No, the overall data suggests that because of the higher wages that have evolved for public sector Canadians—and there are now more unionized government workers in Canada than unionized private sector workers—those higher wages and richer benefit plans are inflating and creating what unions want to call their “wage advantage”. But I'm not personally familiar with a study that successfully pulls the private sector reality apart from the government sector reality.
On May 7th, 2013. See this statement in context.