Wouter J. den Haan - LSE Macroeconomics Summer Courses


Macroeconomics Summer Courses - August 2011

#2 Solving DSGE Models with Heterogeneous Agents and Bounded Rationality. August 22-26

NEW in 2011:
  • Macroeconomic models with learning
  • Additional ways to model boundedly rational agents
  • Model in which rational firms will "follow" irrational firms

Prerequisites:
  • Some basic knowledge about DSGE models, e.g., know what an Euler and a Bellman equation are
  • Some rudimentary knowledge on programming with Matlab
  • Some knowledge on solving DSGE models with a representative agent like Dynare and value function iteration

Course outline 2011:

Monday - Theory of models with rational heterogeneous agents

  • Overview: This morning we discuss some theoretical aspects of models with heterogeneous agents, such as the (lack of) aggregation in models with heterogeneous agents, the set of state variables when you cannot aggregate, and whether a recursive equilibrium exists. Heterogeneity often complicates the analysis. Occasionally, the complexity can be avoided by clever modelling. We discuss some examples. Another issue discussed is the importance of the number of agents. There are models in which there are a really large number of agents and there are models in which there are only a limited number of different agents. We discuss when it is appropriate to restrict the number of different agents and when the results would be misleading. We also start with the numerical analysis by discussing an algorithm to solve models with heterogeneous agents when there is no aggregate uncertainty.
  • Topics:
    • Aggregation
    • Approximate aggregation
    • Cross-sectional distributions as state variables
    • Incomplete markets
    • Aiyagari model
    • Solving the Aiyagari model using iterative methods
    • Models with patient and impatient agents
    • The new-Keynesian model when the heterogeneity among its agents is not ignored
  • Applications & exercises: In the afternoon, you are asked to solve a simple model with a continuum of heterogeneous agents in which agents are hit by idiosyncratic shocks and agents have limited ability to ensure themselves against them. You are asked to investigate the relationship between uncertainty and aggregate savings and to understand that this relationship is quite different in general equilibrium than in partial equilibrium.

Tuesday - Solving and simulating models with rational heterogeneous agents

  • Overview: In the morning we teach you the most popular algorithm to solve models with heterogeneous agents, namely the Krusell-Smith algorith. Simulation plays a key role in sovling and analyzing models with heterogeneous agents. Since there are so many agents it may even be costly to just simulate the model using stochastic simulation (at least if you want to generate accurate series). We teach you a faster and more accurate way to simulate models with heterogeneous agents. You are also taught a simple alternative solution procedure, namely the Xpa algorithm that avoids the simulation step of the KS algorithm when solving the model. We will also show you that you can even implement this algorithm using Dynare (and a bit of extra programming).
  • Topics:
    • Krusell & Smith algorithm to solve models with heterogeneous agents and aggregate uncertainty
    • Xpa algorithm to solve models with heterogeneous agents and aggregate uncertainty
    • Solving models with heterogeneous agents and aggregate uncertainty with Dynare (and a bit of additional Matlab programming)
    • Solving the Aiyagari model (equilibrium interest rate and distribution) in one step
  • Applications & exercises: In the afternoon you will solve a simple equilibrium model with rational heterogenous agents. We will investigate how the aggregate series in the model with heterogeneous agents compare to those generated by corresponding models with a representative agent.

Wednesday - Learning

  • Overview: The assumption that agents are rational is an interesting benchmark, but for sure will not be appropriate in many applications. Models where agents (try to) learn the structure of the economy or at least learn some key laws of motion as time goes by are a sensible alternative. Within the class of bounded-rationality models, models with learning are probably the least ad hoc. Replacing rational expectations with a learning algorithm can do a lot more than dampen or magnify fluctuations a bit. In particular, whether an equilibrium is stable or not can crucially depend on how agents form expectations.
  • Topics:
    • Bayesian learning
    • Least-squares learning
    • Learning and the parameterized expectations algorithm
    • Learning and asset pricing (Adams-Marcet)
    • Expectational stability (E-stability)
    • Multiple equilibria
    • Learning of exogenous and endogenous variables.
  • Applications & exercises: TBA

Thursday - Bounded rationality and heterogeneous beliefs in DSGE models

  • Overview: Models often assume that agents are rational because it is a convenient way to let agents be forward looking. The ability of agents to be forward looking (i.e., think through how current events will affect the future) is essential to understand well how fiscal and monetary policy affects the economy. We discuss some alternatives to rational expectations that allow agents to use economic insights when making predictions about the future. Next, we discuss two popular ways to model the behavior of agents when agents are passive and follow simple rules, namely some agent-based models and the Bernoulli infection model. The interesting aspect of these models is that they can generate interesting dynamics even if the rules followed are simple but heterogeneous. The disadvantage of these models is that all agents are quite dumb. It is a strong assumption that everybody is always rational, but it seems equally strong to assume that nobody in the economy is (roughly) as smart as the academics who make models. We will show how to solve models in which a fraction of the agents is boundedly rational (or just kind of dumb) and a fraction is truly rational. In contrast to what is done in the literature, our rational agents truly are rational and take into account the behavior other types of agents just as we (as model builders) do. We will show that the tools learned on Monday and Tuesday can be used to solve these models as well. As an application, we look at models in which some agents are overoptimistic (or overpessimistic) and we will investigate the question whether it is possible that the other agents in the economy will follow these irrational beliefs.
  • Topics:
    • Models with rule-of-thumb agents
    • Agent-based models
    • Bernouilli epidemiological model
    • Calculation costs
    • Finite horizon learning
    • Combining agent-based simulations with forward looking rational agents
    • Solving agent-based models with also some truly rational agents
  • Applications & exercises: TBA

Friday - Bounded rationality and heterogeneous beliefs in DSGE models continued

  • Overview: See the description of the Thursday lecture
  • Topics:
    • See the topics of the Thursday lecture
  • Applications & exercises: TBA