The recent paper by Chetty et al. finds that the regression of kids' income rank on parents' income rank has a coefficient of 0.3. (See Figure 1.) That implies an R2 for the regression of 0.09. In other words, 91 percent of the variance is unexplained by parents' income.
I would be willing venture a guess, based on adoption studies, that a lot of that 9 percent is genetics rather than environment. That is, talented parents have talented kids partly because of good genes. Conservatively, let's say half is genetics. That leaves only 4.5 percent of the variance attributed directly to parents' income.

Now, if you let me play a bit fast and loose with the difference between income and income rank, these numbers suggest the following: If we had some perfect policy invention (such as universal super-duper pre-school) that completely neutralized the effect of parent's income, we would reduce the variance of kids' income to .955 of what it now is. This implies that the standard deviation of income would fall to 0.977 of what it now is.

The bottom line: **Even a highly successful policy intervention that neutralized the effects of differing parental incomes would reduce the gap between rich and poor by only about 2 percent**. [Bold in original]

This is from Greg Mankiw,

"How much income inequality is explained by varying parental resources?"
And it would take many decades to achieve that 2 percent. ]

For example, the Forbes 400 averages about 66 years old. So, if Mayor De Blasio's pre-K plan to Fight Inequality Now swept the country in 2014, then half of the Forbes 400 would be affected by 2076.

If you read the original paper you see that the 'coefficient' of 0.3 is the "rank-rank slope" rather than the correlation coefficient. The authors report a standard error in the rank-rank slope of just under 0.01 but I could not find a correlation coefficient. However, on eyeballing the graph in Figure 1 it is immediately obvious that the R squared is much higher than 0.09.

Isn't this analysis subject to the same flaws about income inequality cited by Scott Sumner?

In an addendum to his blog entry, Greg Mankiw addresses the very misunderstandings expressed above by commenter Chris Kerr.

It still fails to answer the question of why we should care about income inequality instead of just plain income, or better yet, wealth and lifestyle.

Unless jealousy is your main worry, I just don't see it...

@David Cushman,

Thanks, David.

@Thomas Sewell,

It still fails to answer the question of why we should care about income inequality instead of just plain income, or better yet, wealth and lifestyle.Sure, but not every article and blog post is about what you want it to be about. For those who do care about income inequality--and I, like you, am not one of them--Mankiwâ€™s post is very important.

Unless jealousy is your main worry, I just don't see it...Well, relative status *is* important to pretty much all primates, including man, so designing policy that pretends it has no import may not be ideal.

There is significant evidence that genetics determines maximum possible intelligence. Environment determines how close a child comes to that maximum.

It is inappropriate to claim that only 9% of intelligence is due to genes based on correlations of parental income to intelligence.

Chris Kerr;

See the addendum to Mankiw's post. THe figure plots bin averages, and does not show the within bin variation.

The square of the coefficient equals R2 when the variance of X and y are equal.

I would think that the only income advantage from having rich parents would be interest on inheritance.

Richer parents might be able to hire tutors and have better connections and provide an environment with more of what schools are looking for but the children should be less motivated due to the inheritance and I would think that would prevail.