This is a really tough one. But let’s think about this praxeologically for a moment:
In a capitalistic economy the government acts as a market participant and spends accordingly. In an economy where wages and prices are flexible then, regardless of the level of government spending, wages will adjust and involuntary unemployment will disappear. Therefore we can determine a priori that in the long term government spending cannot directly affect the rate of unemployment except in the ways that it actually affects growth from what it otherwise would have been. This, however, is not directly measurable. One cannot say, merely based upon the level of SPENDING how high or low unemployment will be. Alterations which the government makes could increase or decrease the employment level.
However, this is not what we are seeing, we are seeing the short term effects of government policy in a shifting economy where wages are not especially flexible. We can tell, once again a priori, that if governments taxes from areas which are more capital intesive and spends in areas which are more labor intensive that employment will be positively affected, however unless the government spending is actually a productive force like infastructure or something of the like, then real wages will decrease through a general rise in prices. This could, or could not actually result in negative unemployment growth, however it would most certainly result in a greater unemployment that would otherwise be the case.
By this reasoning I would actually consider this analysis somewhat plausible. However, a very, very important fact is left out. Government spending as a percentage of GDP tends to rise with business cycles because of the fact that even though overall revenue decreases budgets do not. If you look most of the major spikes in spending and unemployment correlate with business cycles, and then during times of relative growth both of these things decrease, suggesting that government spending is not increasing at the same rate as GDP growth. I’m not sure then if this is the case of post hoc, because a reason is given but it leaves out other major events, or non sequitur for a similar reason, because what is said does not necessarily follow.
So we can see that there certainly are major things wrong with this analysis, indeed I find the most important one to be the fact that he leaves out state and local expenditures and focuses only on the federal government which is leaving out a good 40 percent of the issue by today’s standards.
I’m also exceedingly dubious about his ‘real GDP graph’
So overall, interesting idea but I find a lot of stuff really flawed.