The Capital Creators, Piketty and Growth Theory

Something new has happened in economics this month: an influential academic book has been written. Actually, I should say something old has happened because there was a day that academic economists wrote books that had influence. My guess is that it has been about four decades since someone has put original research in the form of an overarching thesis into a book and had that turn out to be highly influential (since, say, Oliver Williamson or, some would say, John Sutton, more recently, for an exception proving the rule). To be sure, academic economists write books that are influential but almost all of them are translations of research for either a popular audience or students. They generally shy away from a broad thesis unless they admittedly move into a more speculative realm.

Thomas Piketty’s book, Capital in the Twenty-First Century, comes, therefore, as somewhat of a surprise. It is most definitely an academic book (or as Solow calls it “a serious book”) published by a University press (Harvard) and my guess is that its 600 plus pages full of graphs and notes would never have been published by anyone else. At its heart is scholarship and a couple of decades of research. But it is not a textbook. It has a thesis: inequality is getting worse and, in fact, is so extreme that if you believe in democracy something needs to be done about it. The thesis is only half proven. The proof — and it is hard to imagine it being derailed — is that inequality within advanced economies is getting worse and one can’t really pretend that anything other than a return to inequality of the 18th century is going on. But the missing bit is precisely why. There are lots of contenders but ultimately the cause seems widespread but with inter-country differences. And with this unresolved, we are not really able to work out what, if anything, we should do about it even if Piketty is convinced that doesn’t matter.

If there is one thing that this teaches us is that there is still a healthy return to writing a book of this kind. Not only has it been widely discussed but it currently sits atop the best seller list at Amazon. I can’t remember another book written by an academic economist that has reached that height (perhaps Freakonomics but even there I’m not sure). But there is more to the story than just that. First, there is a story of scholarship that has emerged somewhat unrestrained from the usual rules that bind academic publication in economics. Second, there is a cost to that: of attribution to those who investigated this issue in the past and why they stopped. Third, there is a benefit of forcing focus on the issue if only to identify shortcomings in our picture that should be an embarrassment to the profession. I’ll deal with each of these in turn.

Unrestrained Scholarship

I’m an economist of the same vintage as Piketty. But I cut my teeth on a tradition at my undergraduate institution, the University of Queensland, that emphasised the history of economic thought. So I learned economics as much from reading books (especially old ones) than I did from reading academic articles. The books that were written prior to 1980 had a life to them. Pick up a book like Knight’s Risk, Uncertainty and Profit, Schelling’s The Strategy of Conflict or Simon’s Sciences of the Artificial and you were forced to look at issues in a different way. There was formal modelling at the heart of these works but also a license to speculate about where research might head and what it might find. And it wasn’t just that these writers could use more colourful language but that speculation was permitted at all.

Modern academic articles have banished speculation. It is pretty much considered a sin and certainly not something that will get past an editorial process. Piketty has used his book to unleash speculation again and most academic economists have been, at best, unable to process it and, at worst, annoyed and consternated by it. But I say, at worst, as a reflection of them rather than Piketty. Because consternation was surely his intention. I too was consternated until I realised that was the point.

Bob Solow’s ever sober approach highlights precisely what is and is not speculation on Piketty’s part. Namely, what is speculative is the prediction of where inequality is heading and that it is based on a “rich get rich dynamic” (Solow’s term) or what one might call a Matthew Effect. But it is not unreasonably so. One might imagine the argument here that Piketty perhaps should have laid out his argument in the same way Solow did. However, I think it is worth noting (a) that is a matter of taste and (b) Solow’s argument only exists because Piketty made his argument his way. The whole outcome is the point and not whether Piketty immersed himself in Solow’s dry discourse.

Attribution

There are costs of bypassing the usual filters for academic research. To me, the main one here is attribution and how it can help frame arguments. The main methodological insight from Piketty that allows him to formulate the consequences of the “rich get rich dynamic” is described by Solow in this way:

There is a stronger implication of this line of argument, and with it we come to the heart of Piketty’s case. So far as I know, no one before him has made this connection. Remember what has been established so far. Both history and theory suggest that there is a slow tendency in an industrial capitalist economy for the capital-income ratio to stabilize, and with it the rate of return on capital. This tendency can be disturbed by severe depressions, wars, and social and technological disruptions, but it reasserts itself in tranquil conditions. Over the long span of history surveyed by Piketty, the rate of return on capital is usually larger than the underlying rate of growth. The only substantial exceptional sub-period is between 1910 and 1950. Piketty ascribes this rarity to the disruption and high taxation caused by the two great wars and the depression that came between them.

There is no logical necessity for the rate of return to exceed the growth rate: a society or the individuals in it can decide to save and to invest so much that they (and the law of diminishing returns) drive the rate of return below the long-term growth rate, whatever that happens to be. It is known that this possible state of affairs is socially perverse in the sense that letting the stock of capital diminish until the rate of return falls back to equality with the growth rate would allow for a permanently higher level of consumption per person, and thus for a better social state. But there is no invisible hand to steer a market economy away from this perversity. Yet it has been avoided, probably because historical growth rates have been low and capital has been scarce. We can take it as normal that the rate of return on capital exceeds the underlying growth rate.

Solow uses words where Piketty uses a statement: namely, that r > g. But what was interesting is that “no one before [Piketty] had made this connection.” That surprised me and I embarked on a brief expedition to find out why.

Let me say that my account of the history of economic thought here is a sketch and not comprehensive. But it will establish that these issues were dormant. It begins with the famous Harrod-Domar statement of what “steady state” or balanced growth would look like. In a steady state, there is a stable growth part where all factors of production (labour and capital) grow at the same rate. For Harrod and Domar, they demonstrated that, in the absence of technological progress, this would only occur if s = (K/Y)n where s is the share of income that is saved, K is the capital stock, Y is income and n is the rate of growth of the labour force. Stated this way, there was no mechanism to ensure that this particular outcome arose but Solow would get us part of the way there. Rather than assume — as Harrod and Domar did — that capital and labour are perfect complements (which is historically a recipe for instability in economics) — Solow assumed the usual diminishing returns. This meant that as you invested more capital the marginal return to capital would fall so that (K/Y) would adjust to bring about steady state growth. By the way, diminishing returns to capital were no good thing for the economy. Indeed, as you added more capits (people), output per capita in any steady state would be lower because they would all be competing to eek more out of the capital stock.

But even this was to reveal an issue because there were many possible steady state growth paths all depending on the savings rate, s. The ‘best’ one (i.e., the one that would maximise output per capita) turned out to be the one that ensured that the marginal product of capital (or under competitive markets, its rate of return) equalled the growth rate. Sound familiar? Output per capita is maximised when r = g and, at the time, it was termed “The Golden Rule.” (As I was saying back in the 1960s, some economists had a way with words). The problem is that there was no natural market force that might bring about this outcome. Thus, we could have a situation where r > or < g. r > g corresponded to having a relatively low capital stock whereas r < g corresponded to having a relatively high capital stock.

Those who have read Piketty will note that we run into an issue here. If one wanted to rationalise the Solow growth model with the data, Piketty argues that r > g most of the time (indicating the existence of scarce capital) except during the Great Depression and World War II (at least for Europe) and the 1950s (for the US) where correspondingly, the amount of capital would be relatively abundant. Maybe that is a classification issue (just which capital was productive when) but Piketty’s account and the Solow model do not appear to sit comfortably together. Indeed, Solow said as much when he argued that diminishing returns would eventually cause r to fall at a greater rate than g:

This is Piketty’s main point, and his new and powerful contribution to an old topic: as long as the rate of return exceeds the rate of growth, the income and wealth of the rich will grow faster than the typical income from work. (There seems to be no offsetting tendency for the aggregate share of capital to shrink; the tendency may be slightly in the opposite direction.) This interpretation of the observed trend toward increasing inequality, and especially the phenomenon of the 1 percent, is not rooted in any failure of economic institutions; it rests primarily on the ability of the economy to absorb increasing amounts of capital without a substantial fall in the rate of return. This may be good news for the economy as a whole, but it is not good news for equity within the economy.

The point is an important one: Piketty’s argument relies on a lack of diminishing returns to capital. This has important implications that I will return to below.

Before doing so, I wanted to point out that these implications of the Solow model for income and wealth distribution had been explored before. Luigi Pasinetti drew some of the chords together but it was a PhD student at MIT in the mid-1960s that was most obsessed about the implications of the Solow model for income distribution. What the young Joseph Stiglitz found in a paper subsequently published in Econometrica was that there were actually strong forces bringing about a more equal distribution of income but that there was also the possibility of a steady state growth trap that had with it an associated increasing inequality of income as the capital share of income grew. This happened when the capital to labour ratio was relatively low. There is certainly a plausible case that the US in the 1950s found itself on the good steady state and that something has shifted it to the bad steady state today.

Piketty did not refer to this work and the papers that followed it at all. That is one of the costs of bypassing the system. But that is too bad because, if he did, he would have seen that Stiglitz justified the very sort of taxes Piketty is now advocating and demonstrated how they might be employed to both bring about a more equal income and wealth distribution and a higher rate of growth. Instead, Piketty has been left open to the fair criticism that his proposed wealth tax is simplistic and not thought out. By contrast, there was past research that did some of this work.

Actually, it is worth noting here that Piketty does more than not use theory to justify his approach, predictions and policy recommendations. He argues (at least in my reading) that he shouldn’t be required to do so. That is one of the benefits of being less restricted but it comes at considerable cost. One cost is that without theory, it is hard to justify both predictions of the future and also policy recommendations and their likely effects (another form of prediction). Only theory can help make that argument and help us understand what we need to know in order to act.

But the other cost is that theory helps ensure that our explanation of the past is internally consistent. As noted earlier, Piketty’s argument relies on there being a lack of diminishing returns to capital. The alternatives are obvious — increasing returns to capital as my co-blogger Erik Brynjolfsson has been arguing for so forcefully recently. In other words, Piketty’s argument requires there to be capital creators — that is, people who find ways to deploy the wealth of the rich in ways that forestalls the otherwise likely effect of diminishing returns. But who are the capital creators and, if they are there, aren’t they also likely to be the ones increasing g? Put simply, if you don’t believe in diminishing returns, how is it that you are also pessimistic about the long-run rate of growth? It seems to me there is an inconsistency here.

The Opportunity

That said, I can’t have my cake and eat it to. I’m arguing that Piketty’s approach to scholarship is refreshing because it removed a constraint that has been harming the advancement of economic knowledge: namely, the ability to speculate. But similarly I am arguing that people are going to have a problem with that — including me. While that is a problem with Piketty’s thesis, at the same time, it is a feature of Piketty’s process. It forced me, for one, to think about and go back and see what economists had said on this issue. That I found something useful is the whole point. But that it has been decades since those leading lights of the profession — who thought this an issue important enough to think about it (a) at the beginning of their careers and (b) when the inequality was not nearly as bad as it was to become — tells me that we needed this. For income inequality is something we know hardly anything about in a deep way. To be sure, we now know enough to realise that it is there and not going away as many had hoped. But we have no idea why or what, if anything, we should do about.

Piketty’s book lays down a hypothesis that should hopefully focus many to start asking these questions. And, as I have already indicated here, the theory that we have does not appear to line up with the facts and so there is much more work to be done. Let alone the fact that our chief microeconomic theory on wealth ownership predicts that rentiers shouldn’t own this capital at all for efficiency reasons (I am thinking here of Grossman-Hart-Moore).