No, I'm saying the tax you pay doesn't add anything new to the tax pot, as the money to pay it already comes from the tax pot.
Interesting idea, I wonder if it would be more efficient to exempt public sector employees from income taxes and just reduce their pay accordingly.
that way you eliminate the cost of sending out the money, recollecting it then sending it out again, insted just sending out the money they don't normally collect back resulting in no loss of income to the employee.