In imperfectly competitive settings, a firm's price depends on its own costs as well as those of its competitors. We demonstrate that this has important implications for the estimation and interpretation of pass-through. Leveraging a large input cost shock resulting from the fracking boom, we isolate price responses to firm-specific, regional and industry-wide input cost shocks in the US oil refining industry. The pass-through of these components vary from near zero to full pass-through, reconciling seemingly disparate results from the literature. We illustrate the policy implications of rival cost pass-through in the context of a tax on refinery carbon emissions.