Professor Bainbridge has graciously responded to my attempt to de-mystify for him the so-called “transition costs” of moving from Social Security to personal accounts. I made the point that there is no additional fiscal burden when those who opt-out of paying the payroll tax today also opt-out of receiving enough future benefits. “Enough” here means “enough to completely repay the Treasury debt that replaces their payroll taxes with accumulated compound interest.” The transition then requires no additional taxes (or benefit cuts) and consumes no potential tax cut.

Another way to put the point, as I noted on Saturday, is to recognize that the Treasury’s borrowing does not represent new debt, but merely a debt swap. The future dollars that would have been paid to the retirees who opted-out are now to be paid to the holders of the replacement Treasury debt. (The obligation to make a future Social Security benefit payment is a debt in the relevant economic sense, whether or not the accounting rules require the government to record it as such.)

In response to this point, the good professor offers a “quibble”. Let me take it piece by piece.

Professor Bainbridge writes:

As I understand it, Social Security is effectively funded on a pay as you go basis in which current workers taxes are not saved but rather are used to pay benefits to current retirees (ignoring the voodoo economics of the trust fund).

Correct.

Accordingly, switching to private accounts will immediately reduce Social Security revenues as some current workers opt for them. As a result, the government will have to borrow now.

Correct. The federal government will now have to borrow by issuing Treasury bonds. It will owe principal and interest payments to the holders of those bonds. But correspondingly, it will be relieved of the obligation to make equivalent future SS benefit payments.

The government will also have to pay interest on the debt starting immediately. In contrast, the offsetting reduction in benefits will not take effect for many years, when those workers who opted for private accounts finally retire.

The Treasury could avoid the need to pay interest in the short term, before the reduction in benefits takes place, by issuing long-term zero-coupon bonds. Or equivalently, if it issues ordinary coupon bonds, it can roll over the maturing coupon-payment part of the debt until the benefit reductions kick in. Either way, the present value of the stream of payments on the Treasury debt remains equal to the present value of the reduction in SS benefits.

So here's my question for White: do you have hard data showing that the present discounted value of the future reduction in benefits at least equals the present discounted value of the bonds and interest paid on them? If not, what I learned about capital budgeting tells me it's a bad deal. No?

I’m not sure what “hard data” means in the context of a hypothetical scenario, but I take it that the question is: how can we be sure that the PDV of the benefit reductions equals the PDV of the stream of bond payments? The answer is simple. We can be sure by setting the “price” of opting-out (the ratio of future benefits foregone to payroll taxes removed) at the Treasury’s borrowing rate. If the Treasury can borrow at a 3% real interest rate, then a worker who opts-out $100 in payroll taxes today also opts-out $100 * (1.03)^n in future benefits, where “^n” means “raised to the nth power”, n being the number of years until the benefits were due.

The Bush plan sets the opt-out rate at 3%. That’s clearly on the high side, as Arnold Kling has noted, because the Treasury is currently paying only about 2% real for 20-year money in the indexed bond market.

Professor Bainbridge adds:

Anyway, does anybody really think that you can sell this idea to the public?

Well, who knows? But it's hard to see why anyone non-spiteful would oppose it, once they understand that (1) opting-out is optional – anybody who wants to is free to remain in the traditional Social Security system, and (2) no matter how many people opt-out, their opting-out doesn’t imply any need to increase taxes or cut benefits for those who remain. The hard part will be getting the public to understand these points.

Let me be clear about (2). Social Security has a future funding gap which will not be closed without either hiking its stream of tax income or lowering its stream of benefit outgo. My point is that allowing opt-out into personal accounts, at a price equal to the Treasury's borrowing rate, does nothing to widen (or narrow) that gap.

As far as the funding gap goes, I agree with Professor Bainbridge that “the best solution would be to raise the retirement age and switch the benefit calculation to price indexing,” i.e., close the gap entirely by lowering the stream of benefit outgo. I say this even though I myself have reached the age of AARP eligibility. (I almost said "regrettably reached", but then I considered the alternative.)