Pay as You Go vs. Investments

Is Social Security a Ponzi scheme? If by Ponzi scheme you mean early “investors” are paid using “investments” made by later “investors”, the answer is yes. If by Ponzi scheme you mean unsustainable pyramid scheme the answer is no. Social Security is sustainable as long Congress behaves itself, and actually pays the internal part of the national debt when it comes due. The internal debt should be paid from general revenues, so the Baby Boomer demographic hump need not be paid for with higher FICA taxes if the government actuaries did their job correctly.

The difference between Social Security and a Ponzi scheme is the rate of return. Ponzi promised unreasonable rates of return and thus robbed later investors. Social Security promises much less, so using the less emotionally charged term “pay as you go” is more appropriate.

But note the price the working class pays for a pay as you go program that is safe and stable: low returns. There are no investments other than the trust fund to handle demographic bumps, and that fund is invested in government bonds.

The Return on Pay as You Go

Consider first a static economy, with no inflation, no population growth, and stable wages. Under these conditions the rate of return for a pay as you go system is exactly zero, the same as putting money in a mattress. Social Security is purely insurance against living longer than average, with the benefits paid for by those who die younger than average. (Social Security also transfers some wealth between those making professional class wages over a long career to those making lower class wages.)

If most people live only a few years after retiring, the lack of investment return is acceptable. FICA taxes can be low because the ratio of retirees to workers is low. As people live longer after retirement, however, the money at stake grows. Now we are demanding that the working class fork over a significant fraction of their wages with no investment return. And even in a static economy, real interest rates are not zero. To the degree which investment rates are nonzero a pay as you go system widens the gap between the rich and working class. If the effect is small, then the safety provided by Social Security is worth the price. If it is big, then progressives and liberals should seriously consider an alternative, such as a forced savings plan or a flat free money for seniors program coupled with large IRA allowances.

Of course, the effect just described applies to a static economy, which is rather artificial. But before you dismiss it entirely, keep in mind that for most of human history economies were largely static. Sustained population and per capita economic growth are phenomena of the Industrial Revolution. Environmentalists keep warning us that this revolution is coming to an end, that we need an economy that works under conditions of low or even zero growth. They may be overly pessimistic, but it might not hurt to be prepared.

Back in the real world, Social Security does provide positive returns because the economy is growing. When the population grows we have more incoming workers to pay for current retirees. When real wages grow, FICA taxes increase faster than cost of living allowances. The Social Security Administration provides a handy-dandy worksheet which includes a table to scale yesterday’s wages with respect to nominal wage growth. Column C is the multiplier. According to the table, wages have grown 14.77 times (in nominal dollars) from 1951 to 2009. According to the Bureau of Labor Statistics calculator, the dollar shrank by a factor of 8.25 during the same period, giving us a real wage gain of 1.79.

Pay as You Go vs. the Dow Jones Industrial Average

We have the government’s estimate of wage growth, both nominal and real. Let us compare it with investments. Is the working class paying a high price for the windfall which Social Security’s earliest retirees received? To answer the question, I threw together some C++ code to compare tables of various indices from Yahoo Finance with the wage adjustments provided by the Social Security Administration. My calculations are a bit crude compared with those used by professional finance wizards, so they shouldn’t be used for retirement planning or final policy decisions. They are meant to be illustrative, to spur further discussion and study by people who do this sort of thing as their day job.

YearIndex FactorMultiplierNominal Rate of Return %Adjusted MultiplierAccumulated Adjusted MultiplierN YearsAccumulated Adjusted Multiplier x 10.6%
20001.291.000.001.001.0010.11
19991.361.000.000.951.9520.21
19981.433.4862.313.145.0930.54
19971.514.0346.423.448.5240.90
19961.605.1841.124.1812.7051.35
19951.676.6037.755.1017.8061.89
19941.747.8934.435.8523.6572.51
19931.798.4630.516.1029.7583.15
19921.809.0827.586.5136.2693.84
19911.9010.1025.696.8643.12104.57
19901.9711.2524.207.3650.48115.35
19892.0611.8122.447.3957.87126.13
19882.1414.4122.238.6966.56137.06
19872.2413.1719.837.5874.14147.86
19862.3916.4920.028.9083.05158.80
19852.4622.2520.6811.6794.711610.04
19842.5625.4720.2412.84107.551711.40
19832.7124.9918.9311.90119.451812.66
19822.8433.6319.5315.28134.721914.28
19813.0032.1018.2613.80148.522015.74
19803.3033.4417.5513.07161.602117.13
19793.6035.5017.0012.72174.322218.48
19783.9236.7816.3912.10186.422319.76
19774.2333.8015.3110.31196.732420.85
19764.4830.4814.248.78205.512521.78
19754.7936.8314.439.92215.432622.84
19745.1540.1514.2010.06225.482723.90
19735.4532.6312.917.72233.202824.72
19725.7931.3712.316.99240.192925.46
19716.3633.9012.156.88247.073026.19
19706.6839.5912.267.64254.723127.00
19697.0134.2711.406.31261.023227.67
19687.4233.1410.945.76266.783328.28
19677.9334.0310.695.54272.323428.87
19668.3734.7410.435.35277.673529.43
19658.8732.709.964.76282.433629.94
19649.0335.799.945.11287.543730.48
19639.4041.7410.095.73293.273831.09
19629.6347.0710.146.31299.583931.75
196110.1143.139.655.50305.084032.34
196010.3248.859.726.11311.194132.99
195910.7246.869.385.64316.824233.58
195811.2560.269.766.91323.734334.32
195711.3563.069.647.17330.904435.08
195611.7060.899.346.71337.614535.79
195512.5267.039.346.91344.524636.52
195413.1088.529.758.72353.244737.44
195313.17108.609.9710.64363.884838.57
195213.90110.039.7910.21374.094939.65
195114.77116.159.7010.14384.235040.73

Let us start by looking at a good year to retire: 2000. In the third column we have a rough value for the gain of a Dow Jones Industrial Average based index fund from each year to the end of 2000. These are rough values. I don’t figure in any dividends or fees. For Dow values, I took the end of month values from Yahoo Finance and averaged over the course of each year. That’s a simple average, not a dollar cost average in order to err on the side of being conservative. As we work our way down the column the value of investing and waiting appears huge. A dollar invested in 1982 is worth twelve upon retirement. Applying a simple continuous compounding formula, we get the average annual rate of return for each year’s investment in the third column. Once again, the numbers appear too good to be true, thanks in part to our old friend inflation.

I could have adjusted these numbers for inflation, but that would not be the correct scale to compare with a pay as you go program. Instead, I scaled the multipliers with the adjusted wage multipliers given by the Social Security Administration (Column 2). For nearly every year the Dow did significantly better than the wage adjustment factor, over five times better for 1982! Column 5 sums up these multipliers as we go back in time. For a worker who has a flat adjusted wage over 35 years, a Dow based index fund would provide the equivalent of 100 years of pay as you go. That’s nearly a factor of three! To translate into dollars, multiply this column by the OASI tax rate (5.3% each for employer and employee when Congress isn’t “stimulating”) to get Column 8, and then multiply by the final nominal wage. A worker who works 35 years at a constant wage relative to the market which comes out to $20,000 per year in 2000, retires with roughly a quarter million dollars.

That was for a good year, not using most scientific of stock indices. Let us take a bad year, 2009, when the market was bottoming out from the Great Recession. Our table is now:

YearIndex FactorMultiplierNominal Rate of Return %Adjusted MultiplierAccumulated Adjusted MultiplierN YearsAccumulated Adjusted Multiplier x 10.6%
20091.001.000.001.001.0010.11
20081.001.000.001.002.0020.21
20071.021.4618.871.433.4330.36
20061.071.6817.251.575.0040.53
20051.121.8315.081.636.6350.70
20041.161.8612.461.618.2460.87
20031.212.1312.641.7610.0071.06
20021.242.1010.581.6911.6981.24
20011.261.908.011.5113.2091.40
20001.291.806.541.4014.60101.55
19991.361.846.091.3515.95111.69
19981.432.247.311.5617.51121.86
19971.512.597.921.7119.22132.04
19961.603.339.252.0821.31142.26
19951.674.2510.332.5423.85152.53
19941.745.0810.832.9226.76162.84
19931.795.4410.593.0429.80173.16
19921.805.8410.383.2433.05183.50
19911.906.4910.393.4236.47193.87
19901.977.2310.413.6740.14204.25
19892.067.5910.143.6943.82214.65
19882.149.2710.604.3348.15225.10
19872.248.479.713.7851.93235.50
19862.3910.6110.274.4456.37245.98
19852.4614.3011.095.8162.18256.59
19842.5616.3811.186.4068.58267.27
19832.7116.0710.685.9374.51277.90
19822.8421.6311.387.6182.13288.71
19813.0020.6410.816.8889.01299.43
19803.3021.5010.586.5295.523010.13
19793.6022.8310.436.34101.863110.80
19783.9223.6510.206.03107.903211.44
19774.2321.739.625.14113.033311.98
19764.4819.609.024.37117.413412.45
19754.7923.689.314.94122.353512.97
19745.1525.819.295.01127.373613.50
19735.4520.988.453.85131.213713.91
19725.7920.178.123.48134.703814.28
19716.3621.808.113.43138.133914.64
19706.6825.458.303.81141.944015.05
19697.0122.047.733.14145.084115.38
19687.4221.317.462.87147.954215.68
19677.9321.887.352.76150.714315.98
19668.3722.337.222.67153.384416.26
19658.8721.036.922.37155.754516.51
19649.0323.016.972.55158.304616.78
19639.4026.847.152.86161.154717.08
19629.6330.277.263.14164.304817.42
196110.1127.736.922.74167.044917.71
196010.3231.417.043.04170.085018.03
195910.7230.136.812.81172.895118.33
195811.2538.757.173.44176.345218.69
195711.3540.557.123.57179.915319.07
195611.7039.156.923.35183.265419.43
195512.5243.106.973.44186.705519.79
195413.1056.927.354.35191.045620.25
195313.1769.837.585.30196.355720.81
195213.9070.757.475.09201.445821.35
195114.7774.687.445.06206.495921.89

Pay as you go looks better. For over a decade the adjusted multiplier is less than one. However, it picks back up and over 35 years the accumulated multiplier exceeds the number of years by a factor of 57/35 = 1.63. Even in a bad year, investing appears to be better than pay as you go. But let us check another index.

S&P 500 vs. Pay As You Go

The same calculations using the same techniques were done for the S&P 500 index. I just took the values from Yahoo, averaged the end of month values over each year and scaled against wage growth. I leave it as a homework assignment to determine how an actual index fund compares and whether dividends needed to be added in or not. The S&P 500 did even worse than the Dow for those retiring at the end of 2009. But still, a worker making a constant adjusted wage over 35 years would be entitled to 49.5/35 = 1.4 times the amount of pay as you go.

YearIndex FactorMultiplierNominal Rate of Return %Adjusted MultiplierAccumulated Adjusted MultiplierN YearsAccumulated Adjusted Multiplier x 10.6%
20091.001.000.001.001.0010.11
20081.001.000.001.002.0020.21
20071.021.4618.871.433.4330.36
20061.071.6817.251.575.0040.53
20051.121.8315.081.636.6350.70
20041.161.8612.461.618.2460.87
20031.212.1312.641.7610.0071.06
20021.242.1010.581.6911.6981.24
20011.261.908.011.5113.2091.40
20001.291.806.541.4014.60101.55
19991.361.846.091.3515.95111.69
19981.432.247.311.5617.51121.86
19971.512.597.921.7119.22132.04
19961.603.339.252.0821.31142.26
19951.674.2510.332.5423.85152.53
19941.745.0810.832.9226.76162.84
19931.795.4410.593.0429.80173.16
19921.805.8410.383.2433.05183.50
19911.906.4910.393.4236.47193.87
19901.977.2310.413.6740.14204.25
19892.067.5910.143.6943.82214.65
19882.149.2710.604.3348.15225.10
19872.248.479.713.7851.93235.50
19862.3910.6110.274.4456.37245.98
19852.4614.3011.095.8162.18256.59
19842.5616.3811.186.4068.58267.27
19832.7116.0710.685.9374.51277.90
19822.8421.6311.387.6182.13288.71
19813.0020.6410.816.8889.01299.43
19803.3021.5010.586.5295.523010.13
19793.6022.8310.436.34101.863110.80
19783.9223.6510.206.03107.903211.44
19774.2321.739.625.14113.033311.98
19764.4819.609.024.37117.413412.45
19754.7923.689.314.94122.353512.97
19745.1525.819.295.01127.373613.50
19735.4520.988.453.85131.213713.91
19725.7920.178.123.48134.703814.28
19716.3621.808.113.43138.133914.64
19706.6825.458.303.81141.944015.05
19697.0122.047.733.14145.084115.38
19687.4221.317.462.87147.954215.68
19677.9321.887.352.76150.714315.98
19668.3722.337.222.67153.384416.26
19658.8721.036.922.37155.754516.51
19649.0323.016.972.55158.304616.78
19639.4026.847.152.86161.154717.08
19629.6330.277.263.14164.304817.42
196110.1127.736.922.74167.044917.71
196010.3231.417.043.04170.085018.03
195910.7230.136.812.81172.895118.33
195811.2538.757.173.44176.345218.69
195711.3540.557.123.57179.915319.07
195611.7039.156.923.35183.265419.43
195512.5243.106.973.44186.705519.79
195413.1056.927.354.35191.045620.25
195313.1769.837.585.30196.355720.81
195213.9070.757.475.09201.445821.35
195114.7774.687.445.06206.495921.89

Wealth to the Working Class?

Even retiring on a bad year, a conservative portfolio does better than wage growth. So in theory, a combination of index fund investing coupled with buying an annuity upon retirement should be better than Social Security on average. Some people would still do better with Social Security since there is wealth transfer within wage and demographic classes. But none of the transfer is between truly rich and working class. From what we see so far, Social Security shrinks the gap between upper middle class and lower class retirees, but widens the gap between the rich and upper middle classes.

But we haven’t factored in all the variables yet. How does a privately managed annuity compare to Social Security?

And what about those laborers who “invest” in lottery tickets? We could force them into conservative accounts in the fashion of Chile’s retirement system. But this concentrates investment decisions in the hands of government regulators. The alternative we favor here is free money for seniors seniors funded out of general revenues (vs. regressive labor taxes). Let the lower classes live for the day without having to invest for retirement, and let the upper middle classes make their own investment decisions. We can disperse economic power while still providing a generous safety net for all citizen retirees.