Social Security Part I: Insurance and Risk Premiums

Much of the Social Security ground has already been covered. For example, one well-established fact is that there is no Social Security crisis (the Daily Howler has also been very good on this point.) If nothing is changed and economic growth turns out to be in the fair to middling range then the trust fund will be exhausted in about 50 years. Of course, in 50 years, we’ll all have personal flying devices and robot vacuum cleaners. In the meantime, there are real problems to worry about: nuclear proliferation, global terrorism, the declining dollar, jobs, and the massive general fund deficits.

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.(*)

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.

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.

On the other hand, those with bad luck or insufficient income will not have a nest egg at retirement. Because of Social Security, instead of facing the risk of zero income at retirement, they are guaranteed income sufficient to subsist.

This is precisely like the insurance example I worked through above: people with good outcomes will wish they hadn’t paid into the insurance fund; those with bad outcomes will be glad they did. Ex-ante, everyone benefits from the insurance. Overall, society is better off because risk is reduced; because people are risk-averse, the gains are quite large.

Now, the quick-witted or contrary will point out, inter alia, that other forms of insurance are successfully provided by the market. Why should the government step into this particular market and not others? This post is already too long, so I’ll save that for another time. But in case you can’t wait, Mark Kleiman explains one such market failure.

One final point: all of the privatization plans I’ve seen discussed would replace Social Security with a defined contribution style system in which the more a person makes, and the luckier that person is, the more that person will have at retirement, and vice-versa. The insurance function of pooling and attenuating risk is totally removed; or, more accurately, reversed. To see the effects of this, run through the numbers above, but add a minus sign throughout.


(*) If you’re initially tempted by the job with uncertain income, imagine that you are offered a job that pays $100k, with the following condition: every Christmas, you and your boss flip a coin. If it’s heads, you get $25,000. If it’s tails, you pay $25,000. This scenario gives equal odds of yielding an income of $75k and $125k, but most people would choose a job that pays $90k with certainty over the coin-flipping job. Of course, that’s identical to paying $10,000 to avoid the +/-$25,000 risk.

(**) To convince yourself that the magnitudes are not way off, note that homeowners pay about $1,500 per year simply to avoid the very low (less than 1/1000) risk of fire destroying their house.