Higher-order effects in asset-pricing models with long-run risks

This paper shows that the latest generation of asset pricing models with long-run risk exhibits economically significant nonlinearities, and thus the ubiquitous Campbell--Shiller log-linearization can generate large numerical errors. These errors in turn translate to considerable errors in the model predictions, for example, for the magnitude of the equity premium or return predictability. We demonstrate that these nonlinearities arise from the presence of multiple very persistent processes, which cause the exogenous states to attain values far away from their long-run means with non-negligible probability. These extreme values have a significant impact on asset price dynamics.