Course Description

This graduate-level course teaches the key building blocks of solving, analyzing and estimating structural macroeconomic models. Students are shown how to use Dynare, but also how to write their own Matlab programs to solve and analyze models. Importantly, the course also focuses on practical problems that researchers run into when using these techniques.

Monday – Linearization techniques

The first lecture teaches you how to solve dynamic stochastic macroeconomic models using linearization techniques. We start with “do it yourself” methods and then move to a more general theory of perturbation. The latter is implemented using Dynare – a free perturbation software.

Topics

• State variables and policy rules

• Linearization and Perturbation analaysis

• Certainty equivalence

• Dynare

Exercise 

In the first coding session, you will be asked to solve a simple DSGE model using both DIY methods and Dynare. 

Tuesday – Analyzing models and an intro into parametrization

The second set of lectures discusses how to analyze linearized solutions of macroeconomic models. We begin by discussing how to simulate your model, how to compute impulse response functions and how to estimate business cycle statistics. Finally, in this lecture we move towards discussing the parameterization of macroeconomic models. We do so by discussing calibration and various alternatives.

Topics

• Simulation, impulse responses

• Filtering and business cycle statistics

• Calibration example

Exercise

In the second exercise, you are asked to write a program to investigate how one can generate sufficient volatility in the unemployment rate in a simple matching model (i.e. how to solve the Shimer puzzle). 

 
Wednesday – Estimating linearized models A

This is the first of two lectures on estimating macroeconomic models. In this lecture, we teach you a powerful tool – the Kalman filter. This tool allows you to estimate unobserved components in time-series and, as such, it plays a key role in the estimation of macroeconomic models with Maximum Likelihood and Bayesian estimation. We will teach you how to calculate the likelihood of a model given the data and we’ll discuss some tricky issues you may run into in practice, such as stochastic singularity.

Topics

• Kalman filter and the state-space form of macroeconomic models

• Maximum Likelihood

• Avoiding the singularity problem

Exercise

 In the coding session, you are asked to estimate a time series model of the labor market and document how matching efficiency dropped during the Great Recession in the U.S.

Thursday – Estimating linearized models B

Building on the tools learned on Wednesday, this lecture gives you an introduction into Bayesian estimation. A key challenge of Bayesian estimation is the evaluation of the posterior and to tackle this problem, we introduce you to the basics of Markov Chain Monte Carlo (MCMC) techniques.

Topics

• Bayesian estimation

• Markov Chain Monte Carlo methods

• Metropolis and Metropolis Hastings algorithms

Exercise

In this exercise you are asked to estimate a dynamic model, extract the unobserved components, and discuss which shock was most important for which recession.

Friday – Moving towards non-linearity

Friday's lecture will cover two distinct topics. First, we will use the methods from Monday's lecture - DIY linearization - and show how these can be used to solve linear models with a "nonlinear flavor" (through exogenous, or endogenous, regime switches). Second, we will introduce the Bellman equation, and discuss how to solve it using value function iteration. 

Topics

• Regime switching and occasionally binding constraints

• Value function iteration

Exercise

In this last exercise, you are asked to solve a stochastic Ramsey growth model nonlinearly, using value function iteration.