For U.S. annual data that include WWII, the estimated multiplier for defense spending is 0.6-0.7 at the median unemployment rate. There is some evidence that this multiplier rises with the extent of economic slack and reaches 1.0 when the unemployment rate is around 12%. Multipliers for non-defense purchases cannot be reliably estimated from U.S. macroeconomic time series because of the lack of good instruments. Since the defense-spending multiplier is typically less than one, greater spending

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... ends to crowd out other components of GDP. The largest effects are on private investment, but non-defense purchases and net exports tend also to fall. The response of private consumer expenditure differs insignificantly from zero. For samples that begin in 1950, increases in average marginal income-tax rates (measured by a newly constructed time series) have a significantly negative effect on real GDP. We lack reliable statistical evidence on how this response divides up between substitution effects from changes in tax rates versus income effects from changes in government revenue. *This research was supported by a grant from the National Science Foundation. We particularly appreciate the assistance with the marginal tax-rate data from Jon Bakija and Dan Feenberg. We also appreciate research assistance from Andrew Okuyiga and comments from David Romer and Jose Ursua. 1942, 17.2% in 1943, and 3.6% in 1944, followed by two negative values of large magnitude, -7.1% in 1945 and -25.8% in 1946. Thus, World War II provides an excellent opportunity to gauge the size of the government-purchases multiplier; that is, the contemporaneous effect of a change in government purchases on real GDP. The favorable factors are: • The principal changes in defense spending associated with World War II are plausibly exogenous with respect to the determination of real GDP. • These changes in defense spending are very large and include sharply positive and sharply negative values. • Unlike the many countries that experienced sharp decreases in real GDP during World War II (see Barro and Ursua [2008, Table 7]), the United States did not have massive destruction of physical capital and suffered from only moderate loss of life. Hence, demand effects from defense spending should be dominant in the U.S. data. • Because the unemployment rate in 1940 was still high, 9.4%, but then fell to a low of 1.0% in 1944, there is some information on how the size of the defense-spending multiplier depends on the amount of slack in the economy. The U.S. time series contains two other war-related cases of major, short-term changes in defense spending. In World War I, the defense-spending variable (blue graph in Figure 1 ) equaled 3.5% in 1917 and 14.9% in 1918, followed by -7.9% in 1919 and -8.2% in 1920. In the Korean War, the values were 5. 6% in 1951, 3.3% in 1952, and 0.5% in 1953, followed by -2.1% in 1954. As in World War II, the United States did not experience much destruction of physical capital and incurred only moderate loss of life during these wars. Moreover, the changes in defense outlays would again be mainly exogenous with respect to real GDP.