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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](https://chat.stackexchange.com/rooms/122523/discussion-on-question-by-matt-black-is-the-usa-this-unequal). – 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
  • 1) 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

1 Answers1

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In the 4th quarter of 2020 the net worth of US households was $122,886,624 million.

The number of US households was 128.451 million.

Therefore, the mean net wealth was $956,681

Total personal income was $19,502,071 million.

Therefore, the mean income per household was $151,825.

In Andersen's hypothetical world where all households have the same wealth and income, the median income/wealth is the same as the mean income/wealth (this is a simple statistical consequence of a symmetric, flat distribution). So the published claim about median income is broadly correct.

(In the above "income" is much more than salaries, profits, interest, dividends and capital gains, for example "employer contribution to government social insurance", and net payments from "social security", "medicaid", "medicare", "unemployment insurance", "veteran's benefits", etc., while personal income taxes are not subtracted out.)

matt_black
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DavePhD
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    Rather than just state the numbers, it would be good to use them to *evaluate* the specific statements in the question. As I read it: Andersen's numbers are approximately correct, and if anything may slightly understate the extent of inequality (differences between median and mean). – nanoman Apr 01 '21 at 08:18
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    Note that of the 19.5 trillion $ income only about 11.7 trillion are wages, the rest is other income like capital gains. For example if you owned your and my house and I pay you 1000$ to live in mine, stating that our average income is 500$ is quite misleading. If we each owned our houses, our average income would be 0$ instead. – quarague Apr 01 '21 at 10:04
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    Downvoted. The question asks about median net worth and income. This answer specifies values for the mean net worth and income. Mean and median can be very different for a skewed probability distribution. Both net worth and income are rather skewed in the US. Median net worth is about $100K rather than one million, making net worth an extremely skewed statistic. Household income was $78K in 2020 rather $152K, making income also quite skewed (but not nearly as skewed as net worth). – David Hammen Apr 01 '21 at 10:58
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    @DavidHammen See my comments on the question. I think it is indeed appropriate to evaluate Andersen's claim by computing mean income and wealth, because Anderson is considering a hypothetical where the total income and wealth are equally distributed, which is a way of *defining* the mean. – nanoman Apr 01 '21 at 11:19
  • @DavidHammen That is probably the point of the book, that income and especially wealth are strongly skewed. If a society is unequal but in a balanced way, it is pointless to compare mean and median. It does not make a difference in the numbers whether everybody has 500$ or one third has 0, one third has 500 and one third has 1000$, the mean and median are the same in both cases. But the first case is clearly more equal than the second case – Manziel Apr 01 '21 at 11:38
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    @DavidHammen: In a hypothetical world like Andersen is discussing, where everyone has the same net income, the mean net income is equal to the median net income. – Michael Seifert Apr 01 '21 at 12:00
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    @DavidHammen, you seem to entirely miss the point so let's spell it out in a comment: The question was about "What would happen to the median household income were US income and net wealth were distributed evenly across households?" In that case the median is equal to the mean (as is the highest, the lowest etc). So to compute the mean income and mean net worth is exactly as computing the median income or net worth under the proposed redistribution. The computation is thus entirely accurate and does not make any mistake confusing median and mean. – Kvothe Apr 01 '21 at 12:01
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    Perhaps the entirely obvious implication that the mean that DavePhD computed is also the median in the proposed hypothetical could be made more explicit. – Kvothe Apr 01 '21 at 12:02
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    @quarague The quote in the question says "income from all sources", so it's not just wages. – Barmar Apr 01 '21 at 12:43
  • @Barmar True. I'm not saying the answer is wrong, I'm just pointing out that it is not really a meaningful quantity the way OP wants to use it. – quarague Apr 01 '21 at 12:54
  • @DavidHammen The question changed after I answered it. The question specially asked for "mean" when I answered. See the edit history of the question. – DavePhD Apr 01 '21 at 13:50
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    @DavePhD your answer is still correct. The mean and median are the same for an equal distribution where every US household has $151,825. Whether you use the word mean or median for it is besides the point, really. – Lio Elbammalf Apr 01 '21 at 14:05
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    @quarague It's not really clear that "wages" appear out of thin air, either. Surely we have the same problem if I pay you to clean my house vs doing it myself. – user3067860 Apr 01 '21 at 14:13
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    The only answerable version of the OP's question is to treat it as an elementary statistics exercise divorced from reality. It ignores the fact that if everyone's income and net worth *was* equal, the economic situation of the USA would be completely different. (Obvious example: would Elon Musk have been *able* to found Tesla and SpaceX, with a personal net worth less than USD 1m, even if he had still wanted to?) – alephzero Apr 01 '21 at 14:58
  • Comments deleted. The comment fields are NOT the place to argue your personal views of economics. They should be focused on improving the answer. There is chat (linked under the question) for such discussion. – Oddthinking Apr 01 '21 at 16:41
  • @alephzero so what? – henning Apr 03 '21 at 20:52