« What to Do About Sea Level Rises. | Main | Don’t These People Have Editors? »

May 09, 2005

Krugman’s Numbers.

Trivial point from Paul Krugman’s column today:

Suppose you're earning $60,000 a year. On average, Mr. Bush cut taxes for workers like you by about $1,000 per year. But by 2045 the Bush Social Security plan would cut benefits for workers like you by about $6,500 per year. Not a very good deal.

Well, I dunno Paul. Assume a couple of things (hey, this is a blog post, not a position paper), like you collect SS for 15 years (Age 65-80...not absurd). So $6,500 a year is $97,500 in total. Looking at this calculator, how much do you need to save over 40 years in order to have that $97,500? At a 5% return (I don’t think that Krugman’s numbers are correcting for inflation, so the investment figures don’t need to. 5% including inflation is well within the numbers for likely returns that Krugman himself has given us before.) it looks like you have to save $63.41 a month, or $760 a year.

Is $760 less than $1,000? Why, yes, indeed it is. So you could either have an extra $240 a year each year, or you could save all your tax cut and get more than your SS would pay you.

I don’t know about the distinguished Professor but I think that’s a reasonable enough deal, don’t you?

(Note, this is all predicated on the idea that I haven’t cocked up the investment calculation, something that I am not at all sure of.)

Update. Looking at some of the comments it might be worth explaining a few things. I assumed that Krugman’s numbers were that the income levels mentioned were for a lifetime. That assumption may be wrong but I think is is the cumulative value of your SS contributions that determines your benefits, not your final salary?  I’m pretty sure that if you look up the numbers you’ll find that it is only someone who makes SS contributions on $60k for a lifetime who would lose $6,500, rather than someone on the more normal earnings trajectory of $20k to start, rising to $60 k near the end.

Secondly, (and this also depends upon your cumulative contributions being the determinant of your benefits) so what if your income stalls for a year or five? You go back down to $20k a year? Your benefits are protected. You get exactly the same benefits accruing as anyone else on $20k. When you have a higher income, yes, your benefits fall relative to the current system but then so do your taxes, and certainly up to the $60k defined as middle class the returns on your investments are higher than those on SS.

Krugman’s math here is simply wrong.

Update II. Damn, I missed something. The Walmart worker didn’t get a tax cut because they don’t pay income tax. They only pay FICA.

May 9, 2005 in Trivia | Permalink


TrackBack URL for this entry:

Listed below are links to weblogs that reference Krugman’s Numbers.:

» Krugman Mangles The Numbers Again--Updated! from Lifelike Pundits
This is what passes for deep thinking on the left: Let's consider the Bush tax cuts and the Bush benefit cuts as a package. Who gains? Who loses? Suppose you're a full-time Wal-Mart employee, earning $17,000 a year. You probably... [Read More]

Tracked on May 9, 2005 7:11:37 PM

» Krugman's Social Security Analysis Flaw from Brainster's Blog
I did a quickie spreadsheet, assuming one started investing $1,000 per year at 5% interest (including inflation) from age 25-64, after which the person would start drawing down $6,500 per annum. Here are the first couple rows of the spreadsheet: [Read More]

Tracked on May 9, 2005 7:23:22 PM

» Krugman on Social Security redux from The Journal Blog
At the risk of beating a dead horse to death, I wanted to return for a moment to yesterday's Krugman post, and an alternative point of view that one of my commenters brought to my attention. [Read More]

Tracked on May 10, 2005 3:46:42 PM

» Krugman Mangles The Numbers Again--Updated! from Lifelike Pundits
This is what passes for deep thinking on the left: Let's consider the Bush tax cuts and the Bush benefit cuts as a package. Who gains? Who loses? Suppose you're a full-time Wal-Mart employee, earning $17,000 a year. You probably... [Read More]

Tracked on Jun 13, 2005 11:10:25 PM


I've already replied to your post over at my site here, but I'd like to add something to that. There's nothing wrong with your arithmetic, but I question the realism of your assumptions.

You suggest looking at Krugman's "middle" example, and doing the math to see how long it would take to save enough to offset the cuts once they retire.

Yes, if you could save $1000 per year for 40 years, that would do it, but that kind of implies someone already making $60,000 per year at the age of 25, which is kind of uncommon, don't you think?

The more relevant point is that you stopped at 15 years of SS to show there was still a benefit. What if you pushed it out to 20 years? Suddenly, it's not so good a deal, is it?

Compare that with someone who gets an extra $50,000 per year for 40 years, and only loses $9,400 per year after retirement. Yeah, that's going to last a wee bit longer than 20 years, isn't it?

In short, this scheme is heavily tilted towards the rich, just as Krugman suggested.

Posted by: CC | May 9, 2005 6:06:31 PM

The problem here is that your example relies on you being absolutely sure that you're going to die at 80. What you need to do is look at current life annuity rates, for which I do not currently have a good source in the US.

Posted by: dsquared | May 9, 2005 6:22:57 PM

If your point is that the middle class individual in this case could be saving $240 under the new plan you seem to be short-sighted. Also keep in mind that the figures you came up with is under ideal market circumstances. It seems that you cannot see the forest through the trees. Krugman's point is that Mr. Bush's plan heavily favors the rich, just like the rest of his fiscal policies. For a more informed look at the economy check out the post on Warren Buffet's opinion of the economic climate.


Posted by: Dissenter | May 9, 2005 6:26:18 PM

Krugman is cooking a horse and rabbit stew. If you combined his tax cuts with the education reform, it tilts to "the rich"; if you combine the tax cuts with spending on the environment, or energy, or just about anything, it tilts towards "the rich".

But in the case of Social Security, unless we were going to fund Soc Sec out of general revenues, the "tax cuts for the rich" did not undermine it, and would not have been available to save it.

Now, if Krugman's agenda is to oppose all other reforms and wait for the day when we fund Soc Sec from general revenues, fine, but he should say so.

Posted by: Tom Maguire | May 9, 2005 6:38:28 PM

Excellent post, Tim. I think Tom's right on the central flaw in Krugman's analysis, but your post points out that a $1000/year cut in taxes now for $6,500 in benefit cuts way in the future might actually be a good deal. I ran a spreadsheet calculation assuming 5% interest, $1,000 contributions from 25-64, then $6,500 withdrawals. Balance still in the account after the distribution at age 80? Almost $110,000.

Posted by: Brainster | May 9, 2005 6:46:37 PM

It seems to me that youare making some huge assumptions here, not least of which is that it will be a relatively rare individual who would, in fact, take that $1,000 and save it for their retirement. You also assumes that the individual in question will be making that amount of money from day one of their working life and keep on making that amount, never suffer a layoff, never be pushed to the edge of bankruptcy due to a sudden major illness, and never have children (who are quite expensive all by themselves).

Most normal people don't make their financial decisions the same way that corporate boards do.

As others here have pointed out, these calculations look good on paper but human beings don't normally operate that way and so these assumptions aren't realistic.

And the favor-the-rich tilt that Krugman points out isn't really disproved by your numbers.

Posted by: The Journal Blogger | May 9, 2005 6:46:53 PM

You guys it seems to me are approaching social security as an insurance investment scheme which it was never intended to be. Its an entitlement, a reward given to individuals who spent a lifetime contributing in one way or another to the culture and are guarenteed not to face retirement from the wage earning game in poverty. The language with which you frame the topic with is everything and it is from that language that the supposed problems with SS arise.

Also, Krugman is still correct in assessing that there would be no problem with social security funding except for the Bush tax give away. I agree with The Journal Blogger that your "facts and figures scrawled" do not disprove Krugman's positions.

Posted by: cul | May 9, 2005 10:45:40 PM

Lots of problems here. Let's start from the smallest (facts and arithmetic) and work our way up to the conceptual flaws.

Social security benefits are calculated based on a wageearner's 35 highest paying years, indexed roughly for inflation. I say roughly, because SS's index doesn't follow rates of inflation exactly, but calculates benefits according to its own formula. This formula already reflects both inflation and something like a savings rate. All of this info can be found at http://www.ssa.gov/pubs/10070.html.

What this means is that even in the face of inflation, Social Security benefits generally perform about as well as (and often better than) traditional savings accounts. Your assumptions don't reflect this indexing of social security at all. If the next forty years are anything like the last forty years, the $60,000/yr worker's benefits will be indexed by a factor of 7.31 -- $438,000 in 2045 dollars. And it will all count towards SSN benefits, since the max income is currently $87,900.

This also means, re: some of these comments, that social security benefits don't dip if you have a year (or five) with low or no income: your top 35 years knock out the rest. Savings certainly would dip in a rough patch.

The fact that benefits max out at a certain income level takes the teeth out of any attempt to progressively reduce benefits, without increasing the maximum or the payroll tax. The $88,000 and up club, which ranges from the middle class to the ludicrously rich, all pay the same FICA and all get the same benefits. The progressive rate at the bottom of the spectrum just flatlines here.

Finally, Krugman's example of the $60,000 worker isn't really about tax cut savings versus Social Security benefit cuts. It's more about a comparing the guy or girl making $60,000 to the millionaire with the $50,000/year benefit from the tax cuts. When you factor in indexing, the $60,000/year worker almost certainly loses.

But let's apply the same mathematics you used to the millionaire. He/she loses $9400/year in social security benefits: over 15 years, that's 141,000. No small sum. But if they invest their annual tax cut at 5% interest, they'll have over $6.3 million dollars in the bank. I'm sure they'll get by just fine.

Posted by: Tim | May 10, 2005 12:04:12 AM

It's idiotic to assume a 5% real return on a riskless investment. Show me where it is right now. I want to buy as much as possible. There is no 5% TIPS and never will be. If you don't know what a TIPS is then you should go find out before shooting off your mouth (or keyboard).

Posted by: elliottg | May 10, 2005 5:05:37 AM

All SS numbers are real numbers by the way so Krugman's 6500 is, by definition, adjusted for inflation. It's less clear to me the effect of inflation on the tax savings. Regardless, the skew towards the rich is incontrovertible.

Posted by: elliottg | May 10, 2005 5:09:29 AM

All SS numbers are real numbers by the way so Krugman's 6500 is, by definition, adjusted for inflation. It's less clear to me the effect of inflation on the tax savings. Regardless, the skew towards the rich is incontrovertible.

If this is a duplicate, I apologize for the typepad bug that reported an error the first time.

Posted by: elliottg | May 10, 2005 5:10:40 AM

Elliot G, the stock market in the US has traditionally returned far in excess of 5% per annum. If you look at Fidelity's webpage and check the returns of mutual funds over the last ten years, you will find that only 27 of 948 funds had an annual return (after fees) of less than 5%. Over half (570) had an annual return of over 10%. Not risk-free, but then even US Treasuries are not considered risk-free.

Posted by: Brainster | May 10, 2005 5:56:25 PM

The point about the upper-middle class doing relatively worse compared to the rich with this change is correct. That's why, incidentally, that while benefit cuts to change Social Security into a welfare plan, one ensuring a basic level of sustenance for all, ought to be combined with rolling its funding into the main tax structure rather than keeping FICA separate.

Posted by: John Thacker | May 10, 2005 7:37:27 PM

Brainster, you need to think about inflation adjusted vs. real returns and risk adjusted vs. riskless returns. After you have made the appropriate adjustments, consider if your critique makes sense.

Posted by: elliottg | May 10, 2005 7:51:34 PM

Elliot G, you seem like a bright fellow, but inflation-adjusted returns are real returns (non-inflation adjusted returns are nominal returns). And there is no such thing as a "riskless" return, not even a savings account with government savings insurance (since the government could always go broke). Yes, there is less risk involved in those accounts than in the stock market, but over the long haul, the real risk is that you haven't been invested in the stock market while others have.

And take a look at Krugman's article and let me know if he's talking real or nominal returns, would you? The answer of course is that you can't tell, because Krugman is a very sloppy writer for someone who supposedly is an economist.

Posted by: Brainster | May 11, 2005 12:19:21 AM

Brainster, you're right, I made a typo on the inflation adjusted - I meant to say nominal. Your 5% from fidelity are nominal returns so useless for analyzing the numbers and the handwaving about risk is ridiculous. You must be one of those Republican charlatans. It's pretty obvious that the benefit cuts are real dollars. For the tax cuts he is imprescise since the $1000 is today's dollars, it matters less as to whether it is real or nominal unless you are trying to make the BS argument that it's a good deal for the 60k wage earner.

Posted by: elliottg | May 11, 2005 1:07:28 AM