The Upper Middle Class Is Doing Fine, Better Than They Should Be Doing

David Callahan wrote a post here on Demos last week titled "Falling from the Upper Middle Class: New Data on Downward Mobility." Drawing upon data from the massive Chetty et al study on social mobility, Callahan argues that rich and upper middle class kids are facing downward mobility, causing them to be less well off than their parents. I have to disagree. A deeper look into the data actually shows that upper middle class kids are not only doing fine, but are actually doing much better than they should be.

To see why this is the case, it is first necessary to understand what kind of mobility the Chetty study is actually measuring. There are two basic ways to talk about social mobility: absolute mobility and relative mobility. Absolute mobility measures your income against your parents income. If your parents made $40,000/year when you were a kid and you make $40,001/year as an adult (assume these figures are adjusted for inflation so they are comparable), then in absolute terms, you have experienced upward mobility. If you make $39,999/year, then you have experienced downward mobility. The Chetty study as detailed in the New York Times report is not measuring absolute mobility.

Instead, the Chetty study is measuring relative mobility. While absolute mobility is a fairly straightforward concept, relative mobility is a little harder to grasp. Rather than compare your income to your parents' income as absolute mobility does, relative mobility compares your location in the income distribution to your parents' location in the income distribution. So for instance, if your parents' income placed them right in the middle of the income distribution (i.e. the 50th percentile), and your income places you at the 51st percentile, then you have upward mobility. If your income places you at the 49th percentile, then you have downward mobility.

There are two important things to note about relative mobility for our present purposes. First, relative mobility is totally detached from absolute mobility. It is possible (and in fact common) to make more money than your parents, but still be lower in the income distribution than they were. How? Because everyone else's income can move up even further than your income did. So you can do better than your parents in absolute terms, but do worse than them in relative terms. Second, relative mobility is an entirely zero-sum game. Think of it like a line of 100 people. The only way for someone to move up in the line (cut in front of others) is for others to move back in the line. If you support upward line mobility for some, you also necessarily support downward line mobility for others. There is no other way to do it because that's how relative mobility works.

With all of that throat-clearing out of the way, we can come back to the question of the plight of upper middle class kids. Callahan notes the following in his post:

According to the study, the more money your parents make, the less likely you'll make the same amount. If your parents earned $75,000 -- placing them in the 61st percentile of earners -- you'll be in the 56 percentile, on average, a modest generational dip in fortunes. But if your parents made $130,000, placing them in the 87 percentile, you'll be in the 64th percentile, on average. That's a much bigger fall downward. But the biggest downward mobility on average is for kids born into the top 1 percent -- who end up, on average, in the 68th percentile, a full 31 percentile points below their parents.

In sentence one, you can already see a problem. It is not possible to determine from relative mobility data whether someone is making the same amount of money as their parents. Amounts are the domain of absolute mobility, which is not what Chetty and friends are measuring. It is, as explained above, very possible to have downward relative mobility and upward absolute mobility.

More than that, if we are going to try to squeeze some meaning out of a group's relative mobility, we have to first determine what it ought to be in the first place. So, for example, ask yourself this: where, on average, should kids born into the 87th percentile wind up as adults? Well, in a perfect world of perfect social mobility, those kids would wind up equally fanned out across the entire income distribution. Some would be on the top, some would be on the bottom, and the rest distributed evenly in between. If that is what happens to those kids, what would the average of all of their outcomes be? What would their average adult percentile be? The answer is the 50th percentile.

In a society with perfect relative social mobility, the average outcomes of all kids at all starting points will always be the 50th percentile. This is not because every kid winds up with literally the same income. Rather, it is because if kids from every given starting point have an equal chance of winding up in every possible ending point (from the 1st to 99th percentile), the average outcome of kids from any given starting point will always be right in the middle, i.e. the 50th percentile. In the same vein, if you randomly distributed 100 people into a single-file line, their average place in the line will always be the middle of the line.

So kids born into the 87th percentile in NYC (one of the group's Callahan uses as an example) should, on average, wind up in the 50th percentile (just like kids born into any other percentile). But, in fact, kids born into the 87th percentile are winding up, on average, in the 64th percentile. That is, they are doing better than they should be. They are net beneficiaries of our rigged system of social advancement.

For those that believe in every child having an equal chance at every social position, the way to interpret Chetty's average relative mobility data is fairly straightforward. If a group of kids' average outcome is greater than the 50th percentile, they are the winners of our system of social immobility. If their average outcome is less than the 50th percentile, then they are the losers of our system of social immobility. How big a winner or loser they are can be determined by looking at how much above or below the 50th percentile their average outcome is.

With this understanding, the data in this blockbuster study clears up quite nicely and reaches exactly the conclusion you'd expect it to: the richer you are, the more rigged the game is in your favor. Rich and upper middle class kids, rather than tumbling and struggling to hold on, are actually doing unjustly well, at least insofar as relative social mobility goes.