Although the sources, extent and physical impacts of the future climate change are highly uncertain, available dynamic economic assessments implicitly assume that economic agents perfectly know them. Perfect foresight, rational expectations or active learning are standard assumptions underlying simulated results. To the contrary, this paper builds on the assumption that economic agents may suffer for a while from limited knowledge about the average and variability of physical impacts of climate change. Using a world dynamic and stochastic general equilibrium model, our simulation results show that identifying the average physical impact is much more crucial than its variability. This finding is robust to the level of risk aversion of economic agents. The rate of pure time preference of economic agents more significantly affects the economic impacts. We also find that the value of information may be negative in the short to medium run.