If inherited genetically-based IQ were the source of the extra edge that the children of the rich get in our society, than we would expect a parent with 4 times average lifetime full-time earnings--say $200,000 a year--to have a kid with a lifetime average income of $51,500 instead of the average of $50,000. But it is not $51,500. It is $150,000.
What he is doing (read the whole post) is arguing that number that are less than one, when multiplied together, approach zero. So the correlation between my percentile in IQ and my kids' percentile in IQ will be less than one. The correlation between someone's percentile in IQ and their percentile in the income distribution is also less than one. Multiply the two together, and you get a small number. But the actual correlation between parent income and kids' income is high. Ergo, there must be some social transmission of inequality, which, for someone of Brad's inclination, means that there is an opportunity for technocrats to step in and "fix" the distribution of income.
Is this argument a swindle? What bothers me about the DeLong story is that if you multiply enough small numbers, then the predicted heritability of anything approaches zero. It's the definition of regression to the mean. After enough generations, all heritable characteristics should even out. But they don't. What actually happens?