Pareto, Taleb and the tails of income distributions

I am reading Nassim Taleb’s Antifragile and then I went back to rereading parts of his extraordinary Black Swan. The Black Swan’s blurb by Daniel Kahneman, “The Black Swan changed my view of how the world works” is fully justified. It will remain one of absolutely indispensable books, a huge epistemological advance. Antifragile is, perhaps, an even more ambitious book because it aims to make systems (including people) antifragile, that is thriving in conditions of (what Taleb calls) “opaque randomness”. So, it is broader in scope and has a  prescriptive part that The Black Swan  does not.

Here I would like to address one of the two themes of Taleb’s that find immediate resonance among people who work on income inequality and globalization: the former one. I  leave globalization for another post.

Taleb’s contribution here is absolutely crucial. Distributions that have long right-end tails, as distributions of income, and especially wealth, do, have both their mean values and inequalities heavily dependent on extremes. Moreover for the extreme events, as Taleb keeps on writing, standard deviations are all but irrelevant. So the distributions cannot be fully described by the mean and variance as we generally tend to do in inequality work. (If the variance, as Taleb writes, reflects lack of knowledge about the mean, then irrelevance of the variance implies lack of knowledge about the lack of knowledge, Rumsfeld’s “unknown unknown”.) 

Statisticians who work on inequality have long known, heuristically, how much our results, from Gini to Theil to income shares, depend on the extreme values, and they tried to “solve” this by getting rid of extremes by truncating the values above some maximum.  This so-called “top coding” was done until a few years ago by the US Census Bureau in its Current Population Surveys, the prime source of income distribution data for the United States, and a methodological primer for many other countries. Since household surveys are random samples, the idea was not to let extreme values that may be sampled in one year, but  not in many others, “unreasonably” affect both the mean and inequality statistics. For example, if you surveyed Bill Gates this year but never before and never again (which is  very likely since people with his wealth are extremely rare), this year’s US mean income and  inequality will turn out extremely high. You would then have hundreds of research papers and doctoral dissertations written about what special economic policy made US inequality shoot up while, of course, the true reason was the sampling.

Nassim is a big fan of power laws that apply to the distributions after a certain point (“crossover point”). This too has been used in practice by combining lognormal distributions that would hold up to a certain (high) income level with a Pareto, power law, distribution that would hold afterwards. (A distribution follows the Pareto law if for every x percentage increase in income, there is αx decrease in the percentage of recipients of such high incomes. α is the Pareto “constant”.) Alternatively, some people (most notably Viktor Yakovenko here) have combined exponential and Pareto distributions: the first would be a distribution that applies to wage earners (the bottom 95% of the population), the second, to capitalists (the top 5%). Anwar Shaikh in his monumental Capitalism used that “combined” distribution to discuss the relationship between income inequality and financial crises.

But where I part ways with Nassim is on the constancy of the α, which is implied in Mandelbrot’s fractile approach on which Nassim builds. I am not writing here about Pareto’s idea of constancy of α across places and time. This has been disproved enough (to see how empirical distributions look, pl. check my earlier post on Pareto, here). I am writing about the empirical fact that when we look at income distributions, depending on what part of the top we consider, α changes. I was interested in this several years ago, did quite a number of runs on empirical distributions, but never followed this up. What I did was to plot a relationship ln H(y) = A –α ln y where H is the inverse cumulative distribution, y = income, α = Pareto “constant” or “guillotine” (because it “cuts” the number of recipients as income is raised), over gradually smaller parts of the top: first for the top 20%, then for the top 19%, then for the top 18% etc. all the way to the top 1%.  I do not expect that the guillotine would stay equally steep.

In some cases the slope of the line may be negative (= α increases in absolute terms) if the distributions near the very top tend to be more “rarefied” than the distributions across the entire top 20%.  As shown in Figure below, this is the case of the United States. If you have only 100  people with incomes above several hundred million dollars, then increasing the threshold by (say) 10%, would make perhaps 20 or 30 of them fall below the new threshold. In the middle, very “dense”, part of income distribution, you can increase the threshold by 10% and very few people, percentage-wise, will drop out: perhaps only 1%. So, around the top, the guillotine would be -2 or -3, in the middle it would be -0.1.

But in the cases of Germany and the UK, whose distributions look almost identical except for the top 1%, the Pareto guillotine becomes less in absolute amount as we approach the top. The distribution around the top is more dense.      

In other cases, like Egypt, shown in the graph below with Italy and the same data for Germany, the Pareto constant is lower (in absolute amounts) almost throughout the entire top 20%. Egypt’s distribution is “denser” than German and Italian (almost) throughout. Weirdly, Italy comes closest to what Pareto would have believed.

The key point is that the power law works with unequal intensity even over the portion of the distribution where we believe it should apply (that is, above the “crossover point”). Thus in the equation above, we should write α(y) rather than a plain α.

The difference in the levels of the guillotines between Egypt and Germany/Italy illustrates another point: less sharp guillotines (if they were to hold throughout the entire distribution) like Egyptian will be associated with higher overall inequality because they imply thicker tails. Sharper guillotines imply less thickness in the tails and thus less inequality. This is expressed in the fact that Gini of a Pareto distribution is equal to 1/(2α-1) and that as α in absolute amount increases (i.e., distribution gets rarified), Gini goes down.

Where does it leave us? At a modified fractal approach: as we slice income and wealth distributions further and further, the same phenomenon does not repeat itself  with equal intensity but, depending on the distribution, with greater or lesser intensity. The Pareto constant varies so much that one wonders how the term “constant” can be applied to it at all.      

Preface to the Russian edition of "Global inequality"

I am delighted that one of the first published translations of my book is in Russian.  There are, I believe, two reasons why Russian readers might find the book interesting and relevant.

First, as the title suggests, the book deals with the changes in world income distribution during the era of “high globalization” that runs from the fall of the Berlin Wall to the outbreak of the Global Financial Crisis in 2008 (and in some instance covers also the period up to 2011). It was an extremely dynamic and turbulent period. The major parameters of the Europe/US vs. Asia relationship have changed, not only because of the remarkable rise of China, that in terms of total GDP calculated at purchasing power, had by now outstripped the United States as the largest economy in the world, but also because many other populous Asian countries have followed an equally successful  growth trajectory.  A couple of numbers suffice to show the scale of change in relative economic power:  between 1988 and 2015, the average per capita income of “non-rich” Asia (that is, Asia that excludes Japan and South Korea, and oil-producing countries of the Middle East) has been multiplied by a factor of 4.5, while the Western per capita income has increased 50%.  After the financial crisis, the  change is even more striking: Western incomes in 2015 are only 2.4% higher than in 2007 while “non-rich” Asia has gained 58%.

The three- or  four-century old relationship between the level of economic development in the western shores of the Eurasian landmass (Europe) and the eastern shores of the Eurasian landmass (China) is thus undergoing a rapid process of change. We are participants and witnesses to a major  economic and political “rebalancing” between Europe (inclusive of the United States) and Asia. This rebalancing, if continued for another generation, will bring the relative income levels of the Western and Eastern shores of Eurasia to the point where they were prior to the Industrial Revolution, that is approximately equal. Such a remarkable development is easily observable in individual incomes, captured by household surveys used in this book to look at the evolution of global income distribution. While people in the middle of the global income distribution (who are from the Western point of view still relatively poor) have experienced more than the doubling or tripling of their real incomes, people in the rich world’s lower parts of income distributions (the “working classes” of the West) have seen very little real growth. This is particularly clear for the three most important Western economies: the United States, Germany and Japan. But the top income groups (the famous top 1%) in the West have done extremely well. This has created the cleavage between the fortunes of the top and the fortunes of their working class or lower middle class compatriots. The fruits of globalization were clearly not equally shared amongst the citizens of the rich countries. And this, combined with migration pressures which are also a reflection of uneven global distribution of income between the countries,  have led to the tumultuous political developments of the last couple of years and the rise of right-wing nationalist and populist parties.

The second reason why the Russian reader might find the book relevant is because Russia was directly or indirectly involved in all key developments discussed here. The end of Communism and the beginning of the “high globalization” in the late 1980s were clearly related. The rough sketch of the geo-economic changes that occurred in the past quarter century indirectly  highlights the position of Russia that straddles  the Europe-Asia divide. It will, if the current developments continue,  find itself geographically between the two richest and most dynamic parts of the world economy, each at one end of the Eurasian continent. This creates obviously challenges for the country and shows a huge importance of fast economic growth, lest the continental landmass of Eurasia (composed mostly of Russia, Ukraine and Central Asian countries) remain at much lower level of income than the maritime edges. Finally, the within-national inequalities that have played such an important role in recent political developments in the West have not passed by Russia. The enormous economic inequality that followed the end of Communist regime in Russia has in the past ten years been to some extent reduced in the income dimension while the concentration of assets remains so high that it puts Russia among perhaps three to five countries with the greatest inequality in wealth. It is quite likely that the wealth concentration in today’s Russia is greater than it was one hundred years ago, before the beginning of World War I.

The concentration of wealth in Russia is also connected with rather hesitant formation of the middle class. It is somewhat of a truism that social stability often  depends on having a sizeable middle class. This is not because one becomes “virtuous” and democratic simply by having a “middling” or comfortable level of income, but because the middle class tends to favor protection of property rights against possible expropriation of those who are poorer, and to favor the rights of political decision-making against those who are richer and can “buy” their way into political power. I believe that, even if the book does not directly mentions this with respect to today’s Russia, the reader can readily see that the two crucial issues are acceleration of economic growth of the country as a whole and strengthening of the middle class internally. The reader will recognize that this is an agenda not dissimilar to that of Sergei Witte some 120 years ago.

These two messages may sound obvious or well-known to the Russian reader but the important point is to realize that here they are not derived alone, that is in isolation from the rest of the world, but rather on the contrary, directly from the empirical study and the analysis of worldwide movements in income and thus in economic power.

In this way, I dare to believe, the book may make a small contribution toward better understanding of our world—the understanding which should hopefully help the next generation live materially richer and more peaceful lives.

 Washington, 30 December 2016.

A short note on Skidelsky’s interpretation of Schumpeter

Yesterday I enjoyed reading and then retweeted the newest piece that the grand Robert Skidelsky has written on the (sad) state of economics today. It is an extraordinary tough and accusatory piece and while the accusations may be at times slightly overdone, Skidelsky’s last sentence that “the economists are the idiot savants of our time” can be I think reasonably thought to apply to many of us (economists). Moreover, Skidelsky’s position is supported by the views of the profession’s greatest minds, men who were without fail, men of erudition and multiple talents, often involved in politics, journalism and quotidian rough-and-tumble.

Dismissing this as having been the product of economics’ infancy where Renaissance spirits could prosper while today’s economics has advanced so much that specialization is unavoidable is not a sensible defense of fach-idioten. It is not because economics by its very nature is a social science that must, in order to be relevant and to contribute to its key objective, namely to the improvement of people’s ordinary lives, include the knowledge of, and display familiarity with, all the neighboring disciplines, primarily history, economic history, philosophy, sociology and psychology. Thus, as I think Keynes is supposed to have said (or at least this is implied in the introduction to his essay on Marshall) that “one is  bound to be a poor economist is he/she is only an economist”.

There is one point however where I think Skidelsky’s overstretches his case. It relates to Schumpeter and Skidelsky’s claim that Schumpeter “also attacked the view of the economy as a machine. Schumpeter argued that a capitalist economy develops through unceasing destruction of old relationships.”  While the second sentence is, I think, accurate especially if we think of Schumpeter’s key contribution to economics (written when he was a young man) “Theory of Economic Development”, the previous sentence about Schumpeter being a critic of those who see the economy as a machine is more controversial. In fact, in his monumental “History of Economic Analysis” (HEA) no economist gets as much praise as Walras for his general equilibrium.  Here is Schumpeter (HEA, Chapter V, $1, p. 827, 1980 edition):

[Walras’] system of economic equilibrium, uniting, as it does the quality of revolutionary creativeness with the quality of classic synthesis, is the only work by  an economist that will stand comparison with the achievements of theoretical physics. Compared with it, most of the theoretical writings of that period—and beyond—however valuable in themselves and however original subjectively, look like boats beside a liner…it is the outstanding landmark on the road that economics travelled toward the status of a rigorous exact science.

And Schumpeter then goes on to criticize Walras for paying as much attention to his applied economics dealing with social justice as to his general equilibrium masterpiece.

Now, to the extent that modern economic analysis has grown out of Walras’ general equilibrium (and I think that it seems a pretty uncontestable proposition) it is wrong to enlist Schumpeter among those who would have necessarily disagreed with the direction taken by modern economics.  It is quite possible, of course, that Schumpeter might still disagree, believing that what was useful as a theoretical  construct, ended up being interpreted by the epigones as an accurate representation of reality. But this is obviously something that is just a matter of speculation.

Why do we have this “problem” with Schumpeter? Because in his own work, Schumpeter shows a duality, or even a contradiction, between his often unquestionable endorsement of “economics as physics” in HEA where it is hailed as an unambiguous progress toward economics becoming an exact science, and scarce use of this approach in Schumpeter's own work. His “Theory of Economic Development” is indeed in its structure very abstract and arid, somewhat similar to Ricardo’s “Principles” (of  whose methodology, by the way, Schumpeter was very critical in HEA), but is not mathematical at all. His “Business Cycles” is heavily empirical but shows scant relationship to Walras and is generally anti-theoretical. (I have to confess that I tried three times to read his “Business Cycles” and that I always failed. It seems almost unbelievable that such a splendid writer and beautiful mind produced a work--which moreover he originally saw as a competitor to “The General Theory”—of, yes, such messiness and unreadability.)

The bottom line is, in my opinion, that Schumpeter’s positon is at least ambiguous. He was at the same time a great admirer of the very abstract general equilibrium approach, and his own practice of economics paid no attention to it at all.

Liberation from the shackles of space

The new book “The Great Convergence” by Richard Baldwin is a contribution to globalization studies, economics of development, and trade economics. I more confidently speak of the former two than of the third but I think that even that could be justified.

There are several aspects of Baldwin’s book that are worth emphasizing. The first is a novel and persuasive way of defining the three historical eras of globalization as made possible successively by the reduced cost of transporting (i) goods, (ii) information, and (iii) people. The story goes as follows. When transportation of goods was perilous and expensive, production and consumption coincided geographically: communities consumed whatever they produced. As we know from even the most developed pre-modern societies like Rome, trade was limited to luxury items and wheat. But Rome was an exception: in most pre-modern societies trade was minimal.

Then came the Industrial Revolution that importantly for our story lowered transportation cost of goods. This made shipment of goods to faraway destinations possible and gave us the first globalization, or the “first unbundling” as Baldwin calls it: goods were produced “here” and consumed “there”.  This also gave us other things that economists take for granted: development as national production of goods through all its stages, trade as consisting of nation A exporting a good to nation B, theory of growth that sees nations advancing from production of food to manufactures. Although Baldwin does not say it, practically all the tools of modem economics are still influenced by the way the first unbundling occurred.

The second unbundling (and the second globalization) comes when the control and coordination of production is done “here” but actual  production of goods is done “there”. Notice the difference: first you unbundle production and consumption, then you unbundle the production itself.  The unbundling of production was made possible thanks to the IT revolution that allowed companies to design and control processes from the center while delocalizing the production to hundreds of units or subcontractors dispersed around the world. These are the famous “global supply chains”. Reduced cost of transportation of information (basically, ability to coordinate and control regardless of distance) is for the second unbundling what reduced cost of shipment was for the first.

A couple of things are worth noticing regarding the second unbundling. First, huge importance of institutions. When globalization was just exports of goods, institutions in the country to which the goods were exported did not matter much: whether institutions “there” were good or bad, the exporters were paid (about) the same.  This is no longer the case with the second unbundling.  When the production is delocalized, the quality of institutions, infrastructure or politics  in the recipient country matters enormously to the center. If designs are stolen, produced goods impounded, travel of people between the center and the offshore location made difficult, the entire production structure of the company collapses. For the center, the quality of institutions in the offshore location becomes  almost as important as the quality of institutions locally.

Second, technological progress in the offshore locations now takes an entirely different hue than in the past. While in the past developing countries  were trying to induce foreign investors to share their know-how, now the center (mother company) has all incentives to make sure the best technology is used because the offshore location has become an integral part of the center’s production chain.  This is an enormous change: rather than begging or incentivizing the rich country’s company to transfer technology, now the owner of that technology is herself keen to transfer to the offshore location as much of it as possible.

The great convergence from which the book takes its title, that is the remarkably fast growth of Asia, can thus be understood to have been made possible by an improvement in institutions and much greater transfer of technological know-how. And with both being directly related to the second unbundling. To put it simply: Asia grew thanks to globalization.

Baldwin’s story here clearly links with development economics. The old-fashioned view of development was “stage-based”: following upon the way England, and later US and Japan developed, it viewed countries as going through the import-substitution stage with significant tariff protection, then developing exports of simple manufactures and gradually moving into more sophisticated products. This was the idea that underlay most of development policy between the 1950s and 1980s. South Korea, Brazil and Turkey were the best examples. But in the 1990s, with the second globalization things changed. What became crucial for success was no longer to develop by own economic policy through various stages, but to become part of the global supply chains organized by the center (the “North”).

Baldwin’s argument changes the way we interpret Asia’s success in the current era: China, India, Indonesia, Thailand  are not repeating Korea’s experience, but are the trail-blazers of a new way to development that, by integrating one’s economy to the “North”, leapfrogs over several technological and institutional stages. To grow, it becomes crucial to be part of global supply chains. The most successful countries in the second globalization are those that due to institutional factors, skill and cost of their labor, and geographical proximity to the “North” are able to become an integral part of “Northern” economy. Baldwin’s  interpretation inverts (rightly, in my opinion) the old dependencia paradigm which held that “delinking” was the way to develop. On the contrary, getting “linked” is what made Asia traverse in a remarkably short  span of time the road from absolute poverty to middle income status.

What would be the third globalization? The ultimate (at least from today’s perspective) unbundling will come with the ability of labor to move seamlessly. This will happen when the costs of moving labor become low. For many operations that require physical presence of a person, the cost of temporarily moving that person to a different location is still high. But if the need for physical presence in a faraway location is solved  through remote control, as we already see in the cases of doctors performing operations remotely,  then labor may become globalized too. The third unbundling, that of labor (as an input in the production process) from its physical location, makes us think of migration and labor markets very differently: if tasks which now require physical presence of a worker can be done remotely by a person at any point on the globe, then migration of labor may be of much smaller importance. Through the third unbundling we can achieve a global labor market that may mimic the way the world would look with a fully free migration.

By placing today’s globalization in the context both of the previous globalization and of what may be the next one, Baldwin allows us to see the economic progress of the past two centuries as a continuum driven by the successive facilitations of movement of goods, information, and people. It also allows us to glimpse a utopia where everything can be quasi instantly and almost costlessly moved around the globe: the ultimate  victory over the constraints of place and location.