Unemployment insurance (UI) extensions can have broad effects on labor markets by changing search effort, creating or destroying jobs, and boosting aggregate demand. I analyze a natural experiment created by a federal UI extension enacted in the United States during the Great Recession and measure the effect on state-level employment. I exploit a feature of this UI extension whereby random sampling error in a national survey altered the duration of unemployment insurance in several states, resulting in random variation in the number of weeks of unemployment insurance available at the state level. Point estimates of the impact of this UI extension imply that unemployment insurance raises employment growth. Although I cannot conclusively rule out an elasticity of zero, I can rule out substantial negative effects. I also document several issues with previous attempts to measure the total effect of UI extensions on employment.