October 2005

Robust Estimation and Control Under Commitment

Lars Peter Hansen, Thomas J. Sargent

In a Markov decision problem with hidden state variables, a decision maker expresses fear that his model is misspecified by surrounding it with a set of alternatives that are nearby as measured by their expected log likelihood ratios (entropies). Sets of martingales represent alternative models. Within a two-player zero-sum game under commitment, a minimizing player chooses a martingale at time 0. Probability distributions that solve distorted filtering problems serve as state variables, much like the posterior in problems without concerns about misspecification. We state conditions under which an equilibrium of the zero-sum game with commitment has a recursive representation that can be cast in terms of two risk-sensitivity operators. We apply our results to a linear quadratic example that makes contact with findings of T. Ba?ar and P. Bernhard [H?-Optimal Control and Related Minimax Design Problems, second ed., Birkhauser, Basel, 1995] and P. Whittle [Risk-sensitive Optimal Control, Wiley, New York, 1990].

Journal: Journal of Economic Theory|Volume: 124|Issue Number: 2|Pages: 258-301|Tags: Risk, Robustness and Ambiguity|Export BibTeX >
  title={Robust Estimation and Control Under Commitment},
  author={Hansen, Lars Peter and Sargent, Thomas J},
  journal={Journal of economic Theory},
January 2005 | Chapter

Intangible Risk?

Lars Peter Hansen, John Heaton, Nan Li
Pages: 111-152|Title of book: Measuring Capital in the New Economy|Editor(s): Carol Corrado, John C Haltiwanger, and Daniel E Sichel|Place of Publication: Chicago|Publisher: University of Chicago Press|Series Name: NBER Studies in Income and Wealth|Tags: Uncertainty and Valuation|Export BibTeX >
  title={Intangible Risk},
  author={Hansen, Lars Peter and Heaton, John C and Li, Nan},
  booktitle={Measuring Capital in the New Economy},
  publisher={University of Chicago Press}
April 2003 | Article

Robust Control of Forward Looking Models

Lars Peter Hansen and Thomas J. Sargent

This paper shows how to formulate and compute robust Ramsey (aka Stackelberg) plans for linear models with forward-looking private agents. The leaders and the followers share a common approximating model and both have preferences for robust decision rules because both doubt the model. Since their preferences differ, the leader’s and followers’ define a Stackelberg equilibrium with robust decision makers in which the leader and follower have different worst-case models despite sharing a common approximating model. To compute a Stackelberg equilibrium we formulate a Bellman equation that is associated with an artificial single-agent robust control problem. The artificial Bellman equation contains a description of implementability constraints that include Euler equations that describe the worst-case analysis of the followers. As an example, the paper analyzes a model of a monopoly facing a competitive fringe.

Journal: Monetary Economics|Volume: 50|Issue Number: 3|Pages: 581-604|Export BibTeX >
  title={Robust Control of Forward-Looking Models},
  author={Hansen, Lars Peter and Sargent, Thomas J.},
  journal={Journal of Monetary Economics},
March 2003

A Quartet of Semigroups for Model Specification, Robustness, Prices of Risk and Model Detection

Evan W. Anderson, Lars Peter Hansen, Thomas J. Sargent

A representative agent fears that his model, a continuous time Markov process with jump and diffusion components, is misspecified and therefore uses robust control theory to make decisions. Under the decision maker’s approximating model, cautious behavior puts adjustments for model misspecification into market prices for risk factors. We use a statistical theory of detection to quantify how much model misspecification the decision maker should fear, given his historical data record. A semigroup is a collection of objects connected by something like the law of iterated expectations. The law of iterated expectations defines the semigroup for a Markov process, while similar laws define other semigroups. Related semigroups describe (1) an approximating model; (2) a model misspecification adjustment to the continuation value in the decision maker’s Bellman equation; (3) asset prices; and (4) the behavior of the model detection statistics that we use to calibrate how much robustness the decision maker prefers. Semigroups 2, 3, and 4 establish a tight link between the market price of uncertainty and a bound on the error in statistically discriminating between an approximating and a worst case model.

Journal: Journal of the European Economic Association|Volume: 1|Issue Number: 1|Pages: 68-123|Tags: Risk, Robustness and Ambiguity, Uncertainty and Valuation|Export BibTeX >
  title={A quartet of Semigroups for Model Specification, Robustness, Prices of Risk, and Model Detection},
  author={Anderson, Evan W and Hansen, Lars Peter and Sargent, Thomas J},
  journal={Journal of the European Economic Association},
  publisher={Wiley Online Library}
May 2002 | Article

Robust Permanent Income and Pricing with Filtering

Lars Peter Hansen, Thomas J. Sargent, Neng E. Wang

A planner and agent in a permanent-income economy cannot observe part of the state, regard their model as an approximation, and value decision rules that are robust across a set of models. They use robust decision theory to choose allocations. Equilibrium prices reflect the preference for robustness and so embody a “market price of Knightian uncertainty.” We compute market prices of risk and compare them with a model that assumes that the state is fully observed. We use detection error probabilities to constrain a single parameter that governs the taste for robustness.

Journal: Macroeconomic Dynamics|Volume: 6|Pages: 40-84|Tags: Risk, Robustness and Ambiguity|Export BibTeX >


title={Robust Permanent Income and Pricing with Filtering},

author={Hansen, Lars Peter and Sargent, Thomas J. and Wang, Neng E},

journal={Macroeconomic Dynamics},





publisher={Cambridge Univ Press}


March 2002 | Article

Robustness and Pricing with Uncertain Growth

Marco Canetti, Lars Peter Hansen, Thomas J. Sargent, Noah Williams

We study how decision-makers’ concerns about robustness affect prices and quantities in a stochastic growth model. In the model economy, growth rates in technology are altered by infrequent large shocks and continuous small shocks. An investor observes movements in the technology level but cannot perfectly distinguish their sources. Instead the investor solves a signal extraction problem. We depart from most of the macroeconomics and finance literature by presuming that the investor treats the specification of technology evolution as an approximation. To promote a decision rule that is robust to model misspecification, an investor acts as if a malevolent player threatens to perturb the actual data-generating process relative to his approximating model. We study how a concern about robustness alters asset prices. We show that the dynamic evolution of the risk-return trade-off is dominated by movements in the growth-state probabilities and that the evolution of the dividend-price ratio is driven primarily by the capital-technology ratio.

Journal: Review of Financial Studies|Volume: 15|Issue Number: 2|Pages: 363-404|Tags: Risk, Robustness and Ambiguity|Export BibTeX >
  title={Robustness and Pricing With Uncertain Growth},
  author={Cagetti, Marco and Hansen, Lars Peter and Sargent, Thomas and Williams, Noah},
  journal={Review of Financial Studies},
  publisher={Soc Financial Studies}
December 2001 | Chapter

Generalized Method of Moments Estimation: A Time Series Perspective (published title “Method of Moments”)

Lars Peter Hansen

This entry describes empirical methods for estimating dynamic economic systems using time-series data. By design, the methods target specific feature of the dynamic system and do not require a complete specification of the time-series evolution. The resulting generalized-method-of-moments estimation and inference methods use estimating equations implied by some components of a dynamic economic system. This entry describes the statistical methods and some applications of these methods.

Title of book: International Encyclopedia of the Social and Behavioral Sciences|Editor(s): N. J. Smelser and P. B. Bates|Place of Publication: Amsterdam|Publisher: Elsevier|Tags: Econometrics|Export BibTeX >
  title={Generalized Method of Moments Estimation: A Time Series Perspective},
  author={Hansen, Lars Peter},
  journal={International Encyclopedia of Social and Behavioral Sciences},
May 2001 | Article

Robust Control and Model Uncertainty

Lars Peter Hansen, Thomas J. Sargent
Journal: American Economic Review|Volume: 91|Issue Number: 2|Pages: 60-66|Tags: Risk, Robustness and Ambiguity|Export BibTeX >

Author = {Hansen, Lars Peter and Sargent, Thomas J.},
Date-Added = {2014-12-29 19:53:18 +0000},
Date-Modified = {2014-12-29 19:53:18 +0000},
Journal = {The American Economic Review},
Month = {May},
Number = {2},
Pages = {60-66},
Title = {Robust Control and Model Uncertainty},
Volume = {91},
Year = {2001}}

February 2001 | Article

Acknowledging Misspecification in Macroeconomic Theory

Lars Peter Hansen and Thomas J. Sargent

We explore methods for confronting model misspecification in macroeconomics. We construct dynamic equilibria in which private agents and policy makers recognize that models are approximations. We explore two generalizations of rational expectations equilibria. In one of these equilibria, decision makers use dynamic evolution equations that are imperfect statistical approximations, and in the other misspecification is impossible to detect even from infinite samples of time-series data. In the first of these equilibria, decision rules are tailored to be robust to the allowable statistical dis- crepancies. Using frequency domain methods, we show that robust decision makers treat model misspecification like time-series econometricians.

Journal: Monetary and Economic Studies |Volume: Special Edition|Tags: Risk, Robustness and Ambiguity|Export BibTeX >
  title={Acknowledging Misspecification in Macroeconomic Theory},
  author={Hansen, Lars Peter and Sargent, Thomas J},
  journal={Review of Economic Dynamics},
May 2000 | Chapter

An Appreciation of A.W. Phillips

Lars Peter Hansen and Thomas J. Sargent

A way to honor A. W. Phillips is to describe the continuing influence of one of his enduring contributions to economic dynamics, his remarkable 1959 Biometrika paper about how discrete time observations can be used to restrict a continuous time linear model. That paper precisely described what later came to be known as the problem of `aggregation over time,’ set forth a framework for studying it, and achieved useful characterizations of it. Phillips’s 1959 paper partly shared the destiny of John F. Muth’s two 1960 and 1961 papers about rational expectations. It took years for other economists to recognize how much more could be done with their ideas. In 1960, both Phillips and Muth were far ahead of most other economists in their understanding of the technicalities of time series analysis, and their appreciation for its potential applications to economic dynamics.

Title of book: W.H. Phillips: Collected Works in Contemporary Perspective|Editor(s): Robert Leeson|Publisher: Cambridge|Export BibTeX >
  title={An Appreciation of AW Phillips},
  author={Hansen, Lars P and Sargent, Thomas J},