I have referenced this data from Russ Roberts before. It compares poverty rates from 1967 and 2003. During that time, aggregate poverty has barely improved - from 13.3% to 12.8%. Here is what poverty rates look like, by family type:
There have been gains against poverty, across the board, since 1967. The largest decline has been among unwed mothers. This has been a shared success between a much stronger safety net for vulnerable households and a richer society in general with more opportunities for all family types.
The next graph shows the total number of poor families, by family type, as a proportion of the total. (Blue bar is 1967. Red bar is 2003.)
Here is a graph of the change in family composition over that time. Note that in 1967, more than 50% of families were two-parent families with children who were not poor.
People are complicated. Maybe instead of Picketty, we should be reading Peltzman.
There are a lot of complicated things going on here, at the bottom of the income distribution, including demographics and age-related effects, Pelzman effects related to higher incomes, female empowerment, and a better social safety net. What we almost certainly are seeing to some extent, is the counterintuitive statistical product of a wealthier, more generous society. And, it has very little to do with "r".
Here is a graph of the number of households, categorized by the number of earners in the household.
It is followed by a graph of the average household income, by number of earners. Going from zero to one to two earners in a household roughly doubles the average income with each earner. And there are more one-earner and zero-earner households, and fewer two-earner households, than there used to be.
Oh, one last thing. That black line way down at the bottom is domestic corporate profit (after tax) per household. Yep, that's it. That's basically "r". Can you believe that little black line way down at the bottom of that graph is responsible for so many of America's hardships?
That black line is turning America into pre-Victorian England!
Unfortunately, we can tax corporations until the last one leaves for Switzerland, and it's not going to do much, revenue-wise. The real money is with those two- and three- earner households. Higher taxes on the marginal income in those households, in reality, are going to fall largely on working women.