Microsimulation for Public Policy. Experiences from the Swedish Model SESIM

Higher education in Sweden is free of admission charges and the government also provides loans and cash benefits to students. The sum of loans and benefits should in principle cover student housing, food, insurances and study material during forty weeks of a year, but in practice the cost of living for an average student has from time to time exceeded the support provided by the government. The cash benefit is about one third of the total, while two thirds is a loan.⁵ Before 2001 a student did not have to start repaying the loan until he/she had a job and labor incomes. Then 4 per cent of the tax assessed income was deducted as interest and payment towards the principal. If the loan was not fully repaid at the age of 65, it was remitted. ⁶

An issue of policy interest was thus to predict the share of students that would never fully repay their loans and the total cost to the government of this remittance. The first version of SESIM was used for this purpose. The study, Ericson and Hussénius (2000), utilized the potential of SESIM to simulate the whole life-cycle and compute life-cycle incomes net of taxes and the charges for the study loans. In cross-sectional studies grants to students who have no or only low incomes are typically shown to equalize the distribution of income, but in a life-cycle perspective this result is not that obvious. A second objective of the study was thus to evaluate how the life-cycle return to education depended on the length of studies and on gender.

Assuming that the conditions at the end of the 1990s prevail in the future, the model was simulated until it reached a steady state in which the number of births equaled the number of deaths and the population shares in each status were constant. Then people were followed until they died. In this way the results were not influenced by population changes and fluctuations in the supply of higher education. The simulations were also done using the assumption of no growth. The reason was that in a growing economy tax scales and benefits will have to be adjusted, and in the absence of rules for automatic adjustments one would have to predict what politicians would do in a distant future. To avoid this problem no growth was assumed.

Total income was defined in the following way: The sum of labor incomes, pensions, incomes of capital, study loans and cash benefits to students, less the sum of income tax, tax on capital incomes, repayments towards the principal of study loans, and interest on these loans. Labor income included earnings, sickness benefits, parental benefits and unemployment compensation. Pensions included old-age pensions and disability pensions, but not occupational pensions.⁷

Life-cycle income is the sum of all total incomes from the age of 16 until the person dies. They were only computed for those who were simulated to reach the age of 60. Table 1 gives life-cycle incomes by length of schooling and by gender using the assumption that the interest rate on study loans was 1.3 per cent. We find that males have higher life-cycle incomes than females and that more schooling increases life-cycle income. The excess rate of return to university training relative to no university is higher for females than for males. The explanation is that the difference in length of working life between those with a university degree and those without is higher for women than for men. Women also live longer and thus enjoy the pension benefits for a longer period.

Table 2 displays how the share of students with loans who get their loans remitted at the age of 65 depend on interest rate, gender and length of schooling. The results are quite sensitive to the assumption about interest rates. Females have much higher remittance rates than men. The explanation is that they work less in the market and get lower incomes. The rate also increases with the duration of the studies because the loans then increase in size and the time span with market work becomes shorter.

Even with moderately high interest rates these shares are pretty high and the total amount remitted is of about the same size as the total of all cash benefits. The government decided already in 2001 to make the rules governing repayments less generous, such that almost all students would have to repay their loans completely before the age of 65.

Which are the redistributive effects of taxes, transfers and non-cash benefits? To what extent do these effects depend on the length of the perspective – a year or a life-cycle?

To what extent does the redistribution performed by the public sector reallocate resources between individuals, and to what extent does it result in an intrapersonal redistribution, for instance from working life to old age?

These issues were studied using the capability of SESIM to simulate whole life-cycles. The results can be found in SOU 2003:110 (2003); SOU 2004:11 (2004) and in Pettersson and Pettersson (2007). The authors claim that a life-cycle perspective is indispensable when designing new taxes and benefits. If it is forgotten in favor of only a short-term perspective, one will not see that the long-run effects of a new policy might not become those intended.

Total income was defined as disposable income less indirect tax paid divided by an equivalence scale, plus non-cash benefits without equivalence scale adjustment. Life-cycle income was then defined as the mean of all total incomes over the life-cycle.

Table 3 displays how the Gini coefficient depends on income concept. Life-cycle incomes are more equally distributed than annual incomes, and total income is more equally distributed than disposable income, which in turn has a Gini coefficient that is about half of that of market incomes. Taxes and benefits thus have a major equalizing impact on the income distribution.

The authors also decompose the Gini coefficient into a weighted sum of concentration indices to investigate how the various income sources contribute to the total Gini. They find that most income sources, such as social security, transfers to family and children, student benefits and income taxes are progressive both annually and in the life-cycle. Market income, occupational pensions, expenditures for old-age care and indirect taxes are regressive.

The only major income source which shifts from progressive to regressive when one goes from annual incomes to life-cycle incomes is old-age pension. In a cross-section of annual incomes old-age pensioners usually have lower incomes than average, but in a life-cycle perspective high pensions are based on high incomes, and high-income earners also tend to live longer than average.

Even if almost all income sources have the same type of impact on the Gini coefficient for annual as well as life-cycle incomes, the relative contribution to the Gini depends on time horizon. For instance, the regressive effect of market incomes is less on life-cycle incomes than on annual incomes, while the regressive effects of disability pensions and income taxes are higher on life-cycle incomes than on annual incomes.

This study also analyzed who is gaining and who is losing over the life-cycle by the public sector. Those who get more transfers and non-cash benefits than taxes paid will have a net gain. In this part of their study the authors did not only include direct taxes but also indirect taxes and social security contributions to the extent that the sum of all taxes paid equaled all benefits received for each cohort. They thus assumed each cohort to be financially balanced over the life-cycle. Furthermore, all economic resources of a household were divided equally among all household members, ie no equivalence scale was used. Table 4 summarizes some of the findings.

There is redistribution from men to women. Women have lower incomes and thus pay less in taxes. They receive more benefits such as maternity and family benefits, and at least partly because they live longer, they get more health care and social care.

There is also a clear redistribution from high to low-income households. The latter pay much less in tax and receive more in transfer payments, while non-cash benefits are more evenly distributed.

There are clear age profiles in the payments between the households and the public sector. Taxes are predominantly paid in working age while benefits are received in the beginning and in the end of the life cycle. Child and family benefits and education come early while old-age pension and health and social care come at the end of life. The balance of payments from and to the public sector starts to become positive at the age of 55, but the cumulative net payments do not become positive until the age of 87. There is thus redistribution from individuals with a short life to those who live long.

Finally, the authors also investigated to what extent redistribution through the public sector resulted in transfers of resources between individuals. They found that only about 18 per cent of the total redistributed was truly a reallocation between individuals, while 45 per cent was annual intra-personal reallocation (benefits in a year were self-financed through own taxes in the same year) and 38 per cent life-cycle intrapersonal reallocation (old-age benefits were self-financed by taxes paid earlier in the life-cycle).

Almost 50 per cent of total production in Sweden is redistributed annually through the public sector. This is done by taxes and fees that are returned to the population in the form of benefits, transfer payments and public consumption. As we have just seen most of the annual redistribution is returned to the same individual – immediately or later in life, for instance as pensions – while a smaller share is redistributed between individuals.

Much of this redistribution builds on an implicit contract between generations. The working population pays taxes and fees to finance childcare, schooling, pensions, health care and old age care - services which are primarily consumed by younger and older people - hoping that their children will do the same when they grow into working age. When the size of birth cohorts varies the issue of redistribution between generations arises. For instance, the large post World War II baby boom cohorts had to put up with large school classes and a fierce competition to enter into universities. Their benefits per capita were thus reduced. These cohorts are now retiring and wondering if they will get the generous pensions they have been expecting. In another 10-15 years they will get to the age when they will need much more health care and social care. Will the government be able to continue providing these services? The children of the baby boomers, cohorts which are smaller in size, might ask if they have to pay for the increased provision of public services to their parents by much increased taxes.

To address these issues a study was started within the Ministry of Finance (Pettersson et al., 2006) with the task to assess the size of any redistribution between now living generations. They also tried to estimate the total life-time consumption potential of a birth cohort, defined as life-time income adjusted by any transfer to or from other generations through the public sector.

The idea was to compute a life-cycle balance account for each individual of all payments from the individual to the public sector and all payments from the public and services provided by the public sector. These balances were then summed for each birth cohort. An obvious problem is that we do not have observable data covering the whole life-cycle of an individual. The solution was to use the pieces of data that existed and supplement with simulations from the SESIM model. The cohorts studied were born in 1930-2009.

Individual longitudinal register data exist from 1968, but more completely from 1987. Transactions before then were imputed using the latest know distribution and totals from the national accounts as well as various other sources. All transactions after 2004 were simulated by SESIM.

The motivation for this micro(simulation) approach was the following:

1. Even if a cohort had a positive (negative) balance, all cohort members might not have it. There might have been some groups within the cohort which had been in advantage (disadvantage) while others had not. With a microsimulation approach one can analyze the distribution within cohorts.

2. The precision in the simulations of future taxes and transfers becomes much better in a microsimulation approach compared to a more aggregate one, because most tax and benefit systems are non-linear.

3. The microsimulation approach permits the analyst to quite flexibly study the balances for other subgroups than birth cohorts, which makes it easier to understand the outcome and make error corrections.

There are a number of fundamental problems the analysts had to address, and the reader is referred to their report for a discussion. Here I will only briefly mention a few. First, all transactions with the public sector, whether they are with the business sector or a foreign agency, are in the end considered to benefit the private consumer. For instance, expenditures for the defense, roads, etc are allocated as benefits across all individuals. Likewise, all incomes of the public sector are debited to the household sector.

Second, some kind of discounting is needed to make balances from different years comparable. It is relatively easy to index by a consumer price index⁸ , but one might also like to correct for the real growth of the economy. This becomes especially clear when one compares consumption potentials.⁹ The authors have chosen to discount with an index of GDP per capita in current prices.

Third, some incomes (and benefits) are individual while others are given to the household. In this study the authors have chosen to assume that there is redistribution within the family such that all family members including children live on the same standard. All incomes are thus allocated equally to all household members and likewise for public consumption. If, for instance, a child goes to a public daycare center at a cost for the taxpayers of say 100 000 SEK per year, these 100 000 are split equally between all family members.

SESIM only simulates the household sector incomes, taxes and transfer payments. The share of the public sector not covered by SESIM was simulated using a macro model called FIMO, and the result was distributed to the individuals in the household sector. It is a model based on the national accounts which simulates annual public incomes and expenditures at a rather detailed level for the government, local governments and the pension system. It also includes the most important macro-economic variables such as GDP, the labor force, prices, interest rates etc. and the population by gender and age groups. The core of FIMO is an aggregate representation of the rules for taxes and transfers. The model does not allow the population to adjust endogenously to changes in taxes and benefits, but such changes have to be imposed on the model exogenously. SESIM and FIMO were run in parallel using the same exogenous assumptions about population changes, productivity, prices and interest rates. For instance, the real wage rate was assumed to increase by 2 per cent annually, the labor force participation rate was set to 80 per cent in the age bracket 16-64, consumer prices were assumed to increase by 2 per cent annually and the interest rate on financial assets was 3 per cent. The sum of all individual taxes and transfer payments simulated in SESIM did not always agree exactly with the corresponding items in the national accounts and in FIMO. The difference was then distributed equally across all adults.

All simulations assumed unchanged policy, ie the tax system and the rules for transfer payments that applied in the beginning of the current century were assumed to remain unchanged. However, some transfers are not indexed, and some are only indexed by the CPI. In order not to decrease the welfare state all transfers and benefits were indexed by the annual average change in wage rates.

The simulations also assumed that the public finances were stable throughout the entire simulation period, ie the public debt as a share of GDP should be about the same at the end of the simulation period as at the beginning. The budget target of a surplus of 2 per cent over a business cycle was also enforced. Real welfare expenditures per capita were assumed unchanged while the effects of the demographic changes were allowed to go through fully. The budget target was maintained through the tax changes.

The welfare state has grown and the expenditures for transfer payments and for public consumption have increased. To finance the growth of the welfare state taxes have increased from about 10 per cent of GDP in the 1930s to about 50 per cent in the 1980s. After that and in the simulated future the GDP shares of taxes, transfers and public consumption stay approximately constant.

Both transfer payments and public consumption primarily benefit the elderly. The public pension system has expanded and become more generous and health care and old age care has also increased. Most of the tax burden is, however, carried by the working population, in particular those in the age bracket 40-65.

Figure 2 displays the public sector balances by birth cohort. One might have expected some to be negative and some positive, but they are all positive. The explanation is that the public debt was assumed to be a constant share of GDP, and in combination with economic growth increasing debt makes this result possible. We should thus compare the relative size of these bars. The generations with a relative gain are those born in the 1930s, 1950s and 1980s, while the large baby boom cohorts of the 1940s and 1960s are relative losers. Those born in the 1930s paid relatively low taxes but were able to get the benefits of the increasing welfare state. Those born in the 1980s paid relatively little in tax because they started to work late and were assumed to retire early and use their increased longevity for leisure. The generations of the 1950s paid marginally more in taxes compared to those born in the 1940s but got more both in transfer payments and public consumption. The baby boom cohorts of the 1940 worked a rather long life and thus paid relatively much in tax, while they had to compete for the benefits from the public sector.

Figure 2

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The results suggest that the increased pressure on the public sector from the large cohorts has not been met by increased taxes but rather by a reduction in the benefits. The same is true for the children of the baby boom cohorts, those born in the 1960s. The youngest cohorts are also losers in these computations. The explanation is that they pay relatively high taxes but get less of future pension benefits. They were assumed to retire at the age of 65, and if the retirement age does not increase with increasing longevity the current pension system will pay out lower pensions.

Within all generations there are individuals who gain from the public sector and others who loose. In fact, this intra generation redistribution is much larger than the inter generation redistribution.

This study also shows that the average consumption potential by cohort – adjusted for price changes and growth – is completely dominated by the market incomes, while the modest intergenerational transfers through the public sector means relatively little. The results suggest that those who were born in the late 1930s and in the 1940s had a little higher consumption potential than the other generations. The explanation is that these generations came out from the schools into a labor market with a high demand for labor and very little unemployment. They got well paid jobs, were able to save and borrow to buy a home, which then increased in value. Although the baby boomers might have lost in the redistribution game through the public sector they were not losers in a wider perspective.

Most of the taxes an individual pays in a life-time go back to the same individual in the form of transfer payments and public consumption. Only about 20 per cent of the taxes an average individual pays result in redistribution to someone else, and most of this redistribution goes to someone in the same generation rather than to someone in another generation.

This study is limited to redistribution through the public sector and does not include private transfers such as inheritance and inter vivo gifts. Nor does it include indirect behavioral effects of public policy, for instance, increased public expenditures on schooling, which increases the educational standard of the population, might lead to different decisions as to work, incomes and wealth accumulation. The informal sector is not included either. In the older generations it was common among women to work at home. Not including this kind of informal work underestimates the consumption potential for the older generations.

Simulating the future with SESIM and FIMO made it possible to fill in the gaps of missing data. Because both models could be calibrated to the same demographic scenario and used the same macro-economic assumptions, it was possible to run the two models in parallel. A closer integration of the two models might have opened for a more realistic distribution of public consumption than equal distribution to everyone.

The results obtained also depend on assumptions about the costs for health care and public care and in particular on the assumption that everyone retires at 65. The increase in the costs of health care and social care is difficult to predict, because they depend on the introduction of new drugs and new treatments and on the ability of the care organizations to increase productivity. New drugs and new treatments are often expensive, but they might increase productivity.

The assumption that everyone, who retires with old-age pension, does it at the age of 65 is unrealistic. The share of people who retire early is not small. It would have been interesting to allow people to retire both before and after 65 in the simulations. SESIM now includes a model with this facility (c f section 3.5). If the incentives of the new pension system and the current policy to give large tax rebates to those who work after the age of 65 make the younger generations stay longer in the labor market, the redistribution between generations would have come out differently.

After the introduction of the new pension system research and policy interest has focused on the behavior of the system, in particular when the large baby boom cohorts retire and age. Interesting issues were: What share of GDP will the pension expenditures take? Will the system stay in financial balance, or will the brake reduce pensions? Which compensation rates will the retired get, and will the inequality of pension incomes increase?

SESIM has been used to simulate the future path of the pension system. This has been done for the European Union Ageing Working Group (see for instance Sundberg, 2006), the medium-term planning of the Ministry of Finance (SOU 2004:11, 2004, p. 11), in preparing for a new administration of the pension system (SOU 2006:111, 2006, p. 111) and by independent scholars (se for instance Flood, 2007 and Section 3.5 below).

The results show that the expenditures for public pensions will take an increasing part of GDP as the baby boom cohorts retire and will reach a maximum of almost 15 per cent around year 2040 (Diagram 6.2 in Sundberg, 2006). With the assumptions made the pension system will generate a surplus every year until 2050, although a declining one, and the financial assets of the system will thus increase. According to these simulations it would not become necessary to hit the brake. However, these simulations are now history, because the current financial and economic crisis has changed the scenario completely and the brake will become enforced already in 2010.

The simulations also show that the compensation rate will decrease for the younger generations unless they chose to retire later. With increasing longevity, the notional pension capital will have to cover a longer period and the annual pensions will then have to decrease.

Flood (2007) demonstrates that variations in retirement age and return on financial assets are more important for the young cohorts than for the old. He computed replacement rates for disposable income¹⁰ and showed that for people born in 1940 and with incomes in the middle of the income distribution, the replacement rate at the age of 68-72 was 73 per cent if they retired at the age of 63, but 81 per cent if retired at 67 – a difference of 8 percentage units. For people in the same income class but born in1960, the replacement rates were 56 and 66 respectively – a difference of 10 percentage units.

If the retirement age was 65 but the annual return to financial assets was either 3 per cent or 7 per cent, the replacement rates for those born in 1940 were 73 per cent and 76 per cent respectively – a difference of 3 percentage units. For the cohort of 1960 the replacement rates became 55 and 73 percent respectively – a difference of 18 percentage units!

The explanation to the differences between the two cohorts is that the 1940 cohort mainly gets its pensions according to the old system and time has not permitted them to accumulate large funds in the funded part of the new system.

The focus in SESIM on demography, income generation, taxes and pensions makes it a good tool to analyze the properties of the pension system and the outcome for the retired compared to those working.

The practice in the Ministry of Finance to restrict the retirement age to be the same for everyone highlights the properties of the pension system but lacks in realism. Similarly, the return on financial assets is assumed to be the same for everyone, while data suggest that there is a large individual variation in return. This becomes especially important in the simulation of the funded part of the pension for the young cohorts, because its contribution to the total pension will become much larger for them compared to older cohorts. There is thus reason to believe that we now underestimate the individual inequality in pension income.

SESIM could relatively easy be changed to accommodate these features. In fact, varying retirement age is already allowed in the version of SESIM discussed in Section 3.5 below, while individual differences in return remain to become implemented.

Like most Western countries Sweden faces population ageing. For instance, the old-age dependency ratio (population 60 and over relative to population 20-59) will increase from about 0.4 in year 2000 to about 0.65 in 2050 according to Eurostat. Statistics Sweden predicts that the number of women who are 65+ will increase by 48 per cent from 2000 to 2040 and the number of men who are 65+ by 79 per cent. Those who are 80+ will increase even more, the number of women by 58 per cent and the number of men by 118 per cent.¹¹ Even if the number of men is predicted to increase faster than the number of women, the share of elderly women will still exceed that of men. The share of 80+ women was 65 per cent in year 2000 and is predicted to become 57 per cent in 2040. Even if these numbers suggest a major shift in the age distribution from working age to old-old age, the situation of Sweden is not that extreme compared to, for instance, the South European countries and Japan.¹² Their age pyramids will by 2050 have transformed into urns!¹³

Population ageing will put burden on the pension system, the health care system and on social care. The expenditures for both public pensions and occupational pensions will increase quite a lot, while the population in working age will remain almost constant. This raises the question whether the pension system will be able to deliver the pensions people are expecting or if the compensation rate will decrease. Will the retired share of the population maintain its income standard relative to the working population?

Even if retired are able to maintain their income standard on average, the new pension system shifts more of the burden of risk from the entire collective to the individual pensioner compared to the old system. We may thus in the future face an increased problem with old-age poverty, which of course will become even worse if the relative income standard of the retired decreases.

Pensions are definitely the most important source of income for the elderly, but many of them also have capital incomes, and compared to previous cohorts the baby-boom cohorts are relatively wealthy. To get a more complete picture of the standard of living for the elderly one would not only have to simulate their future pensions, but also their wealth.

The age distribution of health care expenditures is heavily concentrated to the elderly. An increase in the number of elderly, in particular old-olds, will thus lead to a rather dramatic increase in these expenditures unless there will be a matching increase in the productivity of the health care industry.

Similarly, the expenditures for social care are much higher for the old-olds than for those in the age bracket 65-75. Those who need to be cared for in special homes for elderly, in particular those who need care 24 hours a day, generate very high expenditures for the local municipalities. For this reason, one has tried to shift from institutionalized care to help at home, ie one or more times a day attendants visit the old person at home to help with dressing, food and cleaning. The result is that almost everybody who today lives in so called special housing is demented.

A large share of the care for elderly is still done by relatives and neighbors, in particular by wives to elderly men and by children. Will it in the future become possible to for relatives to continue doing so, and would it become possible to shift even more of the care burden from the public to relatives?

An important issue is how we in the future will finance the expected increase in expenditures for health care and social care. Will tax increases become necessary, or can we shift more of the expenditures to the users of the care services by increasing the user-fees? If we do so, will those in most need of care be able to pay for it?

Are there other policy measures which could ease the balance between the future demand for resources and the supply? Policy measures which have been discussed are an increase in the pension age, activities which increase the health status and survival of the elderly, increased incentives for kin to provide care for their elderly, measures to increase labor supply such as increased immigration and incentives for those on sick benefits and disability pension to return to the labor market, and finally, measures to increase economic productivity.

Around year 2000 an independent group of scientists decided to analyze these policy issues. The project got the nick name “The old baby-boomers”. Our choice of scientific approach was guided by the following considerations. We needed an approach by which we could simulate the consequences of population ageing for at least 40 years. We would thus have to rely on a demographic model which in a realistic way could age the Swedish population. Our approach must also include a detailed and realistic replica of the tax and benefit system, and in particular the pension system. The approach chosen should not only be able to simulate means, but whole distributions, and at the same time provide consistent macro aggregates. It must also be able to capture many different aspects of behavior such as labor supply, geographical mobility, demand for housing, demand for health care and social care etc, and tell us to what extent the increased demand for care will become balanced by increased labor force participation, work, incomes and taxes. We should be able to focus on selected target groups, such as the poor or those in special need of care and get estimates for these groups which were consistent with the estimates for the rest of the population. To accommodate this we needed a model structure which captured the heterogeneity in behavior of people. We also wanted to follow selected birth cohorts over time to see if their situation changed as they aged, and finally, it was important to be able to time any peak in the demand for care or in the incidence of poverty.

Taking all this into account there is hardly any better approach than a microsimulation approach. But to build a new large scale microsimulation model is a major undertaking which requires a team of scientists from different academic disciplines representing various types of expertise. It takes time and large resources, which we did not have. For this reason, we looked for an already existing model which could give us a basic demographic model, the tax- and benefit system and a computer infrastructure. The SESIM model of the Ministry of Finance satisfied our demands, and we were fortunate to reach an agreement of co-operation with the ministry, which permitted us to use their model and also to extend it with new submodels. Implicit in our agreement was that the Ministry could use any additions to SESIM that we would design.

The version of SESIM that existed at the turn of the century missed many of the behavioral models we needed to analyze the various aspects of population ageing. Our first task was thus to start a number of studies to design and estimate the models we needed. We have supplemented SESIM with new models which simulate the following aspects of individual or household behavior: a) the progression of health as people age, b) sickness absence, c) early retirement with disability benefits, d) old-age retirement, e) geographical mobility and tenure choice, f) incomes of the elderly, g) wealth of the elderly, h) utilization of hospital care, and i) utilization of old-age care. A detailed description of this work is given in Klevmarken and Lindgren (2008). Here we will only briefly review three models to give the reader an idea of the types of models used and of some of the special problems involved in designing models for microsimulation. The three models are the models for utilization of hospital care, retirement and the stocks of wealth.

Almost all hospital care in Sweden is publicly provided at small user-fees. There is thus no regular market for the services of hospitals. Excess demand is manifested in queues. Politicians may or may not react to these queues by increasing resources to the health care sector. When estimating a model to capture the utilization of the services of hospitals the resulting estimates will thus in general depend both on the demand and supply of these services. When using such a relation for simulations one has to assume that the public will accommodate an increased demand in about the same way as they have done historically.

In SESIM we have estimated a model for the utilization of inpatient care, see Bolin et al. (2008a) The dependent variable is the number of days a person has spent in a hospital in a year. Most people never spend time in hospital while for a few we record very many days. The distribution is thus much skewed with a high frequency at 0. The kind of model chosen was a so called zero-inflated negative binomial model. Explanatory variables were variables capturing health status, number of inpatient care days last year, age, schooling, if divorced, relative income (individual income relative to population mean), geographical region, if born in Sweden, gender and an interaction between gender and relative income, and finally if the respondent is female and had a child less than one year old. The choice of variables was guided by previous literature and experience, see Bolin et al. (2008a). One might note that relative income was used rather than real income. In microsimulation it is often problematic to use income as explanatory variable, because if there is economic growth and the simulation is carried out for a long period, the income variable might drive the results completely at the end of the simulation period. For this reason we have frequently opted for a relative income measure.

The model was estimated separately for those above 50 years and for those 50 years or younger. We also estimated models without the lagged dependent variable, because there were no data about inpatient care in the 1999 LINDA data set. We thus needed to impute this variable in the start year 1999. The static model was also used when new individuals entered the population.

Figure 3 displays the utilization of inpatient care by age and gender for selected birth cohorts. The diagram shows the sharp increase in utilization among the old-olds, in particular for men, but also the simulation uncertainty at the end of the life-cycle when relatively few have survived.

Figure 3

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Figure 4 displays the evolution of the total number of inpatient days by gender until 2040.

Figure 4

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The retirement models distinguish between retirement with disability pension and with old-age pension. The former is considered primarily driven by ill health, while old-age pension is at least partly driven by economic incentives. Individuals who have been ill for a long time and are unable to work can get disability pension. At the age of 65 it is automatically turned into old-age pension. The typical pension age in Sweden is 65 and the pension systems have been designed such that people normally will retire at this age. It is though usually possible to take an early pension already at 61, but at a reduced compensation rate. The Swedish pension system has three “pillars”: the social security pensions which usually give a compensation rate at about 60 percent; the occupational pensions which give another 10 per cent for most retirees, and private pensions which are equivalent to private savings.

Before September 2001 most employees had to retire no later than at the age of 65. Contracts between employers and unions gave the employers right to discontinue the employment contract for those who reached this age. Parliament has now taken a law which shifts this threshold up to 67. The peak age of retirement is still 65, however. The old contracts and social conventions thus determine this peak, while early retirement is a decision subject to economic incentives.

Early retirement via the disability insurance was modeled using a discrete choice model (Bolin et al., 2008b). The choice of explanatory variables reflects our view that exit from the labor market via the disability insurance is involuntary and determined by the health status. The explanatory variables thus capture health risks rather than economic incentives.

The literature on retirement suggests a few different approaches to model old-age retirement, see for instance the discussion in section 4 of Bolin et al. (2008b). We might distinguish between the life-time budget constraint approach, the option value approach and the hazard model approach. In the life-time budget constraint approach each individual faces a discontinuous or kinked life-time budget constraint and is assumed to choose the retirement age which gives the utility maximizing combination of leisure and life-cycle income. In the option value approach each individual is assumed to compute the expected gain (loss) in utility from postponing retirement one or more years. The hazard model approach is a reduced form approach which usually only considers information one period ahead. The probability to retire for a person who is currently active is typically a function of annual wage earnings, pension accruals and pension wealth, health status, age and gender.

The first two approaches are very computer intensive, and for this reason difficult to include in a microsimulation model. Even with modern fast computers simulations would take too long. The limited information available in SESIM and its intrinsic chronological structure also contributed to our decision to use a discrete choice model for early old-age retirement as well as for retirement via the disability insurance.

When looking at data the research group discovered that some individuals, who retired before 65, got a higher pension than their contracts stipulated. A closer analysis of the retirement situation revealed that some employees, typically in the age bracket 55-65, got early retirement offers from their employers, so called “golden handshakes”. This was a way to get rid of white-collar employees and reduce the expenses for both salaries and pension contributions, which tend to increase with increasing age. To estimate a discrete choice model for the private decision to retire without taking these offers from employers into account would in general bias the estimates. For this reason, a model for the probability to get an offer was also estimated and made part of the entire model structure.

When simulating the retirement model, we start with withdrawal through the disability insurance. The population at risk consists of everyone in the labor force. After those who are simulated to get disability insurance have been dropped from the labor force, those who remain are at risk for early old-age retirement. Those who remain in the labor force at the age of 65 are all assumed to retire at that age. The model can be simulated with and without early retirement offers from employers. It is also possible to extend the age span for market work beyond the age of 65.

Figures 5 and 6 give examples of simulation output. The first of these figures show the simulated population shares in work, old-age retirement and on disability insurance from year 2000 to 2040. The share in old-age retirement will increase from about 18 per cent in 2000 to about 25 percent in 2040, while the share in work decreases from 45 per cent to 42 per cent. The marginal decline in the share of disability insurance is probably the combined result of population ageing and the fact that disability insurance is converted into old-age pension at the age of 65.

Figure 5

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Figure 6

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Figure 6 displays the evolution of the average retirement age under two alternative scenarios. One is the base scenario when everyone is assumed to go into old-age retirement no later than at the age of 65. The alternative scenario extends this age limit to 70. In the first case the average retirement age remains at a level just below 64 years. In the alternative scenario the retirement age grows to a steady state between 66 and 67 years.

When simulating the evolution of the distribution of wealth it is not possible to use a conventional portfolio allocation model that can be estimated from a single cross-section of data. Such a model would give too much volatility in the simulated data. We needed a model which uses information about the stock of assets last year and then simulates any changes. We also needed a model which at least distinguishes between owner occupied housing, tax-deferred pension savings, study debts, other debts and other assets, because taxes and benefits would depend on this categorization. From an analytical point of view, it might have been desirable also to distinguish between risky and less risky assets, and one might also have preferred to distinguish between mortgages and consumption credit. Data limitations and the fact that the main focus of our study did not require a detailed brake down of financial assets made us settle for the following groups of assets: owner occupied housing, other real estate (mostly vacation houses, farm- and forest properties, and apartment complexes), tax deferred pension savings, other financial asset, study loans and other debt.

The distributions of these assets are heavily skewed, and many households do not hold all of them. One has to consider these properties of data when formulating and estimating models, so the simulated distributions are able to replicate them. Figure 7 gives a view of the model structure and the simulation path. Financial wealth precedes real wealth and debts because if a household has financial assets, it might influence any decision about buying new property and taking up debt. The model also systematically distinguishes between those who have an asset and those who do not. In the first case a dynamic model is applied, while in the second a two-part model is used. The two-part model includes a discrete choice model which determines the probability to acquire the asset and a regression type of model which determines the amount acquired. Most of these models were estimated from longitudinal LINDA data.

Figure 7

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Our efforts to estimate a dynamic model for other real estate were not successful. The process was dominated by few but rather large changes in holdings and it turned out that a simple random walk replicated observed data as well as any model we could come up with. Owner occupied housing was treated somewhat differently. A geographical move implies new housing and for this reason decisions to buy a new house or an apartment were modeled and simulated jointly with these moves. Also households which remained in the same area were exposed to a nonzero risk of buying new housing. If a household was simulated to buy a new house or an apartment the market value of the property was simulated as a function of geographical area, floor area, financial wealth, income and demographic variables. This is thus a reduced form relation capturing both the two most important supply variables (geographical area and floor size) and demand variables (wealth, income and family type)

Study debts are loans offered to college and university students by the government. We assumed that the take up rate was 100 per cent and that students borrowed as much as they were allowed to do. Study debts are increased by a certain interest rate determined by the government, and repayments of principal and interest depend on the former student’s income according to rules programmed into SESIM. Thus, no stochastic model was thus applied in this case.

To model changes in other debt than study loans was not that simple because the distribution of change in debt had rather fat tails. For instance, the median change was 0 and the mean 13 000 SEK, while the largest observed increase was 77 millions and the largest decrease 97 millions! The final decision became to estimate a sequence of models: A random effects probit model for the probability of taking up a loan if the household had no loan previously, a random effects GLS regression of the logarithm of new debts given that the household had no debt in the previous year, a random effects probit model for the probability to stay in debt, and a random effects GLS regression of the logarithm of debt for households that continue to have debts.

All models were estimated with data at the 1999 price level, and all simulations were also done at this price level. Afterwards assets and debts were inflated by exogenously imputed interest rates and price increases on real property.

Figure 8 gives an example of the results of these simulations. The average cross-sectional age-wealth profile for the years 2000-2004 shows the well-known reversed U-shape with a peak at about 65. The simulations then show that the peak moves to the right and disappears at the end of the simulation period.

Figure 8

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Our basic simulation scenario includes certain assumptions about the macro indicators which are fed into the model exogenously. For the period 1999-2004 we have used observed values. After 2010 the following assumptions apply:

• Annual rate of change in inflation (CPI): 2.00 %

• Annual average increase in real wage rates: 2.00 %

• Short-term interest rate: 4.00 %

• Long-term interest rate: 5.00 %

• Dividends: 2.50 %

• Rate of change in prices of stocks and shares: 3.75 %

• The market value of single-family houses: 3.50%

For the period 2005-2010 these rates were allowed to adjust from the last observed rate to the constant rates above. Demographic changes were aligned to the basic predictions from Statistics Sweden and the average unemployment rate was aligned to the medium-term forecasts from the Ministry of Finance.

In addition to this basic scenario, we have run a number of alternatives to investigate the sensitivity of the results and explore policy alternatives. They will be explained below at the same time as key simulation results are explained and commented.

Let us start with the health status of the population, which is measured with an index based on self-reported health and self-reported ability to carry out work and other tasks. It takes on four values ranging from full health, good health and bad health to severe health. The simulations show a marginal decline in health status among the elderly as we approach year 2040. In the age bracket 50-74 the share with severe illness increases from 7 per cent to 10. Among women who are 74+ the share increases from about 28 per cent to 35. The health of the oldest men also decreases a little but not as much as for women. (See Figure 9!) These changes reflect the observation that the current health status among young adults is somewhat less than it was for the same age group of previous cohorts, due to for instance, increased obesity, allergies and mental problems.

Figure 9

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The increased number of elderly and the (marginal) decrease in health status will increase the demand for health care. The first panel of Table 5 shows that the average number of days in hospital per year and person 65+ will increase marginally. This is a result both of the increase in the average age of this group and of the decrease in health status. The table also shows the result of two alternative scenarios. First, we increased the health progression of the elderly by adjusting the health index for those aged 40-90 proportionally to their age minus 40 and the calendar year minus 2000 in such a way that a 90-year-old person in 2040 will have the same health as an 80 years old in the base scenario. This implies that the improvement in health comes gradually and is largest for the elderly. The result was that the average number of hospital days was simulated to decrease rather than to increase. In this scenario the death rates were, however, kept at their old age-specific values. If health status increases one might expect that the death rates would decrease. For this reason, the third scenario combines the increase in health status with a decline in age-specific death rates. After year 2010 and after the age of 35-40 each individual was assumed to have the death risk of a 5-year younger person in the base scenario. To avoid excessively old persons the death risks after the age of 100 was eased upwards towards the levels of the base scenario. The result is a rather dramatic increase in the average number of hospital days. The explanation is that we get an agglomeration of very old persons at the end of the simulation period.

The second panel of Table 5 shows the combined effects of the change in the average number of days and the population increase in the age segment 65+. The total number of days in hospitals for people 65+ will in the base scenario increase by about 70 per cent, in the improved health alternative only by 43 per cent, and when the death rates decrease the number of hospital days increase by as much as 142 per cent. The assumed decrease in death rates might be exaggerated, but these simulations show that the results are rather sensitive to the death rates. If the health status of the population improves such that people survive to very old age, but they then will be in need of much health care, we will in the future experience an explosive increase in demand for health care from the old-old.

We will also expect an increase in social care of the elderly. Figure 10 shows the simulated number of elderly with around-the-clock care for the period 2000-2039 by age group in the base scenario. We find that the number of old people who get this kind of institutionalized care will increase from about 70 000 to 160 000. It will increase in all three age groups but most among the very old. There are similar but not quite as dramatic changes for home help, see Figure 11.

Figure 10

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Figure 11

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Using data on average cost per person and hospital day and annual averages per person for institutionalized care and home-help, and the assumption that these numbers will increase by the average increase in the real wage rate, we have computed total expenditures for these three forms of care, see Table 6. The table gives estimates for three years. We find that the total will increase in real terms by a factor of 3.6. To understand how much this is we should have been able to simulate the future budget for the public sector, but SESIM is not able to do it. The model, however, simulates how much everyone pays in direct taxes, and we have thus put the total of these expenditures relative to the sum of all direct taxes from the household sector. The result is displayed in the second column of Table 6. We find that the expenditure share will increase from about 20 per cent in 2000 to 36 per cent in 2040. This suggests that the increased expenditures for health care and social care due to population ageing will become an increased burden to the public budget.¹⁴

Let us now turn to the income and wealth of the elderly. Figure 12 shows the simulated average taxable income for retired relative to the average taxable income of the working cohorts of age 20-64 for a few selected birth cohorts as they age. Everyone is assumed to retire no later than at the age of 65. At this age relative income lies in the interval 75-80 per cent. As the elderly age, their relative income decreases. The drop in income around the age 70 is a result of our assumption that the funded components of the pensions are paid out during the first five years. An individual can choose to have them paid out for a longer period or life-long. Had we chosen such an alternative the kink at age 70 had been smoothed. We find that the relative income of these cohorts decreases down to about 50 per cent at the age of 80. The explanation is that the pension system is “front loaded”. Pensions are indexed by a wage rate index to make them follow the income changes of an average worker, but each year 1.6 percentage units are subtracted, which implies that the income standard of the elderly will deviate more and more from that of workers as the elderly age. We might also note that the curves of the older cohorts lie higher than those of the younger. The main explanation is that the younger cohorts will on average live longer and their pensions will thus have to be paid out for a longer period. Their annual pension will then have to decrease, unless they retire later.

Figure 12

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Because the group 65+ age and because younger cohorts get relatively lower pensions the relative income of the whole group 65+ will decrease. This is seen in Table 7, but for a different income concept – equivalized disposable income. Relative income decreases from about 70 per cent in 2000 to about 55 per cent in 2040 in our base scenario. If we allow people to work in the market until the age of 70 the situation improves. Relative income then only drops to about 62 per cent. The explanation is that the group 65+ will have market incomes, which are higher than pensions, for a few more years, and that the pension will be paid out during a somewhat shorter period.

The low relative income at the end of life raises the issue of poverty. We have defined poverty as having an equivalized disposable income less than 50 per cent of the median of the adult population. Figure 13 shows the poverty rate for a few cohorts as they age. It is very low among working age people, just a few per cent, but increases a few years before the typical retirement age of 65. In the age group 55-65 there are relatively many on disability pension and on early old-age pension, which are relatively low. Immediately after 65 the poverty share goes down because the general old-age pension with a guaranteed minimum raises the income standard. As people grow older the poverty rate increases because their relative income standard decreases as demonstrated above. The youngest cohorts have the highest poverty rate for the same reason that they have the lowest relative income. When they get into the 80:s the poverty rate gets as high as 20 per cent.

Figure 13

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The resources of the elderly are not only determined by their pensions and other incomes but also by their assets. The baby boom cohorts are relatively wealthy, a wealth that could be liquidized and used for consumption, health care and social care. In SESIM we have simulated the evolution of the wealth distribution and we have already seen a snapshot of the results in Figure 8. The simulations show that the peak is pushed to the right and up, and at the end of the simulation period there is almost no peak at all. The curve is an increasing trend. This implies that SESIM simulates that the elderly will keep their wealth rather than to consume it. The shift in the peak is not just an artifact built into SESIM. It can be observed in data, see Figure 1 in Klevmarken (2006).

An important social policy issue is if those in most need of care will have income and wealth that could cover their expenditures for these services, or if the neediest also are those with the smallest resources. In SESIM we can distinguish between those who use care services and those who do not, and we can also see what income they have and how wealthy they are. Table 8 responds to the question: “What income do those in most need of care have?”

Most elderly belong to the first or second income quartile. In year 2000 46.7 per cent of those who did not use any social care belonged to the first income quartile, ie the 25 per cent with the lowest incomes, while as much as 65-70 per cent of those who used public social care belonged to the same quartile. Our simulations suggest that the situation will become even worse in 2040. By then 75 percent of those who use public social care will belong to the first income quartile. These results suggest that those who are in need of public social care will not have the incomes needed to pay for these services, either privately or by increased taxes.

Table 9 shows, however, that the elderly are relatively better off in terms of wealth. In 2000 40 per cent of those who did not use any care belonged to the 4^th quartile and about 30 per cent of those who used home help or were institutionalized. Only a few per cent belonged to the first quartile. In 2040 the inequality of the distribution is simulated to increase, the population shares in the first and fourth quartiles increase.

From these results it is obvious that we will get a rather large group which is income poor. Some of them will however have some wealth, but that is not true for everybody. At the end of the period the share of the elderly that will both have low incomes and no wealth is simulated to increase. Table 10 shows more specifically the poverty rate among the elderly when we define poverty as having an equivalized disposable income less than 50 per cent of the median equivalized income of the entire population and an equivalized net worth less than 50 per cent of the median equivalized net worth of the whole population. Simulation results are shown for the base scenario and when the maximum pension age is increased from 65 to 70 years. In 2000 the poverty rate was low, about 1.6 per cent for all elderly 65+. It was about 1 percentage unit higher among institutionalized elderly. According to the base scenario these numbers will increase to 2040. The poverty rate for all elderly is simulated to become 14.5 per cent and for those who use social care one or two percentage units higher. If the maximum pension age is increased and people chose to retire later the poverty rate will not increase as much. In our alternative scenario we would get about 8 per cent poor among all elderly and among the institutionalized about 12 per cent would become poor. These numbers are also sensitive to our growth assumption. Higher growth and lower unemployment will reduce poverty while lower growth and higher unemployment will increase it, see Klevmarken (2008b) Table 20.

These results suggest that we will get a relatively large share of elderly who will not have the means to pay for the health and social services they will need. Today family members and kin provide a large share of the help to elderly. Wives in particular help their husbands and daughters help their old mothers. Will this resource be available also in the future and help to ease the expected increased pressure on the public sector? To answer this question we have simulated the domestic migration between different parts of the country and measured how closely children live to their parents. A necessary condition for being able to help one’s parents on a more regular basis is that the child lives within commuting distance to the parent. Figure 14 shows how the share of elderly who live in commuting distance from the nearest child will decrease. The explanation to this result is that geographical mobility has increased. Young people move to get education and never return home, and young people also leave the rural areas and move into the major metropolitan areas, where it is easier to find a good job. When we looked more closely at the numbers behind Figure 14 we found that the share of single fathers and mothers who lived close to their children was smaller than the share of couples. Unfortunately, singles are in more need of help than couples. Our simulations thus suggest that we cannot expect children to do more for their parents than they already are. On the contrary, they can rather be expected to do less.

Figure 14

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• If the same share of elderly as currently will get access to health care and social care in the future, the supply of these services would have to increase at the same rate as the age groups concerned. (Inpatient care by 70 per cent, home help by 50 per cent and institutionalized care by 80 per cent.)

• The expenditures for these services tend to increase faster than the tax revenues from households. This will imply reallocation of resources within the public sector, higher taxes or increased user-fees.

• The income standard of those who are retired will decrease as they age relative to the working generations. Younger birth cohorts will get lower relative incomes than older cohorts unless they retire later.

• A large share of the very old will get so low incomes that they become poor. This group will not have the means to pay for care.

• The baby boom cohorts of the 1940s are relatively wealthy and they will according to our simulations keep their wealth also when they age. This is a potential source to fund increasing care expenditures, but a large share of this wealth is tied up in housing.

• We will, however, have a relatively large group of care needing elderly who both have low incomes and very little wealth. This group will not be able to afford higher charges for care.

• We should not expect that children and other relatives step in and substitute for public care.

• Increased immigration is not very effective in balancing the increased burden of care for our elderly.

• Much more effective is an increase in the average retirement age, the ability to maintain high economic growth and good public health.

• Our simulations are sensitive to changes in the death rates. Low death rates for “young old” may - depending on the health status of the elderly – result in an increasing number of very old and heavily care dependent persons.