I have a question about the calculation of GDP measures. The question is perhaps easiest to understand if we consider calculating calculating GDP using the income approach (see here), but might arise under different approaches.
If I understand matters correctly, the basic idea is to add up everyone's income, where 'income' means 'pre-tax income'. For example, if we are talking about a worker's salary, we are talking about their pre-tax salary. This seems to have strange implications when considering public sector employees, who are both paid by the government but also 'pay back' the government via income taxes. More specifically, it seems to imply that the government can boost GDP by paying public sector employees more while increasing the amount of tax that they pay.
To provide a concrete example, suppose that the government pays someone \$100,000/year and exempts them from income tax. (I understand that governments sometimes do this for certain roles.) Suppose now that they decide to instead pay them \$150,000/year and bill them \$50,000/year in income tax (let's say that this is the impact of removing the tax exemption). Am I right that this will increase GDP by \$50,000?