## Saturday, February 28, 2015

### What remains of Pareto?

My class on personal income distribution theories (within-nations) begins with Pareto. Pareto will indeed  be for ever part of such classes because he was the first economist to have been seriously interested in empirical analysis of inter-personal inequality.  Before him,  economics was about functional income distribution which, of course, makes sense if you assume that all workers are at subsistence, all capitalists rich, and all landlords even richer. Then, you do not need to bother with inter-personal inequality. It is just a transformation of factoral income distribution. (This is, I think, most obvious in Ricardo who cannot  even conceive of a possibility of wages ever going above subsistence—except temporarily to precipitate the Malthusian movement. The advantage for modeling—since Ricardo’s “Principles”  are in reality an exercise in verbal modelling—is that you have one fixed quantity and you can then let others vary).

It is just a minor simplification to say that Pareto thought that there was an iron law of income distribution, namely that inequality did not change whatever social system was in power.  It gave consistency to his theory of the circulation of the elites, because whatever elite be in power (land-owning, capitalist or bureaucratic), income distribution would be the same although the people who would be rich or poor would be different.  It was a serious critique of the idea that Marxist socialism would reduce  income inequalities.

What remains of Pareto’s claim?  Several things are clear now--more than a century after Pareto defined his power law and showed that the percentage of recipients of a given income decreases in proportion as that income threshold is raised.

"Pareto's law" does not apply to any entire income distribution. A typical empirical inverse cumulative function is shown on the vertical axis of Figure1. (Explanation: the highest number on the vertical axis is 1, that is 100% of the distribution, or in log terms log of 1=0. The corresponding number on the horizontal axis is the minimum income. Interpretation: 100% of people have an income higher than the minimum. As you increase income on the horizontal axis, the percentage of people with income higher than x goes down.)

If you try to fit a straight line (with both axis in logs), it gets you nowhere: the fit is like R2=0.01. So, we can forget about entire distributions following a power law. (Pareto was not aware of that because he used fiscal data from various European cities and regions which, of course, referred only to the incomes of the rich for which, as we shall see, the fit of the Pareto line is good.)

Figure 1. Pareto line fitted across the entire income distribution

And here is the thing. A straight line can almost  always be drawn, and in a meaningful fashion, across the top 1%, top 2% or top 5%, or even top 10%.  On the vertical axis in Figure 2 you have these top percentiles (in logs) with lines drawn at top 5% and top 1%. On the horizontal axis, you have the threshold incomes (such as:  top 2% begins with income level x, top 1% begins with income level x+y etc.). When  you link the two, you get a straight line.

But the problem is that the straight line, or rather its slope, changes depending on whether you draw it across top 10%, top 5%, top 2% or top 1%. In Figure 2, I show the Pareto line drawn over the top 5% from the same distribution that we just used in the previous graph. It does a relatively good job. But if I were to draw the line across the top 1% (rather than top 5%), its slope would have been very different. We would normally, I think, expect that the line would get steeper (the fat tails are less fat) as we move towards the very top of the distribution. But it does not always happen. In this example, it certainly does not: the line drawn over the top 1% would be flatter than the line drawn over the top 5%.  Sometimes, the very top is the fattest part of an income distribution.

Figure 2. Pareto line drawn over the top 5% of income distribution

So, neither (1) does Pareto constant exist across the entire distribution, (2) nor is it the same across different countries, nor (3) is it the same across different top percentiles of a given income distribution. You would think that Pareto’s contribution was almost nil.

But this is not the case. We use Pareto whenever we need to extend the line to the part of the distribution about which we have no information. For example, if I have percentile data (all 100 of them), but would like to estimate the share received by the top 0.1%, I would then draw a Pareto line over the top 5% (or 10%; this is my call) and extend it all the way to the top 0.1%. That would give me an estimate for the top 0.1% income share.

Second, Pareto is also useful for revealing data anomalies. Consider this example in Figure 3 using US micro data (CPS, year 2008). US Census Bureau practices top-coding, which means that top incomes are artificially reduced. Drawing a Pareto line reveals this. Instead of households continuing to “exist” in very high income areas (all the way to the right), their numbers abruptly drop and the richest households (whom we would expect to exist according to the Pareto fit) are just not there at all. Why are they not there? Because the Census Bureau decided to simply “truncate” their incomes.

Figure 3. Pareto line used to show anomalies in the data

Third, Pareto’s power law is indispensable for all non-symmetrical distributions, of which income or wealth are among the best examples. These are the distributions where the presence of high values does not decrease nearly as fast as implied by Gaussian distributions.  Pareto’s law and power laws in general play an important role in Nassim Taleb’s “Black Swan” (an impressive and absolutely essential book about which I might write in a different post). So, we owe a lot to Pareto.

Finally, what remains of Pareto’s sociology? He does not seem to be very much taught at universities these days, and his books are difficult to find. Many are out of print and extremely expensive (yet, you can get them on Amazon and elsewhere). What he said of Marxist socialism proved half true and half false. Socialist systems indeed created a “new class”, with incomes depending on bureaucratic position and no longer on ownership of assets. But socialism also succeeded in reducing the spread of income which Pareto believed impossible.

He was always an uncomfortable  writer. (Raymond Aron in his discussion of Pareto explains it extremely well.) Pareto’s writing style was atrocious (I just borrowed from the library his “The mind and society” and it is quasi unreadable). And he was a very unusual person: a mathematician, an engineer, steeped in Greek and Latin, and ancient history, for whom (as Schumpeter wrote) 4th century BC Athens was much more real than contemporary United States or Russia (let alone China).
He was also that very unusual breed: a conservative with anti-religious feelings. I think that he was basically a nihilist. But that would seem to be a good philosophy to have in our age of globalization: atomistic individuals, caring only about own gain and loss, not believing in any community or religious ties, and thinking (as Pareto did) that all religions, grand social theories and the like are simply fairy tales. Far from what Pareto called “logico-experimental” theories, religion peddled in “theories transcending experience”. But, he believed, chastened by reality and being of somber disposition, that every ruling class has to justify its power by resorting to such fairy tales. So we cannot have a society without fairly tales, and yet we know that all fairy tales are false.

## Sunday, February 22, 2015

### Trends in global income inequality and their political implications

[This is the transcript of a talk I give at the conference on inequality organized by the Fondazione Centesimus Annus at  the Vatican in May 2014.]

Thank you very much, Professor Curzio. I will stand up so that you would be able to see the PowerPoint. I would like to thank you for the invitation. I am obviously delighted to be here, and I would also like to thank my commentators, Professor Lui and Professor Pastor, who will speak afterwards.
I would also like to ask the Chair to let me know when I am three minutes off my beeping time, because I would like to wrap up with something which is relevant, I believe, for the session and the conference that we are attending today.
And now let me go over a review of the facts that many of you do know, but which, I think, are useful to see perhaps once more.  First, over the last twenty five years, in most countries in the world, there has been  an increase in inequality.
In Figure 1 here I am showing the changes in the Gini  coefficient, which is a measure of inequality, such that when it goes up it means that there is greater inequality. In two-thirds of the countries, most notably in the United States, the United Kingdom, China and Russia, there was a large increase in inequality.

Figure 1. Ginis in the late 1980s and around now

The exception - and I will not have time to speak about that today - is Latin America, in particular Brazil; which is very unusual because these countries are countries with a very high level of inequality. That high level is finally going somewhat down, whereas  in many countries as, for example in Sweden which is a country with a low level of inequality, inequality has gone up. There is thus a certain amount of convergence in within-countries’ inequalities.
That is maybe better shown if you look at this comparison in Figure 2 between the late 1980s and today.  Countries are represented by the dots.  All the dots that are above the 45-degree line are the cases where you had an increase in inequality. And when we make the dot size reflect the population size of the country, then it is even more striking because really big countries like China and India and the United States, and Nigeria and Russia, all registered an increase in inequality.
Figure 2. Ginis in the late 1980s and around now

This, of course, raises many issues which are well known, so some of them, in order to save on time, I will just read off from the slides.
I would like to mention one issue, namely interaction between perception of inequality and  actual measurement of inequality. It seems to me that at some point when a society starts seriously to discuss the topic of inequality and when measurements of inequality are done and published, people suddenly realize that there is really more of it than they thought.  I think a good example of that is the Arab Revolutions, where we really could not find in measurable terms, increases of inequality in Egypt or Tunisia, but where the perception of inequity and inequality had certainly gone up in the past 20 years.
Another issue is social separatism of the rich. I will not explain it as I think the term itself is very clear. And then of course another issue is tax evasion and hidden wealth of the rich, whose magnitudes  we are only really trying to guess now.
Now, in a sort of contradictory movement, we have had at the same time the fact that between country inequality, although very high by historical standards, has been on the decline. And the reason for this is very high growth rate of China in particular, but  also of India, Indonesia, Vietnam.
Essentially China was the force that was driving the decline in between-country inequality and thus  in global inequality for the past 30 years.  However, inequalities between countries are still huge. Just how huge they are I hope to show  in one  although a bit complex graph. The graph (Figure 3) shows the following: on the horizontal axis, you take everybody in a given country divided into 100 groups (called “percentiles”) from the poorest group, number 1, to the richest, which is group 100.
And then you ask, “Okay, this is really the poorest people in such and such country. How do they stack up  within the global income distribution? Where are they?” Now, this is shown on the vertical axis: you put there everybody in the world, in similar one hundred groups, from the poorest to the richest.
I will show the situation for only a few countries, but obviously this can be done  for  all countries that I have in my sample, that is more than 120. Take the United States, which is a rich country. And then start with the poorest people in the United States who are on the far left on the horizontal axis. They are very poor in the United States, but when you put them in the global income distribution, they come to something like 54th percentile. So they are richer than one half of the world! And then of course, as you go on with the next poorest group in the US and further on, they of course  are all richer and richer, higher placed globally, and finally the 12% of the richest Americans are all part of the global top 1%.
Figure 3. Different countries and income classes
in global income distribution in 2008

This is not very different for countries like Italy or Germany or France. I think in Italy too there would be something like 3% of the richest Italians who will be part of the global top 1 percent. But compare that –and I could have taken many other countries here, for example from Africa—with a poor country like India and then you get a very striking figure. We knew of course that people who are poorest in India are also among the poorest in the world, but we may not have been aware that the richest 1% of people in India (it is 12 million people though) are really, in terms of their average per capita income, coming just at the level of what may be called the lower middle class in the rich, advanced countries. This illustrates the immense income gaps that still exist between the nations.
Even what is  considered the middle classes in those poorer countries are by Western terms relatively poor. It is important to keep this in mind.
I have several other countries in the Figure here. I will skip them for the sake of time. Of course, the interesting case is that of Brazil because Brazil combines the poorest people in the world at the very bottom, and the richest people, those who belong to the global top 1%. And just to clarify, I am not really talking here about billionaires and oligarchs, because oligarchs don’t participate in household surveys. So we are talking here about large groups of very well-off people, fairly comfortable and living well.
So what happened to the global inequality? It is the product of these two things that I have just shown, of within-country and between-country inequalities. As a short cut in order  to have an intuitive feeling about how global inequality changed, I think it is useful to focus on the three elements or forces that  determine what happens to the global inequality.
First, I would like to emphasize the enormous role played by China. Until about the year 2000 China alone was the force that reduced global inequality. The other two forces that explain movements in global inequality are within-country inequalities, which as we have seen, mostly increased in the past 25 years, and convergence or divergence of mean country incomes. Here many poor countries, in particular those in Africa, have not been catching up with the rich world until 2000. After that date, the situation changed and we currently experience convergence of mean country incomes: poor countries’ growth rates tend to be higher  than the growth rates of the rich countries.
So how does it look on the global level, when we look at global inequality only? This is shown by the green dots (Figure 4). Please have a look at them now. The horizontal axis is time: the vertical axis is a measure of inequality. We focus on the green dots. They give us the estimates of global inequality among all people in the world where calculations are done as if they were all part of one country.
Figure 4. Three concepts of international inequality, 1952-2013
We  adjust for the differences in price levels because in poorer countries the price level is lower; poor countries’ incomes thus get a boost compared to the situation where we would just convert their local currency incomes into dollars at the current exchange rates. Let me also note that in these 120 plus household surveys which follow broadly the same, well-established UN methodology of data collection, we are including between 10 and 11 million of individual observations of incomes.
The level of global inequality is very high: Gini is 70, which is much higher than Gini of any individual country. It is a higher than South Africa’s Gini which is, as you know, the most unequal major country in the world.
But there is one more element that you can see there: at the very end of this period, and now I have some other preliminary results for 2011 which I did not put on this graph as well, the green dot (Gini) is lower than it was some ten years ago. We hope to see there the beginning of a decline in the global  level of inequality.
Now I would like to say this: this is a historical moment. Although for the past we do not have household survey data, we do have some rough estimates of what was global inequality around 1820 or 1850 and all the way to 1970-1980 when we begin to have household surveys from most countries in the world. I will not go now into how we made these guesses for the past, but they are educated “guesstimates”, not made by one person.
We know that there was a steady increase in global inequality from 1820 to around the middle of the 20th century. The increase was at first driven by the Industrial revolution; but it was also driven by the simultaneous stagnation of incomes in China and India and Africa. The gaps continued to widen in the first half of the 20th century, when many of the future Third World countries were colonies and did not experience economic growth.
Now, for the first time since the Industrial revolution we have a slight reduction in global inequality, perhaps even the beginning of a stronger and steadier decline. I don’t think that we need to exaggerate the importance of this change. It is indeed a welcome change and it is extremely hopeful. I think we should be gratified that it has happened, but we should not only focus on what may be called the “Delta Economics”, that is looking only at  the changes and forgetting about the levels. Because we should not forget that the level of global inequality is extraordinarily high by any measure  you use.
A slight technical issue which has a bearing on what I just said about the possible beginning of a decline of global inequality. In our data we are including most of the world, but our numbers are still underestimates of the real level of inequality because many poor countries that are in civil wars or where the data cannot be gathered (essentially those  in Africa) are not well represented. As you can see in Figure 5, the population coverage in the data for global inequality, which I  have just discussed, is 78% in Africa in 2008 and 70% in 2011. And you can be sure that these 22% or 30% of the missing people in Africa are really mostly very poor people in very poor countries. Thus if we could include them, there is little doubt that global inequality would go up.
Figure 5. Population coverage by household surveys
Now,  I want just to show one more graph which is I think is an important one because it shows the change between 1988 and 2008, at different points of the global income distribution. And then I would like to go into three political or moral issues which I believe can be derived from  I have said so far.
So here is the graph (Figure 6). I am sorry that I have too many graphs, but that is the reality of the world for  somebody who works with numbers. Here, on the horizontal axis, you have again the percentiles of the global income distribution, from the poorest on the left of the axis to the richest on the right. On the vertical axis  I show the real increase in income between 1988 and 2008.
Figure 6. Real income growth at various percentiles of global income distribution, 1988-2008

Now the interesting part is that at income levels around  3 to 7 international dollars per day, you have large percentage  gains between 1988 and 2008. And that is essentially among the people whom one can call,  broadly, the  Asian or Chinese middle class. These are fairly poor people by Western standards, but they have had large increases in their incomes over the past 20 or 25 years.
The interesting part of the graph are also people who are at a fairly high position by world standards, around the 80th global percentile, but who  have not seen much of the increase in their incomes. These are the middle classes of the rich world.
If you look at the data that we have for Japan, Germany, the United States, there was a clear stagnation of median incomes in those countries. So the question then becomes –and I will not go into it today –are these two developments related? Is the stagnation of the incomes of the middle class in rich countries somehow related to the emergence of the new global middle class?  This is obviously a very important question, perhaps one of the most important for today’s world.
What you can also see in this graph is, at the very top, large income increases, in percentage terms and even much more in absolute terms, of the global top one percent.
This is essentially what we now see in the global income distribution. First, we have the emergence of what is called by some the Global Middle Class. I don’t like the term very much because I believe that by saying ‘middle’ we give a misleading impression of people who live with relative ease, of what may be Western middle class income. But these are people who are just above the global poverty line, people living with incomes of 4, or 6, or 10 international dollars per day. They are significantly better off than they were 20 years ago, but they also can slip back into poverty.
So let me go now into the three issues that I mentioned before.  I discussed them  in my writings individually but I put them together for this conference: the issues of justice and politics. The first one is what I call the “citizenship rent”; the second is the issue of migration, and the third is the hollowing out of the middle classes in rich countries. Let me start with what I call the citizenship rent.
Given the fact that most of income inequality in the world can be explained by income gaps between countries, and that if I were to take incomes of all the people in the world I would be able to explain perhaps about one-half of the variability in these incomes with only one variable—the country where a person lives, you directly come to the issue of the citizenship rent.
In other words, people who live or are born in rich countries, do receive in some sense an income, a life-long income which is derived from an accidental fact of the place where they were born.  The key issue is then, should we start talking about global inequality of opportunity? Of course we talk about inequality of opportunity all the time within individual countries, because we don’t think that people, who are of different gender or race or were born in one part of the country rather than  another, should be treated differently. But we forget the issue of global inequality of opportunity. Not all of us, but sometimes I think most of us do forget. Does quest for equality of opportunity end at nations’ borders?
Now of course there are arguments against caring about global equality of opportunity, and again I will not have the time to talk about that, but Rawls, no less, has taken a position which can be interpreted largely to be against the concern with global inequality or even global inequality of opportunity. Why? Because it goes against the right of national self-determination.
I think we should be aware that there are there two goods, and like many times in life, there may be a trade-off. We cannot get both goods,  global equality of opportunity and national self-determination, but we should be at least aware that there is such a trade-off..
If we were to care only about inequalities within nations, as Rawls would like us to do, then  a global optimum would be simply a summum of individual country optima: that is, of countries’ own optimum inequality levels.
The problem with that is that it would leave untouched the main cause of today’s global inequality: gaps between countries’ mean incomes. If you reduce national inequalities but mean differences between US and Mexico, Spain and Morocco, Italy and Libya remain as they are now, you will not have reduced by much the global inequality. That is a key issue.
Let us see it in terms of numbers (Figure 7). If total current inequalities are equal to 98 Theil points (this is just another measure of inequality, similar to Gini) and you imagine, just for the sake of the argument, a totally unrealistic scenario  where all individual countries have reduced within-country inequalities to  zero, the global inequality number will go down  to only 68. So you will have reduced global inequality by one-third. This is not much. To really make a dent in the reduction of global inequality you have to have poor countries grow faster than the rich, or poor people from those countries move to the rich world.

Figure 7. Global inequality in Real World, Rawlsian World, Convergence World…and Shangri-La World (year 2008)
And that is my second issue, over which I will go very quickly because of lack of time. We should see where the issue of migration comes from. It does not come out of the blue. It is a derivative of large between country gaps that exist today. As we have seen, a key thing for the reduction of global inequality is  poor countries catching up, in terms of income levels, with rich countries. But if this  is not feasible, or  is not sufficient alone, then migration comes in. From the point of view of human development writ  large, it is the same whether a poor individual becomes richer in his or her country, or he/she moves to another country. Consequently the issue of migration, I think, has to be put on the table, not only because there is more migration now than before, as we know in Italy every day, but because it is an issue which is derived logically from our concern with global inequality.
Finally, I would put on the table an issue which was already implied in what I said before: it is the question of political decision-making. Increasingly, our income and employment are determined by global forces. At the same time, we have political life organized within nation-states and the stagnation of middle-class incomes in the rich countries.
The latter would not be a problem if the world had one political authority. Actually the developments over the past 20 or 25 years are relatively good because lots of poor people have become better off and those who lost are a group which is relatively well off. But the question is, in a political world composed of nation-states, entirely different. It is the following: these whom globalization failed are within their own constituencies, their own nation states, important and they may not like a globalization that  keeps their incomes stagnant. So there I see two dangers at the national level: one is populism and the other one is plutocracy. With the first one you mimic democracy and roll back globalization. You probably also lower the income growth rate of the poor people in emerging economies. With the second one (plutocracy), you continue with globalization at the cost of making national democracies largely meaningless. Well, we have here another trade-off!
I want to finish my talk  by reiterating  what I have basically said before. First, to reduce global inequality you need fast growth of poor countries, particularly in Africa but also in poor parts of Asia and in poor parts of Central and South America. This is absolutely crucial. Second, we have to see how to have greater migration, preserve good aspects of globalization, and not make national democracies meaningless.  Third, we need to make those who are not benefiting from globalization in rich countries, those whose incomes have been stagnant, better off through within-national redistributions. These are the three key political issues in the future years.
Thank you very much.