Integrated assessment models (IAMs) typically ignore the impact climate change could have on economic growth. The damage functions of these models assume that climate change impacts have no persistence at all, affecting only the period when they occur. Persistence of shocks is a stylized fact of macroeconomic time series and it provides a mechanism that could justify larger losses from climate change than previously estimated. Given that the degree of persistence of climate impacts is unknown, we analyze the persistence of generic shocks in observed GDP series for different world regions and compare it to that of the leading IAMs. Under the working hypothesis of interpreting the direct impact of climate change as such shocks, the implications for growth are investigated for two RCP scenarios. The way of introducing climate shocks to GDP in most IAMs can be interpreted as assuming an autonomous, costless, large and effective reactive adaptation capacity.