Stumbling and Mumbling has an interesting post;
There are three “headline” measures of government activity, which my chart shows.
One is the output of government services - health, defence, education etc - which shows up within the output measure of GDP.
Another is government consumption, which comes in the expenditure measure of GDP.
And a third is overall central government current spending, which is reported in table PSF3 of the public finances; in my chart, I’ve deflated this by the GDP deflator.
And here’s the queer thing. The correlation between annual changes in these three measures is low; no higher than 0.26 since 1984Q1.
How come? One reason is that central government spending includes debt interest and welfare payments, which the other two don’t.
Another reason is that government consumption includes spending on procurement which is excluded from output.
Public Service Output, Input and Productivity: Healthcare
Public Service Output, Input and Productivity: Education