Although I wouldn't be surprised if there's data to support what you stated, I also thin it's possible there are other confounding attributes.
Many government employees are motivated by different factors. Somebody who is motivated by pay would likely gravitate towards the private sector and starting their own business. Somebody motivated by service may be more apt to apply to government jobs. For instance, I would seriously doubt mathematicians who work for intelligence agencies are lower-skilled; this is probably an occupation that selects for other traits.
I am also aware of a LOT of former government employees who start their own companies but it's not clear how much of their success is due to skills vs. network effects.
Many government employees are motivated by different factors. Somebody who is motivated by pay would likely gravitate towards the private sector and starting their own business. Somebody motivated by service may be more apt to apply to government jobs. For instance, I would seriously doubt mathematicians who work for intelligence agencies are lower-skilled; this is probably an occupation that selects for other traits.
I am also aware of a LOT of former government employees who start their own companies but it's not clear how much of their success is due to skills vs. network effects.