Matt has what is probably the single best, focused technical critique of Piketty. Here are his concluding remarks:

Compared to the grand scope of Piketty (2014), the objective of this note has been quite narrow: to systematically explore the relevant evidence on diminishing returns to capital. Technical and uninspiring as this question may be, it is an essential step in knowing whether the prediction of rising capital income and inequality through accumulation—a prediction that gives Capital in the Twenty-First Century its title—will really come to pass. And given the evidence here that Piketty (2014) understates the role of diminishing returns, some skepticism is certainly in order. But rejection of this specific mechanism does not constitute rejection of all Piketty (2014)’s themes. Inequality of labor income, for instance, is a very different issue—one that remains valid and important. Capital itself remains an important topic of study. Among large developed economies, the remarkably consistent trend toward rising capital values and income is undeniable. As Sections 3.3 and 3.4 establish, this trend is a story of rising capital prices and the ever greater cost of housing—not the secular accumulation emphasized in Capital — but it has distributional consequences all the same. Policymakers would do well to keep this in mind.

The full piece is here (pdf), excellent and on target throughout.

To be perfectly frank on this one, Matt here is completely correct and Piketty has not produced any effective response to this point, either within the book or without. The internal response “I still think we need to worry about inequality therefore I side with Piketty” simply represents a misunderstanding of Matt’s argument. Piketty’s mechanism of accumulation, as laid out in his book, is simply the wrong mechanism for understanding growing inequality, both theoretically and empirically. And it is a shame that the Giles critique from the FT has attracted so much attention because it has distracted everyone from the more serious problems with the argument of the book.