I don't know if it's a good strategy to deduce from flat wages that there isn't a shortage in supply of STEM workers. In fact, it is more than likely that the 'replacement STEM workers' for Americans (i.e., immigrant workers) come cheaper. If there is a 'market force' of labor shortage, which brings wages up, there's a counteracting force of 'cheap labour', which brings the wages back to where they were. Essentially, if you pick 'wage behavior' and 'number of employments' as your two metrics for deducing something, you may be underestimating the dimensionality of your 'state-space'.
After looking at EPI's paper, the wages graphs vary around in an errorbar of about 100%, which is incidentally how much the number of employees graphs vary, too. Without actual errorbars, correlating two quantities with a similar-looking 'statistical spread' would lead to an underestimated total (or propagated error