Post-Modern Standards Slip; Kevin Drum Gets Snippy

Is it possible to have high stock market returns even though slower workforce growth means lower economic growth?

Paul Krugman says it is "mathematically impossible".  In a recent post, Kevin Drum stated that high returns are "only feasible if long-term economic growth is also very strong."

[Now, there is a standards issue here - when a mathematician says that he can "prove" something, it means one thing; when a social scientist says, for example, that his latest work "proves" that abortion has gone up under Bush, it may simply be an attempt to gull the gullible.  Mathematicians look down on other disciplines as lacking rigor; because they use the high priced math, economists like to look down on the social scientists, and feel quite pleased with themselves when they prove, for example, that a country can not export capital while running a trade deficit.

But of course, if Krugman does not bring the conventional standards of economics to his popular writing, then when he says "mathematically impossible", he is not writing as an economist, but simply using pundit-type rhetoric to say "my fervently held opinion".  And I suppose the case can be made that Krugman's columns are written to a lower standard.] [Added for emphasis for the non-mathematically inclined].

Now, let's be fair - Drum has shown admirable intellectual flexibility on this point - in earlier waffles, he has said that a forecast of high returns with low growth is "hard", and "You can probably do this if you're willing to fiddle with a spreadsheet long enough, but you'd have to twist your brain into a pretzel in the process."

We don't choke on pretzels here!  Our position has been clear - higher corporate profitability (as a share of GDP) can lead to a higher return on capital.  Could it happen in a slow growth environment?  Could workers, whose labor protections have been gutted by Republicans since Reagan, lose a bit of their wage share of the GDP pie to Benedict Arnold CEOs threatening them with outsourcing?  Could tax-slashing Republicans protect their corporate cronies from paying their fair share of taxes?

I say it is possible (so does Paul Krugman, and I suspect other Dems have muttered these points from time to time.)

Now Brad DeLong has joined in with a post and paper saying that I am right, at least conceptually [and he is quite explicit about that in this follow-up].  The devil is in the details, of course, and it would be nice if the Social Security Trustees would trouble themselves to produce a forecast consistent with their asserted 6.5% return on capital so we could assess its plausibility.

But all this back and forth (and, I suppose, being wrong) has triggered a temper tantrum from Drum.

POST HOC BULLSHIT....Tom Maguire has been pestering me for several days to comment on his theory that — contra Paul Krugman and others — it's quite possible to have both a low-growth economy (meaning that Social Security finances are in bad shape) and high stock market returns (meaning private accounts would be great). I'm not an economist and therefore couldn't offer him a detailed response, but my approximate answer was, sure, it's possible for that to be true (up to a point, anyway), but hardly probable.

"Pestering?".  I prefer "dialoguing" myself, but if attempting to rouse Drum from his intellectual torpor is "pestering", well, guilty as charged.  And as to his "approximate" answer being "possible but hardly probable", even that much of a modification from his (most recent) position may come as a surprise to his readership, who may interpret "only feasible if long-term economic growth is also very strong" somewhat differently.

But the Drumbeat continues:

...the problem with Tom's argument is that it's just a random post-hoc effort to explain away a problem the privatizers hadn't thought of before (or had been able to ignore). In other words, it's part of the genus bullshit.

Ahh!  He puts up a post encouraging a response; Krugman issues a public challenge; and then anyone who responds is engaged in "post hoc bullshit".  Is this the new blogosphere, or the "Reality Based" Version thereof?  Puts a bit of a damper on the exchange of viewpoints.

Of course, Drum can also assume that non-respondents are ducking the question, or stonewalling.  Actually, I ignored this for months, because it seemed to be an argument from the genus "strawman".

And what is so unrealistic about my scenario?  Increased profitability and reduced taxes for the corporate sector are "bullshit"?  Odd to hear Drum say so - what is the standard Dem position on that?

Throw in mobile, global capital, and one wonders just why Krugman and Drum are so wedded to their notion that the equity risk premium is an increasing function of projected workforce growth.  Drum might want to pester someone and find out how that theory works - we are all curious.

But why do I bother?  In Drum's version of a discussion, any response will just be post hoc bullshit.  Having failed to anticipate every possible question he might ask, any answer he doesn't like will be subject to a similar dismissal.

Which is fine, since I am feeling a bit dismissive myself.  I actually had a different question of my own.  Let's go to Drum:

...intellectual honesty requires that you be consistently gloomy or rosy. Unfortunately, there's been precious little of that in the privatization debate.

I didn't think he needed to be lecturing anyone on intellectual honesty then, and I am quite sure of it now.

MORE:  If Drum would care to read Brad DeLong's paper (sorry, no, not the summary), and these two posts by me, perhaps he could explain to us just how it is that I am engaging in "post hoc bullshit" while Brad DeLong is advancing the intellectual ball.

Folks who take the trouble to follow the arguments might notice the occasional parallel in our thought processes, which Prof. DeLong was kind enough to acknowledge.

UPDATE:  One more wack at the pinata - if we accept the emerging consensus, based on the DeLong paper, that Krugman's "mathematically impossible" meant something a bit different, then I suppose we might also note that, in my post that Drum went off on, I included this caveat, cleverly labeled as such:

Now, obvious caveats - these numbers and examples do not, and can not, *prove* that the US stock market is correctly valued, or that the dividend yield must remain at 1.5%, or that foreign investment by US corporations *must* grow to some number by some date.

However, what these numbers *do* prove is that a perfectly coherent, mathematically consistent explanation of current share prices, earnings yields, and dividends yields is available.  Toss in foreign investment, and we offer this in refutation of the various "HAIRy" models that attempt to "prove" that stocks must fall.

Maybe on the po-mo Left, standards of mathematical proof have taken a bit of a drubbing, but I am holding the line.  As is Brad DeLong, I see.

And in an earlier post, I did make this Not So Bold Prediction:

My impression of this debate is that sometime soon, Krugman's supporters (if they can be coaxed forward - they stood up and cheered when he wrote this) will explain to me that "mathematically impossible" means "Not, in Krugman's opinion, very likely".  C'mon - even on sports talk radio, no one says that it is mathematically impossible for the Orioles to win the pennant.

Standards, people, what are the standards to which we hold Paul Krugman?

Comments

[GT]

Tom,

I think you've made some good points on this topic and it's been very interesting reading the different back and forth. But in the end I have to agree with most of what KD says, as I myself wrote similar things before.

Your whole argument is based on things that could happen but for you which you provide no evidence they will happen. If you read, as I suspect you did. PK's "mathematically impossible" comment literally then you can consider yourself the winner. But I never read that comment literally and find that point much too specific to be of any use.

I, and I suspect many others including Delong, read PK's comments as meaning that given the starting conditions the two projections were inconsistent with what we know of the world. Which is what Delong shows in much more detail in his paper. (Yes, you could argue that PK should have said that instead of saying mathematically impossible. To me that's just quibbling with words but to each his own).

In the end that's the main issue for me and why KD is correct in saying this is post hoc bullshit (even if he could have used other words). The only way your model works is if things that nobody considers likely happen in the next 75 years. But nobody on the privatization camp ever said, until confronted by PK and Dean. No privatizer ever explained that their model might require a stock market crash or the US running huge trade surpluses for decades, even when there was no evidence that would happen.

[TM]

Well, as to why folks might be ignoring Dean, as I intend to:

(a) the mechanism for forecasting the equity risk premium is hardly generally agreed;

(b) few economists take 75 year forecasts of the stock market real seriously;

(c) few economists take other economists who forecast imminent market collapses real seriously - there is that annoying Efficient Market concept.

SO, let's sum up the Krugman position - we don't know the equity risk premium, but I think it is lower than someone else does; we can neither prove nor observe its level, but since I am right, the market is due for a swoon.

Compelling.

Oh, and I am begging you to stop with this new waffle - well, of course Krugman was talking about the Soc Sec forecasts specifically, he didn't mean generally. I have already gotten it in an e-mail [UPDATE - from soneone else, as may not be obvious], and believe me - it is embarassing for you, and annoying for me.

No reader of the English language can tell me that Krugman meant "for these specific forecasts, it can't be done" when he wrote stuff like this:

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.

...But privatizers need that high rate of return for 75 years or more. And the economic assumptions underlying **most projections** for Social Security make that impossible.

The Social Security projections that say the trust fund will be exhausted by 2042 assume that economic growth will slow as baby boomers leave the work force. The actuaries predict that economic growth, which averaged 3.4 percent per year over the last 75 years, will average only 1.9 percent over the next 75 years.

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.

The price-earnings ratio - the value of a company's stock, divided by its profits - is widely used to assess whether a stock is overvalued or undervalued. Historically, that ratio averaged about 14. Today it's about 20. Where would it have to go to yield a 6.5 percent rate of return?

Look, I have seen and heard enough, thanks. I think I have a fairly clear grasp of lefty math now. Here we go:

2+2 = Bush Lied.

3+3 = Bush Lied

2+3 = Bush Lied

And so on.

And the lefty grammar lesson has been helpful as well: "mathematically impossible for any forecast" means "not likely for most forecasts, because Bush Lied".

It has been an educational week.

[J Mann]

I don't get Drum's "post hoc" argument at all - this debate has all played out before, and with the same arguments raised on both sides, during the Bush-Gore campaign. (See, e.g., here.)

Drum's complaint appears to be either that (1) because Tom didn't personally raise these arguments in 2000, his reasoning is "bullshit," or (2) because Drum didn't personally follow these arguments back in 2000, they're "bullshit."

[Jim Glass]

If you read, as I suspect you did. PK's "mathematically impossible" comment literally then you can consider yourself the winner. But I never read that comment literally...
~~~

If "mathematically impossible" isn't meant to be read literally, then what the heck would be?

"When we say that it is 'mathematically impossible' that 2+2 = 37, we mean of course that it is relatively unlikely in what we deem to be the most probable foreseeable circumstances."
~~~

"I, and I suspect many others including Delong, read PK's comments as meaning that given the starting conditions the two projections were inconsistent with what we know of the world..."

Well, yeah, if you take a starting position of dividends at 3% and stock appreciation tracking profit growth with profit growth tracking purely domestic GDP growth, and *assume* that in spite of *the major predicted change* in the economy neither of these will change for 75 years(!) -- that is, in spite of the declining opportunity to reinvest in the US due to the fall to 2% of domestic GDP growth, you assume neither dividends nor foreign investment will rise -- well then the original relationship becomes unsustainable. Duh.

One might even say then that it becomes literally mathematically impossible.

Of course, from the 1800s through 1980 dividends averaged 5%. If that condition returns so stock appreciation of 2% matches the growth rate of profits....

[Crank]

I always wondered what it would take to piss you off, TM. Now we know.

[J Mann]

There's nothing that stops the hypothetical private accounts from hypothetically investing in foreign indexes, right?

If Krugman (1) assumes that stock returns are locked to GDP growth; and (2) assumes that there are some parts of the world experiencing 10%+ GDP growth, then it's a pretty simple effort to solve the problem . . .

[GT]

Tom,

Most of my acquaintances and friends would laugh at the idea that I am a lefty. Some would actually cry in frustration. In any case I can ony speak for myself so I don't know whose lefty math you have in mind.

All I know is that you made many good points but I still think you miss the bigger point.

[capt joe]

great post, we can all take something away from this whether we like it or not.

Sometimes you just can't argue with rhetoric and indocrination.

GT, I don't know. I have read a lot of your posts and it surprises me to no small degree that you do not consider yourself a leftie. I would have made that assumption. But maybe they just apply the conventional ruler that they themsleves are middle of the road (as do we all).

[Cecil Turner]

"All I know is that you made many good points but I still think you miss the bigger point."

It seems to me that the person making the assertion bears the burden of proof (in this case a mathematical one). The requirement for a mathematical proof is for the statement to be true in every instance, and a single example where it doesn't hold true disproves it. (The usual technique is to run all the variables to zero and then to infinity in order to find a spot where the result is ridiculous--commonly known as "reductio ad abusurdum.") But in this case, Krugman didn't even bother with the proof, just made an assertion, and TM's example clearly shows it to be incorrect. Shifting the burden away from Krugman, and asking TM to show his scenario is likely, is nonsensical. Krugman's "mathematically impossible" statement is clearly false.

This whole argument leaves me cold, anyway. It starts with a questionable assumption of much lower GDP growth, and ignores the fact that any investment return will surely be more than the phony pay-ourselves-interest-from-the-general-fund (on money already spent) that accounts for the current "trust fund" calculations. There are legitmate arguments against privatization, but extrapolating from Krugman's faulty assertion isn't one of them.

[GT]

Krugman's "mathematically impossible" statement is clearly false.

I already conceded that. So why repeat it?

[GT]

capt joe,

It's all in the definition.

[Patrick R. Sullivan]

"No privatizer ever explained that their model might require a stock market crash or the US running huge trade surpluses for decades, even when there was no evidence that would happen."

That's just DeLong exagerating what's going to happen because he's pissed that Tom is right and Krugman is wrong.

Jim Glass and I have been explaining the point for years, and specifically to you GT, at Arnold Kling's blog. Dsquared remembers it.

Btw, it looks like Kevin Drum is beginning to slowly catch on, because he's moved his position to favoring privatization, if it's some other plan than Bush's.

[capt joe]

there's a definition? Sort of like Open Source Definition?

curious.

[Victor]

Quick & likely stupid question about DeLong's paper... where does the low 1.7% dividend yield come into play?

His concluding sentence in the Ramsey model is that this value is 'low' relative to 'normal' therefore the SSA must be wrong.

I have to plead ignorance on this one. Anyone out there who can help?

Also, how well does the Baker parameterization fit the past 100 years?

[GT]

Patrick,

You predicted a stock market crash?

I was unaware.

[Jim Glass]

"If Krugman (1) assumes that stock returns are locked to GDP growth; and (2) assumes that there are some parts of the world experiencing 10%+ GDP growth, then it's a pretty simple effort to solve the problem ... "
~~~

Of course, the whole issue is a red herring -- what matters is the return to US investors, not US corporations. If investors in 2035 can invest in the Vanguard Greater China and India Diversified Growth Fund, who will care if US growth stocks are limited to 2%?

BUT ... how are stock returns in foreign markets going to be 25% higher than in US ones for 75 years? I've asked this repeatedly of the DeLongiacs but have never gotten an answer.

There's surely no reason why world profit and GDP growth should slow like in the US over 75 years, quite the contrary -- so the Krugman/Baker formula mandates traditonal 7% equity returns in the world, yet they say only 5% in the US?

How do international economists propose to explain such divergent returns from the same investments in open, connected markets? I haven't seen an answer yet.

[GT]

Jim,

As with Tom I have to choose between accusing you of being unclear or admitting I don't underdtand what you are saying, so I will pick the former.

What is your question?

[Cecil Turner]

"Krugman's "mathematically impossible" statement is clearly false.

I already conceded that. So why repeat it?"

Well, in the first place your concessions were qualified (e.g., "that's just quibbling with words"). In the second, you seem to be confused about the purpose of TM's model. He's not trying to predict the most likely outcome, merely demonstrate Krugman's conclusion is wrong (which he did). There is no "bigger point" on this subject: TM is not asking you to base privatization arguments on his model, merely to discard any arguments that rely on Krugman's faulty assertion.

[Jim Glass]

"Well, as to why folks might be ignoring Dean..."

If we are talking about Baker, as opposed to Howard, I actually followed him back when he first went off on this line and economists *were* responding to him, and he kept rejecting their answers and sending those who answered him challenges 10x as long as his original one.

After a while I got the impression that they learned to ignore him the way I learned to ignore certain people on usenet. As the polite option.

But that was just my subjective impression.

[Jim Glass]

Krugman...

"The actuaries predict that economic growth ... will average only 1.9 percent over the next 75 years.

"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."

... What the heck is he talking about? Profits have never grown at the 6.5% steadily, but only at the real rate of the economy, just like he said.

So is he saying stocks *couldn't* have provided a 6.5% return for the past 200 years -- as they actually have -- because that would have required profits to grow faster than the economy for the last 20 decades???

[Jim Glass]

Look, if one really wants the short form response to the Krugman/Baker challenge, here it is:

Total annual return on stocks = R = 6.5 points annually = X points appreciation + Y points dividend yield.

Hold R at 6.5, set X at the rate of GDP growth (= growth rate of profits) and solve for Y.

"Mathematically impossible"?

Done.

[GT]

Jim,

I think that is a good point and why I a) conceded the point but b) think that a literal reading is wrong.

To me this boils down to this:

1)PK said X (1.9% growth and 6.5% returns) is mathematically impossible.

2) Tom and others (including Brad delong) show that X is is not mathematically imposible. Yours is as good a summary as any.

3) But nobody explains why, even if X possible, there is any reason to believe that X is likely. To me that is the crucial point.

[Patrick R. Sullivan]

"As with Tom I have to choose between accusing you of being unclear or admitting I don't underdtand what you are saying, so I will pick the former."

I think that is the wrong choice.

[Victor]

Nevermind about my 1:01 PM question: I believe I've answered it. The Social Security Trustee's don't require a 1.7% D/P ratio, but DeLong and Baker do to keep things at a steady state. It's kind of interesting because Baker has historically argued that the Social Security Trustees assumptions are consistent with a much higher D/P ratio ... http://www.cepr.net/publications/ss_economist_test.htm

Notice also that there is an entirely different way to phrase this problem.

* The Trustees assume that economic growth will be 1.8% below its recent average, because population growth will be 1.8% below its recent average. They also assume that the equity premium will be .7% below it's post 1960- average. Alternatively, over the longer-haul, you could say that their equity premium assumption is 2.6% below the historical average (post 1889). All the while, of course, the real kicker is that they assume the real interest will be higher.

Therefore, one very simple way to reconcile this entire debate is to assume that the real interest rate returns to pre-1981 levels -- which interestly includes a period of time in which we had a debt-GDP ratio greater than 100% (WWII). This is also consistent with a lower CPI-risk premium.

Of course, reconciling the argument in this fashion would make the Trust Fund look much, much worse (solvency is very dependent upon the real interest rate assumption), which is probably why it has not been seriously examined.

[TM]

I always wondered what it would take to piss you off, TM. Now we know.

LOL. OK, Crank, we can't say my first comment lacked for authenticity. And I haven't even read the whole thread, but I am going to apologize to GT now, before I read his comeback. (Hey, I can always re-edit my commentrs - its my blog).

[Jim Glass]

"But nobody explains why, even if X possible, there is any reason to believe that X is likely. To me that is the crucial point."

Noting the effect of discussions of probability on an impossibility theorem, we can consider this.

#1) For 200 years investors have priced equity to produce a 7% return (as per Siegel, Ibbotson, et. al.)

Why would they change now? Absent a reason, we have no reason to believe they will.

Also, profit growth and gains in stock appreciation have reasonably closely tracked GDP growth through history, PK is right about that.

So, if investors still price equity to return 7% as they always have, and if stock appreciation tracks GDP growth as it always has, and thus becomes 2%, then dividends become 5%. QED.

Which of those conditions seems unlikely?

Granted, this is the extreme case that ignores international investment that can let dividends rise by less in the real world.

But still, what really seems so *improbable* and *unlikely* about that, in light of the real-world history of 100+ years of 5% dividends through the 1970s?

And contrary to what I read over at DeLong's, this hardly implies any great misvaluation of stocks or misreporting of profits, or market price collapse or anything like that, as we are talking about 75 years and the adjustment could take place over the first 20.

I dare say that in 1970 the idea of a drop in dividend yield to the 1% of the 1990s would have seemed a lot less plausible than a rise to 4% in the 2020s looks today.

#2) The Krugman proposition of course gives no justification for any decline in stock returns in the rest of the world, (other than in the other geriatric nations, which over 75 years will be a distinct minority).

Thus, by predicting a drop in stock returns in the US, it predicts that a large *gap* will appear between return on equity in the US and return on equity in the rest of the world where return does not fall -- with return in the US being substantially lower over the sustained long run.

Does that seem *very likely* in open, connected, globalized markets?

Or does it seem more likely that rates of return on equity will equalize across global markets -- with return in US equity equalizing if necessary through a combination of higher dividends (though not as high as through most of history) plus more income earned from abroard, as opportunities for profitable investment increase abroad relative to the US?

I have a hard time imagining how an international economist would expect a permanent rate of return gap to arise between markets rather than equalization of return.

And if one wants to do so, I'd really like to read an explanation of it that makes it seem *probable*.

The only alternative option seems to be that Krugman thinks the slowdown of GDP growth in the US will reduce stock returns everywhere else in the world where growth is a lot higher, for 75 years, so no gap will develop. But that doesn't seem very likely to me.

[TM]

From GT, on the question of the equity risk premium:

3) But nobody explains why, even if X possible, there is any reason to believe that X is likely. To me that is the crucial point.

I agree that it is the crucial point.

However, as I took his column, Krugman is saying, based on current dividend yields, P/Es, and projected growth rates, he can prove that the equity risk premium must be less than 6.5%.

My point is that he can't prove it - this is the whole "mathematically impossible" debate.

If he, or DeLong, or someone else wants to come back and say, well, I think it is unlikely to be 6.5% for the following reasons, well, fine - I happen to think it will be 5%, and said so a few weeks ago.

But I am not claiming that I can prove that it will be 5%, or won't be 6.5%, or much of anything else. I have an opinion, and reasons, and others may differ.

And if people really are intent on insisting that Krugman was simply expressing an opinion about what the equity risk premium might be, well, he expressed it pretty strongly.

Which is why I eagerly await the day when Drum expounds on his theory of the equity risk premium as an increasing function of projected population growth. Of course, in the DeLong paper, that specific point is addressed and dismissed - DeLong describes the current consensus as considering the equity risk premium formula to *not* include a work force growth term.

However, Drum and Krugman should model away; then I can dismiss it as post hoc bullshit. Hah!

[Joe Mealyus]

"However, Drum and Krugman should model away; then I can dismiss it as post hoc bullshit."

But Kevin Drum's (more) complete put-down is: "....the problem with Tom's argument is that it's just a random post-hoc effort ... it's part of the genus bullshit."

The "post-hoc" and "bull****" are not the real insult - note carefully that word "random." Talk about loaded. Or lazy. Did Ahab randomly choose a white whale? Did Napoleon randomly choose Russia?

Anyway I like that Drum finishes by saying "stock market returns of, say, 4% or 4.5% don't provide quite the sizzle of 7%, but they still make a perfectly reasonable story." Why "model away" when you can just conclude?

I thought Krugman's original column was excellent - making an interesting point, and not one that any old columnist could make. It will be interesting to see how the thinking evolves on this. "Mathematically impossible" was over-the-top, sure, but perhaps no other opportunity availed itself for the (necessary) expression of thunderous outrage.

[Aaron]

Also, what about situations where American companies like P&G who earn profits in China.

Their US Stock Market return increases because of this great performance and the domestic issue is unimportant.

Do you think Intel will rely on the US domestic market for most of its profits in 2050?

[dsquared]

then dividends become 5%

Jim, Tom; remember that there are bounds placed on the dividend yield because the payout ratio can't go above 100% (or at least, not outside of oddball financial restructuring stories which aren't sustainable on an ongoing basis).

If the div. yield starts at 1.7%, with the payout ratio at around 40%, then the highest it can go assuming a constant stock price is 4.25% (and of course, at this level there would be no net investment and thus even a 2% capital growth assumption would be suspect). In order to get the dividend yield any higher you have to assume a one-off markdown in equity prices. I haven't done the calculations, but someone ought to dot and cross the i's and t's here; some things may or may not be mathematically possible, but there are definitely arithmetic constraints that need to be satisfied.

btw, Jim, this also applies to a lot of your points about foreign versus domestic stock returns (btw, I don't quite understand the point of that excursion, or where Krugman might have said what you're claiming he said). If the return on capital is, for the sake of argument, 7% overseas and 5% domestically, then the way in which equity returns "equalise in a global capital market" would be to mark up the price of foreign equities relative to domestic ones, so that going forward returns would be equal, but the existing holders of foreignequities would indeed realise a superior return over the holding period. Remember that Dow 36K was based on the assumption of lower long term stock returns, not higher.

[dsquared]

Look, if one really wants the short form response to the Krugman/Baker challenge, here it is:

Total annual return on stocks = R = 6.5 points annually = X points appreciation + Y points dividend yield.

Hold R at 6.5, set X at the rate of GDP growth (= growth rate of profits) and solve for Y.

See, this is why the short form doesn't work, which is why Krugman and Baker concluded (erroneously) that no longer form could work.

If we take X as 1.9, to be consistent with the SSA projections, then Y has to be 4.6. But there is another set of constraints to do with the payout ratio:

Dividends/profits <= 100%
Current dividends/profits ~=40%
Current dividend yield ~=1.7%

These constraints, taken together, seem to place an upper bound on Y of 4.25%.

That's why, as Tom has shown, in order to get to the 6.5% returns assumption you have to make alterations to the SSA base case; effectively you have to come up with something like a profit share assumption (Maguire) or a foreign earnings assumption (Glass/Sullivan) or a one-off markdown in stock prices (Samwick/DeLong) or a wedge between accounting earnings and cash (DeLong), which justifies an assumption either that profits can grow faster than 1.9% or that a dividend payout above 100% of accounting earnings is possible.

[dsquared]

(I'd note that the easiest and most sensible way to square this circle would be to pick a more sensible growth rate, under which assumption the "crisis" wouldn't exist and we could still get our 6.5% real equity returns).

[Dave]

Tom --

I confess that this conversation has made my head hurt. In my always simple-minded way of approaching things, dividend payout rates, stock buybacks, and all that stuff are just a diversion -- the different ways in which the total return to capital might be received.

Why complicate things? In our workhorse model of economic growth -- the so-called Cass-Koopmans-Ramsey extension of the Solow model -- the rate of return to capital exceeds the sum the growth rate of the GDP whenever the saving rate in the economy is "not too high." I think everyone would agree that this is the right condition for describing the US economy. (Andy Abel, Greg Mankiw, Larry Summers, and Richard Zeckhauser formally argued this to be the case in a 1989 article that appeared in the Review of Economic Studies -- I don't think anyone is arguing things have "improved" since.)

Brad DeLong is on the right track in the paper linked from the post you link above (the URL is below), as he actually writes down a growth model to make his point. But he sort of obscures the Cass-Koopmans result by writing down a model with an infinitely-lived representative agent -- an odd choice because,as a first approximation, social security will be neutral in such a world. If you want this done right, you have to go the route of Larry Kotlikoff, Kent Smetters, and Jan Walliser (link provided below). Playing with the arithmetic of all the various ways that people might collect capital returns -- which, again as a fist approximation, shouldn't matter for squat -- just mucks things up.

Cheers -- da

DeLong's exercise: http://www.j-bradford-delong.net/movable_type/pdf/20050212-Baker-Krugman.pdf

Kotlikoff, Smetters, and Walliser:http://econ.bu.edu/kotlikoff/KSW.pdf

[Dave Altig]

Sorry for the typos in that previous post -- I really should use that "preview" button.

[TM]

Dave - I think I agree. Waaay back in my first response to this, I noted that I am not fan of dividend-based models, since the point of Miller-Modigliani is that a firm's dividend policy is "merely" a financing decision that doesn't drive the value of the firm.

And I also noted something similar, which I will toss out for D Sq, who said this:

(and of course, at this level [100% of profit paid as dividends] there would be no net investment and thus even a 2% capital growth assumption would be suspect).

My quarrel with that is, we have capital markets, and I have never understood the corporate sector to be self-financing - surely, if national savings are reinvested in new capital, the capital base will grow faster than would be projected by [Investment = Profits - Dividends]. A slight revision would be the well recognized Investment = Savings, where Savings can come from household income.

That was one of my early objections to Dean Baker's specific methodology, as well.

Now, relatedly, it may well be that the equilibrium between savings and investment changes as our population, or the world's, ages - maybe not many 80 year olds are buying 30 year bonds, and place a higher value on current consumption (and maybe the estate tax encourages consumption over saving, if you can't take it with you, and you can't pass it on).

And I suspect a grand model could pick all this up.

Anyway, I am now irked with myself - in my soon to be revised post above, I will point out that there is a standards issue in play here - mathematicians claim to prove things, social scientists claim to prove things, and callers to sports talk radio claim to prove things.

Although mathematicians look down on everyone, economists like to imagine that they used the high priced math, and actually do "prove" things - DSquared proved (not for the first time) that a country cannot be an exporter of capital while running a trade deficit.

Well, we are not arguing that point anymore - it is not his opinion, it is accounting identities.

So, when Krugman says a certain economic relationship is "mathematicaly impossible", we might think that out of respect for his profession and his peers, he would maintain the standards of his profession. In which case, he erred on a somewhat important point of macroeconomics.

Or, we can agree that when Krugman writes for the popular press, he does not burden himself with the weight of his profession - when he writes that an economic relationship is "mathematically impossible", he is wrting as a fan, not an economist, and one can not rely on his economic reputation as standing behind that.

Either conclusion works for me (surprisingly).

And at the bottom of the post Kevin went off on, I did say this:

Now, obvious caveats - these numbers and examples do not, and can not, *prove* that the US stock market is correctly valued, or that the dividend yield must remain at 1.5%, or that foreign investment by US corporations *must* grow to some number by some date.

However, what these numbers *do* prove is that a perfectly coherent, mathematically consistent explanation of current share prices, earnings yields, and dividends yields is available. Toss in foreign investment, and we offer this in refutation of the various "HAIRy" models that attempt to "prove" that stocks must fall.

[Paul Zrimsek]

Like most forms of political foolishness, Krugman's "mathematically impossible" turns out to be adapted from Monty Python: "There is NO cannibalism in the Royal Navy. None whatsoever. And when I say 'none' I mean there is a certain amount."

[dsquared]

My quarrel with that is, we have capital markets, and I have never understood the corporate sector to be self-financing - surely, if national savings are reinvested in new capital, the capital base will grow faster than would be projected by [Investment = Profits - Dividends].

But this does the opposite of helping square the circle; it increases GDP growth but doesn't improve equity returns; if you're paying for your own dividends with stock issuance (either through stumping up for the equity issue, or through being diluted) then you have to knock that off your return, surely? Or if the investment is financed by borrowing, then you're bumping up the leverage of the corporate sector and making the returns work by taking on more risk.

In a macro framework we've got to be thinking of net dividends (I think Brad has already sorted this one out?), or we've got to just look at earnings yields rather than dividend yields (in which case Baker's point is made rather starkly; one either has to come up with a reason why the PE ratio should continue to increase, or come up with some decent story about earnings from outside the USA or by expropriation from labour).

[TM]

if you're paying for your own dividends with stock issuance (either through stumping up for the equity issue, or through being diluted) then you have to knock that off your return, surely?

Well. I'm 0-1 against DSq with the foreign trade point, but this could even the score.

Just a sidebar for clarity: I think we have all agreed that depreciation has already been taken out of Profits.

So, the question would be, if a firm, or "the economy", wants to build a new power plant to power economic growth (not just cover depreciation on an existing power plant), doesn't that have to come out of a corporation's cash flow?

Or, if the power company issues new shares to finance the new construction, doesn't that dilute the equity of current shareholders?

Well, bit of a cheat, but illustrative - we could set up a brand new company, sell shares, build a plant, and sell power. The currently existing power company stays at its old size, the new one covers the new market (and, we have presumed, earns a responsible return on capital).

Shareholders in OldCo were not diluted; the capital markets financed NewCo; NewCo earns a good return.

Or, if OldCo takes on this new project with new equity financing, the number don't change, we just consolidate companies - a newish, larger OldCo has new equity financing and a new plant, earns higher profits, but still earns the same average return on all its capital.

That, anyway, is my story.

Obviously, a lot of investment takes place in a less lumpy way - GM does not do a share issue to upgrade a machine tool line - but the principle should work.

In a macro framework we've got to be thinking of net dividends...

Well, I am saying no. How about that?

(For folks at home - I like D-Squared's track record, but don't be afraid to bet on me on this one. The tote board, as I see it:

(a) they are talking at cross purposes, but will sort themselves out: 20%

(b) TM is right - Investment = Savings rules! Households can save too, from their 57% slice of the GDP pie we have been calling Wages: 50%

(c) DSq is right - financing for new growth has to be counted against the return on existing capital: 30%

I am betting me, big.

[joe mealyus]

dsquared: "(I'd note that the easiest and most sensible way to square this circle would be to pick a more sensible growth rate, under which assumption the "crisis" wouldn't exist and we could still get our 6.5% real equity returns)."

But then what if you throw in "more sensible" (okay, pessimistic) demographic projections? The crisis is back, isn't it?

[Joe Mealyus]

"Or, we can agree that when Krugman writes for the popular press, he does not burden himself with the weight of his profession - when he writes that an economic relationship is "mathematically impossible", he is wrting as a fan, not an economist, and one can not rely on his economic reputation as standing behind that."

A more interesting question to me, is if Gore had won in 2000 and was now (making a Clinton-like appeal for the center, perhaps) pushing a Soc Sec partial privatization plan not totally dissimilar to George's - whether you might not pick up the paper and see Krugman take a very (or more fairly, perhaps, somewhat) different tack with respect to the ideas of Dean Baker.

Isn't the question you're really asking whether he's writing as a Stalwart Opponent or as an economist?

Btw Gary Becker's piece in today's WSJ is very good. Of course he doesn't give a rat's ass about the central issue of the PK/JOM debate.

[dsquared]

Tom; the hidden assumption which you might or might not want to criticise here is that new securities sell for the same valuation as old securities.

In general, I'm beginning to see why Dean Baker insisted on everyone using concrete numbers; they help a lot to keep things clear. Look at it this way:

In the hypothetical economy you're talking about, we assume that every company pays out 100% of its cashflow as a dividend and new securities are issued to savers to fund investment.

In this economy, pretty obviously, the rate of return on savings is the dividend yield.

But there is a wedge between the dividend yield and the return on (physical) capital; shares might or might not be trading at a premium or discount to book. And we currently find ourselves in a position where that wedge is material and positive; if the current dividend yield is 1.7% and the current payout ratio is 40% (neither of which stylised numbers I have checked, btw, so there might be an angle here), then if companies paid out 100% of their cashflow then the dividend yield would be 4.25%.

Now if we apply this to your OldCo/NewCo example, we can see this wedge in action. OldCo is paying out a dividend yield of 4.25%. That dividend can't grow because OldCo has no net reinvestment, but we can float NewCo. NewCo needs capital of X and has a return on capital of Y%, but if we assume that NewCo also pays out all its cashflow as a dividend, then the assumption that NewCo is valued the same as OldCo means that NewCo will float at a price of (XY/4.25%). This is the price at which investors in NewCo get the same dividend yield (= total return, as we have set up the model to have no capital growth) as they could get in OldCo.

Now we can see here that 1) the difference between X, the price of the capital assets and (XY/0.0425), the flotation price of NewCo, is a windfall gain to the entrepreneur who floated NewCo and 2) if all that savers can do is invest money in stocks that pay a 4.25% dividend yield that never grows, there's no way that they're going to make a 6.5% return.

Things get a bit more complicated if you assume that OldCo owns NewCo; I then need to assume that NewCo's return on capital is no greater than OldCo's (I think' I haven't done the sums on this one) in order to get the same or a similar result. But the central issue is Brad DeLong's point; starting from valuations as they are, the wedge between the return on capital and the dividend yield means that we have to have capital growth[1] in order to get to the 6.5% return, and that capital growth has to come about as a result of profits growth.

I might have gone wrong here; in particular, I haven't done the sums for the case in which OldCo owns NewCo (ie, OldCo issues seasoned equity to build the new plant). But the central intuition is that you are buying shares today at a particular dividend yield, that this dividend yield implies a premium to book value, and that premium to book value can only be made consistent with an expected 6.5% growth rate if you assume a certain rate of profits growth. Therefore, you either need to start off by marking down this premium to one which assumes a lower rate of profits growth (Samwick) or come up with a way of making that rate of profits growth consistent with 1.9% GDP growth.

[1] Capital growth in this model comes from the fact that if a company retains earnings to reinvest in projects, the shareholders of that company are effectively buying new capital assets at a price of X, rather than a price of XY/k (where k is the discount rate, generalised from the dividend yield above)

[mcdruid]

Seems to me, what Senor Maguire is saying is that the Baker-Krugman conundrum could be solved either by (a) overseas investment in faster growing economies and/or (b) increased corporate profits probably gained at the expense of worker wages.

I don't know about (a) (though I am curious if this requires all of the rest of the world to grow at a faster rate, or just niche markets - and if the latter, can they handle the entire investment?), but (b) is clearly wrong.

After all, the crux of the Social Security "problem" is that the number of US workers will decline. A worker shortage is not consistent with declining wages, at least under a normal supply curve.

[dsquared]

though I am curious if this requires all of the rest of the world to grow at a faster rate

It doesn't. All you need is for the rate of return on capital overseas not to be too much lower than in the USA. There is a global adding-up constraint if we are to assume that foreign countries are also able to solve their retirement problems, but neither side of this debate is committed to either side on that question.

[dsquared]

Apropos of nothing, sporting trivia:

C'mon - even on sports talk radio, no one says that it is mathematically impossible for the Orioles to win the pennant.

I think that this is true for all major US sports, but in Europe and the UK we have leagues with promotion and relegation (and we have players bought and sold on a free market! no salary caps!). For this reason, toward the end of the soccer season, the gap between your team's accumulated points and the bottom (or top) three in your division is very important and there is often a point at which it becomes "mathematically impossible" (or even "mathematically inevitable") for you to be relegated or promoted.

[mcdruid]

dsquared,
rate of return on capital overseas not to be too much lower than in the USA.

I'm not getting this. It seems to me that if I'm selling to market A at 6.5% returns, and it drops to 4%, and I switch half my business overseas, to market B, I'd need to make 9% there to keep up.

Further, it seems another of Baker's points has gone unremarked in this thread: the increase in P/E ratios from 14.5 to 20. This alone drives returns on investment down some 27%.

[dsquared]

McD; the increase in PER and its affect on investment return is what I mean by "the wedge between the return on capital and the dividend yield above".

[TM]

there is often a point at which it becomes "mathematically impossible" (or even "mathematically inevitable") for you to be relegated or promoted.

We have the famous "Magic number" in baseball, which is the remaining number of (Yankee wins plus Red Sox losses) that make a Yankee win of the AL East a mathematical certainty.

SO I should have had a qualifier about "right now", when we await the day that pitchers and catchers report, the standings are equal, and hope is everywhere.

And the NHL is cancelled! Does it get any better?

[mcdruid]

D^2, I understand that increasing PEs are one way out, I'm just asking if Maguire's calculations take into consideration that current PEs require extra "post-hoc bullshit" effort to get back to the magic 6.5%? I really just don't understand Glass's contention that a WW 4% rate lets a US company go higher.

In addition, according to my calculations, World GDP has averaged 12%/year (9% percapita) increase from 1950 to 2000, but drops to 4.1% (2% percap) for 80-00 and 3.5% (1% percap) for 90-00. (Data from http://www.eco.rug.nl/%7EMaddison/Historical_Statistics/horizontal-file.xls) Glass seems to think this trend will reverse, despite the drop in the US projections.

[dsquared]

The idea is that you need to look at the growth rate not of the overseas economy, but of that part of it which is owned by domestic companies.

For example, think of a country whose only industry is a single oil well that isn't growing at all and has a 6.5% dividend yield. If a US company makes a return of 6.5% on capital and invests 100% of earnings in buying shares in the oil well, its earnings will grow at 6.5% until it owns the entire well. That's the sort of idea.

[cholo]

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