For U.S. annual data that include World War II, the estimated multiplier for temporary defense spending is 0.4–0.5 contemporaneously and 0.6–0.7 over 2 years. If the change in defense spending is “permanent” (gauged by Ramey's defense news variable), the multipliers are higher by 0.1–0.2. Since all estimated multipliers are significantly less than 1, greater spending crowds out other components of GDP, particularly investment. The lack of good instruments prevents estimation of reliable multipliers for nondefense purchases; multipliers in the literature of two or more likely reflect reverse causation from GDP to nondefense purchases. Increases in average marginal income tax rates (measured by a newly constructed time series) have significantly negative effects on GDP. When interpreted as a tax multiplier, the magnitude is around 1.1. The combination of the estimated spending and tax multipliers implies that the balanced-budget multiplier for defense spending is negative. We have some evidence that tax changes affect GDP mainly through substitution effects, rather than wealth effects.

The coefficient of relative risk aversion is a key parameter for analyses of behavior toward risk, but good estimates of this parameter do not exist. A promising place for reliable estimation is rare macroeconomic disasters, which have a major influence on the equity premium. The premium depends on the probability and size distribution of disasters, gauged by proportionate declines in per capita consumption or gross domestic product. Long-term national-accounts data for 36 countries provide a large sample of disasters of magnitude 10% or more. A power-law density provides a good fit to the size distribution, and the upper-tail exponent, α, is estimated to be around 4. A higher α signifies a thinner tail and, therefore, a lower equity premium, whereas a higher coefficient of relative risk aversion, γ, implies a higher premium. The premium is finite if α > γ. The observed premium of 5% generates an estimated γ close to 3, with a 95% confidence interval of 2 to 4. The results are robust to uncertainty about the values of the disaster probability and the equity premium, and can accommodate seemingly paradoxical situations in which the equity premium may appear to be infinite.