Paul Krugman has pointed out, here and here that the meme that most of the inequality we have been experiencing of late has much to do with differences in educational attainment is bogus. Mankiw responds in typical fashion by changing the standards by which that claim is judged. Krugman presented solid evidence that the returns to education have been declining. To which one should add that if we did a real ROI calculation the returns have gone negative. Mankiw counters by saying that may be true but if you do not have an education you are less likely to get a chance to become the top 1%.
The difference between the two as near as I can tell is that Krugman demonstrates that buying a lottery ticket has worse odds of paying out than ever before and Mankiw’s master stroke is apparently that if you don’t buy a lottery ticket you have no chance at winning.