Saturday, December 7, 2013

Administration and actuarial values: Why huge government programs are more efficient than the private market

Image: This is a post about risk (source)

To keep this blog approachable, I'll have to define a few terms. Skip the following indented section if you already know:
  • A defined benefit pension is one where an employer agrees to pay a specific dollar amount each month to an employee from the time she retires to the time she dies.
  • A 401(k) is a type of defined contribution pension. Unlike the defined benefit pension, the employee has no guarantee of income once she retires. That depends on how much money she and her employer put into it, and the performance of the stock market before she retires. It's called a defined contribution pension because--rather than getting a guaranteed defined benefit from the plan--employees get a guaranteed defined contribution to the plan. This defined contribution is the "employer match" to an employee's 401(k). Of course, many employers don't actually offer an employer match; their "defined contribution" is zero and the employee is responsible for funding their entire account.
Let's skip all the philosophical arguments of whose responsibility retirement security should be and ask the question. Which model is more efficient?

The National Institute on Retirement Security issued a report examining that very question. They found that one defined benefit pension plan can cover 1000 employees at 45% less cost than 1000 individual defined contribution retirement plans for those same employees.

It's worth noting that defined benefit pensions are basically a thing of the past. Only current retirees and people very close to retirement have them in the private sector. In the public sector, Republicans' favorite domestic boogey man is public sector pensions, and they're targeted for cuts even in blue states. (No, public worker pensions are not unaffordable. No, public worker pensions didn't bankrupt Detroit). In short, defined benefit pensions are a thing of the past for almost everybody.

As one might assume, there would have to be some extremely compelling reasons to switch to a retirement model that's almost twice as expensive. I wrote here on the reasons for this transition; none of the winners are employees or retirees.

So, why are defined benefit pensions so much more efficient? NIRS provides three reasons:
[Defined benefit pensions a]chieve higher investment returns as compared to individual investors because of professional asset management and lower fees – resulting in a 26% cost savings.
My other recent post on retirement security explains the issue of fees. The other side of this issue is administrative. My company, for example, works with an investment firm that offers us employees something like 50 different funds to invest our 401(k) money in (all of them actively managed, of course). Obviously, there many redundant costs in these 50 accounts that could be cut if all employees pooled their money in one fund rather than all of us taking a swing at one or more of the 50 different funds. Additionally, the principle of economies of scale applies. A single person in charge of a defined contribution account doesn't have much bargaining power, but professional administrators in charge of a massive pension fund of thousands of people have far greater bargaining power.

But wait! Social Security has even lower administrative costs than even the best pension plan; see the footnote my post on the "401(k) revolution" for a more information about Social Security having far lower administrative costs than private pensions. When more people enroll, defined benefit pension plans become less expensive per enrollee. Why not have a defined benefit pension plan that contains the entire country so that savings are maximized? In practice, this really does work. Large government plans, because they can cover so many people, really are administratively more efficient than private pensions (even defined benefit pensions).

But there is further strength in numbers. As explained in this post, individual retirement accounts involve a great deal of luck. If the stock market happens to be doing well when you want to retire, you'll be set. If it's doing bad, you're screwed, losing 30% or more of your monthly retirement income. Either you accept poverty in your retirement, or you continue working until the stock market recovers.

But pension plans with many enrollees don't need to be concerned about the strength of the stock market when a single individual retires. The plan need never be concerned with the short term; the only factor that matters is the long term, and this is a far more efficient investment strategy. NIRS estimates that this gives the defined benefit pension model a 5% savings over the defined contribution model; in reality, it's difficult to put a price on the fact that workers have the security of knowing they can retire when they want to, and won't be forced to accept a 30% (or more) reduction in retirement income, or else be forced to continue working into their golden years, waiting for the stock market to recover.

The other major source of savings for defined benefit pensions has to do with actuarial values:
[Defined benefit pensions a]void the problem of “over-saving” by pooling the longevity risks of large numbers of individuals – resulting in a 15% cost savings.
Pension plans might not look like insurance, but they are. Indeed, Social Security's official name is Old Age, Survivors, and Disability Insurance. And when we talk about insurance, we have to talk about actuarial values.

Let's say that Bob is in charge of his own retirement (ie, he's got a 401(k) instead of a defined benefit pension). How much money does Bob need to save for retirement? To keep things simple, let's say that the average employee lives to be 75, which we'll assume is exactly 10 years of retirement. Let's also assume that 10 years of retirement costs exactly $100,000.

So if the average person lives long enough to enjoy 10 years of retirement at a cost of $100,000, Bob should save $100,000, right?

Wrong. What if Bob is an outlier and lives to 95? That's 20 years more retirement, or 30 years of total retirement, at a cost of $300,000. $100,000 might be enough, but it might not be. Bob's actuarial value is $300,000; he's got to save $300,000 to know he's good for retirement. All of Bob's coworkers need to save $300,000 for retirement, even though only 1% of them will actually live to 95 and need that much money.

What Bob and his coworkers should do is each save $100,000 for retirement, with the agreement that the leftover money from people who die before 75 goes to pay for the people who live past 75. Since 75 is the average life expectancy of Bob and his coworkers, the leftover money of people who die before reaching 75 will be enough to cover the people who live past 75. If everyone saves as though they'll live to 75 but pools their resources, there will be enough for everybody. Everyone only needs to save $100,000 instead of the tremendous burden of saving $300,000, meaning they can live fuller lives before retirement.

In other words, each person by herself has an actuarial value of $300,000; but when risk is pooled over the entirety of Bob's workplace, each individual's actuarial value falls to $100,000. Pooling of risk is the advantage the defined benefit model holds over the defined contribution (401(k)) model.

Of course, the agreement I described where Bob and his coworkers only save $100,000 is essentially what a defined benefit pension plan does; defined contribution pensions cannot do this.

(If you're wondering why NIRS says that lower actuarial values provide only a 15% savings, it's because NIRS assumes the employees are eligible for Social Security, which does much of the heavy lifting of retirement security. In our simplified example, Bob and his coworkers didn't have Social Security, so the difference had a much bigger effect on actuarial values).

The government can do it better still
My hypothetical with Bob is oversimplified in many ways, but notice that we assume that Bob's coworkers exactly match his country's life expectancy curve. In other words, their pension plan, as described, only works if the average life expectancy is less than or exactly equal to 75, and not a day more. This is easiest to see in graph form:

The horizontal axis is age at death, and the vertical axis is the percentage of people. The black curve represents the population distribution. In Bob's country, 40% of people die at the age of 75; 75 is also the average age at death for people in Bob's country. A very small number of people live past 90; an equally few number of people are unlucky and die at 55. The most likely age at death is 75, and that is also the average age at death--that's for the entire country, represented by the black curve.

As we said above, we expect the average age at death of the employees at Bob's company to be 75, because that is what is normal for Bob's country. In that case, the age-at-death distribution for Bob and his coworkers would be exactly the population distribution--smack on top of the black curve. That is the most likely outcome. But it's very much possible that Bob and his coworkers have a distribution that is different from the population curve. If, for example, they die in a distribution not of the black population curve, but in the distribution of the red curve, their pension plan will be in serious trouble. The average age at death for the red distribution is 80; clearly, the pension plan will run out of money if they've only saved enough money for the average age at death to be 75.

It's also kind of a problem if their age at death distribution is the blue curve. If that happens, the pension plan will have money leftover when everyone dies. While that's good for the pension plan, it's bad for the people who paid into it. They could have paid less and enjoyed that money while alive.

So, to guard against the chance that Bob and his coworkers beat the odds and their average life expectancy exceeds 75, they should all save $120,000 instead of $100,000. If they all save $120,000, the most likely outcome is that their pension plan will have money leftover when they all die. While that would be less than ideal, it's better than the pension plan running out of money if their average life expectancy exceeds their country's average life expectancy of 75. So, their actuarial value is not $100,000, but higher, at $120,000 (which is still way less than $300,000, each employee's actuarial value alone).

But what if Bob's company combined with another large company, doubling the number of participants in the retirement plan? As more people join, the probability that their distribution will differ from the population distribution falls (in statistics, this is known as the law of large numbers). In other words, if the number of people participating in Bob's pension plan doubles, the age at death curve is more likely to look like the black curve, and less likely to look like the red or blue curves. That means that there is less of a chance that the average age at death will exceed 75, meaning each person will need to save less money. Now, $115,000 per participant will probably be enough. If they keep adding participants to the plan, the actuarial value will keep getting lower and lower (that's the law of large numbers). If enough people participated, perhaps the actuarial value really could be lowered to $100,000.

Even better is the situation in which the government levies taxes on workers in order to guarantee every person in the entire country retirement security as long as they live. By combining the entire country into one retirement plan, the actuarial values are as low as they possibly can be. Actuarial values fall as more people enroll; having Bob's entire country enrolled means the actuarial values are as low as they possibly can be. The private market can't offer this type of saving, because no private plan can possibly cover everybody.

This situation with actuarial values is seen over and over. The American private health insurance/health provider market is unbelievably inefficient--33 cents out of every dollar spent on health care in the American private market is spent on administration--several times that spent on government-run health insurance programs, like Medicare, Medicaid, the VA, and the national health systems of other countries. Even in the private market, the bigger the insurer, the lower their administrative costs, and greater ability to bargain lower costs for their enrollees. In insurance, bigger is better, and you can't get bigger than every single person in the country.

This makes sense for other social democratic programs that look even less like insurance, such as universal child care. Aside from the high cost, companies don't like to offer child care as a benefit because it's difficult to guess just how expensive it will be. As an employer, your employees could have very few children, or each employee could have a family of ten. It's not good to promise benefits you later find you can't afford; it's also not good to have a fund of money set aside that you don't use--investments in new machinery could have been made, employees could have been given a raise, etc. Because there's a tremendous range in liabilities, it's difficult for an employer to offer child care benefits. On the other hand, this problem doesn't exist if the government guarantees child care to every child. The fertility rate at an individual company may deviate from the national fertility rate; a nation's fertility rate won't deviate from the national fertility rate because it is the national fertility rate.

For childcare, economies of scale also plays a role: it's cheaper per child to cover an entire nation of children compared to just the offspring of the employees of one company. Diapers and juice boxes can be bought in enormous bulk orders, training and administrative responsibilities can be consolidated, etc.

Actuarial values also explain why paid parental leave and is best provided by the government. If we know the national fertility rate, we can set aside enough money for all the paid parental leave we need for the year. But a company's fertility rate could differ significantly from the national fertility rate, creating the potential for unfunded liabilities or unutilized resources. The same goes for extended sick leave--in a given year, any individual company may get many have several employees who experience significant health problems and require an extended leave of a month or more, or they may have none. However, at the national level, this happens at a predictable rate. By contrast, sick and vacation days are best provided by individual employers; if you offer your workers 10 days of vacation and 12 sick days per year, you know exactly how much that will cost, and can plan accordingly.

The greatest strength of social democracy is the fact that everyone is covered. That's great for the people living within a social democratic country, and--because so many redundant administrative costs are eliminated and actuarial values are as low as they can possibly be--that's great for lowering costs and saving money. It's not that we can't afford to cover everyone--it's that we can't afford not to cover everyone.

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