I do, however, trust Per Krusell and Tony Smith to have given it a fair reading, because Krusell and Smith have long track records as diligent and thoughtful scholars. And their analysis appears to devastate both Piketty’s model and his prediction that income inequality is destined to grow explosively over time.
All of Piketty’s predictions depend on his assumptions about how much people save. The simplest respectable model (that is, a model that economists generally feel comfortable using for many purposes, and which fits fairly well with observations) says that we save a fixed percentage of our incomes — say 30%. (There are also more sophisticated models in which this percentage can change as economic conditions change.)
Piketty, by contrast, assumes that our net saving is a fixed percentage of our net incomes, where “net” means “after subtracting depreciation of our assets”. That’s a very different assumption, and, according to Krusell and Smith, not at all a plausible one. It’s implausible first because it has extremely odd implications. Most notably, it implies (though this is not immediately obvious) that if economic growth slows to zero, we will eventually choose to save 100% of our incomes(!!). Beyond that, Krusell and Smith argue in considerable detail that, compared to the more traditional models, Piketty’s does a poor job of fitting the last seventy years’ worth of data.
According to Krusell and Smith, Piketty demonstrates correctly that under his assumptions, slowing economic growth must lead to massive inequality over time. But under the far more plausible assumptions found in modern textbooks and modern research papers, that conclusion goes away. In fact, after substituting those assumptions, Piketty’s arguments yield something like the opposite conclusion — as growth slows down, changes in inequality become pretty much negligible.
If this analysis is right — and given the identities of the authors I’ll be very surprised if it’s wrong — then there appears to be very little reason to buy into Piketty’s story. That doesn’t mean he’s wasted his time. We learn a lot by making a variety of different assumptions and figuring out where they lead us, even when the assumptions are ultimately unsupportable. But a serious intellectual exercise is not the same thing as a serious prediction.