Climate change and mitigation policies pose considerable risks to the economy and to financial sectors. And that is why climate change is also relevant for central banks. Why governments are in the driving seat, there should be also a role for central banks. And indeed, there is an increasing number of major central banks around the world that are exploring strategies on implementing climate change considerations into their monetary policy frameworks. In our research, we wanted to understand better how effectively climate change can be addressed by central banks or what is the role central banks can play in their impact. To this end, we have developed a two-sector integrated assessment model with green or clean and dirty input factors. This is a global model and we consider green quantitative easing being the tool available for central banks. So how do we define green quantitative easing? We make some very extreme assumptions. Namely, we define green quantitative easing as a full and sudden portfolio shift of the outstanding stock of privately issued bonds held by central bank towards bonds issued by only clean firms. We have basically three main results. First, we find that green quantitative easing is effective, although its impact is moderate. Concretely, we show that with green quantitative easing, the increase in global temperature can be reduced by 0.04 degree of Celsius by the end of the century. What second result is when comparing green quantitative easing with the carbon text, which is widely considered as being the most effective instrument, we find that a carbon text is four times more effective than green quantitative easing. Thirdly, we find that green quantitative easing and the carbon text are complementary instruments. There are some non-linearities due to substitution effects for green and dirty input factors, which are partly of setting each other, but in net terms, both instruments can be considered as being complementary. Our research confirms that there is a role for central banks to address climate change via green quantitative easing. At the same time, governments have much more powerful tools at hand to address climate change. That is why we argue green quantitative easing should be used as a complementary tool that should support government action.