Piketty’s Second Fundamental Law of Capitalism

20 Jun, 2014 at 10:43 | Posted in Economics | 4 Comments

When Piketty introduces this law in the text of Capital in the Twenty-First Century, he abbreviates it in the form β = s/g for the benefit of the general reader. But he then follows up that introductory statement with several pages of explanatory text and warnings to the reader that make it clear that that his intent is only to describe the value toward which β would converge in the long run, if s and g remain relatively constant. Unfortunately, the abbreviated statement of the law has thrown many people off. Economists are in the habit of using equilibrium methods to turn long-term asymptotic limits of processes that evolve over time into unchanging constraints on some idealized steady-state equilibrium. So rather than use the inherently dynamic accounts of wealth, income and the capital-to-income ratio that are partially explained above, and that Piketty uses to study the dynamical evolution of the structure of economic inequality as it evolves over time, some commentators have instead gone right to a steady-state model in which β is set constantly equal to s/g, and from which they then fallaciously deduce immediate (and absurd) changes in β from the fluctuations in s and g. This is quite far from Piketty’s intent and misrepresents his framework.
Since part of the point of the Second Fundamental law and its surrounding framework is to analyze what happens as the capital-to-income ratio increases over time, not what happens in the less usual conditions when it is stable, the focus on steady-state conditions seems to me misguided. For example, if a society begins in 2014 with a capital-to-income ratio of 4, a savings rate of 10% and a growth rate of 1.5%, then even if the savings rate and growth rate remained constant indefinitely, it would take a very long time for β to get near its limiting value of s/g = 6.7. Specifically, β would not get to within 10% of s/g until the year 2115; it would not get to within 5% of s/g until the year 2159; and it would not get to within 1% of s/g until the year 2159. The distance between the present value of β and the present value of s/g is a measure of the present strength of the “force” pushing the capital-to-income ratio higher. Since some of the forces generating inequality depend on the rapidity with which β is increasing, it is the strength of this force and the direction in which β is moving that are important. Piketty’s Fundamental Law should not be interpreted as the statement that β is approximately equal to s/g. Under ordinary conditions β can be quite far from s/g. That’s part of the point.

Dan Kervick


  1. It’s not a law. It’s an identity. Jeez.

    • That is not an identity, Phil. I do not think you know what an identity is.

  2. Does housing capital contribute to inequality?
    An essay on Thomas Piketty’s Capital in the 21st Century∗

    Odran Bonnet, Economics Department, Sciences Po and LIEPP

    et al.

  3. Lets not get to Nik Piketty
    But there is something a tad hickety pickety
    in a law about Capital
    that is so neo-classical as to be mechanical
    all of this is a bit too rickety

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