Nonemployment is often posited as a worker's outside option in wage setting models such as bargaining and wage posting. The value of this state is therefore a fundamental determinant of wages and, in turn, labor supply and job creation. We measure the effect of changes in the value of nonemployment on wages in existing jobs and among job switchers. Our quasi-experimental variation in nonemployment values arises from four large reforms of unemployment insurance (UI) benefit levels in Austria. We document that wages are insensitive to UI benefit levels: point estimates imply a wage response of less than $0.01 per $1.00 UI benefit increase, and we can reject sensitivities larger than 0.03. In contrast, a calibrated Nash bargaining model predicts a sensitivity of 0.39 – more than ten times larger. The empirical insensitivity holds even among workers with a priori low bargaining power, with low labor force attachment, with high predicted unemployment duration, among job switchers and recently unemployed workers, in areas of high unemployment, in firms with flexible pay policies, and when considering firm-level bargaining. The insensitivity of wages to the nonemployment value we document presents a puzzle to widely used wage setting protocols, and implies that nonemployment may not constitute workers' relevant threat point. Our evidence supports wage-setting mechanisms that insulate wages from the value of nonemployment.