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It seems like discussion of Piketty’s Capital has run its course and much of the commentary has moved on (though not necessarily from the broader topic) so now is as good time as any to peer back and reflect on how the debate around the book ended (if such a thing can be summarized). From my own vantage point, the debate about the book (not necessarily the discussion) stalled out around a single question, so I will do my best to restate and clarify that question so as to focus where more evidence and argument is needed, should this be a conversation anyone wishes to resume. None of this is new, exactly, but it’s worth recanting given the importance of the question and the stakes surrounding it.

Around 1800 AD, living standards in some countries began to rise substantially, and over the past 200 years, that rise (as measured in GDP per capita) has been on the order of a factor of 50. This generally seems to correlate with other indicators of increased living standards to a degree that, with some exceptions (such as thinly-populated resource-rich countries) it is generally, though not universally, accepted practice to use GDP per capita as a good-enough shorthand for broad living standards. Whatever the case, exactly how and why this increase transpired is still a matter of debate, in no small measure because most people would find it desirable to replicate the phenomenon in those areas that have not yet experienced it. Indeed, some countries that did not begin experiencing the phenomenon in its initial emergence have experienced it since, leaving, essentially, three groups of countries – those who have experienced it, those who have not, and those in transition.

Piketty’s book, while not exclusively, overwhelmingly is focused on the first kind of country. A compelling portion of his narrative is documenting that transformation, yet the broader focus of the book is on what has transpired since that transformation was consolidated in the era following the Second World War. There are two key factors to be documented. The first is that the countries that have fully experienced this transformation are themselves not ‘complete’ in this regard – average living standards (recent economic troubles excepted) continue to rise and are generally, though not universally, expected to continue to rise in the absence of extreme calamity on the scale of global catastrophic climate change. The second is the change in the distribution of income – since a moment of ‘peak equality’ in roughly 1970, most of the countries Piketty analyzes have seen a sharp increase in inequality, the specific degree of which dependent on method of measurement but whose general contours is not really disputed. This, Piketty and many other believes, poses a problem for these countries that is not alleviable solely by continuing increases in average living standards or aggregate wealth and income growth.

Piketty devotes a lot of space to developing a simple model of how the aggregate quantity and distribution of capital can drive income inequality. This remarkably simple model requires only three input variables – the growth rate of the economy, the average return to capital, and the savings rate (perhaps better phrased as the rate of capital formation relative to national income) – to generate a long term prediction of two key ratios: the ratio of capital to income, and the capital share of national income. From there, wealth inequality can be used directly to compute a floor on income inequality – for example, if 1% of the population owns 50% of the national wealth and the capital share of income is 30%, then that 1% captures, at a minimum, 15% of national income.

And here we arrive at the crux of the debate. Piketty’s model implicitly assumes a certain exogeneity between those three input variables and the two ratios they converge towards, ie, that they are not inherently correlated with each other. This exogeneity poses a fragility in Piketty’s model and a challenge to mainstream economic theory. The fragility is that, if they are strongly correlated (in the direction such correlation is expected), and especially if there is iterative feedback between them over time, then Piketty’s model no longer produces outcomes in which wealth inequality drives income inequality. The key example here is the average return to capital; were it to fall in proportion to the rise of total capital accumulation, then the capital share of national income would be invariant to the quantity of capital, and thus largely undermine the mechanism by which present wealth inequality drives future income inequality. Furthermore, were this anticipatable decline in the in return to capital to drive a decline in savings, the capital/national income ratio would converge at a substantially smaller value than that projected by extrapolating from the initial period. This further depresses the likelihood of ever-increasing wealth-driven income inequality.

This is also precisely the challenge to mainstream economic theory. These correlations and feedbacks are precisely what are predicted by fundamental, strongly-held ideas about economics held by economists; most centrally that investment behavior is driven by that most central economic force, supply and demand. Piketty, however, is not simply laying down an alternative model, but an empirical challenge to this challenge. The most crucial assertion made by his model – that the return to capital fails to decline in proportion to the supply of capital – is not simply a theoretical alternative but one derived from the meticulously researched and calculated estimates in his unprecedented data. As I myself pointed out in my write-up of Piketty’s book, the data show that the return to capital is sufficiently resilient to its accumulation to justify Piketty’s model. At least, that is, without controlling for any additional factors.

And here is where debate stalled, with one side asserting that theory demands these variables be tightly correlated, and the other side responding that empirics demonstrates that they are not. The problem, of course, is that macroeconometric panel empirics is extremely sensitive to model specification, to the point of being perhaps the perfect example of how any decent statistically-versed researcher with strong priors can generate the outcomes from the data they which to receive. Certainly it is more than possible to generate a superfluity of complex models demonstrating the theoretically-predicted correlations, and these models will collectively have zero persuasive power because it is trivially easily to create as many or more equally-plausible equally-complex models that demonstrate the obvious.

Why does this all matter, to the degree it’s worth recounting in such detail to the tune of a thousand words? Because it strikes directly at the heart of the most important argument for tolerating high income inequality.

There are basically three arguments in favor of tolerating high income inequality, which I will attempt to summarize as fairly as I can.

  •  The ‘Just Deserts’ Position: incomes reflect the inherently just outcomes of markets. Beyond a certain threshold to prevent the worst form of miseries, it is therefore a violation of justice to take from the deserving and distribute to the undeserving.
  • The ‘Pink Salt’ Position: income inequality is irrelevant except to the irremediably envious, resentful, or spiteful. What matters is preserving and increasing human happiness, which is largely driven by civil liberties, non-market institutions such as family and community, and the secondary impacts of economic progress.
  • The ‘Golden Egg’ Position: income inequality may be ceteris paribus bad but aggregate economic growth is extremely good to a degree that in most plausible scenarios swamps income inequality. Furthermore, income inequality and economic growth may be conjoined outcomes of our economic system and cannot be modified independently. Therefore, we should be extremely cautious about attempting to alleviate income inequality through policies that slow the rate of economic growth, as this may reduce not just aggregate utility but the utility of those benefiting directly from redistribution.

It will shock nobody to hear that I reject outright the first argument in the strongest possible terms, and the second in quite strong terms as well. Indeed, I believe that the majority of Americans, and certainly the majority of voters in developed countries, disagree with those arguments as well. It is that third argument that gives pause to many – including, to a degree, me (though that pause is still far from convincing in my own case). The average person living in a developed country today as compared to a person living in that same country in 1800 is vastly better off, and it is not impossible to imagine that the average person living in a developed country in 2100 will be vastly better off than that average person today. Impeding our shared progress in that regard could simultaneously defer developments that improve the quality of most lives while simultaneously deferring developments (like innovation in renewable energy sources and storage) that could mitigate or reverse the worst consequences of economic growth to date.

This all converges on something of an ironic surprise. In this debate, it has been the left that has been advocating, implicitly or explicitly, on behalf of the resilience of capitalism (broadly defined) and its ability to deliver human prosperity, whereas it has been the right that has claimed, implicitly or explicitly, that capitalism and the prosperity it delivers is fragile, so much so that even increasing post-market redistribution (as opposed to pre-market regulatory redistribution through minimum wages, stronger protections for unions, and abridging the current rights and privileges of lenders and shareholders) could, to use a tired aphorism, kill the goose that lays the golden eggs. This ideological positioning isn’t wholly novel, and whether it is instrumental and ephemeral or representative of something larger remains to be seen; but it is notable, and worth pondering for what it says about the state of both the contemporary mainstream left and right movements in the United States (if not beyond).

stewie "david ricardo" griffin

Linking to Dylan Matthew’s generally-excellent piece on the correct way to manage one’s personal finances, Matt Yglesias says “stocks are on average a much better long-term investment than houses.”

This, of course, is an increasingly common view in the “internet wonk community” (one I consider myself an member of), distinct from the related and equally-prevalent view that ‘homeownership should be much less subsidized than it it now.’

This is also a view I take issue with, which you’d already know if you read my big Piketty #thinkpiece – you read my big Piketty #thinkpiece, right? right? – and one that I think needs a little elucidating and defending in detail.

There are three basic reasons that buying a house is a vastly better investment than current wonkpinion suggests. The first is that making large leveraged investments can pay off hugely even if the underlying growth rate of the purchased asset is slow. Let’s demonstrate.* Let’s take an average American buying an average house in an average way – $200,000 purchase price, 20% down, 4% closing costs, 5% interest rate. Now let’s say the value of that house grows reeeeeeeally slowly – just 0.3%/year, which just so happens to be the compounded annual growth rate of the Case-Shiller index since 1947.

If our average American sells their house after 10 years, their initial $48,000 equity investment will become $67,691.08 – which means their equity grew at a CAGR of 3.5%! If they sell after 15 years, they’ll net $92,209.57, which is a CAGR of 4.45%. Hey, that’s a lot higher than the 0.3% growth rate of the house’s price itself, isn’t it?

It sure is! The amazing power of leveraged investments is that you can turn a little bit of equity into a large return, as Matt Yglesias notes concisely here. Here, in fact, is a nice little graph demonstrating the implied return rate of selling your house after making regular mortgage payments for a given number of years, given the interest rate paid, assuming that meager 0.3% growth rate:

n33ds m0Ar l3vr1j

After 13 years, you’ll get a 3% return even at a very high interest rate; at 19 years, you’ll get a 4% return. In fact, you can assume zero growth and still get a substantial return on your initial investment – as long as you don’t count the regular payments on the debt.

Hey, what about the regular payments on the debt?

Good question! This brings us to my next two points. Because if leveraged investments are so awesome, why don’t we empower (and perhaps subsidize) average people to make large leveraged investments in stocks, which have a much larger underlying growth rate? Beyond all the other problems with that idea (not that nobody has pitched it), the thing about a house is that it has an unusual counterfactual. If you buy stocks with leverage, in theory the payments on the debt should come out of your savings, creating a counterfactual of simply saving and investing that money. But the counterfactual to owning is renting. This creates some curious conditions that lead to my next two points in favor of buying a house – inflation protection and subsidies.

There is obviously some connection between the purchase price of a house (and therefore the amortized monthly payment on the mortgage) and the rent it could fetch – regardless of where you fall on the capital controversy that dare not speak its name, there must be some fundamental link between the price of an asset and its expected returns. However, a mortgage is detached from the imputed rent (the flow of sheltering services) a house delivers, and therefore is nominally frozen in a way that rents are not. So therefore even if a mortgage today is substantially more expensive than the rent payment on an equivalent housing unit, in thirty years even very low inflation will change that drastically. Just 2% average annual inflation entails an 80% increase in the price level over three decades, meaning the annual mortgage payment declines by nearly half over that time. Rent, in the meantime, keeps going up (except in rare cases which can entail its own problems), at least as fast as inflation. Therefore even a mortgage whose monthly payment is more expensive than a rent payment today will be much cheaper than renting in a few years.

Aha, you might say, but there is a problem with this – the magic of compound interest means that the difference-in-monthly-payment savings accrued today by the renter will be much more valuable in retirement than the parallel savings accrued years from now by the owner. This is true! But that’s where the subsidies kick in. Our primary national subsidy for homeownership is to allow mortgage-payers to deduct the interest portion of their payments from their income – and the amortization structure of mortgages means the share of payments comprised of interest are highest right when the mortgage begins, and declines until the loan expires:

interest on your interest

This benefit comes when “housing” costs – really, housing-purchase-debt costs – are at their highest, also because earlier in life is when incomes are their lowest. It is difficult – very difficult – to defend the home mortgage interest deduction as currently structured, as such a large portion of the benefit goes to such a small and disproportionately well-off group. It is worth considering, though, whether the idea at the core of the program is sound. And either way, whether you think we should have them or not doesn’t mean that you don’t consider them when considering what constitutes a good investment under the status quo.

Of course, I haven’t even touched on imputed rents once a house is fully-owned (or, conversely, actual rents), which are of course the most important return to a house, well beyond the capital gains discussed heretofore. But this leads to the most important conclusion: not that houses are such a great investment per se; just that they’re a great investment for people without a lot of capital because of their unique pathway to leverage. If you had half-a-million dollars, should you buy a house (or apartment) to rent or a portfolio of financial products? Almost always the latter. But if you only have an order of magnitude less than that to your name, it may make sense to buy something with a lower return (not to mention wholly undiversified) because you can lever up. Just another way that large capital concentrations can secure higher returns – or at least exercise more freedom of action.

Spreadsheet, as always, attached – calculate your own expected returns on your housing investment!

House Investment

*All of these numbers are real and net-of-depreciation unless otherwise noted.

I’ve been working on collecting some longer thoughts on Piketty’s book now that I’ve finished it (so yes, keep your eyes open for that) and in the meantime I’ve been having fun/getting distracted by playing around with his data, and especially the data from his paper with Gabriel Zucman, which, you know, read, then play too.

One thing I realized as I was going through is that Piketty and Zucman may have incidentally provided a new route to answer an old question – were America to at last make reparations for the vast and terrible evil of slavery, how much would or should the total be?

What is that route? Well, they provide certain annual estimates of the aggregate market value of all slaves in the United States from 1770 through abolition:


As you can see, the amount was persistently and stunningly high right through abolition.

Now, without wading too much into heck who am I kidding diving headfirst into the endlessly-resurrected Cambridge Capital Controversy, the price of capital is determined in large part by the income it generates; so the market value of an enslaved person was an implicit statement about the expected income that slaveholders receive from the forced labor of their prisoners. So we can (by imputing the intervening annual values in their time-series, which I did linearly, which may not be a great assumption but it’s what I did so there it is) compute the real aggregate dollar market value of slaves from 1776-1860, then impute the annual income produced by, and stolen from, America’s slaves. For that, I used 4%, being conservative with Piketty’s 4-5% range.

Then you have two more steps: firstly, you have to select a discount rate in order to compute the present value of the total of that income on the eve of the Civil War in 1860; then you have to select a discount rate to compound that through 2014.

Well, that’s where things get interesting. For now, let’s pick 1% for both of those discount rates (which I am doing for a reason, as you will see). That makes the value in 1860 of all the income stolen by the Slave Power since the Declaration of Independence said liberty was inalienable roughly $378 billion*. That $378 billion, compounded at 1% annually for 154 years, is worth just about $1.75 trillion.

But those discount rates are both low – really, really low, in fact. Lower than the rate of economic growth, the rate of return on capital, and lower than the discount rate used by the government. When you increase those discount rates, though, you start to get some very, very, very large numbers. If you increase just the pre-1860 discount rate to 4%, for example, the 1860 figure leaps to over a trillion dollars, which even at a discount rate of 1% thereafter still comes to well over four-and-a-half trillion dollars today. Even vaster is the increase that comes from increasing the post-1860 rate, even if you leave the pre-1860 rate at 1%. At 2%, today’s bill comes due at just under $8 trillion; at 3%, $35 trillion; at the government’s rate of 7%, it comes to over $12.5 quadrillion. That’s over six times the entire income of the planet since 1950, a number that even if we concluded it was just – and given the incalculable and incomparable horror of slavery as practiced in the antebellum United States, it’s difficult to say any amount of material reparation is adequately just – is in practice impossible to pay.

There are three conclusions I think are worth considering from the above analysis:

1) First and foremost, slavery was a crime beyond comparison or comprehension, since compounded by our collective failure to not only to make right the crime as best we are able but to not even make the attempt (not to mention Jim Crow and all the related evils it encompasses).

2) Compound interest is a powerful force. Mathematically, obviously; but also morally. These large numbers my spreadsheet is producing are not neutral exercises – they are telling us something not only about the magnitude of the grave injustice of slavery but also the injustice of failing, year after year, to begin to pay down our massive debt to those whose exploitation and suffering was our economic backbone. And that only refers to our material debt; our moral debt, although never fully repayable, grows in the absence of substantive recognition (or the presence of regressive anti-recognition).

3) Discount rates tell us a lot about how we we see our relation to our past and our future. The Stern Review, the widely-discussed report that recommended relatively large and rapid reductions in carbon emissions, became notable in good part because it triggered a debate about the proper discount rate we should use in assessing the costs and benefits of climate change policy. Bill Nordhaus, hardly a squish on the issue, notably took the report for task for using a very low discount rate – effectively, just over 1% on average.

It is hard to crystallize precisely the panoply of philosophical implications of how discount rates interact differently with different kinds of problems. In the case of climate change, a low discount rate implies that we today should place a relatively higher value on the costs future generations will suffer as a consequence of our activity, sufficiently high that we should be willing to bear large costs to forestall them. Commensurately, however, a low discount rate also implies a lower sensitivity to the costs borne by past generations, relative to the benefits received today. High discount rates, of course, imply the inverse in both situations – a greater sensitivity to the burden of present costs on future generations and the burden of past costs on present generations.

There is no consensus – and that is putting it lightly – over what discount rates are appropriate for what situations and analysis, and whether discount rates are even appropriate at all. And when we decide on how to approach policies whose hands stretch deeply into our past or future, it is worth considering what these choices, superficially dry and mathematical, say not just about inputs and outputs, but also the nature of our relationship to the generations that preceded us and those that will follow.

Data attached:

piketty slave reparations

*2010 dollars throughout.

So late last year Matt Yglesias found a simple and concise way to create a good-enough estimate of the value of all privately-held American land, using the Fed’s Z1. He did not, however, go on to take the most-obvious next step, which was to use FRED to compile all the relevant series to calculate the entire time-series.

I have taken that bold step. Behold – the real value in present dollars of all privately held American land since FY 1951:

it's good to have land

Oh, look – a housing bubble!

But because this is the Age of Piketty, why stop there? Thanks to the magic of the internet and spreadsheets, all of the data Piketty relied on in his book is freely available – and perhaps even more importantly, so is all the data Piketty and Zucman compiled in writing “Capital is Back,” which may be even more comprehensive and interesting. So using that data, I was able to calculate land as a share of national income from 1950-2012. Check it out*:

 this land is my land; it isn't your land


Oh look – a housing bubble!

And why stop there? We know from reading our Piketty that the capital-to-income ratio increased substantially during that time, so let’s calculate the land share of national capital:


image (5)

Oh look – a…two housing bubbles?

It’s hard to know what to make of this at first glance, but after two decades steadily comprising a quarter of national capital, land grew over another two decades to nearly a third of it; and after a steep drop to under a fifth of national capital in less than a decade, just about as quickly rebounded, then plummeted even faster to under a fifth again.

So the question must be asked – why didn’t we notice the first real estate bubble, just as large (though not as rapidly inflated) as the first? There are two answers.

The first answer is – we did! Read this piece from 1990 – 1990! – about the “emotional toll” of the collapse in housing prices. Or all these other amazing pieces from the amazing New York Times archive documenting the ’80s housing bubble and the collapse in prices at the turn of the ’90s.

The second answer is – to the extent we didn’t, or didn’t really remember it, it’s because it didn’t torch the global financial system. Which clarifies a very important fact about what happened to the American economy in the late aughties – what happened involved a housing bubble, but wasn’t fundamentally about or caused by a housing bubble.

For context, here’s the homeownership rate for the United States:

get off my property


The 00’s housing bubble clearly involved bringing a lot of people into homeownership in a way the 80’s bubble did not; that bubble, in fact, peaked even as homeownership rates had declined.

There are a lot of lessons to learn about the 00s bubble, about debt and leverage and fraud and inequality, but the lesson not to learn – or, perhaps, to unlearn – is that a bubble and its eventual popping, regardless of the asset under consideration, is a sufficient condition of a broader economic calamity. Now, it does seem clear that the 80s housing bubble was in key ways simply smaller in magnitude than the previous one; it represented a 50% increase as a ratio to national income rather than the doubling experienced in the aughties even though both saw land increase similarly relative to capital. But there have been – and, no matter the stance of regulatory or, shudder, monetary policy, will continue to be – bubbles in capitalist economies. The policy goal we should be interested in is not preventing bubbles but building economic structures and institutions that are resilient to that fact of life in financialized post-industrial capitalism.

*Piketty and Zucman only provide national income up through 2010, so I had to impute 2011-2012 from other data with a few relatively banal assumptions.

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.

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.

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!

Something that annoys me in the minimum wage debate is that the anti-minimum wage folks assume that labor markets (not “the labor market” – there is no “the labor market”) works like other markets.

It doesn’t.

And there are really, really good reasons for that! But let’s just look at one facet/outcome of that.

If you asked me “in an ideal world, what would be the price of [just about anything],” my answer would be “nothing!” Food? Free! Furniture? Free! Clothing? Free! Computers? Free! Because free implies a defeat of scarcity – that one day we will have replicators and 3d printers and servile robots and abundant clean energy and almost all goods and services will be without cost. That’s utopia.

But if you asked me, “in an ideal world, what would be the price of labor,” I would never, ever say free. Because what economists call “labor” most people call “time” – a finite, substantial quanta of someone’s finite time on Earth.

The right way to think about this is the Star Trek universe, where almost all goods and services are provided costlessly by machines but people still put their time and effort into creative or rewarding projects, the kind of stuff we call today “artisinal production.” That stuff still “costs,” but its mostly a gift and barter economy where people brew their own delicious beer and give it to friends or trade it for delicious, home-distilled bourbon.

Now, the price of labor in our own, non-utopian world, has effects, large and small, on lots of things, and its not obvious what the best balance between the returns to labor vs. capital are, or the best mechanisms for obtaining them. But we also shouldn’t be trying to ceteris paribus drive down the price of labor like we should the price of chocolate or power cords or other commodities.

And because of the totally different way “labor” is conceptualized, and because of the totally different implications and underlying meanings of labor markets, they just don’t work like normal markets in so many key ways.

Put it this way: nobody thinks it’s morally wrong to prefer a brownie to a blondie or white fudge to dark fudge, but people do think its wrong to hire based on skin color. In fact it’s illegal, for very good reason.

When individuals have to cut back on expenditures, they don’t like it, but they do it; but bosses (at least good ones) agonize over firing employees and really loathe doing it.

When individuals have the chance to bargain or get a great deal on a good, they leap at the chance; but even when the economy is bad, employers do not take the opportunity to renegotiate salaries downward. If they have to, they’d rather lay off 5% of their workforce then give everyone a 5% pay cut.

And, just to finalize, think about how much people invest their self-worth into their career. Not that they should. But inevitably many do.

So labor markets are just not really like markets for goods and services at all, and people who insist that “fundamental laws of economics” mean that increased minimum wages absolutely must ceteris paribus reduce employment are making fundamental errors.

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