I decided to look at the impact this would really have over the population; particularly, whether the program is self-sustaining or not and, if not, by how much.
According to the Social Security Administration, the effective interest rate paid on 'deposits' is currently 4%.
This graph conveniently covers the working life of those currently retiring; 45 years.
Since everything I'll do here is interest rate-sensitive, my brother suggested that I back this up with treasury bond and prime rate data.
The 10-year treasury rate is shown below and the 30-year rates are higher:
...and the prime rate:
The basic shapes are quite similar to the first curve (from the SSA) with the first one having the lowest (most conservative) peak of the three; I'll use that one even though the SSA should arguably have invested in 30-year bonds.
There are similar charts for other Social Security details; minimum wage, tax rate, Social Security interest rates and the Social Security Wage Base (the maximum income subject to the tax).
I used the total Social Security tax rate (employee plus employer; currently 12.4%; table above shows only the employee half) and interest over the last 45 years to calculate the total Social Security savings of a life-long minimum wage earner.
In the first year, the savings is the annualized wage (assuming 2080 hours/year) times (twice) the tax rate, times one-half of the year's interest rate (half rate to account for the average of the year's withholding); except for 2011 and 2012 when the employee side was reduced by 2 points while the employer side remained unchanged.
In successive years (up to retirement), the savings is the sum of the first year's savings with interest plus the next year's wage (assuming 2080 hours/year) times (twice) the tax rate, times one-half of the year's interest rate.
After retirement, the accumulated savings is depleted by the calculated yearly benefit and at least partially replenished by the interest income on the balance; I assumed an interest rate of 4% going forward from 2012.
I used annual compounding instead of continuous compounding because it also produces a more conservative result.
I used the Social Security benefit online calculator and tediously put in 45 years of minimum wage incomes to find the current benefit.
I was surprised to find that the benefit was $916/month; I had guessed $300/month in the previous post. I must recant my guesstimate from my previous post; the average lifetime minimum wage earner will accumulate savings of just under $200,000 over 45 years, not $83,000.
In addition, if we assume that the interest rate stays at 4% during the expected 15-year benefit period (even though rates are rising), there is nearly $130,000 left after death, not $29,000. Allowing this to be inherited would be a very big deal for poor families. This would really help close the wealth gap; combining it with elimination of the regressive fuel, sales and property taxes would elevate many poor folks quickly.
I did the same exercise for someone starting at twice minimum (college or skills assumed) and ending in the 50th percentile; this is about $42,000/year right now.
However, if we again assume that the interest rate stays at 4% during the expected 15-year benefit period, the interest income exceeds the benefit and there is nearly $570,000 left after death. Also a really nice inheritance; Mom and Dad could leave over $1 million if they both worked; many do but never reap their just rewards.
I did the same exercise for someone starting at twice minimum (college or skills) and ending in the 10th percentile; this is about $142,000/year right now. For this case, the Wage Base was also employed to limit contributions.
However, if we again assume that the interest rate stays at 4% during the expected 15-year benefit period, the interest income far exceeds the benefit and there is nearly $2.25 million left after death. This group is getting totally hosed.
WTF?
This is a shocking set of results, to say the least. I have been led to believe that Social Security benefits are so crappy because we are always paying for those who came before us. However, the analysis above tells a radically different story.
By my calculations (described below), the fund has produced a surplus from every crop of workers since those who retired in 1998 and I see no reason to believe that this has not been the case for a lot longer.
It looks like we contribute far more than enough to account for the paltry $2.7 trillion in the Social Security trust fund.
How much more? Using the wealth/income distribution curve developed in my last post and the three data point from above, we can make a good, yet conservative estimate of the total accumulated Social Security savings of the group born in 1947 and retiring last year; the crop of 1947.
How Much Did The Crop of 1947 Save?
All we have to do to estimate the total savings of this group is curve-fit the inflection points (between work and retirement) of the three curves above to the wealth/income curve below and integrate the area of the curve thus found.
The process involves summing the areas of rectangles under the curve as shown below (some of you will no doubt recognize this process from long-ago Calculus classes).
The vertical value is $/person and the horizontal value is population (people) so the area of each rectangle produces $.
Here's the wealth/income curve from my last post. I multiplied the curve by a constant to get a good fit to recent gross personal income data statistics; good alignment of individual percentile points and an area under the curve of $8.6 trillion (gross personal income in US) last year.
The curve-fit result is shown below. I used the savings points calculated in detail above (10th percentile=$1.6 million, 50th percentile=$565,000 and 20th percentile=$200,000) and fitted them conservatively to a graph with the same Y = X^-0.8 formula as the wealth/income curve above.
The fitted curve (in blue; 'Saved') is always below the reference (in red; 'Curve-Fit') to be sure I didn't over-estimate the crop savings as a whole.
To get the area under the curve (the integral), we just multiply the estimated savings of each group to the number of members in each percentile; each 5-percentile group has 5% of the number of people born in 1947 (2,858,000) in it; 142,900 people per 5-percentile group.
Again, to be conservative, I didn't start to integrate until the 10th percentile since I'm not sure how many of the top 9 percentiles actually pay in to the system at all; many probably never worked a day in their lives.
The result; $1.32 trillion.
The Problem
Here's where I have a problem.
If the crop fro 1947 saved $1.32 trillion and there are 44 more such groups currently paying into the system (those born between 1948 and 1992) and preceding crops left a balance (gathering interest) and we currently pay out about $0.8 trillion/year in benefits, how can it be that the trust fund has a balance of only $2.7 trillion?
Shouldn't the balance be more like $30 trillion?
What Should the Trust Fund Balance Be?
This question is also a tough one but not as tough as the last one; no curve-fitting or integration required.
To solve it, I needed the GDP data from 1952 to 2012, the average Social Security benefits for the last 15 years and the yearly birth rates from 1932 to 1992. I went back to 1952/1932 since some of those folks (born in 1932 and now over 80 years old) are still beneficiaries. I didn't count those over 80 or those under 20; I called it a push since the over-80 crowd is already figured into the life-expectancy figure (bell curve distribution) and the under-20 crowd has earnings near zero (and are highly underemployed).
Using the 1947 crop as a baseline for savings-per-crop, I assigned a potential savings for other crops equal to the 1947 savings scaled first by birthrate ratio (to the crop of 1947) and then by GDP ratio of the year they entered my workforce to the year the 1947 crop entered (the 1947 crop entered in 1967).
You can see that GDP growth (blue curve) tracks population pretty well but I also used the trend-line (black curve) to graph actual GDP growth since 1952 (by shooting for $1.58 trillion in 2012). The curve after 2012 is a guess and somewhat improbable given the lackluster state of the economy.
This is a shocking set of results, to say the least. I have been led to believe that Social Security benefits are so crappy because we are always paying for those who came before us. However, the analysis above tells a radically different story.
By my calculations (described below), the fund has produced a surplus from every crop of workers since those who retired in 1998 and I see no reason to believe that this has not been the case for a lot longer.
It looks like we contribute far more than enough to account for the paltry $2.7 trillion in the Social Security trust fund.
How much more? Using the wealth/income distribution curve developed in my last post and the three data point from above, we can make a good, yet conservative estimate of the total accumulated Social Security savings of the group born in 1947 and retiring last year; the crop of 1947.
How Much Did The Crop of 1947 Save?
All we have to do to estimate the total savings of this group is curve-fit the inflection points (between work and retirement) of the three curves above to the wealth/income curve below and integrate the area of the curve thus found.
The process involves summing the areas of rectangles under the curve as shown below (some of you will no doubt recognize this process from long-ago Calculus classes).
Here's the wealth/income curve from my last post. I multiplied the curve by a constant to get a good fit to recent gross personal income data statistics; good alignment of individual percentile points and an area under the curve of $8.6 trillion (gross personal income in US) last year.
The curve-fit result is shown below. I used the savings points calculated in detail above (10th percentile=$1.6 million, 50th percentile=$565,000 and 20th percentile=$200,000) and fitted them conservatively to a graph with the same Y = X^-0.8 formula as the wealth/income curve above.
The fitted curve (in blue; 'Saved') is always below the reference (in red; 'Curve-Fit') to be sure I didn't over-estimate the crop savings as a whole.
To get the area under the curve (the integral), we just multiply the estimated savings of each group to the number of members in each percentile; each 5-percentile group has 5% of the number of people born in 1947 (2,858,000) in it; 142,900 people per 5-percentile group.
Again, to be conservative, I didn't start to integrate until the 10th percentile since I'm not sure how many of the top 9 percentiles actually pay in to the system at all; many probably never worked a day in their lives.
The result; $1.32 trillion.
The Problem
Here's where I have a problem.
If the crop fro 1947 saved $1.32 trillion and there are 44 more such groups currently paying into the system (those born between 1948 and 1992) and preceding crops left a balance (gathering interest) and we currently pay out about $0.8 trillion/year in benefits, how can it be that the trust fund has a balance of only $2.7 trillion?
Shouldn't the balance be more like $30 trillion?
What Should the Trust Fund Balance Be?
This question is also a tough one but not as tough as the last one; no curve-fitting or integration required.
To solve it, I needed the GDP data from 1952 to 2012, the average Social Security benefits for the last 15 years and the yearly birth rates from 1932 to 1992. I went back to 1952/1932 since some of those folks (born in 1932 and now over 80 years old) are still beneficiaries. I didn't count those over 80 or those under 20; I called it a push since the over-80 crowd is already figured into the life-expectancy figure (bell curve distribution) and the under-20 crowd has earnings near zero (and are highly underemployed).
Using the 1947 crop as a baseline for savings-per-crop, I assigned a potential savings for other crops equal to the 1947 savings scaled first by birthrate ratio (to the crop of 1947) and then by GDP ratio of the year they entered my workforce to the year the 1947 crop entered (the 1947 crop entered in 1967).
 |
| Birth Rates |
 |
| GDP Growth Percentage |
The GDP data scales the wages of prior and successive crops so that the potential contributions of later groups increases appropriately. Again, a conservative estimate since personal income used to be a substantially greater share of GDP than it is now.
Once I got this data, I further scaled the potential contribution of each crop as follows;
For those over 65, I added to their potential contributions the difference between interest income on per-crop savings since retirement and their average Social Security benefits; year by year over the last 15 years multiplied by the crop size to get an actual contribution. This was really tedious.
For those under 65 it's a bit trickier. Since savings growth over time is decidedly non-linear, I normalized the 10-percentile growth curve from above to 1.000 for retirement day and then for each crop I multiplied the potential contributions by the normalized fraction over the 45 years they've contributed to get an actual contribution.
The end result is plotted against birth year........drum roll please....
I get a Social Security Trust Fund balance of $51.8 trillion; not $2.7 trillion.
As noted, the horizontal axis is the birth year of the various crops of people; it ends in 1992 because that crop is just starting to contribute.
The curve starts to flatten out in the early 1960's because of the drop in birthrates and because the savings growth of those born after 1960 is just starting to blossom, having not joined the workforce until 1980. The curve will start an upward trajectory again in a few more years.
As noted, the horizontal axis is the birth year of the various crops of people; it ends in 1992 because that crop is just starting to contribute.
The curve starts to flatten out in the early 1960's because of the drop in birthrates and because the savings growth of those born after 1960 is just starting to blossom, having not joined the workforce until 1980. The curve will start an upward trajectory again in a few more years.
The result is higher than my guess of $30 trillion because the retirees of the last 15 years left $9 trillion behind (or, were denied $9 trillion of their own money) and also because the area under the non-linear growth curve is quite a bit higher than for straight-line growth.
What the f___!
How is This Possible?
Aside from the larger question of 'where's the other $49.1 trillion?", this large balance is based on the beauty of compounded interest.
If you go back and look at the 1st graph in this post, your eye should tell you that the average interest rate of the last 45 years is easily 6%. The actual average is 7.08%.
So start with the minimum wave in 1967 of $2,912/year and a withholding of $227.14 for that year.
Then multiply the withholding by 1.0708^45 (29.36) to get $6,670 as the value of that first year's withholding. Repeat 44 times with a slowly increasing minimum wage and decreasing exponent and you get a big number. Multiply that by millions of people per crop and dozens of crops and you get stupidly big numbers like $51.8 trillion.
Where's the Other $49.1 Trillion?
This one has me totally stumped.
My first guess was that the government pissed away the contributions as soon as they were received and never paid any interest and is now claiming it is only on the hook for what it stole.
However, when I do that math (withhold the historical Social Security rates on 41% (bottom 90% of earners) of half of the historical GDPs (personal income is currently about half of GDP but was a higher percentage in the past) I still come up with $5 trillion, not $2.7 trillion. This tells us the principal has also been substantially spent.
However, when I do that math (withhold the historical Social Security rates on 41% (bottom 90% of earners) of half of the historical GDPs (personal income is currently about half of GDP but was a higher percentage in the past) I still come up with $5 trillion, not $2.7 trillion. This tells us the principal has also been substantially spent.
My friend Steve asked if it might be because of labor participation rates or women in the workforce but the Bureau of Labor statistics shows that the current rate (thanks to the mass thievery of 2007-2008) is roughly the same percentage of population as the average of the rates over the last 60 years; higher percentage of women, lower percentage of men but with the same overall proportion.
I wrote to the Social Security Administration and asked:
"I think that the group that retired last year (born ~1947) had amassed savings of at least $1.3 trillion on top of $9 trillion left over from the 15 previous groups. When added to the savings of all successive groups with interest, I get about $52 trillion. Where did it go?"
I'm still waiting for an answer.
On the Accuracy
I'd have to say that my numbers are conservative (and therefore on the low side) for these reasons:
I'd have to say that if the Social Security Trust Fund balance is understated by $49 trillion, then the National Debt is underestimated by the same amount; it is really closer to $66 trillion.
The good news is that we become our own biggest creditor; not China.
The bad news is that annual debt service must increase from $300 billion to $1.2 trillion and that, at that rate of payment, the debt will take a loooooooooong time to repay.
The worse news is that this revered (by liberals) program to help the poor is actually serving to keep them poor by stealing their hard-earned savings.
How Can It Be Fixed?
"I think that the group that retired last year (born ~1947) had amassed savings of at least $1.3 trillion on top of $9 trillion left over from the 15 previous groups. When added to the savings of all successive groups with interest, I get about $52 trillion. Where did it go?"
I'm still waiting for an answer.
On the Accuracy
I'd have to say that my numbers are conservative (and therefore on the low side) for these reasons:
- Conservative interest rates
- Annual instead of continuous compounding
- Conservative curve fit
- Did not include top 9% of earners (more than half of all income)
- Did not include those under 20 years of age
- Personal income was historically a much larger fraction of GDP but was treated as a constant ratio
- Otherwise used government-supplied numbers
I'd have to say that if the Social Security Trust Fund balance is understated by $49 trillion, then the National Debt is underestimated by the same amount; it is really closer to $66 trillion.
The good news is that we become our own biggest creditor; not China.
The bad news is that annual debt service must increase from $300 billion to $1.2 trillion and that, at that rate of payment, the debt will take a loooooooooong time to repay.
The worse news is that this revered (by liberals) program to help the poor is actually serving to keep them poor by stealing their hard-earned savings.
How Can It Be Fixed?
- Get Congress' hand out of the till.
- Start individual withholding accounts for all Americans using Social Security numbers as a means to keep them separate and transferable after death.
- Pre-populate the accounts of those still working with the correct amounts.
- Increase the current annual benefits paid to 1/15th of the correct savings.
- Pay death benefits to those who got ripped off; everyone.
- Follow my Grand Bargain plan to reduce government spending and pay off the now gargantuan National Debt of over $60 trillion.
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