One not totally pointless point is that New Keynesians talk about G minus steady state G in theory (which means G minus some sort of trend in data). The work horse NK models have Ricardian equivalence so the timing of taxes doesn't matter.
But I am a paleo Keynesian, so I should look at something else. I should look at G-cT where T is taxes minus transfers (such as pensions) and c is the marginal propensity to consume which I have estimated to be about 1/3. Note that this is not at all equal to the deficit G-T. It is true that Keynesians have used the full employment (or "structural") deficit as a fiscal policy variable, but this never made sense for any Keynesian model (including the original IS-LM dated 1937).
Being totally lazy, I look at real G + 0.5 times the Federal budget deficit divided by the GDP deflator. This means that Federal G appears 1.5 times, state and local G appear 1 time and federal taxes minus transfers appear -0.5 times. I call this variable silly.
The recovery started in 2009q2 and I look at growth rates starting then (with growth from 2009q2 to 2009q3). The correlation between the growth rate of real GDP and the growth rate of silly is 0.22 which is considerable smaller than the correlation of the growth rate of real GDP and the growth rate of real G.
Here is the scatter
bothers me even though it is just one data point.
*this is not a typo. I assume the reader, if any, will be singular.