Summer School on Heterogeneous Agents in Macro Models
Lake Como School of Advanced Studies

Organized by the Department of Economics, Management and Statistics (University of Milano Bicocca)

Petr Sedláček
University of Oxford


This course teaches state-of-the-art techniques to solve and analyze dynamic stochastic general equilibrium (DSGE) models with heterogeneous agents. After a short refresher on solution methods for representative agent modesl (such as perturbation and projection), the course provides students with an understanding of (i) workhorse algorithms to solve models with heterogeneous agents with(out) aggregate uncertainty (such as the Krusell-Smith algorithm), (ii) different simulation methods and accuracy tests, (iii) alternative solution algorithms (such as Reiter’s hybrid method) and (iv) an introduction into continuous time models and their solutions.Throughout the course, students will learn how to implement the covered material in practice using Matlab and Dynare (where possible). Participants should use their own laptop.

Day 1 – Introduction and Aiyagari model

• Introduction
• Quick refresher of basic solution techniques (perturbation and Dynare, projection and PEA)
• Solving the Aiyagari model – workhorse heterogeneous agent model WITHOUT aggregate risk

• Solve Aiyagari model using Dynare
o Using penalty function and the bi-section method

Day 2 – Krusell-Smith algorithm

• Krusell-Smith economy – workhorse heterogeneous agent model WITH aggregate risk
• Solving the individual’s problem
• Approximating (time-varying) distributions
o The aggregate law of motion

• Solve Krusell-Smith economy using Dynare
o Using stochastic simulation

Day 3 – Krusell-Smith continued and Alternatives

• Practical issues in Krusell-Smith algorithm
o Alternative simulation methods
o Convergence and accuracy tests
• Introduction into alternatives to Krusell-Smith
o Explicit aggregation
o Hybrid methods

Day 4 – Explicit aggregate and hybrid methods

• Explicit aggregation
• Hybrid methods:
o Parametrizing distributions of microeconomic agents
o Perturbation and aggregate distribution dynamics
• Solving heterogeneous agent models in Dynare

• Solve model with ex-ante heterogeneous firms using Dynare

Day 5 – Continuous time

• Introduction
• Basic concepts and models
o Solow growth model
o Search and matching model
• Basic solution methods
• Extending to models with heterogeneous agents

• Solve Solow growth model in continuous time