From de Rugy:
There are few studies on the issue, but two have found that government spending shrinks the private sector, at least a little. Looking at war spending, Harvard University's economist Robert Barro estimates that the multiplier of government spending is 0.8: when the government grows by $1, the private sector shrinks by 20 cents. Also, using a variable that takes into account the fact that military spending is anticipated several quarters before it actually occurs, the University of San Diego's Valerie Ramey has shown how U.S. military spending influences GDP and estimates that the multiplier of government spending is between 0.6 (when World War II data is excluded) and 1 (when it is included). Thus both papers support the "crowding out" hypothesis.