The achievement of economic and environmental sustainability largely depends on technological change. The literature has theoretically and empirically investigated the extent to which Green technological progress is influenced by varying policy stringency and country commitments, with recent relevant literature advancements predominantly on the microeconomic side. Theory and evidence suggest that countries policy actions might have heterogeneous impacts on technological progress, depending on institutional and economic conditions, among which trade relationships assume a strong importance. The paper investigates whether inventions-policy relationship are heterogeneous across countries, on the basis of a country OECD panel dataset that covers green patents, R&D, human capital, policies and trade over 1983-2013. It also analyses whether inventions inducing spillovers exist, in the form of stimulus a country might receive from the policy actions operated by its main trade partners. Internal and External policies can produce technological effects. Various panel models that take into account for serial correlation and slope heterogeneity are implemented: random coefficient models, constrained and unconstrained seemingly unrelated regressions, which can convey individual country coefficients, and average mean group estimators that capture country heterogeneity by including averages and common factors within the vector of covariates. The statistical and economic meaning and feasibility of cross country heterogeneous effects is the main aim of the paper. Results show that heterogeneity and serial correlation matter. Though the constraints posed by the reduction of poolability are somewhat binding, strong heterogeneity emerges with respect to the effects of R&D, trade and environmental policies towards the generation of green patents. Individual ‘innovation function' with idiosyncratic features and different ‘models' or clusters are drawn out by the analysis. This signifies that parametric specifications that address cross section heterogeneity and time related factors might enhance both the statistical robustness of results and their specific policy relevance.