This paper focuses on tenure driven productivity dynamics of a firm-worker match as a potential explanation of "unemployment volatility puzzle". We let new matches and continuing jobs differ by their productivity levels and by their sensitivity to aggregate productivity shocks. As a result, new matches have a higher destruction rate and lower, but more volatile, wages than old matches, as new hires receive technology associated with the latest vintage. Our contribution is to produce model driven stickiness of old jobs’ wages which does not rely on ad hoc assumptions on wage rigidity. In our model, an aggregate productivity shock generates a persistent productivity difference between the two types of matches, creating an incentive to open new productive vacancies and to destroy old matches that are temporarily less productive. The model produces a well behaving Beveridge curve, despite endogenous job destruction, and more volatile vacancies and unemployment, without a need to rely on differing wage setting mechanisms of new and continuing jobs. Price rigidities do not alter the basic mechanism and the transmission of monetary policy shock is very similar to the standard New Keynesian model with search frictions.