In this post I will employ a statistics-based argument that money begets money. Don’t worry, I’ll get back to blathering unquantifiable bullshit soon, but this is worth it!
Angela Duckworth is a world-class research psychologist at the University of Pennsylvania who is famous for her work on grit (perseverance and determination). When she is not traveling around the world giving hilarious lectures, she is my statistics professor, which is pretty awesome for me.
In our last class, she was describing what you can learn about data just by looking at its shape on a graph. For instance, why is the “normal distribution” important? What causes the curved shape that you see below to come about? She showed us this 6 second video in which thousands of little beads are poured over a bunch of nails. When a bead hits each nail, 50% of the beads will go right, and 50% will go left. There are many more paths to get to the center of the distribution, and those on the wings have to be really un/lucky and get bounced the same way each time. And, because there are so many beads and so many factors involved, they tend to balance themselves out and by the end you get a perfectly normal distribution—the bell curve. In other words, the normal distribution is a result of a bunch of unbiased factors that sort out any given population.
So, I wondered, what is the pattern of income distribution in the United States? If it was a normal distribution, that would mean the top of the bell curve would be $51,914, the median income of the country (2011 US Census). Within one standard deviation (the average distance from the median income), you would find 68.2% of the country, as we did in the graph above and in the probability machine video. That majority would be flanked by 27% on the sides with about 4% in the extreme wings. In general we would want the standard deviation to be small, as this would point to greater income equality; people’s incomes would be closer to each other. As you can see in the graph below, more of the population is in the wings for the dark blue line, which would mean incomes would be further away from each other. The light blue line would be preferred, where people have less disparate incomes.
But what we see in the United States today is not close.
The data is skewed left. I scoured the internet for a graph that was 100% representational of our income distribution, but that proved to be as likely as finding a to-scale model of the solar system: it’s just too big. Those big bars on the right need to be spread out like the rest of the graph all the way to casino tycoon Sheldon Adelson who made about something around 7.2 billion this year (Forbes). Which means this graph is only representational of 0.0027% of the US household income distribution curve. In other words, if this graph spans 6 inches across your screen, you would need a computer screen 18,000 feet wide to see the full distribution (0.5ft/0.000027).
What does this mean?
Let’s go back to the youtube video and the beads bouncing off the nails. From the basic statistics that I understand, radically skewed distribution implies that the history of beads matter. If the the bead had bounced lucky last time, it was more likely to bounce lucky again, and vice versa. This makes sense to me. It is much more difficult to go from an income of $30,000/year to $40,000/year, than it is to go from $1,000,000,000/year to $1,000,010,000/year. In other words, the further down the road to wealth you are, the more likely you are going downhill.
So, I have advice for those looking to make more money; the first step to making money is having money. The rich get richer. Of course, there are plenty of exceptions.
I am sending this post to Professor Duckworth and my assistant professor, Peggy Kearn. I want to hear what they think and see if there are any other conclusions we might draw from the shape of income distribution in America.
March 19th, 2014 at 4:31 AM
I’m hoping I can use your two blue line diagram (the bell curves) for a non-commercial presentation on inequality–is this image yours? Any chance I can use it under Creative Commons?
March 22nd, 2014 at 2:09 PM
They are not my images. I just found them online. best of luck and let me know if I can be of any more use.
November 1st, 2012 at 10:04 PM
Einstein was a dyslexic without the cranial acromegalia (LITFU) to pull it off, for I expect my ivy league education friend to be sparring with voodoo in the shadows of our parasympathetic nervous system – parse bits of magic, display for me the entrails of fairies, dissect our devils and pin the wings of better angels. What ever happened to all that quantitative triple-blind-bound-and-spanked data you promised us? If most of these helpful tidbits your shilling are up for philosophical debate then what are you gleaming from your studies besides an opinion that can probably be snagged from somewhere in the six rows of self-help books at my local Barns and Noble?
Like you pointed out at the end of one of your older posts: this is all pretty intuitive is it not? Having a favorite thing to look at that makes us feel better is as old as art, opinions, and boobs. And fabulous blogs like yours. Thank you internet for one stop shopping.
November 1st, 2012 at 10:21 PM
oh, and “second” my ass Ben, T Swift doesn’t count as a band GFYS.
November 9th, 2012 at 3:25 PM
1) I am not blogging about what I am learning, but what I want to blog about. 2) very little in cutting edge science can be said with nuance. 3) You can make fun of my height, the size of my nose, my foolish stutter, or the length of my toes, but if you mess with how awesome my program is, you will make me mildly annoyed for a second, and then I’ll pat you on the head and give you a treat. It’s hard to stay angry when you are so cute.
November 11th, 2012 at 11:51 AM
1 & 2 I’m sorry, I just get so excited thinking about what you’re learning I just what you to tell me everything. My rusty manners in combination with Code Red Mountain Dew often get the better of me when delicately trying to provoke my friends into hurtful arguments. I’ll work on my subtlety.
3, you’ve got the physical parameters of an mid-level character from a Jewish version of The Wind and The Willow.
November 11th, 2012 at 11:09 PM
lol…great one liner. Not quite as good as “your posts are like deployments to Afghanistan…” but nonetheless superb.
October 27th, 2012 at 10:49 PM
Back in my academic prime I learned about circles, squares, squished circles, lines, segments, and I think what we’re dealing with is a ray, the x axis, the horizontal line, it’s a ray and rays just aren’t very compliant at producing symmetry, and without symmetry curves just kinda suck balls at being bell shaped. (we’re not on the gold standard: wealth generation and earning potential is infinite for all intents and purposes, while there are limits to how indebted a person can become before people stop giving them money.) Outliners only have room to pop up in one direction (no pun intended in reference to best band ever! Louis Tomlinson you suck balls at nothing!). Any country’s distribution-of-annual-income chart will look baseball-cap shaped, won’t it?
Your egalitarian beads may default to judicious symmetry when falling through nails, but for humans equality is an elective synthetic frequently antithetical to social homeostasis. I don’t know if I really believe in any part of that last sentence but it felt good to write. (no, I agree with the fist 2/3rds of it.) Conclusion: Equality is only intrinsic to humans if you pick them up and drop them from the same spot, thank you Jeremy Clifton.
Your posts are like deployments to Afghanistan, it’s getting harder and harder to figure out the point 🙂
October 27th, 2012 at 11:36 PM
That last line was RIDICULOUSLY hilarious. I laughed my ass off. Alicia ran over to see what I was laughing at.
You have points, some of them good. I liked your ridiculously well-worded sentence in the middle…how did that happen? I was kinda blown away by your brilliance and verbosity.
But shiny foreheads have a way of piercing the fog. First, as Wilkinson talks about, more egalitarian societies are actually more stable than non-egalitarian ones. So allowing the rich to get more and more wealthy does not lead to homeostasis happiness and wealth. It leads to revolutions, recessions, and resentment.
I say ’the point’ in the first line. I’m simply arguing that wealth begets wealth. If circumstances favor you, than circumstances are likely to favor you in your next set of circumstances. While I though this before, it turns out that this is a statistical reality (I think) with no room for ideology (I think). Second, I agree with you that there is no room to be an ‘outlier’ on the poor side of the income distribution, but that in itself is interesting. Only the wealthy stand out and poverty is mundane.
For our society has decreed in full throated calls that “wealth generation is infinite” and that Sheldon Adelson deserves the 21 billion he has made over the last three years through his casino empire. That is the sort of productivity we need in this country, and it should be rewarded with 140,000 times the annual salary of a teacher. Teachers, after all, are only teaching our kids, and badly too, with their collective bargaining and bratty unions. But Adelson educates our hearts.
October 29th, 2012 at 8:52 PM
Jer, you can educate my heart all night long. Just keep talking standard deviations to me, you filthy filthy man. I also LMFAO’d at Eric’s line. (pun very much intended in reference to the *second* best band ever). Truly tragic that such whit (lulz) is wasted upon the blogosphere. In serio, though, I like your quantifiable bullshit just as much as your unquantifiable. Maybe more. kudos bars.
October 30th, 2012 at 1:27 AM
I hate missionary kids who are culturally literate. I had to LTFU (Look the fuck up) LMFAO and the band.
I’ll try to keep my musings as quantifiable as is reasonable. But as Einstein said, some of the most important things can’t be measured, like how much I enjoy your comments on my blog ; )
October 26th, 2012 at 4:47 PM
Way to normalize your distributions. Interesting way to think of how it is easier to make 10k more when you are very rich. Also, it would have been easy to make your own graph of the US income distribution using a program like excel.
October 26th, 2012 at 4:16 PM
The saddest part of that graph is that it peaks between $15-$20k.
October 27th, 2012 at 9:54 PM
indeed! It would be less upsetting if the peak was closer to what some might consider “middle class”.