AN EVALUATION OF SOCIAL INSURANCE SAVINGS ACCOUNTS

AN EVALUATION OF SOCIAL INSURANCE SAVINGS ACCOUNTS Stefan Fölster [1] The Swedish Research Institute of Trade (HUI) Stockholm, Sweden Abstract Many countries have reformed, or plan to reform, their pension system, often replacing defined benefits with some sort of savings account. In recent years proposals have been made to apply personal savings accounts also to other elements of social insurance, such as unemployment insurance, social assistance or parental leave compensation. This paper evaluates the consequences of replacing these systems with an insured social insurance savings account. Effects on marginal tax levels and income distribution are analyzed using both income panel data for Sweden and a simulated sample. Introduction In many countries reforms of pension systems are discussed or actually implemented. A common trend is to move from public, pay-asyou-go schemes with defined benefits toward funded systems in which contributions are defined and deposited in some form of personal savings account, and benefits depend on the return to the assets invested. In the wake of these reforms growing interest has focused on personal savings accounts as a way of organizing other types of social insurance or social expenditure than just the retirement income system. In Sweden, for example, educational savings accounts are being implemented. In Chile unemployment savings accounts are being introduced. [2] Individual health accounts have been analyzed and proposed. [3] Proposals for more comprehensive savings account based reforms have also been made (e.g. Snower & Orszag, 1998; Fölster, 1998). An example of a more comprehensive system in existence is the Singa- Public Finance and Management, 1(4), 2001 pp. 420-448.

An Evaluation of Social Insurance 421 porean Central Provident Fund, originally designed to increase savings and to provide retirement security. It has since been extended with a number of schemes, e.g. saving for medical needs, financing of higher education, insurance of dependents and a variety of other social needs. [4] The basic idea of a more comprehensive system is that mandatory payments into a social insurance savings account (SISA) replace most of the taxes currently used to finance benefits. In this paper benefits are taken to include unemployment benefits, social assistance, sickness benefits, disability benefits, parental leave, child benefits, housing benefits, and subsidized student loans. In order to separate issues the old age pension system is excluded. Withdrawals from the account are regulated, and can be made during spells of unemployment, sickness and other events. Throughout this paper it is assumed that withdrawals from the account equal benefits paid in the current system. After retirement the individual freely disposes over the balance on the account. The account is insured in the sense that the state covers all debt on the account. Much of the economic debate on pension accounts has focussed on the problems associated with a transition to a funded system. In this paper, however, we assume that the social insurance accounts are not funded, but merely consist of accumulated drawing rights. By way of introduction this paper describes some of the theoretical arguments made for an account system. Then the current Swedish social insurance is compared to a savings account based system using two empirical approaches. One consists of an analysis of a panel of individuals over the period 1976-1996. Since this empirical analysis does not cover the entire life cycle, and does not allow an exact calculation of how marginal tax effects change, it is complemented with simulation of a large number of individuals over the life cycle, designed to represent the actual population. [5] This also provides a test of the reliability of the two approaches. A crucial concern in evaluating such a reform is that it may be inequitable. Social insurance based on personal savings has often been viewed as incompatible with the aims of welfare states, partly because

422 An Evaluation of Social Insurance countries like Singapore that have savings account based systems provide very little redistribution. To the extent that redistribution is added to a savings account based system, one might be concerned that the gains in terms of lower marginal taxes are diluted. The Swedish social insurance system is among the world's most generous, yielding one of the most equal income distributions net of taxes among OECD countries. Using Sweden as a reference thus provides a tough test of whether a savings account based social insurance can combine a reasonable income distribution with lower marginal taxes. Even if a comprehensive account based social insurance may have some advantages, implementation would face formidable perhaps insurmountable political obstacles. In the conclusion therefore a number of the smaller account proposals, such as the educational learning account, are briefly described. A Basic Principle Behind Savings Account Based Social Insurance Social insurance has two basic functions. One is to provide insurance against risks; the other is to help individuals to redistribute income over the individuals life cycle. In most public social insurance systems both of these functions are financed with tax revenue. The aim of a savings-account based social insurance is to rely on mandatory individual savings instead of taxes to cover redistribution over the lifecycle, and to insure income over the life cycle rather than day by day. The central idea is instead to provide a more efficient insurance arrangement that provides protection against large risks, but reduces the need for tax financing, and in particular reduces marginal tax effects. An account based social insurance induces a number of economic effects. More complete theoretical analyses have been presented (Fölster & Trofimov, 1999; Orszag & Snower, 1997; and Orszag, Orszag, Snower & Stiglitz, 1999). Here we focus on some of the main aspects. Assume initially that there is symmetric information between the individual and the insurer. In the beginning of each period both the individual's wage w t during period t as well as expected future values of

An Evaluation of Social Insurance 423 wt are common knowledge. The individual pays m t which can be either a tax or an insurance premium. After that he learns his actual income y t which may be lower than w t due to income losses. At the same time new information about the likelihood of future income losses is revealed. He then receives compensation x t for income losses and consumes c t. Between periods the person earns interest 1 + r, and for simplicity it is assumed that the discount factor β equals 1/(1+r). [6] Expectations, conditional on time t information before y t is revealed, are denoted E t. Thus E 0 y0 refers to the expected value of y0 in the first half of period 0, before y0 is revealed. To keep things simple we assume an infinite horizon. Consumers maximize a standard intertemporal utility function: max E0 t=0 β t u (ct) (1) Assume initially that there is no moral hazard. The individual cannot avoid declaring income, reduce work effort or otherwise influence own income losses. A universal welfare state system will typically finance social insurance with an income-related tax or non-actuarial insurance premium, m t = τ y t. The tax rate τ is assumed to be proportional and constant over time. In return the individual receives a compensation x t = (w t - y t ) (1 - τ ). Suppose that in this system the initial expected value of tax payments must balance the expected payments of compensations: E0 t=0 β t τ yt = E0 t=0 β t (wt - yt)(1- τ) (2) If wt were constant and the information about expected values of yt remained constant, this would constitute an efficient arrangement. Given a concave utility function the individual's utility is maximized with a constant consumption stream, in this case wt (1 - τ). In fact, however, wt can vary and information on expected values changes between periods. As a result the tax an individual pays in any period will differ from the actuarial premium. In addition the consumption stream is no longer constant, and therefore no longer pareto opti-

424 An Evaluation of Social Insurance mal even though the state would care nothing about rearranging payments to provide a constant consumption stream. A similar problem arises for a voluntary insurance. [7] Assume that the insurer is risk neutral and competitive, and can borrow or lend at the interest rate r. Risk neutrality implies that individual income loss is a perfectly diversifiable risk. Competition among insurers is assumed to imply zero economic profits. Then the pareto-optimal insurance contract can easily be found under the assumption that complete contingent-claims markets exist. At time 0 the individual sells claims to his income stream and buys contingent claims to cover income losses. Then the individual's time 0 budget constraint is E0 t=0 β t ct = E0 t=0 β t yt (3) Maximizing utility (1) subject to this constraint yields first-order conditions that specify a constant consumption level c at every date and in every state. Solving the budget constraint with constant consumption gives c = r βe0 t=0 β t yt (4) The time 0 contingent claim contract is, however, not time consistent. As soon as new information on expected values of future y t is revealed, insurers will try to get rid of individuals with deteriorating prospects. This effect could possibly be avoided with the help of regulation. More bothersome is what happens if the individual's prospects improve. The individual will then cancel the insurance, making it impossible for the insurer to cross-subsidize those with income losses. Thus, a voluntary social insurance requires lifetime ties in order to work. Such lifetime ties to private insurers are probably in conflict with legal principles in most current welfare states. Cochrane (1995) suggests a mechanism for the related case of health insurance that could solve the problem of time inconsistency. The essence of the approach is to adjust the insurance premium in every period to reflect changed information on expected income losses, and at the same time require side payments each period that reflect the present value of changes in expectations of income losses. Thus an individual whose prospects deteriorate would receive a payment from the

An Evaluation of Social Insurance 425 insurance company equalling the net present value of increases in future income losses. Vice versa the individual would have to make a payment to the insurance company if prospects improve. In order to enforce the contract in a situation where individuals can go bankrupt Cochrane's mechanism requires a savings account in which savings at any time equal the possible payment that a client may have to make to the insurance company. Thus the time inconsistency problem can potentially be solved with the help of a savings account. An obvious way around the time inconsistency problem in both Cochrane's mechanism and the universal welfare state arrangement is to introduce a mandatory, public, actuarial insurance. The insurance premia would then be set as implied by (3) and (4), while the time consistency problem is suppressed since it is impossible to switch insurance company. So far, however, the analysis misses the essence of the welfare state dilemma. Social insurance, whether privately or publicly arranged, remains susceptible to moral hazard. In fact, the presence of moral hazard is the main motivation for attempting to keep marginal effects low. Assume that an individual can influence his income stream in a way that the state or insurer cannot detect, for example by pretending to be sick or unable to find employment. Let the new income stream y t ' be the result of the individual's utility maximization. Let utility be a function u(ct',l(yt - yt')) of consumption c't and the additional leisure l(yt - yt') that the individual gains by manipulating his income from yt to y't. The utility function satisfies the condition that for a constant consumption level a voluntary income loss is preferred, since it allows more leisure. This implies that yt' < yt. Further, if xt' compensates for the entire income loss s.t. xt'= (wt - yt')(1 - τ), then the individual's utility maximization implies yt'(xt') = yt'( (wt - yt')(1 - τ) ) = 0. In order to avoid this a deductible must be introduced. We assume that the deductible is determined by a rule D that assigns a particular Dt in every time period, conditional on variables such as wt, yt' and other variables, but not on yt which is assumed to be unknown to

426 An Evaluation of Social Insurance the state or insurer. The compensation paid is then xt' = (wt - yt')(1 - τ) - Dt. Assume a public, mandatory, actuarial insurance that, apart from the deductible, allows a constant consumption stream. Going through the same steps that led up to (4), the individual's consumption in any period with moral hazard and a deductible becomes c't = -Dt + rβε0 t=0 β t (y't + Dt). (5) Since yt' is decreasing in Dt a lower deductible lowers the individual's consumption stream. Since the insurer or the state still makes zero profit and is therefore indifferent to the size of the deductible, the socially optimal design of the system can be found by maximizing the individual's utility w.r.t. the rule D that determines the size of the deductible in each period. In doing so there is an important constraint. In most welfare states there are strong social preferences and stated policy aims to protect everyone from falling below a minimum standard of living. Thus in each period the individual must have a minimum to live on, call it MIN. This limits the size of the deductible. The maximization problem is then as in (6), where y' as defined above is the individual's optimal choice of declared income. max E0 t=0 β t u(c't,l( yt - y't)) w.r.t. D s.t. Dt y't (1 - τ) MIN (6) Since the condition must be met for any yt' it is clear that it is quite restrictive. The constraint can be made less restrictive, however, by introducing a savings account. We assume a very simple version of the savings account based social insurance, designed to make the point even in the infinite period model. Assume that a deposit is made on the saving account in any period in which income yt' exceeds MIN. The balance on the account is, in a sense, the individual's money, and the individual earns interest. In every period an annuity based on the balance in the account is returned to the individual. [8] Yet the individual's expected value of making the mandatory deposits on the account is of

An Evaluation of Social Insurance 427 course smaller than the actual deposits since expected future withdrawals must be taken into account. The size of the deposit on the account in any period is At and the maximum amount is governed by a rule A which we do not need to specify to make the point. Similarly, withdrawals from the account are governed by a rule V that determines a withdrawal Vt in any period. The withdrawal is zero if either the balance on the account is zero or if the constraint in (6) is violated. Otherwise the withdrawal Vt is positive. Since this means that the deductible can be completely or partly paid with a withdrawal this means that the new restriction for the maximization problem (6) becomes Dt y't (1-τ) - MIN + Vt (7) Clearly this constraint is less restrictive, which means that the deductible can be made larger in the account system than would otherwise be possible. The model does not say much about the size of the effect. Intuitively it is obvious, however, that this depends on the probability distributions of wt and y't. If the world divides into individuals that never have an income loss (y't = wt) and individuals that have a complete income loss in every period, then the account will make little difference. Those with persistent income losses, persistently never have any balance on their account which implies that Vt = 0 in any period. Restriction (7) is then identical to the restriction in (6). A crucial question for the empirical section is therefore how many people have such persistent income losses. A major insight in recent economic research is that life-time income tends to be much more equally distributed than income in any particular year. This is shown in a number of studies. [9] An OECD study, for example, indicates that the majority of individuals in the lowest income quintile in 1986 had moved up five years later. In fact, one in five had moved up at least two quintiles. [10] A Swedish study that estimated income distributions over the entire life cycle concluded that the lowest quintile only had 31 percent lower life time income than the highest quintile, while annual incomes were four times higher in the highest quintile than in the lowest. [11]

428 An Evaluation of Social Insurance The Empirical Approach The empirical analysis aims to show how incomes and marginal taxes would be affected by the social insurance savings account (SISA) using an actual and a simulated population. A limitation of this analysis is that it only examines the direct effects of the social insurance system, ignoring behavioral changes that may be induced. Since empirical estimates of individuals' adjustment to changing marginal tax rates vary widely any assumptions about the size of these effects would be somewhat ad hoc. Instead, our simulation of direct effects lends itself to the interpretation that a change of social insurance system that, for a given income distribution, induces the largest direct reduction of marginal tax rates, also induces the most favorable indirect effects. Design of the personal savings account As in the previous section wage income before taxes is denoted yi,t where the subscript i denoting the individual is now made explicit. The sum of government transfers is denoted xi,t. Two complications in the data are that taxes are not proportional, and that some government transfers are taxed, while others are not. The income taxes paid on wage income and taxable government transfers is denoted Ti,t. Disposable income for individual i during year t is Ii,t = yi,t + xi,t - Ti,t (8) The account system requires each individual to save a fraction of his or her wage income in SISA. For simplicity it is assumed that payments into the account replace a share α of current income taxes and that rules for these payments are the same as for income taxes, so that Ai,t = αti,t. [12] Similarly, allowed withdrawals from the account follow rules similar to those that govern current transfer systems, so that withdrawals are Vi,t = xi,t. To simplify calculations it is assumed that withdrawals Vi,t are taxed in the same way as xi,t is in the current system, but the tax revenue is part of Ti,t of which a share α is deposited in the account. A consequence of these assumptions is that one of the arguments often made for accounts - giving the individual greater flexibility - is ignored here. In this simple version of the account the disposable income in the account system equals disposable income in the

An Evaluation of Social Insurance 429 current system up until retirement. The difference lies in the accumulation of assets on the account. The balance on the account (b a i,t) then develops as in (9). b a i,t = (1+r)b a i,t-1 + Ai,t - Vi,t (9) The rate of interest r, and the individual discount rate, are subsequent calculations assumed to equal the rate of GDP growth. The only insurance element in this account system is that negative balances at retirement are canceled. The costs of this insurance is financed as part of the tax (1-α)Ti,t that is not deposited on the account. In the empirical analysis reported below a tax of 4 percent on incomes turns out to be sufficient to finance the insurance. Since Ti,t is progressive, the tax in SISA is also progressive. Still, switching to the account implies a significant tax cut for a large share of the workforce who expect to have a positive balance on the account at retirement. But a person who expects a negative balance on the account at retirement would consider the entire payment into the account a tax. A constraint applied in the empirical analysis is that the government budget balance in the savings account system is the same as in the current system. Table 1 shows the costs, in percent of GDP, of the social insurance systems that are replaced by SISA.

430 An Evaluation of Social Insurance Table 1 Benefits and public services encompassed by SISA. Benefit Unemployment benefit 1 Parental leave Sick benefit Child benefit Social assistance Housing benefits Student loans 2 Disability benefits 3 Total Program s cost in terms of % of 1995 GDP 3.7 1.5 1.3 1.2 0.93 0.62 3.2 12.45 1 Includes benefits for training during unemployment (AMU) 2 Net of repayments 3 Includes early retirement and work injury The database LINDA is a longitudinal Swedish data set containing information on 300 000 individuals and members of their households. The sample of individuals is representative for the population during the period 1960 to 1995. The core of the data are the income registers (Inkomst- och Förmögenhetsstatistiken) available annually from 1968 to 1995, and population census data available every fifth year from 1960 to 1990. For each year information on all family members of the sampled individuals are added to the data set, but they are included only for as long as they stay in the family. While LINDA primarily consists of a panel, the sample outflow has been matched by a representative inflow, so that the included individuals are both longitudinally and cross-sectionally representative of the population. Of the 300 000 individuals available each year, about 100 000 are in the sample over the entire period from 1968 to 1995. For practical purposes the sample can not always be used over the entire period, as the data become richer over time. From 1968 there

An Evaluation of Social Insurance 431 is is annual information on income, but some components of income, such as social assistance, are shown separately first after 1977. For most of the analysis described below we therefore focus on the period 1976-1996, and on the group of people who were 18-34 years old in 1968. They were 46-62 years old in 1996. While the database is rich in some respects, it is also limited in other respects. For one, it does not cover entire working life cycles, and therefore does not give a complete picture of the effects an account would have. Further, the database does not lend itself to calculations of marginal taxes since the tax- and social insurance systems have been changed so many times during the observed period. Therefore we compare the results from the database with those from a simulated population. The simulation The calculation is based on a simulated population of 1000 persons. [13] Life cycles begin at age 20 and end at death. There are four steps in the construction of the simulated population: 1. First, the distribution of pre-tax simulated wages is determined. The simulated population is divided into six groups (male, female with no secondary education, secondary education and tertiary education respectively) using the frequency distributions in the actual population. [14] For each group the mean wage in year t is determined as mt = mg + θt - δt 2 (10) This yields the typical parabolic income pattern over time. mg is a constant that differs for each of the six groups. In addition the individual s wage wit differs from the mean by a random walk process. Let uit be a random variable which is distributed independently of income and previous proportional changes; then if zit = log(wit /mt) the generating process can be written as zit - zi,t-1 = uit (11)

432 An Evaluation of Social Insurance If uit has a constant variance of σu 2 and if σt 2 denotes the variance of zit then (11) implies that σt 2 = σ0 2 + tσu 2 (12) and the variance of the logarithms of income in each year grows linearly over time. Therefore information on the variance of earnings in different age groups provides estimates of (12). Estimates of the parameters in (8) and (10) were jointly estimated using a maximum likelihood method (as done e.g. in Cameron and Creedy, 1995). [15] The simulated wage distributions are consistent with estimates obtained in various studies that analyze wage panel data. [16] Note that in our simulations we assume that there is no productivity growth. 2. To generate lifetime earnings first pre-tax wage is calculated for each individual, rewriting (11) as wit = w i,t-1 exp[(mt - mt-1) + uit] (13) This can be used to generate the wit's given a set of random variates from an N(0,σu 2 ) distribution. [17] Capital income and capital taxation is ignored in the simulation of individual income streams, but enters the state's balanced budget requirement described later. Subsequently after tax earnings Iit are calculated as Iit = wit - T(K it) + x(k it) if i is working - T(Kit) + x(k it) if i is sick, retired, on parental leave, in tertiary education, involuntarily unemployed, or voluntarily not working. Here T(.) is a schedule of taxes and/or deposits on the personal account, and x(.) is a schedule of benefits and/or withdrawals from the personal account. Both depend on a vector Kit that describes the individuals' history in terms of earnings, employment record, number and age of children and other aspects that determine tax and benefit rates. These are described further below and in the appendix. Family

An Evaluation of Social Insurance 433 history, which typically is the most complicated part in a life cycle simulation, has been considerably simplified here. Since Swedish tax and benefit rules with few exceptions are geared toward the individual with no regard to marital status we have for the most part ignored marital status. [18] Thus individuals in the life cycle model are not "matched" to each other to create families. Each individual has children with a certain probability and bears half the costs associated with children, e.g. child care fees. 3. It is assumed that all people retire at 65 years of age, unless they fall ill and enter early retirement. The age of death is determined randomly according to the actual distribution of mortality. This differs for men and women, but is assumed to be independent of other variables. 4. Sickness, voluntary and involuntary unemployment, parental leave, and tertiary education are determined as follows. We assume that spells of sickness are equally likely for all categories at all stages in life, but that the duration of spells varies according to a probability table which depends on sex, age, current income, and the share of previous 5 years during which the individual has been either sick or unemployed. [19] Spells of sickness beyond three years of length are assumed to imply early retirement. Individuals that retire early do not work at all until they reach the age of 65 when all individuals enter normal retirement. Spells of involuntary unemployment and voluntary non-work are randomly assigned based on probability tables where the length of the spell depends on age, income, sex and the share of previous 5 years during which the individual has been either sick or unemployed. [20] Occurrence of childbirth is determined randomly according to the actual distribution. It is assumed that when a child is born a mother is on parental leave 90 percent of 1.25 years (the time compensated by parental leave insurance) and a father 10 percent of 1.25 years. This corresponds to aggregate statistics. Participation in tertiary education is determined randomly according to aggregate frequencies as described above. A person engaged in tertiary education is assumed to participate for five years, during age 20 to 24. A weakness of such simulation models is that they do not capture all cross-effects well. For example, no account is taken of how education may affect sickness or the probability of having children. As one meas-

434 An Evaluation of Social Insurance ure of robustness, however, a study using an alternative technique creating life cycles by splicing together panel data yielded similar distribution of life time income, unemployment and sickness (ESO, Ds 1994:135). Using the simulated income pattern and the simulated work history, payments into the social insurance in the form of payroll taxes and income taxes are calculated. The exact tax- and social insurance rules applied in the simulation are shown in the appendix. Then income before and after transfers is derived. [21] Results There is an important difference between the population in the database LINDA and the simulated population. The actual population in the database mirrors the economic and social changes that have taken place over the two decades. In contrast the simulated population builds on career patterns as measured in the mid 1990ties. It would therefore not be surprising to find significant differences between the populations. One important difference that is easily corrected for is the fact that the database population is registered over two decades only. The balance on the account will therefore tend to be smaller than for the simulated population which is available over the entire working life. To achieve comparability a random sample is taken from the simulated population that has the same age distribution as the LINDA population had in 1976. The account balance is then shown twenty years later (denoted comparable simulation below). By and large differences between the database sample and the simulated sample in the comparable simulation turn out to be quite small. A number of descriptive parameters are easily compared. In terms of average income and variance of income there are, for example, no statistically significant differences between the samples in the database and the simulation. Table 2 shows the account balances excluding the insurance or redistribution in 1996 for the Linda population, for the comparable sample from the simulated population, and for the simulated population at the end of their entire working life from age 18 to age 64. In table 2

An Evaluation of Social Insurance 435 the samples are divided into deciles according to the final account balance. It is important to keep in mind that these are not equivalent to income deciles. Even people with low annual incomes can end up with high balances if they have long working lives and few withdrawals. Table 2 Account balance before insurance in 1996, average balance per decile, thousand kronor Decile LINDA Comparable Simulation Simulation age 18-64 1-1729 -1734-2627 2-621 -699-947 3 36 84 142 4 47 138 262 5 89 147 308 6 160 235 425 7 334 396 582 8 493 437 629 9 711 662 1041 10 1353 1431 2398 The share of people that end up with negative balances on the account is 15-17 percent, as shown in table 3. This can be contrasted with Feldstein and Altman s (1998) analysis of an unemployment savings account using the Panel Study of Income Dynamics in the U.S. They find that 5.2-7 percent would retire or die with negative balances (depending on the version). One important difference is that in their study all people initially included in the sample work. In our sample in contrast, all people who due to various disabilities never work are included. Another important difference is of course that SISA has a wider scope. Interestingly, however, net government payments required to support those who end up with negative terminal balances are at around 30 percent of current social insurance transfers no higher than in the Feldstein and Altman sample. The explanation for this seems to be that in the Feldstein and Altman sample many of those who end up with negative terminal balances have frequent spells of unemployment. SISA, in contrast, covers so many types of social insurance that are used

436 An Evaluation of Social Insurance by people with little unemployment who pay their own way using the account. Table 3 Analysis of SISA with alternative samples, percent. LINDA Comparable Simulation Simulation age 18-64 Negative terminal balance 16.2 15.1 17 Negative balance ever 38 34 57 Net government payments as percent of current social insurance transfers 29 28 31 As mentioned previously the population in LINDA does not allow a calculation of marginal tax rates, since the tax- and social insurance systems have been changed so many times over the two decades. In the simulation, however, marginal effects can be calculated. They are derived by letting each simulated person earn 100 kronor more during one year at a time. Then the relation between the 100 kronor increase in gross earnings and the sum of increased current and future net earnings yit can be calculated as 1/100 * t=j Iit in the current system, and as 1/100 * t=j Iit + bi64 in SISA. [22] This expression is defined as the marginal tax rates and are shown as an average over all individuals and over all time periods j = 18.65. Table 4 shows what happens when the current system is replaced by SISA in the three samples. The marginal tax rate includes marginal effects in the current system of progressively increasing fees for public services and decreasing subsidies. The marginal tax rate is first shown as an average for all people and then for different income groups. [23] Income is here defined in two ways. First, deciles for distribution of lifetime income (after taxes and subsidies) are shown. In the current system marginal tax rates are highest for high income earners, due to

An Evaluation of Social Insurance 437 progressive taxation, and low income earners due to progressively reduced subsidies. With SISA marginal tax rates are much lower and more equal for all deciles except the first decile. The reason is that people in the first decile at retirement tend to have less on their account than the minimum guaranteed amount. As a result they still have some incentive to earn income as this raises the guaranteed pension, but the incentive is naturally much lower than for someone who ends up with more than the guaranteed amount on the account. Table 4 Marginal tax rates including VAT and marginal effects of benefits, in percent of gross income (before employers tax). Marginal tax rate in percent Current system SISA SISA without insurance Average for all 74 61 49 Average for deciles in terms of life time income 10th decile 5th decile 2nd decile 1st decile 80 67 75 94 59 60 67 88 46 48 51 53 Finally we turn to effects on the income distribution. Table 5 shows the account balances for deciles of disposible income over working lives.

438 An Evaluation of Social Insurance Table 5 Net present value of switching to SISA per decile of disposible incomes during working life, thousand kronor. Decile Life time disp. income LINDA Comparable Simulation Simulation age 18-64 1 3560-64 -95 2 5116-79 -139 3 5899-95 -157 4 6460-119 -186 5 6989-24 -33 6 7519-38 -51 7 8088 47 59 8 8784 72 117 9 9880 95 145 10 13171 200 333 As table 5 shows there is some effect on the overall income distribution. The incomes of the highest life time income deciles would be bolstered by about 2.5 percent (based on the simulation 18-64). It should be noted, however, that behavioral effects are not accounted for at this stage. In light of the large improvements in incentives reported above, there should be considerable behavioral effects that improve outcomes for most groups. Further, some of the people with high life time incomes actually have low wages, but work many years. Thus not all of the people who gain are high income earners in any particular year. These results on overall income distribution do not preclude existence of redistributionary effects between groups of people that do not perturb the overall distribution. We have performed a number of tests of such effects, but reporting these falls beyond the scope of this paper. A rough characterisation is that people gain with personal savings accounts who work many years at a low wage, which in the current system means that they pay in a lot over the course of their life time, but receive fairly low compensations when they are e.g. sick or unemployed. On the other hand people lose with personal savings accounts who work only few years at a high wage, which means that they receive high

An Evaluation of Social Insurance 439 compensations in the current system even though they pay in rather little over the course of a life time. Conclusion A comprehensive account such as SISA is probably too complex to appear on any political agenda (although it exists in Singapore, and a number of Swedish firms are introducing more comprehensive accounts on a voluntary basis). Rather, the analysis above can be seen as a way of analyzing what the aggregate effect of introducing a number of smaller, and more specialized, accounts would be. As a way of concluding some of these specialised accounts are briefly described. Educational savings account In Sweden an educational savings account has been debated and, in fact, embraced by several political parties, labor unions and employers. Currently a number of firms are introducing educational savings accounts on a voluntary basis even though tax rules are not yet particularly favorable. [24] The Swedish government is expected to propose more favorable tax treatment in the coming year. In England "educational learning accounts" have been advocated by Tony Blair, and have been under consideration by the government. The problem that an educational savings account aims to solve is that a growing group of people need additional education throughout their career. Employers' willingness to pay such education is often below what is socially optimal because of the risk that the employee will leave with the human capital investment, perhaps to a competing firm. Most people's own financing of such education is limited by liquidity. Also student loans are often not enough to finance education and living expenses later in life when many have high expenses for children and housing. The need for complementary education cannot be easily met by public subsidies because experience shows that such offers are often taken up by people who seek a break rather than an investment in their future career. The basic idea of an educational savings account is that employees and employers contribute to the individual savings account. [25] Contributions to the account should be tax free. Savings on the account can be used to finance education and income support during education.

440 An Evaluation of Social Insurance Withdrawals that are made to finance the costs of education are tax free, while withdrawals that are made for income support are taxed as income. The balance on the account at retirement can be freely withdrawn or used to bolster one s pension. When an employee changes employer she takes the account with her, but retains only the part contributed by herself, while the employer retains his/her contributions. Flexibel work accounts A growing number of firms across Europe have flexible numbers of hours during a workweek, depending on business fluctuations that affect the firm s workload. The wage for excess hours is accumulated in the account and can be withdrawn in terms of fewer hours or cash at a later time. Unemployment savings account An unemployment savings account has been discussed in several countries (e.g. Orszag & Snower, 1997) and appears to be under implementation in Chile, at least in a limited version. In the most simple version each employee saves a fraction of her wage on the individual unemployment savings account. As in the case of the educational account contributions can be split between the employee and the employer. If the individual loses her job she may withdraw an amount from the account that corresponds to unemployment compensation in traditional systems. If the funds in the account are not sufficient to pay the benefit, the government lends the necessary amount. At retirement a positive balance on the account can be withdrawn, or used to top up pensions. The government cancels the debt of those who reach retirement age with negative account balances. With this system all unemployed individuals receive the same cash amounts during spells of unemployment as they would under existing unemployment insurance rules. Their full protection is thus maintained. Any person who expects to retire with a positive balance completely internalizes the cost of unemployment benefits. For individuals who expect to retire with negative balances additional unemployment has no greater personal cost than in current unemployment insurance. Therefore an unemployment savings account will have little effect if unemployment over a lifetime is concentrated to a small

An Evaluation of Social Insurance 441 group of individuals who also tend to end up with negative balances on their account. But if unemployment spells more commonly affect people who work most of their life and expect to end up with a positive balance, then the account can lead to substantial reduction of public outlays for unemployment insurance and improved incentives. In order to study this question empirically Feldstein and Altman (1998) analyzed how Americans represented in the Panel Study of Income Dynamics would have fared under an unemployment savings account system. The analysis indicates that merely five percent of employees would retire or die with negative account balances, and that only about half of all benefits from the savings account would be paid to such individuals. Most individuals have positive account balances even after their unemployment spell. In the end the unemployment account would save more than 60 percent of the current taxpayer burden, not counting dynamic effects due to improved incentives. Further, effects on income distribution are shown to be quite small. Family policy savings account Most welfare states have extensive provisions for families, often including parental leave compensation, compensation when children are sick, childcare subsidies, child allowance and other subsidies. Yet having children is not a traditional "insurable event" and, in fact, a large majority of people have at least one child during the course of their life. In the Swedish debate several political parties have argued that a fixed sum should be placed on a restricted account when a child is borne. From this account the parents could then withdraw money. One point of this proposal was to make the use of subsidies more flexible, allowing e.g. a shorter parental leave period in return for more child care. Another point was to give the same parental leave compensation regardless of current income. In Denmark a true savings account has been proposed (e.g. Morgen, 1995). The idea is that part of wages are saved on a family policy account. The equivalent of all family policy subsidies can then be withdrawn from the account. One can even borrow from the account. But when a certain debt limit is reached further withdrawals are financed by a public insurance.

442 An Evaluation of Social Insurance Health account In many countries the fraction of health costs that patients pay themselves has increased in recent years. This development has often been necessitated by a lack of public funds. But often it is also seen as a way of reducing demand for health care above and beyond what is medically necessary. A problem with this approach has been, however, that a large fraction of families have almost no liquid savings and find it hard to make even small payments, especially if they are not anticipated. A risk is therefore that demand is cut even for medically necessary treatment. As a solution to this dilemma some economists have recommended combinations of catastrophic health insurance with individual health accounts. The central idea is that individuals pay health care costs below a certain deductible from the individual health account; costs above the deductible are paid by the insurance, which may be private or public. Assets remaining in the account when the individual retires are then available for other purposes. The motivation for the parallel saving and insurance plans is that each individual spends his or her own money for medical care except when treatment is very expensive. Thus the desirable features of a larger deductible is combined with a mechanism that creates reserves from which individual expenses can be paid. An important question is whether such a plan is inequitable. To the extent that individuals experience different health shocks over many years, the plan could lead to large differences in account accumulations. If illness over working life is distributed very unequally the plan could look like a savings account for the healthy, and self-insurance for the ill. In order to investigate how equally medical expenses are distributed over working life Eichner et al. (1996) use health insurance claims data to calculate the effects of a health account system. They show that medical expenses over an entire working life are more evenly distributed than is often assumed. More than eighty percent of the people in the sample would retain over 50% of their contributions. Only five percent would retain less than 20% of their contributions.

An Evaluation of Social Insurance 443 Notes 1. The author is grateful for help and comments to Dennis Snower, Mike Orszag and Robert Gidehag. 2. Unemployment accounts have also been analyzed by Orszag and Snower, 1997, Feldstein and Altman, 1998, and Orszag, Orszag, Snower and Stiglitz, 1999. 3. See for example Eichner et al, 1996. 4. See Asher, 1994, for a description of the Singaporean Provident Fund. 5. The simulation is similar to that used in Fölster, 1999. 6. The argument is not affected by varying interest rates or by assuming a finite number of periods. 7. For the case of health insurance these problems are analyzed in Diamond, 1992, pp. 1238-39, and Cochrane, 1995. 8. In a model with a finite working life the balance on the account would be returned as well at retirement. 9. Examples of such studies are Björklund, 1989, and Aaberge et al, 1996. 10. OECD, 1995. 11. Hussenius and Selén, 1994. Living standards may be even more equal because public services are subsidized more for low income earners, and because low income earners more often live in areas where housing costs are low. 12. The account system as implemented here implies that the public sector loses income taxes, which instead are deposited on the individual accounts. On the other hand the accounts are used to finance all household transfers except old age pensions. Public consumption would be financed with what currently is the em-

444 An Evaluation of Social Insurance ployers tax, although this could be converted into income tax if wages are raised to their current gross levels, before employers tax. 13. The simulated population is similar to that used in Fölster, 1999. 14. The distribution of these variables are provided by the Swedish Central Office of Statistics for 1990. 15. Estimates obtained are σ0 2 = 0.173; σu 2 = 0.0049; θ = 0.0311; δ = 0.00071; m male, no sec ed = 8.91; m male, sec ed = 9.54; m male, tert ed = 10.3; m female, no sec ed = 8.70; m female, sec ed = 9.14; m female, tert ed = 9.8; 16. In particular Björklund, 1993 and Gustafsson, 1994. 17. To generate wage in the first period wil for example, suppose that vi is randomly selected from the standard normal distribution N(0,1), and use wil = exp(m1 + vi σu). 18. Exceptions are social assistance payments that are conditional on the spouse's income. This is implicitly handled in the simulation by using a probability of being eligible for welfare given that the individual is out of work and does not have unemployment insurance. 19. The probability tables are provided by the Swedish Health Insurance Authority for the year 1990. 20. Data underlying the probability table are provided by the Swedish Labor Market Board. 21. Transfers are calculated in a simplified manner. Additional negotiated compensations are ignored. 22. Effects via the public pension system have been taken into account. 23. Importantly, the marginal tax calculations are based on an expost reasoning. Ex-ante people will of course not know how incomes and withdrawals develop over their life time, so that the

An Evaluation of Social Insurance 445 actually perceived marginal tax rate will be based on expectations of future developments. 24. Some 50 firms have introduced educational savings accounts during 1999. Typically around one third of the employees choose to participate. 25. A specific proposal is presented and analyzed in Fölster, 1994. References Aaberge, R., Björklund, A., Jäntti, M., Palme, M., Pedersen, P., Smith, N., and Wennemo, T. 1996. Income inequality and income mobility in the Scandinavian countries compared to the United States. Discussion Paper no. 168. Statistics Norway, Research Department. Asher, M.G. 1994. Social security in Malaysia and Singapore practices, issues and directions. Institute of Strategic and International Studies. Malaysia. Atkinson, A.B. 1987. Chapter 13: Income maintenance and social insurance. Auerbach, A.J. & Feldstein, M (red.), Handbook of Public Economics, vol II. Elsevier Science Publishers. Björklund, Anders. 1993. A Comparison between Actual Distributions of Annual and Lifetime Income: Sweden 1951 92. Review of Income and Wealth, 39, pp. 377 86. Björklund, A. 1997. Income distribution in Sweden: What is the achievement of the welfare state? Mimeo, SOFI. Stockholms Universitet. Björklund, Anders och Palme, Mårten. 1997. Income Redistribution within the Life Cycle versus between Individuals: Empirical Evidence using Swedish Panel Data. Working Paper nr 197. Handelshögskolan i Stockholm. Blomquist, S. 1981. A comparison of distributions of annual and lifetime income: Sweden around 1970. Review of Income and Wealth, 27, pp. 243 264.