Yesterday at the New School in New York, I attended a lunch
talk given by Hagen Krämer (University of Karlsruhe, Germany). His short paper deals with Piketty’s
by now famous r>g proposition. Hagen, like several others, including Debraj Ray with whom some time ago I
had a discussion on this topic, argues that an important missing part in Piketty is propensity
to save out of capital income. (He acknowledge though, quoting from “Capital in
the 21

^{st}century”) that Piketty is aware of its importance.The point is of course simple. In the classical world, which Piketty follows, it is assumed that the entire return to capital (r) is reinvested. Thus the return on capital is the same as the growth rate of capital. Why this is a reasonable simplifying assumption I have written here. (And this classical assumption gave rise to Joan Robinson famous quip that “capitalists earn what they spend, and workers spend what they earn.”)

But then suppose that capitalists decide to spend some of their r on fancy cars and yachts. There would be a split between the rate of return on capital (which is still r), and the rate at which capital grows (which will be now equal to r*=sr where s is the average saving rate out of capital income). It is then very clear that if capital does not increase as fast as output, the share of capital income in total net output (Piketty’s alpha) may not increase. It is at its most obvious if we assume that s=0. Then capitalists spend their entire income, the capital stock does not grow at all, and if the growth rate of output (g) is positive, the capital/output ratio will go down, and Piketty’s alpha will decline. Notice that all of this happens while r>g still holds in the background (on the production side).

Ergo, you can have r>g, and neither increased share of capital income in total income, nor increased income inequality are guaranteed. Then, Hagen derives the conditions under which s is just sufficiently high to guarantee that capital increases faster than output which in turn ensures a rising share of net income going to capitalists. Let’s call this required rate s

_{e}.

In a final step, Hagen compares s

_{e}with the actual saving rates of the top 1% and 10% (who now double as capitalists) in Germany, UK and the US. He finds that s

_{e}is generally higher. This means that, with the existing parameters, Piketty positive feedback process of rising inequality is unlikely to take off. But in the future, with new values of the parameters (say, higher saving rates among the rich or higher β) the dynamic of increasing inequality might be launched.

The value of the Hagen’s paper is that it highlights the fact that savings matter. It also shows that even if r>g, an increasing inequality is not guaranteed so long as savings of capitalists are not high enough.

In a somewhat related paper, that I wrote a few weeks ago and just posted on the Web, I take a somewhat different tack to the problem. I note that even the rising capital share (with the standard assumption that capitalists reinvest their entire r) does not guarantee the increase in inter-personal income inequality. In other words, to go from a rising capital share (in functional income distribution) to the rising inter-personal inequality, you need two additional steps. They are usually satisfied in practice, so we seldom think of them, but they are nevertheless important. The first is that capital income needs to be more concentrated than labor income. If, for example, capital income were distributed equally across the population (with Gini=0) then however much capital share increases, it will not lead to higher inter-personal inequality but would rather lower it. The second thing which needs to be satisfied is that people who receive capital income are also rich (in terms of overall income). That is almost always the case, but theoretically it need not be. For example, if capitalists were poor, then an increase in capital share would reduce inter-personal income inequality.

I then consider how the transmission (or “pass-through”) from greater capital share to greater inter-personal inequality works in three ideal-typical economic systems: (a) socialism where capital income is distributed equally, (b) classical capitalism where capitalists have only income from capital (and are rich) and workers have only income from labor (and are poor), and (c) new capitalism where the same people are both capital- and labor-rich. I derive elasticities of transmission in each of the three cases. If the elasticity is 1 then each percentage point increase in capital share leads to a Gini point increase in inter-personal inequality (this is the maximum “pass-through”). If elasticity is 0, then capital share can increase without adding anything at all to inter-personal income inequality. I end by looking at how high are these elasticities in today’s economies. As the graph shows, today’s economies have an elasticity that lies between 0.4 and 0.6. It means that as capital share rises from say, 35% of total net income to 36% (where it is now in the United States), Gini will increase by about half a point (say, in the US, from 42 to 42.5). Moreover, as the graph shows, the elasticity has had a tendency to increase over time which means that personal income inequality in rich countries is becoming more sensitive to the rise of capital share in total income.

A way to reduce the elasticity is to broaden ownership of capital. (Recall that when capital is distributed equally per capita, capital share can rise to 100% without affecting income distribution.) We are of course very far from that point since Gini of capital income is about 0.8 in the United States and all rich countries, but if wealth concentration is reduced, either through participation of workers in profit-sharing or subsidies to small investors, or broader access to housing, or debt forgiveness for the poorer groups, the elasticity (or the “pass-through”) will become less.

Let me end with two key messages.

1. It is seldom appreciated that the rising capital share (from
the functional income distribution) does not guarantee a rising inter-personal
Gini. How much will a rising α affect Gini depends on concentration of ownership
of capital and association between capital and total income (are people with
high capital income also rich).

2. In affluent societies where, by definition, capital-output
ratio is high, it becomes imperative to broaden ownership of capital lest its
rising share lead to unsustainable levels of inter-personal income inequality.
This is also one of the messages in my forthcoming book “Global inequality: A new approach for
the age of globalization”: policies in “new capitalism” need to focus on equalizing endowments, including
wealth, not as much on redistribution of
current income via taxes.