Don't underestimate the institutional and personal corruption factor. When the government outsources to contractors, there is an automatic revolving door between the government insiders and the contracting firms. The government workers put in their time at the relatively lower pay scale, and when they get out they just end up sitting on the other side of the same table at a much higher salary. Everybody knows how it works, and as long as nobody rocks the boat they get to retire with both a government pension and a second income and retirement plan.
In some areas it moves even faster and nobody waits for retirement. If you want to work on Wall Street with an MBA/law degree and you can't get in, just go work for a government regulator. Four of five years of that under your belt and you end up being hired by the same firms you used to regulate. It's possible that this route will pay as well as going directly to the private sector.
It's not as obvious as working with on project Z in government and then directly going to a contractor who works on Z, although that often happens. It's more that the contractors know they need to hire a certain number of people who have previous government managerial experience if they are going to make a credible bid for the job.
I've seen this in person working for military contractors. To even get considered you need to have retired officers of a certain rank. When it comes to the corporate level, the requirement is having generals on you board of directors, or in management. In one case I saw a general who had a big part in the Iraq war get on the board of directors because the company wanted to go over the billion dollar mark in sales. They were starting to compete with the big boys, and without "contacts" they knew they would never get their. As far as I know it worked.