Extreme events are one of the main channels through which climate and socio- economic systems interact. It is likely that climate change will modify their probability distributions and their consequences. The long-term growth models used in climate change assessments, however, cannot capture the effects of short-term shocks; they thus model extreme events in a very crude manner. To assess the importance of this limitation, a non-equilibrium dynamic model (NEDyM) is used to model the macroeconomic consequences of extreme events. Its conclusions are the following: (i) Dynamic processes multiply the extreme event direct costs by a factor 20; half of this increase comes from short-term processes; (ii) A possible modication of the extreme event distribution due to climate change can be responsible for significant GDP losses; (iii) The production losses caused by extreme events depend, with strong non-linearity, both on the changes in the extreme distribution and on the ability to fund the rehabilitation after each disaster. These conclusions illustrate that the economic assessment of climate change does not only depend on beliefs on climate change but also on beliefs on the economy. Moreover, they suggest that averaging short-term processes like extreme events over the five- or ten-year time step of a classical long-term growth model can lead to inaccurately low assessments of the climate change damages.