This happened yesterday:

Then this:

And you can read the rest of the conversation from there (it was actually quite civil), but for the purposes of this post, it brought me back to the Piketty Simulator I ginned up a little while back to test Piketty’s second law, and I expanded it. And what do you know – Hendrickson is roughly 50% right. And figuring out exactly why gets at the heart of Piketty’s project. Check it out:

Piketty Simulator

So if you open up the spreadsheet and play with it yourself – and you should! spreadsheets are fun! – you should know a few things. Firstly, continuing my stated opposition to grecoscriptocracy, I have changed Piketty’s alpha and beta, the capital share of national income and the long-run equilibrium capital/income ratio, to the Hebrew aleph (א) and bet (ב). I have also created a new variable of interest, which I assigned the Hebrew gimel (ג), which we’ll get to a bit later.

In the spreadsheet, you can set initial conditions of the following five variables – the initial levels of capital and national income, and Piketty’s r, s, and g – the return on capital, the savings rate, and the growth rate. The spreadsheet then tells you a few things, both over the course of three centuries (!) and the long-term equilibrium.

Firstly, it tells you א and ב. Secondly, assuming invariant wealth shares, it tells you the share of national income that goes to the “rentier class” given any given wealth share.

The other thing it tells you, which is key to the first part of this discussion, is ג, which can be best defined as the capital perpetuation rate; it is the percentage of the “r” produced by capital that needs to be saved in order to maintain the existing ב. It can be defined, and derived, in two ways. The first is g/r, which is intuitive; it can also be derived as s/א, which may be less intuitive, but it also really important. Because it shows both why Hendrickson is wrong and why he was right.

The key to Hendrickson’s point is that is really important to the inequality path. Which is correct! But the other point is that inequality can, and will, rise regardless of s so long as r>g and Piketty’s big assumption is true. More on the latter later, but play with both math the simulator first.

The math first - s/א is a clear way to derive ג: it’s the ratio of the share of national income devoted to capital formation divided by the share of national income produced by existing capital. But if you decompose it (fun with algebra and spreadsheets in one post – I’m really hitting a home run here) you’ll see that since א=r*ב and ב=s/g then you’ve got in the numerator and the denominator and it cancels out. That’s why I put both derivations of ג - ג and ג prime – in the spreadsheet; even though one is directly derive from the savings rate, you can change s all you want and ג remains stubbornly in place. Other things change, but not ג.

This is important because it decomposes exactly what Piketty is getting at with his r>g inequality. Essentially, there are two different things going on. One is the perpetuability of capital, the other is the constraint on capital-driven inequality. As you change in the spreadsheet, you’ll see that the rentier share of national income changes accordingly as the long-run ב increases; you’ll also notice that “rentier disposable income” changes accordingly. Hey, what’s that? It’s the amount of income leftover to rentiers after they’ve not only not touched the principal but also reinvested to keep pace with growth.

And indeed, you’ll see if you change and g that as they get closer and closer, regardless of  how large the capital to income ratio is the rentiers need to plow more and more of their returns from capital into new investment to ensure their fortunes keep pace with the economy. Indeed, if r=g, then rentiers must reinvest 100% of their capital income or else inexorably fall behind the growth of the economy as a whole.

In summary, Piketty’s r>g is telling us whether the owners of substantial fortunes – think of them as “houses,” not individual people – can maintain or improve their privileged position relative to society as a whole ad infinitum. Given and gs tells us how privileged that position really is. Even with a 50% savings rate (!), if g = 4% while r = 5% then even though a rentier class that owns 90% (!) of national capital captures 56% of national income, they can only dispose of just over 11% of national income or else they will be slowly but surely swallowed into the masses. On the other hand, if s = 6%, fairly paltry, but g is only 1% relative to r‘s 5%, then rentiers only capture, initially, 22.5% of national income; but they can spend 18% and still maintain their position; if they spend just the 11% above, they can start increasing their already very privileged position (though this model doesn’t account for that).*

So Hendrickson is both right – you need to incorporate s to compute the long-run inequality equilibrium, while also wrong in that, so long as we’re not yet at that equilibrium, r>g can and, at the very least likely if not necessarily inevitably, produce rising inequality. So while the share of national income that goes to creating new capital limits the ability of capitalists to increase their capital income to the point where it truly dominates society, so long as r > g, they not only need never fear of losing their position, but also through careful wealth management and, defined very relatively, frugality, expand it over time, at least until they hit the limit defined by s.

But therein lies the rub. All these simulations, which echo Piketty’s work**, operate from a central fundamental assumption that, if altered, can topple the entire model (both Piketty’s and mine) – that r, s, and g are exogenous and independent. Now, Piketty himself doesn’t exactly claim that, but he does claim (both in Capital and in some of his previous, more technical economic work) that both theoretically there are many compelling models in which they largely move independently, especially within “reasonable” ranges, and in practice these values have been fairly steady over time and that changes in their medium-to-long-term averages, to the extent they are interconnected, have sufficiently low elasticities that, for example, r (and therefore א) decline slower than ב increases and therefore the dominance of capital increases. He derives this a little more technically in his appendix on pgs. 37-39, and discusses it in his book around pages 200-220; you can also check out this working paper to show how a production function with a constant elasticity of substitution > 1 can not only theoretically produce a model consonant with his projections but also matches the trend in Western countries over the past few decades.

These assumptions in many ways cut deeply and sharply against a lot of different assumptions, theories, and models about the economy that many people hold to, advocate for, and have a great deal of influence. And demonstrating conclusively or empirically how related they are can be maddeningly circular and also ripe territory for statistical arcana that most people don’t understand and, as Russ Roberts has pointedly noted, even those who do don’t really find convincing. But fundamentally, if you believe that r, g, and s are sufficiently independent and exogenous, you can view income distribution as a largely zero-sum game set by systems that states can to a substantial degree alter without changing those values; but if you view them as connected in vital feedback loops, you may be loathe to tax r for fear of depressing s and thereby depress g; your game is negative sum, not zero. How you view this bedrock question, a question hard to resolve conclusively through either theory or empirics, is going to determine a lot of what you take away from Captial.

*I’d love to create a model that shows variant rentier shares of national wealth and national income over time, but that’s not for this post, at least.

**One thing Piketty doesn’t stress but this spreadsheet makes clear is just how long the processes Piketty describes take to play out. Given the default society I plugged into the spreadsheet – r=5%, s=12%, g=1%, C=3, NI=1 – a rentier class that own 90% of total wealth, while projected to capture over half of national income in the long run, only captures ~14% initially; after 50 years, it is still capturing less than 30% of national income; and even after two centuries, it is still 6% of national income short of it’s long-run equilibrium, which is quite a bit. Obviously expecting fundamental aspects of society to be invariant for that long in our post-industrial world is probably very unrealistic, but it gives you a sense of the scale of the dynamics this book is grappling with.

So Tom  Kludt, totally inadvertently, laid down a challenge yesterday afternoon:


Faced with a challenge, I responded the only way I knew how – comprehensively and a little cantankerously:


As you can see, the chart speaks in many ways for itself – from 2-6% of wideouts rocking a 1X on their back from ’99-’03, the percentage skyrocketed at nearly 20%, or 5pp, each year since, hitting nearly 60% in the most recent season. And if you weight it by games played (I’m counting the playoffs), it’s similar if not even starker:

nfl wide receiver jersey numbers gw

Fewer than 3% of WR-games are played by guys sporting teens until ’04, when the number leaps to 9% and climbs at the same ~20%/5pp rate.

And, of course, Kludt, is right: Keyshawn is Patient Zero, being the only wideout to play a full season before 2004 with a 1X jersey.

What’s a little curious is that the quality of receivers wearing a 1X jersey is lagging behind the quantity. Below is a graph (since ’04 so we’re not just looking at KJ) of the percentage of total games played, catches made, yards acquired, and TDs caught by guys wearing a teen jersey:


So without getting too much into measuring football player quality, one would imagine that, if quality were equal, the share games played would be exactly equal to the share of the other major stats – but that’s not happening. With the exception of ’09, which was just TDs, in every year WRs with 1X jerseys are racking up slightly but consistently fewer catches, yards, and scores than their 8X counterparts relative to the number of games their playing. Why this would be, I couldn’t say, but there you have it. So when you’re drafting your fantasy team this year and you have no other way of deciding between two equal wideouts in the late rounds, go with the traditionalist.



Among the various fallout of Facebook’s odd consumption of Oculus is the growing notion that the various individuals who provided Oculus with ~$2.4mm in funding via Kickstarter in exchange for, well, stuff, but importantly, not equity, equity that presumably would have returned perhaps an order of magnitude more than its cost following Facebook’s purchase. The Times has the summary; Gamespot has the longer and more thoughtful musing; and Barry Ritholtz has the primal scream.

I’m going to go ahead and acknowledge #slatepitch here, but everyone complaining about this is, for the most part, wrong. Nobody was lied to or deceived. Everybody who pledged to the Kickstarter campaign signed a perfectly transparent contract exchanging their money for a concrete, well-defined deliverable, knowing full-well that “hey, maybe somebody who succeeds in designing a revolutionary improvement over existing VR helmets maybe has a big-dollar idea on their hands.” If the Ouya wasn’t a stupid idea and instead had been purchased by Apple or Roku or Amazon for billions (or even hundreds of millions) I’m sure we’d be hearing the same complaints, and they’d still be wrong. Even in the realm of “nominally transparent but fishy exchanges,” this falls well short of “old people paying subscription fees to AOL” or “Herbalife.”

Part of what is incensing people about this, crucially is the scale – crucially because it shows where the real injustice lies. There are, on Kickstarter, many projects to help “kickstart” people’s board game designs, music albums, and short films – should that board game then get picked up by Rio Grande, or that album picked up by XL, or that short film get a contract for expansion into a feature by The Weinsteins, well, isn’t that the point of Kickstarter? You help someone “kickstart” their project, and their dreams, to help them succeed at bringing some cool new creation into the world and hopefully leverage that success into a more-fulfilling career. And maybe that project, and their subsequent career, will be a more lucrative one then the more mundane pursuit they were engaged in before Kickstarter helped them find their break. And that’s OK! You didn’t ask for equity, you didn’t get it, you dig the board game or the T-shirt and life goes on.

But the investors in Oculus, collectively, just made two billion dollars.

And therein lies the real injustice. Kickstarter funders of Oculus may be thinking “hey, I pitched in to help you make a great idea happen, maybe even to make you personally financially successful, but I did not sign up to make you a billionaire.” But that gets us back to the real injustice – there shouldn’t be  billionaires! The fact that a twenty-something dude who figured out how to strap your parent’s basement to your face is now going to live a life of immense luxury, free of all wants and able to pursue any material dream, largely because another billionaire twenty-something thought “hey, I really want to wear my parent’s basement on my face,” is totally outrageous. But it only highlights the vastly deeper flaws in our current socioeconomic system, which allows and indeed catalyzes the accumulation of vast wealth by a tiny minority on relatively arbitrary bases. Nobody who gave to Oculus on Kickstarter is, or almost certainly will ever be, a billionaire. And many of them may and likely will in their lives face substantial economic hardship, hardship that would have been largely avoidable if we had a society committed to supporting the broad majority of people at the expense of the 0.1%. But right now we don’t have that society, and that’s the real injustice.

Ryan Avent had a fantastic post Tuesday dismantling the rationale of the Fed, and specifically Jeremy Stein, for basically casting macroeconomic improvement to the wind for the sake of ill-defined financial stability. If you read Ryan’s post you’ll see precisely why this is backwards and, indeed, as likely as not to backfire.

The relatively meager contribution I’d like to make to the discussion is simply this – if the Fed truly believes that financial instability, despite being wholly absent from their legal mandate, is sufficiently important to trade off other desirable outcomes to pursue, then they should pick a target. One of the better decisions the Fed has made in recent years is more openly and rigorously defining targets – specifically, clearly defining the thresholds in widely-available and transparent measures of unemployment and inflation that may lead the Fed, once crossed, to raise interest rates, and disclaiming any potential rate raises before then. If the Fed wants us to take their approach to financial stability seriously, they should pick a variable or index and a threshold value and announce it. Absent doing so, we’ll all have to wonder whether less rigorous impulses undergird the Fed’s eagerness to find new reasons to raise interest rates even as unemployment is high and inflation low.

Piketty cites two fundamental laws of capitalism. The first one is, truly, a law, and indeed as he says an accounting identity, but the second “law” is really more of a tendency. It suggests that the long-term path of the capital/income ratio (which he calls β but I’m going to call ב becuase we need notation diversity) is equivalent to the ratio of the trend savings rate and the trend growth rate (absolute, not per-capita, importantly). This is nothing Piketty doesn’t mention, but it’s worth stressing that this tendency can take a looooong time to manifest. A society beginning with a ב  of 1 and a trend savings/growth ratio – and thus a long-term predicted ב  - of 4 will take over a generation to build a ב  of 3; the same society with a trend savings/growth ratio of 6 will take over 80 years to surpass a ב of 5.

Anyway, if you’re the kind of nerd I am, you’ll want to play around with the formulae too. Spreadsheet attached; enjoy.

capital 2nd law convergence

Piketty says something in a way that sounds like he takes it, as so many do, as axiomatic:

“…growth always includes a purely demographic component and a purely economic component, and only the latter allows for an improvement in the standard of living.”

The nit I’d like to pick with this received trusim is marginal relative to its broad accuracy, but is still worth noting – there are economies of scale to absolute population. These manifest in two interrelated ways – consumption and investment choices that are only “unlocked,” if it were, when total population crosses certain thresholds, and future per-capita-growth that results from past choices that were contingent upon absolute population.

I can illustrate these by giving three examples – one purely the former, one purely the latter, one a mix.

A purely “unlocked” choice would be a more specialized service that could not achieve scale relative to fixed costs without a large enough absolute population given a fixed share of population interested in the service. Think “shop that only sells customized meeples” or more conventionally “Latverian restaurant.” This doesn’t affect to the level of per-capita income or output, now or in the future, but improves living standards by providing a greater diversity of quality consumption options.

A purely future-oriented choice might be an aircraft carrier. Today, nobody benefits. But in the long term, if an aircraft carrier in the most optimistic framing maintains peace, security, and a stable order, this allows for greater per-capita growth (and fewer destabilizing interruptions) in the future, though in the present it registers as output that brings little utility to the public at large. Obviously two things must be noted –  military investment does not always increase peace, security, and stability; and even assuming it does, there are many, much more cynical, interpretations of how military power projection leads to future per-capita growth for the projectors.

A mixed choice would be cet bruyant objet du désir, a large subway system. It both increases consumption options and quality available to present individuals – lots of people prefer riding trains! – while also being an investment that increases long-term per-capita-growth rates.

This is not the most important point in the world, but since Piketty made it I found it a good time to quibble with it.


I’m getting into the good stuff in Piketty’s 2001: A Capital Odyssey and will have plenty to blog about; in the interim, though, I did a little research of my own. I was digging into CPS data for other reasons and figured, “hey, look, there’s questions about capital income!” So I quickly crunched the numbers on whether, not how much (which is top-coded anyway), American households claim positive gross capital income, by year. And lo and behold:

capital income includes rent


The fraction of American households claiming any gross capital income has declined substantially since Wall Street, from just over two-thirds in the late ’80s to just under half today. There is a hiccup, which is that the rent question asks net of expenses, but if you exclude rent and just examine dividends and interest you get a close-to-identical response.

capital income excludes rent


What’s more remarkable is the uniformity of the trend – while both the levels and the rate of change differed from state to state, every state saw a decline, and almost every state saw the same pattern of steady decline the nation as a whole did. The below chart shows the total percentage-point decline from ’88-’13 in each state:

decline by state


Quick note on Wyoming: the disparity between the two measures is due to one funky data point, in which 2013 capital income jumped 22 percentage points from 2012 to 2013. Included for rigor’s sake, but I’d be surprised if that wasn’t just a blip; otherwise, Wyoming’s trend is very similar using both measures. Also, Alabama is a slightly odd case, as it seems to be the only state that saw a sustained period of increase, from around 45% to 55% in the first decade, and down to below 40% after. Also worth noting that decline isn’t correlated with levels:

capital income level by state


Anyway, more evidence for the concentration of capital ownership! Hooray!


“To put it bluntly, the discipline of economics has yet to get over its childish passion for mathematics and for purely theoretical and often highly ideological speculation, at the expense of historical research and collaboration with the other social sciences. Economists are all too often preoccupied with petty mathematical problems of interest only to themselves. This obsession with mathematics is an easy way of acquiring te appearance of scientificity without having to answer the far more complex questions posed by the world we live in. There is one great advantage to being an academic economist in France: here, economists are not highly respected in the academic and intellectual world or by political and financial elites. Hence they must set aside their contempt for other disciplines and their absurd claim to greater scientific legitimacy, despite the fact they they know almost nothing about anything.”

Thomas Piketty, Capital in the 21st Century

This post from CAP alum Zaid Jilani on the RT-ness of CAP has been making the rounds lately. before I say anything further I do want to emphasize that it took no small amount of courage to make these kinds of disclosures about his former employer and that kind of courage (assuming the disclosures are true) is to be commended.

But methinks his conclusion – in which RT stares deeply into CAP’s eyes and says “We’re not so different, you and I” – is at once too naive and too cynical.

Institutions are institutions. They have processes; they have hierarchies; they have external pressures; they have revenue sources to maintain. To some extent, indeed, they are all alike. In this way no media institution is truly “independent” and in this way of course CAP is like RT.

But in so many ways that matter CAP is totally unlike RT. RT is propaganda. RT spews a steady stream of distortion and untruth. CAP doesn’t! There may be internet conflicts between ideological progressives and politically-minded institutionalists but to use the beleaguered football field metaphor, they’re fighting between the 40 yard lines while RT is in the red zone. CAP was fighting over how strenuously to stress a difference with a President over war; RT’s position is, automatically, Putin’s position, 100%, always.

One of the best posts I’ve ever written was this one, about how differences in degree become differences in kind. Comparing CAP to RT makes a point about the nature of institutions, but it’s a much shallower one than Jilani thinks it is, and it obscures the differences and those are actually the more important part.

When I read Erik Kain’s post yesterday about how the Ouya has essentially failed, my immediate response was “well, of course, the video game industry is drawing dead.” Let me explain what I mean.

When technological innovation leads to a new product class that catches in, there is an initial phase called the adoption phase which is characterized by large and rapid growth, continued innovation, and something of a mania around the product and industry. We saw that with video games in the ’90s.

But when an industry becomes mature, sales plateau as the product becomes a more banal part of everyday life and the mania generally declines. This can sometimes be wrenching for an industry, especially since what worked before no longer works now. They may fail to realize that no amount of innovation can change the total magnitude of the industry relative to life in general, just compete within the bounds of that magnitude. Firms whose models were built implicitly around a continuation of the adoption phase will fail.

To give you a concrete example, here’s car sales per thousand souls in the US since Ted Turner bought the Braves:


Beyond the extreme sensistivity to business cycles, what you see is that, despite the fact that the quality improvements in American cars since the days of Nader’s Raiders has been extraordinary in safety, comfort, fuel efficiency, pollution mitigation, and other cool accessory features, it hasn’t convinced Americans to buy more car overall. This pattern is clearly taking hold in the video game industry:

Screen Shot 2014-03-08 at 8.00.29 AM

Now, let’s be a little clear here – mobile gaming has done a lot for the category of industry we’re calling “video games.” But that’s because it expanded the boundary of what video games were, not because it convinced people to spend more time playing what, up through 2007-08, we referred to as “video games.” My mother plays plenty of Candy Crush Amazing Epic Super Saga: Incredible Journey of Candy Gilgamesh or whatever but that hasn’t convinced her to take up Halo (though the image of my mother pwning and trash-talking on XBox Live is pretty hilarious). In a sense, this growth is illusory insofar as you are considering the growth of console and PC gaming. That’s really clear when you look at this:

Screen Shot 2014-03-08 at 8.00.56 AM

Video games, methinks, have entered the phase in their life where they are no longer stealing American hours from other activities; indeed, if anything, the rise of Netflix, board games, and some backlash against video games probably means equilibrium per-capita video game hours will end up settling at a lower number than they currently are. The Ouya was implicitly premised on the idea that it wasn’t competing with existing consoles; it wasn’t doing what they were doing better or differently, it was trying to convince people to do something new. But for most people, if they weren’t playing video games, they were just doing something else. The Ouya was drawing dead because video games are drawing dead. That doesn’t mean the industry is going to implode; it just means its moved on to fierce competition for limited market share rather than explosive overall growth.

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