Some thinks that World War II offers an example of a situation where fiscal stimulus worked. But the World War II analogy is highly misleading for any discussion of a peace-time economy. The deficits were run during an all-out war when 40 percent of GDP was spent on munitions, the military made most of the allocation decisions in the economy, over 15 percent of the workforce was in harm's way in the military, there were widespread wage and price controls, and rationing ruled the day. In essence, the World War II deficit experience tells us more about fiscal stimulus in the Soviet Union's command economy during the Cold War than it does about the modern U.S. mixed economy.
From Ethan Ilzetzki, Enrique Mendoza, and Carlos Vegh, here is a new paper (gated) on fiscal multipliers (shorter, ungated version here, powerpoints here, slides here, ungated but slightly older version here):
We contribute to the intense debate on the real effects of fiscal stimuli by showing that the impact of government expenditure shocks depends crucially on key country characteristics, such as the level of development, exchange rate regime, openness to trade, and public indebtedness. Based on a novel quarterly dataset of government expenditure in 44 countries, we find that (i) the output effect of an increase in government consumption is larger in industrial than in developing countries, (ii) the fiscal multiplier is relatively large in economies operating under predetermined exchange rate but zero in economies operating under flexible exchange rates; (iii) fiscal multipliers in open economies are lower than in closed economies and (iv) fiscal multipliers in high-debt countries are also zero.
That's zero as in "two times zero equals zero," or "1/2 times zero equals zero too" or even "-0.5 times zero equals zero." I don't think the multiplier is zero for the United States, but very likely it's zero in a bunch of places.