Chapter 28. Challenges for Central Banks’ Macro Models In this chapter we discuss a number of challenges for structural macroeconomic models in the light of the Great Recession and its aftermath. It shows that a benchmark DSGE model that shares many features with models currently used by central banks and large international institutions has difficulty explaining both the depth and the slow recovery of the Great Recession. In order to better account for these observations the chapter analyses three extensions of the benchmark model. First we estimate the model allowing explicitly for the zero lower bound constraint on nominal interest rates. Second we introduce time variation in the volatility of the exogenous disturbances to account for the non Gaussian nature of some of the shocks. Third and finally we extend the model with a financial accelerator and allow for time variation in the endogenous propagation of financial shocks. All three extensions require that we go beyond the linear Gaussian assumptions that are standard in most policy models. We conclude that these extensions go some way in accounting for features of the Great Recession and its aftermath but they do not suffice to address some of the major policy challenges associated with the use of nonstandard monetary policy and macroprudential policies.