A review of the literature on fiscal multipliers:
Barro (1984) ≈ 0.6 U.S. defense spending increases in WWI, WWII, Korean War.
Hall (1986) ≈ 0.6 U.S. defense spending, 1920-42, 1947-82.
Ramey (2011) 0.6-1.2 U.S. defense spending, 1939-2008, estimates based on defense-news variable, short-run versus long-run, deficit financed.
Fisher and Peters (2010) greater than 0 U.S. defense spending, 1948-2007, estimates based on stock returns of defense contractors, cumulative effects over 5 years for 1959 over 5 years for 1959-2007.
Barro and Redlick (2011) 0.4-0.8 U.S. defense spending, 1917-2006, short-run versus long-run, temporary versus permanent (based on defense news), deficit-financed, applies to increases or decreases.
Hall (2009) ≈ 0.5 U.S. defense spending, 1930-2008.
Owyang, Ramey, Zubairy (2013) ≈ 0.6-0.9 U.S. (1890-2010) and Canada (1922-2011) defense spending, based on defense news, short-run versus long-run, deficit financed, interactions with unemployment rate.
Kraay (2012) 0.5-0.7 Uses timing of World Bank loan disbursements to 29 developing countries, 1985-2009, short-run.
Nakamura and Steinsson (2012) ≈ 1.4 U.S. defense spending across U.S. states, 1966-2006, responses of state real GDP over two years. Note: one reason the state spending multiplier was higher was that spending was nearly free, coming from current or prospective taxes levied mostly on residents of other states.
Cohen, Coval, Malloy (2011) less than 0 Federal spending in U.S. states, driven by states’ political power in U.S. Congress, effects on corporate investment and employment and on state GDP and total employment, 1967-2008.
Wilson (2012) greater than 0 ARRA cross-U.S. state spending except for UI, 2009-10, effects on state employment.
Chodorow-Reich, et al. (2012) greater than 0 ARRA cross-U.S. state spending on Medicaid, 2009-10, effects on state employment.
https://www.imf.org/external/np/seminars/eng/2013/fiscal/pdf/barro.pdf
Guo, Liu, Ma (2016) 0.6 local fiscal multipliers using annual data for 1800 China counties.
http://www.sciencedirect.com/science/article/pii/S0147596715000578
Fishback and Kachanovskaya (2015) debunked the multiplier during the Great Depression: "To estimate the impact of federal spending on state incomes, we develop an annual panel data set between 1930 and 1940. Using panel methods we estimate that an added dollar of federal spending in the state increased state per capita income by between 40 and 96 cents. The point estimates for nonfarm grants are higher and for AAA farm grants are much smaller and negative in some cases. The spending led to increase in durable good spending on automobiles but had no positive effects on private employment."
https://www.cambridge.org/core/journals/journal-of-economic-history/article/multiplier-for-federal-spending-in-the-states-during-the-great-depression/D98013D970C3CF4C1D2D56D873172ADB
"Given increasing trade integration and the adoption of flexible exchange rate arrangements particularly the adoption of inflation targeting regimes our results cast doubt on the effectiveness of fiscal stimuli. Moreover, fiscal stimuli are likely to become even weaker, and potentially yield even negative multipliers, in the near future, because a large number of countries are now carrying very high public debt ratios."
http://www.sciencedirect.com/science/article/pii/S030439321200116X
"Using Japanese financial data that provide enough observations under the good and bad regimes of financial conditions, we find that fiscal multipliers are smaller in the bad regime than in the good regime."
http://www.tandfonline.com/doi/abs/10.1080/13504851.2017.1299098
"Using phase diagram analysis, we prove that the aggregate capital stock at the time of expiry of fiscal stimulus is lower than it would be without a deficit spending program."
http://onlinelibrary.wiley.com/doi/10.1111/geer.12090/full