the pre-miums affordable this deductible has been increasing over the previous years from e150 in 2008 toe375 in 20153. Additional insurance can be entered into, providing coverage for other medical treatments such as dental care.

The largest portion of health care costs for the elderly, are the costs arising from long term care, or old age care. Together with long term care for disabled, this is financed

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Data from Independer, a comparison site for financial products:

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through WLZ taxes4. Every citizen pays an income dependent tax (9.65% of income, fixed at a maximum ofe3,241 in 2015). Just like the first pillar pension premiums, the long-term health care costs are financed on a PAYG basis. Each year, the government anticipates the costs, and sets this percentage accordingly.

Since the year 2000, health care expenditure has increased drastically. Before 2000 the costs of health care were strictly managed, but the quality of health care was low and waiting lists were long. In the following years, large improvements were made by allocating more collective funds to the health care sector. Maintaining a high quality proves to be difficult. Between 2000 and 2013 health care spending doubled, and the portion of government spending increased from 10.5% in 2000 to 14.6% in 2013, as can be seen in the left panel of Figure 2.1. In order to explain this increase, two factors can be separated: the price of health care and the volume of health care. Prices are rising fast as a consequence of the Baumol effect, first described in Baumol and Bowen (1966). This effect describes labour productivity in the health care sector improving slower than in other sectors, even though wages have to be increased to keep attracting employees. This causes labour costs to rise rapidly. According to Van der Horst et al. (2011), the volume of health care is mostly dependent on the age composition of the population and the average income. Improving life expectancy shifts the weight of the population more towards the elderly, a group with more health care needs. The development of price and volume can be seen in the right panel of Figure 2.1.

Figure 2.1: The left panel shows the evolution of health care costs as a percentage of Gross Domestic Product (GDP) over time. The right panel shows the development of volume and costs of health care as an index, where 1998 is set to be 100. Calculations are based on data by Statistics Netherlands.

Depending on the growth assumptions for health care spending, the CPB estimates that by 2040 the total costs of health care will double or even triple, consuming a large part of the expected increase in income over those years, see van Ewijk et al. (2013), therein Chapter 3. To make matters worse, the Dutch dependency ratio (the number of people above 65 divided by the number of people in the working age of 15-64 years) has been increasing over the previous years, and is expected to rise further over the coming decade. Figure 2.2 shows this Dutch dependency ratio. A high dependency ratio and a mostly publicly funded health care system cause high taxes on the working, decreasing disposable income and possibly decreasing labour participation.

The expected increase in people of over 65 also has major effects on the number of people in nursing homes. Although the number of people in institutions has decreased somewhat over the previous years, a prognosis by Statistics Netherlands shows this number will increase over the coming years. The increase is mainly driven by people over 80 years old. Figure 2.3 shows this prognosis, the parts in pink and green represent people above the age of 80 years.

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Figure 2.2: The evolution of the dependency ratio: the number of people above 65 divided by the population in the working age. Prediction from the year 2015, calculated by the International Insurance Center (IIC)

Over the last few years the Dutch government has acknowledged these impending threats to the economy and sustainability of the current system. The goal is to slow down the growth of these expenses, whilst maintaining a high standard and wide accessibility. Need-less to say this is nearly impossible, and some compromises will have to be made. Two directions can be distinguished: a shift from uniform health care to a more differentiated range, and a shift from collective financing and mandatory insurance to a system with more private financing.

Recently, out-of-pocket payments have been introduced for wealthy people living in nurs-ing homes, amountnurs-ing up to a maximum close toe27,000 per year. Another way of shifting to private financing is increasing the deductible in basic health care insurance, as men-tioned earlier. The uniformity of health care has not yet undergone large changes, since solidarity and equality are valued highly in the Dutch system. A shift to a free basic qual-ity and a more expensive better qualqual-ity system could be one of the ways to reduce public spending in the future however. Different approaches could have a big impact on financial planning decisions, as they might change the desire for insurance and liquidity. Chapter 4 will provide more information on current health care costs, and defines a number of future scenarios to incorporate these changes in the model.

Figure 2.3: A prognosis of the institutionalised population, where different colours represent different age groups. Especially nursing home use by people over 80 years old is expected to double over the coming 45 years. Data by Statistics Netherlands.

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3.

Modelling the retirement phase

As mentioned before, analysing the effects of financial planning decisions will be done using a life cycle model. In this study, only the retirement phase is considered, starting at the pension age. The life cycle model can be seen as a model for inter-temporal choice, extended for implementing uncertainty about costs and life expectancy. For the cohort receiving their first pension payments in 2015, the incrementally increasing pension age is equal to 65 years and three months. Because only whole years are simulated in the life cycle model, a retirement age of 65 is used from here on.

Since the goal of this research is to calculate optimal financial planning decision and not to explain the observed lack of annuitisation, expected utility theory based on Von Neumann and Morgenstern (1944) is used rather than prospect theory. In order to use the expected utility model, preferences are assumed to be defined by a utility function, and agents are assumed to have a desire to maximize their expected utility. According to Kahneman and Tversky (1979) the driver for insurance demand under prospect theory is not risk aversion but overestimation of small probabilities by agents. Explaining the observed lack of third pillar annuitisation this way is beyond the scope of this research.

3.1 Life cycle model

The model is based on the assumption that a decision maker maximises his expected utility over the rest of his life, by deciding on his consumption for every time period. Since it is widely used in similar research, a utility function from the power family is adopted, characterised by a Constant Relative Risk Aversion (CRRA). For a positive amount of consumption and a risk aversion greater than one, the utility function is defined as:

u(Ct) =

C_t1−γ

1 − γ , for γ > 1. (3.1)

A higher value of γ represents a higher risk aversion. Since only the retirement phase is modelled, the time horizon is t = 0, ..., T − 1, with t = 0 corresponding to the retirement age of 65 years and T − 1 = 45 corresponding to the assumed maximum attainable age of 110 years. Then for stochastic consumption C0, ..., CT −1, the life cycle model can be

defined as: V (C0, ..., CT −1) = E "_{T −1} X t=0 βt t−1 Y s=0 ps ! u(Ct) # , (3.2)

where β is the time preference discount factor and ptis the 1-year probability of surviving

to period t + 1, conditional on survival up to period t. Now V (C0, ..., CT −1) is the overall

expected lifetime utility, discounted to the moment of retirement using the time preference discount factor and survival probabilities. Maximising this expectation should provide the optimal consumption path for a decision maker. This utility function is time separable, neglecting possible effects of habit formation. The consumption decision in a time period is dependent on the amount of wealth available to the decision maker. To prevent a transfer of wealth from one time period to another, there is a borrowing constraint:

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where Ct is the consumption, Wt is the wealth at time t, Yt is the income for period t,

and Htis the amount of health care spending in period t. The amount of wealth which is

not used for consumption will earn a return over the upcoming time period, available for consumption on the start of the next period. There are many theories on how this return should be calculated. For example, Peijnenburg et al. (2011) offer the choice to put a part of the savings in risky assets and have the rest earning the risk-free rate. As a full model of market movements is beyond the scope of this research, a simplification is made and all the savings earn the constant, risk-free rate rf.

Apart from earning a risk free rate of return, next period’s wealth is determined by the income and health care spending. Since only the retirement phase is modelled, income is limited to the income from lifelong annuities, purchased upon retirement. Given a certain initial capital at age 65, the decision maker decides on the percentage of wealth he wants to annuitise, and what portion of wealth he wants to keep liquid. The price of a lifelong annuity is actuarially fair, meaning it is determined only by the expected payments, so the insurer does not add a profit margin or risk premium. The composition of health care costs is given in Chapter 4, these costs are treated as an exogenous variable. So, the wealth in period t + 1 is given by:

Wt+1= (Wt+ Yt− Ht− Ct)(1 + rf). (3.4)

The order of events is as follows:

1. Savings from last period earn the risk-free rate, 2. Annuity payment is received,

3. Health care costs are paid, 4. Consumption decision is made.

As health care costs may be high, consumption could fall below a socially accepted stan-dard of living or even become negative. To incorporate a system of social security, con-sumption in a time period can never be smaller than some fixed amount Cmin.

3.2 Choice of parameters

In order to be able to estimate the life cycle model, parameter values have to be chosen. Since the data set used for this research is not as complete as the data used in De Nardi et al. (2009), estimating the values using regression techniques is not possible. Fortunately there is enough relevant literature on this topic, so parameters can be set accordingly. First of all, the utility function requires a risk aversion coefficient, γ. De Nardi et al. (2009) estimate that this value is close to 4 for their data. Peijnenburg et al. (2011) choose a value of 5, consistent with their previous studies. Brown (2001) uses survey questions to translate risk preferences into risk aversion categories. He finds that two thirds of the sample falls in the highest category of risk aversion, described with a γ of 5. The other third of the sample is evenly distributed over three classes with lower risk aversion, described with coefficients 2.9, 1.5 and 0.7. Taking these three papers into account, γ = 3 is used as a benchmark in this paper. In Chapter 5 the effect of other risk aversion parameters on the results will be shown in a robustness analysis. For the time preference discount factor, the value β = 0.96 is chosen, in line with research by Peijnenburg et al. (2011). Since currently risk-free interest rates are historically low, rates varying from 1% to 3% are considered, with 3% as the basic scenario. Bequests are not implemented in the model, because De Nardi et al. (2009) conclude that they have no significant effect on the outcomes.

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To describe Dutch mortality, data by the Dutch Actuarial Society (AG) is used. Adopting a Lee-Li mortality model, historical Dutch mortality and mortality in comparable European countries are taken into account to generate a best estimate prediction for the future. The one-year survival probabilities psin the life cycle model can be calculated from these

mortality rates, given gender and age. Using the mortality rates and some interest rate term structure, the actuarially fair price of an annuity can be calculated. Since guideline 2004/113/EG by the European Union prohibits gender specific pricing of annuities, and this law became binding on the 21st of December 2012, annuities are priced using gender neutral mortality rates. To create a realistic setting, a margin for costs and profit is included. This surcharge is assumed equal to 3% of the present value. The price of a lifelong annuity for a person aged 65, paying e1 at the beginning of every year the annuitant is alive is then given by:

¨ a65= 45 X t=0 1 1 + rf t tp65 ! ∗ 1.03, (3.5)

where tp65 is the probability a person aged 65 survives for t more years. For a fixed

in-terest rate of 3% and gender neutral mortality rates, the premium is approximately equal toe16.13. The yearly annuity income Yt can be calculated by multiplying the available

wealth upon retirement by the fraction annuitised, and then dividing by this premium. As mentioned before, a system of social security keeps people from going bankrupt or living under a socially accepted standard. A married person receives roughlye9,000 per year in net AOW payments. Because rent and some other costs have to be paid from this, Cmin is set toe6,000 to reflect actual minimum consumption.

3.3 Description of the simulation program

In order to simulate the model and see what financial planning decisions are optimal under different circumstances, a program is needed. To limit the programming time, the Matlab program as described in appendix B of Biewald (2009) is used as an outline. The life cycle model is optimised using a dynamic programming algorithm. Working back from the last time period to the first, a series of small optimisation problems is solved recursively. This method was first described by Bellman (1957), and the recursive relations are therefore called Bellman recursions. By doing these optimisations, the optimal consumption decision can be calculated for each value of disposable money, given the remaining number of time periods.

The next phase is to simulate realisations, to see the effect of different inputs. A number of agents is created, assigning a starting capital, a gender and a starting health status. The agents go through an entire lifetime, encountering health status changes, health care costs and an uncertain time of death. For a sufficiently high number of agents, the average outcomes will converge to the expected value. Maximising the average lifetime utility by changing inputs like the fraction annuitised, gives an indication of the optimal financial planning decision for a person facing retirement. Specific retirement strategies can also be derived for people from different classes, for instance a healthy rich female or an unhealthy poor male. A full version of the Matlab program with some explanation can be found in Appendix C.

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4.

Modelling health care costs

4.1 Cure and Care

When considering health care costs, two main categories can be determined. One is the curative health care, aiming to cure people of their illnesses. Examples of such health care are doctor visits, dental care, medication and midwifery. Almost everyone encounters this kind of health care at some point. The left panel of Figure 4.1 displays the average cura-tive (cure) costs per age, for both men and women. This data comes from an overview of invoiced health care costs for 17 million insured in the year 2012, collected by Vektis.

Figure 4.1: The left panel shows the division of the 2012 curative care costs in Euros per age and gender. The right panel shows the division of the 2006 long term care costs in Euros per age group and gender. Both are corrected to 2015 prices using Dutch CPI.

Cure costs start of high, reflecting the health care most newborns need in their first year. Afterwards the costs tend to rise with age, although a slight decrease can be noticed around 85 years. Beyond this point, increasing age and diminishing health status limit the options for extensive curative care. The hump in women’s health care costs around 30 years reflects the extra health care needs of women during their pregnancy and after giving birth. The rising health care costs with age do present a somewhat distorted image, since most curative health care costs are made in the year prior to passing away. At higher ages, mortality is a lot higher and therefore health care for the elderly tends to be costly. For this study, the relevant health care costs are the ones made in retirement, so from the age of 65. These cure costs average around e4,900 a year, but costs for long term care can far exceed this amount. Long term care includes costs arising from nursing and medical assistance, staying in an institution like a nursing home, nursing care at home, and many other services aimed at making life easier when one can no longer care for him or herself. From data by Statistics Netherlands, in 2006 a person could expect an average ofe74,237 in long term care costs in his remaining lifetime (in 2015 prices). The increase of long term care (care) costs with age is very high, as depicted in the right panel of Figure 4.1. This data about AWBZ spending comes from the website of the Dutch Ministry of Health, Welfare and Sport, and is collected by RIVM and Statistics Netherlands.

4.2 Spread

Not every individual encounters the same health care costs over the course of his or her lifetime. The division of average health care costs per age and gender is therefore not suffi-cient to model the uncertainty in health care spending. Data from Statistics Netherlands,

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based on the data set used by Wong (2012)5, shows that the top centile accounts for more than half of the expected lifetime long term care costs upon retirement, as can be seen in Figure 4.2. The top 1% averages over e750,000. Figure 4.2 also shows a division of total long term care costs into intramural care (inside an institution like a nursing home) and extramural care (nursing care at home). It is clear that the intramural care is by far the largest driver for both the total costs and the spread. At an average cost of roughly e60,000 for a one-year stay in a nursing home, being institutionalised has a big impact on the financial situation of a pensioner. Curative care has a lot less skew distribution, according to van Ewijk et al. (2013), the top 20% accounts for roughly 35% of cure costs.

Figure 4.2: Spread of extramural, intramural and total old age care costs. Each bar represents 10% of the observed population. A large right hand tail can be observed.

This large uncertainty about future health care costs and being unable to keep living at home is currently taken away by collective public financing of long term care through WLZ taxes. Dutch people living in a nursing home only pay a small amount out-of-pocket. If this would not be the case, saving up substantial amounts of money to ensure being able to pay for possible old age care costs would be far from optimal. Many pensioners would pass away with a large amount of wealth left unspent. In a world with less solidarity, higher own contributions or a more differentiated care system, long term care insurance could provide a solution.

4.3 Health status effect

Apart from age and gender, health status has a large influence on personal health care spending. By quantifying this factor, a better simulation of the lifetime cycle model can be achieved in a later stadium. To assess the health status of an individual his own perception can be used, the so called self-perceived health. Since such a classification of health status is quite broad and subjective, this could cause a misrepresentation of reality. Another way of defining the health status is to look at function limitations. Severe limitations such as not being able to eat a meal or take a bath are strong indicators for long term care use. Intuitively, the presence of limitations in everyday activities caused by bad health will increase the use of health care services. The exact effect can be quite difficult to estimate, since survey data and health care expense data have to be combined. To simplify calcu-lations three health statuses are used, equivalent to Reichling and Smetters (2015). The aim of these statuses is to model the dynamics of nursing home use among the population. Because old age care in nursing homes is by far the biggest source of health care risk in retirement, they are assumed to be the only factor. Dividing the total long term care costs over the total number of years spent in nursing homes will then give the average one year price of nursing home care.

5

A data set describing a sample of the old Dutch National Health Service participants. Prices are scaled to 2015.

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According to data by Statistics Netherlands, almost 5% of the population over 65 years is living in an institutionalised household. This means they are met in their daily needs on a professional level. Although this number also includes prisons and refugee camps, the nursing home population accounts for the largest part of these households, especially at high ages. Therefore the percentages in Table 4.1 are considered to be equal to nursing home use. The chance of living in a nursing home rises fast with age. Women are clearly over represented at higher ages, as a result of their higher life expectancy. According to the AG2014 mortality table, a man aged 65 in 2015 has a 12% chance of reaching the age of 95, whereas a woman has a chance of 22%.

Male Female Total 65 - 69 years 1.0% 0.9% 0.9% 70 - 74 years 1.3% 1.5% 1.4% 75 - 79 years 2.3% 3.4% 2.9% 80 - 84 years 5.1% 9.0% 7.4% 85 - 89 years 11.3% 19.8% 16.9% 90 - 94 years 22.8% 34.3% 31.3% 95 years or more 36.7% 50.9% 48.3%

Table 4.1: Institutional population per age group and gender. Data by Statistics Netherlands. In order to calibrate the health statuses to fit the Dutch population and estimate the development of the health care status over time, longitudinal survey data is essential. The Survey of Health, Ageing and Retirement in Europe (SHARE) offers such data. This large project started it’s first wave of interviews in 2004, in eleven countries including the Netherlands. Participants in the retirement age are interviewed on a long list of subjects, one of which is their physical health. Table 4.2 shows that for the latest and biggest wave of SHARE, it turns out women are indeed over represented in the age over 65, accounting for 52.5% of the total respondents. This is especially true in the higher age groups, with a percentage of females rising over 86% for ages above 95.

Age group

Total 65-69 70-74 75-79 80-84 85-89 90-94 95+

Male % in age group 48.3% 47.3% 51.5% 46.3% 41.2% 38.6% 13.3% 47.5% Female % in age group 51.7% 52.7% 48.5% 53.8% 58.8% 61.4% 86.7% 52.5%

Table 4.2: Division of men and women over the age groups in wave 5 of SHARE.

In the SHARE questionnaire, the presence of several limitations is inquired. These limi-tations are divided into two categories: light limilimi-tations and heavy limilimi-tations. The exact SHARE questions and a list of both light and heavy limitations can be found in Appendix A. It turns out the best approximation of nursing home use is to classify people with two or more heavy limitations as health status h3: living in a nursing home. People experiencing none of these difficulties, both heavy and light, are classified as h1: healthy. The rest of the population, having some limitations but not two or more heavy ones is classified as h2: impaired but not severely. This last health status does not invoke health care costs, and can be seen as a transition status between healthy and institutionalised individuals. Since people with severe limitations in basic activities obviously have a lower life ex-pectancy than healthy individuals, the mortality rates should reflect this. Robinson (2002) calculates the difference in mortality that arises from eight different health statuses. Using an exponential formula, mortality probabilities can be calculated given health status, gen-der and age. Because there has been a big decrease in mortality for all ages over the last 20 years, a correction has to be applied to these rates in order to make them realistic for

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use in 2015. Mortality rates are multiplied by a factor 0.3 for ages up to 85, and for higher ages they are multiplied with 0.4. As can be seen in Appendix B, simulation shows these rates and the transition probabilities described below produce an overall mortality curve similar to that of AG2014, for individuals aged 65 in the year 2015. Because Robinson (2002) only calculates mortality rates for an age up to 100 years, after this point the rates are smoothly extrapolated in a way that complies with the AG rates.

4.4 Fitting to the data

Because of the persistence of function limitations, autocorrelation in the health statuses has to be taken into account. Using the different waves of SHARE data, transition probabilities can be modelled. A discrete time Markov chain is used because of its autocorrelation properties and easy implementation in later simulation. Since the waves are published once every three year, the third power root of the observed transfer probabilities matrix approximates one-year transfer rates. Because the transfer probabilities change with age, a separate transition matrix is calculated for each age group. A lack of observations for the age group 95 years and older means this group has to be merged with the 90-94 years group, so one transition matrix is used for ages 90 and higher. Figure 4.3 shows the evolution of health statuses as age progresses. Besides these transition probabilities some starting probabilities are also needed. By observing the division of health statuses in the youngest age group, the chance of starting in a healthy state is 63.2%; 35.3% starts of in an impaired state at 65, and 1.5% is already in a nursing home at retirement.

Figure 4.3: The evolution of health statuses as age progresses. The left panel describes a man starting in a healthy state at age 65 and the right panel a man starting in a nursing home.

By simulation, the expected number of years of nursing home use for an individual aged 65 can be shown to be equal to 1.06. According to the data described in section 4.2, the expected long term care spending is equal toe74,237 in 2015 prices, resulting in an average price of living in a nursing home for one year of roughly e70,000. The simulated spread of lifetime long term care costs at retirement now closely fits the observed spread, as can be seen in Figure 4.4.

Figure 4.4: The simulated and the observed spread of lifetime long term care costs at age 65 in percentiles. The simulation only allows for whole years in a nursing home, causing steps in the graph. Observed spread data by Statistics Netherlands.

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4.5 Future scenarios of health care financing

In order to see what the effect of changes in the financing of health care are to the optimal financial planning decisions by pensioners, some scenarios have to be constructed. Most of the following scenarios are based on the study of Knoef et al. (2014).

1) No old age care costs scenario:

In this scenario all out-of-pocket old age care costs are assumed to be zero. This implies that all costs are financed collectively, without any extra contributions for people in bad health. This scenario serves as a benchmark, where full annuitisation will probably be optimal since there is no need for liquidity and the agent only faces longevity risk. 2) Current financing scenario:

For long term care costs, out-of-pocket payments are based on the WLZ legislation. The figure that the yearly amount of contribution is based upon is the sum of all income, increased with 8% of current wealth. Up to 12,5% of this amount has to be paid as own contribution, capped at e2,284.60 a month. So mandatory own payments can be substantial, even though the amount and quality of care are equal for everyone.

3) Total old age care costs scenario:

In this scenario all payments are out-of-pocket, representing a system with no collective financing. Because old age care costs could quickly surpass financial means, a minimum consumption level has to be maintained to keep individuals from going bankrupt. This scenario is the opposite of the basic scenario, the most extreme form of self financing. 4) Separation of living and old age care scenario:

In order to keep old age care affordable, only the costs of care are collectively financed, and the costs of living have to be paid out-of-pocket. This way, people have more control over their living conditions and might be able to better choose a care situation that works for them. The costs of living in a nursing home are estimated to bee500 a month. So a total ofe6,000 has to be paid out-of-pocket when living in a nursing home for a full year. This scenario is based on plans by the Dutch government, that are currently put on hold6. 5) Lifetime maximum payment scenario:

The first part of old age care costs has to be paid out of pocket, up to a fixed amount. After this limit has been reached, all old age care costs are collectively financed. As in other scenarios, there is a minimum consumption level that prevents unacceptable financial losses. This scenario is based on the system Great Britain plans on imposing from 20177. In those plans the threshold is set to £100,000. Apart from a cost reduction, the goal of this scenario is to encourage saving for old age care. In order to create a solidary system, for this research the maximum amount is set to 10% of the wealth upon retirement. 6) Mandatory long term care insurance scenario:

If long term care insurance would be available, buying such a product could take away the uncertainty of health care expenses. Two cases can be considered, mandatory and voluntary. Mandatory insurance will have the same effects as collective financing, equally dividing the costs among everyone. Voluntary insurance will be especially interesting for people expecting high health care costs, so adverse selection effects have to be considered. For this research only mandatory insurance will be taken into consideration. Premium payment takes place every year, conditional on the survival of the agent. The premium amount is calculated as a reversed annuity (without surcharge). In order to create a solidary system, the present value of premiums is again set to 10% of the retirement wealth for this research.

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Retirement wealth

Since in some of the scenarios the own contribution depends on the household wealth of a pensioner, it is important to look at this in the SHARE data set. A range of questions about assets, savings and debts is asked to at least one member of each household. From these categories, the imputations ‘household real assets’, the value of real estate, business and cars minus mortgages, and ‘household financial assets’, the sum of savings, bonds and other investments minus financial liabilities are constructed. The sum of these two amounts makes up the ‘household net worth’, which is used in this research. Figure 4.5 shows the division of the first two categories of wealth among the age groups8. Wealth decumulation with age can clearly be observed, although there is a slight difference between real assets and financial assets. Real assets decrease more steadily than financial assets. This could be an effect of selling real estate, the desire to leave a bequest, or the desire to keep a financial buffer for uncertain times.

Figure 4.5: Decumulation of average household wealth in Euros after retirement. The left panel shows the mean value of real assets, whereas the right panel shows financial assets.

The minimum consumption level ofe6,000 is equivalent to a retirement capital of e96,804 at the retirement date when a discount rate of 3% is used. So even an individual that has no savings at the retirement date has a retirement capital of almoste100,000. Table 4.3 shows a rough division of retirement capital over the population, derived from SHARE.

Savings: e 0 e 100k e 250k e 400k e 650k Retirement capital: e 100k e 200k e 350k e 500k e 750k Occurrence: 35 % 15 % 25 % 15 % 10 %

Table 4.3: Division of retirement capital over the SHARE survey population.

Certainty equivalent consumption

In order to provide insight into the effects of these scenarios on the actual expected con-sumption by pensioners, the Certainty Equivalent Concon-sumption (CEC) measure is used. To compute this, the average expected utility is calculated back to consumption in Euros. Inverting formula 3.1 and 3.2 gives a formula for the CEC for γ > 1:

CEC = u−1   1 PT −1 t=0 βt Qt−1 s=0ps · V (C ∗ 0, ..., C ∗ T −1)   , with (4.1) u−1(x) = 1 (1 − γ) · x 1 γ−1 for x 6= 0, (4.2)

where V (C₀∗, ..., C_{T −1}∗ ) is the average expected utility for a scenario. Because the units of this measure are Euros, the outcomes can be compared more intuitively.

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5.

Simulation Results

This chapter contains the results acquired from Matlab simulation. The first part covers the optimal fraction of annuitisation for different scenarios. Hereafter, the effects of different scenarios of future old age care financing on consumption and collective spending are examined. Finally, the sensitivity and the robustness of the results with respect to the input parameters are calculated.

5.1 Optimal fraction of annuitisation

When no out-of-pocket health care costs are considered, full annuitisation yields the high-est certainty equivalent consumption, for every simulated amount of retirement capital. Figure 5.1 shows the CEC for the fractions between 0%, equivalent with no annuitisation, and 100%, equivalent with full annuitisation.

Figure 5.1: The average certainty equivalent consumption for annuitisation levels ranging from 0% to 100% in the scenario without any out-of-pocket health care costs.

Figure 5.2 shows that for the full costs scenario, the most extreme case of out-of-pocket payments, this result does not change. Since the intermediate scenarios will not change the optimal fraction either, from here on only full annuitisation of retirement capital is considered. The strong benefit of a higher fraction of annuitisation does decrease under the full costs scenario.

Figure 5.2: The average certainty equivalent consumption for annuitisation levels ranging from 0% to 100% in the scenario with full out-of-pocket health care costs.

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5.2 Comparison of future financing scenarios

Table 5.1 shows the simulation outcomes for each of the scenarios defined in Chapter 4. In order to be able to compare the scenarios, their relative change with respect to the cur-rent financing system is also listed. For each combination of financing scenario and starting capital 100,000 simulations were performed. The standard parameters as determined in Chapter 3 and 4 were used.

Scenario Retirement CEC Relative to Collectively Relative to capital current financed current Current financing e 200k e 12,332 - e 72,744 -scenario e 350k e 21,566 - e 72,299 -e 500k e 30,853 - e 69,820 -No out-of-pocket e 200k e 12,389 + 0.5% e 74,682 + 2.7% payments e 350k e 21,707 + 0.7% e 75,331 + 4.2% e 500k e 30,989 + 0.4% e 73,489 + 5.3% Full old age e 200k e 11,704 - 5.1% e 68,510 - 5.8%

care costs e 350k e 18,113 -16.0% e 57,291 -20.8% e 500k e 22,298 -27.7% e 47,993 -31.3% Lifetime maximum e 200k e 11,917 - 3.4% e 70,357 - 3.3% payment scenario e 350k e 19,487 - 9.6% e 65,658 - 9.2% e 500k e 25,323 -17.9% e 60,273 -13.7% Separation of living e 200k e 11,825 - 4.1% e 67,866 - 6.7% and care costs e 350k e 21,361 - 1.0% e 67,239 - 7.0% e 500k e 30,707 - 0.5% e 67,862 - 2.8% Mandatory insurance e 200k e 11,120 - 9.8% e 48,430 -33.4% scenario e 350k e 19,459 - 9.8% e 28,561 -60,5% e 500k e 27,836 - 9.8% e 9,619 -86.2%

Table 5.1: Simulation results for the six scenarios, for three starting values of retirement capital. The third column represents average certainty equivalent consumption, and the fifth column represents the average amount of health care costs that have to be financed collectively per person. For both values, the percentage of change with respect to the current scenario is given.

Apart from the no health care costs scenario, all future financing scenarios realise a de-crease in collective financing. This does come at a cost however; the drops in the expected consumption level are large, especially for the more wealthy individuals. Scenarios that make own payments dependent on long term care use do not succeed at lowering the collec-tive costs whilst maintaining an acceptable consumption level. The mandatory insurance scenario does achieve this. Because the premiums are dependent on the retirement capital, the drop in consumption is equal for all levels of wealth. The decrease in collective costs is substantial, and rising for larger values of retirement capital.

Surprisingly, for high retirement capitals, the decrease in expected consumption for the lifetime maximum scenario is larger than 10%. A possible explanation is that in the manda-tory insurance scenario the payments are spread out over time, whereas they can be realised in a single year in the lifetime maximum scenario. This sudden drop in utility has a large effect on the average utility, and thus on the CEC.

Using the division of retirement capital mentioned at the end of Chapter 4, the total decrease of collective financing can be calculated. Table 5.2 lists the collectively financed part for both the current scenario and the mandatory insurance scenario. The last col-umn shows the weighted average; it turns out using 10% of the retirement capital to pay insurance premiums decreases the collective costs of old age care by 48%.

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Retirement capital e 100k e 200k e 350k e 500k e 750k Weighted average Current scenario

collective part e 74,605 e 72,744 e 72,299 e 69,820 e 67,594 e 72,330 Insurance scenario

collective part e 67,934 e 48,430 e 28,561 e 9,619 e-23,593 e 37,265

Table 5.2: The collectively financed part for both the current financing scenario and the manda-tory insurance scenario. The last column shows the weighted average, using the division of re-tirement wealth from Table 4.3.

As can be seen in table 5.1, there is a trade-off between the CEC and the amount left to be financed through taxes. To provide insight into this trade-off, this amount is divided proportionally among the elderly population. The firste 100k is exempted from tax pay-ments. A yearly tax is calculated by dividing by the average life expectancy. The resulting CEC in table 5.3 shows that some scenarios cause a transfer of wealth. Both the separation of living and care and the mandatory insurance scenario transfer some money from the poorer to the richer. Furthermore, the full costs and the lifetime maximum scenario cause a far greater decrease in CEC than in collective payments. This has a large, negative effect on all wealth classes. For the full costs scenario, the net CEC for the highest wealth class even drops more than 50% compared to the current financing scenario.

Scenario Retirement Gross CEC Yearly tax Net CEC capital Current financing e 100k e 6,369 - e 6,369 scenario e 200k e 12,332 e 1,639 e 10,693 e 350k e 21,566 e 4,097 e 17,468 Collective: e 500k e 30,853 e 6,556 e 24,297 e 72,330 e 750k e 46,174 e 10,653 e 35,521 No out-of-pocket e 100k e 6,198 - e 6,198 payments e 200k e 12,389 e 1,688 e 10,701 e 350k e 21,707 e 4,220 e 17,487 Collective: e 500k e 30,989 e 6,752 e 24,237 e 74,495 e 750k e 46,446 e 10,972 e 35,474 Full old age e 100k e 6,184 - e 6,184 care costs e 200k e 11,704 e 1,388 e 10,316 e 350k e 18,113 e 3,470 e 14,643 Collective: e 500k e 22,298 e 5,552 e 16,746 e 61,253 e 750k e 26,250 e 9,022 e 17,228 Lifetime maximum e 100k e 6,200 - e 6,200 payment scenario e 200k e 11,917 e 1,528 e 10,389 e 350k e 19,487 e 3,819 e 15,668 Collective: e 500k e 25,323 e 6,110 e 19,213 e 67,411 e 750k e 34,727 e 9,929 e 24,798 Separation of living e 100k e 6,205 - e 6,205 and care costs e 200k e 11,825 e 1,575 e 10,250 e 350k e 21,361 e 3,937 e 17,424 Collective: e 500k e 30,707 e 6,300 e 24,408 e 69,503 e 750k e 46,239 e 10,237 e 36,002 Mandatory insurance e 100k e 5,995 - e 5,995 scenario e 200k e 11,120 e 844 e 10,275 e 350k e 19,459 e 2,111 e 17,348 Collective: e 500k e 27,836 e 3,378 e 24,458 e 37,265 e 750k e 43,084 e 5,489 e 37,595

Table 5.3: The trade-off between Certainty Equivalent Consumpion and yearly taxes for the six scenarios. Collective costs are assumed to be fully paid by the elderly. Tax is divided proportion-ally, with an exemption of the firste 100k of retirement capital.

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5.3 Sensitivity analysis

Interest rate

In the previous simulations, an interest rate of 3% has been used. Since interest rates are currently historically low, the sensitivity of these results to a lower interest rate should be considered. In order to do so, the same simulations are performed for interest rate levels of 2% and 1%, keeping all other values equal. To decrease simulation time, only the intermediate retirement capital value ofe 350,000 is considered. Table 5.3 lists the results.

Scenario: 3% interest 2% interest 1% interest CEC Collective ∆ CEC ∆ Collective ∆ CEC ∆ Collective Current e 21,566 e 72,299 -10% - 1% -19% + 0% No costs e 21,707 e 75,331 -10% - 1% -19% - 2% Full costs e 18,113 e 57,291 - 7% + 4% -14% + 9% Lifetime max. e 19,487 e 65,658 - 8% + 0% -17% - 1% Living costs e 21,361 e 67,239 -10% + 1% -20% + 2% Insurance e 19,459 e 28,561 -10% +18% -19% +30%

Table 5.4: Certainty equivalent consumption and collective financing for different interest rates. All simulations assume the intermediate retirement capital ofe350,000.

A lower interest rate erodes the value of pension savings, because lifelong annuities become more expensive. Therefore, the CEC decreases for lower interest rates. This also causes an increase in the part of old age care costs that has to be financed collectively, because pensioners have less money available to pay out-of-pocket costs. Especially the mandatory insurance scenario is sensitive to a decrease in interest rates, because the amount of in-surance premium drops when the annuity price rises. When interest rates are low and are expected to go up over the coming years, making the annuitisation choice at the pension age could be unfavourable. With the current low interest rates, being able to (partially) delay the annuitisation choice is likely to provide a more favourable outcome.

Minimal consumption level

Changing the minimum consumption level will only have an effect for scenarios with large ou-of-pocket costs. For other scenarios, the consumption level for someone with a retirement capital ofe350,000 will not move below the threshold Cmin. Table 5.6 shows

that for the full costs scenario the CEC decreases and increases sharply with Cmin. For the

other financing scenarios effects are relatively small. The effect on the collectively financed part is also small, because the decreased threshold only affects a few of agents.

Scenario: Cmin= 6,000 Cmin= 3,000 Cmin = 9,000 CEC Collective ∆ CEC ∆ Collective ∆ CEC ∆ Collective Current e 21,566 e 72,299 + 0% - 1% + 0% - 2% No costs e 21,707 e 75,331 + 0% - 1% + 0% - 4% Full costs e 18,113 e 57,291 - 29% - 5% +11% + 5% Lifetime max. e 19,487 e 65,658 - 15% - 2% + 6% - 1% Living costs e 21,361 e 67,239 + 0% + 0% + 0% + 1% Insurance e 19,459 e 28,561 + 0% + 1% + 0% + 0%

Table 5.5: Certainty equivalent consumption and collective financing for different Minimal con-sumption levels. All simulations assume the intermediate retirement capital ofe350,000.

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5.4 Robustness check

Risk aversion

For the basic simulations, a risk aversion of γ = 3 was chosen. The risk aversion parameter influences how individuals value their utility under uncertain conditions. So for the scenario with no out-of-pocket health care costs, or scenarios where costs are relatively certain or manageable, the risk aversion parameter will have only a small effect. As can be seen in Table 5.4, the CEC values for the full costs scenario and the lifetime maximum scenario change considerably for different parameter values. The outcomes are valued differently, even though actual costs and consumption do not change.

Scenario: γ = 3 γ = 2 γ = 4

CEC Collective CEC ∆ Collective CEC ∆ Collective Current e 21,566 e 72,299 e 21,584 - 3% e 21,571 - 3% No costs e 21,707 e 75,331 e 21,735 - 2% e 21,686 - 1% Full costs e 18,113 e 57,291 e 19,814 + 1% e 15,658 + 0% Lifetime max. e 19,487 e 65,658 e 20,655 - 2% e 17,503 - 1% Living costs e 21,361 e 67,239 e 21,427 + 1% e 21,287 + 1% Insurance e 19,459 e 28,561 e 19,463 + 4% e 19,465 + 1%

Table 5.6: Certainty equivalent consumption and collective financing for different risk aversion parameters. All simulations assume the intermediate retirement capital ofe350,000.

A higher risk aversion parameter could negate the optimality of full annuitisation. Sim-ulation shows that this is not the case for γ = 4 however, as the CEC for the full costs scenario is equal toe15,658 for full annuitisation and e15,464 for 90% annuitisation.

Time preference factor

Altering the time preference discount factor will change the relative importance of future consumption to current consumption. This will mainly have an effect for financing sce-narios that cause an inconsistent consumption over the lifetime. For instance under full annuitisation, for the no old age care costs scenario the consumption is equal for every time period. This means the effect of a change in the time preference factor is cancelled out by the change it causes in formula 4.1. Table 5.5 shows that changes resulting from variations in the time preference factor are small; consumption only varies a percent or less for all scenarios.

Scenario: β = 0.96 β = 0.95 β = 0.97

CEC Collective ∆ CEC ∆ Collective ∆ CEC ∆ Collective Current e 21,566 e 72,299 + 0% - 2% + 0% - 1% No costs e 21,707 e 75,331 + 0% - 2% + 0% - 2% Full costs e 18,113 e 57,291 + 1% + 0% - 1% + 0% Lifetime max. e 19,487 e 65,658 + 1% - 1% + 0% - 1% Living costs e 21,361 e 67,239 + 0% + 0% + 0% + 1% Insurance e 19,459 e 28,561 + 0% + 0% + 0% + 3%

Table 5.7: Certainty equivalent consumption and collective financing for different time preference discount factors. All simulations assume the intermediate retirement capital ofe350,000.

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6.

Opportunities in the field of life

and health insurance

As described in Chapter 4, continuing the current system of old age care financing un-altered will lead to unbearable WLZ premiums for both the retired and the working population. The pay-as-you-go structure requires a lot of solidarity between generations. While working, a large part of the income flows to the elderly, and future generations must be trusted to finance future costs the same way. Since demographic developments have put pressure on this solidarity between generations, other systems of old age care financing are worth looking into.

6.1 A funded old age care system

Chapter 5 showed that saving a relatively small amount of 10% more retirement capital can cut the part of old age care costs that has to be financed collectively by half. This implies that a system where individuals can save up money to either finance their own old age care costs or to buy insurance for it upon retirement could relieve the stress off government finances. In such a system, a number of choices has to be made. A position paper by AG (2013) explores these choices, and the impact a funded old age care system has on government finances. The main choices are whether the funded system should be mandatory or only voluntary and encouraged, and if the savings should be considered as collective or individual claims. An individual saving system can be compared to the life-time maximum scenario as defined earlier. Simulations showed that this way of additional financing decreased collective spending by 7%. A collective system, such as the mandatory insurance scenario defined earlier has a much larger effect: it decreases collective costs by 49%. So a collective funded system would be much more sustainable when faced with increasing old age care expenditure than an individual funded system.

As is the case with pensions, a funded system provides protection against demographic shocks. A larger generation will save more money, and a smaller generation is not re-sponsible for the large generation’s old age care costs. A funded system does have some drawbacks; low interest rates, high inflation and disappointing investment returns could cause the savings to lose value and be insufficient to cover old age care expenses. As pro-posed in Kortleve (2013), the system could be layered, like the Dutch pension system. The first layer of such a system provides basic health care, and is financed collectively on a pay-as-you-go basis. This ensures that everyone will be taken care of, albeit in a more aus-tere manner than now. This first layer provides protection against inflation, inaus-terest rates and investment returns. On top of this, several old age care systems could be introduced, both mandatory and collective (second layer) and voluntary and individual (third layer).

Because older generations have paid their AWBZ premiums for a long time, and will not have any accumulated savings under such a new system, a gradual transition should ensure no generation is paying an unfair amount. Both systems would then have to coexist at first, causing WLZ premiums to go up on the short term. On the long run however, premiums will be much lower than the current projections, given steady investment returns and inflation and interest rates around the long term average. A full analysis of this transition problem can be found in the position paper by AG mentioned earlier.

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6.2 Combining life insurance and old age care insurance

With the current, abundant old age care financing system, private insurance for such costs does not exist in the Netherlands. In the United States, collective financing of old age care costs is often not sufficient. Here private long term care insurance does exist. The market for these insurances is small however, and premiums are generally high. The in-ability for this market to expand could be caused by information problems. Individuals often know their health status best, and the people buying insurance are those who expect to encounter large care costs. The vicious cycle of increasing premiums and attracting rel-atively more ‘bad risks’ is referred to as adverse selection. The insurer has to preform an extensive screening to determine the long term care risk of an individual seeking insurance, to determine an adequate premium. Insurance is often only partial, covering less than half of the actual costs.

At the same time, this adverse selection causes problems in the field of life insurance. In the market for private lifelong annuity products (the third pension pillar), a ‘bad risk’ is someone with a high life expectancy. At an undifferentiated premium, only healthy peo-ple will buy these products, as they expect to live longer than average and feel they can benefit from the insurance contract. This again leads to increasing premiums. Currently there are strict regulations on the screening that insurance companies can perform prior to issuing a life insurance product. Despite these restrictions, the hassle of going through the process can cause people not to seek insurance, even though it might be favourable for them.

As mentioned in Bodie (2002), creating a bundled risk annuity could resolve this prob-lem. An insurance product providing both a steady, lifelong income and compensation for possible nursing home costs would provide a pensioner with complete protection. Such a product would not only cause the (perceived) need for liquidity to disappear, the adverse selection effects of the life and health insurance part would offset each other. Healthier people benefit more from the lifelong certain income, and unhealthy people benefit more from the insured medical cost. To increase pensioners wealth, or decrease government spending through by lowering first pillar and WLZ payments, the pool of insured should be sufficiently large to have this offsetting effect. This can be achieved by offering such an insurance as an option to people facing their retirement. If costs and benefits are listed comprehensively by every insurance provider in a uniform way, such bundled risk annuities could quickly become a new standard for pensioners. Murtaugh et al. (2001) explore this opportunity into further detail.

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7.

Conclusion and Discussion

This study was set out to find ways of improving both the Dutch pension system and old age care system, by matching pensioners’ preferences to possible future old age care financing scenarios. The rapidly increasing number of elderly will put a large burden on the working population over the coming years if the current financing system is continued unaltered. Even though the strong desire for a solidary system makes introducing higher out-of-pocket payments difficult, a more sustainable system could provide stability for many decades to come. This would provide both young and old with more confidence in their retirement. Therefore the goal of this research was to determine what the optimal financial planning decisions are for pensioners, and how different, more sustainable future financing scenarios affect pensioners and decrease collective spending.

7.1 Optimal financial planning decision

A pensioner faces two main risks, longevity risk and the risk of high health care costs. Buying annuities is an efficient way to cover the longevity risk. The mortality premium an annuity yields makes it a very efficient financial product, especially at high ages where mortality is high. Annuitising all the retirement wealth does leave a pensioner without any liquidity, especially in the early stages of retirement. Possible out-of-pocket costs for old age care could decrease consumption greatly when no financial buffer is present. So upon retirement, the fraction of annuitisation is a deliberation between more efficiency or more liquidity. The life cycle model with its utility assumptions can express this complicated choice into one value of expected utility upon retirement, thereby providing a powerful tool for comparing retirement choices.

Simulation showed that both for a scenario without any out-of-pocket old age care costs as for a scenario where all costs have to be paid out-of-pocket, full annuitization yields the highest utility. The relative preference of annuities over liquidity does decrease when out-of-pocket costs are introduced, but the mortality premium is high enough to maintain optimality of full annuitisation. Because the rest of the simulated scenarios are all in be-tween no costs and full costs, the optimal financial planning decision for pensioners, given the used data and assumptions, is to annuitise their entire retirement capital for every scenario of old age care financing.

7.2 Sustainability

How sustainable are the proposed financing scenarios? Currently an average lifetime amount of e71,690 has to be financed collectively for every retired person according to the used data. The spread in old age care costs is high, the top 10% is responsible for more than half of the old age care costs. Because of this, scenarios that link out-of-pocket payments to realised old age care costs can only decrease collective spending by a small proportion. Reducing old age care spending to a sustainable level this way would greatly reduce the quality of life of the unlucky few that spend longer periods of time in nursing homes.

By collectively saving money for old age care in an equivalent way to the current pension system, collective costs can be reduced drastically. By saving only 10% of the retirement capital and converting this to an annual premium, costs can be reduced by as much as 48%. Such a funded old age care financing system is less vulnerable to demographic shocks,

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however low interest rates or high inflation could pose a new threat. Next to the funded part, a basic, pay-as-you-go part could provide protection from this, like the first pillar in the Dutch pension system.

7.3 Discussion and further research

Because inflation rates were not integrated into the life cycle model, sensitivity to changing inflation has not been investigated. Inflation protection is an important aspect of pensions, although over the previous years inflation compensation has proven to be difficult because of low interest rates and low coverage ratios arising from this. Inflation in health care costs is even higher than the general price inflation, causing the problem with old age care costs to be even bigger than described here. Further research could be done into the effects of inflation on these financing scenarios and the optimal retirement choices associated with them.

In line with related research the CRRA utility function was adopted in the life cycle model, although this might not be the best way of modelling the retirement phase. Be-cause the function is time separable, it neglects the effects of habit formation and the decreasing desire for consumption as age progresses. Including these behavioural aspects could improve simulation results. However, having a non time separable utility function means the Bellmann recursions can no longer be used, so then much more computational force would be needed to solve the life cycle model.

Over the coming years the retirement age is increasing incrementally to 67 years, and will be linked to the life expectancy from 2020 on. A higher retirement age could have an effect on the optimal retirement choices, as care costs could move closer to the retire-ment date leaving less time to build a buffer. However, as life expectancy rises and health improves, this effect might also be reversed. Projecting the results of this thesis into the future could be an interesting extension.

The question remains why annuitisation levels stay low, even though annuities yield high returns and out-of-pocket costs are limited. Adding a bequest aspect or higher surcharges for costs and inefficiency might explain this. Further research could focus on retirement products that decrease the perceived need for liquidity, are much more easy to understand and are offered on a large scale in a uniform way, or even as a default option. When pen-sioners get more value from their retirement capital, their consumption can be higher and social security has to support less people. This could stimulate economic growth, and de-crease the pressure on intergenerational solidarity. As the bundled risk annuity proposed in Chapter 6 might provide a solution to some of these problems, this idea could be explored into more detail.

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Financial planning decisions under changing long term carefinancing