A note on “maximum” US inequality

A couple of days ago, Brad DeLong wrote a nice post (here) contrasting Dean Baker’s view of the main drivers of inequality today (rents to the financial sector, to the “liberal” professors, rents to patents and copyrights and high pay of CEOs) vs. a simplified Piketty’s view based on the elasticity of substitution of capital for labor in excess of 1 (and thus remaining high rate of return to capital despite higher K/income and  K/L ratios). The implication of Dean Baker’s view is that the current inequality is somewhat of an anomaly, related to the way  capitalism (especially in the US) has evolved in the past three decades.  According to Piketty, however, increase in inequality obeys some deeper laws. In my forthcoming book, I do take the position that it indeed obeys some “deeper laws” but I think that these “deeper laws” have to allow for Baker’s rents as well.

However what motivated me to write this post is an often-repeated assertion, made sometimes as a critique and at other times (and by other people), as a praise, that Piketty’s “system” implies that an endless increase in inequality is possible or even likely under capitalism.  Now for people who work on inequality, an increase that would go on “forever” and/or be “without a limit” is simply an impossibility. There are no societies in general, much less advanced societies, where Gini would be close to 1, or where the share of the top 1% would be (say) 90%. It is just that as societies become richer, the expectation of what the social minimum is rises, the “automatic inequality stabilizers” kick in, and even if rich countries differ in terms of their levels of inequality,  none of them has, or could conceivably have, inequality that would come close to the upper bounds of Gini, Theil or top 1% measures. So if inequality cannot increase “forever”, it has to have some other upper bound. Heuristically, we could say that the upper bound may be around the point at which the US is now, because no modern rich country (countries with GDP per capita in excess of $30,000) had ever had  income inequality as high as today’s US.  So, we could say, based on our experience to date, that a Gini above 0.45 for an advanced democracy would be very, very unlikely.

But if we go back to the world of simple models, let’s see what Piketty’s own would tell us. First, start with the steady-state capital-income ratio (Piketty’s beta). As countries get richer (and short of wars), we can expect that β will increase. Today, Switzerland probably has the highest β in the world. It is about 6.5. Suppose that the US steady-state rate of  growth (of total GDP) is 1.5% per annum and its saving rate 15%. We do it so just to make it simple, so that we can say that at some future date US steady-state β would be 10 (15/1.5). (Note: I really do not believe that in the real world we shall ever see a steady-state β, not a steady-state economy at all; but it is a useful construct to have in order to organize our thoughts better.) Suppose further, as argued by Piketty, that the rate of return on capital remains 5%. Well, this simply means that one-half of net income (10 times 0.05) will belong to capital-owners.

Now, the overall Gini coefficient is equal to the sum of the shares of labor (capital) multiplied by their concentration  coefficients (similar to the Ginis). We also know that the concentration coefficient of capital income in the US today is about 0.6, and that, under the extreme circumstances and as the share of capital in net output increases, it might go up to 0.7-0.8.  The concentration coefficient of labor income is about 0.4 and is unlikely to increase. Then, the maximum Gini that we can expect becomes (0.5 times 0.7-0.8) + (0.5 times .0.4) = 0.55-0.6.  This is inequality level of today's Brazil and Colombia. Thus the maximum inequality that we can imagine for the United States would be inequality that exists today in parts of South America. It implies an increase of US inequality by  a third—not a trifling matter. But it does not imply an “infinite” increase in inequality.

This short exercise helps us, I think, better focus our minds. The choice in the US today is ether to curb further increases and try to bring US level of inequality in line with what existed In the country some 30 years ago (which is by no means easy), to be satisfied if inequality no longer increases,  or to let inequality move to South American levels. But the real bounds to inequality do exist. Unlike real income, inequality cannot keep on rising (even in theory) forever.