This paper shows that the available stylized facts on productivity dynamics, such aspersistent cross-sectoral heterogeneity, do not allow to solve an identification problemregarding the impact of common drivers - such as General Purpose Technologies (GPTs) - oneconomic growth. The evidence of persistently heterogeneous productivity performances isconsistent both with a GPT-driven model, and with a model characterized by purelyindependent and idiosyncratic sectoral dynamics. These results are obtained within a simpletheoretical framework, and illustrated with reference to measures of concentration of thesectoral contributions to aggregate total factor productivity growth.