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## Not Like Musical Chairs

Imagine a 20 person economy. In this economy, we can arrange all of the income earners from lowest-earning to highest earning in increments:

 Person 1 \$10.00 Person 2 \$10.50 Person 3 \$11.03 Person 4 \$11.58 Person 5 \$12.16 Person 6 \$12.76 Person 7 \$13.40 Person 8 \$14.07 Person 9 \$14.77 Person 10 \$15.51 Person 11 \$16.29 Person 12 \$17.10 Person 13 \$17.96 Person 14 \$18.86 Person 15 \$19.80 Person 16 \$20.79 Person 17 \$21.83 Person 18 \$22.92 Person 19 \$24.07 Person 20 \$25.27

The average income in this economy is \$16.53. The median income in this economy is \$15.90. Suppose you take a snapshot of this economy today, and then revisit it 20 years from now and then in 20 years you find that the median income and average income calculations are exactly the same. Does this imply that individuals in this economy are no better off 20 years from now than they are today?

Not at all. In fact, you learn almost nothing from the summary statistics I presented above. It might be the case that individuals are considerably worse off, better off or somewhere in between. Consider how a typical hierarchy works. College students graduate and elevate into the \$10 job that Person 1 has today. In each year the oldest person (assuming salaries are aligned with age here) retires, and this allows each younger worker to move up the income ladder by one spot. So in year two, the original Person 1 now earns \$10.50, and Person 19 now occupies the spot of Person 20 and earns \$25.27. If the rate of entry of college grads is equal to the rate of exit of retirees, then what you’d see is that every year a person’s living standard increases by 5% and all at the same time the average living standard of the population remains unchanged. So, if we were able to track people over time, a person starting out as Person 1 would end up 153% better off by the end of the period – this is most certainly different than what the aggregate statistics would tell us.

Of course, this could work the other way too! It might be the case that every worker is experiencing a 5% decline in wages each year, but that on average living standards are getting no worse. Further, if the rate of entry into the professions exceeds the rate of exit, it is likely that we’ll see stagnation in wages. On the other hand if the rate of exit exceeds the rate of entry, then we’d likely see increases in wages beyond what I show here.

What is unusual is that so many people seem to confuse aggregate statistics for individual well-being. What is more unusual is that many academic departments actually work this way. Very few faculty members (that I know of) complain about the stagnation in their own wages over time, even as global departmental budgets remain unchanged. So long as retirements and new hires are matched up, every faculty member can enjoy raises year after year after year while the department budget remains unaltered. Is it really so hard to imagine this happening at a larger level? Indeed, the publicly available data that follows people over time provides more evidence for this view than for the “life is no better today” view.

### 4 Responses to “Not Like Musical Chairs”

1. Rod says:

But what about the top one percent who got all that money by blind luck? Shouldn’t he (of course it’s a he because of the glass ceiling) get his income taxed at a 70 percent federal rate, a 12 percent rate in New York state and a ten percent rate in nYc? And then there’s an 8 percent sales tax, cigarette taxes, Bloomy fat and carbohydrate taxes, and if you take a walk, they tax your feet.

And why shouldn’t a Women’s Studies major get a corner office and make a hundred grand straight out of college?

2. Speedmaster says:

Well, what I get from this is that the top 2 people should be dragged around the UR campus behind a chariot like Hector for their “top 10%” ways.

After that? #s 17 and 18 should always keep their backs to the wall.

3. jb says:

I don’t know much about income mobility but want to learn more. This helps. Does this suggest that even if we had a zero growth economy, that as long as the rate of entry to the workforce is equal to the rate of exit, that it’s conceivable all individuals could see an increase in their “ranking”? (with the median and mean remaining unchanged?). Maybe “conceivable” is not strong enough. Or maybe I am missing something…

4. Michael says:

My guess is that for a period of 20 years for a relatively free economy (with social mobility), about 6 or 7 of the people in the original bottom 10 are now in the top ten, 6 or 7 of the people in the top ten or either in the bottom ten, retired, or dead, and the rest are new people just entering the market. Just a guess; if it’s any other system but some form of free market, the top ten are probably either the same top ten or the children of top ten. Same with the bottom (see North Korea).