Green transition is important for the economics of the OECD countries and their transition to cleaner production. This paper estimates a knowledge production function consisting of a system of innovation inputs, innovation outputs, and productivity with feedback effect from productivity on innovation investments. The model accounts for productivity shock, endogeneity of inputs, and their simultaneity and interdependence. Productivity shock is a latent unobserved component that is specified in terms of observable factors. The model is estimated using Bayesian methods organized around Marco Chain Sequential Monte Carlo iteration techniques also known as Particle Filtering. For the empirical part, the paper uses balanced panel data covering 27 OECD countries' green innovation and patents activities observed during the period 1990–2018. Our empirical results show evidence of significant heterogeneity in productivity and its relationship with its identified determinants. The paper also discusses the implications of these results for OECD countries’ green growth strategies.