Who Would Like To Bet On Paul Krugman?

[LATE UPDATE:  I claim the Dean Baker "No Economist's Left behind" Cup here.]

How one could make money from writing a blog has vexed greater minds than mine.  And how one might make money by *reading* them has been truly puzzling. 

Until now.

I have a longish, confusing-ish post making a point about Social Security, economic growth, and returns on capital that, when understood, is so obvious folks will wonder what the discussion was about.

However, my point stands in direct contradiction of a column written by Paul Krugman, and (so far) has not found support anywhere in the blogosphere.

So, my proposition - I will pick out a couple of key phrases that summarize the Krugman argument, and put my money where my mouth is.  If a consensus emerges that I am correct, you pay; if, OTOH, I am wrong, I pay.  The technical term for this is "wager".  (Let's just add, VOID where PROHIBITED!  And for those who prefer, settlement can occur in the form of a donation to a charity of the winner's choice, subject only to a "nothing embarrassing, no hideous mailing list" type of restriction.)

Now, frankly, I ought to be the underdog here - we are talking about macroeconomic forecasts, and Paul Krugman is who he is (I am who I am, too, but what is that?)

And, as regular readers know, there is a certain "stopped clock" quality to my criticism of Paul Krugman.  Oh, I may think I score the odd success, but frankly, if Krugman said "Good morning", I would probably put up a post saying it's nighttime in Tokyo, and wondering how a guy with a reputation as an international economist could possibly overlook that trivial and obvious fact.

Well.  The wagers.  Despite my heavy underdog status, I will put these up at even money.  $100 on this one:

...the numbers the privatizers use just don't add up.

Let me inflict some of those numbers on you. Sorry, but this is important.

Schemes for Social Security privatization, like the one described in the 2004 Economic Report of the President, invariably assume that investing in stocks will yield a high annual rate of return, 6.5 or 7 percent after inflation, for at least the next 75 years. Without that assumption, these schemes can't deliver on their promises. Yet a rate of return that high is mathematically impossible unless the economy grows much faster than anyone is now expecting.

Emphasis added.  In my post I demonstrate that higher growth at a low return on capital does not increase the return on capital (no, seriously - Krugman really is on the other side of that proposition, although he probably does not realize it).

SO, the bet - I win your money if: 

(1) some credible economists emerge to endorse the notion that the return on capital question is separate from the economic growth question (i.e, taking the low growth/low return scenario and increasing growth does not automatically turn it into a high return on capital scenario, but rather, can simply turn it into a high growth/low return on capital scenario); that the projected return on capital depends a lot on how you forecast returns on capital (I'm really on a limb with that one); and, here we go, that there are mathematically possible and economically plausible scenarios where we have low labor force growth and low (1.7%) productivity growth, but high stock market returns.  I am not even holding out for more foreign income on this point, although I suppose I could.

Just to handicap this a bit, I will even tell you the winning argument: the return on capital is determined by the income flowing to capital (the income share of capital) and the level of capital employed.  In the high growth scenarios, we need to model levels of investment (replacement plus new investment), a capital/labor ratio (those new workers need capital to be productive), and an income share to capital.

What folks will realize, upon reflection, is that the return on capital will only go up if the relative capital deployed falls, or the income share of capital rises.  The notion that either of these ratios must be directly dependent on labor force growth or productivity growth will not be sustained - in fact, their behavior is a result of modeling choices.  In short, higher growth does not automatically increase the return on capital.

Having settled that, folks will ask what might increase the return on capital.  Increasing the income share is an obvious way. 

So, in a low growth environment, suppose that productivity growth is 1.7% per year, but for two years, real wages are *flat*, so that the increased income from the increased productivity goes to capital.  The income share of capital will rise from roughly 8 to 11%, which will take the return on capital from 5% to 6.5%.  Bingo.

Is that laughably implausible?  These folks are worried about *falling* real wages (here, too, but  not at Heritage!) - for my forecast to work, all I need are two years of stagnant real wages.

So, a fine bet, yes?  Takers are invited to enlist in the comments section.  Should be an easy $100.  Krugman versus The Minuteman!  Help me out, help yourself out, win my money!

You want more?

In the long run, profits grow at the same rate as the economy. So to get that 6.5 percent rate of return, stock prices would have to keep rising faster than profits, decade after decade.

That may or may not be true as an historical fact, and who cares?  Shall we wager on this:

(2) profit growth is not the same as return on capital; a firm, or an economy, can have high profit growth with a low return on capital, or low profit growth with a high return on capital.  (HINT: Don't forget dividends!)

Go ahead - if we find a consensus that my statement is false, you win.  Make it another $100.  Now, does my statement directly contradict Krugman's?  It certainly runs counter to the spirit of his statement, I think.

Let's have one more.  This is excerpting Krugman:

They can rescue their happy vision for stock returns by claiming that the Social Security actuaries are vastly underestimating future economic growth. But in that case, we don't need to worry about Social Security's future: if the economy grows fast enough to generate a rate of return that makes privatization work, it will also yield a bonanza of payroll tax revenue that will keep the current system sound for generations to come.

Alternatively, privatizers can unhappily admit that future stock returns will be much lower than they have been claiming. But without those high returns, the arithmetic of their schemes collapses.

(3) For $100 - the preceding from Krugman is false.

In fact, low-growth scenarios with high stock market returns and an early distress for Social Security (Trust fund exhaustion by 2042 or sooner) are easily developed; high growth scenarios with low stock market returns and deferred trust fund exhaustion are also easily developed.  In fact, although growth is an issue for Social Security (since the number of retirees doesn't grow, at least right away), it need not be for stock market returns.

Let's do (3) for $100, even though it is very close to (2).  And I am not going to get all quibbly about folks whining "no fair, an income share of 11% is too high, Krugman didn't mean that, and it's not reasonable".  He didn't say "reasonable"; he said it can't be done with low growth, and that only high growth led to salvation. 

He also says that high growth scenarios improve capital returns, but that will only be the case if the income share to capital rises, or the relative level of capital deployed falls. And that is surely not what he said in the excerpt, where he talks only about growth.  If Krugman will allow (by implication) a higher income share to capital in high growth scenarios in order to make his statement about higher returns true, then he must be willing to contemplate a higher income share to capital in a low growth scenario.  Fair's fair.  Let's play (3) for another $100.

OK, as I said, this is a fine chance for someone to commercialize their blogging, or blog-reading.

I would love to take people's $300.  Dare I say, Bring it on!

MORE: Even though no one asked: I believe that growth is good, and that it is certainly easier to project high returns on capital in a higher growth environment; I suspect that the 6.5% real return folks talk about for equities is high; I believe that Dean Baker's fundamental point, that the Soc Sec Trustees ought to either explicitly forecast a return on capital, or back out the return on capital implied by their forecast, is excellent; I believe Oswald acted alone; and I believe that the Soc Sec Trustees have an institutional bias towards low-ball forecasts.

UNRELENTING:  Dare we do equations?  The formatting will be brutal, but why not?  See the continuation.

UPDATE:  No takers?  I should track down some of the folks who cheered Krugman last week.  Here is Ian Walsh; and here is Kevin Drum's take:

Typically, they assume long-term returns of 6.5-7%, but returns like that are only feasible if long-term economic growth is also very strong. The problem is that if long-term growth is strong, Social Security isn't in trouble in the first place:

...Privatizers assume that stock market returns for the next 75 years will be as high as they have been for the previous 75 years. For that to happen, economic growth for the next 75 years also needs to be roughly as high as it has been for the past 75 years.

Well, well, well.

GDP = Output = Workers x (Output/Worker); Output/Worker = Productivity
Profit = Output x Income Share to Capital = Workers x Productivity x Inc Sh to Cap
Capital = Workers x (Capital/Worker)

Higher growth comes from adding workers (workforce growth), or increasing output per worker (productivity growth).

SO: Return on Capital =

[Workers x Productivity x Inc Sh to Cap] / Workers x (Capital/Worker)

Is it obvious that increasing growth by adding workers to this mix does not increase the return on capital?  Since "Workers" appear in the numerator and the denominator, they cancel.  This relects the notion that increasing the scale of an operation does not change the return on capital (unless something is *not* scaling the same way).

Productivity is trickier (and my verbal formulation may be off a bit). Basically, as Output per Worker rises, the Capital team captures some of the benefit.  (Normally, I should add, productivity is associated with "capital deepening", where it takes more capital to make workers more productive.  I am setting that aside here, since it makes it harder for productivity to turn growth into a higher return on capital).

So, in this formula, if the old Return on Capital was 5%, and the increase in productivity is 1.7%, the new Return on Capital will be (5.0%) x (1.017) = 5.085%.  Keep that up for 16 years with no capital deepening, and the Return on Capital will rise to 6.5%.  Patient capital, indeed.  And remember, we are assuming that, down in the denominator, (Capital/Worker) is not changing.

Suppose we increase Productivity so that it grows by 2.7% per year.  Now, the Return on Capital will grow from 5% to 6.5% in just 10 years.  And when will it stop growing?  Ahh, we have a bit of a glitch here - without some more elaborate assumptions about the relationship of capital to labor and output, the Return on Capital will just keep going up.  However, any reasonable adjustment I make will slow the (already slow) improvement in the Return on Capital, so I stand by my point that the most plausible place to look for an improvement in the Return on Capital is not growth, but the Income Share to Capital.  Increase the Income Share to Capital, and that can solve the Return on Capital problem right away.

As modeled here, higher growth achieved by adding workers does nothing for the return on capital; higher growth through higher productivity reduces the time it takes the return on capital to grow to the target, with an unlikely assumption about capital deepening.  So yes, growth can solve the Return on Capital problem eventually, depending on what one assumes about the relative capital deployed (as I noted originally).

 

Comments

[creepy dude]

"If a consensus emerges that I am correct, you pay; if, OTOH, I am right, I pay."

Yep. Financial wizard you are. Krugman's toast.

[Al]

Paging Brad DeLong!

[Drew]

Well, I understood "Paul Krugman" "wrong" and "social security." Normally, when I see all those together, I can agree with the context of the article, so I'm going to guess that you're probably right.

Any chance of printing something like this in terms that an idiot like me can understand?

[George M. Behr]

Thought you were trying to get me on a 'sucker' bet:

"If a consensus emerges that I am correct, you pay; if, OTOH, I am right, I pay"

I think you meant "OTOH, I am wrong, I pay".

[MattJ]

If I were Krugman, I would represent myself as a credible economist, endorse my own opinion, and take all your money.

Or woould that be cheating?

[Patrick R. Sullivan]

"some credible economists emerge"

Ay, there's the rub.

But, don't accept any bets from Australian economists.

[TM]

if, OTOH, I am right, I pay"

I think you meant "OTOH, I am wrong, I pay".

Oh, man, someone will pay for that. COPY BOY! GET ME REWRITE!

[T J Sawyer]

I quit reading Krugman's latest rant when he got to "... 6.5 or 7percent after inflation ... a rate of return that high is mathematically impossible." Seems I had just finished reading the year 2000 book, Valuing Wall Street, in which the authors present Wharton economist Jeremy Siegel's extensive work showing that the average real return (after inflation) has been surprising stable at guess what - 6.75% Is this worth maybe $110 alone?

[Geek, Esq.]

Can I bet on Krugman being wrong, and Donald Luskin being even worse?

[Crank]

Looks like Krugman should go brush up on this essay's point about how people who won't use multi-variable equations shouldn't write about economics.

As for me, you lost me at a few points, but I believe I understand the central ideas here. Let's see if I can summarize these points without mischaracterizing them:

#1: Krugman contends that it "is mathematically impossible" to have growth in returns on stocks in the neighborhood of 6.5-7% without very high levels of growth in the economy as a whole, higher than any reasonable current estimate. TM contends that it is possible, and that this can occur if corporations hold down wage growth and thus pass on to investors much or all of the benefits of economic growth. You would think that liberal/Democratic pundits would grasp this zero-sum-game workers vs. capital dynamic as a possibility. As TM has noted before, this scenario becomes more plausible when you consider the possibility of capital invested in low-wage foreign markets.

If TM is right, not only is this a possible outcome, but it is one in which it becomes uniquely desirable for laborers to become capitalists to offset their vulnerability to stagnant wages. Which explains why #3 is wrong too: since private accounts are an investment in the international stock and bond markets while the current pay-as-you-go means (on a macro level) an investment in domestic payrolls, any scenario in which (a) wages don't keep up with profits or (b) jobs go offshore is likely to throw off the 1:1 relationship of returns on capital:payrolls, and thus defeat Krugman's tidy syllogism.

#2, I'm not sure I understood, however. I think Krugman is saying that corporate profits (before, or after payment of interest to bondholders?) determine the return on capital to the corporation's owners. I get that you say this is not necessarily so, but I'm not sure I followed why.

[Don Luskin]

The answer is so much simpler than this. Krugman is wrong even using his own numbers. As I wrote here -- http://www.nationalreview.com/nrof_luskin/kts200502021117.asp -- his 3% dividend/repurchase yield plus 3.4% GDP growth gets you there no problem. And by the way, I have the history of corporate earnings growth back to 1900, and it very closely tracks GDP growth. My NRO article yielded an response from Dean Baker, the loony leftist economist whom Krugman quoted, and he conceded that I was right, but emphasized that the "real" point was that you can't get there from the low GDP growth figures that the actuaries use. And so now Tom has arisen to show that you can, or at least to argue that. I tend to think that you cannot. For Tom to be right, in other words for the return to capital to be so disproportionate as to close the gap, you would have to experience what Baker and Krugman talk about -- p/e ratios rising to heights that are unprecedented, and staying there. Not to say that it's impossible, but there is surely no reason to expect it; quite the opposite. To see what I mean, you could call the NASDAQ bubble of 1999/2000 a case in which the "return to capital" was "disproportionate" in the way that Tom posits. So it can happen. But it is unlikely to last.

If I were forced to make the case, I would look to non-US sources of earnings. The easiest way for profit growth to exceed GDP growth would be for US-domiciled companies to earn increasing fractions of their profits from non-US sources.

[yetanotherjohn]

I did a quick google search. Between 1926 and 1999, the return was 11% for the US Stock market average. As another example, 1963 to 1993 was 11.83%.
Now, I don't know what the productivity gains where from 1926 to 1999, but I would be amazed if it was anywhere close to 11%. So I'm not sure how you can link productivity to expected return.

[Pat Curley]

Luskin had some fund with that same column. He points out that Krugman talks about 3% dividends and 3.4% real growth; by definition that indicates a 6.4% return.

I have also commented that a company's share price can increase faster than its sales if it makes use of long-term fixed rate debt; something that is well-known to commercial real estate investors.

[ArminTamzarian]

I get 3.9% real growth in the DJIA from the June 1932 low of 42 to the February 2003 low of 7750, using the GDP deflator. Dividend yield over that period isn't below 3%, so there you go, 7% real stock returns. Are there any broader historical indexes anyone's put together?

Coincidentally, real GDP growth from trough to trough, 1933 to 2001, I get as 4.0%. Krugman's numbers are going to be a little off if he's going from 1929 to 2004.

Why is real GDP growth supposed to be so much lower than 3.4% over the next 75 years? Real per capita GDP growth from 1933 to 2001 was 2.9%. Are we expecting less than 0.5% population growth?

[TM]

Are we expecting less than 0.5% population growth?

IIRC, we are - 0.2% workforce growth springs to mind, although I am hazy as to the relevant time period.

[Tim Worstallt]

I go with Don Luskin. Global capital markets mean that the link between growth in US profits does not need (in fact won’t) to track growth in the US economy. It should, dependent upon how global those markets really are, track global GDP growth.

[ArminTamzarian]

"IIRC, we are - 0.2% workforce growth springs to mind, although I am hazy as to the relevant time period."

I checked the Census website: 0.6% growth in the 20-64 group over the next 45 years.

[CBKiteflyer]

Question: Can somebody explain to me whether the "proof" that Michael Kinsley offers at http://www.latimes.com/proof is related to Krugman's claims?

[CBKiteflyer]

Question: Can somebody explain to me whether the "proof" that Michael Kinsley offers at http://www.latimes.com/proof is related to Krugman's claims?

[Jim Glass]

"I have the history of corporate earnings growth back to 1900, and it very closely tracks GDP growth.... If I were forced to make the case, I would look to non-US sources of earnings.

"The easiest way for profit growth to exceed GDP growth would be for US-domiciled companies to earn increasing fractions of their profits from non-US sources. "

~~~~~

The simplest solution is to have world GDP be the relevant GDP.

If world GDP grows at 4% over the next 75 years that's two extra points and there we are -- back to the stock market's 7% return.

(If anyone wonders why this should be the case in the 21st century when it wasn't in the 20th, well, there were little things like Communism and socialism taking most of the world out of the market, a couple of World Wars, capital controls, Smoot-Hawley and its like ... but past record is not a reliable indicator of future performance.)

There has been some suggestion that markets equalize when they come into contact.

If Krugman had consulted with someone who knew something about international economics, instead of Dean Baker, he might have picked up on that idea.

[TM]

I go with Don Luskin. Global capital markets mean that the link between growth in US profits does not need (in fact won’t) to track growth in the US economy.

Jim Glass made that point right out of the chute, and I got there a day later. Weirdly, I initially dropped it from this post for expository purposes (although it may have reappeared after a subtle revision).

As to the question about Kinsley's proof, I would say he is making a different point, that personal accounts don't change total savings, and so they are a glorious wash.

[Randall]

What a fool you are. Nice to be at Princeton, and know you are not.

[TM]

I'm sorry, Randall, was there a specific point with which you care to disagree? They are numbered (1), (2), and (3) for your convenience.

[spencer]

The intermediate ss case assumes about 4% nominal gdp growth. To get 10% nominal stock returns under that scenario you have to have some combination of the following developments:

1. PE rises to levels suggested by Krugman
2. after tax earnings share of the pie rises from around 6% of gdp to around 35% of gdp
3. firms regularly pay out over 100% of earnings in dividends. This is under a scenario where you return to a pre WW II type market where dividends acount for the bulk of returns.

One of more of these variables has to grow much faster then nominal gdp year after year after year-- you can not get away from that conclusion..

[Retief]

Back to Algebra you go. There are not two instances of the variable "Workers" in your equation but three. You can't cancel just two of them and have the other one disapear on its own. You noted this one sentence before you tried to do it:

Capital = Workers x (Capital/Worker) or C=W(C/W)

Then you give us your return on Capital

SO: Return on Capital =

[Workers x Productivity x Inc Sh to Cap] / Workers x (Capital/Worker)

or Return on Capital = WPI/(W(C/W))

You have just noted that you denominator simplifies to C, giving you Return on Capital = WPI/C. Which leaves you with no W in the denominator. As any basic Algebra student can tell you, one can cancel the two Ws but that will also leave you with Return on Capital = PI/(C/W). When you multiply by the inverse you get right back to WPI/C. Multiplying C by W/W can have no lasting effect on the W in the numerator.

Maybe we should think twice before daring equations.

[Paul G. Brown]

Tom-

Over on Brad DeLong's site, you commented:

"All somewhat beside the point - can we find someone to defend Krugman's assertions, please? My money is waiting."

Dude. You just did defend Krugman.

Paul Krugman's first analysis suggests earnings growth at 1.9% and stock dividends and buybacks at 3%. So, we can project real returns to be 4.9%. [Nominal returns of 7.9%].

You said (in same comment thread): "In fact, if "6" is the over/under, I would bet "under" - I picked 5% a few days ago (and now I am stuck with it, I guess...)."

4.9% - PK, 5% - Tom.

Meanwhile, "2004 Economic Report of the President, invariably assume that investing in stocks will yield a high annual rate of return, 6.5 or 7 percent after inflation".

Well break out the accordian, folks, cos' we're all gonna polka!

[dsquared]

How do you reinvest dividends in this model? If the amount of capital employed is presumed constant, what are the dividends being invested *in*?

Btw, Retief is dead right above; both arithmetically and economically, adding workers in your model *does* increase the return on capital. If you have a fixed amount of capital and a constant marginal productivity of labour and you add more workers, return on capital increases. It's the same phenomenon as having a fixed number of workers and a constant marginal efficiency of capital; adding more capital increases productivity.

[TM]

Gents, do not take me to task for my failure to re-state my assumptions for the umpteenth plus one time Here is what I said earlier in the post:

In the high growth scenarios, we need to model levels of investment (replacement plus new investment), a capital/labor ratio (those new workers need capital to be productive), and an income share to capital.

What folks will realize, upon reflection, is that the return on capital will only go up if the relative capital deployed falls, or the income share of capital rises.

Now, *IF* we are assuming a onstant capital/labor ratio (as I said), then d-squared's objection disappears, and Retief's observation that not all of the workers cancel is a part of my point - if the C/W ratio is kept constant, then adding workers to get more growth also requires more capital, and the return on capital does not change.

[Sorry, this was a very late response - I think d-squared and I must have moved on to a follow-up post].