Criticism and Summary of Capital in the 21st century

For your convenience, this is the criticism surrounding Capital in the 21st century  and the summary of the book in the Economist (Sanjay posted this before I believe).
Below is what I find most relevant to the first 6 chapters (including intro, which provides a great overview of different schools of thoughts):
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“Capital” makes three big contributions in its 577 pages. First, Mr Piketty, a pioneer in using tax statistics to measure inequality, painstakingly documents the evolution of income and wealth over the past 300 years, particularly in Europe and America. In doing so, he shows that the period from about 1914 to the 1970s was an historical outlier in which both income inequality and the stock of wealth (relative to annual national income) fell dramatically. Since the 1970s both wealth and income gaps have been rising back towards their pre-20th-century norms. There are surely a few snafus in these statistics, but this work has transformed understanding of the history of wealth, with eye-popping results. Who knew, for instance, that the annual value of inheritances in France has tripled from less than 5% of GDP in the 1950s to about 15%, not all that far from the 19th-century peak of 25%? As a piece of empirical sleuthing, the book is indisputably brilliant.

Mr Piketty’s second contribution is to come up with a theory of capitalism that explains these facts and offers a prediction of where wealth distribution is heading. His central claim is that the free-market system has a natural tendency towards increasing the concentration of wealth, because the rate of return on property and investments has consistently been higher than the rate of economic growth. Two world wars, the Depression and high taxes pushed down the return on wealth in the 20th century, while rapid productivity and population rises pushed up growth. But without such countervailing factors, Mr Piketty argues, higher returns on capital will concentrate wealth—especially when, as now, an ageing population means that growth should slow.
Mr Piketty’s expectation of rising wealth concentration is not outlandish. However, it is a prediction based on extrapolating from the past, not an inherent model of capitalism. He assumes that the returns to capital will not fall substantially even as the stock of wealth rises. That may prove to be true, but the Piketty prediction is a hypothesis, not an iron law.
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