Let me pull this apart, piece by piece. The stimulus will increase the GDP number, regardless of where the money comes from or goes into - it's adding to the system. The fallacy here is that GDP is measures productivity - it measures money flow - and the stimulus, by definition, is a flow of money, completely irrespective of any change in productivity. It's also why stimulus is "better" than tax cuts - tax cuts remove a flow of money, whereas stimulus creates one, with the true end result being equivalent.
The creation of jobs is a likely consequence of this money flow. What is not seen is the businesses and jobs not created on account of the lack of need to fix the economy. For instance, it would be a fantastic time to start a bank, if the insolvent ones weren't simply going to be bailed out, but it turns into a terrible time to start a bank if you know that your competition is going to get government money for nothing and you won't. The same misallocation will occur on an individual level with such a stimulus package... and the most likely result will simply be a fudged GDP number that is even less of a reflection of productive output. When the misallocation is stopped, on voluntarily or per force, a reversion to where things were going will occur, only now the business that would have been created for recovery will not exist - instead there will be completely different ones that were feeding on the stimulus.
So how about the whole more jobs thing? As I mention in the last post, government-created demand for hole-diggers can solve all unemployment issues. You could even increase the working week to 50 hours with all this demand for hole-digging! Most people would rather work less time for the same return, so the good here is increasing productivity, not increasing jobs. Few arguments are made for productive output being increased by stimulus, and they either rest on "GDP goes up => Productivity goes up", refuted earlier or "More people working => More productivity", which fails the hole-digger example and fails further when you consider that companies having to compete with the labour demand for hole-diggers and hole-digger admin staff and safety inspectors and all may not be able to employ as many people, so productivity will go down.
I have established that stimulus is probably a bad thing, if you consider the long-term effects on productivity or personal wealth, even if it's free. It's not free - where does the money comes from? Either it comes from debt (selling all citizens in the future into slavery) or from printing (stealing from the utility of money). Both of these are traditional, and horribly frightening when practised to a large degree. Selling too much debt makes the slavery approach absolute, as everyone works to no personal gain, and stealing too much results in devaluation as money becomes worthless, the end result of which is hyperinflation.
The governments seem to think that throwing money at the problem will make things better, a policy that has never worked in the past. The more the better, borrow or print, it's all good! We have the people sufficiently scared, they'll let us do anything, so let's live large! Why is it so difficult to learn from history?
"Progress, far from consisting in change, depends on retentiveness. When change is absolute there remains no being to improve and no direction is set for possible improvement: and when experience is not retained, as among savages, infancy is perpetual. Those who cannot remember the past are condemned to repeat it." - George Santayana
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