This is a linkpost for /r/discussion/lw/ov1/putanumonit_contra_noah_smiths_bad_argument_for_a/
The most interesting thing here (I think) is the proposal to measure inequality by computing a Gini coefficient on log incomes rather than raw incomes. This seems like a fairly natural thing to do and it seems plausible that it produces a metric that does a better job of identifying actually-harmful inequality. But isn't the fact that scaling all incomes by a constant factor -- hence adding a constant to all the log-incomes -- changes the metric a fatal objection?
Does anyone have a reasonable argument for when inequality is worse than absolute poverty, and what decisions one should make based on a dispersion measure in the first place? IMO, the fatal objection is that it's pointless to pick a measure without being able to describe its use.
edit: this model should also include a reasoning that it makes ANY sense to measure by national boundary, as opposed to globally, by language group, by age cohort, or some other natural grouping.
a reasonable argument for when inequality is worse than absolute poverty
Rather seldom, I'd think. I would expect serious attempts to measure when one is worse than the other to fall foul of the usual problems around interpersonal utility comparisons etc., and if any econometric measure has been dealt with rigorously enough to make those problems go away, I haven't heard of it.
I think one can at least make a reasonable argument for why inequality is (sometimes) bad; then figuring out whether any given instance of it is worse than any given instance of absolute poverty "only" has those usual problems to contend with. Inequality is (sometimes) bad for at least the following reasons.
Empirically, even after reasonable attempts to avoid confounding with absolute poverty, inequality at the country level has been found to correlate with all manner of social ills. See e.g. Pickett & Wilkinson, The Spirit Level. (I make no claim that everything in that book is right, but it makes a reasonable argument.)
Human brains (non-human brains too, I think) operate by comparisons. Someone who feels worse off than others around them will almost always feel bad as a result. Greater inequality means more people feeling more worse-off than others. This doesn't operate only at the country level, but within-country comparisons tend to be more salient than cross-country ones because of e.g. media with national scope. (I don't claim that country-level inequality is the only sort that matters; it may well not be the sort that matters most. But it's one sort that matters, and it has the dubious advantage of being somewhat measurable because relevant statistics are available.)
Some resources are approximately fixed in quantity for quite fundamental reasons. One example (whose scope happens to be that of a single country) is influence over lawmaking. In so far as these resources are tradeable for money (political influence isn't formally, but is to a great extent in practice) inequality in money translates into inequality in access to these resources, which (because the total amount is fixed) more or less implies absolute poverty. So, e.g., most people have very little political influence. (Democracy can be thought of as a sort of UBI for political influence. Unfortunately it often doesn't work very well for that purpose, e.g. because with first-past-the-post elections many people are in "safe" constituencies and their vote has negligible effect.)
For the avoidance of doubt, (1) the existence of adverse consequences of (some) inequality does not imply that measures to reduce inequality are always a good idea (because they may themselves have other adverse consequences) and (2) the existence of such adverse consequences doesn't mean that any particular measure of inequality exactly tracks their severity. (In particular, Jacob may well be right that something like his "logini coefficient" tracks them better than the Gini coefficient does.)
So, what decisions should one make based on a dispersion measure? Probably none, directly. Rather, if you see that (say) your Gini coefficient is high, or that it's increasing, that should be a cue to look for the sort of effects described above and see whether they're bad or whether they're getting worse. What to do if so will vary from case to case.
You're getting at some interesting things which mostly support my argument against Gini, not necessarily for Logini. I agree that what we should be doing is minimizing those social ills you mentioned, not trying to move numbers on a chart. Unfortunately, making people more secure, providing cheap housing for poor people and ensuring that democracy is more representative would have no impact on Gini which to a large extent is driven by how much the top 1% makes.
I think the top 1% basically have their own economy. They make their money from capital gains and global corporations, they spend their money on luxury goods and zero sum things like Park Avenue penthouses. Besides taxes, most things that would affect normal people (minimum wages, public services, housing markets, employment shifts) don't affect the 1% and don't really move Gini.
What would a natural choice of 0 be on that log? I would nominate bare subsistence income, but then any person having less than that would completely wreck the whole thing.
Maybe switch to inverse hyperbolic sine of income over bare subsistence income?
I don't know if it's a fatal objection, it's the main thing differentiating Logini from regular Gini. Logini isn't a "pure" measure of inequality, but I argue that measuring pure inequality is not very useful.
First of all, there's no such thing as "pure inequality". Gini measures just "reported income, within country, household aggregated" inequality or something equally full of caveats. Asking for inequality without qualifications or context gets you nowhere, so why not combine absolute prosperity with income distribution? I don't think Logini is a better econometric formula in some abstract sense, just that it correlates closer with what we should care about (life quality).
I think you may be misunderstanding my objection, which has nothing to do with any notion of purity.
Suppose you measure the "logini coefficient" in some country. Immediately afterwards, they decide that instead of denominating their currency in Foobars, which is beginning to produce slightly silly results after many years of inflation, they will switch so that the New Foobar equals 1000 Old Foobars.
Suddenly everyone's income is nominally 1000x less. All your logs will decrease by whatever log-to-your-chosen-base of 1000 is. And this will completely change the "logini coefficient". Even though nothing has really changed.
There may well be a good answer to this objection. Perhaps there's a good case to be made for taking the unit of money to be, say, the price of a mass-produced loaf of bread or something. (The "good case" might be something like "meh, there's no particular justification for this, but it produces results that seem like they make sense".) But prima facie, a metric whose value can change drastically because of a change that makes literally no real difference seems problematic.
I think that most macro indicators will be vulnerable to random changes in currency denomination, which is why (as you suggested) economists don't look at just nominal value. If you're tracking changes in Logini from 2007-2017 you could convert everything to 2007 Foobars, or you could use the "loaf of bread" approach and adjust for Purchasing Power Parity. PPP is the standard way to compare currencies across time and space, it's not perfect but it gives reasonable results.
Is there any reason to interpret the coefficient by itself, rather than relative to other coefficients of other areas/times? If you were comparing coefficients you would of course use the same real-adjusted currency. If you aren't comparing, I don't see the point of the coefficient nor the problem with it changing due to the income units used.
I'd have thought you'd want to be able to say things like "if the coefficient is at least 0.618033989 then you should give very serious thought to whether you have a problem".
And it's all very well to say that if you were comparing then of course you would use a common currency for both -- but in practice I doubt it would work that way. If you compare two countries' GDPs, you look them both up, do a single currency conversion, and compare the numbers. You can't do that with logini; if you know that a country's logini is 0.739085133 when computed using pounds sterling in 2017, that is not enough information to convert it into US dollars in 2020 (even in 2020 when you know how much the dollar is worth then).
I suppose that if logini coefficients took off then people computing them might pick some standard-for-all-time currency and convert to that. Which is more or less equivalent to my suggestion of using something like the price of a loaf of bread as a unit, except a bit more arbitrary.
Yep,the correct link is here but unfortunately I can't edit the post now. I'm pretty sure I posted the URL in the right place, but not sure enough to swear that it's a bug. Maybe because I accidentally posted it to drafts first? Usually I post links straight to discussion.