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In his book (Evil Geniuses) about how the USA got where it currently is, Kurt Andersen speculates about how far wealth and income inequality has risen in the last few decades.

He attempts to visualise in concrete terms the implications by using this thought experiment. What would happen to the median household income were US income and net wealth were distributed evenly across households? (Andersen, Kurt. Evil Geniuses (p. 301). Ebury Publishing. Kindle Edition. ):

In this imaginary America 2, every household has a net worth of $800,000 and an annual income from all sources of $140,000.

In his words, the current distribution of US wealth and income looks like this:

The absolutely middle American economically, somebody with more than the poorer half of Americans and less than the richer half, lives in a household where the earners earn $64,000 a year and have a net worth of $100,000.

Are Andersen's illustrations for the extent of US wealth inequality correct?

matt_black
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  • Comments are not for extended discussion about personal economic theories; this conversation has been moved to chat. – Oddthinking Apr 01 '21 at 00:53
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    ... Since household income (or wealth) is presumably positively correlated with household size, your median would be artificially high in this comparison. The median that weights all households equally (comparable to Andersen's mean) would be lower, and the inequality would actually be even bigger. Of course ignore this if your statement "the median person lives in a household..." was not precise. Also, arguably households are not the best way to measure inequality in the first place, precisely because of the household size effect (is it "bad" that some households are larger than others?). – nanoman Apr 01 '21 at 08:35
  • To all those pointing out that median isn't the same as mean: yes. The claim and title should always have been median. My original title misstated this but I have now corrected it. – matt_black Apr 01 '21 at 11:02
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    @matt_black Sorry, but I think that confuses things further. Andersen's numbers are how much each household would have in the hypothetical case that income and wealth were distributed equally. That is just another way of defining the mean of the current actual distribution. The hypothetical distribution has no variation and so its mean and median are equal to that same number. The difference between the mean and median of the actual distribution is a measure of inequality among households. I thought that was why you were comparing Andersen's numbers to the actual median. – nanoman Apr 01 '21 at 11:06
  • @nanoman Yes, mean and median are the same in the hypothetical. But his claim compared that to the median of the current distribution and the title and claim should reflect that. Though pointing out the difference between mean and median of the current distribution would be useful as many will use the wrong number in discussion. – matt_black Apr 01 '21 at 11:11
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    @matt_black Okay, but I think your previous phrasing "Is the mean household income in the USA $140K...?" was fine because that is what Andersen effectively claimed. And it was the correct basis for the calculation in DavePhD's answer. Andersen just gave a longwinded explanation (in terms of imaginary redistribution) of what the mean means. – nanoman Apr 01 '21 at 11:18
  • @nanoman That wasn't my phrasing of the claim, that was oddthinking's edit. Which misstated the claim. Andersen compares the current median with the hypothetical median (which, in a flat distribution, is the same as the mean). But the comparison to the current situation (where mean and median are very different) was clearly a comparison to the median. – matt_black Apr 01 '21 at 11:22
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    @matt_black Sure, I'm just emphasizing the important relation "hypothetical mean (and median) = current mean". So "difference between hypothetical median and current median" is mathematically equivalent to "difference between current mean and current median". – nanoman Apr 01 '21 at 11:27
  • Yes, it was me that added the term mean. If that didn't match the claim, that is all on me. My apologies. 2) I remain surprised that his claim is about median: the mean would illustrate his point more clearly, and DavidPhD's answers shows that his numbers match the mean pretty closely (probably dated). 3) It would be good to quote the book where the author indicates median is intended.
    • – Oddthinking Apr 01 '21 at 16:37
  • @Oddthinking I've added the explicit quote from Andersen that clearly shows he is talking about median (which he describes without using the term itself but its definition). – matt_black Apr 01 '21 at 16:44
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    @Oddthinking See my other comments -- the point is that OP's description of the book makes it clear that Andersen is describing a hypothetical equal distribution of income and wealth, keeping the national total fixed. That's enough to make the calculation unambiguous (if every value is the same, then the mean and median are the same -- and specifically equal to the mean, not median, of the real data). – nanoman Apr 01 '21 at 16:53
  • @matt_black In that case, I consider Andersen's own comparison slightly misleading for reasons stated in my first comment on this question. – nanoman Apr 01 '21 at 17:13
  • If you divide up wealth by household like the author does, you're encouraging larger households to split up into multiple smaller households. More households means an ever increasing divisor so even if his numbers are correct, they won't be for very long. – bta Apr 01 '21 at 19:25
  • @bta Irrelevant. the question was about a way of illustrating how big wealth inequality is now (and whether it was numerically correct) not a serious proposed solution to the problem where we have to worry about the consequences. – matt_black Apr 01 '21 at 20:18
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    @bta FWIW, it's well known among economists that household size/composition is relevant to interpreting household income. Serious discussion on household incomes commonly uses "equivalised income", where the raw HH income is adjusted according to household size to make comparisons more meaningful - e.g. a single adult earning $100k might be considered on a par with two adults and two kids earning $210k under the OECD-modified equivalence scale. I have no idea whether Andersen is assuming equivalised numbers here. – GB supports the mod strike Apr 01 '21 at 23:46
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    Dear commenters: Everyone acknowledges that this hypothetical thought experiment is not stable; it is irrelevant and you do NOT need to tell us again. We all agree IN THE HYPOTHETICAL WORLD median and mean are the same; it is irrelevant and you do NOT need to tell us again. We all understand the illustrative analogy is not a perfect model; it is irrelevant and you do NOT need to tell us again. – Oddthinking Apr 02 '21 at 03:51
  • matt_black: I thank you for your recent edit, but when I read it I draw the opposite conclusion to you. It states the median household income is $64K, but the imaginary world household income is $140K. I conclude the imaginary world income refers to the mean, and I read @DavePhD's answer as confirming that (within error bars of different sources from different years). I closed it while we work out what the claim is. – Oddthinking Apr 02 '21 at 03:56
  • @Oddthinking With a totally flat income distribution (the imaginary world), the median is exactly the same as the mean. Andersen's chosen comparison in the real world is the "middle american economically" which is the definition of the median. So the claim compares medians. – matt_black Apr 02 '21 at 09:13
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    I think I see the confusion: you made two different edits to the title which had the effect of reversing each other. The question title now is effectively "If we set the median income in a fictional USA to be the same as the mean income of the USA in reality, would that median income be $X?" That is an identical question to "Is the mean income of the USA $X?" Why not use the simpler wording? – Oddthinking Apr 03 '21 at 02:32
  • @Oddthinking While you are correct (because of how the median of the hypothetical world is calculated) this confuses the calculation with the comparison Andersen wanted to make. We all agree on the calculation but I wanted to stick with Andersen's wording as he was trying to make an illustration for people who don't understand statistics. The title and question accurately report his version of the claim. – matt_black Apr 03 '21 at 13:03
  • I've reopened, even though I don't like the wording. Now @DavePhD's answer is back to being on-topic and ready to be accepted. – Oddthinking Apr 03 '21 at 16:04