Income inequality is one of the major issues in this year’s presidential election, and there is no shortage of statistics to convey just how dire the status quo is. Below, I’ve gathered a few examples:

- Bernie Sanders says top 0.1% have almost as much wealth as the bottom 90%
- Top 1% pay nearly half of all federal income taxes
- Richest 1% earn biggest share since Roaring ’20s
- As union membership has fallen, the top 10% have been getting a larger share of income
- An Economic Cancer: The Top 1% Earns More Than the Bottom 50%

You get the idea. It seems there is almost no way to talk about income inequality (or tax policy) without resorting to the use of statistical aggregates (1%, 10%, etc.). The results of any such analysis can be jarring, and lead to many interesting questions. Is it really fair that 0.1% of population should possess 90% of the nation’s wealth? Should the top 1% really make more than the bottom 50%? Can the government do something to ensure income is more broadly among the population?

While these are all interesting questions, they rely on two very important assumptions:

- “The Top x%” group contains a consistent group of individuals over time.
- Extreme income inequality, among different income brackets, is an aberration.

The problem with these assumptions may not be immediately obvious, but it will become clear if we try out a slightly protracted thought experiment. Using broad statistical aggregates seems to be a reasonable way to describe these issues. However, it breaks down quickly under any scrutiny.

To illustrate this problem with statistical aggregates truly are, I decided to run the numbers on a hypothetical economy–the economy of Equalistan–that is completely equal by design. Here are the key assumptions driving Equalistan:

- Everyone starts work at age 23 at a starting salary of $40k per year. No one is unemployed after this age.
- Combining the effects of annual salary increases and promotions, it is assumed that everyone’s salary increases by 5% per year.
- Each person saves 5% of their income each year, which is added to their wealth
- Each person earns a 5% return on their accumulated wealth. (And to make the math easy, this is calculated off the wealth at the end of the previous year).
- Everyone starts off at age 23 without any student loans and without any wealth of their own.
- Everyone retires promptly at age 65.

Now, it may be correctly argued that the assumptions driving my imaginary society are unreasonable. I would readily agree. However, I hope we can all agree that such a society would be a veritable utopia for those concerned about income inequality.

So let’s see the results:

Note that in this table, all of these calculations are somewhat conservative, because they only include the working population. By assumption, no one is unemployed, and retirees are excluded from these percentages.

In spite of this conservative approach, and the explicitly equal nature of the society imagined, the statistical aggregates still paint a darker portrait. The 1% is well under control it would seem. But it’s still the case that the top 10% owns dramatically more than the bottom 50%, and the top 20% makes almost 50% more than the bottom 50% does. What accounts for this?

Well, the most important fact is that in Equalistan, as in real life, older, more experienced, people tend to make more money than their younger counterparts. Older people are also likely to have accumulated more wealth, which, in the absence of Federal Reserve shenanigans, will generate meaningful returns on their investments each year. This wealth accumulation effect naturally contributes to income disparity, even though it is presumably not a feature of a market economy that we want to eliminate for ourselves

What all of this tells us is that using statistical aggregates like the top 1% or top 10% is deeply unhelpful. Some economists and politicians like this approach because the data is easy to access and it produces neat headlines. And in a very literal way, it does define the extent of income inequality.

But when we talk about income inequality, the inequality at any point in time is not the real issue. What we really ought to care about are poverty and social mobility. If no one was in poverty, it is my contention that we would not care how much the top 5% earned. Similarly, if even people from poor backgrounds had an equal chance to make it to the top, it would matter much less to everyone just how much those people made.

Of course, neither of these features describe the world in which we actually live. Poverty still exists and social mobility is not as strong as we would like. But if we are going to understand and evaluate progress on these issues, a good first step would be to use meaningful data. After seeing the thought experiment above, the bottom 100% of people should agree that mere rhetoric about “top 1%” isn’t sufficient.