Working for the government can be great, depending on who you work for and whether or not it fits your personality, but don't be deluded into thinking that the majority of government employees have cushy, high paying jobs.
Note: Politicians and Senior Executive Service employees are a different story, many of them are overpaid and ineffective at their jobs.
GS-15 = O-6 (Colonel/Navy Captain)
GS-14 = O-5 (Lt Colonel/Commander)
GS-13 = O-4 (Major)
GS-12 = O-3 (Captain, this is the journeyman level for engineesr)
GS-9/11 = O-1/2 (Lt's, apprentice stage)
GS doesn't start at 9, though. The lower grades are typically limited scope, no supervisory responsibility, office jobs (secretaries, mail room, clerk, data entry, etc.). Or they're training positions, straight out of college an engineer may be a GS-5/7 and after 2-4 years a GS-11/12. They don't really have a clean comparison to military ranks, that I know of.
They do, but you have to start going into the enlisted ranks for best comparisons. GS-7 might be E-6/E-7, GS-5 would be E-4/E-5, etc.
If you look at responsibility, it seems to fit.
Likewise just as D.C. has peculiar effects on the military rank of typical workers, so does it have peculiar effects on the civilian grade of workers, due to the position classification principle of "scope of effect".
But the Navy normally uses O5 to command ships of similar crew size. Very rarely, even O4... it all depends on what exactly the ship is, and what the expected mission set of that ship is.
Obviously the Navy wouldn't slot a random O4 into minesweeper command even though it's a small ship, so you're really talking about a "better than average" O4 even for those, it just reflects back to how scope of responsibility can change things even for the Navy.
The base salary would double. However they'd be left without a pension, and other benefits though I think the pension is easily the largest monetary value.
Let's use as an example someone with 20 years of federal service and a highest 3 years salary of $150k. The FERS benefit is roughly 1.1% * 20 * 150k = $33k/year. That's a 25-year annuity of $450k. To accumulate $450k over 20 years, that's about $12k per year, or 8% of income. People who serve longer will get a bigger pension, but the nature of the $100k+ positions in the federal government is that they require advanced degrees, extensive work experience in the private sector, etc, which limits the overall length of service.
If you're an educated professional (say an antitrust economist at the DOJ), you'll make a lot less money in federal service even accounting for benefits. On the other hand, if you're a document clerk, you'll make a lot more.
1. Microeconomics is seriously, perhaps completely, wrong; or,
2. Federal employees are much more motivated by non-financial rewards, such as the satisfaction of public service, than the rest of us, and are, therefore, better people than the rest of us; or,
3. They couldn't make more in the private sector, and would probably make less.
Take your pick.
There are people who enjoy public service, that doesn't make them better or worse than the rest of us. I served in the Army for almost a decade, it doesn't mean I'm better than anyone.
The "can't make it in the private sector" argument is ridiculous. Everyone who has ever worked at a sizable organization, both for the government and in the private sector, has known someone that was completely incompetent yet still remained employed. Sometimes people just slip through the cracks, it doesn't matter where you are. What's funny is that on one hand we have civilians saying that federal employees couldn't make it on the outside, and on the other side whenever someone gets out of the military, there will be those who say its because that person "couldn't cut it." It's childish and counterproductive nearly all of the time.
Two reasons that come to mind that you haven't mentioned are free travel and a stable employment situation. Right now things are kind of screwed up, but generally speaking, government jobs are stable. You might have to move, but at least you know that you'll have a job unless you give them a good reason to let you go.
One of the smartest people I know has been a software engineer for about 5-7 years, he gets treated like crap at his private sector company, and makes well below market value. I honestly have no idea why he stays at his company, but I do know enough to realize that I won't be able to explain it with a mathematical model.
Second, if you want to be an infantryman, fly a jet, work with missiles, etc, most of the jobs are military. And there are subcultures found only in the military that some people find very appealing. The models are smart enough to consider such factors.
But the motivations and cultures of the military and civilian employment writ large are VASTLY different. Lumping the civilians in with the military and declaring it all good is way too simple. There are huge chunks of the government where the work is really no different than similar work in the private sector.
The postal service and UPS is only one example -- there are some unique functions and activities in USPS, out in rural areas, but the vast majority of it is pretty much the same as USPS. Wanna bet that postal workers are paid more than USPS workers? Or on their turnover ratios?
It isn't too hard to see the best parts of the government, they're pretty interesting and do important stuff. But those parts make a surprisingly small fraction of the total activity.
There are also other, less appreciated aspects: e.g. federal employees work is in the public domain by default which means a lot of people can work on open-source software without fighting corporate culture:
The number of jobs where that's true is a small subset of the number of jobs which pay more in the private sector.
The other big factor you're missing is the stability: if you have a family, disabilities or health problems, etc. something like the startup scene is a lot less appealing compared to a job where there are legal mandates against death-march project management. Given the skew towards mid-to-senior level positions, I'm also sure that a lot of people saw the appeal of an employer which has strict rules against age discrimination, too.
This is not to say that they couldn't make more money but that they're making tradeoffs for the likely future value based on their personal risk exposure. Arguably #1 is true but really it's irrelevant because anything as complicated as your career seems outside of the scope of microeconomics.
I've worked both sides of the fence, so I'm not flinging arrows.
The sheer number of government employees is amazing especially when you consider you have to add on top of these numbers those at state, city, and local, levels.