Formulation, Estimation and Policy Analysis in New Keynesian DSGE Models

By Lawrence J. Christiano

  

 

Overview

The objective of this course is to develop the tools for building a New Keynesian open economy model, estimate it and use it to do policy analysis. In practice, models must be designed to match the particular circumstances of a country and they must be constructed so that they are adequate for the particular policy questions of interest. This means that no single model will serve all purposes. For this reason, we will focus on foundations, so that students have the ability to go to the drawing board to design a model that suits their needs. 

Certain key features of open economy New Keynesian models are easiest explained in a closed economy context. So, we will start with the open economy to discuss issues like (i) how to model price-setting frictions (the defining characteristic of NK models) and (ii) address related problems about aggregation over heterogeneous agents. Given the objectives of the course, we will not shy away from technical details. Still, we’ll draw a line and some details will be relegated to separate portions of the handouts. The easiest way to access these portions of text is to read the files in pdf form. Those versions of the files (and more) are provided below. Still, it will be useful to have hardcopy of the lectures during the class for note-taking purposes.

We may get to a discussion of financial frictions, and I have included some material on that subject. However, I suspect that we will at best only be able to do a brief overview of that important topic.

Computer exercises will give students hands-on practice in the use of Dynare to solve, estimate and analyze dynamic models.

 

Lectures

1) The simple New Keynesian (NK) lecture 1 and lecture 2 on model without capital (background: my handbook chapter; Journal of Economic Perspectives paper, interview and this). We will stress the key role in short term economic dynamics of aggregate demand, and the importance of good policy for guiding it. We will evaluate inflation targeting from this point of view.

a) This is a follow up on lecture 2. It: (i) illustrates the undetermined coefficients solution method described in lecture 2, (ii) discusses the relationship between the nominal rate of interest and inflation (Fisherian versus anti-Fisherian relationship). Another follow-up shows how the computational findings at the end of lecture 2 can be demonstrated analytically.

b) Handout (this will not be discussed in lecture) on linearization as a tool for solving models (a more in depth discussion appears here).

c)  Derivation of linearized NK Phillips curve.

d) A series of exercises in NK_exercise.pdf (found in the zip file here) accomplishes three things (you can find the pdf file, as well as the associated Dynare code, cgg.mod, here).

i)    Gives students experience with Dynare for solving and simulating models.

ii)  Gets to the heart of the New Keynesian models by exploring its basic underlying economic principles.

iii)        Shows how ‘news’ shocks might cause an inflation targeter to drive the interest rate in the ‘wrong’ direction and inadvertently trigger an inefficient stock market boom (Slides, manuscript; and section 3.2 of handbook chapter.)

e) Our equilibrium conditions do not include the government budget constraint, the profits of the firms and the details of the household budget constraint. In part, this is due to our assumption of lump-sum taxes. In part it is because Walras’ law allows us to summarize these equations with the resource constraint. This is a brief summary of this well-known fact in the context of our simple model.  

f)   Other, related materials.

2) Estimation of DSGE models (the handout makes some references to this note on model solution and here is a note on the appropriate acceptance rate for the MCMC algorithm).

a) State space representation of a model.

b) Elements of Bayesian inference (Bayes’ rule, MCMC algorithm).

c)  A simple example to illustrate Bayes’ rule.

d) Exercise that illustrates the MCMC algorithm is in the pdf file, MCMC_exercise that can be found in the zip file found here).

e) We will use Dynare to estimate a version of the closed economy model using macroeconomic data from India. We will use the estimated model to consider the problem of using a model for forecasting and doing conditional forecasting. There is a range of forecasting situations that we could consider. We’ll look at how to address the question, “what will happen if we raise the interest rate by x basis points for the next year?” (For a more extended discussion of various types of conditional forecasting see this, section 2 (b).)

3) Extending the NK model to the open economy. This is a drastically simplified version of the model used at the Riksbank and described in here. Code to generate graphs in the lecture notes. Code that estimates the open economy model using Armenian data and reports forecasts in 2 (e) above.

4) A very informal review of financial frictions literature: frictions arising from problems in the non-financial business sector and frictions arising from problems inside the financial sector. We probably will stop at this point.

5) A more formal approach to financial frictions arising from problems in non-financial firms. (Probably will not get to this.)

a) Micro foundations for the Costly State Verification (CSV) approach (zip file with code for the computations, and a version of the  slides with more extensive derivations). The CSV model is used as a friction on the asset side of a bank’s balance sheet.

b) Integrating CSV into a New Keynesian model and the results of Bayesian estimation of the model using US data (CMR, JMCB 2003, AER 2014).

i)    The model.

ii)  The importance of risk shocks and news on risk.

iii)        The response of monetary policy to an increase in interest rate spreads.

iv)        Carefully documented (thanks to Ben Johannsen) Dynare code for replicating the material in this presentation.

c)  Financial frictions on the liability side of banks’ balance sheet. Two-period exposition of Gertler-Karadi/Gertler-Kiyotaki model in which the financial frictions stem from bankers’ ability to ‘run away’ (section 3 of reading, handout).

6) Financial frictions emerging from inside the banking sector: an informal review. Summary of Gertler-Kiyotaki AER2015 (here is a more extended set of lecture notes). The focus here will be on shadow banking, which grew very large in the US in the 2000s. (Probably will not get to this.)