Short answers, pulled from the story.
The fiscal multiplier is the ratio of the change in national income to a change in government spending. When the government spends an additional dollar, that sum becomes income for workers and suppliers, who in turn spend a portion of it, generating further income and consumption in a chain reaction. When the multiplier exceeds one, the total increase in national income is larger than the original government outlay.
The existence of a multiplier effect was first proposed by Richard Kahn, a student of John Maynard Keynes, in 1930 and published in 1931. Kahn developed the theory to support a public works scheme proposed by Lloyd George during his 1929 election campaign, showing that much of government expenditure would be recouped through higher tax revenues and reduced unemployment insurance costs.
In July 2008 testimony to Congress, economist Mark Zandi estimated the multiplier for a temporary increase in food stamps at 1.73, the highest of any policy option he reviewed. The International Monetary Fund found that multipliers were in the 0.9 to 1.7 range since the Great Recession, compared to the 0.5 value their models had assumed. Italian economists estimated values from 1.4 to 2.0 when dynamic effects were included.
The IMF admitted in October 2012 that it had used multiplier assumptions of around 0.5 in forecasting, when the actual range since the Great Recession was 0.9 to 1.7. The UK Office for Budget Responsibility relied on the IMF's underestimated figures when projecting the economic impact of austerity. The Trades Union Congress estimated this error meant the OBR may have under-estimated the economic damage from UK austerity policies by 76 billion pounds.
Crowding out is the argument that deficit-financed government spending pushes up interest rates, discouraging private investment and reducing private economic activity by roughly as much as the government has added. Studies of sports stadiums have found multiplier values below one, consistent with crowding out. However, economists argue crowding out is less likely during recessions, when private investment is already constrained and financial markets are hoarding cash rather than lending.
Spending targeted at low-income households tends to produce higher multipliers because those households spend a larger fraction of any income addition quickly. In the 2008 congressional testimony, a temporary increase in food stamps had the highest estimated multiplier at 1.73, while general aid to state governments had the lowest spending multiplier at 1.36. Tax cuts consistently showed lower multipliers than spending increases in the same analysis.