Pension Policies

Abstract

This chapter analyzes the effects of population aging on pension policies. With population aging raising the cost of providing Social Security benefits, should Social Security’s benefits in the United States and some other countries be raised because they are relatively low or should they be lowered as part of a reform to restore solvency? While these questions are ultimately political, since either approach is economically feasible, this chapter argues that economics has something to say about the likely effects of population aging on pension policy, focusing on policy for unfunded Social Security programs. This chapter presents a model based on shadow prices and constraints that permits an analysis of the effects of population aging on inter-generational transfers through Social Security, using the tools of standard price theory. The model is based on recognition that the old-age dependency ratio acts as a shadow price for Social Security benefits in a pay-as-you-go system. The chapter also addresses the question as to what would be a sustainable benefit formula in the long-term for Social Security, given the prediction that (at some point) further increases in the payroll tax rate are politically unacceptable. It considers issues of political sustainability. A Social Security benefit formula or automatic adjustment formula that is financially sustainable may not be politically sustainable. That situation could occur if it leads to a decline in the benefit replacement ratio that is politically unacceptable, necessitating further changes in the Social Security program. In addition, the chapter considers issues relating to raising the age of eligibility for Social Security benefits. Rather than attempting a global focus, this chapter focuses on high-income countries like the U.S., with some reference to less developed countries.

I have received helpful comments on part of this chapter from Marion Boisseau-Sierra and Didier Blanchet.

Appendix: Shadow Prices and Constraints

This section presents a formal model for analyzing these issues relating to population aging and Social Security policy. With pay-as-you-go financing, Social Security faces the budget constraint that the annual inflow of revenue must equal the outflow of benefits

$$ \mathrm{BN}=\mathrm{twL} $$

(26.1)

where B is the average annual benefit, N is the number of Social Security beneficiaries, BN is total annual benefit payments, t is the payroll tax rate, w is average annual wage income, L is the total number of Social Security covered workers and twL is total annual Social Security contributions. This constraint is a hard or fixed constraint that is determined by the financing requirements of a pay-as-you-go system. In addition to this constraint, two soft constraints are defined by the differing views of the population as to the acceptable role of government in providing retirement benefits. The first soft constraint is that there is a maximum acceptable level for the Social Security payroll tax rate t_max, so that the actual payroll tax rate must be less than or equal to t_max.

$$ \mathrm{t}\le {\mathrm{t}}_{\mathrm{max}} $$

(26.2)

People differ as to what that rate is, and its level thus depends on the political strength of the different viewpoints, and varies across countries. Sweden, for example, has adopted the policy that all future adjustments to its Social Security system will be made through changes in benefit levels, with the Social Security payroll tax rate having reached its maximum acceptable level (Turner, 2004).

In addition, a politically determined minimum acceptable level for the generosity of Social Security benefits also acts as a soft constraint. The generosity of Social Security benefits is typically measured by the Social Security replacement rate, which is the ratio of Social Security benefits to wages $\frac{\mathrm{B}}{\mathrm{w}}$. Thus, there is a minimum acceptable replacement rate ($\frac{\mathrm{B}}{\mathrm{w}}$)_min, with the actual replacement rate being greater or equal to that rate.

$$ \frac{\mathrm{B}}{\mathrm{w}}\ge \left(\frac{\mathrm{B}}{\mathrm{w}}\right)\min $$

(26.3)

In Sweden, because all adjustments to Social Security are made by cutting the generosity of benefits, the replacement rate has declined over time. At some point, it can be predicted that the replacement rate will fall to a level that the political consensus is that further cuts are not politically acceptable.

The old-age dependency ratio for Social Security is the ratio of beneficiaries to covered workers $\frac{N}{L}$. It is widely recognized that an increasing old-age dependency ratio, which is caused by population aging, increases the difficulty of financing Social Security benefits.

Equation (26.1) can be rewritten in terms of the level of the average individual’s tax payments.

$$ \mathrm{tw}=\mathrm{B}\frac{N}{L} $$

(26.4)

The shadow price to the individual for a marginal increase in Social Security benefits is the marginal increase in the worker’s tax payments tw with respect to a marginal increase in benefits B for current retirees. Using that insight, Turner (1984) showed that the old-age dependency ratio acts as a shadow price p for Social Security benefits in the context of a pay-as-you-go system.

$$ \mathrm{p}=\frac{\mathrm{N}}{\mathrm{L}} $$

(26.5)

To demonstrate the intuition of this concept, when the ratio of beneficiaries to workers is one to ten, it costs each worker USD 0.1 to raise the average benefit level by USD 1. By comparison, when the ratio is one to two, it costs each worker USD 0.5 to raise the average benefit level by USD 1. A similar shadow price can be calculated for Federal spending on the young, but total spending on the young is roughly 20% as large as spending on those age 65 and older (Burtless, 2015), and is not considered here.

These constraints and the shadow price can be used to form the basis of an analysis of the level of Social Security benefits as it is affected by population aging. The demand for the level of Social Security benefits can be written as a function of workers’ earnings w, the shadow price p of Social Security benefits, and the real interest rate.

$$ \mathrm{p}=\frac{\mathrm{N}}{\mathrm{L}}\kern0.5em $$

(26.6)

Increases in the wage rate increase the demand for Social Security benefits, while increases in the shadow price of Social Security benefits reduce the demand for benefits. Increases in the real interest rate reduce the demand for Social Security benefits because they increase the demand for financial assets. The demand function can be written in a percentage change form as

$$ \mathrm{E}\left(\mathrm{Bd}\right)=\mathrm{a}1\mathrm{E}\left(\mathrm{w}\right)+\mathrm{a}2\mathrm{E}\left(\mathrm{p}\right) $$

(26.7)

where E is the percentage change operator (the derivative of the natural logarithm), a₁ is the income elasticity of demand for the level of Social Security benefits, which is positive, a₂ is the price elasticity, which is negative, and it is assumed for simplicity in this analysis that the real interest rate is constant, and thus drops out of the percentage change equation. Other parameters could be added to the demand function, such as a demand for income redistribution, but factors that do not change over time would drop out from the dynamic demand function.The pay-as-you-go constraint can also be written in percentage change terms as

$$ \mathrm{E}\left(\mathrm{BN}\right)=\mathrm{E}\left(\mathrm{twL}\right) $$

(26.8)

Equation 26.8 is a dynamic budget constraint. It indicates that for Social Security to maintain financial balance over time, the growth rate in total real benefit payments must equal the growth rate in total real payroll tax payments.

Splitting the dynamic budget constraint into its component parts, Eq. 26.8 becomes

$$ \mathrm{E}\left(\mathrm{B}\right)+\mathrm{E}\left(\mathrm{N}\right)=\mathrm{E}\left(\mathrm{t}\right)+\mathrm{E}\left(\mathrm{w}\right)+\mathrm{E}\left(\mathrm{L}\right) $$

(26.9)

The growth rate in total Social Security contributions (the right-hand side of Eq. 26.9) equals the sum of the growth rates of the payroll tax rate, average real wages, and the labor force. The growth rate in total benefits (the left-hand side of Eq. 26.9) equals the sum of the growth rate of benefits per beneficiary and the growth rate of beneficiaries. Expressing the equation in terms of the percentage change in average benefits gives

$$ \mathrm{E}\left(\mathrm{B}\right)=\mathrm{E}\left(\mathrm{t}\right)+\mathrm{E}\left(\mathrm{w}\right)+\mathrm{E}\left(\mathrm{L}\right)\hbox{--} \mathrm{E}\left(\mathrm{N}\right) $$

(26.10)

Because the policy interest concerning benefit levels relates to the replacement rate $\frac{\mathrm{B}}{\mathrm{w}},$ Eq. 26.10 can be rewritten as

$$ \mathrm{E}\ \left(\frac{\mathrm{B}}{\mathrm{w}}\right)=\mathrm{E}\left(\mathrm{t}\right)\hbox{--} \mathrm{E}\left(\frac{\mathrm{N}}{\mathrm{L}}\right) $$

(26.11)

To maintain a constant replacement rate (E $\left(\frac{\mathrm{B}}{\mathrm{w}}\right)$= 0), the payroll tax rate must grow at the same rate as the increase in the old-age dependency ratio. If the tax rate has reached its maximum acceptable level so that no further increases are possible (E(t) = 0), the change in the replacement rate is not determined by the income and price elasticities of the demand for Social Security benefits but by the requirements of the pay-as-you-go budget constraint.

$$ \mathrm{E}\ \left(\frac{\mathrm{B}}{\mathrm{w}}\right)=-\mathrm{E}\left(\frac{\mathrm{N}}{\mathrm{L}}\right) $$

(26.12)

Equation 26.12 indicates that in that situation, the percentage change in the Social Security replacement rate equals the negative of the percentage change in the old-age dependency ratio. Since with population aging, the rate of growth of the old-age dependency ratio is positive, the policy outcome must be that the replacement rate will decline at the same rate that the old-age dependency ratio is increasing.

Assuming that the payroll tax rate has not reached its maximum acceptable level, the effect of policy changes on the benefit replacement rate can be analyzed in terms of the levels of the wage and price elasticities. The benefit demand Eq. 26.7 can be rewritten in terms of replacement rates by subtracting the percentage change in wages E(w) from both sides of the equation

$$ \mathrm{E}\ \left(\frac{\mathrm{B}}{\mathrm{w}}\right)=\left(\mathrm{a}1-1\right)\mathrm{E}\left(\mathrm{w}\right)+\mathrm{a}2\mathrm{E}\left(\mathrm{p}\right) $$

(26.13)

where the superscript D indicating demand has been suppressed for notational simplicity. If the wage income price elasticity a₁ equals one, the outcome of policy reform on the Social Security replacement rate will depend entirely on the price elasticity a₂. With a negative price elasticity, because of the increase in the shadow price (increasing old-age dependency ratio), the policy reform will result in a decreasing Social Security replacement rate. Thus, under conditions of population aging, a necessary condition for policy reform to result in an increase in the Social Security replacement rate is for the income elasticity of demand for Social Security benefits to be greater than one. For example, depending on the percentage changes in income and in the old-age dependency ratio, the policy reform outcome could be an increase in the generosity of Social Security benefits, as measured by the replacement rate, if the income elasticity were sufficiently high and the price elasticity sufficiently low (in absolute value). According to the intermediate estimates of the U.S. Social Security actuaries, real covered wages will grow by 1.17% per year between 2015 and 2035. Over that period, the number of OASDI beneficiaries per 100 covered workers will rise from 36 to 44, or by about 1% a year (U.S. Social Security Board of Trustees, 2015). With these growth rates, if, for example, the income elasticity was 1.2 and the price elasticity was less than 0.2 in absolute value, policy reform would result in an increase in the benefit replacement rate. The greater the degree that people consider that there are no good substitutes for Social Security benefits and that Social Security benefits are a necessity, the lower would be the price elasticity in absolute value. Because the employer half of the payroll tax payment is not salient to workers, that may lower the price elasticity. However, the more that people consider private savings and pensions to be a substitute for Social Security, the higher would be the price elasticity.

In sum, this model analyzes reform due to population aging affecting the generosity of Social Security benefits in a price theoretic framework, with the outcome of reform depending on the income and price elasticities, along with the associated changes in income and the shadow price. With population aging, reform will result in an increase in the generosity of Social Security benefits only if the price elasticity is sufficiently small in absolute value and the income elasticity exceeds one.

Requirements for Financial Sustainability in Social Security Financing

This section addresses the issue of the financial sustainability of Social Security. Are the benefit formula and the financing mechanism together sustainable over the long-term?

The mathematics of pay-as-you-go systems clarifies the role of indexing implicit in Social Security benefit formulas with respect to both economic and demographic changes, such as population aging. It indicates what type of benefit formula or automatic adjustment mechanism is needed to maintain sustainability of Social Security financing.

We begin the analysis of this section by returning to the dynamic budget constraint as expressed in Eq. 26.10.

$$ \mathrm{E}\left(\mathrm{B}\right)=\mathrm{E}\left(\mathrm{t}\right)+\mathrm{E}\left(\mathrm{w}\right)+\mathrm{E}\left(\mathrm{L}\right)\hbox{--} \mathrm{E}\left(\mathrm{N}\right) $$

(26.10)

For countries where the payroll tax rate t is fixed (E(t) = 0), having reached the maximum level considered politically acceptable, the dynamic constraint for a sustainable benefit formula can be seen in Eq. 26.14.

$$ \mathrm{E}\left(\mathrm{B}\right)=\mathrm{E}\left(\mathrm{w}\right)\hbox{--} \mathrm{E}\left(\frac{\mathrm{N}}{\mathrm{L}}\right) $$

(26.14)

Equation 26.14 can be interpreted as a dynamic benefit formula that is consistent with sustainable pay-as-you-go financing when the payroll tax rate is fixed. It indicates that a sustainable Social Security program with pay-as-you-go financing would have benefits growing at less than the real wage earnings growth rate. They would grow at the rate of real wage earnings growth less an adjustment for the rate of growth in the old-age dependency ratio. Adjustment mechanisms or benefit formulas that are not consistent with Eq. 26.14 will not be sustainable over the long run. Because the U.S. Social Security benefit formula has benefits growing at the rate of the real wage growth rate over the long term, Eq. 26.14 indicates that the U.S. Social Security benefit formula is not sustainable with population aging and a fixed payroll tax rate. Of course, it is possible that the payroll tax rate will be increased in the future.

In sum, the Social Security budget constraint limits countries’ Social Security options. If countries have decided that they will not raise the Social Security payroll tax rate, their choices are further limited. Because of falling birth rates and increasing life expectancy at older ages, the number of beneficiaries is growing faster than the number of workers. In this situation, the Social Security budget constraint indicates that countries must reduce the generosity of Social Security benefits relative to wages. With a fixed early retirement age, this means that the replacement rate must fall. With population aging, benefit formulas and automatic adjustment mechanisms that are not consistent with this constraint will ultimately fail to be sustainable. Increasing the early retirement age is a policy option for dealing with the effects of population aging on Social Security systems that was discussed in this chapter.

The assumption of a fixed payroll tax rate appears to apply for some countries, where it appears that the payroll tax rate has reached its maximum acceptable level, and can be predicted to eventually apply for most countries after future increases have caused the rate to reach the highest level that is politically feasible. Even in those situations, however, there may be people who disagree with the political consensus and favor instead maintaining the replacement rate (E(B/w) = 0) so as to preserve the level of generosity of the Social Security program. In that case, Eq. 26.10, with rearrangement of terms, becomes

$$ \mathrm{E}\left(\mathrm{t}\right)=\mathrm{E}\left(\mathrm{N}/\mathrm{L}\right). $$

(26.15)

Thus, if the replacement rate is fixed so as to maintain the generosity of the Social Security program, the payroll tax rate must increase at the same rate as the old-age dependency ratio.

This analysis thus far has taken the old-age dependency rate as being determined by demographics, given a fixed Social Security benefit claiming age (retirement age). However, an alternative approach is to raise the eligibility age for Social Security benefits. From Eq. 26.11, if both the replacement rate and the payroll tax rate are considered fixed, Social Security solvency can still be maintained by raising the eligibility age over time so as to keep the old-age dependency rate constant

$$ \mathrm{E}\left(\mathrm{N}/\mathrm{L}\right)=0. $$

(26.16)

Equation 26.16 assumes that raising the eligibility age is done in such a way that benefits received at the new age are the same as those received at the previous age. It should be noted that this is a partial equilibrium analysis, and does not take into account effects of raising the retirement age on the capital-labor ratio, and thus on real wages and the fertility rate.

Application to the U.S. Social Security System

The basic U.S. Social Security benefit formula maintains a constant replacement ratio over time and thus can be represented in dynamic (percentage change) terms as the following:

$$ \mathrm{E}\left(\mathrm{B}/\mathrm{w}\right)=0 $$

(26.17)

This benefit formula is sustainable without increases in the payroll tax rate, so long as the old-age dependency ratio is stable or declining. Thus, the Social Security benefit formula was stable for years while the Baby Boom generation was swelling the ranks of the workforce and the old-age dependency ratio was declining.

The current Social Security benefit formula is no longer sustainable with a fixed payroll tax rate because the old-age dependency ratio is increasing, which implies a replacement rate that declines over time at the same rate as the increase in the old-age dependency ratio, as shown in Eq. 26.12.

Calculations using the intermediate assumptions for the 2015 Trustees Report indicate that between 2015 and 2035 the old-age dependency ratio is projected to increase at roughly 1% per year (U.S. Social Security Board of Trustees, 2015, 2019). Using Eq. 26.12, this implies that the replacement rate for financial sustainability must decrease at 1% per year. This conflict between the actual Social Security benefit formula and a sustainable formula is one way of viewing the inherent problem in financing under the current U.S. Social Security benefit formula with the constraint of a fixed payroll tax rate.

Thus, the financial unsustainability of the U.S. Social Security program can be viewed as being due to a flaw in its benefit formula that does not adjust to an increasing old-age dependency ratio. The current demographics of an increasing old-age dependency ratio plus the political economics of a seemingly fixed payroll tax rate dictate that the U.S. Social Security replacement rate must fall. It is not possible to maintain the current generosity of Social Security with an increasing old-age dependency ratio and a fixed payroll tax rate.

An Alternative Model

Voting models provide an alternative approach to analyzing the issue of what will happen to the future level of U.S. Social Security benefits. A simple model would indicate that the greater the number of beneficiaries and people near retirement age relative to younger workers, the greater the likelihood that benefits will be increased because that is in their own narrow self-interest. An implication of this model is that the large Baby Boom generation would force high Social Security payroll tax rates on their children to finance increased Social Security benefits for themselves. However, given the inter-connectedness of different generations through families, it seems implausible that the Baby Boomers would want to do this. Also, given a median voter model, it seems implausible that they would have sufficient voting power to achieve that outcome if they desired it.