## Potpourri

==> Just an announcement, kids, I’m scaling back my frequency of posts at Mises CA; I’m just too busy. If you want to take your hand at it, feel free to pitch ideas to them at contact@mises.ca. They often get picked up by ZeroHedge if that matters.

==> Someone else made a print version of Barta and my Bitcoin book. Silas and I only benefit from the transmission of knowledge… (Remember if you want the free PDF, go here.)

==> A new NBER study suggests that part of the “surprising” US performance last year was due to the ending of unemployment benefits. Here’s a Reason review, but TL;DR if you stop paying people to not have jobs, then fewer people will not have jobs.

==> Can’t remember if I linked to this? Peter Lewin (an expert on Austrian capital theory) chimes in on Piketty.

==> I don’t have time to deal with this, but if you want to see another perspective, Mike Konczal tries to defang Scott Sumner’s laughing over the sequester and Keynesians.

==> An interesting autobiographical note from one of the authors of *The Market for Liberty*, fantastic book that I reviewed very favorably (here–thanks to Darien for finding the link).

The three factors, I think, behind the strengthening of the recovery were:

1. Expiration of unemployment benefits.

2. End of regime uncertainty regarding Obamacare.

3. The beginning of the end of private-sector deleveraging.

“E. HardingThe three factors, I think, behind the strengthening of the recovery were:”

The recovery we observe today would not even exist had it not been for the Keynesian stimulus from 2009-2011 and the interventions to stop the financial system from collapsing.

Had a “liquidationist” solution been pursued in 2008, large numbers of banks would have collapsed in 2008-2009 and million of deposit savings would have been lost, and a depression as bad as or worse than the 1930s would have resulted.

My thoughts on the UI study, if you’re interested: http://factsandotherstubbornthings.blogspot.com/2015/01/new-research-on-unemployment-insurance.html

What are your thoughts on Lewin? I am finding his post very hard to follow. It’s like he’s trying to work with about a third of a Solow model. And I don’t get why he’s equating the capital share of income with the level of inequality.

Ah well, one could

alsoquestion whether, evenifcapital’s share of income approaches 100%, that capital is driven by demographic trends and inheritance into increasingly fewer hands. And therefore whether Piketty’s assumptions about capital’s share strictly increasing over time wouldnecessarilyimply increasing inequality. But if those assumptions themselves don’t hold, what’s the point of questioning Piketty’s demographic and inheritance assumptions? Redundantly proving he’s wrong?I’m not entirely sure I follow. I guess my bigger confusion is that the capital share is not inequality according to Piketty (or anyone!), he noted some increase in the capital share over the twentieth century but doesn’t think it will increase continually. I’m just confused by Lewin’s whole spin on what Piketty is saying.

If r > g (which Piketty belabors as a “fundamental law”) the capital share should grow to approach 1, right? I’m confused how you think Piketty thinking r is strictly greater than g,

doesn’timply he thinks the capital share grows indefinitely?To get from there to ever increasing inequality, you need certain auxiliary assumptions, about demographics and inheritance, yes. But I’m surprised to hear you think he

doesn’tstart by essentially arguing that capital’s share grows toward unity (and then work from there, to inequality from auxiliary assumptions).I suppose I’m not understanding why you think r > g implies the capital share of income goes to 1, or why you think Piketty thinks this. Can you provide a page number maybe?

I thought Piketty said alpha is the capital share of income, and that alpha = r x beta, where beta is the capital stock divided by income. Then beta is equal to s/g where s is the savings rate. So alpha = (rs)/g. I don’t understand why you think (or why you think Piketty thinks) that this goes to 1 merely because r > g.

I think I’ve just misunderstood the math. Still, see Phil’s comment below, which I think partially justifies my confusion.

Phil points you to a chart that shows convergence to a beta of 700%, which Piketty says is the equilibrium value. You are thinking of alpha. Alpha is equal to r*beta. So the convergence to beta=7. If we take his long-run typical r of about 0.05, that implies an equilibrium alpha (what you’re interested in) of 0.35.

Take a look at figure 6.5. What are the alphas converging towards?

Phil’s graph does not show an increase of either the capital stock or capital’s share of income going to infinity, it simply doesn’t.

Now I’ll agree, if someone didn’t read Piketty and the discussion of why he thinks beta will converge to an equilibrium level of 700%, then that figure that Phil shares might suggest something different.

Andrew – Piketty does in fact predict a continuous and pronounced worldwide growth of the capital stock vis-a-vis income. This is a slightly different way of capturing the predicted effect than examining – say – yearly returns on capital as a share of total income, but he uses it to illustrate the underlying mechanism of r>g and all that he wishes his reader to take away from it. That was the entire point of the second half of his figure 12.4 (the first half being an artificially pronounced trough that he achieved through statistical manipulation to bolster his false historical narrative)

http://piketty.pse.ens.fr/files/capital21c/en/pdf/F12.4.pdf

Piketty does predict a stabilization…of the *savings* rate. But this is also explicitly identified as an assumption that he makes. Relax that assumption, things change pretty dramatically. Or even hold to that assumption, and he still asserts a sustained divergence in C-I ratios. 700% is not the magic convergence number – it is only where he supposes things will be at the end of his century long projection based on what he assumes to be the worldwide savings rate. The convergence is only on that assumed savings rate of about 10%.

But don’t take my word for it. Take Piketty’s own description from the two relevant places where he brings this up.

Chapter 5:

“I also assume that the savings rate will stabilize at about 10 percent in the long run. With these assumptions, the dynamic law β = s / g implies that the global capital/income ratio will quite logically continue to rise and could approach 700 percent before the end of the twenty-first century, or approximately the level observed in Europe from the eighteenth century to the Belle Époque. In other words, by 2100, the entire planet could look like Europe at the turn of the twentieth century, at least in terms of capital intensity. Obviously, this is just one possibility among others. As noted, these growth predictions are extremely uncertain, as is the prediction of the rate of saving. These simulations are nevertheless plausible and valuable as a way of illustrating the crucial role of slower growth in the accumulation of capital.”

Chapter 12:

“In the central scenario for the evolution of the global capital/income ratio that I discussed in Chapter 5, I assumed that the savings rate would stabilize at around 10 percent of national income as this international convergence process neared its end. In that case, the accumulation of capital would attain comparable proportions everywhere. A very large share of the world’s capital stock would of course be accumulated in Asia, and especially China, in keeping with the region’s future share of global output. But according to the central scenario, the capital/income ratio would be the same on all continents, so that there would be no major imbalance between savings and investment in any region. Africa would be the only exception: in the central scenario depicted in Figures 12.4 and 12.5, the capital/income ratio is expected to be lower in Africa than in other continents throughout the twenty first century (essentially because Africa is catching up economically much more slowly and its demographic transition is also delayed). If capital can flow freely across borders, one would expect to see a flow of investments in Africa from other countries, especially China and other Asian nations. For the reasons discussed above, this could give rise to serious tensions, signs of which are already visible.

To be sure, one can easily imagine scenarios much more unbalanced than the central scenario. Nevertheless, the forces of divergence are much less obvious than in the case of the sovereign wealth funds, whose growth depends on windfalls totally disproportionate to the needs of the populations benefiting from them (especially where those populations are tiny). This leads to endless accumulation, which the inequality r > g transforms into a permanent divergence in the global capital distribution.”

He suggests savings at 10%, g at just under 1.5% at the end of the century which gets you to his “could approach 700 percent” figure.

One thing he definitely has not said and that you have definitely not demonstrated him saying is that the capital share will continue to increase.

Your chapter 12 quote is about the distribution of the capital stock NOT the capital share of income. It’s important to keep these concepts straight.

Andrew this is very easy to sort out. To get alpha going to infinity you need s or r going off to infinity or g going off to zero (or less). Piketty clearly doesn’t make a case for any of that. Alpha and beta are pinned down. They were in the Solow model. They are in Piketty.

Actually I’m not entirely sure how to think about this in the context of long run negative growth, so don’t quote me on that last part.

No Daniel, the Chapter 12 quote is about the Capital/Income RATIO depicted in the accompanying Figure 12.4, to which it directly refers. I never represented it as a presentation of the capital return share of income, and in fact stated otherwise when I introduced 12.4 above.

For someone who quite rudely just insinuated to Andrew that he “didn’t read Piketty” and therefore made an erroneous representation of him, your own erroneous readings of both Piketty, not to mention others with whom you converse, are as palpable in comparison as they are astounding in this context.

12.4 is the ratio to income. Andrew asked about capital’s share of income. Your quote refers to the distribution of capital’s share of income.

Here’s The Market For Liberty on mises.org: https://mises.org/library/market-liberty-1

And here it is on amazon.com: http://www.amazon.com/The-Market-Liberty-Morris-Tannehill/dp/0930073088

Thanks I should’ve thought of that too, Darien, but I was referring to a book review I wrote for Mises.org. I have an old URL for it, but it’s broken since they revamped the website.

Sorry, Bob; I misread you. Is this the review you’re after? https://mises.org/library/society-without-government

Yes thanks!

I realize that reading comprehension is not your friend, Daniel, but:

(1) 700% is nothing more than where he expects C/I to be 100 years from now IF his assumption of the savings rate convergence at 10% holds true. It is the product of a forecast made using that assumptions – IOW where he expects it to end up after a century – not the stable equilibrium that you purported it to be in your comment above. See:

“*With these assumptions,* the dynamic law β = s / g implies that the global capital/income ratio will quite logically continue to rise and could approach 700 percent before the end of the twenty-first century”

(2) Piketty is pretty clear in recognizing the possibility of capital accumulation continuing, especially as one relaxes the assumptions

“This leads to endless accumulation, which the inequality r > g transforms into a permanent divergence in the global capital distribution.”

(3) Simply holding the 10% rate constant and continuing Piketty’s own projection model forward another decade to 2110 results in the ratio quickly breaking north of 700%. It would not do so if this were a stable equilibrium as you claimed above.

(4) As a brief aside, Piketty’s forecast “model” is chock full of the same sort of amateurish back-of-the-envelope contrivances that plague the rest of this chart and should be evaluated accordingly, even if the 10% savings assumption is accepted.

Always such a treat to talk to you Phil.

1. Right, it’s the projection to the end of the century. Plug in the figures for beta and show me how beta keeps increasing, then we can talk. It’ll take the century to converge, it’s true. Nothing in the determination of beta suggests r > g pushes it to infinity. If you disagree explain your reasoning.

2. The distribution of capital is not the same as the capital share of income. I pointed this out to you above, I don’t know why you’re repeating it.

3. Which g are you plugging in? I don’t see how you get this. If you are using a g other than something just shy of 1.5 it may keep going a little longer but you’re going to level out somewhere along there.

1. There appears to be a substantial divergence between how Piketty actually calculated his forecast and how you *think* he calculated his forecast, Daniel. You seem to be accepting his model, adding in a few additional assumptions that your misreading of his text leads you to believe to be a part of it, and working backwards to his forecast from there. What we actually have in Piketty though is the product of a base assumption (the 10% savings rate convergence) coupled with a very rudimentary linear projection, a bunch of ad hoc guesstimation to fill in the gaps, and an intermittently applied rolling average overlaid on top of the whole thing.

2. Seeing as I did not equate it with the capital share of income and in fact said the exact opposite upon introducing Figure 12.4 to the discussion, I’m not sure what you’re even talking about and would accordingly defer to my previous assessment of your reading comprehension skills.

3. See #1 above. How you think Piketty performed his forecast is a very different thing from how he actually performed his forecast. If you keep his forecast model at the 10% savings convergence after 2100, hold the world dist. ratios constant to where he set them, and assume a stable continuation of his world income trend, then yes – the ratio goes north of 700% in 2110.

And for fun I’ll add in:

4. You repeatedly asserted above that 700% is an “equilibrium value” or some sort of similar stabilization point. Yet Piketty’s text makes no such claim, and only enlists this number to suggest that some 90 years from now it’s about where he expects the world’s C/I ratio to be at. So if not a misreading of Piketty even as you chastised another poster for supposedly failing to read the same, where exactly are you getting this “equilibrium” business from?

re: “You repeatedly asserted above that 700% is an “equilibrium value” or some sort of similar stabilization point. Yet Piketty’s text makes no such claim.”

Check the discussion of beta=s/g starting on page 166. Beta is a long-run value. On page 169: “the law beta=s/g is the result of a dynamic process: it represents a state of equilibrium toward which an economy will tend if the savings rate is s and the growth rate g, but that equilibrium state is never perfectly realized in practice.”

This is not some radical contribution. We’ve had these steady state equations since at least 1956 (maybe Ramsey had them in the 20s – I’d have to double check that). It’s really stupid that we’re arguing this point.

re: “So if not a misreading of Piketty even as you chastised another poster for supposedly failing to read the same”

Can you please stop repeating this? I don’t know why you have this need to make things up about me. I never said that.

I did say someone that didn’t read the book might interpret your chart in the way that you were trying to spin it. But of course that’s not the only way to misunderstand the chart. If you read the book and forgot it you’d misunderstand. If you read the book and didn’t understand it you’d misunderstand, etc.

I was having a nice conversation with Andrew before you came here. Please stop inventing insults of Andrew and putting them in my mouth.

Daniel – I’m not taking issue with Piketty’s growth rate beyond noting it is an assumption. I’m not questioning his savings rate beyond – again – noting that it carries an assumption. And I’m not asserting anything about his modeling of the two separate and apart from the empirics of his forecast.

I am, however, questioning *your* assertion that they settle at an equilibrium that is specifically 700% and specifically coincides with the year 2100 on his Figure 12.4, as none of that is evident in Piketty’s own claims. So while you may be unsure as to why we’re arguing the point, I am unsure why you are now evading an explanation for a very specific and erroneous claim that you made and reiterated at an earlier point in this thread.

As to my other remark, you stated “if someone didn’t read Piketty and the discussion of why he thinks beta will converge to an equilibrium level of 700%…” Leaving aside the aforementioned issue that the 700% equilibrium convergence is your own invented – and now evaded – construction, the clear insinuation of that remark is that persons who disagreed with your assertion – i.e. Andrew at that point of the conversation – must not have read Piketty.

Since you plainly don’t enjoy being called out for making such insinuations (or for that matter your habit of baselessly attributing errors of method, comprehension, competence, qualification, or even basic calculation practices to others you criticize), my advice to you on this point is simple: quit inserting such blatantly uncharitable and derogatory insinuations about any and every interlocutor you face on this subject. They are needless, and only serve to start the conversation on a footing from which it is difficult to ever recover. And given your own challenges of comprehension when it comes to Piketty as has been amply documented above, they are also more than a tad hypocritical to be coming out of such a self-unaware source.

Guys, for the record, I think that Daniel is right that I was wrong about the math-just a bad misunderstanding on my part. On the substance and on reflection, r > g by itself, doesn’t imply an ever growing capital share. That requires additional auxiliary assumptions. I certainly got the

impressionthat was what was being claimed. I now think I may have misunderstood that, too. However:It still seems to me that Piketty would logically have the capital share of income growing for at least the next several decades. And looking at his projection I see no continuous decrease in the rate of increase of the capital/income ratio, so I don’t see on what basis the value is expected to stop increasing at 700%? If that’s what Piketty’s model assumes, then it doesn’t look like he used his model to make his projection. What gives?

re: “so I don’t see on what basis the value is expected to stop increasing at 700%”

beta=s/g

s is about 0.1

g is about 0.015

Andrew – All fair on the math issues. My original point was to note the different metric of his C/I ratio does indeed show a fairly aggressive expansion of the capital stock as an implied effect of r>g.

But yes – I also want to know where Daniel’s assertion of the stabilizing 700% equilibrium comes from. Because (1) this does NOT actually appear in Piketty’s claims and (2) it seems to be the result of a misreading of Piketty’s related assumption that the savings rate will stabilize at 10% worldwide in an adjoining passage.

Let me ask you two this: precisely where do you think Piketty got his 12.4 figure???

Having not

personallyexamined his spreadsheet for that graph, I plead ignorance and agnosticism. I only note that it doesn’t look like it comes from a model that you describe.Andrew is correct. It may be loosely informed by his model. The assumptions of that model also determine its shape and where he expects its end point to be in 2100. But it is constructed from several specific components that fill in the trend, and do so in a way that fits his story. Specific components include:

1. Historical estimates of global output, which are then weighted regionally across the century & projected forward according to where he anticipates the weights going (there are HUGE gaps and other problems in the regional btw – as in sufficiently large to undermine the reliability of the whole thing). The forward projections are also mostly a continuation of his own guesstimations, with a little averaging overlaid in a few regions.

2. Historical data on the capital stock by region. He only has actual data for the US & Western Europe across the whole series, and Japan/Aus/NZ since 1970, so the rest is guesstimated or – in the communist regions – simply hard coded in according to an a priori ideological claim about the position of capital in a communist society. These too are projected forward post-2010, most of it through simple guesstimation of where he thinks it will be.

3. Historical data for total world output (giving him the income part of the ratio) and a projection of where he thinks it will go through 2100.

4. Piketty’s savings rate assumptions, which show all regions of the world converging on 10% by 2080.

He then projects where he thinks the C/I ratio will be in 2100 and uses the above, in cumulative, to backfill in the trend lines. The 700% is a product of that projection, attained through where he sets his savings assumption and g. It is not, however, a fixed equilibrium around which the world will automatically stabilize.

Perhaps also worth reiterating that Piketty himself does NOT consider 700% an equilibrium – rather it is only an outcome that happens IF he sets his assumptions around the 10% savings rate and specific levels of output growth across the century. Change either of those things and it could be higher (or lower) in any given year. IOW, Daniel seems to be taking the assumptions Piketty used as if they are fixed and drawing his claimed equilibrium out of their projected results. Yet Piketty himself tells us the assumptions are NOT fixed:

“Obviously, this is just one possibility among others. As noted, these growth predictions are extremely uncertain, as is the prediction of the rate of saving. These simulations are nevertheless plausible and valuable as a way of illustrating the crucial role of slower growth in the accumulation of capital.”

Therefore 700% is not an equilibrium, but a product of his forecasting.

He does call it an equilibrium – I gave it to you above – and yes of course an equilibrium value changes when the values of the parameters change.

No Daniel. He says his “second law” represents an equilibrium state that “is never perfectly realized in practice” in a passage some 20 pages prior to the figure you are projecting an equilibrium onto. When he gets to that actual figure though, he readily concedes that it is a *product* of his prior assumptions, and not an equilibrium onto itself. So either Piketty did not mean what he plainly said when he described his figures as “uncertain” and only a “possibility” among many outcomes, or you are borrowing from an earlier passage to append something to the one under consideration.

In any case, the result of your claim is intrinsically circular. You cannot predict conditions X & Y will hold 100 years from now and plug them into a formula producing result Z, then assert that the result Z thereby validates inputs X & Y and is somehow now an equilibrium state towards which X & Y gravitate. Piketty – to his credit – does not make that step. You seem to believe otherwise.

Phil you’re acting like if we don’t know the future with exact certainty then it can’t be an equilibrium. You have a very different understanding of what an equilibrium is in economics from mine. I’ll stick with mine.

I don’t even follow what you’re trying to say in the second paragraph.

Daniel – What I’m saying is that by all appearances, your theory of equilibrium seems to proceed as follows:

Step 1: Make wild guesses about what the global savings rate AND output will be 100 years from now.

Step 2: Derive a world C-I ratio for 100 years from now from the guesses in Step 1.

Step 3: Produce a trend line between the present day and that guess-derived ratio from Step 2 by way of connect-the-dots.

Step 4: Assert that the ratio from Step 2 exhibits innate stabilizing characteristics and label it an equilibrium

Step 5: Use that newly labeled equilibrium from Step 4 to assert that the connect-the-dots exercise from Step 3 represent a convergence upon the derived ratio of Step 2.

(Disclaimer: Piketty only follows this line of construction through Step 3 and then caveats it with an admission that its premised on wild guesses. This is to his credit.)

Try this instead:

1. Derive steady state equations for the capital stock relative to income.

2. Forecast the parameters that contribute to the steady state.

3. Plug them in and get forecasted capital stock relative to income.

That’s to get his long run equilibrium. I don’t know if the path to get there was projected or if he had some kind of balanced growth path with the same forecasted parameters or what.

Forecasts are always dicey. Piketty says as much which is good. But that’s the exercise.

Unless you are asserting that there is a stabilizing effect in the world growth rate at 1.5% (in which case you should also be prepared to offer a reason) there’s something missing from your purported equilibrium. Simply calling something a “forecast” or an “equilibrium” does not make it so. Thus we actually have something more along the lines of:

1. Make wild guesses about where savings and output will be 100 years from now

1a. Label aforementioned guesses “forecasting” even though they don’t employ any standard forecasting model and are actually just rough guesses

2. Plug them in to get your C/I ratio.

2a. Also label this a “forecast” even though it’s made from the same wild guesses

3. Let Piketty play connect the dots to tie them back to the present.

3a. Plead ignorance of this, but accept its results nonetheless.

4. Ascribe an equilibrium convergence to the product of the above, ignoring that it lacks any innate stabilizing character and is only one of many possible results determined entirely by the wild guesswork undertaken in Step 1.

“Daniel seems to be taking the assumptions Piketty used as if they are fixed ”

Never said it. Not ever. Not once.

If the assumptions are not fixed, then the 700% is not an “equilibrium” but a product of those forecasting assumptions. Is that what you believe now?

It seems like there are two “equilibriums”: an equilibrium savings rate, which is pulled out of thin air(???) and an

impliedequilibrium Capital/Income ratio,giventhat equilibrium savings rate.But again, looking at figure 12.4, it doesn’t look like the rate of increase is decreasing as fast or as continuously as it should if it’s converging on 700%.

BTW, Daniel, I just realized, .1/.015 = 6.6 repeating, not 7. This seems like even stronger indication that the function used to create the graph isn’t converging to Piketty’s beta, it’s already about there and has a significant positive slope.

Just under 7 is what he says and as I noted above the long run g is just under 1.5 putting beta somewhere above 6.666.

Ya 2100 value in the chart s 667% which is 0.1/0.015.

Piketty’s referenced equilibrium is a theorized global convergence in the savings rate. He supposes this will happen around 2180 at 10%. The 667 is NOT an equilibrium onto itself, but a product of that savings rate plus another contingent assumption of what world output will be in 2100. If we simply change the assumptions around (say savings converges at 15% instead, or a different growth in output), we could literally set it at any number we want for the resulting C-I ratio…which further affirms that it’s not an equilibrium =)

re: “The 667 is NOT an equilibrium onto itself, but a product of that savings rate plus another contingent assumption of what world output will be in 2100.”

I assume you mean growth rate, not output itself right?

Yes – it’s the equilibrium product of those parameters. Beta=s/g

Actually Daniel, if you look at his spreadsheet he is using an estimate of world output in 2100 to get to the rate of growth and calculate his world C-I ratio, so it is ultimately contingent on an assumption about where world output will be in 100 years. An equilibrium requires stability. Simply plugging in wild guesses does not yield stability, as changing any of them even slightly can dramatically alter the result.

re: “Actually Daniel, if you look at his spreadsheet he is using an estimate of world output in 2100 to get to the rate of growth and calculate his world C-I ratio”

Hence, “I assume you mean growth rate”

The actual level of output doesn’t enter into beta.

re: “An equilibrium requires stability. Simply plugging in wild guesses does not yield stability, as changing any of them even slightly can dramatically alter the result.”

You are confusing the equilibrium value of beta with our estimate of the equilibrium value of beta. The latter is of course just an estimate.

I predict that the dispute between Phil and Daniel will tend to infinity as the year approaches 2100.

As this discussion is rapidly descending into a semiotic dyslexia of Kuehnian pedantry, I’ll simply note:

1. Future world output is one of the (very) few things in Piketty’s spreadsheets even approximating a regular forecast. As his highly variable growth rates are derived directly from this forecast, that rate and the calculation derived from it is directly contingent on his output prediction, which is what I stated.

2. Daniel previously and repeatedly asserted that a stabilization occurs at Piketty’s specific 100 year forecast of a 700% C/I ratio. Above this was described as a “convergence” at 700%. On a related blog post, he asserts that it “will level off at around 700%.” It is therefore only reasonable to interpreted as an ascription of equilibrium characteristics to Piketty’s specific estimate.

3. Since that estimate is wholly contingent on the aforementioned guesses about the savings rate & world output 100 years from now, calling that an equilibrium is absurd on a number of counts. Why 2100 and not 2050, when the same formula would presumably apply? Why not a growth rate of 3%? Why not a global convergence around a savings rate of 12%? Bottom line: there is nothing innately stabilizing about the year 2100 or Piketty’s estimated C/I ratio in that year, and to assert otherwise is to both misunderstand what he’s doing to achieve his projection and attribute an equilibrium claim to him that he did not in fact make.

4. The lack of a declining slope in the decade before 2100 also strongly suggests that Piketty is not attempting to show a convergence at the point that Daniel repeatedly claimed. Rather, Piketty is simply forecasting where he thinks the ratio will be in a century. Piketty’s book – to its rare credit – openly acknowledges this ambiguity in ways that Daniel’s original comments, at least, did not.

5. What I actually believe we have here is this: Daniel, by way of the aforementioned affliction of semiotic dyslexia, misread Piketty’s reference to a theorized global convergence in the savings rate at about 10% (a plausible but not airtight claim) as a theorized convergence around his Figure 12.4’s *particularized* end point. In doing so he ascribed equilibrium conditions to that end point that Piketty himself never claimed. In the ensuing conversation, that original particularized claim has morphed into an ascription of a general equilibrium to Piketty’s 2nd law on account of a passing theoretical reference to it as such – qualified by an admission that this equilibrium characteristic is never realized in practice – at an earlier point in Piketty’s text, though also one that does not assert the particularized stabilization claim about 700% in the year 2100 that Daniel originally and mistakenly attributed to Piketty’s text.

The primary remaining question is therefore whether Daniel still believes that 700% (or 667, if we go by the exact calculations on the figure) is a particularized equilibrium convergence point for Piketty’s C/I ratio. If he does indeed believe this, it is fair game to then ask (a) how he reconciles this convergence with the strong positive slope immediately preceding it, (b) why this convergence occurs in 2100 and not 2050 or 2150 or any other date, (c) why this convergence occurs at the savings rate and world output levels Piketty uses for 2100 and not any other possible level, and (d) what theorized characteristic explains the predicted future stabilization of the world growth rate – a figure that has historically exhibited fluctuation – which would be necessary for the claimed future C/I stabilization to occur, either in its particularized form in 2100 or at any other future moment.