Joseph Stiglitz writes about the top 1%  in Vanity Fair. I will try to comment on more of the article at some point, but it starts off like this:
It’s no use pretending that what has obviously happened has not in fact happened. The upper 1 percent of Americans are now taking in nearly a quarter of the nation’s income every year. In terms of wealth rather than income, the top 1 percent control 40 percent. Their lot in life has improved considerably. Twenty-five years ago, the corresponding figures were 12 percent and 33 percent.
So compared to 25 years ago, the share of income going to the top 1% has doubled, from 12% to almost 25%. But the conclusion that Stiglitz draws, does not follow. It does not follow that their lot in life has improved considerably. There’s no “their” there. The people who were in the top 1% 25 years ago are not the same people in the top 25% today. The numbers that are quoted are two snapshots at two different times. The correct statement is that the people who are in the top 1% today earn a larger share of the income pie than the people who were in the top 1% 25 years ago.
How would Stiglitz answer this? Perhaps he would say it’s mostly the same people and that I am nit-picking. Or that the people who are in the top 1% today may not have been in the top 1% 25 years ago but they were close. They were maybe in the top 5%. So his statement is close enough for an article in Vanity Fair. Yes, his statement is imprecise, but it captures what is going on.
My counter would be that many of the people in the top 1% today were not even in the work force 25 years ago. LeBron James. Sergey Brin. Mark Zuckerberg. The imprecision allows Stiglitz to imply that the 1% are a coherent group that does stuff to maintain or grow their economic power. But it’s not true. Yes, some of the top 1% are politically adept. They work in the financial sector. Or in law firms that work in and around New York City and Washington DC doing stuff related to government power. But some and maybe much of that growth in the economic power of the top 1% is due to productivity.
Finally, I would point out that when you actually follow the same people over time, the gains at the top (and the bottom) do not mirror the changes in the two snapshots:
This picture is from a study that’s part of the Pew Economic Mobility Project . This study follows the same people over time over roughly a 30 year period:
Family incomes in the PSID sample were measured in 1967–1971, when parents had an average age of 41years, and again in 1995–2002, when their adult children had an average age of 39 years.
The gray bars are from the period 1967-1971. They represent the parents. The scarlet bars are the kids.
And notice that the overall change between generations is an increase in real terms (corrected for inflation) from $55,600 to $71,900. That’s an increase of 29%. And the inflation correction probably overstates inflation. Not exactly the Great Stagnation. There is ZERO gain in the top quintile. I know. The top quintile is not the top 1%. But my point is that if you look at the share going to the top quintile between 1969 and 1999 as two snapshots, you’d find big gains for the top quintile that is misleading in the same way the Stiglitz inference from the data is misleading.
This is from InfoPlease  that gets the data from the Census Bureau. I assume it’s right–it mirrors what we hear over and over again. The top of the income distribution appears to get all of the the gains or at least the biggest gains:
Source: U.S. Census Bureau
Notice that all of the quintiles, except the top quintile get smaller shares between 1970 and 2000, roughly the time covered by the Pew study. But the Pew Study comes to the exact opposite conclusion. The lowest quintiles got the biggest gains WHEN YOU FOLLOW THE SAME PEOPLE. Using the Census data over time tells you NOTHING about what “they” (the top whatever percent) had happen to “them” over time.
It is also worth pointing out that the pie is not constant. So you’re well-being can grow even when your share of the pie falls if the pie is getting sufficiently larger.
Here is an earlier post  on the same topic reacting to a similar claim by Justin Wolfers.