The bad news is right in the abstract:
[P]olitical power is self-perpetuating: legislators who hold power for longer become more likely to have relatives entering Congress in the future. Thus, in politics, power begets power.Basically, they find that political office can, indeed, be inherited in the US -- that no only is it an advantage to come from a political family, but that it's even more of an advantage to come from a well-established political family. The nice twist in this paper is that while they are not able to demonstrate exactly why that happens (they suspect name recognition and contacts, both of which make sense to me), they do show that whether it is that helps kids from political families succeed is about the political environment, not the kids themselves. In other words, it's not that political talent runs in families; it's that once someone from a family makes it in politics, everyone in that family has a better chance of joining her.
The good news, however, is that dynastic politics has been steadily fading in American politics:
The proportion of legislators with relatives in Congress has significantly decreased over time...while 11% of legislators were dynastic [previous relative in Congress] between 1789 and 1858, only 7% were dynastic after 1966.The big caveat here is that their data only run through 1996. Beyond that, since the Civil War the Senate has had a lot more dynastic politicians than the House (and, for what it's worth, my count of contemporary dynastic Senators is consistent with where their trend line ends in the 1990s). The South has had quite a few more than the rest of the nation -- which in turn meant that for a century or so Democrats were more likely to be dynastic than Republicans, but that gap faded once the South started electing Republicans (see their Figures 1 and 2). But, yes, the dynasties are fading. My favorite table (3) in the paper shows the top 15 political dynasties in Congressional history -- did you know that Henry Clay was part of a political family that sent 17 Members to 72 Congresses between 1789 and 1978? Anyway, of these 15 families, only three are current, soon to be two. The last Kennedy is about to leave Congress, however, although there's still a Frelinghuysen, and Connie Mack IV is part of a hundred-year dynasty.
I think we can put some of this to rest. Politicians from families that produced other politicians do have advantages in American politics. It's also unusual for Americans; the paper shows that legislators are much more likely to make it a family business than other occupations. But it is not a new trend, or suddenly increasing rapidly. To the contrary, it goes back to the earliest days of the republic, and has steadily faded over time, and the best evidence is that it continues to fade today.