Notes on "Is Piketty’s ‘Second Law of Capitalism” Fundamental?" by Per Krusell and Anthony A. Smith

Is Piketty’s ‘Second Law of Capitalism” Fundamental?

Per Krusell and Anthony A. Smith

Oct.21 2014

In "Capital in the Twenty-first Century", Thomas Piketty uses what he calls “the second fundamental law of capitalism” to predict that wealth-to-income ratios are poised to increase dramatically as economics’ growth rates fall during the twenty-first century. This law states that in the long run the wealth-to-income ratios equals s/g, where s is the economy’s saving rate and g is its growth rate.

Argument against:

It holds the net saving rate constant as growth falls, diving the gross savings rate to one as growth goes to zero.

It is inconsistent with both the textbook growth model and the theory of optimal saving: in both of these theories the net saving rate goes to zero as growth goes to zero.

Both of theories privido a reasonable fit to observed data on gross and net saving rates on the US, whereas Piketty’s does not.

Contrary to Piketty’s second law, both of these theories predict that wealth-to-income ratios increase only modestly as growth falls.

Piketty’s first law:

Capital’s share of national income, y, is r* k/y,

r:  return to capital

k: aggregate stock of capital

Inequality in capital holdings > Inequality of all of income.

In the LR k/y=s/g?

The capital-to-income ratio is s/(g+d)

d: depreciation of capital