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This paper studies the role of expectations and monetary policy in the economy's response to climate actions. We show that in a stochastic environment, without the standard assumption of the perfect rationality of agents, there is more uncertainty regarding the path and the economic impact of a climate policy, with a potential threat to the ability of central banks to maintain price stability. Market beliefs and behavioral agents increase the trade-offs inherent to the chosen mitigation tool, with a carbon tax entailing more emissions uncertainty than in a rational expectations model and a cap-and-trade scheme implying a more pronounced pressure on allowance prices and inflation. The impact on price stability is worsened by delays in the implementation of stringent climate policies, the lack of confidence in the ability of central banks to keep inflation under control, and the adoption of monetary rules tied to expectations rather than current macroeconomic conditions. Central banks can implement successful stabilization policies that reduce the uncertainty surrounding the impact of climate actions and support the greening process while remaining within their mandate. • This work investigates how expectations can shape a green transition. • Without fully rational agents impacts of climate policy are more uncertain. • Carbon taxes and cap-and-trade's drawbacks are enlarged by non-fully-rational agents. • Delayed action and low credibility in central banks cause major inflationary pressure. • A reactive monetary policy can reduce uncertainty on climate policies' impacts. [ABSTRACT FROM AUTHOR]