Perpetual growth, the labor share, and robots

ABSTRACT

The recent literature on the economic effects of machine learning, robotization and artificial intelligence suggests that there may be an upcoming wave of substitution of human labor by machines. We argue that these new technologies may lead to so-called perpetual growth, i.e. growth of per capita income with a non-progressing state of technology. We specify an exact parameter threshold beyond which perpetual growth emerges, and argue that ongoing technological change may bring the threshold in reach. We also show that in a state of perpetual growth, factor-eliminating technological progress reduces the role of labor in the production process and that this leads to a rising wage rate but ever-declining share of wage income. We present simulation experiments on several policy options to combat this inequality, including a universal basic income as well as an option in which workers become owners of ‘robots’.

KEYWORDS:

• Perpetual economic growth
• economic effects of robots
• labor share in income
• income distribution

JEL CLASSIFICATION:

• O41
• O33
• E25
• P17

Acknowledgements

We thank three anonymous reviewers, Luc Soete, Thomas Ziesemer, Adriaan van Zon, Pierre Mohnen and participants at the UN Expert Group Meeting on ‘Accelerated Technological Change, Artificial Intelligence, Automation and their Implications for Sustainable Development Targets’ (Mexico City, 26–27 April 2018) for comments on an earlier version. The views expressed and any remaining errors remain solely our own.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 The emphasis on the pure employment effects is especially strong in the popular debate following Frey and Osborne. For example, The Guardian headlined ‘Robots are the ultimate job stealers. Blame them, not immigrants’, (https://www.theguardian.com/commentisfree/2018/feb/14/resentment-robots-job-stealers-arlie-hochschild) while Mother Jones warned that ‘You Will Lose Your Job to a Robot—and Sooner Than You Think’ (https://www.motherjones.com/politics/2017/10/you-will-lose-your-job-to-a-robot-and-sooner-than-you-think/).

2 We use the terms ‘robots’ to colloquially refer to a set of technologies that Frey and Osborne (2017) describe as ‘machine learning’. See the next section.

3 Aghion, Jones, and Jones (2017) provide a model of automation in which ρ < 0, and in which the conclusion on the share of wages in GDP differs sharply from the one that we draw in Section 6. In their model, the share of automated labor tasks keeps growing for ever, but never becomes one. Because labor and capital are complementary, labor remains asymptotically necessary, and therefore imposes a burden on the economy that is similar to Baumol’s cost disease. The share of wages therefore does not decline in the steady state.

4 A brief comment on the interpretation of our K_s production factor and its relation to perpetual growth seems in order. So far, we interpreted K_s as pure capital, in which a certain exogenous state of knowledge is embodied, but which, in a perpetual growth regime, only accumulates and does not change in nature. Alternatively, we can think of K_s as a stock of disembodied knowledge, which firms combine with capital K_o and labor. In such an interpretation, the growth regime described in this section would still require R&D (which is the accumulation of Ks). Marchese and Privileggi (2019) show how the generation of this kind of disembodied knowledge is compatible with competitive markets, and how growth in such a context leads to a declining share of labor in total income, as it does in our model (this is explored in the next section).

5 Using a production function very similar to ours, DeCanio (2016) estimates the elasticity of substitution between robots and human labor at which the labor share begins to decline. His estimations point to a value of the substitution parameter (ρ in our case) between 0.4 and 0.5.

6 Our simulation is crude in that it taxes all capital income at an equal rate. Guerreiro, Rebelo, and Teles (2019) discuss and analyze a number of more sophisticated options for using tax instruments to combat income inequality with rising automation.