http://economistsview.typepad.com/economistsview/2011/03/social-security-is-not-welfare.html
https://archive.is/8Y8Yl
In his blog post Thoma references another blog post that gives details of a hypothetical risk pool, in an attempt to prove that Social Security functions like an insurance policy.
One reader of Thoma's blog pointed out the obvious error of comparing Social Security to an insurance policy, and Thoma simply instructed the commenter to read this link he referred to in his article —
http://angrybearblog.com/2004/12/social-security-part-i-insurance-and.html
https://archive.is/FWRVE
The reader's comment is worth reading, since it gives a better description of Social Security than the one Thoma provides — and one that isn't countered by Thoma's blog post, or the post he instructs the commenter to read --
Curt Doolittle said...
Pretty big error in logic you have going on there.
We can insure against fire, because not every house will burn.
We can, all of us, contribute a little, for the very few who need it.
If we require fire insurance, we do not create a moral hazard, we create a virtuous cycle of fire-reduction.
If we insure against old age, we must insure everyone, because nearly everyone will become old.
We must all contribute a great deal, because almost all people will need it.
If we require old age insurance, we create a moral hazard, whereby people do not save, and money is spent rather than saved and invested.
Social security is a transfer program.
If it were a forced savings program it would be a form of insurance.
It cannot be a risk mitigation program because risk mitigation requires a probability of less than 'certainty'. Therefore it is NOT a risk mitigation program.
It is an inter-generational, risk inducing, fragility-inducing, moral hazard.
if you want to make a social security program, enforce savings on everyone, and redistribute some portion of the very top to the very bottom.
We can insure against fire, because not every house will burn.
We can, all of us, contribute a little, for the very few who need it.
If we require fire insurance, we do not create a moral hazard, we create a virtuous cycle of fire-reduction.
If we insure against old age, we must insure everyone, because nearly everyone will become old.
We must all contribute a great deal, because almost all people will need it.
If we require old age insurance, we create a moral hazard, whereby people do not save, and money is spent rather than saved and invested.
Social security is a transfer program.
If it were a forced savings program it would be a form of insurance.
It cannot be a risk mitigation program because risk mitigation requires a probability of less than 'certainty'. Therefore it is NOT a risk mitigation program.
It is an inter-generational, risk inducing, fragility-inducing, moral hazard.
if you want to make a social security program, enforce savings on everyone, and redistribute some portion of the very top to the very bottom.
Mark Thoma said in reply to Curt Doolittle...
Read the AB link.
So let's look at the blog post that Thoma keeps referring to, to see if it is as convincing as he seems to think.
The credibility of the author of this post is given away in the first paragraph quoted below, in the statement that Social Security is solvent 'conditional on minor adjustments'. Social Security already earns a negative return when compared with other alternatives, so this language describing Social Security's solvency hides the obvious point that the only way Social Security can remain solvent is by making everyone who contributes poorer — given that they are already losing part of their retirement savings by contributing to Social Security at all --
http://angrybearblog.com/2004/12/social-security-part-i-insurance-and.html
https://archive.is/FWRVE
...
As mentioned already, the basic solvency of Social Security (or solvency conditional on minor adjustments) is established, so I’d like to instead address the basic merit of the program. My argument centers on the fact that Social Security is really insurance. In fact, the phrase “Social Security” is typically used as shorthand for “Social Security Retirement Insurance.”
What’s so special about insurance? As it turns out, the vast majority of the population dislikes risk, and will pay money (e.g., insurance premiums) to avoid the consequences of risk. I’ve surveyed my students and asked whether they would prefer a job that has equal odds of paying $75k or $125k (expected income = $100k) to a job that paid $90k with certainty. Almost all prefer the $90k, meaning they would pay up to $10k (by having an expected income of $90k instead of $100k) in order to not have to face income swings of +/-$25k; many would pay more.(*)
...
Pay special attention to the use of the phrase 'equal odds' in the description above of the risk being insured against in this hypothetical risk pool — given that the author is attempting to make the case that Social Security is insurance, there is already a large potential problem in his argument.
http://angrybearblog.com/2004/12/social-security-part-i-insurance-and.html
https://archive.is/FWRVE
...
In such a situation, if people can pay less than $10,000 to avoid such risk then real economic value is created. And in fact, this happens in the real world all the time. Consider a group of 100 people, each of whom faces this hypothetical gain or loss of $25,000. Let’s see how they can benefit by pooling risk.
First, what is the social cost of the risk faced by this group of people? By hypothesis, it’s worth $10,000 to each of them to avoid the +/-$25,000 risk. So the mere presence of this risk creates a cost of 100 * $10,000 = $1,000,000. If we can figure out a way to reduce this risk, there’s the potential to create an additional $1m (100 people at $10,000 each) in value for this group.
How does a risk pool work? With just 100 people, there is near mathematical certainty (about .997, based on the sum of 100 Bernoulli draws, which follows a binomial distribution) that a minimum of 35 people will “win,” gaining $25k. The vast majority of the time at least 40 will win and, on average, 50 will win and 50 will lose. Should only 35 people gain $25,000 while 65 lose $25,000, then the group will have lost (35 – 65)*$20k = $600,000. Thus the simplest form of insurance entails each member paying a premium of $6,000, creating a pool of 100 * $6,000 = $600,000 to cover the group’s potential losses.
...
Notice that there is a huge problem in the calculations in the last paragraph quoted above, which are intended to show an unusually high payout from the risk pool (a worst case example), where 65 participants made $75,000 (vs. 35 making $125,000), and so well over 1/2 of the risk pool participants had to file a claim against the pool for that lost $25K. The 35 people who had the optimum outcome and 'won' the $25K won't file a claim against the risk pool — they'll simply pay their premium again, assuming they wish to continue their coverage to avoid the worst case outcome of only earning $75,000 (following the assumptions given in the quotes from the blog post).
So, to compute the payout from the risk pool when 65 people file claims, you simply multiply the number of claims by the dollar amount of those claims — in this case, 65 * $25,000, or $1,625,000.
In short, this risk pool of 100 policy holders will pay out on average 50 * $25,000, or $1,250,000 every policy period, given the assumption that each participant had equal odds of making $75,000 in a given period, and so incurred the hypothetical $25,000 loss.
This would require each member of the risk pool paying a minimum policy premium of $12,500, since it would be unreasonable to assume that fewer than 1/2 of the policy holders would file claims, given that it is equally likely that each policy holder earns either $75,000 or $125,000 (again, per the hypothetical example).
It makes sense that the policy premium for the average case would be 1/2 the coverage amount, given the assumption of the hypothetical example that each policy holder has equal odds of filing a claim for any given period — so in order for the risk pool to even have a chance of remaining solvent, it must at a minimum collect 1/2 of the coverage amount from every policy holder, since in most policy periods at least 1/2 of the policy holders will be forced to file a claim for the coverage amount.
The example calculation in the blog post of 65 losers and 35 winners, showing a group loss of $600,000 makes no sense (for consistency the blog post should show the group loss as (35-65)*$25k = -$750,000, but it still wouldn't be meaningful), since the 35 who 'won' only share in the loss with the policy premiums they paid — the risk pool must pay for the covered losses from the premiums already collected, and so the policy holders who did not incur a covered loss are not filing a claim and have no effect on the payouts required by the risk pool.
For the example given in the blog post, where 65 claims were filed, the risk pool would have to pay $25,000 to 65 policy holders. If the risk pool did not collect at least $1,625,000 in total premiums for all the policies ($16,250 per policy holder), or did not have enough capital in reserve to cover any shortfall, the pool would not be able to pay those claims, and it would become insolvent.
Why would anyone claim that an insurance policy premium of $6,000 dollars from 100 policy holders (for a total of $600,000), would cover a loss to 65 policy holders of $1,625,000 (65 claims for $25,000)?
A risk pool has to be managed to handle a worst case loss, so even a policy premium of $12,500 is too low for this hypothetical pool, given that this is the expected payout per policy holder — a risk pool has to collect more in premiums than the most likely payout to avoid going bankrupt, so the policy holders must pay more than $12,500 for this hypothetical pool to even have a chance of working.
So clearly, the first paragraph quoted below is false — $6,000 won't come close to funding a risk pool where every policy holder has a 50% chance of filing a claim for a coverage amount of $25,000 --
http://angrybearblog.com/2004/12/social-security-part-i-insurance-and.html
https://archive.is/FWRVE
...
That is, if each member pays $6,000 for insurance, they can create a pool large enough to cover the group’s losses even in the worst of states. (Should the worst of states not occur, the balance can be repaid to the group as dividends, pushed into the next year’s pooled funds, or retained by the insurer as profits.) Stated differently, without insurance each member of the group faces a risk of income as low as $75,000. By pooling risk, no member of the group faces a risk of income below $94,000.
Moreover, as more people join the risk pool, the law of large numbers tells us that the risk is reduced further and further. In fact, with 10,000 people in the risk pool, the premium required to cover the group’s maximum total losses (in all but about 3/1000 cases) is only $500, instead of $6,000. That is, with a reasonably large group of people sharing risk, each can pay $500 and the risk is entirely eliminated. How much economic value is created by this? As I explained earlier in this post, real people in the real world are willing to pay amounts in the $10,000 to $15,000 range to avoid income swings on the order of +/-$25,000. But in the presence of insurance, these 10,000 people only have to pay $500. So in this hypothetical example, insurance — risk-pooling over a large group of people — creates $9,500 in economic value per person. (**)
What does all of this have to do with Social Security? Those who are hard-working, fortunate, and not too profligate will have a large nest egg at retirement and Social Security will account for only a small portion of their retirement portfolio. This is tantamount to paying for insurance and then not needing it. This happens all the time — every year someone fails to get sick or injured and, while surely happy in their good health, would have been better off not buying insurance. That’s the nature of insurance: if you don’t need it, then you’ll always wish you hadn’t purchased it. Only in the context of retirement insurance is this considered a crisis.
...
Also notice that the second paragraph quoted above is false.
That is, the Law of Large Numbers tells us nothing that allows us to reduce the policy premiums as the number of policy holders increases, since the Law of Large Numbers simply states that if an experiment for a particular random variable is repeated a large number of times, the average of the results should approach the expected value. For example, if you flip a fair coin millions of times, you will find that you get very close to an equal number of heads and tails — even though there can be long runs of consecutive flips that repeat one side of the coin.
If you estimated the probability of a real-world random event at 50% (as in this hypothetical risk pool), you could prove that your estimate was correct by performing (or observing) a large number of trials. If as the number of trials grew, the average of all the results didn't trend toward your expected value, you would know your estimate was incorrect. But even if an estimated probability matches the outcomes in the real-world, that doesn't mean a long sequence of outcomes can't happen that don't match the expected value.
Using the hypothetical risk pool as an example, the Law of Large Numbers tells us that after a very large number of policy periods has passed, the number of claims filed should get closer and closer to: (1/2 the number of policy holders * the number of policy periods) — that is, a claim will be filed on average 1/2 the time, if policy holders really do have a 50% chance of losing $25,000 (of earning only $75,000), as given in the quoted description of the hypothetical risk pool. But this doesn't mean it's impossible for a large number of consecutive policy periods to pass where well over 1/2 the policy holders incur the $25,000 loss and must file claims.
So for the hypothetical risk pool, a policy premium of $12,500 is still too low, regardless of the number of policy holders, since with a real-world claim probability of 50%, after a large enough number of policy periods, it's highly likely that at some point there will be a run of consecutive policy periods where well over 1/2 of the policy holders file claims, and without a large reserve the risk pool will become insolvent, since in that case much more than 50 * $25K would be required to cover the claims. The Law of Large Numbers tells us that over the long haul, the total amount paid by this risk pool will trend toward the expected value of a 50% payout rate, given the assumption of equal odds for a loss or a gain to policy holders. That is, the total will trend toward: ((1/2 the number of policy holders * $25,000) * the number of policy periods). The Law of Large Numbers does not tell us that a large number of consecutive worst case losses are impossible because the number of policy holders is increasing.
Assuming that a long run of a particular outcome for a random variable decreases the probability of that outcome in the future is called the 'gamblers fallacy'.
That is, consecutively flipping heads 10 times has no effect on the probability that heads will come up on the 11th flip, since each flip is an independent event.
In any case, it is clear that there is nothing in this hypothetical risk pool example to support the claim that Social Security is insurance.
Never mind that the numbers this author uses in his example do not make any sense, and are not supported by anything he wrote — why would he use a 50% probability for an example he was attempting to relate to a forced U.S. government retirement plan that pays to everyone who reaches the age of 70, when the life expectancy in the U.S. was estimated to be over 77 years, as of 2004, when that post was written? Obviously, using 50% as the probability for a hypothetical event that you're attempting to relate to a real life probability that is close to 100% makes no sense.
This author's risk pool example does not work, because the numbers he uses do not cover the risk he described, but if you plug a 90% probability for filing a claim into his example it really blows up, and makes it obvious why this comparison is nonsense — you cannot use a risk pool to insure against a near certainty, because everyone who participated in such a pool must pay in the full cost of that outcome.
In a previous post on Social Security, I mentioned the nonsensical example of 'Grocery Insurance', to illustrate the point that you would not try to create an insurance plan to cover a cost that everyone incurs all the time — it would make no sense, since it would do nothing but increase a cost that you had to incur by necessity, by adding the additional cost of managing the risk pool.
So no one would buy 'Grocery Insurance' (even if it existed), because such insurance would cost more than the covered groceries (such an insurance plan would not remain solvent, if this were not the case), and so purchasing such insurance would reduce the quantity of groceries that one could purchase.
Social Security has exactly the same effect. Since the government does not invest surplus Social Security contributions into productive investments that earn a positive return to taxpayers (taxpayers must pay any interest on the government securities held in the 'trust fund', so those securities are a liability to taxpayers, not an asset), the costs to run the Social Security administration to perform the transfer payments only reduce the amount that retirees would have, had they been able to simply save that money in a private account. That some contributors receive more from Social Security than they contributed in payroll taxes does not alter the situation — without a steadily increasing population, Social Security cannot pay more to any participants than they have contributed, without taking the difference from other taxpayers. Social Security is a negative sum game — in that sense it is like insurance, but bad insurance that rarely covers the full cost of a loss — but that is a damning criticism, not cause for celebration.
And notice how the author attempts to dismiss criticisms of Social Security — as if people are calling it a crisis only because some had to pay into it, but ended up not needing it, rather than the real point, that the so-called trust fund only contains claims on future taxpayers — that is, U.S. government securities, which are a liability to future taxpayers, that do nothing to fund future retirement costs.
Given how bad Mark Thoma's blog post is, it is not surprising that a post he refers would be just as bad (if not worse).
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