Arnold Kling

The Budget Debate, VI

PRINT
Peak Load Pricing and Mental T... The Budget Debate, VII...

[Update: Bernard Yomtov convinced me that the CBPP did not make the error I suggested below. Instead, the way that they accomplished the swindle is explained in this post.]

As a share of GDP, increases in future Medicare and Social Security benefits are much larger than the tax cuts enacted by the Bush Administration. The figures are roughly 10 percent of GDP and roughly 2 percent of GDP, respectively.

However, the Center on Budget and Policy Priorities compares the present value of future entitlement shortfalls to the tax cuts. This method, cited in the New York Times by Paul Krugman, uses an interest rate to discount future dollars to present dollars. Since the entitlement shortfalls are farther in the future, they are discounted more heavily, which reduces their magnitude. According to Krugman and to the CBPP, this shows that the present value of the shortfalls in Social Security in Medicare comes to less than $10 trillion, which makes it smaller than the revenue foregone by the Bush tax cuts.

(For a basic introduction to interest rates and present value, go here. For a discussion of present value calculations in the context of the Federal Budget, see the discussion of generational accounting here.)

With discounting, the choice of the interest rate is crucial. A low interest rate would artificially diminish the magnitude of the Bush tax cuts. A high interest rate would artificially diminish the value of the future entitlements.

What is a good interest rate to use? As this article shows, this is a difficult issue. However, almost all economists would agree that a real (inflation-adjusted) interest rate is more appropriate than a nominal interest rate. Most economists would agree that the best estimate of the long-term real interest rate is the rate on inflation-indexed Treasury securities, or TIPS, which currently is about 2 percent.

What interest rate did the CBPP use? The answer is buried, quite literally, in a footnote that says only


Assumes level of GDP and interest rates projected by the Social Security actuaries

I did a search to try to find the interest rate projected by actuaries. I found this document from the year 2000, which gives an interest rate of 6.9 percent. I found this answer using a query on the Social Security web site, which gives an interest rate of 6.4 percent.

These are nominal interest rates, not real discount rates. They are three times the rate that one should use, so that they completely distort the relationship between present and future budget actions. Using an interest rate over 6 percent artificially reduces the impact of future entitlements relative to near-term tax cuts. I am certain that if one re-did the calculation with a more reasonable interest rate--less than 2 percent--then this would show that it is the entitlement shortfalls that exceed the tax cuts in their impact.

To put this another way, if an interest rate over 6 percent can be assumed, then switching Social Security and Medicare to private accounts earning that rate will have the appearance of tripling the rate of return that individuals earn. If the Bush Administration were to use such an interest rate to justify a privatization proposal, I am sure that Krugman and the economists at the CBPP would be the first to cry "foul."

For Discussion. What hidden assumptions might distort a calculation that is expressed in terms of the share of GDP rather than in terms of present value?


Comments and Sharing


CATEGORIES: Social Security



COMMENTS (26 to date)
Bernard Yomtov writes:

It is appropriate to use real interest rates to discount constant dollar figures, and nominal interest rates to discount current (not inflation adjusted) dollar figures. It's not clear to me whether the 75-year estimates are inflation-adjusted or not, so I don't know which rate should be used, but it certainly should be consistent with the projections.

Jane Galt writes:

No, it's not appropriate to use a nominal discount, because the shortfalls themselves will be inflation adjusted through COLA.

Patrick R. Sullivan writes:

Paul Krugman today:

" What this means is that the revenue that will be sacrificed because of those tax cuts is not a minor concern. On the contrary, that revenue would have been more than enough to 'top up' Social Security and Medicare, allowing them to operate without benefit cuts for the next 75 years".

What happened to the "real assets" in the trust fund? To the "transition cost" of a privatized system?

Jane Galt writes:

More broadly, the government takes its revenue (roughly) as an inflation adjusted percentage of GDP, and the payouts will also be inflation-adjusted, so any inflation washes out. Moreover, since the US treasury is assumed to have virtually zero default risk and thus borrows at the risk-free rate, the nominal rate should be the time value of the money (the real rate) plus the nominal inflation rate, which pegs the inflation expectation the CBPP is using at near 5%. The figures they're getting from Social Security, even if they are inflation adjusted (which I doubt, for the same reason -- it's irrelevant what the inflation rate is, because the revenues and the outlays should be inflating at roughly the same rate), are not adjusted for any 5% inflation in a time when we're currently worried about deflation.

Bernard Yomtov writes:

Not sure I understand your point, Jane.

Suppose the govt says it's going to give me $1000 plus COLA a year from now. Assume a 2% real interest rate and inflation of 3%, so the nominal rate is 5% (plus a smidgen). With my 3% COLA I'm going to get $1030, which has PV of $980.95 at the nominal 5% rate.

If we operate in real terms, using today's dollars, my payment is $1000, and discounting that at the real 2% rate gives $980.40, the same amount as above after allowing for the aforementioned smidgen.

Where's the problem here, as long as contributions and earnings rates are also treated consistently?

Arnold Kling writes:

Bernard, I agree that nominal magnitudes should be discounted at nominal rates, and real magnitudes should be discounted at real rates.

When you compute something as a share of GDP, that is a real magnitude. Therefore, it should be discounted at a real rate.

The Trustees' report speaks almost entirely in terms of ratios to GDP. It appears to me that what the CBPP folks were doing was taking the share of GDP from the Trustees' report and discounting it at a nominal rate. If so, then that is exactly the wrong thing to do.

Bernard Yomtov writes:

Arnold,

You say,

"When you compute something as a share of GDP, that is a real magnitude. Therefore, it should be discounted at a real rate.

The Trustees' report speaks almost entirely in terms of ratios to GDP. It appears to me that what the CBPP folks were doing was taking the share of GDP from the Trustees' report and discounting it at a nominal rate. If so, then that is exactly the wrong thing to do."

I agree. It would be wrong. I said as much in my first comment on the matter, which I considered unexceptionable.

Still, I'm far from convinced they did this. First, it would be an elementary error, and since they take figures from Social Security, it might imply that Social Security was making the same mistake.

Of course you could do the % of GDP calculation in nominal terms if you wanted to. Estimate nominal GDP and nominal amounts of tax cuts and entitlements, then discount back with a nominal rate. Not a great way to do it, but if you're looking for a comparison with someone whose already done it that way it might be best.

I do fault the authors for not being clear about their methods.

Jane Galt writes:

It's not exactly an "error". The CBPP is a policy tank devoted to protesting tax cuts and entitlement reform.

I'm pretty sure the Social Security numbers are in real terms, but I'll check. I was confused about your earlier point. Basically, the point I was making is this: we don't care what the nominal numbers are for Social Security, unlike a corporation borrowing, because both inflow and outflow are a percentage of income. What we care about is the relationship of inflow to outflow. The gap and the ratio are much larger for the entitlement reform than for the tax cuts. To the extent that discounting is appropriate, it is appropriate to discount at the real rate, both for the reasons Arnold states, and because the only opportunity cost of the money is prepaying debt; none of the other government expenditures contemplated are going to increase national income the way private investments do. Since the US government will see its income grow pretty much in line with inflation, while the value of the debt erodes, the appropriate discount is the real value of the extra interest payments, which seems to be, as Arnold points out, around 2%.

Now, assuming we did want to use nominal rates, where the hell do they get 6+%? The government's not taking out a personal mortgage; it's issuing risk free debt. Expected inflation would have to be in the 4-5% range for their discount rate to be close to accurate. We're worried about deflation right now, and the Fed hasn't shown any inclination to print its way out of our sovereign debt; nor would it be likely to until very far along in the entitlements crisis. My private student loans are pricing considerably below what the CBPP thinks the US government will be paying.

Bernard Yomtov writes:

Technically, I think they can use any nominal rate they want, as long their inflation assumption matches it. In the example I gave above, you could use 5% inflation and a 7% nominal rate, and still get the same answer. After all, the inflation rate is just a scaling factor, and washes out, as you pointed out.

The important thing is consistency and a sensible underlying real rate.

Jim Glass writes:

We can start with the interest rate issue. But also be aware of the "hide the liabilities" issue.

Krugman says this is an "actuarial" analysis of liabilities "like a private insurance company would use". That is patently false.

The 75-year cut-off date for the projection causes true net liabilities to be greatly *understated* by counting payments made into the system by people who today are young or unborn *without* counting liabilities owed to them after the 75-year date on the liability side. This is cash-basis analysis with an artificial cut-off date, not actuarial analysis. It is counting income *but not* associated liabilities! If any private insurance company "actuarially" computed and reported its net liabilities this way, its top executives would wind up in the cell next to the guys from Enron and Worldcom.

To quote the Analystical Perspectivs on the Budget at http://www.whitehouse.gov/omb/budget/fy2004/ [pages 47-48]
~~~
"Limiting the calculations to 75 years understates the deficiencies, because the actuarial calculations omit the large deficits that continue to accrue beyond the 75th year. The understatement is significant, even though values beyond the 75th year are discounted by
a large amount...[ large indeed -- especially with a more realistic interest rate]

"In fixing the horizon at 75 years, most of the taxes of these future participants are counted without a full accounting for their expected benefits, much of which will be received beyond the 75th year.

"For Social Security, the present value of benefits less taxes in the 76th year alone is nearly $0.1 trillion, so the omission of these distant benefits amounts to several trillion dollars of present value...."
~~~

So, first, Krugman is omitting "several trillion dollars" right there. Then note that a future liability in year 76 alone that is still $100 billion in today's money *after being discounted for 75 years* (and plug in your more realistic interest rate here)will be HUGE then. And without privatization of some sort that allows it to be financed with real economic savings, it will all have to come out of current taxes.

And because the financial imbalance in SS is biggest and growing in the out years after #75, even if you *did* truly close the 75-year gap today without such Krugman-like gimmickry, after just one year passed on the calendar making number 76 number 75, we'd have a new $100 billion funding gap again, growing every year forever.

And of course this doesn't cover Medicare, for which the same thing applies on an even larger scale.

Now with a true *actuarial* analysis all this would be all accounted for and the truth would be evident. But the 75 year gimmick slips trillions of liabilities that will be piling up like a mountain then under the rug and out of sight today.

*No way* is the actuarially measured deficit closed. It's like saying: "I can fully cover my current living expenses for X years with no problem at all using this financial program [which plunges me into total liquidation in year X+1]"

But wait, it gets better! Look at the year-by-year discounted to current value bottom-line numbers from the Analytical Perspectives., Table 3-3:
~~

Social Security and Medicare liabilities (combined) $ trillions
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2000 2001 2002
Net present value for past,
present and future participants ................... 12.0 15.8 16.4
~~
First, that's a lot more than Krugman said -- but more importantly, it rose by fully $4.4 trillion in just two years! That's an average of more than $2 trillion PER YEAR! Each Year! Forever?? Compare that to Bush's tax cuts to see what's driving future deficits.

And I won't even get to Krugman's heroic assumption that all the general revenue represented by Bush' total beginning-to-fantasized-end tax cuts, if in fact collected, SHOULD be used for nothing but (a futile effort at) closing the funding gap for SS and Medicare, by, ahem, "topping them off". ;-) That's a whole 'nother story.

Patrick R. Sullivan writes:

The interest rate and inflation assumptions are not the scam as much (as Jim Glass has pointed out in another forum) as the "75 year cut off".

Here's how Krugman is really deceiving everyone. Take a person who is born in 2011. Assume he enters the work force in 2033, and pays SS taxes for 45 years (and his employers' match it) until he retires at age 67. That person would be eligible for his benefits in the year 2078.

But according to Krugman's malarkey, those benefits would be $ 0! This person's 45 years of payroll taxes ARE being counted in Krugman's scenario. As are the taxes paid by anyone born in later years. But their benefits are made to magically disappear.

Jim Glass writes:

Re interest rates. I think that our host is exactly right that any the market rate that is used as a discount rate is going to be too high, maybe by 2x or 3x.

The key (to me) is that since SS is 100% "paygo" through tax collections and not financed with any real economic savings, in figuring its future cost to the economy it's not right to use a market interest rate as a discount rate because it's not going to get a market interest rate -- it doesn't even get the rate on federal bonds. It gets zip.

It would seem that you have to calculate the expected growth of SS in dollar terms and and the expected growth of GDP, or maybe better National Income, in dollar terms, since that's where the all financing will be coming from.

If one expects real GDP (or national income) to grow 2.5% or 3% a year, I'd think that would be the appropriate discount rate -- which over 75 years or longer makes a *big* difference even compared to the rate on federal bonds.

If SS were privatized and financed with savings, then a market rate would be appropriate.

Note: That's for figuring the cost of financing SS *to the economy*. If one is figuring the value of future benefits *to recipients*, say relative to their contributions, then a market interest rate is appropriate.

That produces a pretty brutal result too for today's young. E.g, take a look at http://www.ssa.gov/OACT/ASKACT/part2.html
Figure the lifetime rates of return on those.

Jim Glass writes:

... as Jim Glass has pointed out in another forum ...

And here too. I'd saved bandwidth and provided a link, if there was a link.

Bernard Yomtov writes:

CAUTION: Partisan shot coming.

The scam Krugman is being accused of is easily understood by referring to Bush's methods of underestimating the size of his 2001 tax cut by assuming that the cuts would be fully rescinded in 2011. Or refer to Mitch Daniels telling us the Administration wasn't projecting past five years because that far out was too uncertain.

End of partisan shot

If you're going to complain that the SS analysis leaves out important numbers 76+ years out, then you have to include the tax cut effects 76+ years out. After all, the point of the study was to compare the two.

achilles writes:

Hmm, very interesting but I think Jim is either completely misleading us or completely misreading Table 3-3 in the '04 budget.

The 3.5 trillion number that Krugman quotes is similar to the 3.4 trillion number that appears under the first heading in Table 3-3. The much larger number of 16.4 trillion at the bottom of table 3-3 is a sum of Social Security and Medicare comes from a number for Medicare ($13 trillion) that is much larger than the number Krugman (or the SSA) gives.The higher number has NOTHING to do with the issue that Jim raises: which is the 75 year cutoff. The President's budget does a 75 year "actuarial calculation" just as the SSA does. It does say this method has limitations because of what happens after year 76 but the numbers in Table 3-3 do NOT include anything happening after year 76. Take a look 16.4 trillion is just the sum of $3.4 trillion in SS and $13 trillion in medicare. Also the $4 trillion increase that he is so worried about is not in a re-calculated SS liability but in the medicare liability calculated in the budget.

The much higher ($13 trillion instead of $5 trillion) for medicare comes from how the full cost of SMI is included in the calculations for Table 3-3 even though there is no mandated coverage of all those costs. Again this has nothing to do with Year 76+ and beyond just that the president's budget includes all of SMI while SSA only assumes SMI funding at current levels.

Also, I think it is a little unusual to claim that nominal dollars should not be discounted using nominal interest rates just because we are using PASYG system. I agree with Bernard and Jane and Arnold that the right number should be closer to 5-5.5% instead of 6.25%. My guess is that SSA uses a moving average of 30 year T-bond yields as the risk free rate, with the resulting average being higher now than what we would expect to see in the future.

Jim Glass writes:

Bernard:

Re the "sizing" of the tax cut. You are quite right, except it's true for cost and revenue estimates for all tax and expediture items enacted by Congress. It ain't a Bush thing, that's how the budget process works. A gross dollar number covering an arbitrary number of years gets put out for the cost or revenue raised, often selected for political benefit, and telling the public nothing useful. Even experts have to try to figure out the real meaning.

There are also a good number of "extender" items that Congress intends to keep in place forever but which expire every two years or so. This has the double benefit to Congress of keeping their cost out of the budget numbers more than two or so years out, and keeping the lobbyists coming back making campaign contributions every two years to see they get renewed. (They are fondly known as "annuity" items by staffers).

I've always been in favor of putting the government on accural accounting under GAAP rules. Of course, they don't listen to me but Greenspan came out strongly fot it too in his last round of testimony. (The cash basis accounting method used by the US governmet is illegal for the owner of a good-sized candy store and could send him to jail, literally). Though it won't happen until someplace hot freezes first, for obvious political reasons. That's one thing both parties agree on with no problem.

Achilles:

I don't know what objection you are making if "Table 3-3 do NOT include anything happening after year 76" is part of it. I mean, that's the point!

Krugman wrote that the numbers he cites "estimate the 'actuarial balance' of Social Security and Medicare the same way a private insurance company would."

That's malarky. Any private insurance company that estimated the 'actuarial balance' of its annuity obligations by counting reciepts on the plus side *without* counting liabilities attached to those very same receipts, just because they were payable more than an arbitrary number of years out, would end up with its executives residing in the cell next to the candy store owner's.

"I agree with Bernard and Jane and Arnold that the right number should be closer to 5-5.5% instead of 6.25%."

Our host can speak for himself, but the way I read him he wrote: "I am certain that if one re-did the calculation with a more reasonable interest rate -- less than 2 percent..."

achilles writes:

Jim, you made a big deal about Krugman ignoring everything after year T+76 which would greatly inflate the unfunded SS deficit, then posted the $16 trillion number and said "that's a lot more than what Krugman said".

I was just pointing out that the two things are not connected: the $16 trillion figure in Table 3-3 is a lot larger than what Krugman said it was but that has nothing to do with year 76+, it has to do with the WH decision to take the full cost of medicare's SMI into account. That is what I was pointing out. Your post gave the impression that if you took year 76+ into account you would end up with the $16 trillion number, I was clarifying that misimpression.

To your second point regarding the definition of 'actuarial value'I am not an actuary so I can't judge the validity of your definitions. My only observations are that in a PASYG system you can never get a number that satisfies your definition (for any finite duration), since there will always be a generation that has paid in but is waiting to be paid out. Regardless, Krugman's (and the CBPP's) definition of 'actuarial balance' is exactly the same as the SSA and the White House's definition of actuarial balance as presented in the header of Table 3-3. So you may be right and have a better way to do the calculations, but in that case the economists at the SSA, the White House and the CBPP are all wrong, not just Krugman who is reporting their numbers.

As to discounting, Arnold in the comments section made the following clarification
"Bernard, I agree that nominal magnitudes should be discounted at nominal rates, and real magnitudes should be discounted at real rates."
That pretty much speaks for itself. Initially, I think Arnold (quite reasonably given the imprecise nature of the CBPP piece) assumed that the real quantities (i.e. the ratio to GDP) was being discounted at nominal rates. This of course would be wrong. if you look at the CBPP piece though the asterisk for the vague footnote is in the nominal $ column and not the % of GDP column, indicating that the authors are in fact discounting nominal numbers using nominal interest rates (as they should). The number they use is about 75-100 basis points higher than what one would expect but over 75 years that number does not make a big difference (about a year's worth of deficits between discounting at 5.5% instead of 6.25%)

Bernard Yomtov writes:

Jim,

"Re the "sizing" of the tax cut. You are quite right, except it's true for cost and revenue estimates for all tax and expediture items enacted by Congress. It ain't a Bush thing, that's how the budget process works. A gross dollar number covering an arbitrary number of years gets put out for the cost or revenue raised, often selected for political benefit, and telling the public nothing useful."

Yes but. The Bush approach was particularly duplicitous (surprise), even by these standards. He did not just cut off the estimate after 10 years, standard if not particularly rigoprous practice. As I understand it he cut it off after nine years by providing that the cuts would be reversed in year 10. Nobody with an ounce of brains would believe such a thing, and in fact, of course, the drive to make the cuts permanent began almost immediately after they passed.

Patrick R. Sullivan writes:

" If you're going to complain that the SS analysis leaves out important numbers 76+ years out, then you have to include the tax cut effects 76+ years out."

While it is possible that even paranoids can have real enemies, it is Constitutionally unlikely for George W. Bush's Administration to control taxes after January 2009.

In just the last quarter century, the top marginal tax rate has gone from 70% to 50% to 28% to 33% to 40% to (iirc) 36%. Does anyone think there will be a similar "flexibility" in SS benefits?

Bernard Yomtov writes:

Well, the tax cuts will still be there after Bush is gone. So what you're saying is it's OK for Bush to make a giant fiscal mess, because future administrations will be there to clean it up.

Come to think of it, that is the story of Bush's business career, so why not his Presidency?

Patrick R. Sullivan writes:

" Well, the tax cuts will still be there after Bush is gone."

As Milton Friedman famously said, "there's a tax bill every year". And Reagan's tax cuts lasted how long after he was gone?

Bernard Yomtov writes:

Jane wrote,

"It's not exactly an "error". The CBPP is a policy tank devoted to protesting tax cuts and entitlement reform.

I'm pretty sure the Social Security numbers are in real terms, but I'll check. "

That's a pretty harsh accusation, Jane. Don't you think you might check before making it? I did check, via the simple device of sending an email to the authors. To summarize, they used nominal figures, as Social Security does, and nominal rates. So they are neither idiots nor charlatans.

Bernard Yomtov writes:

Patrick,

Again, you're saying it's OK because someone will clean up Bush's mess, as Bush Sr. and Clinton cleaned up Reagan's.

Arnold Kling writes:

I now believe that the CBPP did not use discounting of nominal magnitudes using a real interest rate. What they did was at least as underhanded. I will have a full post up on this.

Jim Glass writes:

"My only observations are that in a PASYG system you can never get a number that satisfies your definition (for any finite duration), since there will always be a generation that has paid in but is waiting to be paid out."

Well gosh, love the parens -- any misleading calculation will get you a misleading result, eh?

OTOH, it is routine to estimate actuarial balance for Paygo systems by looking at future income and liabilities on an open ended basis, discounting them to current value. Which, contrary to what Krugman says, is what real insurance companies do.

And if you do project for only a finite time period, it is easy to add an annotation explaining the reality, as the Perspectives does but the Krugman doesn't.

"Regardless, Krugman's (and the CBPP's) definition of 'actuarial balance' is exactly the same as the SSA and the White House's definition of actuarial balance as presented in the header of Table 3-3. So you may be right and have a better way to do the calculations, but in that case the economists at the SSA, the White House and the CBPP are all wrong, not just Krugman who is reporting their numbers."

Except Krugman says he *is* using the better way by calculating the balance "the same way a private insurance company would do", which he is not doing. You keep missing this point.

In addition Krugman is comparing these numbers to a tax cut on the scope of the Bush tax cut proposals and saying the Bush proposals are *bigger*. Nobody at he SSA or White House say any such thing. And it's not true.

Look, GAO projects that Medicare and Social Security expenditures just by themselves will grow by about 14 points of GDP by 2050, to about 22 points of GDP -- compared to an entire federal budget of only 20 points of GDP today -- from about 8 points of GDP now.

Is Krugman really saying that the Bush tax changes would amount to *14% of GDP* in 2050? Compared to an entire federal government operating before the changes at 20% of GDP? C'mon.

achilles writes:

Hey, I was very explicit about my lack of actuarial knowledge in my post. Clearly, that was not enough to stop Jim from deleting my disclaimer, then quoting the subsequent sentence and having a 'feel good' moment from making snarky remarks about my use of parens to make 'misleading' statements. Very classy but then again what else is new.

Comments for this entry have been closed
Return to top