On page 10:
Jason Furman:
Moreover, economic theory is unclear about whether slowing growth would in fact result in a rise in r – g. In general when growth rates fall, the ratio of capital to income rises, and the increased prevalence of capital drives down the rate of return on capital. Whether the return on capital falls more or less than the growth rate depends on how substitutable capital and labor are, with less substitutability meaning that the extra capital will be less useful thus driving its return down more. Unfortunately, the degree of this substitutability has not been clearly established, although Piketty's assumption that it is sufficient to prevent a large fall in the rate of return on capital is a plausible reading of the aggregate data.
In addition, the return on capital is also determined by individuals’ willingness to provide funds, that is, to save, and with slower consumption growth on the horizon (in part because of longer periods of retirement), individuals should be willing to save more for a given rate of interest—further driving down the interest rate and the return on capital.
As a result it is ambiguous whether or not r – g would increase or decrease as a result of lower growth rates. In fact, many standard economic models imply that r would fall by more than g so that lower growth rates would actually lead to a reduction in r – g and consequently push in the direction of less inequality.
It is worth noting that, separate from Piketty’s argument about increases in the capital share, it is plausible that continuing increases in income inequality within capital income in the United States will occur simply as a result of the large increases in inequality within labor income that have already occurred.
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