A few months ago, I wrote a post called “Equality of Opportunity: Part I.” Like a good movie executive, I left open the possibility of a sequel. In fact, the end of that post was the Economics Blog equivalent of a cliffhanger.

The cliffhanger was that the definition of equal opportunity I laid out didn’t really work. The definition was: “People who put in the same amount of effort, should achieve the same outcome, regardless of their circumstances.” The problem was with the word amount.

The question raised at the end of that post was simple: what if kids in more challenging circumstances aren’t able to devote the same amount of effort as more advantaged kids? For example, teens with college-educated parents are almost twice as likely to spend at least 10 hours a week doing homework as those with non-college educated parents. The reason is not laziness on the part of teens with less-educated parents. Instead, these teens were simply more likely to work for pay. You know, because their parents might be struggling economically.

So, if we imposed the definition of equal opportunity above, what would happen? Well, students with less-educated parents would get worse educational outcomes than kids with more-educated parents. And, under that definition, we would be fine with that outcome. After all, the more-advantaged kids put in more effort towards school work. Right? Actually, I would argue that this logic is wrong.

What is Effort?

Is effort really best defined as the amount of time put towards a certain goal? For example, is one hour of homework with no other responsibilities equal to one hour of homework when one is also working a part-time job? Or, when one student is studying with a professional tutor, while another labors alone? I think not.

The clear truth is: circumstances affect effort. And, this fact is the fundamental problem with the definition of equal opportunity I laid out above. Our advantaged student may be able to work 10 hours a week on homework without cracking a sweat. On the other hand, our less-advantaged student may struggle to get to 5 hours a week. Unfortunately, under our current definition of effort, we would view the advantaged student as working “harder.” And, the advantaged student would be rewarded, reinforcing that advantage across generations.

Before continuing, it’s worth noting — the goal of ensuring equal opportunity is not the same as ensuring equal outcomes. In an excellent article on defining equal opportunity, John E. Roemer puts it thus: “equality of opportunity finds no moral bad in inequality of final condition across individuals ascribable to differential effort.” Inequality in outcomes is fine, as long as it is due to differential effort. What I am arguing is that we need to think about effort differently.

Redefining Effort

Luckily, a small tweak in how we think about effort can make a big difference. Imagine a group of students who one might call “advantaged.” They do not need to work to help support their families. They go to high-quality schools and face few distractions. Their parents can afford professional tutors. And then imagine a “disadvantaged” group, that lacks these benefits.

Now, define effort relative to others in the same circumstances. We would now assume that the student who spends the most hours on school work in the advantaged group is working just as hard as the student with the most hours from the disadvantaged group. The advantaged student may work more hours. But, some of those extra hours reflect their relative advantage. If the hardest working disadvantaged student were in the advantaged student’s shoes, we would assume that they would also spend more hours on schoolwork.

Defining effort in this “relative” way holds people responsible only for things within their control. In other words, it recognizes that circumstances affect effort. And, if we use this definition of effort, we will get a definition of equal opportunity with interesting — and testable — implications.

A New Definition of Equality of Opportunity

The new definition of equal opportunity will look very similar to the first. The main difference will be replacing a single word — “amount” with “relative.” Our new definition: “People who put in the same relative effort compared to others in the same circumstances, should achieve the same outcome.” Under this definition, our hardest working advantaged student and our hardest working disadvantaged student would both have the same outcome. So, our society would have to enact policies that ensure both students can graduate from a good college or otherwise have access to a good career.

The nice thing about this definition is that it has a very clear implication: no correlation should exist between a child’s circumstances and their outcomes later in life. After all, within groups defined by circumstances, there will always exist a hardest working person, a second hardest working person, etc. And, under this definition, people in the same relative position should arrive at the same outcome.

Taking the Definition to the Data

Like I said, this definition of equal opportunity has a clear implication. No correlation between circumstances and later-life outcomes should exist. So, can we test this implication?

The answer is yes, and a team of researchers at OppurtunityInsights.org has done it. What they did sounds simple (it’s not!). Basically, they obtained recent tax data on a group of people born in the early 1980s. These individuals are now in their 30s, and the researchers can observe things like income and past college attendance. The researchers then obtained data on this group’s parents’ income in the late 1990s, when the subjects were teenagers. Finally, the researchers merged the parents’ income onto the children’s outcomes to see if any correlation exists. Under our definition, it shouldn’t.

But, of course, a correlation does exist. Below, I have reproduced a figure from a paper by Raj Chetty, Nathaniel Hendren, Patrick Kline, Emmanuel Saez, and Nicholas Turner. The figure shows how parent’s income relates to a child’s likelihood of attending college. Under our definition, the line should be flat. It ain’t. A child whose parents are in the twentieth percentile has a 40 percent chance of attending college. A child whose parents are in the 80th percentile has an 80 percent chance, or twice as high.

Figure 1. Likelihood of Attending College based on Parent’s Income.

Source: Chetty et al. (2014).

Other outcomes are similar. For example, a child born to a parent in the bottom 20 percent of the income distribution has a 10 percent chance of making it to the top 20 percent. For a child born already in the top 20 percent, the chance is three times higher of remaining at the top, or 30 percent.

What’s perhaps more interesting is that certain places have more equal opportunity than others. The map below plots how steep the line from Figure 1 is for various places in the U.S. Dark red means a steeper line, and therefore more inequality of opportunity. The map makes two things clear. One: the south struggles. Two: tremendous variation exists in equality of opportunity even within the U.S. Some places do well, and those places may be worth learning from.

Figure 2. Map of Equality of Opportunity (dark red is more unequal)

Source: Chetty et al. (2014).

The Land of Opportunity?

So, does all this mean that America is not the “Land of Opportunity,” it purports to be? This question is something we all struggle with. On the one hand, we all know of stories of people who start out low-income and climb the ladder. On the other hand, I would argue that we know those stories for a pretty simple reason: they are rare. And, maybe because these stories conform to a narrative we want to believe.

I think a small change to the moniker can help. From “Land of Opportunity” to “Land of Possibility.” I think it’s true that almost anyone can make it to the top in the U.S. The problem is that possibility is not the same as equal probability. Think of it this way. If you are born to parents in the top 20 percent of the income distribution, you need to be in the top 30 percent of your cohort to stay at the top. You can get a “C”. If you are born in the bottom 20 percent, you have to be in the top 10 percent of your cohort to get to the top. You need to get an “A.” If that’s not the definition of inequality of opportunity, then I don’t know what it is.