Over 90% of the grandchildren of top 1% wealth grandfathers did not achieve that level

See The Gilded Age and Beyond: The Persistence of Elite Wealth in American History by Priti Kalsi and Zachary Ward. From NPR's planet money.

"These economists look at wealth dynamics of the richest of the rich Americans during the late 19th and early 20th centuries. They find that the richest of the rich tend to drop in wealth rankings, so they don't stay at the top. However, they do find a relationship between their wealth and the likelihood that their grandkids are in the top 1%. Having a "rich grandparent exponentially increases the likelihood of reaching the top 1%. Still, over 90% of the grandchildren of top 1% wealth grandfathers did not achieve that level." In other words, having super rich grandparents boosts the likelihood that you're super rich, but it's no guarantee. Link to paper"