Estimates of retiree income will be obtained, indirectly and after some analysis,
by basically using the
annuity value function M(r,n)
which gives the value of an investment account after n years
if the investor puts a fixed amount , e.g. one dollar, into the account each
year and the account earns a compound interest or
| Yrs | 4% | 5% | 6% | 7% | 8% |
|---|---|---|---|---|---|
| 10 | 12 | 13 | 13 | 14 | 14 |
| 15 | 20 | 22 | 23 | 25 | 27 |
| 20 | 30 | 33 | 37 | 41 | 46 |
| 25 | 42 | 48 | 55 | 63 | 73 |
| 30 | 56 | 66 | 79 | 94 | 113 |
| 35 | 74 | 90 | 111 | 138 | 172 |
| 40 | 95 | 121 | 155 | 200 | 259 |
| 45 | 121 | 160 | 213 | 286 | 387 |
| 50 | 153 | 209 | 290 | 407 | 574 |
This table shows that if you put one dollar into an account earning a compound return rate of 6% each year for 45 years the account would be worth 213 dollars and if you put in 1000 dollars each year for 45 years the account would be worth $213K. The 45 year saving period gain fits nicely with a 45 year work life (running from age 20 to age 65) where a worker could be putting his payroll tax into an account for his retirement.
The above table can be used to demonstrate that a 4% payroll tax can be adequate for providing superior retiree incomes. Assuming the absence of inflation, suppose that a worker retires after 45 years of earning $30K per year and putting 4% or $1200 into an annuity account each year. Consider the cases where the account earns a compound rate of return of a) 6% and b) 7%. At retirement the account value is in case a) $255.6K and in case b) $343.2K. Now it is shown later in computing appropriate withdrawal rates that if the worker wants to have the account last 20 years after retiring the annual withdrawal rate can be in case a) 8.02% of $255.6K or $20.5K which is 68.3% of his pre-retirement income. In case b) it is 8.63% of $343.2K or $29.6K which is 98.7% of his pre-retirement income. Now if a worker could get at least a 6% compound return rate, and there were no inflation whatsoever, the case for worker retirement accounts would be very evident, and even conclusive considering a 7% compound return rate . When we take into consideration inflation however, the corresponding results will not be quite as good.
Now inflation can and does change wages and the value of the dollar dramatically over a working lifetime of 35 to 45 years. For example, in the 45 year period from 1957 to 2002 the average annual inflation rate was 4.2% (see the Consumer Price Index table in DATA) which meant it took $6.40 to buy in 2002 what $1.00 could buy in 1957! So you can see that it is very important to take inflation into account in determining retiree incomes. This is done by generalizing the annuity function to obtain what is termed the inflated annuity function. The annuity function and inflated annuity function are derived in DATA as appendix material because they are mathematical in nature and also because they are essential to the understanding of personal retirement accounts. The derivations however are just there for the mathematical critics and the general reader need only understand that the above table also provides the multiplier value for account age and effective return rate.
The idea behind the inflated annuity is to assume an
apparent rate of return equal to r + i where r is the real return rate and
i is the inflation rate (using the Inflation Analysis material in OVERVIEW) and
to assume that a worker’s wage is increased each year by the factor
With the above assumptions it is shown in DATA that the worker’s account value after n years is
.04W(1 + i)n-1 M(re, n)
where W(1 + i)n-1 is the worker’s wage after n years (just due to inflation) and M(re ,n) is the multiplier or annuity function based on account age and effective rate of return. This expression for account value reduces to that for an ordinary annuity account if there is no inflation and allows us to see how inflation reduces account value. First, there is a slight reduction in the multiplier values since the effective rate re is slightly smaller than the real rate r. Now a worker’s wage is not necessarily adjusted each year to compensate for inflation although the need for regular adjustments is recognized. There is also the belief that increased labor costs frequently precede and cause rising prices. The expression wage-price spiral suggests that it is difficult to say which came first, so over a long period of years the expression for the final wage appears reasonable (Although it is also reasonable to expect some lag in wage adjustments).
A major problem with the account value expression is that the effective market gain varies over time. Actually, short term values go up and down "like a roller coaster", e.g. the values for 1951 through 1956 were consecutively 8%, 4%, -5%, 31%, 26%, 6% (see DATA). In order to assume these parameters to be constants over a period of time, it is necessary to interpret them as geometric long term average values which can only be determined at retirement time or estimated using past long term averages. Consequently we have to assume a long term value of effective market gain of say, 6% or 7%, to determine a conditional multiplier value. Later it will be shown how market gain, inflation, and effective market gain have varied since 1940 and it will be shown that the 6% and 7% values are reasonable assumptions in a healthy economy. Note that in using the above multiplier table with inflation, the effective compound return rate is used.
Perhaps the best way to look at the account value
of the inflated annuity at the time of retirement is as a
multiple of the worker's annual wage at retirement. If n = 45 (years) and
The calculation of account value so far has only taken into account
inflation. The following example will show how pay raises can
affect retirement income while still using the inflated annuity expression for
account value. Assume a worker works 45 years, his starting annual wage
is W, the annual inflation rate i% is constant, and his retirement account earns
a constant effective return rate of 6 %. Assume further that
at the end of the 5th
year he gets a
This can be computed by considering that the worker has in
effect a second annuity account starting in year 6 and that the payroll tax
going into the second account will be and will continue to be equal to 25 % of
the amount going into the first account (this is generally true unless the
worker changes to a lower job classification). Specifically, in year 6 there will be
.04( .25W(1 + i)44) into the second.
These values are listed in Table 2 below to illustrate how the second account
values compare to the corresponding values of the first account. Also
with the 40% wage increase he has in effect a third annuity account starting in
year 11 and the payroll tax going into the third account will be and continue to
be 40% of the total amount going into the first 2 accounts which is equal to 50%
of the amount going into the first account. Note in Table 2 the account
age or duration is shown for each account and, assuming a 6% effective return
rate, the multiplier values from Table 1 have also been listed.
Final subaccount values are obtained by first multiplying .04 (payroll tax rate) times the size of the wage increase as a decimal fraction of the value of subaccount 1 at the time of the wage increase (e.g. .25 at the end of the 5th year). For subaccount 1 this is 1.0 at the start of the account in year 1. This product is then multiplied by the multiplier value which is determined by the subaccount age and the effective rate of return, and the result is the numerical coefficient in the final value expressions.
All that is needed now in order to compute the full
account value in year 45 is the value of
| Subaccount # | 1 | 2 | 3 |
|---|---|---|---|
| Initial Input | .04W | .25(.04W)(1+i)4 | .5(.04W)(1+i)9 |
| Final Input | .04W(1+i)44 | .25(.04W)(1+i)44 | .5(.04W)(1+i)44 |
| Duration d(yrs) | 45 | 40 | 35 |
| Multiplier (re=6%) | 213 | 155 | 111 |
| Final Value | 8.52W(1+i)44 | 1.55W(1+i)44 | 2.22W(1+i)44 |
| Estimated Value ($) | 170.4K | 31K | 44.4K |
There are two important points to note in the above computation of retirement account value. The first is that by taking 20K to be the inflated value of the starting wage W, we have bypassed the explicit calculation of the inflation effect on the final wage while still taking into account that effect by using a current starting wage. The second point to note is the strong weighting effect that subaccount duration had in computing the final subaccount values. Even though the worker had sizeable wage increases at ages 25 and 30 (assuming the worker entered the workforce at age 20), the two raises together only resulted in 31% of the total account value.
A second example extends the method used to take into account wage increases by estimating the retirement account value of an average worker retiring from the present system in 2002 but assuming that the worker had been working in the new system for the previous 45 years. The goal was to compare the retirement income of this average worker to the average yearly Social Security benefit of $10,656 paid in 2003, which was derived from a Cato Institute report and discussed in PROBLEM. The data used to make this estimate are given in the following table and come from Social Security Administration Table 4.B15, provided by the courtesy of Greg Diez and William Kearns of the SSA. Table 4.B15 data are described in more detail in COSTS where they were used to estimate the transition costs of phasing in the new system
The age groupings in the table below, largely in 10 year age spans, were considered too coarse for estimating final retirement account value so a finer wage versus age profile was constructed from the table data and consistent with them as follows: The average taxable wage for the 20-29 age group was taken to be that of a 25 year old, that for the 30-39 age group was taken to be that of a 35 year old, etc. up through the 50-59 age group. These values are shown in the subsequent table where the constructed wage versus age profile is given in row C. Row B of that table gives the ages for which the average taxable wage is estimated. Using the values assumed for ages 25, 35, 45, and 55, the values for ages 30, 40, and 50 are determined by interpolation, i.e. the value for age 30 is the average of the values for ages 25 and 35, etc. The value for age 20 is determined by extrapolation from the values for ages 25 and 30 and is such that the value for age 25 is the average of the values for ages 20 and 30. The values for ages 60 and 61 are just the values for the age groups 60-61 and 62-64 obtained from Table 4.B15.
| Age Group (yrs) | 20-29 | 30-39 | 40-49 | 50-59 | 60-61 | 62-64 |
|---|---|---|---|---|---|---|
| Average Taxable Wage | 18.3K | 31.6K | 35.1K | 35.7K | 31.2K | 26.5K |
The calculation of the retirement account value for this average worker retiring in 2002 assuming the worker had been in the new system for the previous 45 years is shown in the following table. This calculation is very similar to the calculation of the final account value in year 45 in the first example except that now there are ten subaccounts, the amount of the worker’s total wage that is in each subaccount at retirement in the year 2002 is given, and the percentage wage increases gained earlier in the worker’s work life are given by these final subaccount wages. For example, the average wage for a 25 year old is 57.8% higher than that for a 20 year old so it is assumed that this average worker got a 57.8% wage increase at age 25 and that this increase went into the second subaccount and that this increase amounted to $6.7K in 2002. The percentage increase assumed that this average worker gains at the age given in row B is given in row D and the value of this increase in 2002 is given in row E
Note that Table 4.B15 data show decreases in the average taxable wage of workers starting at age 60. Apparently this is due to some workers starting to work part-time at age 60 or switching to work that is less physically demanding but which pays less. In the calculation of total account value these wage decreases are handled as deficit subaccounts and act to reduce total account value. To understand why they should reduce account value note that, for example, the wage increase that initiated subaccount 8 at age 55 was considered to be maintained until age 65, but obviously it was not. However, the deficit subaccounts here have such short durations that their effect on total account value is negligible.
In order to determine the amount of the 57.8% increase, for example , it is necessary to assume an inflation factor for the 45-year period. Supposing that factor were 5, the starting wage corresponding to the 11.6K would be 2.3K, the corresponding average annual inflation rate would be about 3.7%, this worker’s wage at the end of the 5th year would be about 2.7K, and the increase would be about 1.6K. That seems like a rather large step increase, but if a finer wage versus age profile were available, there would be more subaccounts and the step increases would seem more reasonable. Actually we can construct a finer wage versus age profile that is still consistent with the Table 4.B15 data and doing this for ages 21 through 35 really emphasizes the value of subaccount duration in determining total account value at retirement time. Accordingly this was done and the results are shown in the subsequent table where the sum of the 15 subaccount values (in row H for a 6% effective return rate, in row J for a 7% effective return rate) replaces the sum of the values of subaccounts 2, 3, and 4 in the coarser wage versus age table. That is, $105.6K replaces $92.1K and $134.3K replaces $115.6K.The total account values are then $210K with a 6% average annual effective market gain and $272.8K if we use a 7% value. Now the justification for using the 6% and 7% values in computing these account values at retirement time and how those account values translate into retirement income will be considered later. First we have to look at the numbers in Tables 4 and 5 a little more closely.
| A | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| B | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 | 62 |
| C | 11.6 | 18.3 | 25 | 31.6 | 33.4 | 35.1 | 35.4 | 35.7 | 31.2 | 26.5 |
| D | - | 57.8 | 36.6 | 26.4 | 5.7 | 5.1 | 0.9 | 0.8 | -13 | -15 |
| E | 11.6 | 6.7 | 6.7 | 6.6 | 1.8 | 1.7 | 0.3 | 0.3 | -4.5 | -4.7 |
| F | 45 | 40 | 35 | 30 | 25 | 20 | 15 | 10 | 5 | 3 |
| G | 8.52 | 6.2 | 4.44 | 3.16 | 2.2 | 1.48 | 0.92 | 0.52 | 0.23 | 0.13 |
| H | 98.8 | 41.5 | 29.7 | 20.9 | 4.0 | 2.5 | 0.3 | 0.2 | -1.0 | -0.4 |
| I | 11.4 | 8.0 | 5.5 | 3.8 | 2.5 | 1.64 | 1.01 | 0.55 | 0.23 | 0.13 |
| J | 132.2 | 53.6 | 36.9 | 25.1 | 4.5 | 2.7 | 0.3 | 0.2 | -1.0 | -0.4 |
| A. | Subaccount number. The data for subaccount j are given in column j. |
|---|---|
| B. | Age of worker when subaccount was initiated. |
| C. | Average wage of worker of this age in the year 2002 in thousands of dollars. |
| D. | Percentage wage increase obtained by worker at this age. |
| E. | Initial subaccount value in thousands of 2002 dollars. |
| F. | Duration of subaccount in years (subaccount age at retirement). |
| G. | Multiplier equal to 4% of Annuity Account Multiplier for age F and a 6% effective rate. |
| H. | Final subaccount value G x E in thousands of dollars with a 6% effective rate. |
| I. | Multiplier equal to 4% of Annuity Account Multiplier for age F and a 7% effective rate. |
| J. | Final subaccount value I x E in thousands of dollars with a 7% effective rate. |
| A | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| B | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 |
| C | 12.9 | 14.3 | 15.6 | 17.0 | 18.3 | 19.6 | 21.0 | 22.3 | 23.7 | 25.0 | 26.3 | 27.6 | 29.0 | 30.3 | 31.6 |
| D | 11.6 | 10.4 | 9.4 | 8.6 | 7.9 | 7.3 | 6.8 | 6.4 | 6.0 | 5.7 | 5.3 | 5.0 | 4.8 | 4.6 | 4.4 |
| E | 1.34 | 1.34 | 1.34 | 1.34 | 1.34 | 1.34 | 1.34 | 1.34 | 1.34 | 1.34 | 1.32 | 1.32 | 1.32 | 1.32 | 1.32 |
| F | 44 | 43 | 42 | 41 | 40 | 39 | 38 | 37 | 36 | 35 | 34 | 33 | 32 | 31 | 30 |
| G | 8.0 | 7.52 | 7.04 | 6.6 | 6.2 | 5.8 | 5.44 | 5.08 | 4.76 | 4.44 | 4.16 | 3.88 | 3.64 | 3.40 | 3.16 |
| H | 10.7 | 10.1 | 9.4 | 8.8 | 8.3 | 7.8 | 7.3 | 6.8 | 6.4 | 5.9 | 5.5 | 5.1 | 4.8 | 4.5 | 4.2 |
| I | 10.6 | 9.9 | 9.2 | 8.6 | 8.0 | 7.4 | 6.9 | 6.4 | 6.0 | 5.5 | 5.1 | 4.8 | 4.4 | 4.1 | 3.8 |
| J | 14.2 | 13.3 | 12.3 | 11.5 | 10.7 | 9.9 | 9.2 | 8.6 | 8.0 | 7.4 | 6.7 | 6.3 | 5.8 | 5.4 | 5.0 |
Note that whereas the wage increase in going from age 20 to age 25 and from age 25 to age 30 was 6.7K, it is now one fifth of that or 1.34K per year in going from age 20 to age 30. Similarly the increase is now 1.32K per year in going from age 31 to age 35. The row descriptors from the previous table apply also to this table except that there now 15 subaccounts. These 15 subaccounts, replacing subaccounts 2,3, and 4 of the previous table, have a total subaccount value of 105.6K versus the total of 92.1K in row H and 134.3K versus 115.6K in row J. The step increases of 26.4% to 57.8% now are replaced by smaller step increases ranging from 4.4% to 11.6%, and using the same assumed values of inflation factor and inflation rate , the wage increases range from $310. to $476. per year or hourly rate increases from $.15 to $.24.
Now the basic assumption in the above analysis is that the wage versus age profiles in the 45 years preceding 2002 were essentially the same as for 2002 except that the wage values changed from profile to profile by the corresponding inflation factors. This is something that can be confirmed by the Social Security Administration in addition to providing finer wage versus age profiles. The above analysis with the refined and constructed profile indicated that this average worker had at retirement time an account value of about $210K with a 6% return rate, $272.7K with a 7% return rate, and these values will be used to compute the yearly retirement incomes that this account could provide after first discussing withdrawal rates . At this point it is important to note that 97% of the total account value that this average worker gained is due to his annual earnings between age 20 and 35 (assuming these earnings levels are not reduced prior to retirement). This is due to the strong effect that account duration has on account value.
Now a retiree will generally want to make periodic withdrawals from his
account leaving the balance invested so as to have his account last through his
retirement years. Assume the average market gain a and
average inflation rate i have changed little over the years immediately
preceding retirement and the retiree expects these numbers to remain essentially
the same for the immediate future. Assume also he wants the
account to last k years, e.g. k = 20, and that he wants to increase his
withdrawal amount each year by the factor
(1+i) to compensate for inflation. Therefore if his
initial annual withdrawal is p% of his final account value A, his withdrawal for
the second year would be p(1+i)% of A, p(1+i)2
% of A in the third year, etc. Now he needs to find the maximum value of
p that will allow his account to last k years. It turns out that
the maximum initial withdrawal rate p% is given by the quantity (1 +
re )k divided by the quantity
(( 1 + re )k
+ M( re , k ) )
where re is the value corresponding to the average market gain and
the average inflation rate. Actually, this value of p is such that the account
will last k+1 years before it is empty, allowing the retiree to feel
a little more secure. Note that M (re , k)
is the annuity function making another appearance, and that the value of p is
independent of the account value A. The quantity
( 1 + re
)k is the value of an account after k years earning a compound
return rate re where there is only an initial investment,
e.g. one dollar. The derivation of p is shown in DATA
for the mathematically inclined, and the following table gives the values of
p in percent form for k values of 15, 20, and 25 years, and
for the familiar values of re for those not so inclined.
It is important to remember that the values of the percentage p depend on both
the average gain and corresponding average inflation rate or equivalently on
both re and the corresponding average inflation rate.
Now market gain and inflation rate can change from year to year leading the worker to be very concerned about having his account last for a certain number of years. Since this will almost certainly be a matter of general concern among retirees, it is very likely that the Social Security Administration (SSA) will have become very expert in helping retirees make their accounts last, including recommending annual adjustments in withdrawal amounts to compensate for inflation rate and market gain changes. Note that the average values will usually change much more slowly than annual values. Three or four year average should generally work fine.
Retirees will generally want to make monthly withdrawals, once they have decided on an appropriate annual withdrawal amount. They might want to make special withdrawals at times to pay their property taxes or buy a new car. They could have monthly withdrawals by the IRS as estimated income tax, and they could probably have their monthly withdrawal automatically deposited in their checking account. There could be a lot of flexibility in the way they manage their retirement accounts.
| k / re | 4% | 5% | 6% | 7% | 8% |
|---|---|---|---|---|---|
| 15yrs | 8.25 | 8.79 | 9.34 | 9.89 | 10.46 |
| 20yrs | 6.85 | 7.43 | 8.02 | 8.63 | 9.24 |
| 25yrs | 6.02 | 6.63 | 7.26 | 7.90 | 8.57 |
Consider now the retirement income of that average worker retiring from the present system in 2002 but assuming he had been working in the new system for the last 45 years with 4% of his annual wage going into his retirement account. If the worker's account had earned and continued to earn an effective return rate of 6% he would have $210K in his account and he could start his withdrawals at 8.02% per year or $16.8K and have his account last 20 years or to age 85. With a life expectancy of 17.5 years, which is the average for men and women aged 65, the $16.8K provides a reasonably good comparison with the $10.7K average benefit from the present system and for about 32% of the current payroll tax rate. The $16.8K is also 63% of the $26.5K average wage of workers 62 to 64 years old who are about to retire. That can also be regarded as a pretty decent pension.
If the worker's account had earned and continued to earn an effective return rate of 7% he would have $272.7K in his account at retirement time and he could start his withdrawals at 8.63% per year or $23.5K and have the account last 20 years or to age 85. ( it is convenient to use the pronouns he and his although the worker here is an average worker from the 2002 combined group of men and women workers) The $23.5K is greatly superior to the $10.7K average benefit from the present system and is 89% of the $26.5K average wage of the workers 62 to 64 years old who are about to retire. Later in examining the U.S. economy from 1940 to 2003 it will be seen that an effective return rate of 7% looks reasonable, barring war and stock market depressions like the one we had from 1968 to 1981. Social Security retirement incomes this impressive might cause large corporations to switch from private pensions to using such a new Social Security System to meet their pension obligations.
Another aspect of annuity accounts in general, which is important to note, is how the value of the account multiplier increases with the parameter n, which is a measure of the age of the account in years but which can also be taken as a measure of the total amount invested, e.g. n dollars. In the case of the inflated annuity function, n (in "inflation-adjusted dollars") is regarded as the account input and the account value M(re,n) is the account output, for a given rate of return re and a duration of n years. The annuity account gain is then taken as the ratio of M(re,n) to n and is conveniently expressed as dollars output per dollar input. The table below gives the inflated annuity account gain for several values of return rate and for account age ranging from 20 years to 50 years. The table values show that the account gains for accounts held for 20 years or 25 years are rather low compared to the gains of accounts held for 40 to 50 years and that account gains increase at an increasing rate as account age increases. This is the reason why using personal retirement accounts to supplement present system benefits doesn't make much sense, i.e. they would generally be of short duration. It also indicates that if a worker wants to work more than 45 years, working those extra years can be quite profitable.
| 20 yrs. | 25 yrs. | 30 yrs. | 35 yrs. | 40 yrs. | 45 yrs. | 50 yrs. | |
|---|---|---|---|---|---|---|---|
| 8% | 2.3 | 2.9 | 3.8 | 4.9 | 6.5 | 8.6 | 11.5 |
| 7% | 2.1 | 2.5 | 3.2 | 4.0 | 5.0 | 6.4 | 8.1 |
| 6% | 1.8 | 2.2 | 2.6 | 3.2 | 3.9 | 4.7 | 5.8 |
| 5% | 1.7 | 1.9 | 2.2 | 2.6 | 3.0 | 3.6 | 4.2 |
Going back now to the annuity function M(re,n) we saw that with an effective return rate of 6%, investing an extra $100 per year for 45 years would result in an additional $21,300 in a worker’s retirement account. If a worker at age 40 wants to gain the same additional amount in his retirement account and his account earns the same effective return rate, he has to put an extra $387 in his account each year for the next 25 years, and if the worker was at age 45, it would be an extra $576 each year for the next 20 years. This is because the multiplier value M(re,n) falls off fairly rapidly as the investment duration parameter n is decreased, and this is the basic reason for concluding that a worker’s account value at retirement is essentially determined by the wages he earns between 20 and 35 years of age. If a worker gets large wage increases when he is in his 40’s that will certainly increase the value of his account at retirement time but not as much as he might expect.
To get an idea of what a worker might expect in the way of an annual rate of return on his personal account, assuming his payroll tax money is invested in a broad based stock fund, the end-of-year values of the NYSE Composite Index from 1939 to 2004 were examined (the NYSE Composite consists of over 2000 U.S. and non-U.S. stocks). In order to determine effective rates of return (after inflation) the Consumer Price Index (CPI) data, produced by the U.S. Bureau of Labor Statistics were used. The NYSE Composite Index and CPI data were used to construct tables, shown in DATA, that allow one to determine, for any multi-year interval in the overall period from 1940 through 2003, cumulative market gain (amount of change in the Composite Index), cumulative inflation, and effective cumulative market gain. There are three tables. The first gives the NYSE Composite Index data and corresponding yearly gain factors (1+a) where a is the apparent gain relative to the Index value for the previous year. The second gives the CPI annual inflation factors (1+i) where i is the inflation rate for the year and it gives the cumulative inflation relative to 1940. The third table gives the effective annual NYSE Composite gain factors (1+ re) and the cumulative effective NYSE Composite market gain relative to 1940. Note that (1+a), (1+i) and (1+re) are the gain factor, inflation factor, and the effective gain factor defined earlier in discussing inflation. The variable a is the apparent gain in a one-year investment, the variable i is the inflation rate for the year and re is the effective gain or rate of return. Using the tables to determine the market gain, the cumulative inflation, and the effective market gain for a multi-year period , the geometric average annual market gain, average annual inflation rate, and average annual effective market gain for that period can be computed, and these are the numbers shown in Table 8 below.
The table below shows these numbers for four major periods in years 1940
through 2003 and several sub-periods within three of those major periods in an
attempt to better understand some rather extreme variations. The first major
period is the period 40 – 48 (1940 -1948). These were
years of lend-lease activity, World War II, and post-war readjustment, unlike
any other years in the 63-year period. There was severe gas rationing, over 11
million in the U.S. military at the height of the war, and the vast majority of
manufacturing facilities were devoted to producing war materials. It was not a
good time to invest in the market. The average annual market gain was
The years from 1948 to1963 were very good years in that inflation was very low and market gain was high. The average annual inflation rate for this 15-year period was just 1.6 % and the average annual effective return rate was 8.28% ! This was the period in which the baby boomer generation was born and when many World War II vets graduated from college thanks to the GI Bill. The U.S. Treasury Fact Sheet on the U.S. Tax System indicates the Federal tax burden had been reduced from the wartime high of 20.9 percent to 14.4 percent of GDP by 1950, but the Korean War and the extension of Social Security coverage to the self-employed brought it up to 19 percent by 1952.
The sub-period 63-68 was added to major period number 2 in an attempt to see what might have contributed to or caused the catastrophic inflation losses and complete loss of any effective market gain in the third major period 68-81. In the years 63-68, President Johnson claimed that a minor incident in the Gulf of Tonkin between the U.S. destroyer Maddox and North Vietnamese patrol boats was an act of unprovoked aggression and was given the power, by The Gulf of Tonkin Resolution in 1964, to escalate our involvement in the Vietnamese civil war as the President saw fit. Then the first U.S. combat troops landed in 1965 and our war with the North Vietnamese lasted until 1975 when we left in defeat. Prior to 1965 we had just had military advisors aiding the South Vietnamese. The war lasted 10 years and cost us over 58,000 dead, over 153,000 wounded, and our faith that we could fight a war to a successful conclusion. Also in 1964 President Johnson declared a War on Poverty, which included programs like Head Start and Job Corps, and in 1965 Congress created the Medicare program and passed Social Security Amendments creating the Medicaid programs. These two wars undoubtedly caused taxes to be increased substantially. We can see that the sub-period numbers show that average annual market gains, both apparent and effective, were significantly lower over this 5-year period than the corresponding numbers for the preceding 15-year period. Also the average inflation rate increased to 2.6 %, the annual rate having steadily increased from 1.3 % in 1964 to 4.2 % in 1968.
| Period # | Sub period Span in Years | a% | i% | re% |
|---|---|---|---|---|
| 1 | 40-48 | 4.4 | 7.0 | -2.5 |
| 2 | 48-63 | 10.0 | 1.6 | 8.3 |
| 2 | 63-68 | 8.1 | 2.6 | 5.4 |
| 2 | 48-68 | 9.6 | 1.9 | 7.6 |
| 3 | 68-72 | 2.4 | 4.7 | -2.2 |
| 3 | 72-81 | 1.5 | 9.0 | -6.9 |
| 3 | 68-81 | 1.8 | 7.7 | -5.5 |
| 4 | 81-91 | 11.6 | 4.1 | 7.2 |
| 4 | 81-99 | 12.2 | 3.2 | 8.7 |
| 4 | 81-03 | 9.6 | 3.3 | 6.1 |
The numbers for the 20-year period 48-68 are absolutely great numbers for promoting a Social Security system based on personal retirement accounts The average inflation rate is under 2% and the average annual effective rate of return is 7.6%. If these values could be obtained for 45-year periods, retirement incomes would be roughly 60% higher than those if that rate of return were 6%.
Period 3, years 68 – 81, is best covered by examining sub-periods 68 - 72 and 72 – 81. The first of these coincides with President Nixon’s first term in which he had to deal with both rising inflation and rising unemployment, the latter at 5%, up from 3.5% in the late 60’s. There was considerable interest in the government managing the economy at that time and in 1970, Federal Reserve Chairman Arthur Burns proposed setting up a wage-price review board, composed of distinguished citizens, who would pass judgments on major wage and price increases. In August, 71 a New Economic Policy was put into effect calling for a 90-day freeze on prices and wages allowing time to put new economic expansion policies to be implemented. The public and press were enthusiastic about the policy, the Dow Jones Industrial average had its biggest one-day advance to that date, and Nixon was reelected in 72. Now the table above shows the average effective annual gain for this sub-period was -2.2% but the effective gain table in DATA shows that 69 and 70 were the losing years.
In 73 Nixon reimposed a wage-price freeze in response to increased inflation which put the Government in the business of setting prices and wages. However ranchers, farmers and others rebelled against the controls and most were abolished in April 74. President Nixon resigned from the presidency in 74, due to the Watergate Affair, but as president he had established the Environmental Protection Agency, the Equal Opportunity Commission, and the Occupational Safety and Health Administration, agencies that imposed considerable regulation on our economy and increased business costs. In 74 the effective gain of the NYSE Composite was -35%! That has to be some kind of record! The economy was bad and Nixon's resignation was like the proverbial "last straw".
Succeeding Nixon, Gerald Ford was president from 74 through 76. Inflation was high enough to discourage investment and push capital overseas and into government bonds. In 76 Jimmy Carter was elected president, there was a severe recession and the largest peacetime deficit of $66.4 billion. In 77, Carter’s first order was to pardon draft evaders. In 78, OPEC raised the price of oil 50% causing more inflation. The budget deficit was 48.8 billion and the discount rate was 9.5%. In 1980, the inflation rate was 13.5%, the budget deficit was $75 billion, the discount rate was 16% (13% plus 3% surcharge) and Ronald Reagan was elected president. During the years 68-81 income tax was not indexed for inflation and the high inflation rates caused the tax burden to increase from 19.4 percent of GDP to 20.8 percent.
Reagan’s tax cut, entitled the Economic Recovery Tax Act of 1981, had strong bipartisan support in Congress. It enabled a 25% reduction in individual tax brackets, phased in over 3 years, and indexing for inflation. Also in 81, individuals were given the right to have Individual Retirement Accounts which reduced some of the multiple taxation of individual savings. Inflation rates dropped from 10.3% in 81 to 6.2% in 82, and to 3.2% in 83. Correspondingly the effective market gain increased from -11.1% in 81 to -.3% in 82, and to +18.2% in 83. However these tax cuts led to historically high budget deficits so that the tax cuts were reduced somewhat in 84, especially on the business side. Note in the table below , comparing the average values for the period 72-81 to those for the period 81-91, market gain went from 1.5% to 11.6%, inflation went from 9.0 % to 4.1%, and effective market gain from -6.9% to +7.2%.
The data for the 19-year period 81-99 are comparable to those for the very good 15-year period 48-63. The average annual market gain was 12.2% versus 10% for the 48-63 period and suggests that the economy was even more robust, probably due to the technological change that had occurred in the roughly 35 intervening years. The average annual effective market gain of 8.7% further emphasizes that retiree incomes could be exceptional under the new system.
In the period 99-02 however there was a severe market crash in which many
people lost a lot of money. In many cases these were retirees that had to go
back to work again, at least part-time. Now in 96 Federal
Reserve Board Chairman Alan Greenspan expressed concern about “irrational
exuberance” in the stock market but the NYSE Composite Index and NASDAQ
Composite Index gains in 95 and 96 do not appear to be alarming. The gain
tables in DATA show an orderly decline in annual gain from a peak value in 97 to
roughly zero in 00. These gain tables show many cases where the annual gain
declines from a peak value to a slightly negative value and then rebounds to a
reassuring value in the following year, so this orderly decline did not look
like it would go on to be a crash. However the NASDAQ
Composite Index milestone data 99 show an unbelievable increase in Index value
from 2100 to over 4000 by years-end. The NYSE Composite Index just shows a 12%
gain for 99. That unbelievable data might have convinced many that a crash was
about to occur and might have precipitated it. In 00 the Federal Reserve
increased the discount rate from 5% to 6% but by years-end had concluded that a
crash was occurring and starting in January of 01 rapidly reduced the discount
rate to 1.25% by January of 02. This undoubtedly helped to shorten the market
recovery time. The effective market gains from 00 to 03 were
respectively -2%,
In conclusion, the analysis of the stock market gains and inflation rates over the years 1940 through 2003 show that except for 3 bad periods, due to 3 distinct problems, the average annual market gains would make retirement accounts invested in the stock market very profitable. The years 40-48 were the years surrounding World War II and involved an all-out war effort. In a war of that magnitude loss of life and property are to be expected and market performance would be a minor concern. Looking at the years 68-81 it seems clear that the average annual effective gain of -5.5% over this 13-year period was due to excessive taxation. The excessive taxation reduced the purchasing power of workers causing them to seek higher wages. It increased the costs of producing goods and services causing the producers to seek higher prices. The inability to fully compensate for the excessive taxes, despite minor efforts to reduce taxes, led to higher inflation and lower market gains. After the Reagan tax cuts were passed it took another 11 years to fully recover from the cumulative market losses over the 13-year period, i.e. it took until 1992 to bring the cumulative market gain (relative to or measured from 1940) back up to the value it had in 68. Some of the Reagan tax cuts had to be taken back because they resulted in high deficits. It seems clear that in order to avoid excessive taxes and/or high deficits that we need to limit Government Spending.
Also in view of Federal Reserve Board Chairman Arthur Burns recommendation of a wage-price review board in 1970, for controlling inflation, and Chairman Alan Greenspan's concern about irrational exuberance in the stock market in 96, we need a separate government authority for monitoring the health of our economy, voicing concern about various government actions as to their economic effects, and in general for making recommendations as to the appropriate management of our national resources, including human resources, insofar as it affects our economy. For example, it seems that Congress with its taxing authority has as much control, if not more, over the money supply as the Federal Reserve and it seems obvious from the stock market depression in 68-81 that the Federal Reserve cannot control inflation just by controlling interest rates.
Finally the analysis of market gain together with inflation rates indicates a strong negative correlation between market gain and inflation rate. That is, high market gain and low inflation seem to go hand-in-hand and vice versa. Also it is obvious that a high inflation rate can turn a low market gain into an effective market gain that is negative.
The following internet-available references were used for the discussion of events affecting stock market behavior in the period 40-03:
1. Vietnam War, wikipedia.org
2. The War on Poverty, 1964 – 1968, lexisnexis.com
3. Lyndon Johnson’s War on Poverty, npr.org
4. Modern History Sourcebook, President Lyndon B. Johnson, fordham.edu
5. Nixon Administration Timeline, archives.gov
6. Nixon Tries Price Controls, pbs.org
7. Gerald Ford, wikipedia.org
8. Jimmy Carter, 1976 – 1980, acusd.edu
9. Fact Sheet: History of the U.S. Tax System, ustreas.gov
10. Federal Reserve Discount Rate History, harpfinancial.com
11. U.S. National Debt History, toptips.com
12. Fed Should Have Acted Against Stock Market Bubble, commondreams.org
13. NASDAQ Newsroom, nasdaq.com
14. The Housing Bubble, cepr.net