Persistent stochastic shocks in a new Keynesian model with uncertainty

Both from theoretical and practical viewpoints, I argue that the New Keynesian model's forward-looking IS curve should be derived by quadratic approximation. This leaves uncertainty in the basic three-equation model. After adding exogenous AR(1) processes, I examine the results by numerical simulation. First, I derive a reduced-form solution for the nominal rate of interest which describes the equilibrium behavior under optimal discretion. Focusing on the persistence parameter, the equilibrium will be simulated and compared to the model version containing the certainty equivalence. In a next step, impulse response functions show the adjustments over time after a cost shock. As a result, accounting for uncertainty can lead to lower interest rates of roughly 25 basis points compared to the case without uncertainty.