Emanuel Gasteiger and Klaus Prettner
http://d.repec.org/n?u=RePEc:zbw:fubsbe:201717&r=dge
We analyze the long-run growth effects of automation in the canonical overlapping generations framework. While automation implies constant returns to capital within this model class (even in the absence of technological progress), we show that it does not have the potential to lead to positive long-growth. The reason is that automation suppresses wages, which are the only source of investment because of the demographic structure of the overlapping generations model. This result stands in sharp contrast to the effects of automation in the representative agent setting, where positive long-run growth is feasible because agents can invest out of their wage income and out of their asset income. We also analyze the effects of a robot tax that has featured prominently in the policy debate on automation and show that it could raise the capital stock and per capita output at the steady state. However, the robot tax cannot induce a takeoff toward positive long-run growth.
That paper left me puzzling. I think a lot of the results hinge on the particular production function that has been applied here: infinite elasticity of substitution between robots and humans, unit elasticity of substitution between them and “traditional” capital. I do not think reality is that extreme.
NEP-DGE Blog 
Many thanks for reading our paper and for mentioning it in your blog!
What we found interesting in this context is that – with the same production function – one gets completely different results in the context of a standard Solow (1956) type of growth model and also in a Ramsey-Cass-Koopmans framework. In these cases there exists a long-run balanced growth path with positive per capita income growth (even without technological progress) that is sustained by automation. By contrast, in the standard OLG framework, this balanced growth path vanishes, which is due to the fact that households save only out of labor income and labor income is suppressed by automation.
While the production function we apply conforms to the very definition of automation (as a replacement of labor), we fully agree with your assessment that, on the macroeconomic level, reality is not that extreme. However, the central result goes through even if the strict substitutability between automation and labor is relaxed.
How are robots near perfect substitutes for labor and not general capital? This really puzzles me in this whole discussion of robots taking over. Is it that they have an arm? The fact that they perform a function humans have done before is not sufficient. Then an engine is a robot that replaces human power.
In my opinion, the crucial point is that a robot could do the job it takes over in a fully autonomous way, while a standard machine still needs to be operated by somebody. For example, in case of a self-driving taxi, there is no need for a human driver anymore, whereas switching from a rickshaw to a modern car merely allows the driver to carry more passengers over longer distances during the same time interval. The latter raises labor productivity and the wage of the driver, while the former replaces labor and reduces the wage of the driver.