Some Fundamental Problems with Thomas Piketty's Capital in the Twenty-First Century.

• Author: Rallo, Juan Ramon
• Position: Book review

The publication of Capital in the Twenty-First Century by Thomas Piketty in 2014 has intensified the debate on the relationship between capitalism and inequality. The French economist's fundamental thesis is that the capitalist economic system unleashes a series of processes that will normally lead to an increase in income and wealth inequality:

The overall conclusion of this study is that a market economy based on private property, if left to itself, contains powerful forces of convergence, associated in particular with the diffusion of knowledge and skills; but it also contains powerful forces of divergence, which are potentially threatening to democratic societies and to the values of social justice on which they are based. The principal destabilizing force has to do with the fact that the private rate of return on capital, r, can be significantly higher for long periods of time than the rate of growth of income and output, g. The inequality r > g implies that wealth accumulated in the past grows more rapidly than output and wages. This inequality expresses a fundamental logical contradiction. (Piketty 2014, 571)

More precisely, Piketty argues that within capitalism the net rate of return on capital (r) tends to be higher than the rate of economic growth of aggregate income (g), so that the wealth accumulated in the past increases at a higher rate than aggregate production and, in turn, than wages. That is why the share of net capital incomes within net domestic product (NDP) tends to increase by reducing the wage share. And to the extent that the distribution of net capital income is usually more unequal than that of labor income, the larger share of net capital income would lead to an increase in income inequality.

Piketty bases his conclusion on his own theoretical model and on the empirical evidence he has been collecting throughout his academic life.

His theoredcal model is formed by what he calls "the two fundamental laws of capitalism." According to the first fundamental law (Piketty 2014, 52-55), the share of net capital income within NDP (a) is equal to the net rate of return on capital (r) multiplied by the ratio between capital and NDP ([beta]):

[alpha] = r * [beta] (1)

As a result of this first fundamental law, the progressive capitalization of the economy (measured by [beta]) will lead to an increase in the share of net capital income within NDP.

According to the second fundamental law (Piketty 2014, 166-68), the ratio between capital and NDP is determined in the long run by the ratio of the net saving rate (s) to the growth rate of the economy (g):

[beta] = s/g (2)

That is, the greater the domestic savings and the lower the economic growth, the greater the capitalization of the economy.

Combining these two fundamental laws, we can arrive at the conclusion that the share of capital income within NDP is directly proportional to the net rate of return on capital and the rate of net savings and inversely proportional to the rate of economic growth:

[alpha] = r * s/g (3)

As a consequence, if the net saving rate is kept constant, an increase of r or a reduction of g will result in an increase of [alpha]. Also, if the relative difference between r and g remains constant, any increase in the net saving rate will, in turn, increase [alpha].

On the basis of this simplified economic model, Piketty provides abundant historical evidence in his book that, apparently, shows increases in inequality coincide with a widening of the spread between r and g, while reductions in inequality coincide with a narrowing of the spread between r and g.

Since Piketty published his book, numerous papers have been written with the purpose of analyzing and contrasting the model and the evidence he presents. This article summarizes the main conclusions that the economic literature has found in this respect. Its contribution consists in offering a combined discussion of the problematic hidden assumptions in Piketty's model. (1)

The Problems of the Theoretical Model

The essential problems of Piketty's simple theoretical model derive from the need to complement the two fundamental laws of capitalism with other hypotheses he does not expressly mention, in particular:

1. For a to increase, it is not enough that r > g. The gross rate of saving by capitalists must also be sufficiently high (Acemoglu and Robinson 2015).

2. The net saving rate is not independent of the rate of economic growth (Krusell and Smith 2015).

3. The net rate of return on capital, r, is not independent of the net saving rate (Rognlie 2014).

4. An increase in the share of net capital income within NDP, [alpha], is not enough to increase inequality (Milanovic 2016).

First, the inequality r > g does not necessarily mean that capital income will grow faster than labor income. Because the stock of capital depreciates over time, and because the net rate of return on capital may be reduced as more capital accumulates, it will be additionally necessary to save a sufficiently large portion of gross capital income to replace and increase the stock of capital so that net capital income keeps increasing higher than wage income.

In this regard, it is important to emphasize that...