We present a novel way to model technological shocks, with the feature that it can be biased towards more recently installed production units. We show that at one extreme, the shock is like a neutral technological shock, while at the other end of the spectrum, it resembles investment specific technological shocks, since it affects newly created machines the most. To make these ideas operational, we embed our proposed shocks in a model with putty-clay technology (where the notion of new and old firms is clear). We estimate the process for the shocks requiring that the model replicates the volatility properties of the Solow residual and the overshooting property of the labor share of output. Our estimates point to three factors to be capable of replicating well such overshooting property: putty-clay nature of technology, a time bias in the shocks towards new plants and competitive wage setting.