This paper introduces dynamics in the R&D to innovation and innovation to productivity relationships, which have mostly been estimated on cross-sectional data. It considers four nonlinear dynamic simultaneous equations models that include individual effects and idiosyncratic errors correlated across equations and that differ in the way innovation enters the conditional mean of labor productivity: through an observed binary indicator, an observed intensity variable or through the continuous latent variables that correspond to the observed occurrence or intensity. It estimates these models by full information maximum likelihood using two unbalanced panels of Dutch and French manufacturing firms from three waves of the Community Innovation Survey. The results provide evidence of robust unidirectional causality from innovation to productivity and of stronger persistence in productivity than in innovation.