Yes, your power law analysis is plausible. But I’m concerned about comparing numbers from different surveys. Self-reported net worth might be very different from net worth as observed by wealthx. Also, representative response doesn’t seem very plausible to me. It could well be that wanting to claim to have $100m causes response.
Wealthx makes a distributional claim (p6): 28% of people with 30m+ have 100m+. Only 19% in America (p9).
2^(-1.9) = 26.7%, so the power law that I obtained fits the distributional claim that WealthX makes.
I spent more time looking for data, and I’ve gotten varying estimates for income percentiles.
Thesethreesources say that top 1% of Americans is net worth of ~$7 million.
This reference (2012) says that there are 1.8 million Americans with net worth $2m+.
This source (2014) which says that 1.24 million Americans have net worth of $5m+.
The latter two bullet points seem incompatible with the first: I find this very disconcerting. Any idea as to what’s going on?
The last source above also reports 132,000 Americans with $25m+. This source (2012) reports 107,000 American households with $25+ million.
The WealthX reference that you cited (2011) says that there are only 57,860 people in the US with net worth $30+ million.
There’s some tension between these.
The two points below are in consonance with one another:
A reference (2011) that I cited in my top level post says that there are 81,000 people in the world with net worth $50m+.
The WealthX reference (2011) gives a figure on the order of 100k people with $50m+ worldwide.
The WealthX report on college alumni is from 2013 whereas the other WealthX report is from 2011: stock market fluctuations could have played a major role.
Anyway, if we estimate the number of American $30m+ people in 2013 at 100k, that’s 1 in 3,000 Americans.
Assuming that 50% of $30m+ alumni from top universities (I chose Harvard, Princeton, Yale, MIT, Stanford and University of Chicago) graduated from their undergraduate programs (need to avoid double-counting), and that 75% of them are self-made (in consonance with what WealthX says), one gets a figure of 1 in 200 students for undergraduates from top universities (calculated on my own), so your odds are boosted by 15x. If one looks at billionaires, one has more skewing toward the top schools: I get a figure of 1 in 5000 of becoming a billionaire: maybe odds are boosted by 100x relative to the general population.
Circling back to the Harvard MBA thing, even if there’s not a representative response to the survey, the prevalence of people of a given wealth is bounded below by the response rate. 23% of respondents reported a net worth of $20m+, given that 4% said $100m+ plausibly at least 15% had net worth $30m+, so at least 5% of the class as a whole. Thus, going to Harvard Business School would boost your odds all the way up to 1 in 20 (lower bound), 10x the base rate of undergraduate students at elite universities.
Is this plausible? Each Harvard Business School class is about 50% of the size of a Harvard undergraduate class, and top students who want to do business who chose to do undergraduate locally are more likely to go to a top school for graduate school: each of these factors pushes in the direction of the class being more select for ability. Then there’s the choice of attending: lower caliber students who chose to attend will sometimes have better chances than higher caliber students who choose not to attend. A figure of 1 in 20 seems not unreasonable, but a figure of 1 in 6 or whatever (coming from assuming the survey results to be representative) seems suspiciously high.
I’m disappointed that the figure of $200m+ was off: it was a pretty major update for me when I saw it – it made me think that that promoting effective altruism on elite college campuses, as well as improving the productivity of students at them could have really high expected value. But it was too good to be true – there was major tension between it and information that I had had previously.
I should add that my figures don’t property take into account the ages at which people accumulate the bulk of their net worth. For “number of graduates from top universities” I considered graduates between ages of 22 and 82, but this isn’t appropriate, since most people won’t acquire most of their wealth until later in life (e.g. the average age of a billionaire is 66), so the prevalence of eventual $30m+ people should be something like 2x what I said, and similarly, for members of the general population (where I included everyone, including children) the prevalence should be something like 3x what I said.
So the actual prevalences of eventual $30+ millionaires should be something like 1 in 1,000 (general population) and 1 in 100 (graduates of top universities).
As for billionaires, there are 442 US billionaires, maybe 100 million in the appropriate age range, so 1 in 250,000 of the general population becomes a billionaire, 129 billionaires at the schools that I looked at with ~250,000 in the appropriate age range, cutting by a factor of 2 to account for possible double counting (undergraduate/graduate), we get a frequency of 1 in 4000 eventually becoming billionaires. (About 0.4 billionaires per university class.)
This analysis is quite crude – one would need the actual age distribution and not just the average age.
Yes, your power law analysis is plausible. But I’m concerned about comparing numbers from different surveys. Self-reported net worth might be very different from net worth as observed by wealthx. Also, representative response doesn’t seem very plausible to me. It could well be that wanting to claim to have $100m causes response.
Wealthx makes a distributional claim (p6): 28% of people with 30m+ have 100m+. Only 19% in America (p9).
Very good points, thanks!
2^(-1.9) = 26.7%, so the power law that I obtained fits the distributional claim that WealthX makes.
I spent more time looking for data, and I’ve gotten varying estimates for income percentiles.
These three sources say that top 1% of Americans is net worth of ~$7 million.
This reference (2012) says that there are 1.8 million Americans with net worth $2m+.
This source (2014) which says that 1.24 million Americans have net worth of $5m+.
The latter two bullet points seem incompatible with the first: I find this very disconcerting. Any idea as to what’s going on?
The last source above also reports 132,000 Americans with $25m+. This source (2012) reports 107,000 American households with $25+ million.
The WealthX reference that you cited (2011) says that there are only 57,860 people in the US with net worth $30+ million.
There’s some tension between these.
The two points below are in consonance with one another:
A reference (2011) that I cited in my top level post says that there are 81,000 people in the world with net worth $50m+.
The WealthX reference (2011) gives a figure on the order of 100k people with $50m+ worldwide.
The WealthX report on college alumni is from 2013 whereas the other WealthX report is from 2011: stock market fluctuations could have played a major role.
Anyway, if we estimate the number of American $30m+ people in 2013 at 100k, that’s 1 in 3,000 Americans.
Assuming that 50% of $30m+ alumni from top universities (I chose Harvard, Princeton, Yale, MIT, Stanford and University of Chicago) graduated from their undergraduate programs (need to avoid double-counting), and that 75% of them are self-made (in consonance with what WealthX says), one gets a figure of 1 in 200 students for undergraduates from top universities (calculated on my own), so your odds are boosted by 15x. If one looks at billionaires, one has more skewing toward the top schools: I get a figure of 1 in 5000 of becoming a billionaire: maybe odds are boosted by 100x relative to the general population.
Circling back to the Harvard MBA thing, even if there’s not a representative response to the survey, the prevalence of people of a given wealth is bounded below by the response rate. 23% of respondents reported a net worth of $20m+, given that 4% said $100m+ plausibly at least 15% had net worth $30m+, so at least 5% of the class as a whole. Thus, going to Harvard Business School would boost your odds all the way up to 1 in 20 (lower bound), 10x the base rate of undergraduate students at elite universities.
Is this plausible? Each Harvard Business School class is about 50% of the size of a Harvard undergraduate class, and top students who want to do business who chose to do undergraduate locally are more likely to go to a top school for graduate school: each of these factors pushes in the direction of the class being more select for ability. Then there’s the choice of attending: lower caliber students who chose to attend will sometimes have better chances than higher caliber students who choose not to attend. A figure of 1 in 20 seems not unreasonable, but a figure of 1 in 6 or whatever (coming from assuming the survey results to be representative) seems suspiciously high.
I’m disappointed that the figure of $200m+ was off: it was a pretty major update for me when I saw it – it made me think that that promoting effective altruism on elite college campuses, as well as improving the productivity of students at them could have really high expected value. But it was too good to be true – there was major tension between it and information that I had had previously.
Thanks very much for the exchange.
I should add that my figures don’t property take into account the ages at which people accumulate the bulk of their net worth. For “number of graduates from top universities” I considered graduates between ages of 22 and 82, but this isn’t appropriate, since most people won’t acquire most of their wealth until later in life (e.g. the average age of a billionaire is 66), so the prevalence of eventual $30m+ people should be something like 2x what I said, and similarly, for members of the general population (where I included everyone, including children) the prevalence should be something like 3x what I said.
So the actual prevalences of eventual $30+ millionaires should be something like 1 in 1,000 (general population) and 1 in 100 (graduates of top universities).
As for billionaires, there are 442 US billionaires, maybe 100 million in the appropriate age range, so 1 in 250,000 of the general population becomes a billionaire, 129 billionaires at the schools that I looked at with ~250,000 in the appropriate age range, cutting by a factor of 2 to account for possible double counting (undergraduate/graduate), we get a frequency of 1 in 4000 eventually becoming billionaires. (About 0.4 billionaires per university class.)
This analysis is quite crude – one would need the actual age distribution and not just the average age.
What are the chances of being a billionaire or getting $30m plus if you go to Harvard rather than an elite uni?
And then what about HBS rather than Harvard?