Syllabus for mini-course on robust control and filtering in macroeconomics (to be given at the University of Texas at Austin, March 28-30, April 11-13 2001).

Instructor: Thomas J. Sargent (Hoover Institution and Stanford University)

The course will consist of four lectures. The main text will be `Elements of Robust Control and Filtering for Macroeconomics' by Lars Peter Hansen and myself. The lectures will teach people how to read the difficult parts of the text. The main messages will be what robust control in filtering are about, how they amount to a conservative modification of rational expectations, and how robust decision rules can be constructed easily by solving suitably modified Bellman equations. The Hansen-Sargent manuscript can be downloaded here: rgamesa.pdf The manuscript will be updated occasionally before Dec 1, 2000. The manuscript consists of these chapters:

• Chapter 1: Introduction
• Chapter 2: Basic ideas and methods
• Chapter 3: Elements of linear control theory
• Chapter 4: The Kalman filter
• Chapter 5: Time domain games
• Chapter 6: Frequency domain games
• Chapter 7: A permanent income model
• Chapter 8: A dual robust filtering problem
• Chapter 9: Single agent applications
• Chapter 10: Estimation and decision
• Chapter 11: Robustness in forward-looking models
• Chapter 12: Choosing theta: detection error probabilities
• Chapter 13: Robust taxation

A robust controller treats his model not as true but as a more or less good approximation. He seeks a decision rule that will work well enough over a set of models. One who constructs a robust filter treats his statistical model not as true but as an approximation. She seeks an estimator or filter that will work well across a set of models. Robust controllers and filters can be constructed by simple modifications of the usual Bellman or Riccati equations. The course will display this mostly in the context of linear quadratic models, though extensions to nonlinear models will also be described. We will spend substantial time on robustness in forward looking model. Matlab programs for many of the calculations will be supplied.

Matlab programs that will be mentioned in the class can be downloaded from matlab2 HST, HSW programs

General introductions to robustness in macroeconomics can be found in the following papers. The first two are `popular' while the second two are more advanced. The fourth paper describes non-linear robust control.

• Acknowledging Misspecification in Macroeconomic Theory (with Lars Peter Hansen, August 25, 2000) . The text of Sargent's Frisch lecture at the 2000 World Congress of the Econometric Society; also the basis for Sargent's plenary lecture at the Society for Economic Dynamics in Costa Rica, June 2000.  costa3.ps costa3.pdf
• Wanting Robustness in Macroeconomics (with Lars Peter Hansen, June 10, 2000) This paper is a `nontechnical' (according to Hansen) survey of an approach to building a preference for robust decision rules into macroeconomics.   wanting.ps wanting.pdf
• Robust Permanent Income and Pricing with Filtering, (with Lars Peter Hansen and Neng Wang, August 25, 2000) This paper reformulate Hansen, Sargent, and Tallarini's 1999 (RESTud) model by concealing elements of the state from the planner and the agents, forcing them to filter. The paper describes how jointly to do robust filtering and control, then computes the appropriate `market prices of Knightian uncertainty.' Detection error probabilities are used to discipline the one free parameter that robust decision making adds to the standard rational expectations paradigm. hsw2003.ps hsw2003.pdf
• Robustness, Detection, and the Price of Risk (March 27, 2000) 
  (with Evan Anderson and Lars Hansen) (Formerly known as `Risk and Robustness in Equilibrium ';) This paper describes a preference for robust decision rules in discrete time and continuous time models. The paper extends earlier work of Hansen, Sargent, and Tallarini in several ways. It permits non-linear-quadratic Gaussian set ups. It develops links between asset prices and preferences for robustness. It links premia in asset prices from Knightian uncertainty to detection error statistics for descriminating between models. [ Postscript file ] [ PDF file ]
  

• Robustness and Pricing with Uncertain Growth (January 2001) 
  (with Marco Cagetti, Lars Hansen, and Noah Williams) A continuous asset pricing model with robust filtering of a hidden Markov process. [ Postscript file ]