This is not one of those “he said, she said” where reasonable people can disagree on whether the PCE or CPI is a better price index. This is a pay/productivity gap being invented by using the slowly moving price index (NDP, which is similar to the PCE) to make worker productivity look better, and the faster moving price index (CPI) to make real wages look lower. That’s not kosher. You need to use the same type of index for both lines on the graph.
If you simply don't believe in wage stagnation, then I'm not sure what this whole conversation has been about.
http://taxfoundation.org/sites/taxfoundation.org/files/docs/...
While that graph shows labor's share as stable, many others do not, e.g. in this piece by Jared Bernstein: http://economix.blogs.nytimes.com/2013/09/09/why-labors-shar...
Of particular interest to me is that if you look at the BEA numbers, they split 'labor share' into wages and non-wage compensation (benefits, SS, medicare, etc.) - the latter share has climbed over time to 20%, meaning much of the stability in the "wage share" is just increasing money being paid to Medicare.
It's not clear what's being measured and not in that chart, but, for example, this St. Louis Fed data shows both an increasing Dividend share of GDP and a declining wage share of GDP:
http://qvmgroup.com/invest/2012/09/05/profits-cash-flow-divi...