Have wages kept up with inflation?
Yes and no. Wages have kept up with official CPI, and even exceeded it in recent years.
But then again, official CPI doesn’t really measure inflation. It used to, but during the Clinton Administration the BLS changed the weighting of the basket of goods from simple weighting to geometric weighting. This reduced the weighting of items in the basket that increased in price, and increased the weighting of items that decreased in price. The impact has been pretty dramatic.
The BLS also introduced hedonics, whereby something like a smart phone that was 50% more expensive than its predecessor but had 50% more features was considered to not be inflationary, because we get more enjoyment out of the phone.
The impact, according to Shadow Government Statistics – Home Page is 3–4% per year, which means that wages have fallen against real inflation by around 15% in the past five years.