## Saturday, November 22, 2014

### Intuiting Large Numbers: A Facebook Exchange

I recently had an interesting exchange with a FaceBook friend, a reasonable person with political views very different from mine. He posted something to the effect that he didn't think a free market society could produce a middle class, and supported it with the claim that at the beginning of the 20th century one or two dozen families held most of the wealth. Pretty clearly, judging by past exchanges, his view was that it was the rise of labor unions that changed that situation. I do not know if he had actual data on the distribution of wealth; if he did, I suspect that "wealth" was limited to forms of wealth, such as stocks and bonds, held mainly by wealthy people.

What is more relevant is the distribution of income, so I asked if he had data on that. I also suggested that he was being misled by the inability of humans to intuit large numbers. If a hundred people have incomes of a million dollars a year and a hundred million have incomes of a thousand dollars a year, it looks as though the hundred have most of the income. Simple arithmetic demonstrates that they actually have just under a thousandth of it.

He responded with a graph showing the share of income going to the top one percent, .1 percent, and .01 percent of the population. It did not go back quite to 1900, but extrapolating it the share of the top .01 percent then looked to be about 5%.

The top .01 percent would be about 10,000 people, say 2,000 households. So even after expanding his one or two dozen families by two orders of magnitude, their share of income was still only about one twentieth of the total, making it difficult to see how their existence could have prevented a middle class from coming into existence.

To put the point a little differently ...  . From 1900 to 1905, real GDP per capita increased by about ten percent. So if all of the income of the top 10,000 people in 1900 had been transferred to the rest of the population, their gain would have been equivalent to two or three years of economic growth. If the existence of the rich made the rest of the population too poor to have a middle class in 1900, the problem should have been solved by 1903.

Which I think supports my original point about intuiting large numbers.

At 3:12 PM, November 23, 2014,  terry freeman said...

David, are you familiar with "Why is there no socialism in the United States," by Werner Sombart? He makes the case that the American worker was 2-3 times better off than the German worker, and that the dearness of land in Germany (and, I would add, much of Europe) left workers with few options, while American workers could easily huff off to a farm, and produce enough food for a family, and surplus. I'm not sure his analysis is complete, but I'd call a population of comfortable American workers of that era something like a "middle class."

At 3:35 PM, November 23, 2014,  Anonymous said...

Doesn't total wealth matter a lot more than income for determining class? (And whether a middle class could exist?) The Economist recently ran an article which shows a graph of the wealth held by the top 0.1% compared to the bottom 90%. The 0.1% held more of the wealth in the late 20's and early 30's, but the 90% surpassed them after that. Although just recently, the 0.1% have managed to catch up again.

At 3:36 PM, November 23, 2014,  Anonymous said...

At 3:32 AM, November 24, 2014,  Anonymous said...

David, I believe you're assuming that the only possible mechanism for "keeping down the middle class" is the unavailability of wealth because somebody else is holding onto it.

Remember also that wealth and political influence are mutually attractive. In most "capitalist" nations, people who have somehow become wealthy can easily obtain political influence not available to most; in most "communist" nations, people who have somehow gained a high party/government position can easily obtain material comforts not available to most. Furthermore, this effect could quite plausibly be superlinear -- the top N% in terms of the independent variable acquires MORE than N% of the dependent variable.

While we're at it, the relationship between income and wealth tends to also be superlinear: there are tens of millions of Americans with a steady-though-small income but zero or negative net wealth, while those with a steady large income tend to accumulate more and more wealth.

If so, then the existence of a top 0.01% with 5% of the income might plausibly mean they have 20% of the wealth and 50% of the political influence.

At 8:10 PM, November 25, 2014,  Max said...

"a reasonable person"

"He posted something to the effect that he didn't think a free market society could produce a middle class, and supported it with the claim that at the beginning of the 20th century one or two dozen families held most of the wealth."

Does not compute.

At 5:50 AM, November 27, 2014,  Anonymous said...

Let's attach some actual numbers to my previous comment. According to this paper and this paper, the 0.01% of Americans with the highest income received 5% of the income, held 11% of the wealth, and made over 40% of the [disclosed] political contributions in 2012.

It's unclear, of course, how closely political contributions correlate with political influence. If you assume that political contributions are primarily self-interested, the people making them must be getting something of value commensurate with what they're paying (or at least believe that they are); if you assume that political contributions are primarily altruistic, the relation could be much weaker.

At 4:04 PM, November 28, 2014,  Anonymous said...

Your late father has a youtube video where he talks to the American Education League in Pasadena, CA.
He made a very important point on income distribution and tax policy, that the distribution data is simply based on income reporting. The inequality was squeezed out in the 50's because there were so many ways to shield income under the unrealistic tax brackets at the time.

At 4:08 PM, November 28, 2014,  Anonymous said...

At 1:37 PM, November 30, 2014,  RJ Miller said...

Let's not forget that these are statistical categories and fail to account for the fact that a real person's income fluctuates over time: