If we are to speak of Keynesian economics, then we are talking about fiscal multipliers. I have found a number of references that cover them fairly well. It would be nice to find something a little less technical, as an introduction.
The idea behind fiscal multipliers is that a reduction in taxes or an increase in government spending results in an increase in GDP that is some multiplier of the tax reduction or spending increase itself. The multiplier may range from less than negative one to greater then positive one. The exact value of the multiplier depends on the type and economic conditions.
A key to understanding the fiscal multipliers is that it is the change in taxes or spending that has a multiplier effect, not the absolute level. As well, the multiplier has an initial impact that dies off with time. In theory, given the appropriate set of conditions, the upward multiplier can be greater than one while a following downward multiplier can be less than one. Done right, in theory, they can be used to ratchet up the economy. Of course, as with many things, actual practice is much messier than in theory.
Simple government spending isn't Keynesian nor does in include a fiscal multiplier. A ramp up in defense spending may be done in response to some threat to national defense, and while it will have some fiscal multiplier associated with it, this doesn't mean it was done for the purpose of the multiplier effect. All the fiscal multiplier says is that there is an effect because the economy is a closed loop feedback system with gain. The fiscal multipliers are simply the gain. And there is nothing unusual about this. Nature, and especially engineering, is dependent upon feedback systems with gain. The interesting thing about the economy, and not terribly surprising, is that the complexity results in a gain that changes.
The best way to look at government spending is on a per capita, real dollar basis.
What is notable is that the real dollar, per capita spending began increasing in about 2001.
That spending has multiple purposes and effects. One is simply that it is a percentage of the total GDP, circulating funds around the loop. In the process, it provides necessary services, investment in common goods. In other cases, it seems more like busy work. With the US able to produce all the food necessary for the population with 2% of the work force, and everyone needs to work to buy food. Some of government seems to just keep it all moving. It is hard to tell how much of defense spending is providing an absolutely necessary level of preparedness and how much is just busy work. In terms of a jobs program, it's pretty good. Some of it is simply care-taking, caring for the disabled and elderly. Some of the spending, the continuous increase in real dollar per capita, fits with the fiscal multiplier, a continuous stimulus over years and years.
We shouldn't confuse the fiscal multipliers with all government spending. All government spending is not Keynesian.
The following presentations on fiscal policy and multipliers provides a nice summary
Fiscal Policy Decisions Top 5 Concepts
http://academic.kellogg.edu/mckayg/macro/presentations/MacroPresentation11top5revised.ppt
"This unit discusses the use of fiscal policy tools or levers (basically Keynesian ideas) to restore the economy to full employment. Recessions and inflationary periods are examined. Also discussed are some of the problems associated with focusing only on demand. The following research articles tabulate the fiscal multipliers under varying economic conditions."
This presentation goes over the macro economic theory of fiscal policy tools in changing aggregate demand.
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Fiscal Policy
http://www.markville.ss.yrdsb.edu.on.ca/economics/Fiscal Policy ppt(1).ppt
I haven't read this one but include it for comparison.
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Below are three research papers that I've been able to find. The first is a good overview of fiscal multipliers under varying conditions. The second is a very specific examination of the effect of military spending increases on local regions. The third article examines the effects of multipliers in a very technical analysis. Personally, it is the general form of the response presented on page 31 that provides the most useful "executive summary" information. The rest is a real groaner. I generally read the introduction, a bit into the body, the conclusion, and what tables and graphs I can make sense of.
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IMF Fiscal Multipliers
http://www.imf.org/external/pubs/ft/spn/2009/spn0911.pdf
"What determines the size of the multipliers?
The size of the multiplier is larger if: a) “leakages” are few (i.e., only a small part of the stimulus is saved or spent on imports), b) the monetary conditions are accommodative (i.e., the interest rate does not increase as a consequence of the fiscal expansion), and c) the country’s fiscal position after the stimulus is sustainable."
"Can the fiscal multiplier be negative?
Yes, fiscal expansions can be contractionary if they decrease consumersÂ’ and investorsÂ’ confidence, especially if the fiscal expansion raises, or reinforces, fiscal sustainability concerns."
"What is the size of the fiscal multiplier?
The size of the fiscal multiplier is country-, time-, and circumstance-specific. In the March 2009 IMF staff note prepared for the G-20 Ministerial Meeting, a range of multipliers was used. The low set of multipliers included 0.3 on revenue, 0.5 on capital spending, and 0.3 on other spending. The high set of multipliers included 0.6 on revenue, 1.8 on capital spending, and 1 for other spending. Cross-country VAR estimates of fiscal multipliers in LICs range from negative to 0.5, in part because of higher fiscal sustainability concerns in LICs. However, these estimates can be downward biased because the lack of accurate data leads to attenuation bias. The table below provides a detailed survey of the estimated multipliers."
"Which multipliers should be used in specific applications and projections?
Fiscal multipliers have been calculated for some countries but should be carefully reexamined in light of the current events. The table below summarizes estimates of multipliers, mostly for advanced countries. Country circumstances, however, should be taken into account in arriving at the multiplier for a specific country. The factors mentioned at the beginning should be considered.
A rule of thumb is a multiplier (using the definition ∆Y/∆G and assuming a constant interest rate) of 1.5 to 1 for spending multipliers in large countries, 1 to 0.5 for medium sized countries, and 0.5 or less for small open countries. Smaller multipliers (about half of the above values) are likely for revenue and transfers while slightly larger multipliers might be expected from investment spending. Negative multipliers are possible, especially if the fiscal stimulus weakens (or is perceived to weaken) fiscal sustainability.
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Fiscal Stimulus in a Monetary Union Evidence from US Regions
http://www.columbia.edu/~en2198/papers/fiscal.pdf
"We use rich historical data on military procurement spending across U.S. regions to estimate the effects of government spending in a monetary union. Aggregate military build-ups and draw-downs have differential effects across regions. We use this variation to estimate an \open economy relative multiplier" of approximately 1.5. We develop a framework for interpreting this estimate and relating it to estimates of the standard closed economy aggregate multiplier. The closed economy aggregate multiplier is highly sensitive to how strongly aggregate monetary and tax policy \leans against the wind." In contrast, our estimate \differences out" these effects because different regions in the union share a common monetary and tax policy. Our estimate provides evidence in favor of models in which demand shocks can have large effects on output."
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MEASURING THE OUTPUT RESPONSES TO FISCAL POLICY
http://emlab.berkeley.edu/~auerbach/measuringtheoutput.pdf
"A key issue in current research and policy is the size of fiscal multipliers when the economy is in recession. We provide three insights. First, using regime-switching models, we find large differences in the size of spending multipliers in recessions and expansions with fiscal policy being considerably more effective in recessions than in expansions. Second, we estimate multipliers for more disaggregate spending variables which behave differently relative to aggregate fiscal policy shocks, with military spending having the largest multiplier. Third, we show that controlling for predictable components of fiscal shocks tends to increase the size of the multipliers in recessions."