Sunday, August 10, 2014

It's The Population, Stupid

Here's something that Maitreesh Ghatak (at the LSE) and I wrote together:


The Times of India recently reported, not without a certain self-congratulatory air, that: "The latest wealth index by New World Wealth that looks at multimillionaires — an individual with net assets of at least $10 million — has ranked India eighth in the global rich list, below countries such as the US, China, Germany and the UK but above Singapore and Canada."

This has certainly sent Indian cyberspace into a little tizzy. A common celebratory headline: "India has more multimillionaires than Australia, Russia and France!” And given that the largest number of the world’s poor also live in India, a common admonitory reaction is: "See? Told you so! India is just a corrupt society."

This isn't the first time we've been gobsmacked by the sort of numbers India can generate. Recently, farmer suicides did the rounds, with the already large numbers (around 300,000 since 1995) helped along by the Indian numbering system: read here for why some participants in a recent BBC debate had it wrong by a factor of 10 . All quite understandable: India is so large that nobody has a real sense of the numbers anyway. Which is why the following handy little motto should always be clutched close to heart and brain:

When confronted by a Large Indian Statistic, consider dividing by the population.

We learn from the same source (New World Wealth) that the world has 495,000 multimillionaires, and India has 14,800 of them. Divide: India has just 3% of the world's multimillionaires. It has, however, 17% of the world's people. Suddenly India is looking like it does not have its “fair share” of multimillionaires.

Now, of course, India is a poorer country. The real question is whether India has more than its expected share of multimillionaires once we take into account this fact. To do this in a lot of detail will take some real work, but we’re in a back-of-the-envelope mood for this post. So, whipping out a handy envelope on World Bank letterhead, we carry out some quick calculations.

In 2012 Indian per-capita income was USD 1,550, and world per-capita income around USD 10,235, suggesting that the ratio of Indian per-capita income to the world average is a measly 0.15. Meanwhile, the multimillionaire ratio (India’s share relative to its population) is 3/17 = 0.17. These two ratios are very close, which suggests that neither self-congratulation nor admonition is quite called for at this stage. But we will need to dig deeper.

Let’s think about millionaires for a moment: those with assets of USD 1m or more. According to WealthInsight (see this link), India had 251,000 millionaires in 2012, around 0.02% of the population. The corresponding number for the United States is 5,231,000, around 1.64%. Thus, using the United States as a benchmark, India’s millionaire share in the population relative to the US is 1.22% (the ratio of 0.02 to 1.64). At the same time, India’s per capita income is only 3% of that of the US. So: does India have too few millionaires relative to the United States, after making the income correction? Not really: if two countries have the same level of relative inequality but different mean incomes, a halving of mean income predicts a change in the population incidence of (multi)millionaires by a factor that typically comes down by more than half, the exact prediction depending on the distribution of wealth. This is (in part) because “millionaire” or “multimillionaire” is a threshold concept: a fixed monetary figure (USD1m for the former, USD10m for the latter) has to be crossed. One good way to explore the predicted change is to employ a Pareto distribution of wealth, along with the population-weighted average Gini coefficient for wealth distributions (which is a bit over 0.65, and calculated from this link). Then a halving of per-capita income is expected to lower the (multi)millionaire share of the population by a factor of approximately 2.38. If we really go out on that limb and plummet from the heights of US per-capita income (USD 50,660) to that of India (USD 1,550), we would expect the both the millionaire share and the multimillionaire share in India to be approximately 1.28% that of the United States.

Since the actual millionaire share in India relative to the United States is 1.22%, which is remarkably close to the prediction, India does not appear to be out of line, as far as millionaires are concerned (and after we have corrected for economic differences). But the case of multimillionaires tells a rather different story. In India the multimillionaire share is 0.001% of the population, while in the United States it is 0.058%. Taking ratios, we see that the multimillionaire share in the population in India is 2.06% of the corresponding share in the United States. This number is surely high relative to the prediction of 1.28%.

This parallels findings by Piketty and his colleagues. India does not stand out in terms of income going to the top 1%, but it does in terms of income going to the top 0.1%.  While there is noise in all these data, we would tentatively conclude that India, controlling for economic differences, has “more multimillionaires than it should.” While this may generate applause in some circles, we would therefore side with the admonitory warning bell sounded by Raghuram Rajan.

Country
Relative Income
M-Share
MM-Share
Predicted
Relative Share
Relative M-Share
Relative MM-Share
India
0.03
0.020
0.001
1.28
1.22
2.06
China
0.11
0.094
0.002
6.54
5.71
3.38
Hong Kong
0.72
2.604
0.213
65.88
158.56
370.25
UK
0.75
1.053
0.034
70.08
64.12
58.76
Germany
0.88
1.643
0.031
85.44
100.03
54.62
Japan
0.94
1.656
0.017
92.73
100.85
28.68
US
1.00
1.642
0.058
100.00
100.00
100.00
Singapore
1.01
2.908
0.122
101.06
177.07
212.20
Switzerland
1.60
3.639
0.224
179.66
221.61
389.25
World
0.20
0.167
0.007
13.54
10.18
11.97

Notes and Sources: Relative Income is country per-capita income relative to US per-capita income (from the World Bank Databank). M-Share is millionaire divided by population, in percent, and MM-Share is multimillionaire divided by population, in percent (from Times of India, New World Wealth, WealthInsight, and United Nations). Predicted Relative Share uses Relative Income and a Pareto distribution, along with the population-weighted average of within-country wealth Ginis (approx. 0.67) to generate predicted relative share of millionaires and multimillionaires in each country relative to the United States, in percent.  Relative M-Share and Relative MM-Share are the actual relative shares generated from columns 3 and 4, by expressing those numbers relative to the US numbers, in percent.

Remembering that the United States is itself a country with very high inequality, this is additional cause for concern.  For instance, China comes in below its predicted value for both millionaires and multimillionaires, and countries such as Japan and Germany come in far below the predictions for multimillionaires, as does the world as a whole. Countries with a significantly higher share than their predicted values are Hong Kong, Singapore and Switzerland; see Table.

Take away points? India is poorer than the world average and so naturally has a greater percentage of poor people and a lower percentage of rich people. Yet using the absolute numbers, India has more of almost everything, which is misleading. Indeed, correcting for income differences, India has the “expected share” of millionaires relative to the United States. However, looking at the super-rich, namely, the multi-millionaires, India does have more than its expected share: something not too savory is cooking on the very end of the right tail.

Lesson: for India, always do the percentages, whether for multimillionaires or for farmer suicides. We might then learn something.

Endnote: A previous version of this post contained a cautionary endnote explaining that our rudimentary analysis could be complicated by a proper accounting of threshold effects. Following up on this, we subsequently extended the analysis. 


Tuesday, June 3, 2014

Ray on Milanovic on Ray on Piketty

Branko Milanovic has commented in some detail on a recent post of mine, about Piketty's Capital in the Twenty First Century. My initial urge was not to reply. But I see that Branko's post is getting a fair amount of attention on the net, with a wealth of approving accompanying comments about theorists who know nothing of that grand place, the Real World. 

So here is an attempt to point out why Branko's post is problematic. Not that it will help much with the general public who are (to some extent understandably) distrustful of academic arguments. And we all know it never ends: the title of this post puts me in mind of the little old lady who snapped, "Young man, it's turtles all the way down!" 

Preamble.

At various points Branko claims that I bring to bear a ahistorical, abstract set of arguments on what is a vibrant historical process. In doing so I'm apparently missing all the nuanced depth of Piketty's Laws. It is hard to convey just how strongly I disagree with this position, and I am not going to try. Suffice it to say that there is no substitute for one indispensable tool of debate, and that is logic. So let me take Branko's points, one by one, and attempt to address them logically.

NB. I personally like Branko, and I like his work too. So if what follows sounds hard-hitting, it is all in good spirit. With that Branko, pick up your chhota peg: cheers!

Point 1.

"While r>g may be a feature of all growth models it is still a contradiction of capitalism for three reasons: because returns from capital are privately owned (appropriated), because they are more unequally distributed (meaning that the Gini coefficient  of income from capital is greater than the Gini coefficient of income from labor), and finally and most importantly because recipients of capital incomes are generally higher up in the income pyramid than recipients of labor income."

I agree with all three of these observations. So far, I see no connection between them and r > g. But wait, I've interrupted him, he has more to say:


"The last two conditions, translated in the language of inequality mean that the concentration curve of income from capital lies below (further from the 45 degree line) the concentration curve of income from labor, and also below the Lorenz curve. Less technically, it means that capital incomes are more unequally distributed and are positively correlated with overall income. Even less technically, it means that if share of capital incomes in total increases, inequality will go up. And this happens precisely when r exceeds g."

Ah, here we are: r > g is precisely when the "share of capital incomes in the total increases" (presumably he means increases over time), and then the rise in overall inequality follows from the other assumptions --- his "last two conditions". There are, then, two pieces in his reasoning, and r > g apparently generates a progressive dominance in the share of capital income --- this is the first piece. 


But this piece is clearly wrong, and as I will fully describe in the next point (and have already stated in my earlier article), r > g implies nothing about the share of capital in total income, nor its change over time. For instance, in any model of balanced growth, r > g is entirely compatible with constant income shares of capital and labor. I've said as much in my article, but as there seems to be some persistence of this confusion, see point 2 below.


Dear reader, do not infer from this statement that I believe that the share of capital incomes will not rise. Indeed, I believe that they will rise. I say as much in my post when I discuss the "fourth fundamental law" of capitalism. My only assertion here is that r > g has nothing to do with it.

The second piece of Branko's reasoning is correct. If we assume that capital incomes are more unequally distributed than labor incomes, and if  we assume that the share of capital incomes in the total increases over time, then sure, total inequality will generally climb. But all these "ifs" are endogenous outcomes. Sure, they could be empirically what we observe. And as I have said many times: I fundamentally agree with the empirics. But please, don't tell me that this is some deep theory of inequality when all the "ifs" in that sentence pretty much assume the answer already. I expect the public to swallow it, but I don't expect a serious scholar to peddle it.

In any case, for the 87th time, r > g has nothing to do with any of the reasoning in the paragraph above, and I drive that home (dream on, Debraj!) in my discussion of Branko's next point.


Point 2.

"[r > g] It is indeed a contradiction of capitalism because capitalism is not  a system where both the poor and the rich have the same shares of capital and labor income. Indeed if that were the case, inequality would still exist, but r > g would not imply its increase. A poor guy with original capital income of $100 and labor income of $100 would gain next year $5 additional dollars from capital and $3 from labor; the rich guy with $1000 in capital and $1000 in labor with gain additional $50 from capital and $30 from labor. Their overall income ratios will remain unchanged. But the real world is such that the poor guy in our case is faced by a capitalist who has $2000 of capital income and  nothing in labor and his income accordingly will grow by $100, thus widening the income gap between the two individuals."

Oh dear, here we go again, a repetition of the very same error I've been trying to fix. Let me first make my point in words, and then we'll see where Branko makes his mistake.


Here is the point: income is income is income, no matter where it comes from. Therefore, inequality will increase if the rich save more than the poor. It will stay constant if the rich save at the same rate as the poor. And it will decline if the rich save at a lower rate than the poor.

Relax, dear reader! I know you're itching to say, "but in the Real World only the first of those statements is true." I grant that to you without the semblance of a quibble. But my point was and is that r > g has nothing, absolutely nothing, to do with whether inequality goes up or down. All that matters (in this particular context) is whether the relatively rich save more of their income than the poor, and not the current composition of savings. 

The following thought experiment might help. Remove a rich man's capital wealth completely, but allow him to keep his labor income of $1 million. Meanwhile, find a poor man with some meagre labor income, say $10,000 a year, and present him with a one-time gift of $100,000 in shares, yielding another $10,000 in dividend income. I've now created a situation in which the rich man currently has no capital income, whereas the poor man has 50% of his income from capital income. Does this mean that the poor man's income will grow faster? The answer is: certainly not. It will all depend on who saves more out of his income. It is irrelevant whether that income is earned in the form of capital, or labor.


This discussion yields two lessons:


Lesson 1. Income is income no matter how it is earned, so the composition of income at any date is irrelevant. All that matters is whether the rich save more than the poor.

Lesson 2 (for the 88th time). r > g has nothing to do with any of this. 

Where did Branko make his mistake? It is right here, in this line (and in similar lines after it):

"A poor guy with original capital income of $100 and labor income of $100 would gain next year $5 additional dollars from capital and $3 from labor..."

What the guy makes next year from his capital income is emphatically not $5. What he makes depends on how much of that income he saves. Each dollar he saves will earn him a 5% return, but that does not mean he will have $5 tomorrow simply by virtue of having a capital income of 100 today. That makes no sense.

What's more, he would make that 5% return no matter whether he saves part of his capital income or part of his labor income. That saving would yield him 5%, because that is the assumed rate of return on capital (=savings) in this example.

After all this confusing (and confused) flailing around with r > g, we finally get to something we can agree on:


Point 3.

"Let us be clear: If capitalists were spendthrifts and used all their income on consumption,  there would be indeed no accumulation of capital, we would be in Marx’s simple reproduction, and Debraj would be right. But again this is not the  world we live in.  Not only is the assumption that capitalists save and reinvest 100% of their capital income a standard one in growth models... [i]t also corresponds with empirical data."

I didn't say anything different. I have been emphasizing different savings propensities throughout my article. I completely agree that differential savings rates between rich and poor is an enormous driver of inequality. If you consistently save a larger fraction of your income than I do, and our labor incomes grow at the same rate g, you will become infinitely richer than me as time goes by. I guarantee it. Yet, at the risk of developing a sore throat, let me say it for the 89th time: r > g has nothing to do with it.


Much of Branko's article consists of statements made about my thinking that are odd, to say the least, and I am not sure how to respond to them. But hey, blogs will be blogs, so let's hear:

"Now, why has Debraj gone astray in his otherwise very lucidly argued paper? Because he essentially assumes that economic processes described by theory of growth are abstract and do not take place in a capitalist environment..."


Hmm...and what is this "capitalist environment"? Milanovic barrels on:

"...where indeed the facts are such that capitalists tend to be rich (and not poor), and where such capital owners do not spend all of their income on consumption."

Oh Branko, are you sure you've read what I wrote? Here are some quick extracts from my post:

"richer people can afford to (and do) save more than poorer people. But that has to do with the savings propensities of the rich, and not the form in which they save their income. A poor subsistence farmer with a small plot of land (surely capital too) would consume all the income from that capital asset."

And later:

"[T]he savings rate climbs with higher incomes. This is an important driver of secular inequality. One can pass through several Kuznets cycles, but the rich will always be in a better position to take advantage of them, and they will save at higher rates in the process. The process is cyclical, but not circular." 

It sounds like this aspect of the "capitalist environment" is something that I just might be aware of. (And there's more --- much more --- to be aware of, such as the implacably labor-displacing nature of technical progress, which I discuss in my article.) What Branko is doing is turning a precise discussion, in which I am examining Piketty's Third Law, into a statement about my general ignorance of the capitalist system. Come now Branko. Would you like to examine Piketty's Third Law, or would you like to tell me about the savings propensities of the rich? On the latter we are in agreement. In fact it is far better candidate for a "Law" than any in Piketty's book. But what has the Third Law to do with it? And if it doesn't (as I hope you see by now), my leaving it out is not a hallmark of my "going astray," but rather to discuss things in the only way I know: scientifically.


Conclusion.

In closing, let's get something straight. I've read my Capital (nope, the other Capitaland here's a little secret: the author is a hero of mine for asking some of the greatest questions of all time). As a matter of fact, I am deeply interested in historical processes. I believe I do not neglect them in my work, or I try not to. I firmly believe that capitalism tends to generate ever-widening inequalities, for the reasons that I have outlined in my previous post and that I will expand upon in the near future. And I am not some right-wing stooge dumping on Piketty using abstract mathematical arguments, or an economist who unabashedly believes in free markets. These are simplistic ways to categorize Piketty's critics.

What I do believe in, however, is clear-headed reasoning. There is data --- and a lot of great data in Piketty's book --- and then there is explanation, or theory. When discussing the data, discuss the data. But when doing the theory, let's not slip  "historical truths" or "capitalist reality" in there. If you want to explain something, don't hide behind the skirts of that great seducer, the Implicit Assumption.