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...is how to factor in the number of people employed by 'government contractors'.
It's no secret that in many cases you can take a job once paid directly by the government (federal, state or even local) and hire a pirivate company to use an employee to do the same work. The money still winds up on the government books...but you can count a 'reduction' in government head count. (And the total cost is often higher.)
My feeling is this is where the truer picture lies.