From Charles I. Jones and Christopher Tonetti:

How muchof past economic growth is due to automation, and what does this imply about the effects of A.I. and automation in the coming decades? We perform growth accounting using a task-based model for key sectors in the U.S. economy. Historically, TFP growth is largely due to improvements in capital productivity. The annual growth rate of capital productivity is at least 5pp larger than the sum of labor and factor-neutral productivity growth. The main benefit of automation is that we use rapidly-improving machines instead of slowly-improving humans on anincreasing set of tasks. Looking to the future, we develop an endogenous growth model in which the production of both goods and ideas is endogenously automated. We calibrate this model based on our historical evidence. Two key findings emerge. First, automation leads economic growth to accelerate over the next 75 years. Second, the acceleration is remarkably slow. By 2040, output is only 4% higher than it would have been without the growth acceleration, and by 2060 the gain is still only 19%. A key reason for the slow acceleration is the prominence of “weak links” (an elasticity of substitution among tasks less than one). Even when most tasks are automated by rapidly improving capital, output is constrained by the tasks performed by slowly-improving labor.

And an important sentence from the paper itself:

…, the key gain from automation is that it allows production of a task to shift away from slowly-improving human labor to rapidly-improving machines.

The authors stress that those are preliminary results, and the numbers are likely to change.  For the pointer I thank the excellent Kurtis Hingl, who is also my research assistant.