Suppose that tomorrow all workers entering the work force would be working under a new social security system in which a worker and the worker's employer would each pay 2% of the worker’s annual wage or salary in payroll tax and that money would go into the worker’s personal retirement account where it would be invested in stock funds to provide the worker the worker's retirement income. Surprising as it might seem, the total payroll tax of 4% would provide retirement incomes that are superior to those of the present system, and at 38% the present cost in payroll tax and at 25% the expected payroll tax cost in the near future.
The phase-in of the new system would start a simultaneous phase-out of the present Social Security system. The phase-in would take essentially 45 years if we start it with just those workers entering the workforce, 35 years if we jump-start the system by including those in the present system who are under 30 years of age and putting 4% of all OASDI wages they had earned plus compound interest in their retirement accounts. The vast majority of workers in the present system would retire in this phase-in period. However there would be some that would work on beyond age 65 and even age 70, as there are today. The phase-out of the present system would last 25 to 30 years longer than the new system phase-in. The extra years are needed to see all of the present system workers through their retirement years receiving their pay-as-they-go benefits and because of the increased longevity of the retirees.
During the phase-in period workers in the new system would only differ from workers in the present system in the way their retirement incomes were determined. They would pay the same payroll tax rate as workers in the present pay-as-you-go system. After the phase-in is over, the payroll tax rate that workers in the new system would have to pay would not change abruptly, as the 25 to 30 year remainder of the phase-out might aptly be described as the pay-as-they-go period. Consequently, for a period of 60 to 65 years, workers in the new system would be paying a payroll tax rate substantially greater than 4%. However, after reaching the age of 65 (perhaps earlier) in the new system, workers would be able to retire and receive superior retirement incomes, and this could happen even as the last of the workers in the present system begin their retirement.
Personal retirement accounts would be managed by the Social Security Administration (SSA) to insure a good safe return and this would cause the SSA to gradually evolve into a professional retirement account agency. Disability insurance could be provided for workers in the new system by taking a premium from the worker's retirement account where this premium would decrease as the value of the worker's account increased. The SSA would send annual reports to each worker in the new system listing the amount of money that went into the worker's account that year, the current value of the worker's account, and perhaps an indication of the inflation rate such as the percentage increase of the total amount of money that went into the personal retirement accounts that year (after the phase-in period), which could be interpreted as an increase in the general cost of labor.
Constraints on a worker’s retirement account would be minimal and would be mainly to insure that the worker would not become a burden on taxpayers in retirement years. The worker's retirement account would be the worker's personal property and the residual value of the account upon the worker's death could be left to the worker's heirs. Taking the value of the account in cash at the worker's retirement would be an option but choosing to make annual withdrawals from the account during retirement years, leaving the remainder invested, looks like the best way to manage the retirement account.
The money going into workers’ retirement accounts would cause a shortfall in the money that would otherwise be available to pay the retirement benefits of the present system. This money would have to be replaced by taking money from the General Revenue Fund (largely income tax revenue) and is the principal transition cost. Surplus payroll tax could be used to pay some of this transition cost and taking money from General Revenue could be viewed as cashing in IOUs in the Trust Fund, i.e. taking back previous payroll tax surpluses that were spent as General Revenue but listed as money borrowed from the Trust Fund. The transition cost would be small at first making the jump-start a reasonable option. With the jump-start essentially the first 10 years transition costs are paid up-front, i.e. in starting the system. In general, the annual transition cost would steadily increase in size over the phase-in period as the number of workers in the new system builds up to a more or less steady state value and as many reach the age of 65. The peak annual transition cost occurs at the end of this phase-in period and then the annual transition cost gradually decreases and ends in the following 11 year period (assuming a 16% payroll tax rate). Only in the 15 to 20 years after the transition costs have been paid, can the payroll tax rate be gradually reduced to the 4% level. Transition costs are estimated in COSTS and are discussed in terms of 2002 dollars and as a percentage of the Federal Budget. In order to further view the transition costs as manageable, it is noted here that the peak transition cost is estimated to be $192 billion in 2002 dollars in COSTS and the peak payroll tax surplus amount spent as General Revenue was $156 billion in 2004 (discussed in PROBLEM).
The problems of the present Social Security System are discussed in the PROBLEM page for the purpose of giving people a better understanding of the payroll tax surplus, the Trust Fund, the wage cap, and the significant changes that have been going on in those system variables in the last 7 to 10 years. Major demographic changes are also a major problem for the present system. This problem is essentially twofold. People in the U.S. are living longer and are therefore living longer in retirement. The American Experience Table of Mortality, published in 1949, indicates that only 53% of the 20 year-olds would reach the retirement age of 65 and only 11% of those would live to age 85. The Period Life Table for 2002, put on the internet by the SSA, really emphasizes the impressive increase in longevity. It indicates that 83% of the 20 year-olds entering the workforce will reach the age of 65 and of those, 42% will go on to reach the age of 85 and 22% will live to be 90 years old. Two-thirds of the 90 year-olds will be women. Also there seems to be a problem with our birthrate. This should not be surprising as the number of one-parent families has been increasing and as contraceptives are being increasingly used to limit family size. In 2002 the birth rate reached an all-time low of 13.9 births per 1000 population. It is significant to note that there was a recent high of 16.7 in 1990 and an all-time high of 25.3 in 1957, which was in the midst of the postwar baby boom era (1946 – 1964). Still, the Census Bureau says that the birthrate appears to be adequate. Anyhow, the demographic problem indicates that the pay-as-you-go system is now completely inappropriate for the U.S. and should be replaced as soon as possible because of the rapidly diminishing number of workers per retiree. The new system is independent of this number.
New system retiree incomes are analyzed in the SOLUTION page using the annuity value function and the inflated annuity function. The annuity value function gives the value of an investment account if a constant amount is invested annually in the account for a number of years and the account earns a constant compound interest or rate of return. The inflated annuity function more appropriately takes into account inflation by assuming a worker's wage is increased annually to compensate for inflation so that the amount of payroll tax going into the worker's retirement account each year steadily increases. Both functions are idealized mathematical models but they serve very well to emphasize the strong effect of account duration, as well as the rate of return, on account value. For example, if a worker's account earns a 6% rate of return and the worker chooses to retire after working 45 years rather than 40 years, the worker's retirement account value at retirement time would be 37% higher, just by working that extra 5 years.
It is important to note the simple and common characteristics of the annuity and inflated annuity functions. They both give account value at the end of a chosen number of years as the product of two numbers. With the annuity function the first number is the annual constant investment amount and the second number is a simple multiplier which depends on the account duration in years and the compound interest rate . With the inflated annuity function the first number is the final investment amount, as the investment amount is increased each year by the inflation rate, and the second number is a multiplier which depends on the account duration in years and the effective rate of return (defined in the next paragraph). In both cases the multiplier is the same function so that only one multiplier table is needed for determining multiplier values. In the case of an inflated annuity you use the effective rate of return and in the case of the regular annuity, you use the real rate of return or interest rate. Interest rate and rate of return have the same meaning but interest rate is usually used in connection with a a bank account or loan whereas rate of return is used in connection with investments.
In order to simplify the definition of the inflated annuity function in
SOLUTION a number of terms such as gain factor and
inflation factor are introduced here together with the
corresponding rate of return and inflation rate. These terms are used to
define the effective gain factor and the corresponding
effective rate of return(or effective interest rate),
which is that of gain in purchasing power. All of
these factors are annual factors but they are also used to denote average annual
factors, where so defined. The letter a is used to
denote the apparent market gain, or the
advertised interest in the case of a bank account or bank loan ,and the
gain factor is (1 + a), with the
gain a written in decimal form. The gain factor
gives the dollar output after a year of investment
per dollar invested. Similarly the letter i is
used to denote an annual inflation rate, and the
inflation factor is (1 + i), with
inflation rate i written in decimal form. The quantity
r in the equation (r = a - i) is termed the
real rate of return. It is the amount by which the apparent rate of
return exceeds the inflation rate. The ratio 1 / (1 + i)
gives the amount of purchasing power left in a dollar after
one year with an inflation rate of i%. It also signifies
"What you could buy for one dollar last year now costs (1 + i) dollars."
Multiplying this ratio by the gain factor for the year gives us the
effective gain factor (1 + re ). This can be seen by
substituting the quantity (r + i) for a in the gain
factor and simplifying the product as follows: (1 + r + i) / (1 + i) = (1
+ re) where
It is important at this point to note the difference between arithmetic and geometric averages. The arithmetic average of the sum S of n terms (numbers) is w = S / n and S = n x w. The geometric average w of the product P of n factors (numbers) is the nth root of P and P = wn, i.e. w to the nth power. The nth root of P is found by dividing the logarithm of P by n and taking the antilogarithm of the result. Calculations using logarithms and antilogarithms (aka inverse logarithms) can be be quickly and easily made using a small hand-held computer. This is an essential and inexpensive tool to have these days. In dealing here with gain factors, inflation factors, and effective gain factors, the average values will be geometric averages.
A simple example will illustrate how easy it is to compute an average annual gain, inflation, or effective gain factor. Since they are all computed in the same way, the average annual gain factor for the years 1950, 1951, and 1952 will be computed using the NYSE Composite data given in DATA. The gain factors for these years are 1.2086, 1.1630, and 1.0645 respectively. The triple product 1.2086 x 1.1630 x 1.0645 = 1.4963 gives the cumulative gain or gain factor for the three year period. Using logarithms the cube or third root of 1.4963 is quickly found to be 1.14377 so the average annual gain for this three year period is 14.4%. Now in using the tables in DATA the multiplication is already done for you. For example, to get the cumulative gain for the 25 year period from 1965 to 1990, you simply divide the cumulative gain for 1990 by that for 1965.
It is shown that wage increases due to experience gained can be handled by subaccounts that have shorter durations than the main account. The shorter durations mean the subaccounts will be weighted less in determining final account value. This approach is used, with multiple subaccounts, to compare a new system average retirement income to the present system average retirement income.
Assuming a retiring worker will choose to make annual withdrawals from the worker's account leaving the remainder invested, the worker needs to know how large an annual withdrawal can be made and have the account last a specified number of years. Tables and the equations for handling this problem are given assuming a constant inflation rate and a constant effective rate of return for the worker's account during the worker's retirement years. Of course, the worker would still need to monitor the worker's account value and perhaps make adjustments in the size of the worker's withdrawals. Account management would be the worker's responsibility, but the SSA would provide a considerable amount of guidance.
The NYSE Composite Index end-of-year values and the annual
Consumer Price Index values for the period 1940 - 2003 are presented in
tables in DATA and are used to construct a
table (in DATA) of the annual effective rate of return of the NYSE Composite
over this 63 year period. It shows how the purchasing power of one dollar
invested in 1940 in the NYSE Composite has changed over the years. The most
pleasing results were that the average annual effective rates
of return for the periods 1948 - 1963 and 1981 - 1999 were 8.3% and 8.7%
respectively. There were 2 periods however where the average annual
effective rate of return was negative! For the period 1940 -
1948 it was -2.5% and for the period 1968 - 1981 it was
The derivations of the annuity function, the inflated annuity function, and the maximum withdrawal rate from the retirement account during retirement to have the account last through the retirement period are given in DATA, which also contains the NYSE Composite Index data table, the Consumer Price Index data table, and the resultant effective market gain data table. The tables are all for the period 1940 - 2003 and the data are presented in 2 forms, yearly and cumulative, so that it is easy for the reader to check the summary results shown in the SOLUTION page and to compute similar results for any period in the years 1940 - 2003.
The new system could include the self-employed in a much less expensive manner than they are in the current system (they pay a 15.3% "payroll tax"), and after 40 to 45 years in the system, even less if they are very successful, they could retire and have a good retirement income. When the payroll tax rate gets down to 4%, many more workers might well choose to be self-employed, and it could happen much sooner than that.