Friday, August 29, 2008

More on how the future deficit is caused by over-generosity to past participants

This is a long post, so be sure to hit the 'read more' link to see the whole thing.

We’ve talked a bit here (and here, over at Angry Bear) about how Social Security’s large future shortfalls are a function not of over-generosity to future retirees, but to over-generosity to past ones. This sounds strange and it’s been a bit hard to explain given the data available. But I’ve spent a bit of time converting data in this paper by SSA economist Dean Leimer into a form that might help things make some more sense.

To start, this table shows the program’s deficit over the infinite horizon, measured in the 2008 Trustees Report as $13.6 trillion, or 3.2 percent of taxable payroll over that period. Folks who think the infinite horizon figure is crazy often focus on the, well, infinite part; how can we know, and why should we care, what will happen in the infinite future?

Those of us who think the infinite horizon measure has merit sometimes point out that the deficit isn’t a function of what we project will happen in the way off future, but of what happened in the past. Early participants received much, much more in benefits than they paid in taxes. As a result, the trust fund balance is much lower than it would have been had these early cohorts received only an actuarially fair return (defined as their benefits being equal in present value to their taxes; put another way, it means they would receive a return on their taxes equal to the interest rate paid on bonds on the trust fund).

To back this view, we sometimes point to this table, which breaks the infinite horizon shortfall down more finely. It shows that the $13.6 trillion deficit through the infinite horizon is fully accounted for by the fact that past and present participants received $15.2 trillion more in benefits than they paid in taxes. Future participants are projected to receive $1.5 trillion less in benefits than they’ll pay in taxes, even if Social Security were fully solvent. Add those two numbers together, subtract the current value of the trust fund ($2.2 trillion) and you have the $13.6 trillion deficit.

One question that’s been raised, however, is that the figures for past and present participants includes everyone currently over the age of 16. This means that the earliest participants are lumped together with people just entering the system now, so it’s not clear whether the $15.2 net transfer is really a function of over-generosity to past cohorts or to future ones.
I requested from the Social Security actuaries a cohort-by-cohort breakdown of the figures above, but they weren’t able to provide it. So alternately, I worked with data from Dean Leimer’s paper to convert it to a form more comparable to that show in Table IV.B7. Dean is probably the leading expert on how different cohorts have been treated under the Social Security program and he constructed his figures from SSA data, so I fully trust they’re technically correct. The issues was simply converting them for comparability, which I did.

I should note, however, that the numbers don’t exactly match up because Leimer’s projections of future taxes and benefits was based on the 2002 Trustees Report, which showed a significantly larger deficit than the 2008 Report. I discounted future dollar amounts based on the interest rates in the 2008 Report to keep things as comparable as possible, but the overall deficit is larger in Leimer’s figures due to his matching an older set of Trustees projections. Also note that all individuals born prior to 1900 are lumped together in Leimer’s data.

In any case, first here’s a chart showing real internal rates of return from Social Security for different birth cohorts. As you can see, early cohorts received very high returns while later cohorts received lower ones. Once a cohort is receiving a return below the trust fund interest rate (around 3 percent) the present value of that cohort’s taxes will exceed their benefits. These later cohorts will be net contributors to the system, meaning that they actually help keep the system solvent even if they’ll be the ones holding the bag when it’s going broke.

You may notice that for later cohorts returns tend to rise. Why is this? It’s because these figures are shown under scheduled taxes and benefits, which assumes (unrealistically) that full benefits can be paid at all times. As future cohorts will live longer and longer in retirement, they’ll receive more benefits and so returns will rise. But again, this is unrealistic; in real life, returns will inevitably stabilize.

Now here’s the second chart. It shows net transfers from Social Security by cohort, expressed in present value dollars to make them comparable to the numbers in Table IV.B7. If the dollar figure is positive that means that a given birth cohort received more in benefits than it paid in taxes (all in present value form); if the number is negative, it means they pay more in taxes than they’ll receive in benefits. Again, all this is under scheduled benefits, so solvency doesn’t come into play here.

What the table shows is that early cohorts – particularly those born prior to 1900 – received much more in benefits than they paid in taxes. For the pre-1900 cohorts, the bonus was around $14 trillion. The bonuses decline over time until they’re actually negative beginning with people retiring in the late 1990s. They stay negative for quite a while, and then some distant cohorts are actually slightly positive again (also due to the assumption that they live longer and collect more benefits).

If you add all the cohort figures up, they total around $22 trillion in present value. If you then subtract the current value of the trust fund, the total is around $20 trillion. This is larger than the current infinite horizon shortfall of $13.6 trillion, because the 2002 Trustees projections were more pessimistic.

But I think this basically shows the point we were discussing earlier. The so-called “infinite horizon” deficit has very little to do with what will happen hundreds of years from now and everything to do with what happened in the first 25 years or so that the Social Security program was running. Participants, rich and poor alike, were paid much more in benefits than they contributed in taxes. As a result, the trust fund balance – which should be somewhere around $16 trillion – is only around $2 trillion. This is what drives the long-term deficit.

I think in a way this makes reform easier to understand and resolve. We’ve inherited a ‘legacy debt’ due to over-generosity to prior generations. Whether this over-generosity was justified is an academic question. (Some say yes, to help reduce poverty; I agree there, but much of the legacy debt is due to over-generosity to high income participants, which is harder to justify.) In any case, though, it’s a done deal: the shortfall is what it is, and our only choices are how to deal with it. My argument, which I’ll expand on more fully in the future, is to treat this legacy debt more like a real debt: find the best, fairest and least economically damaging way to pay it off, which may be a way outside of the current Social Security financing structure. But that’s a question for another day.


Bruce Webb said...

Sorry I still don't buy it. We know exactly how much was paid out in various periods from the first check in 1941 to now. You can and I did total Tables IV.A2 and IV.A4 and come up with the following values:

OAS 1941-1956 $25.6 billion
OASDI 1957-1968 $181 billion
OASDI 1969-1980 $793.1 billion
OASDI 1981-1992 $2.476.5 trillion
OASDI 1993-2000 $2.829.3 trillion
OASDI 2001-2007 $6.330,9 trillion

All of those benefits were paid out of then current dollars and are off the books. That if you cast them in PV terms that they would be larger numbers doesn't erase the fact they are no longer liabilities, those checks were cashed decades ago.

Lets apply the calender to this argument. The pre-1900 cohort would have started going off the books by 1968 when the oldest surviving eligible beneficiary would have been 93 years old. At this point total payouts to all parties totalled $206.6 billion. This cohort would have been almost entirely off the books by 1980 with some lingering survivors aged from 81 to 104 years old. Total benefits paid out to that point were $999.7 billion. Large parts of that would have been paid out to people born bewtween 1900 and 1915 and it is not as if the pre-1900 cohort paid no payroll taxes at all. Chart or no chart the idea that unfunded liability of $15 trillion going forward is the result of extra benefits above taxes paid from the portion of the $999.7 billion paid to the pre-1900 cohort is arithmetic nonsense.

If we needed proof we could draw it right from the post:
"I should note, however, that the numbers don’t exactly match up because Leimer’s projections of future taxes and benefits was based on the 2002 Trustees Report, which showed a significantly larger deficit than the 2008 Report."
There is no possible action by the pre-1900 cohort that could move the needle between the 2002 and 2008 Reports either in a positive or negative direction, those people are neither drawing extra benefits or mailing in rebates, whatever their overall impact on the system it was by its nature static between those two periods. If the current unfunded liability number is moving around it is the result of changing assumptions about the future and not about excess collections in the past.

And this is just wrong:
"To back this view, we sometimes point to this table, which breaks the infinite horizon shortfall down more finely. It shows that the $13.6 trillion deficit through the infinite horizon is fully accounted for by the fact that past and present participants received $15.2 trillion more in benefits than they paid in taxes. Future participants are projected to receive $1.5 trillion less in benefits than they’ll pay in taxes, even if Social Security were fully solvent. Add those two numbers together, subtract the current value of the trust fund ($2.2 trillion) and you have the $13.6 trillion deficit."

First the tense in 'received' is wrong. The $17.4 trillion represents the gap between future cost less future taxes for people 15 years and older over the next 100 years. It is offset by an excess in collections going backwards for "past and current participants" of $2.2 trillion REDUCING the unfunded obligation going forward to $15.2 trillion. A clear reading of the table is not that past participants drew $15.2 trillion more out in benefits but that they put $2.2 trillion more in in taxes. You have simply confused the sinners from the sinned against here.

Plus the $1.5 trillion extra projected to be collected from future participants is misdescribed as well. Properly examined this means that cohorts born after 1994 if separated out would be able to fully fund their own scheduled benefits with a relatively modest $1.5 trillion left over, which is to say that long term Social Security will revert to full Pay-Go status.

Maybe I am just too dim to get it but from here the storyline seems 180 degrees reversed from what the dollar figures show.

Andrew G. Biggs said...


Thanks for the comments. Hopefully I can explain better here.

To start, the infinite horizon shortfall as described in Table IV.B7 is by definition the sum of the cohort-by-cohort net benefits (meaning PV benefits minus PV taxes). That is, had I gotten the cohort figures from the actuaries, rather than having to convert older numbers, they would have added up exactly as shown in the table. So in one sense this proves the point by itself: the total infinite horizon shortfall is the sum of net benefits paid to all past and future cohorts. Net benefits to future cohorts are negative (meaning they pay more taxes than benefits) while for past cohorts they're positive. I can't imagine it's possible to attribute the deficit to future cohorts who are paying more than they receive instead of past ones who received more than they paid. This is just a definitional/logical issue.

Second, the numbers you highlight are only of benefits paid. What matters for solvency is benefits net of taxes. The way this translates itself to solvency is through the trust fund balance. Eg., imagine that the government in its generosity decided to pay me 10 times more in benefits than I paid in taxes. Once I'd dead, that payment would be 'off the books,' but the result would be that the trust fund balance would be lower than it should be. Multiply by entire cohorts and you get the picture. If early cohorts had been paid an actuarially fair return, the current trust fund balance would be more than enough to fund the system forever. Again, there's not much empirical disputing of this.

You pointed out how the change from 2002 to 2008 numbers affects things, which raises an interesting point. Future outcomes can affect solvency, as we've seen a number of times. But what happened from 2002 through the 2008 numbers was in large part due to a change in modeling future household benefits. CBO's work showed that future benefits will be lower relative to taxes because of changes in household structure. As women's earnings come closer to men's, the amount of spousal benefits paid out declines. So even given the same amount of earnings and taxes, future benefits will be lower. How does this help solvency? In short, the current system becomes a worse deal for future participants -- because fewer spousal benefits are being paid out, the net benefit paid to future cohorts gets even lower. Does this contradict my earlier point? Not at all: the massive net benefits paid to early cohorts remains, but the total shortfall declines because future cohorts are getting even less benefits relative to their taxes.

Other factors can also help, but I believe modeling changes are the main driver from 2002 through 2008.

The paragraph re confusing the sinners and the sinned against isn't correct because you're thinking about things on an annual cash flow basis than a cohort basis. The current trust fund balance isn't an excess of collections for past/present participants, since they still have a lot of benefits yet to collect. As with my personal example above, the mere fact of a positive trust fund balance isn't meaningful; what matters is the level of the trust fund, which is far lower than is needed to fund promised benefits.

Anonymous said...

brave try Mr Biggs

but bogus from the beginning. the only danger here is that the experts will think they understand it, and the congressmen will think that since they can't understand it they have to go with the experts.

the first fallacy is to treat Social Security as if it was an investment plan. the "overgenerosity" of the payments to the first participants had a lot more to do with the facts of phasing in a pension system, and using it to take up some of the costs of what would otherwise have been ordinary welfare, or the social costs... and economic costs... of allowing the poor elderly... who had lost their savings from the free market depression... to live and die in ugly poverty.

you cleverly count all of that as a cost to social security. forgetting that the people paying into social security were in fact... even as their payments were being used to pay benefits... simply paying in advance for their own benefits.. in an outside the markets system of retirement insurance.

i do not know if your "present value" calculations rely upon the difference in present value between taxes paid now vs benefits paid later... an opitcal illusion that might be justified if there was a a real alternative by which those taxes could be invested and earn the interest rate you assume... and still act as insurance... which there is not.

and that brings us to the bogus conclusion at the end of the curve... while you claim that future participants get less than they paid in, your chart shows that they get more than they paid in... though perhaps less than you say they "could have gotten" if only they had invested and got the percent return you say they could have gotten, if only the insurance had no value to them.

yes, if only.


Andrew G. Biggs said...


Thanks for the polite comment. To be clear, 'less' or 'more' is measured in present value terms where the discount rate is equal to the interest rate earned by the trust funds. So when I say 'less' I mean less than if they'd invested their taxes in trust fund bonds, which are a low-risk, low-return investment.

You're right that any paygo system will pay 'bonuses' to early participants, who collect for a full retirement even if they didn't pay taxes a full working life. But these bonuses need not be nearly as large as they turned out to be, and in fact Roosevelt vetoed legislation that increased bonuses and would have vastly reduced the size of our current shortfall. (He was overridden.)

Your point regarding the insurance value of the plan is valid, but not to the argument made here. The argument HERE is that the future shortfall is a function of large net payments to early generations. That argument is true. Now, you can counter-argue that the future deficit is ok because we should have made those large net payments to past participants, or that the insurance value of the program to future participants is so large that they still get good value from the system. That's fine, but it simply doesn't touch on the argument I'm making here, which is one of accounting.

Bruce Webb said...

"The argument HERE is that the future shortfall is a function of large net payments to early generations. That argument is true."

I disagree. Your formulation implies that the bulk of the future shortfall is the result of past transfers when instead the numbers show it would be the result of future transfers to people born between 1952 and 1993. There is no shortfall at all until or unless the Trust Funds go to zero, which may or may not happen in 2041 (SSA) or 2049 (CBO). If the economy going forward manages to keep revenues ahead of the realities of existing demography that figure for future shortfalls may well shrink or conceivably vanish. Wittingly or not you are trying to describe a contingent future with past definite language.

Arne said...


I understand the math and agree that it is correct, but I question whether it is useful. Since the PV is going up every year by the assumed treasury rate, it will double in 14 years. I do not see that there is any meaningful number to which I can compare that $27T, so it pontless.

If the economy improves and an extra $5T is collected over the next 75 years, it will change the math so that future participants will receive $6.5T less instead of the $1.5T currently projected by the IC model. Again, so what.

I believe that the $13.6T could be compared to the cost of converting the PAYGO program to a fully funded program, but if I never want to do so, I have no use for the number. If a comet crashes into Earth and destroys the SS system, I hardly care whether I have $27T in losses 14 years from now, $200T in losses 100 years from now, or $2x10^23 in losses 1000 years from now. There won't be anyone to collect and it will still be axactly what is cost to start up the SS program in the first place.

Am I wrong?

Andrew G. Biggs said...


You're right in a qualitative sense, which is why I usually don't cite the dollar figure of the deficit (I actually had to look it up again, since I don't use it often). The dollar figure goes up by the rate of interest each year, but the economy also grows albeit at a smaller rate. Usually I cite the deficit relative to the tax base (around 3.2%) or relative to GDP. That figure grows over time, but less fast than the dollar figure.

The $13.6T is close to the termination cost of Social Security (I think that's around $16 or $17T) and is obviously related, though not exactly the same.

Since we're on the topic, this is a good place to address one of Bruce's concerns from over at Angry Bear, that the fact that the future deficit can change based on demographic or economic conditions means that it wasn't caused by over-payments in the past. That's not the case, and hopefully this will explain.

Imagine you had a plain old government debt of $13.6 trillion. That debt doesn't change, except to increase with interest. Our ability to repay the debt, however, does change: if the economy grows then the debt will be smaller relative to the economy and therefore easier to pay. If birth rate rise so there are more people, then the dollar debt to repay doesn't change but there are more people to spread it over so the individual burden declines. Likewise, if people don't live as long as expected, that saves money on Social Security and Medicare payments and we can use that money to help repay the debt. So future conditions do matter, which is why we spend time talking about whether the Trustees or CBO projections are reasonable. But they don't change the fact that we've inherited a de facto debt from earlier generations.