We provide insights into the relationships between technological development, economic growth, and pollution accumulation using a two-sector model of economic growth with endogenous technical change. In the model, output is produced using a polluting resource. Production can be used for either consumption or abatement of pollution. Scientists can be allocated between two research activities: resource-saving and abatement-augmenting technologies. Our results indicate conditional path dependency. Specifically, when the innovative capacity in the resource-saving research sector is sufficiently high, scientists are allocated to improve only the resource-saving technology, independently of the state of the technologies and environment. Consequently, the allocation of researchers is path-independent. When the innovative capacity in the abatement-augmenting research sector is sufficiently high, the optimal allocation of researchers depends on the initial level of the pollution stock or technologies but eventually will be directed to improve the abatement technology. We further characterize the optimal steady-state and off-steady-state dynamics and show that green growth is always socially optimal. By using a two-sector model, we address a lack of attention to multi-sector growth models in neoclassical growth theory and show that distinct results and transitional dynamics can emerge.