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January 28, 2005

Fun with Numbers

Matt Yglesias expresses skepticism about Cato's Social Security Calculator. One objection is over the annuity calculation, which he says is off by about 15%. I don't know that much about annuity markets, but it seems plausible that Cato's using an overly optimistic estimate. One thing to keep in mind is that annuities are sensitive to real interest rates-- the higher the interest rate, the higher the annuity one can expect. Since interest rates are at historic lows at the moment, one might expect that annuities will be more generous as interest rates go up. On the other hand, maybe the financial markets of the future will be awash in capital and therefore interest rates will be lower. Either way, this seems like a 10 or 20% correction to Cato's calculation, still leaving personal account users much better off.

Here's his more serious objection:

Now I think that they get the 5.27 percent figure by assuming that stocks will have an average real annual return of 6.5 percent (this is what the president's privatization commission estimated) and bonds an average real annual return of 3.25 percent (6.5 * .6 + 3.25 * .4 = 5.2). A return of 6.5 percent is not considerably lower than the historical return on stocks. But the estimated figure should be considerably lower than the historical figure for two reasons.

One is that price/earnings ratios have reached a level considerably higher than their historical average. This implies either that stocks are overvalued right now, or else that stocks were undervalued in the past. Either way, it implies slower growth in the future.

The other is that the denominator of the P/E ratio -- earnings -- is related to economic growth. But the future economy is very unlikely to grow as quickly as the economy of the past, primarily because the population will be growing much more slowly. This population-driven slowdown in economic growth is the source of the purported "crisis" in Social Security but its effects will be felt in many areas, including the stock market.

I blogged about the first objection last month, and I think it's a serious objection. So far, I haven't seen a knockout argument on either side of this issue, but I think we have good reason to be worried that the returns won't be as high as 7% in the future.

I think this all misses the point, though. Cato's calculator is clearly a marketing tool rather than a tool for serious public policy analysis. But I think it has some fair-minded assumptions. They chose to use a relatively conservative 60-40 portfolio, despite the fact that many people would likely choose to put 100% of their money into stocks until they get into their fifties, which would give a higher return.

More to the point, even if you grant all of Matt's objections, personal accounts still end up doing better. I whipped up a little calculator of my own, which does the math in a transparent fashion. Cato's calculator says that if I start out at 25,000 at age 25, that I'll end up with a stock portfolio of $406,000 and an annuity of $38,685. My calculator more or less duplicates that result. If we grant all of Matt's objections and use a 4.2% rate of return (60% stocks at 5%, 40% bonds at 3%, with let's say a higher .5% transaction cost), then my personal account still ends up being worth $310,000. And if we assume the annuity pays out a conservative 7%, instead of Cato's assumption of 9%, I would still end up with an annual benefit of about $22,000. According to Cato's calculator, Social Security would pay $15,748 for the same wage profile.

There are various other objections that could reduce this number further, but the point is that even with extremely pessimistic assumptions, you do much better with real economic assets generating wealth in the private sector than you do with a pay-as-you-go system.

Incindentally, I'm not going to try to defend Heritage's calculator. It says my hypothetical 25-year-old would retire with a $900,000 personal account, which seems to require that the full 12.4% payroll tax be invested in the private sector, something that even the insane Ferrara plan doesn't advocate. The closest I can get is with this set of parameters, 5% return and 12.4% set aside, which gives me $824,000 in benefits at age 67. If anyone can figure out which assumptions give you Heritage's result, I'd be interested to see it.

Posted by Tim Lee at January 28, 2005 9:17 AM

Comments

Tim, what about the assumption in the Cato Calculator that personal income would grow at a 4% rate annually until retirement. Did you remove that? Is that assumption built into both the actual social security benefit calculator AND the Cato plan calculator? Or is it part of one and not the other?

Posted by: Jim Henley at January 29, 2005 6:08 PM

Jim,

As you can see from the link above, my calculator allows you to input an earnings growth rate, so you can play around with it and see how lower earnings growth affects the returns.

The reason I didn't blog examples with different earnings growth rates is that writing my own Social Security benefit calculator would be much more complicated than writing the personal-accounts calculator was. So although it can tell you what the expected payout from Social Security would be, it can't tell you the comparable Social Security benefit amount.

The actual Social Security benefit calculator is based on the average of your actual earnings, adjusted using actual wage growth. So it makes no assumptions about future wage growth because it doesn't have to--the formula is entirely backwards-looking.

Here is my same hypothetical worker with wage growth of 1%-- he retires with a final wage under $40,000. (under, I hasten to emphasize, Yglesias's very conservative assumptions about rate of return) With a 7% annuity, he'd get about $13,000 per year, while Social Security would pay (according to a very rough back-of-the-napkin calculation that's probably wrong) about $10,000 per year. The improvement isn't as dramatic as for the wealthier worker, but he still comes out clearly ahead. Also, keep in mind that for very poor workers, Cato's plan includes a minimum benefit provision that would quite possibly be about the same as Social Security's benefits at low income levels anyway.

Finally, I've been meaning to mention that my calculator makes no attempt to factor in recognition bonds, which means that for older workers it substantially understates the potential payout.

Posted by: Timothy at January 29, 2005 6:28 PM

Maybe you can answer the question I had about the Cato calculator (shameless self-promotion link: http://www.steelypips.org/principles/2005_01_23_principlearchive.php#110691569645131685): Why is it that the gender you put in changes the value of the account at retirement?

I understand that women live longer than men, so a difference in the payout value would make sense, but if there's a different strategy being pursued depending on gender, they don't mention it in their footnotes.

Posted by: Chad Orzel at January 30, 2005 10:21 PM

This looks about right; the first move in this particular conjuring trick was made before any of the calculations were set up, by comparing "your SS benefits" versus "your private a/c". The point being that if you wanted to get these on an apples-to-apples comparision, you would need to subtract from your personal a/c, the cost of buying rest-of-life annuities for the current generation of retirees. That would be what you would do if you were obsessed with pretending that an intergenerational transfer system was a kind of investment, which everyone apparently is.

I think that a 7% annuity rate will strike everyone in the year 2040 a incredibly high; even small movements in life expectancy, like closing the gap between the USA today and Japan today, knock seven bells out of annuity rates. But that's a side issue; my view is that this is a thoroughly broken argument, and that defenders of Social Security have got themselves into an almighty mess by pretending it can be won on these terms.

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