Standard macroeconomic models underpredict the volatility of unemployment fluctuations. A common solution is to assume wages are rigid. We explore whether this explanation is consistent with the data. We show that the wage of newly hired workers, unlike the aggregate wage, is volatile and responds one-to-one to changes in labor productivity. In order to replicate these findings in a search model, it must be that wages are rigid in ongoing jobs but flexible at the start of new jobs. This form of wage rigidity does not affect job creation and thus cannot explain the unemployment volatility puzzle.