"Government Workers Make 45% More Than Private Sector Employees"

I see the claim: "According to recent research done by Mark J. Perry, professor of finance and economics at the School of Management of the University of Michigan government employees make on average 45% more than private sector employees." But I would like to find out whether this is simply the average pay, whether it takes into account the differences in jobs, whether it takes into account the high retention rate for public jobs. Just looking at it briefly makes me assume that nothing is controlled for here, but I would be disappointed for an academic to make this claim if that were true.

From the BLS:

State and local government employers spent an average of $39.83 per hour worked for total employee compensation in September 2009, the U.S. Bureau of Labor Statistics reported today. Wages and salaries averaged $26.24 per hour worked and accounted for 65.9 percent of these costs, while benefits averaged $13.60 and accounted for the remaining 34.1 percent. Total employer compensation costs for private industry workers averaged $27.49 per hour worked in September 2009. Total employer compensation costs for civilian workers, which include private industry and state and local government workers, averaged $29.40 per hour worked in September 2009. . . .