Other Material Related to the Analysis of the New Keynesian Model

1. Assignment #9, question 1, accomplishes two things.

a. Gives students experience with Dynare for solving and simulating models.

b. Gets to the heart of the New Keynesian models by exploring its basic underlying principles.

2. Solving and analyzing models using the linearization strategy in Dynare.

a. A simplified discussion of the solution to linear expectational difference equations that we explore with Dynare appears in the class handout. An evaluation of that solution from the perspective of all possible solutions to a linear expectational difference equation appears here.

3. Implications of Assignment #9 for inflation targeting.

a. The rationale for, and possible pitfalls of, the Taylor principle/inflation targeting. Pitfalls will be shown to be possible if there is a significant working capital channel or if ‘news’ shocks are important (see this manuscript for further discussion).

b. The optimality of using the natural rate of interest (especially if news shocks are important) to guide policy, and identifying measurable proxies for it (see background manuscript).

4. Extensions not discussed formally in class:

a. Code for exploring different versions of the NK model and investigating, for example, the relative performance of first and second order perturbation methods for model solution. Here is a simple (no capital, closed economy) NK economy with Rotemberg price adjustment costs. Here is a simple NK economy with Calvo price adjustment. Here is code for analyzing a medium-sized NK model.

b. An alternative to perturbation for solving models is called the extended path method, which – like the perturbation method – has been incorporated into Dynare. A discussion of that method for doing stochastic simulation appears here. Two examples, based on the simple NK model without capital, are considered. In each case, the zero lower bound on the interest rate is binding. One case considers the economic effects of a positive technology shock. The other case considers the welfare and other effects of a government spending shock when it must be financed by distortionary taxes and the government’s intertemporal budget constraint must be satisfied.

c. Using linearized DSGE models to simulate a fixed interest rate path, either because the zero lower bound is binding or as input to a policy briefing (code).

d. A more extensive discussion of Ramsey optimal policy appears here. Possible time inconsistency of monetary policy and the timeless perspective are discussed. The implications of the working capital channel (briefly discussed in assignment 9) are reviewed.

5. Exploring the meaning of the fact that money demand and supply are not included standard presentations of the NK model.