Maybe less than people thought, here is a new ReStat paper by Gillian Brunet:
I use newly digitized contract data on U.S. war production spending between 1940 and 1945 to analyze the macroeconomic effects of U.S. military spending during World War II. I find personal income multipliers of 0.34 over two years and 0.49 over three years. Personal income multipliers can significantly underestimate GDP multipliers, perhaps by as much as 50%. Employment estimates imply costs per year of employment over the same time horizons of $405,013 and $232,268 in 2015 dollars, suggesting that job creation has been limited. I also find evidence of negative scale effects: larger positive spending shocks are associated with systematically lower multiplier estimates.
Via Alexandre Berger. The author’s title is “Stimulus on the Home Front: The Effects of World War II Spending at the State Level.”