A new NBER paper by Daron Acemoglu and Pascual Restrepo finds that "deployment of robots reduces employment and wages, but they caution that it is difficult to measure net labor market effects."
Here is a graph that summarizes their results:
Notice that cities with auto factories such as Detroit and Lansing have above average robot adoption and below average employment growth (actually negative.)
This study reminded me of the 2016 Autor, Dorn and Hanson study of the impact of Chinese trade on local labor markets. Even the time period was the same (1990-2007). As with robots, automation reduces employment in local markets, but this does not tell us much of anything about the effect on aggregate employment. Workers losing jobs in Detroit might migrate to Texas, where jobs are plentiful.
Do we have any evidence of the effect of trade and automation on total employment? Let's look at the unemployment rate from 1990 to 2007 (both were peak years of the business cycle.)
The unemployment rate fell slightly during this 17-year period, and thus provides no evidence that either trade or automation negatively impacted employment. However the unemployment rate is only one indicator, and many people prefer the employment to population (above age 16) ratio:
As you can see the employment ratio was about the same in 2007 as in 1990, and hence the aggregate data shows no evidence that either trade or automation reduced employment during the period studied by Autor, Card and Hanson, as well as Acemoglu and Restrepo.
Of course that doesn't mean these factors have not had a negative effect on overall employment, just that doing so would require a very sophisticated study. Unfortunately, the science of economics has not yet advanced to the point where that sort of study is feasible. And thus we are forced to admit that we simply don't know if there is any effect on overall employment.
But I do think that we know that trade and automation raise real GDP.