"This shows that at almost every age level, the country continued to de-urbanize from 2000 to 2013. Various trend pieces about empty nesters moving to the big city simply aren't reflected in the data."
My experience is that people are overall more willing to trade space for urban convenience than they used to be, but still not so willing/able to trade both space and affordability for it. In places where the suburbs are also stupidly expensive - NY and CA - you don't see it as much. Everywhere else in the US - where property in the suburbs gets dramatically cheaper once you're five, ten, fifteen miles outside the city center - that's hard to resist.
You said "there is in fact a big migration back into the cities" and that's the part that the numbers disagree with.
Instead, there has been a slowdown in the continuing move to the suburbs. And a suburb-centered population is one that still won't move so quickly on transit and the like, at a state and national level.
No, population growth in the burbs alone does not disprove migration into the cities. As I said, skyrocketing costs in the cities are evidence of this. With respect to city transportation infrastructure, wealthier people moving in and developers building up capacity are significant forces in affecting policy.
"This shows that at almost every age level, the country continued to de-urbanize from 2000 to 2013. Various trend pieces about empty nesters moving to the big city simply aren't reflected in the data."
My experience is that people are overall more willing to trade space for urban convenience than they used to be, but still not so willing/able to trade both space and affordability for it. In places where the suburbs are also stupidly expensive - NY and CA - you don't see it as much. Everywhere else in the US - where property in the suburbs gets dramatically cheaper once you're five, ten, fifteen miles outside the city center - that's hard to resist.