Paul Krugman on the "$600 Billion a Year" Number

Paul Krugman tries his hand at showing what's wrong with the Bush-Lieberman "waiting a year to fix Social Security costs $600 billion" number:

Bruce Willis, Asteroids, and Unfunded Liabilities

Sometimes you really have to wonder. It should be obvious that the Social Security Administration’s estimate of the growth of unfunded liabilities says nothing – nothing at all – about the cost of delaying a “fix”, whatever that might mean. But it seems that even many economists – to say nothing of Joe Lieberman – don’t get it.

So here’s an example, to illustrate the point.

Suppose that an asteroid is bearing down on our planet. If nothing is done, it will strike in 2019, inflicting $20 trillion in losses. At a nominal interest rate of 5 percent, that’s a present value of $10 trillion.

If we do nothing about the asteroid, by next year the present value of the future losses from the asteroid strike will be $10.5 trillion. So the “unfunded liability” from the asteroid strike rises by $500 billion a year.

Suppose that there is a way to fix the problem: we can send Bruce Willis into space to blow up the asteroid. So here’s the question: if we wait a year to send Bruce Willis into space, does that cost $500 billion?

Of course not: it could cost either more or less. If waiting a year means that we’ve lost our last chance to stop the asteroid, it costs $10 trillion – the full present value of the avoidable losses the asteroid would inflict. On the other hand, if Bruce Willis can still blow up the asteroid next year (or any year before 2019), there is no cost at all to waiting. In fact, if waiting increases the Willis expedition’s chances of success, there’s a benefit to delay.

In other words, the $500 billion increase in the present value of the future costs from the asteroid says nothing about the costs of delaying action. All it says is that the future is getting closer.

The same is true for Social Security. The future is getting closer, so the unfunded liabilities of Social Security are rising in present value (though not as a percentage of GDP). This says nothing at all about the cost of delaying a “fix.” Those costs, if there are any, depend on the nature of the fix.

And it’s hard to see any costs of delaying the Bush version of a fix. After all, the problem is that in the absence of changes in the system, at some future date Social Security may have to pay reduced benefits. The only thing the Bush plan does to help the system’s finances is – guess what – reduce future benefits. Why does waiting a year to announce benefit cuts that won’t happen for several decades have any cost?

One last point. Lieberman defends himself by saying that unfunded liabilities do too grow $600 billion a year. But that’s not what he said earlier: he said that each year we delay costs $600 billion, which isn’t at all the same thing.

Paul is, of course, right. There is no real economic cost associated with delay by itself: the $600 billion per year number is just a standpoint-of-valuation and choice-of-units effect. There is a real economic cost associated with delay only if delay robs you of the opportunity to undertake the most efficient and effective Plan A and forces you to adopt an inferior Plan B for fixing the problem instead. That's not the case here.

Comments

[Allen K.]

Where is this from?

[chris]

Lieberman's working two jobs just like a blue collar brother without the benefit of a union; he's feeling that falling standard of living too. He's repping the interests of the industry of financial services and the state of Con.

[snsterling]

Most people will not understand the concept of present value and thus not understand the whole presentation. They think of interest as something which adds future value to something in the present rather than something which reduces something in the future when viewed from the present. And this includes most college educated people even those who have taken a class in economics.

This is not the way to debate Social Security in public. You can't use numbers or math in any meaningful way. You have to come up with reasons why a particular approach is right or wrong on a moral basis.

[Sean-Paul]

Brad, you got a link for this?

[RonK, Seattle]

Much better ... but probably too late to get back on the scoreboard.

[Movie Guy]

Well, I have finally read read something meaningful.

The asteroid.

If we are planning to send "Bruce Willis into space to blow up the asteroid", I suggest that we not wait too long. He's growing older.

If we are talking about Social Security, let's send Bruce Willis to the Hill when the debate reaches its momentum. He can blow up the straw house down and then go solve the problem with the asteroid.

I'm sure that Bruce Willis can handle both tasks.

[Movie Guy]

Thanks, Krugman.

All done!

[JR]

The phenomenon under discussion is called "unwinding the discount." This is a plain-vanilla accounting concept, and it's just astonishing that Lieberman doesn't understand it.

[Grep Agni]

This is not an especially good analagy. Moving an asteroid from an earth-intercepting orbit becomes harder the longer one waits. A very small force is sufficient if applied early, but the the closer it comes the more energy is required. Waiting really does have a cost in the asteroid case.

[William Palmer]

On the one hand it's a bad analogy because Bruce Willis isn't really trained to go to space to destroy asteroids.

On the other hand, destroying an asteroid today would be done with the same plasma ray that we would use to destroy the asteroid tomorrow. (Nobody is talking about just altering its course.)

But the first real question is: Is this explanation an exclusive given to Delong by email or was it published somewhere?

The second real question is: If we scream loud enough, will Krugman get his own blog?

The third real question is: If we scream loud enough, will Krugman run for office in 2008?

[Robert Waldmann]

Gep agni Perhaps not a great analogy, but the asteroid has a lot of joementum no ? Also the film is called Armaggedon and you know that Delay has "today might be the day" on the wall of his office, and, you know, the whole debate is about delay.

[spencer]

The other part of the argument that is not discussed in this article is if economic growth is stronger this year then is assumed by the ss commission in making the projections the size of the projected deficit drops.
So the true situation is that as long as we have stronger growth then assumed we actualy save money by waiting.

[anne]

There is considerable danger that the Social Security debate, which is critical, will mask the pronounced deterioration of Medicare's resources is proposed and provisionally passed tax cuts come to being. There seems to be a determination in Congress that either Social Security or Medicare or Medicaid must be severely limited. There is no reason for such limitations other than a wish to set aside the legacy of the New Deal, a legacy of all social benefit programs that have assured middle class America.

[Bob H]

Acting precipitately means that you are basing your fix on population and income projections that are by definition most uncertain. Waiting until these trends become clearer makes possible more accurate projections.
Surely you could afford to wait until 2030 to see how the 2042-2052 projections are holding up.

[johnchx]

I'm generally a big fan of Krugman's work, but I have to say that he's a bit off base here. The $600 billion figure isn't completely meaningless. For the moment, let's set aside the issue of whether it's a good idea to talk about the "infinite horizon" projection at all, and whether the "medium cost" scenario is the right set of assumptions to work with, and focus on the $600 billion on its own terms.

Now, one reasonable (and, I think, valid) interpretation of the infinite horizon "deficit" figure of $10.5 trillion (as of January 2003) is: "How much money would we have to set aside today to pay the planned benefits with no change in taxes, forever?" Now, suppose that instead of coming up with the cash on 1/1/2003, we wait for 1/1/2004. Will $10.5 trillion still do the trick (ignoring changing assumptions)? Of course not. We've missed out on a whole year's worth of interest earnings. So now we have to come up with the original $10.5 trillion, plus the forgone interest. (Aside: it looks like the effective discount rate here is about 5.25%, which seems a bit high compared with 20 year Treasury yields of around 4.8% - 4.9%, but no matter.)

So, yes, "fixing" the SocSec infinite-horizon deficit by the simple expedient of coughing up the money will cost more in 2004 than in 2003, and perhaps something close to $600 billion more.

Does this matter? Interestingly, no, because the discount rate is also a measure of the social time value of money. Put another way, the discount rate means that we are indifferent between paying $10.5 trillion today (1/1/03) and paying $11.1 trillion tomorrow (1/1/04). Why? Because we have plenty of productive ways to use $10.5 trillion for a year. (The argument in favor of investing SSTF balances in the equities market, whether as individual accounts or simply as a diversification of the SSTF's investment portfolio, is that we can get yields that exceed the straight time-value of money. Unfortunately, such yields have exactly one source: risk premia.)

So what about Bruce Willis? Paul usually chooses better analogies. This one is fatally flawed. First of all, the asteroid scenario is one in which the "cost" of not solving the problem (asteroid impact damage) is completely divorced from the "cost" of the solution (Bruce's rocket ship budget). This might be a reasonable analogy for, say, global warming. But for Social Security, it's completely off-base: the magnitude of the problem is EXACTLY the cost of the solution. Second, you'll notice that -- by unspoken assumption -- the cost of Bruce's mission is unaffected by his launch date. Again, not a good match for real social security policy options.

It should be clear that the magnitude of tax increases and/or benefit cuts needed to generate revenues/savings with a specified present value will be smaller if they are effective earlier. What isn't clear is whether that means that earlier is better. One way to look at it is that doing nothing effectively lends $10.5 trillion (or whatever) to the private economy. It's entirely possible that the "yield" on that investment -- in terms of overall economic growth -- will far outperform the yield on T-Bills. In which case, we would see the present value of the Social Security "gap" falling year by year.

In this connection, it's interesting to look at the paragraph in the report of the Social Security Trustees that set off this contretemps in the first place. It doesn't say that a delay "costs" $600 billion. It actually says, "The change to the later valuation date for this report, January 1, 2004, tends to increase the measured deficit, by about $0.6 trillion." More importantly, the next sentence is: "However, the effects of changes in data and methods more than offset this incerease." In particular, the infinite-horizon "deficit" is $0.1 trillion LESS on January 1, 2004 than it was on January 1, 2003.

Yes, you won't hear it from Senator Lieberman, but waiting one year actually "saved" $700 billion, for a net improvement in our position of $100 billion. Not a bad endorsement for a few more years of "inactivity."

[anne]

Nicely done JohnChx, though you are essentially cleverly agreeing with Paul Krugman :)

There is decidedly no change needed in Social Security that will assure reduced benefits until we have a sense of our growth pattern in the coming several years. I would expect growth to be above the Social Security actuaries estimate of 1.9%, and above the 2.2% level that will allow full benefits for generations.

[David]

apni -- acting sooner on the asteroid is more costly and risky than acting later (it's farther away and harder to get to this year, compared to next year). so it depends on how these two things trade; for purposes of this argument, let's assume they're a wash, so Krugman can make his point.

[enfant terrible]

I've heard that Bruce Willis is a conservative, so if you send him to solve the problem, he'll just go off into space on his private account and let the asteroid hit hard.

[ritchie]

"A very small force is sufficient if applied early, but the the closer it comes the more energy is required. Waiting really does have a cost in the asteroid case."

On the other hand, waiting means you need less energy and complexity to reach the asteroid, making the fix cheaper, as well as getting better data about where the asteroid will end up.

Did I get the fizzics right on that?

Likewise, won't we have a better idea is SS is getting closer to being broke or solvent, if we wait a bit?

Did I get the ecognomicks right on that?

[Auros]

JohnChx says:
(((
One way to look at it is that doing nothing effectively lends $10.5 trillion (or whatever) to the private economy. It's entirely possible that the "yield" on that investment -- in terms of overall economic growth -- will far outperform the yield on T-Bills. In which case, we would see the present value of the Social Security "gap" falling year by year.
)))

This can be translated as:
a) The assumptions on which the estimate of present cost was based, were wrong.
b) The real cost is much lower, possibly zero.
c) Every year we continue using the wrong assumptions for the future, but force people to incorporate reality into assessments of the past, the projected future cost will fall.

Which is precisely what's happening. It shows that there's only a "cost" of $600B per year if you're still using assumptions that have already been proven wrong.

[Bernard Guerrero]

Paul's wrong, Brad. The question isn't whether the fix can be implemented later as per the asteroid example, because the damage occurs year by year _in terms of what the next generation has to shoulder_. Cut benefits now, and the generational accounts will be closer to even. Cut later and you can still "fix" the system, but the worker of the future (e.g. my kids) will have to shoulder that much more unreasonable of a burden for all the imlicit calls-on-resources that you and Paul have made explicit by allowing the Boom to retire. Paul isn't right, Kotlikoff is.

Bernard Guerrero

[Mac Thomason]

Let's just send Willis into space anyway and see what happens. Can't hurt.

[ChasHeath]

The plan that is being closed out right now is Plan C, which is the option that allows repaying the various trust funds without a need for large future increases in income taxes.

By running large current deficits, in spite of the large and growing surplusses in various pension trust funds held by the federal government (Social Security, military, and civil pension trusts), we are constricting future choices. In effect, we are giving money to the rich now, in the form of income tax cuts for the rich, in exchange for setting up a future game of musical chairs.

For example, in the future, which choice would we make between these three: a) pay the interest on publicly held debt issued between 2001 and 2010; b) pay Social Security benefits; c) pay for national defense.

By this yardstick, the hypothetical $600 Billion per year of expense we are currently accruing for future Social Security obligations is being siphoned off in the form of current tax cuts for the rich.

[gt]

Bernard,

That just makes no sense.

[bodzin]

At a nominal interest rate of 5 percent, that’s a present value of $10 trillion.I thought in Walton and Rockoff it said there was a rule of 70. That with compound interest, the doubling time times the interest rate will equal 70. If that's the case, it seems that Krugman's numbers are wrong: A current $10 billion cost at 5 percent interest won't double in 10 years, it will double in 14 years. Or am I once more failing basic math?

[Bernard Guerrero]

Sure it does, GT. I don't want benefits reduced at some indeterminate point in the future. At that point, those cohorts that have already accrued additional benefits under the current formula and retired will find it difficult to cede those benefits. Or, rather, the politicians will find it exceedingly difficult to pull those benefits away from them. You can see that effect at work already, with Shrub's pledge not to touch the benefits of anybody over 55.

I'd much rather that we bite the bullet right now and spread plenty of the pain back onto the Boom cohorts that are causing this mess in the first place. Cut benefits and raise the retirement age now, before anybody's received a damned thing. The timing doesn't affect the PV of the cost, but it influences who pays for how much.

[Bruce Webb]

Someone even more wonkish on the Reports than me (and I don't recall the name so can't give the credit) spotted this in the 2004 Report. It is worth citing in full. 2004 Report p.58

"In last year's report the unfunded obligation over the infinite horizon was reported as $10.5 trillion in present value as of January 1, 2003. The change to the later valuation date for this report, January 1, 2004, tends to increase the measured deficit, by about $0.6 trillion. However, the effects of changes in data and methods more than offset this increase. See section IV.B.8 for details.

As noted in the previous section, the $10.4 trillion infinite future open group unfunded obligation may also be expressed as a percentage of the taxable payroll over that period."

Infinite future liability in the 2003 Report was $10.5 trillion. Infinite future liability in the 2004 Report was $10.4 trillion. The $600 billion figure is what the liabililty would have grown if the Trustees were right. In fact the liability shrunk by $100 billion because they were wrong.

Not only is the whole concept of infinite future liability bogus in and of itself, you can take it on its own terms and conclude it is $700 billion less in the 2004 Report than was predicted in the 2003. That $600 billion is a phantom number.

(Though the phrasing is misleading, using "tends" to report a counterfactual is a gross distortion of grammar)

[anne]

Nicely phrased argument on counterfactuals is supposed economic projections :) There is of course not the least reason to limit Social Security benefits based on growth projections that are remarkably pessimistic from an historical perspective. We must be as careful in protecting Medicare.

[Movie Guy]

Anne

How do we protect Medicare?

[anne]

Movie Guy

"How do we protect Medicare?"

A simple and exceptionally important question. Since I started the thought I had better continue and you had better help. I am thinking :)

[mac]

There is one critical piece missing from that article; the future cost of interest on debt assumed today. It was clear to everyone in the Clinton years, that the way to assure social security solvency was first to stop the bleeding of an ongoing deficit, and then to reduce the government's aggregate debt load before the social security obligations made that impossible. It was also obvoius to the conservatives like Norquist, which is why they didn't like the idea of reducing the debt in the first place. It's a spectacular demonstration of un-patriotic behavior, since they are willing to beggar the entire country for their own narrow ideological gains.

"We want to drown the government in a bathtub." If doing so takes us into abject misery, that's just a little collateral damage. Insanely, they are even willing to trust the Chinese Communists to underwrite their stupid games.

[John Morrison]

"Or am I once more failing basic math?"

You're once more failing basic math. :-)

2005 + 14 = 2019, Paul Krugman's year.

[ChasHeath]

The simplest answer to "How do we protect Medicare" is to ask why the GOP blocked health care reform 11 years ago, rather than figuring out a compromise way to solve the escalating crisis of health care when the opportunity was ripe then.

[gym42]

It seems that what is being discussed by Bush (private accounts) is analogous to Bruce Willis pulling a barge full of nuclear waste and throwing it into the astroid, adding more to what will eventually hit the Earth (and causing more destruction).

[johnchx]

anne:

Yes, I basically agree with Krugman's overall assessment of the situation and the policy implications. What I'm quibbling about is (a) the decision to imply that the $600 billion figure means nothing and (b) the contours of the Bruce Willis metaphor.

Paul has a gift for crystalizing difficult ideas into easily grasped metaphors. I just don't think this one measures up to his usual standard.

auros:

I don't think that's quite a fair translation. The question at issue is whether the $600 billion figure means anything *assuming* that the assumptions are correct. Under alternative assumptions, the $600 billion figure doesn't even come up, because there's no problem to fix.

Krugman seems to be implying that the $600 billion figure means nothing, that it is pure scare propoganda. I'm not sure I can go along with that. A year's delay does indeed mean that we would have to come up with an additional $600 billion (or so, ceteris paribus) to "solve" the problem with a lump-sum payment. However, we "should" be willing to do so, since the delay is "worth" $600 billion to us. Put another way, the $600 billion figure is a nice reminder that we *gain* nothing by delay...every penny of "gain" we accumulate from delaying the solution will be taken away when we finally solve the problem.