Brad DeLong's "Finger exercises" provide a simple model to play with, and begins with a discussion of four different possible return rates (r) that might relate to the growth rate (g) in Piketty's models. He then looks at the levels of r, g, and wealth to income (W/Y); the results of the model suggest that at least to some extent, the inverse relationship of return rates to capital and accumulation of wealth does in fact hold.
James K. Galbraith's review provides a number of interesting critiques, and finds that while the book contains good information on "flows of income, transfers of wealth and the distribution of financial resources in some of the world's wealthes countries," it does less well in proposing remedies appropriate to the times, and in clarifying the various meanings of "capital"; he also appears to muddle the precedents of the growth model he uses to drive his argument.
[T]he argument of the critics was not about Keynes, or fluctuations. It was about the concept of physical capital and whether profit can be derived from a production function. In desperate summary, the case was three-fold. First: one cannot add up the values of capital objects to get a common quantity without a prior rate of interest, which (since it is prior) must come from the financial and not the physical world. Second, if the actual interest rate is a financial variable, varying for financial reasons, the physical interpretation of a dollar-valued capital stock is meaningless. Third, a more subtle point: as the rate of interest falls, there is no systematic tendency to adopt a more “capital-intensive” technology, as the neoclassical model supposed.
In short, the Cambridge critique made meaningless the claim that richer countries got that way by using “more” capital. In fact, richer countries often use less apparent capital; they have a larger share of services in their output and of labor in their exports—the “Leontief paradox.” Instead, these countries became rich—as Pasinetti later argued—by learning, by improving technique, by installing infrastructure, with education, and—as I have argued—by implementing thoroughgoing regulation and social insurance. None of this has any necessary relation to Solow’s physical concept of capital, and still less to a measure of the capitalization of wealth in financial markets.
There is no reason to think that financial capitalization bears any close relationship to economic development. Most of the Asian countries, including Korea, Japan, and China, did very well for decades without financialization; so did continental Europe in the postwar years, and for that matter so did the United States before 1970.
And Solow’s model did not carry the day. In 1966 Samuelson conceded the Cambridge argument!DeLong finds fault with Galbraith's critique, and Galbraith responds in the comments on DeLong's post. Chris Bertram reviews Rawls' Economic Justice in light of Piketty over on the Crooked Timber group blog. Paul Krugman has a laudatory review of the book up at the NYRB.
My own first impression is to think that it would be quite difficult to maintain a return on capital much in excess of the growth rate in cases where capital provides nearly all of the factor input of production, at least for the time periods we're talking about (50+ years). I could be mistaken, otherwise if r-g is large for any substantial length of time, then the quantity of capital would greatly exceed the entire output of the economy of which the capital is a part. Mathematically, these two growth rates have to converge as one becomes closer to another. Moreover, we would also expect that r would fall before that, due to diminishing returns. Piketty's exploding models, in which one factor totally predominates seems less appealing than some kind of pendulum model.
We are in a second Gilded Age, according to the evidence, and the question is what to do about it, and how bad might it get?Rather than raising the income tax to confiscatory levels as Piketty reommends, the most promising policy prescriptions available to us at this time seem to be to neutralize the favorable tax treatment of dividends and capital gains relative to wage income, to invest in public goods (both tangible and intangible), and to strengthen the social safety net.
Some questions I'm still thinking about: If wealth and income inequality are increasing in certain economies, but moderating globally, how much of the argument still holds? Has Piketty chosen the correct definition of r? Is Noah Smith correct in saying that this is just a restatement of the robots vs. globalization argument?