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January 05, 2005

Social Security: Something I Don't Understand

Kevin Drum has a CBO chart of the consequences of CSSS Plan 2--Plan 2 of the President's Commission to Strengthen Social Security:

The Washington Monthly: SOCIAL SECURITY PRIVATIZATION IN PICTURES.... Like Ross Perot, we're all about visual aids here at Political Animal. After all, a chart is worth a thousand words, right? So here's a chart everyone ought to pay attention to. As we all know by now, George Bush's favored Social Security privatization proposal is rumored to be Plan 2 of the President's Commission to Strengthen Social Security — known to its friends as CSSS Plan 2. This plan diverts one-third of payroll taxes to private accounts and cuts guaranteed future benefits by one half. (It does a couple of other things too, but these are the biggies.) So: how does CSSS Plan 2 compare to the alternative of doing absolutely nothing? The nonpartisan Congressional Budget Office produced a report last July that examined exactly that. The chart below summarizes their findings.

Source: Congressional Budget Office (2004), "Long-Term Analysis of Plan 2 of the President's Commission to Strengthen Social Security" (Washington: CBO).

The dark blue solid line is for the current system and the dark blue dashed line is for CSSS2. They are both labeled "expected." But they are not expected values. The dark blue solid line does not mark the expected value of benefits--it marks what benefits will be if economic, demographic, and other factors happen to turn out to fall at their mid-range (I'm not sure whether that means mean or median) values. It looks to be the value of the expected economic, demographic, et cetera outcome--not the expected value of the outcome.

The dark blue dashed line is, I think, an even more complex concept. I think it adds together two things: (a) the benefits that the Social Security system will pay out under CSSS2 if economic, demographic, and other factors happen to turn out to fall at their mid-range values, plus (b) the certainty-equivalent value of the returns to private accounts for that high degree of aversion to risk implicit in current financial market risk premiums.

What I cannot figure out is a theory of decision-making under uncertainty which would make comparing these two dark blue lines something that anybody would want to do. I understand expected value. I understand certainty-equivalence for reasonable degrees of risk aversion. I understand CAPM--although in this case I would reject its implicit assumption that people have costlessly managed to lay off the idiosyncratic risk in their portfolios. I even understand certainty-equivalence for the degree of risk aversion needed to match historical market return differentials (although I would reject it too for this purpose). But I don't understand why CBO has done what it has done--if, indeed, I haven't misread what they have done completely. It seems neither fish nor fowl. Unless I'm missing something important, comparing the two dark blue lines gives too pessimistic a picture of the relative value under CSSS2.

Posted by DeLong at January 5, 2005 06:33 PM

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Brad DeLong today correctly questions the wisdom of a particular CBO report on the Commission Model 2. Brad wonders why CBO would mix a certainty equivalent of a personal account with a distribution of other economic and demographic outcomes. I wonde... [Read More]

Tracked on January 6, 2005 05:50 PM


Can you explain further what your confusion is about? I'm unsure how they've calculated the 80% uncertainty interval, but the blue lines themselves seem fairly clear. Both blue lines include estimated OASDI benefits, and the CSSS2 line adds in private account benefits based on a total portfolio return (after administration costs) of 4.9%. Obviously CBO might be wrong about that level of return, but given that assumption it seems reasonable to compare the two lines, doesn't it? After all, you have to use some number to estimate the value of private accounts.

And why do you think the lines are not expected outcome values? I didn't see anything in the report about methodology, so I assumed that's exactly what they were. What do you see that I missed?

In any case, what would you suggest? Is there a better method for comparing expected benefits under different programs?

Posted by: Kevin Drum at January 5, 2005 07:03 PM


I also have a stupid question. Actually a few.

How are they determining the value of the 'personal' account in PSSS2? Are they merely adding the capital in the account to the then-PV of the forthcoming traditional SS benefit? Are they assuming purchase of a single life annuity with it? Are they adding a COLA factor? Would there be one?

Posted by: Lewis Carroll at January 5, 2005 07:55 PM

I thought expected value was a term of art in economics referring to the probability times the payoff.

Posted by: praktike at January 5, 2005 08:35 PM

E(x) = sum x * p(x), discrete
= integral x * p(x) dx, continuous

Posted by: Stoffel at January 5, 2005 11:10 PM

Could it be that one is not meant to compare the two dark blue lines to each other, but to their respective 80% bands?

The current law, except for circa 2050, looks like the expected value hangs out near the center of the 80% distribution. The CSSS Plan 2 expected value is fairly uniformly at the bottom of its 80% distribution, which implies to me that CSSS Plan 2 outcomes are heavily skewed, with a few outliers on a long tail -- usually a sign of riskier policies.

Posted by: Dave at January 6, 2005 01:59 AM

The CSSS2 line is not expected, but risk-adjusted. It shows what the projected benefit is worth, assuming that a dollar of stocks and a dollar of bonds and a dollar of coffee are all worth a dollar.

You would get the same comparison if you took the present values, but discounted risky cash flows at a higher rate (as is always done). But in the picture, the amounts are not discounted, but shown as a % of contemporaneous GDP. That is why the "expected" line is not (and should not be) the expected value of the distribution.

Posted by: enfant terrible at January 6, 2005 06:34 AM

One thing that the shaded components make clear, and which should be a big deal, is that the variability of outcome is far greater under the proposed system than the existing one. We knew that already, but it needs to be a bigger issue in the public debate.

Since Social Security represents some part of one's material standard of living at a time of life when the opportunity to fix a bad outcome is much reduced, I think higher variability is a worse thing in this case than in things that happen earlier in life. If we want our policies to promote good behavior, introducing a random component to retirement funds that is difficult to offset through through behavior (working, learning or savings) seems a pretty bad idea.

Which brings us back to the point that this whole exercise isn't about making the best use of our resources, about maintaining an element of insurance in our national retirement programs, about taking steps to avoid poverty among the elderly. It is about something else -- a windfall to investment brokers, the destruction of useful and successful redistributive programs, undermining the party of the New Deal. Take your pick, or take the whole buffet.

Posted by: kharris at January 6, 2005 06:47 AM

1. Would there be an effort to "cap" medical malpractice awards if the plaintiffs' trial bar gave to the Republicans?

2. Would there be any call for private accounts if Wall Street gave to the Democrats?

Posted by: Ellen1910 at January 6, 2005 06:58 AM

There is an assumption built in here that the Trustees economic projections are based on real world expectations of future economic growth, that is that the Intermediate Cost alternative is in fact a good faith effort at estimating the midpoint of future economic and demographic numbers.

An examination of the numbers over time show that that is simply not true, particularly since the 2000 Report. This can most easily be seen by examining the Low Cost alternative.

The numbers change but the outcome is constant: a fully funded Trust Fund with a constant Trust Fund Ratio. It cannot be an accident that the best guess of the Trustees for future growth pegs their most optimistic estimate at exactly the level needed to fix Social Security. It is always a Goldilocks number, never too hot and never too cold.

The problem for the Trustees is trying to keep some sort of gap. Historically there is some plausible distance between the Low Cost (no fix needed) and Intermediate Cost (accepted "middle" range). In the 2004 Report they were forced to say that 2.7% was the middle and 2.8% was the top. Similar compression is seen in the out years, growth numbers have been screwed down farther than can be plausibly accepted. 1.9% as your "optimistic" estimate for long-term productivity is positively grotesque.

This year the models collapse. You can't plug in a number that shows the system in crisis without having a Low Cost Alternative that shows it to be overfunded, something the Trustees have been avoiding at all costs. But they are faced with an economy that returned 4.0% compared to models that predicted 2.7% and 2.8%, and are faced with replacing 2005 projections that called for 1.8% and 2.1% respectively. The squeeze is on.

But the notion that these were ever good faith estimates of the range of expected outcomes died a long time ago. Coincidentally about the time of the 2001 Report.

Posted by: Bruce Webb at January 6, 2005 07:16 AM


Lovely job. Icky conclusion, though.

Posted by: kharris at January 6, 2005 08:08 AM

What about the numbers in the CBO report (http://www.cbo.gov/showdoc.cfm?index=5666&sequence=0)?

Under the section "Analyzing Alternative Investments," they write, "The individual account proposal in CSSS Plan 2 calls for individual investments in government securities, corporate bonds, and equities. Individuals would be able to select a specific asset allocation. CBO assumes that participants would invest their IAs in the following portfolio:"

In that table, they have "6.8" for "Annual real expected return" of equities.

I'm asking in the context of the conflict that Dean Baker et al. have pointed out (and Bruce Webb has reiterated repeatedly at this weblog) between the assumption of a roughly 7% RRR for equities versus the assumptions on GDP growth in projections for the (unreformed) SS system.

Posted by: liberal at January 8, 2005 08:10 AM

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