The difference between Social Security and an annuity is that Social Security charges too little and promises payouts of too much. It cannot sustain the payouts which are promised in 2014 from revenues available to it in 2014 or the investment returns reasonably possible as a result of those revenues (and its accumulated capital). It must therefore increase the amount of revenues it receives, by a) increasing the SS tax rate and b) increasing the number of people who pay into SS until c) it inevitably defaults on promises to some portion of beneficiaries, for example by adopting e.g. means testing and retroactively stating that people born after a certain day will get the payout they've been promised their entire lives iff they have less income/wealth than $INSERT_CUTOFF and, if they exceed that, they'll receive $CONSOLATION_PRIZE_FORMULA instead.
Did you know that Social Security taxes were once 2.25% of income? Before they were 4.5%? Before they were 6.9%? Before they were 8.1%? Before they were 15.3%? That's where we are in 2014.
To be fair, while Social Security is clearly not an annuity, as of 2014 it isn't yet in default of its obligations. There's some dispute about what year that will inevitably happen. It will not be described as a default when it does, but rather tweaking a few formulas to protect America's most vulnerable citizens.
Edit: Social Security also has some "constructive default" options which are available outside of the program, because it is coextensive with the taxing power of the federal government. For example, SS benefits were once untaxed but are now taxed. There exist plausible ways by which every dollar promised of SS benefits can be "paid" but in which many get immediately recaptured by the government, which avoids formally adjusting the terms of the promise but which is indistinguishable from default in its impact on e.g. your family's budgeting process in 2070.
Another option is inflating away the insolvency. Japan will probably do this. It will pay out every yen of the promised monthly 200,000 yen due to pensioners, but pay it with yen which buy half as many apples as they did back when the pensioners were working.
The similarity that Social Security has to a Ponzi scheme is that they are both ultimately zero-sum games. The difference is that the government can run a zero-sum game forever, because it's the government.
You have a standard lie in your screed above, which when revealed demonstrates exactly how the zero-sum game will shift during our lifetimes to keep Social Security solvent forever and ever, amen. You claim that Social Security has no investments. This is a blatant lie. Social Security has been running a surplus for all of my life, and investing the surplus in trillions and trillions of US government debt, partially because it's the safest investment in the world and probably mostly because it's really convenient for the government.
Ah-ha, I'm sure you're going to say. When the one hand cashes in the T-bills, the other hand will have to pick our pockets to pay for it with more taxation, you're going to say.
Yes. But which pockets the government picks to pay off our internal obligations is extremely important.
Social Security, you see, is funded by a more-or-less flat tax on the first $XYZ,000 of workers incomes. It is basically the most regressive a tax can be, short of it being a fixed dollar amount regardless of income, which usually only happens for licensing fees, but that's another story. On the other hand, the mature T-bills are going to be paid for out of the general fund, the taxation structure for which is honestly one of the more progressive tax bases in the world.
When you combine this with the most probable fixes for Social Security -- dropping the income cap on the tax -- the future of Social Security is quite clear. Social Security is going to quietly shift from intergenerational wealth transfers to intragenerational wealth transfers. Some people in a generation, the poorest, will get back more money from Social Security than they pay in. Some people in a generation, the richest, will pay in more money than they get back.
The difference between Social Security and a Ponzi scheme is that, in a Ponzi scheme, if every group did not statistically get back more than they paid in, they would stop paying into it. Social Security, being involuntary, can collect 15% of $250,000 from a man while telling him upfront and outright he's only getting back 15% of $150,000 after he retires. At this point, a Ponzi scheme would collapse. Social Security will just putter along happily, running exactly as it should.
The difference between a Ponzi scheme and Social Security is that a Ponzi scheme is an investment, while Social Security is an insurance. As an insurance, a statistical loss is expected, but it provides a guarantee, in this case that when you are old you will never be destitute, living on the street eating catfood, or cats and rats when you can catch them.
Since Social Security is clearly not an annuity, calculations based on treating it as if it was (or should be) don't really tell us anything. In particular, where does this idea come from that current revenues have to pay for future benefits? That's not the way Social Security works or ever has worked.
Right, so when our population follows in the footsteps of Japan and Korea, we can just stop paying the benefit/kill all the old people/enslave all the young people.
My default is to suspect arguments that support dismantling social programs now because they might be insolvent in 60 years. Especially when insolvency here means not paying out as much as people expect to receive right now.
> If everyone has one or less children, the population does not grow exponentially.
False. An exponential function, and a growing exponential function, differ only in the value of the exponent.
Here's an equation that predicts future population based on the value of an exponential term:
The equation: pt - p0 e^rt
pt = population at time t
p0 = present population
r = rate of population growth, 1% = .01
t = time
A result at 40 years for a population rate of change of -1.7% per year:
e^(-.017 * 40) = .5066
This result says that, for a population growth rate of -1.7%, after 40 years the population will be about half its present size. It's an exponential result, it's even an exponential growth rate, but the growth rate is negative.
The red trace is an exponential rate of change for r = +1.7%, the green trace for r = -1.7%. Both are exponential results, and both reflect what a population would look like for given r values.
False. Put all your bullshit math aside because that's what it is, bullshit trying to move the goalpost. The statement I made is absolutely factually true. If everyone has one or less children, the population does not grow exponentially.
We're not talking about how to model population growth, or functions, we're talking about whether every couple having one child results in exponential growth and it simply does not. If the population decreases, that is not exponential growth. An exponential result != exponential growth. You are wrong and we are done.
And, everything else aside, all the described rates are exponential.
> We're not talking about how to model population growth ...
WHAT?? Here is what you said: "If everyone has one or less children, the population does not grow exponentially." How exactly is that NOT talking about how to model population growth?
Also, it's "one or fewer children," not "one or less children."
> An exponential result != exponential growth
False in a discussion about population and exponential growth rates, terms you chose.
It's sad that you can't admit that a population decrease is not exponential growth, but your ego clearly can't handle being wrong so troll somewhere else.
Quotation: "The formula for exponential growth of a variable x at the (positive or negative) growth rate r, as time t goes on in discrete intervals (that is, at integer times 0, 1, 2, 3, ...), is xt = x0 (1 + r)^t"
Let me emphasize that for you, in case your eyes are giving out:
"THE FORMULA FOR EXPONENTIAL GROWTH OF A VARIABLE X AT THE (POSITIVE OR NEGATIVE) GROWTH RATE R ..."
Now circle the word you're most unfamiliar with, raise your hand, and the teacher will administer a sedative.
You seem unable to read English. Let me make it clear for you, you're trying to make a lay conversation about population into a math problem which it is not, in doing so you are changing the meaning of lay words into their math definitions and misunderstanding the points being made to you in the same way a scientist means something different by the word theory than a lay person does. Stop talking, stop doing math, and listen, pay attention to context, this is not a math class and as I'm the commenter you replied to, I'm the one who sets the context and I've said not a math conversation; this is a lay conversation, use the lay definition of words.
You've been told numerous times to stop thinking about math and read the words but you clearly don't grok or can't remove your math head and have normal conversation. You're still talking about modelling growth, no one else is or was. Turn off your math head and read the English words using their lay definitions, a decline in population is not exponential growth as a decline in population is not any kind of growth because it isn't growth. If you can't bring yourself to admit that, you are beyond hope.
Secondly, I'm a computer programmer, I understand the math, so stop trying to lecture me on math when you're the one not listening. I can't help it you don't understand the point being made to you because you lack the ability to be aware of the context of the conversation you're in. I know what I'm trying to communicate and I've made it as clear as I can numerous ways; if your brain is unable to work in multiple contexts, that's your failing in understanding how to communicate with others.
If you try and prove your point with equations one more time, or reference them one more time, then you've utterly failed to understand what is being communicated to you and we're done because I don't talk to brick walls who can't think.
Wait, what? Replying to a comment that is clearly about mathematics, with a comment that is clearly about mathematics, is trolling?
The OP's comment, including " ... changing the common definition of exponential by saying the exponent could be 1 or less than one" is (a) mathematical and (b) wrong and misleading. The "common definition of exponential" accommodates any valid argument to exp(x), and to claim otherwise requires a mathematical correction to avoid misleading people.
This is a very disappointing comment line. I know not everyone here is a CS major, but if you're even CS-knowledgable you should understand what an exponential process is. It is not, as many laypeople assume, something that is "very big".
That said, I was not intentionally trolling. I do think it's possible for a SS-style benefit to sustain itself provided that an exponentially growing population, whose exponent is greater than 1, is obligated to pay in.
A country with a stagnant or declining population will probably have trouble.
You may disagree, that's fine.
Nevertheless, any population whose growth (or lack of growth) is defined by the average number of children per member will behave exponentially.
Social security, now that I think about it, does sound much like a Ponzi scheme.