This paper shows that the latest generation of asset pricing models with long‐run risk exhibit
economically significant nonlinearities, and thus the ubiquitous Campbell‐Shiller log‐
linearization can generate large numerical errors. These errors translate in turn 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 highly persistent processes, which cause the exogenous states to attain …

This paper analyzes both the existence of solutions to long-run risk asset pricing models as
well as the practicality of approximating these solutions by the Campbell-Shiller log-
linearization. We prove a simple relative existence result that is sufficient to show that the
original Bansal-Yaron model has a solution. Log-linearization fares less well: we find that for
very persistent processes the approximation errors in model moments can be as large as
50%, and can get such basic facts wrong as the direction of the yield curve. The increasing …