That idea was suggested recently by Bill Gates, though I think you can debate with what degree of literalness. It’s worth a ponder in any case, and here is a recent Noah Smith column on the idea, and here is Summers in the FT, WaPo link here. And here is Izabella Kaminska.
Put aside the revenue-raising issue (which will require some taxes on capital, most likely, including on robots): if we have taken in optimal revenue, is there a separate and additional argument for an additional robot tax? In this context, I would consider “robots” to be capital that is especially substitutable for human labor.
Presumably the claim is that there is either a distributional or an “externalities from a happy human being” reason to slow the rate at which capital is substituted for labor. But if we accept that assumption, should we tax robots or subsidize wage labor?
One reason not to tax the robots is that employers might substitute away from robots and toward natural resources rather than toward domestic human labor. Maybe that doesn’t sound intuitive, but think of paying the energy costs to outsource to another nation and transport the outputs back home.
But the main issue is probably one of incidence. A general problem with a wage subsidy is that sometimes much of its value its captured by employers. For instance if the subsidy takes an EITC form, employers could pay less to their workers, but perhaps many eager workers still would seek the job to capture the somewhat higher net total wage, namely the employer portion plus the benefit. If enough workers are keen to get the pay, employers can claw back much of the EITC boost and still get the work force they need.
Now consider the incidence of a tax on robots. If the elasticity of the demand for robots is high, there will be a big shift away from robots and toward labor (and land and other resources). It is at least possible that workers capture more of the gains this way than from the direct subsidy to their wages. On the downside, the employer fares less well under this scheme.
So it depends on how labor and robot elasticities relate to each other. I don’t know what relationship between the parameter values is likely, but typically in these scenarios just about any result is possible. The robot tax would seem to do best when the elasticity of demand for robots is high, but the corresponding elasticity of demand for labor is low (and differentials in supply elasticities do not offset this). As robots and labor become more substitutable, that difference in demand elasticities is likely to diminish. So if you are going to do this, maybe it is necessary to do it soon, precisely when it does not seem needed.
Your call, but that is the basic set-up of the problem.