The Relationship Between
US Average Wage Growth and Rate of Return
by
William Larsen
4-12-2003
draft
Social Security's Old Age Benefit program uses a predefined formula for calculating benefits. This benefit is directly and proportionately effected by the change in the US Average Wage.
This link takes you to a interactive formula page where you can calculate what it takes to retire. It can help you compute the full value of your Social Security OASI tax.
This reference page provides links to many government web sites with data tables. They include Social Security, United Stated Treasury, Consumer Price Index, Period Life Tables, and more.
Is it critical that as the US average wage increases, that the rate of return the Social Security
Trust fund earns maintains an effective rate of return. If this does not occur, then the amount of
surplus in the year of increased wage growth must increase exponentially.
Table 1
When new cohorts begin work, they begin to contribute as well. This now creates two sources of revenues. New contributions and earnings from the trust fund. There are three categories of change, increasing, constant and decreasing worker to beneficiary ratio.
Increasing worker to beneficiary ratio creates a net cash surplus between new money and expenses. New contributions exceed expenses and the surplus deposited in the trust fund for the day when the ratio may not be as favorable.
Constant worker to beneficiary ratio creates no net cash surplus. New money will equal expenses. The trust fund continues to grow based on earnings only.
Decreasing worker to beneficiary ratio creates a situation where at some point in time new money will be insufficient to pay insufficient. At this point earnings from the trust fund will be needed to pay benefits. If there are no new workers, then the fund will exhaust itself when the last beneficiary dies.
All three categories of ratios have a common theme. They are based on actuarial accounting. In this way risk can be shared between those who live long and those who die young. The problem with life is few know when they will die?
If shared risk is not used, the savings rate of an individual to pay the same benefit as the 5.1% would more. The problem is what life span do you use? 10% of those born will live to age 90, where as 3% live to age 95. Saving 9.2% gives you a slight risk 3% of living past 95 and running out of money. Therefore, people can share the risk by pulling resources together. Saving 5.1% under a shared risk allows the worker to save an additional 4.1% which can be used to increase their living standard, otherwise saving 9.2% will be over saving for a vast majority of people while providing not enough resources in retirement. Saving 18.4% allows you 80% of your resources you enjoyed while working in retirement to age 95.
Social Security
Social Security's tax rate was created without regard to life expectancy, wage growth, inflation or the rate of return it would earn. As such the actual trust fund is insufficient to pay full benefits. Social Security was not based on actuarial accounting. Actuarial accounting would require the rate of growth in the trust fund must be large enough to make up the shortfall in revenues and expenses, but also at the same time increase to keep pace with the rate of change in the shortfall.
An effective rate of return of 2.9% is needed in order to maintain a 5.1% contribution rate. A lower effective rate of return would require a lower benefit or increased contribution rate.
Many analysis have evaluated Social Security's problem. They model them using a "
stochastic
model?
Click LINKS and you find some. In many cases, these analysts use what is referred to as a net
rate of return or real return. In this case the inflation rate is subtracted from the rate of return
earned by social security and this real rate/net rate is used to analyze the cash flow. There are a
number of problems in doing this. The number one problem is inflation is not used to index the
wages used to calculate the initial OASI benefit. The number two problem and could over time
be the number one problem is in compounding this error. Compounding over short periods of
time is not a real problem, but over 75 years, the difference between the two methods can be very
large. Table 2 shows the rate of return their analysis would use. The only time the two methods
are equivalent is when wage growth equals inflation at 3%.
Table 3
However, the most over looked and larger problem, most analysts who have evaluated Social Security's cash flow is in the handling of future benefits. The initial OASI benefit is based off wage growth. Assuming that each cohort will have the same equivalent benefit is wrong. Table 4 shows how far off the analysis can get when not taking into account wage growth in determining future benefits. For example, 4% wage growth and 3% inflation will underestimate the benefit 75 years from now by 106%. See table 4. This is the single largest problem.
Why then do analysts over look the effect of wage growth on future benefits? They may think keeping track of wages for a cohort and calculating that cohorts average benefit is too much work or error prone. Assuming each retiree receives the same value makes the calculation easier. Keeping track of the number in each cohort, their wages over 45 years and then indexing each cohorts benefit by inflation during retirement and on top of this keeping track of how many in each cohort draw benefits may be seen as an insurmountable problem. In my opinion, I think it is relatively easy to keep track of the number in each cohort and their unique initial benefit. This is why my analysis over the years has held steady for twenty years and others analysis are constantly being revised.
Revising an analysis is good, however, a moving average of variables should be used instead of using current values for inflation, wage growth and rate of return.
As a side note, the recent Social Security Administrations projected change in exhuastion of the Social Security Trust fund from 2041 to 2042 was caused by incresing the immigration rate into the United States.
References:
| Table 1
Effective Rate of Return Relationship | |||||||||||||
| Wage Growth | Rate of Return | Wage Growth | Rate of Return | Wage Growth | Rate of Return | Wage Growth | Rate of Return | Wage Growth | Rate of Return | ||||
| 0.00% | 2.90% | 2.00% | 4.96% | 4.00% | 7.01% | 6.00% | 9.07% | 8.00% | 11.13% | ||||
| 0.25% | 3.16% | 2.25% | 5.21% | 4.25% | 7.27% | 6.25% | 9.33% | 8.25% | 11.39% | ||||
| 0.50% | 3.41% | 2.50% | 5.47% | 4.50% | 7.53% | 6.50% | 9.59% | 8.50% | 11.64% | ||||
| 0.75% | 3.67% | 2.75% | 5.73% | 4.75% | 7.79% | 6.75% | 9.84% | 8.75% | 11.90% | ||||
| 1.00% | 3.93% | 3.00% | 5.99% | 5.00% | 8.04% | 7.00% | 10.10% | 9.00% | 12.16% | ||||
| 1.25% | 4.18% | 3.25% | 6.24% | 5.25% | 8.30% | 7.25% | 10.36% | 9.25% | 12.42% | ||||
| 1.50% | 4.44% | 3.50% | 6.50% | 5.50% | 8.56% | 7.50% | 10.62% | 9.50% | 12.67% | ||||
| 1.75% | 4.70% | 3.75% | 6.76% | 5.75% | 8.82% | 7.75% | 10.87% | 9.75% | 12.93% | ||||
| Table 2
Net rate of Return Relationship | |||||||||||||
| Wage Growth | Rate of Return | Wage Growth | Rate of Return | Wage Growth | Rate of Return | Wage Growth | Rate of Return | Wage Growth | Rate of Return | ||||
| 0.00% | 2.90% | 2.00% | 4.90% | 4.00% | 6.90% | 6.00% | 8.90% | 8.00% | 10.90% | ||||
| 0.25% | 3.15% | 2.25% | 5.15% | 4.25% | 7.15% | 6.25% | 9.15% | 8.25% | 11.15% | ||||
| 0.50% | 3.40% | 2.50% | 5.40% | 4.50% | 7.40% | 6.50% | 9.40% | 8.50% | 11.40% | ||||
| 0.75% | 3.65% | 2.75% | 5.65% | 4.75% | 7.65% | 6.75% | 9.65% | 8.75% | 11.65% | ||||
| 1.00% | 3.90% | 3.00% | 5.90% | 5.00% | 7.90% | 7.00% | 9.90% | 9.00% | 11.90% | ||||
| 1.25% | 4.15% | 3.25% | 6.15% | 5.25% | 8.15% | 7.25% | 10.15% | 9.25% | 12.15% | ||||
| 1.50% | 4.40% | 3.50% | 6.40% | 5.50% | 8.40% | 7.50% | 10.40% | 9.50% | 12.40% | ||||
| 1.75% | 4.65% | 3.75% | 6.65% | 5.75% | 8.65% | 7.75% | 10.65% | 9.75% | 12.65% | ||||
| Table 3
Net Difference between the two relationships over 75 years | |||||||||||||
| Wage Growth | Rate of Return | Wage Growth | Rate of Return | Wage Growth | Rate of Return | Wage Growth | Rate of Return | Wage Growth | Rate of Return | ||||
| 0.00% | 0% | 2.00% | -4% | 4.00% | -8% | 6.00% | -13% | 8.00% | -17% | ||||
| 0.25% | 0% | 2.25% | -5% | 4.25% | -9% | 6.25% | -13% | 8.25% | -17% | ||||
| 0.50% | -1% | 2.50% | -5% | 4.50% | -9% | 6.50% | -14% | 8.50% | -18% | ||||
| 0.75% | -1% | 2.75% | -6% | 4.75% | -10% | 6.75% | -14% | 8.75% | -18% | ||||
| 1.00% | -2% | 3.00% | -6% | 5.00% | -10% | 7.00% | -15% | 9.00% | -19% | ||||
| 1.25% | -3% | 3.25% | -7% | 5.25% | -11% | 7.25% | -15% | 9.25% | -19% | ||||
| 1.50% | -3% | 3.50% | -7% | 5.50% | -12% | 7.50% | -16% | 9.50% | -20% | ||||
| 1.75% | -4% | 3.75% | -8% | 5.75% | -12% | 7.75% | -16% | 9.75% | -21% | ||||
| Table 4
Error in Assuming OASI Benefits Constant | |||||||||||||
| Wage Growth
(-) under estimation (+) over estimation of future benefits | |||||||||||||
| Inflation | 0.0% | 0.5% | 1.0% | 1.5% | 2.0% | 2.5% | 3.0% | 3.5% | 4.0% | 4.5% | 5.0% | 5.5% | 6.0% |
| 0.00% | 0% | -45% | -111% | -205% | -342% | -537% | -818% | -1220% | -1795% | -2615% | -3783% | -5445% | -7806% |
| 0.25% | 17% | -21% | -75% | -153% | -266% | -428% | -661% | -994% | -1471% | -2151% | -3120% | -4498% | -6456% |
| 0.50% | 31% | 0% | -45% | -110% | -204% | -338% | -531% | -808% | -1203% | -1768% | -2571% | -3715% | -5339% |
| 0.75% | 43% | 17% | -20% | -74% | -152% | -264% | -424% | -654% | -982% | -1450% | -2117% | -3066% | -4414% |
| 1.00% | 53% | 31% | 0% | -45% | -109% | -202% | -335% | -526% | -798% | -1187% | -1741% | -2529% | -3648% |
| 1.25% | 61% | 43% | 17% | -20% | -74% | -151% | -262% | -420% | -646% | -969% | -1430% | -2084% | -3014% |
| 1.50% | 67% | 52% | 31% | 0% | -45% | -109% | -200% | -332% | -520% | -789% | -1171% | -1715% | -2488% |
| 1.75% | 73% | 60% | 43% | 17% | -20% | -73% | -150% | -259% | -416% | -639% | -957% | -1410% | -2052% |
| 2.00% | 77% | 67% | 52% | 31% | 0% | -44% | -108% | -199% | -329% | -515% | -779% | -1156% | -1690% |
| 2.25% | 81% | 73% | 60% | 42% | 17% | -20% | -73% | -149% | -257% | -412% | -632% | -945% | -1390% |
| 2.50% | 84% | 77% | 67% | 52% | 31% | 0% | -44% | -107% | -197% | -326% | -509% | -770% | -1141% |
| 2.75% | 87% | 81% | 72% | 60% | 42% | 17% | -20% | -73% | -148% | -255% | -408% | -625% | -933% |
| 3.00% | 89% | 84% | 77% | 67% | 52% | 31% | 0% | -44% | -106% | -196% | -323% | -504% | -761% |
| 3.25% | 91% | 87% | 81% | 72% | 60% | 42% | 17% | -20% | -72% | -147% | -253% | -404% | -618% |
| 3.50% | 92% | 89% | 84% | 77% | 67% | 52% | 30% | 0% | -44% | -106% | -194% | -320% | -499% |
| 3.75% | 94% | 91% | 87% | 81% | 72% | 60% | 42% | 17% | -20% | -72% | -146% | -251% | -400% |
| 4.00% | 95% | 92% | 89% | 84% | 77% | 66% | 52% | 30% | 0% | -43% | -105% | -193% | -317% |
| 4.25% | 96% | 94% | 91% | 87% | 81% | 72% | 60% | 42% | 16% | -20% | -71% | -144% | -249% |
| 4.50% | 96% | 95% | 92% | 89% | 84% | 77% | 66% | 51% | 30% | 0% | -43% | -104% | -191% |
| 4.75% | 97% | 96% | 94% | 91% | 86% | 80% | 72% | 59% | 42% | 16% | -20% | -71% | -143% |
| 5.00% | 97% | 96% | 95% | 92% | 89% | 84% | 76% | 66% | 51% | 30% | 0% | -43% | -104% |
| 5.25% | 98% | 97% | 95% | 93% | 90% | 86% | 80% | 72% | 59% | 42% | 16% | -19% | -70% |
| 5.50% | 98% | 97% | 96% | 94% | 92% | 89% | 83% | 76% | 66% | 51% | 30% | 0% | -43% |
| 5.75% | 98% | 98% | 97% | 95% | 93% | 90% | 86% | 80% | 71% | 59% | 41% | 16% | -19% |
| 6.00% | 99% | 98% | 97% | 96% | 94% | 92% | 88% | 83% | 76% | 66% | 51% | 30% | 0% |
"
A stochastic model is a tool for estimating probability distributions of potential outcomes by
allowing for random variation in one or more inputs over time. The random variation is usually
based on fluctuations observed in historical data for a selected period using standard time-series
techniques. Distributions of potential outcomes are derived from a large number of simulations
(stochastic projections) which reflect the random variation in the input(s)."