Climate change is one of the most challenging topics of our generation, with profound implications for society, politics and also economics. The debate regarding the role of central banks and financial regulators in addressing climate-related policies has notably gained importance in recent years. Heterogeneity in the ecological thinking is another crucial aspect that affects households (Bliuc et al., 2015), firms (Leyva-de la Hiz et al., 2019), financial regulators and central banks (Campiglio et al., 2018). In this respect, Hommes and Lustenhouwer (2019) develop a dynamic stochastic general equilibrium (DSGE) model to examine the emergence of (almost) self-fulfilling waves of optimism and pessimism and self-fulfilling liquidity traps in a New Keynesian model with a continuum of heterogeneous expectations. Starting from their contribution, we develop a framework in which expectations are heterogeneous with respect to their level of anchorage around the targets of the central bank. We depart from the standard assumption in the literature under which the level of anchoring is homogeneous for both variables, such as in Hommes and Lustenhouwer (2019), evaluating the model under heterogeneous levels of anchoring around the targets of the central bank, and where brown firms’ expectations are less anchored due to the potential increase of costs derived from green policies. Our preliminary results show that only with anchored inflation expectations, waves are larger than in the case in which only the output gap is anchored, and weak responses to shocks in the brown sector may lead to waves of greenflation.