Will additional government spending "jump start" the economy? We cannot answer this question without some understanding of how fiscal policy works.
In order to explore this question without assuming the answer from outset, I consider two mechanisms: intertemporal substitution and increasing returns.
This is Barro's approach. It says that a temporary increase in public spending crowds out contemporaneous private consumption and investment. Thus, there is no public spending multiplier -- public spending cannot increase GDP MORE than the amount of public spending itself. Public spending does increase GDP because it also crowds out leisure, but it reduces private spending.
This seems to fit the historical data: public spending does seem to reduce private spending.
Believers in a public spending multiplier have not been terribly specific about how this works. If I had to formalize their view, I would use some kind of increasing returns. That is, the benefit from working occasionally is GREATER when others are working more. A leftward shift in the labor supply of some persons thereby reduces labor productivity of the others, which causes others to work less.
The question is -- when is the economy in the range of increasing returns? That is, when will (increased) reduced employment (increase) reduce productivity? Arguably there are a number of recessions (including the Great Depression) when reduced employment harmed productivity. In these cases, we might expect that public spending would raise private sector productivity and thereby raise employment by firms that make private consumption and investment goods.
I blame the believers in public spending multipliers for failing to supply us with more details about how the increasing returns works, because this knowledge would help a lot for targeting the public spending in a way that maximized the likelihood that the increasing returns were exploited. However, in this recession this question is moot.
In THIS recession, productivity is HIGH despite the reduced employment. That is, employment seems to have affected productivity exactly as we would expect if there were DIMINISHING returns (that's the Cobb-Douglas model I wrote about yesterday). Thus, even if I could be guaranteed that public spending would be well-timed in this recession AND public spending had a multiplier in previous recessions, I remain doubtful that public spending will have a multiplier in this recession.
We have to accept that, these days, public spending will crowd out private spending.
[Added: I view "increasing returns" as another way of saying "chain reactions" or "coordination failures." That is, if it were so important to work when others do, then why isn't productivity of today's workers lower because of the 2 million workers that left over the last year? I realize that there are "other things going on", but if the "other things" dominate increasing returns in determining productivity, then why wouldn't the former also dominate in determining the fiscal multiplier?]