"... in areas exposed to industrial robots, between 1990 and 2007, 'both employment and wages decline in a robust and significant manner (compared to other less exposed areas).' "
Well, duh! If you confine your sample to those areas that are being automated then yes you will see decline in the human involvement. I don't think I've heard anyone suggest otherwise and I reckon they'd be pretty stupid to do so. For one thing, why would someone bring a robot in *unless* it was going to be cheaper than using a person over the long term?
Did they examine any areas of the economy which grew over the same period, which might have been where these unemployed or underpaid people were ending up? The period leading up to 2007 looked pretty good on paper for a number of major economies so I suspect that it wasn't all bad news.