A number of readers have posed what is actually a pretty sophisticated question about Social Security reform. They have realized, after reading Martin Feldstein or other sources, that in the long run a pay-as-you-go system can offer retirees a rate of return equal only to the rate of economic growth (work force growth plus productivity growth). Meanwhile, even risk-free investments offer a higher rate of return. Doesn't this mean that pay-as-you-go retirement systems are inherently inferior, and that we should privatize on simple efficiency grounds?

It can seem like a compelling argument. But it turns out that there is a catch - roughly a $3 trillion catch. And the deliberate efforts of would-be privatizers of Social Security to hide that catch in the fine print - not to mention their failure to take that fine print into account in other policy proposals - are what get me angry about this whole issue.

Maybe the best way to explain what's going on is to take a simplified example. Imagine a static economy - no growth in productivity or wages - in which people live two periods. They work for one period, then retire for the second (so you should think of a "period" as something like 30 years). We assume that the real rate of return on private investment is 100% (remember, again, that these are long, multi-year periods), so that one real dollar invested during working years yields two dollars in retirement.

Now suppose that there is a Social-Security type pay-as-you-go system, in which all workers pay some fixed amount - say $1 - which is not invested, but instead used to pay current benefits to retirees. Since given our assumptions the number of workers equals the number of retirees, this means that every individual will put in $1 when young, then get $1 back when retired - a zero rate of return.

So there you have it: a zero rate of return on Social Security, versus 100% on private retirement accounts. Clearly privatization is good for everyone, right?

But you should immediately realize that there must be something wrong with that argument. After all, there isn't any waste in the pay-as-you-go system - it's just transferring money around. So where does the return go?

The answer - which I guess isn't that obvious - is that it goes to pay a hidden debt. When the pay-as-you-go system starts up, there is a generation of retirees who receive benefits without having made contributions. (What this corresponds to in the real world is the very high rate of return received on contributions by early recipients of Social Security.) That debt - equal in this example to $1 per worker - is never paid off; instead, the earnings from each worker's contribution are in effect used to pay the interest on that debt. And that's where the money goes.

Or if all of this is too metaphysical for you, let's just ask what it would take to privatize our simplified retirement system. You couldn't just say to workers "OK, you're free to invest your own money"; somehow you have to find the money to pay for the benefits of the current generation of retirees. That is, you have to find a way to pay off that hidden debt. That's why a straight comparison between the rate of return on private retirement plans and Social Security contributions is meaningless.

In our simplified example, a transition to a privatized system would require an injection of funds from the rest of the budget equal to $1 per retiree. I haven't been able to lay my hands on a precise estimate for the real Social Security system, but I am pretty sure that the cost of paying off the overhang of obligations would be something north of $3 trillion. Which brings me to the reasons why I am angry with the peddlers of privatization proposals, whether full-scale or partial along the lines of the Bush "plan" (scare quotes because there are no details.)

First, the proponents try to pretend that there isn't any cost. In general, they never mention that there is this little debt that needs to be paid off unless forced to. And even then you get a muttered "Well, everyone knows there will be some transition costs", as if we were talking about a minor detail, not a near-doubling of the national debt.

Second, if you are planning to privatize Social Security in whole or in part, you should be making allowances for those transition costs in the rest of the budget. If we think of the Bush proposal as a 1/6th privatization, he ought to be setting more than half a trillion dollars aside over and above the Social Security surplus to pay for those "transition costs". In fact, the Bush tax cuts will use up just about all of the CBO's unrealistic estimate of the non-Social Security surplus over the next decade. If you make a more realistic estimate of the funds available - I've just read a chilling paper by Auerbach and Gale, available from www.nber.org if you have a license - there is really less than $400 billion available for fiscally prudent tax cuts, compared with a true cost for the Bush cuts of around $1.7 trillion. And that's before we get to his Social Security "plan".

None of this says that privatizing Social Security is necessarily a bad idea. But the way that privatization is being sold is spectacularly dishonest, and to propose privatization and huge tax cuts at the same time is spectacularly irresponsible.