I agree with every paragraph there but one. Unfortunately the paragraph I disagree with is the important one.
The practical point made by the Taleb and Douadi paper, put in terms of observations of actual populations, is that for a fixed value of the Gini coefficient, as the population grows, the actual top 1% will come to own an increasing fraction of the total wealth. This will happen not because of any change in the causal mechanisms by which people acquire differing wealth, but just because the population is larger and is statistically likely to explore more of the fat tail. Observing such an increase therefore cannot be used to argue that the rich are being increasingly favoured, unless a correction is first made to account for this effect.
If that is the practical point made by T&D — and I’m not sure it is — it seems to me fallacious. Doesn’t it amount to saying, “the parameters baked into the underlying data-generating process we posit may be constant, so who cares that the actually existing level of inequality is increasing?” It confuses what I really care about (actual inequality) with the imperfect model (the power law) of what I really care about.
There’s also a risk of equivocating about what “the rich are being increasingly favoured” means. If it means “the power-law-producing process which, by assumption, decides people’s incomes & wealth is itself changing over time to favour the rich”, then that would be falsified by the underlying power law being constant over time. If it actually means instead e.g. “the economy will distribute a growing proportion of its output to the rich” or “underlying causal economic processes enable positive feedback loops that engender Matthew effects for income and/or wealth”, then it is quite consistent with the underlying power law being constant over time.
If that is the practical point made by T&D — and I’m not sure it is — it seems to me fallacious. Doesn’t it amount to saying, “the parameters baked into the underlying data-generating process we posit may be constant, so who cares that the actually existing level of inequality is increasing?”
Taleb is not talking about what one might care about, but pointing out some mathematical facts about fat-tailed distributions (distributions with a power-law tail) and quantiles. The population top centile, he shows, can be a substantially biased underestimate of the distribution top centile, even for very large populations (100 million).
Among the consequences of this is that if you take ten countries, each with the same value for the top centile, and aggregate them, the top centile of the combined population may be substantially larger. In that situation, what is the “real” fraction of wealth of the top 1%? The value for any individual country, or the value for the aggregate? Would the answer depend on whether the countries were all economically isolated from each other?
It confuses what I really care about (actual inequality) with the imperfect model (the power law) of what I really care about.
I’ve never understood what people find so objectionable about inequality. Poverty, yes, inequality, no. To me, what is wrong with some people being rich while others starve is only that some starve. It bothers me not at all that among those who are not poor, some are vastly wealthier than others, even though I am not one of them.
If your objection to the richness of the rich is a claim that it is causally responsible for the poorness of the poor, then you are interested in underlying mechanisms described by the distribution.
Taleb is not talking about what one might care about, but pointing out some mathematical facts about fat-tailed distributions (distributions with a power-law tail) and quantiles.
In that situation, what is the “real” fraction of wealth of the top 1%? The value for any individual country, or the value for the aggregate?
Whichever “is relevant to whatever the context is”. If the actual region of interest were the aggregate, the relevant value would be that for the aggregate.
If your objection to the richness of the rich is a claim that it is causally responsible for the poorness of the poor, then you are interested in underlying mechanisms described by the distribution.
The mechanisms entail a particular distribution, or family of distributions, and in this case the mechanisms are underspecified given the distribution. (Hence my pointing out that the phrase “the rich are being increasingly favoured” “is quite consistent with the underlying power law being constant over time”.)
If your objection to the richness of the rich is a claim that it is causally responsible for the poorness of the poor, then you are interested in underlying mechanisms described by the distribution.
The mechanisms entail a particular distribution, or family of distributions, and in this case the mechanisms are underspecified given the distribution. (Hence my pointing out that the phrase “the rich are being increasingly favoured” “is quite consistent with the underlying power law being constant over time”.)
“Increasingly favoured” is a statement about mechanisms. If the mechanisms remain the same as the population increases, then every individual who ends up rich is still working within the same mechanisms. It’s just that when the population increases, chance alone, operating on the same mechanisms, will produce many richer individuals.
Technically, the population top centile is a biased underestimate of the distribution value even for a thin-tailed distribution, but for those distributions the bias is unmeasurably small with country-sized populations.
“Increasingly favoured” is a statement about mechanisms.
When you personally state it, or in general when it’s stated by anyone? If the former, fair enough. If the latter, I disagree (cf. the last paragraph of an earlier comment). As a down-to-earth example, if I lost a game of Monopoly to you and afterwards ruefully remarked that “the dice were favouring you more & more towards the end”, I would not automatically be accusing of having swapped the original dice for a different set of dice partway through the game.
If the mechanisms remain the same as the population increases, then every individual who ends up rich is still working within the same mechanisms. It’s just that when the population increases, chance alone, operating on the same mechanisms, will produce many richer individuals.
Right (accepting arguendo the premise that the relevant mechanisms imply a power law-like distribution with α appreciably less than 2). And in that situation one could react as T&D might, i.e. by arguing that since the mechanisms remain the same, the resulting increase in equality is chimerical. Alternatively, one could react as I would, i.e. by arguing that an increase in some quantitative property of a concrete group of people does not magically become chimerical just because it arises from immutable mechanisms. (This is essentially the disagreement I laid out before between definitions (3) & (4) and definition (2) of the relevant statistical population.)
“Increasingly favoured” is a statement about mechanisms.
When you personally state it, or in general when it’s stated by anyone?
Ok, those words could be used for either meaning—to the confusion of discussion. T&D do say:
So examining times series, we can easily get a historical illusion of rise in wealth concentration when it has been there all along.
which could also be read in either sense. But the population centile and the mechanisms whereby people get rich are what they are. They are both real things, the divergence of which does not make either less real than the other.
I agree with every paragraph there but one. Unfortunately the paragraph I disagree with is the important one.
If that is the practical point made by T&D — and I’m not sure it is — it seems to me fallacious. Doesn’t it amount to saying, “the parameters baked into the underlying data-generating process we posit may be constant, so who cares that the actually existing level of inequality is increasing?” It confuses what I really care about (actual inequality) with the imperfect model (the power law) of what I really care about.
There’s also a risk of equivocating about what “the rich are being increasingly favoured” means. If it means “the power-law-producing process which, by assumption, decides people’s incomes & wealth is itself changing over time to favour the rich”, then that would be falsified by the underlying power law being constant over time. If it actually means instead e.g. “the economy will distribute a growing proportion of its output to the rich” or “underlying causal economic processes enable positive feedback loops that engender Matthew effects for income and/or wealth”, then it is quite consistent with the underlying power law being constant over time.
Taleb is not talking about what one might care about, but pointing out some mathematical facts about fat-tailed distributions (distributions with a power-law tail) and quantiles. The population top centile, he shows, can be a substantially biased underestimate of the distribution top centile, even for very large populations (100 million).
Among the consequences of this is that if you take ten countries, each with the same value for the top centile, and aggregate them, the top centile of the combined population may be substantially larger. In that situation, what is the “real” fraction of wealth of the top 1%? The value for any individual country, or the value for the aggregate? Would the answer depend on whether the countries were all economically isolated from each other?
I’ve never understood what people find so objectionable about inequality. Poverty, yes, inequality, no. To me, what is wrong with some people being rich while others starve is only that some starve. It bothers me not at all that among those who are not poor, some are vastly wealthier than others, even though I am not one of them.
If your objection to the richness of the rich is a claim that it is causally responsible for the poorness of the poor, then you are interested in underlying mechanisms described by the distribution.
The practical import of those mathematical facts lies ultimately in their relevance to features of the concrete world. If they do not bear on features of the concrete world which you or I care about, then they may have intrinsic beauty as mathematical results, but it would be mere misleading mathsturbation to present them as practically significant, as T&D do.
Whichever “is relevant to whatever the context is”. If the actual region of interest were the aggregate, the relevant value would be that for the aggregate.
The mechanisms entail a particular distribution, or family of distributions, and in this case the mechanisms are underspecified given the distribution. (Hence my pointing out that the phrase “the rich are being increasingly favoured” “is quite consistent with the underlying power law being constant over time”.)
“Increasingly favoured” is a statement about mechanisms. If the mechanisms remain the same as the population increases, then every individual who ends up rich is still working within the same mechanisms. It’s just that when the population increases, chance alone, operating on the same mechanisms, will produce many richer individuals.
Technically, the population top centile is a biased underestimate of the distribution value even for a thin-tailed distribution, but for those distributions the bias is unmeasurably small with country-sized populations.
When you personally state it, or in general when it’s stated by anyone? If the former, fair enough. If the latter, I disagree (cf. the last paragraph of an earlier comment). As a down-to-earth example, if I lost a game of Monopoly to you and afterwards ruefully remarked that “the dice were favouring you more & more towards the end”, I would not automatically be accusing of having swapped the original dice for a different set of dice partway through the game.
Right (accepting arguendo the premise that the relevant mechanisms imply a power law-like distribution with α appreciably less than 2). And in that situation one could react as T&D might, i.e. by arguing that since the mechanisms remain the same, the resulting increase in equality is chimerical. Alternatively, one could react as I would, i.e. by arguing that an increase in some quantitative property of a concrete group of people does not magically become chimerical just because it arises from immutable mechanisms. (This is essentially the disagreement I laid out before between definitions (3) & (4) and definition (2) of the relevant statistical population.)
Ok, those words could be used for either meaning—to the confusion of discussion. T&D do say:
which could also be read in either sense. But the population centile and the mechanisms whereby people get rich are what they are. They are both real things, the divergence of which does not make either less real than the other.