Solving the new Keynesian model in continuous time

We show how to formulate and solve the new Keynesian model in continuous time. In our economy, monopolistic firms engage in infrequent price setting á la Calvo. We introduce shocks for preferences, total factor productivity and government expenditure, and then show how the equilibrium system can be written in terms of 8 state variables. Our nonlinear and global numerical solution technique uses the collocation method based on Chebychev polynomials directly computing the continuous-time Bellman equation.