Should-Read: Piketty's elasticity of substitution between capital and labor is, in his model, produced by the constancy of the rate of profit near 5%/year in spite of wide swings in the capital-output ratio. You can't say that substitution parameter is wrong without providing an alternative explanation for the constancy of the rate of profit. Yet very few of Piketty's critics even attempt that:
Diane Coyle: Inequality, revisited: "Recently I’ve been dipping into The Contradictions of Capital in the 21st Century: The Piketty Opportunity, edited by Pat Hudson and Keith Tribe... http://www.enlightenmenteconomics.com/blog/index.php/2017/09/inequality-revisited/
...There is a reasonable consensus among the contributors to these various collections that Piketty’s theorising is flawed (in particular depending on an empirically invalid assumption about the substitution between capital and labour), that his application of a theory about productive capital to the data including housing wealth and financial capital is troubling, and that his call for a global wealth tax is (as Avner Offer puts it in his essay in this book) ‘utopian’. Equally, pretty much all would agree that Piketty, with co-authors, has done a terrific service in putting together the database, and in getting inequality on the agenda of both economists and policymakers.
Pat Hudson['s]... challenge to Capital in the 21st Century is its omission of globalisation and technology as drivers of inequality–if one is thinking about policies to mitigate inequality, r>g isn’t much help. She pinpoints financial markets, and regulatory and political beliefs, as key points of intervention–in other words, the specifics Piketty ignores in his generalisations. Avner Offer focuses on housing, and limiting its tendency to make wealth more unequal through credit controls. The main sections of the book aim to particularise the analysis of inequality by looking at the trends, institutions and politics of different countries – one section on western economies, one on major economies elsewhere. As Luis Bértola points out here, Piketty is very Eurocentric. Having these different national perspectives is a useful contribution...