"Challenging the Empirical Contribution of Thomas Piketty's Capital in the 21st Century" by Phillip W. Magness and Robert P. Murphy is one of the first deep reviews of the facts that I have seen. I haven't read it yet, but the abstract looks promising:
Thomas Piketty's Capital in the 21st Century has been widely debated on theoretical grounds, yet continues to attract acclaim for its historically-infused data analysis. In this study we conduct a closer scrutiny of Piketty's empirics than has appeared thus far, focusing upon his treatment of the United States. We find evidence of pervasive errors of historical fact, opaque methodological choices, and the cherry-picking of sources to construct favorable patterns from ambiguous data. Additional evidence suggests that Piketty used a highly distortive data assumption from the Soviet Union to accentuate one of his main historical claims about global “capitalism” in the 20th century. Taken together, these problems suggest that Piketty’s highly praised and historically-driven empirical work may actually be the book’s greatest weakness.Comments on the paper welcome. If I get a chance to read it I'll post some.