Recent literature has raised the attention on the estimation of time-invariant variables both in a static and a dynmamic framework. In this context, Hausman-Taylor type estimators have been applied, relying crucially on the distinction between exogenous and endogenous variables (in terms of correlation with the time-invariant error component). We show that this provision can be relaxed, and identification can be achieved by relying on the milder assumption that the correlation between the individual effect and the time-varying regressors is homogenous over time. The methodology is applied to identify the role of inputs from "Science" (firm-level publications' stock) on firms' labour productivity, showing that the effect is larger for those firms with higher level of R&D investments. The results further support the dual – direct and indirect – role of R&D.