Tyler Cowen directed me to an interesting question raised in his comment section (by "BC"):
Do federal employees pay income tax on their wages? I know they do nominally, but that tax goes back to their employer, the federal government. So, doesn't that mean that, while their actual salary may be lower than their official nominal salary, they actually don't pay any tax? (NB: this is quite different from a private sector employee whose after-tax salary is less than the pre-tax salary. In that case, the difference between the two does *not* go to the employer, creating a gap between what the employer pays and what the employee receives.)
For example, suppose a private firm and the federal government both value a worker's output at $100k/yr and the tax rate is 20%. The private firm offers the worker $100k and the worker receives $80k after paying taxes. The federal government, however, can offer the worker $125k in nominal salary, *knowing that it will receive $25k back in income tax*. The net result is that the federal government pays $100k and the worker receives $100k after taxes, i.e., the worker earns $100k tax free, $20k more than he or she would earn at the private firm. Another way of seeing this is to note that taxes paid by employees are economically equivalent to taxes paid by employers. So, if employers received rebates for income taxes paid by employees, then the net income tax would be zero. Well, the federal government *does* receive a rebate for all income taxes paid by employees!
Doesn't this mean that taxes are doubly distortive? Not only do they discourage employment by creating a gap between what (private) employers pay and what workers receive -- the usual cited distortion -- they also distort the *composition* of the workforce by allowing the federal government to crowd out other employers.
This is one of those cases where things look very different if you recall the macroeconomic linkages. Let's start by assuming that the government hires the worker away from a comparable private sector job. In that case, the tax paid by the newly hired government worker would be offset by the tax no longer paid on the job he left in the private sector. To make things simple, assume a flat rate tax system. Then total tax revenue is the tax rate times national income. Thus in order for the act of hiring a government worker to result in more total tax revenue, the act of hiring the worker would have to boost national income.
Now we can see that the actual question being asked here is whether or not the act of hiring a government worker causes national income to be higher. Here are some models where that is generally not the case:
3. Real business cycle theory
4. New Keynesian models with a natural rate of output
And here's one model where it may be the case:
5. Primitive Keynesian models of the sort that were discredited during the 1970s
The wrong way to think about these sorts of issues is to look at accounting relationships at the individual level. "Follow the money". The correct way to approach the problem is to think in terms of aggregates such as "national income". Does government hiring cause national income to rise? If so, then you get more revenue.
PS. In some New Keynesian (and RBC?) models you might get a rise in measured national income, as the government worker would make the country poorer, causing labor supply to increase as a way of preventing an excessively sharp fall in consumption. I'm abstracting from that (second order) issue, which gets into questions about the proper way to measure GDP.