What is the impact of Robots on Wages? Yglesias linked modeled behavior .
My take, of course, is that it's impossible to say but that if there are specific jobs robots can do, then there is likely to be short-term wage pressure on those jobs. In the long run, however, I'd discount the idea that this will necessarily have a huge impact on wage inequality. Turns out robots can probably never do the type of face-to-face, human-like interaction which will only become more valuable in the future. Jobs like being waited on, having your house cleaned, getting a massage... Jobs for which the demand will increase more than 1 for 1 with GDP per capita... (I really doubt massage chairs reduced demand for actual massages...) Second point is, robots fall into the "extremely high TFP" category generally, which means they could be subject to digital camera or computer-like price declines, quickly becoming affordable for rich and poor alike.
Long story short is that even cheap-labor replacing technological advance alone necessarily carries no implications for wage inequality. (Could go either way...)
The interesting thing from the Modeled Behavior post was the view that the income difference between the US and Mexico is only due to a change in institutions. Hence, they argue, take a housekeeper in Mexico, put her in LA, and voila, because of the better institutions in LA, she can now clean more houses because she's more productive, thanks to the unique institutions in LA, such as good traffic, that Mexico cannot replicate.
Of course, that is not the case. She would get paid more for the same work because the US is far wealthier than Mexico, and because Americans are wealthier, we can afford to pay more for a housekeeper. Also, there are relatively fewer unskilled workers in the US, so of course the demand-and-supply yield a different equilibrium. The income-level difference could, of course, be primarily a story of institutions, but it need not be the proximate cause of the wage differential any more than the wage differential between Delaware and West Virginia (at $64k to $26k, is similar to the difference between the US $45k and Mexico $15k is necessarily due to institutions. Human capital, history, trade costs, and historical trade costs could all be factors as well...