Well one way is to look at job quitting rates in the Federal government versus private industry.
If Federal employees are staying at their jobs in a full employment economy, then they are voting satisfaction in their pay. If their rate of quitting is greater than private industry, then they probably need to be paid more.
Anyway, I found a BLS chart that tells the story. Bottom line, comparing quit rates for June 2018:
Federal workers are 5 times more likely to keep their job than private workers.
So by and large, Federal employees are happy campers.
