## Research Papers and Computer Programs

### Two monograph

·         Robust Control and Economic Model Uncertainty (with Lars Hansen) (December , 2003) This is a draft of a monograph on robust filtering and control. It adapts H_2, H_\infty, and entropy methods to handle discounted problems. Both single agent and multiple agent settings are studied.  There are new chapters about recursive equilibria in this version.   PDF file

·         Recursive Models of Dynamic Linear Economies (with Lars Hansen) (June, 2004) This is a monograph on linear quadratic stochastic dynamic equilibrium models, how to represent their equilibria and how to extract their econometric implications  mbook2

### Working papers

• Robust Control and Misspecification (with Lars Peter Hansen, Gauhar Turmuhambetova, and Noah Williams) (April 17, 2004).  This paper integrates a variety of results in robust control theory in the context of an approximating model that is a diffusion.  The paper is partly a response to some criticisms of Anderson, Hansen, and Sargent (see below) by Chen and Epstein. It formulates two robust control problems -- a multiplier problem from the literature on robust control and a constraint formulation that looks like Gilboa-Schmeidler's min-max expected utility theory. The paper studies the connection between the two problems, states an observational equivalence result for them, links both problems to risk sensitive' optimal control, and discusses time consistency of the preference orderings associated with the two robust control problems.  [triple34.pdf ]
• Lotteries for consumers versus lotteries for firms, with Lars Ljungqvist ,(October, 2003).   A discussion of a paper by Edward Prescott for the Yale Cowles commission conference volume on general equilibrium theory. Prescott emphasizes the similarities in lotteries that can be used to aggregate over nonconvexities for firms, on the one hand, and households, on the other.  We emphasize their differences.    [ pred4.pdf
• The Conquest of U.S. Inflation: Learning, Model Uncertainty, and Robustness, with Timothy Cogley,(November, 2003).   An adaptive Fed’s model is a mixture of three models. The Fed uses Bayesian methods to update estimates of three models of the Phillips curve: a Samuelson-Solow model, a Solow-Tobin model, and a Lucas model.  Each period, the central bank also updates the probability that it assigns to each of these three models, then determines its first-period decision by solving a Bayesian linear regulator problem’.  Although by the mid 1970s the U.S. data induce the Fed to assign very high probability to the Lucas model, the government refrains from adopting its low-inflation policy recommendation because that policy has very bad consequences under one of the other low (but not zero) probability models.  The statistical model is thus able to explain the puzzling delay in the Fed’s decision to deflate after learning the natural rate hypothesis.  [ inflat13.pdf]
• Bayesian Fan Charts for U.K. Inflation: Forecasting and Sources of Uncertainty in an Evolving Monetary System, with Timothy Cogley and Sergei Morozov (September, 2003).   We use Bayesian methods to estimate a VAR with drifting coefficients and volatilities then construct fan charts that we compare with those of the Bank of England’s MPC.  Our fan charts incorporate several sources of uncertainty, including a form of model uncertainty that is represented by drifting coefficients and volatilities.  [ fantom2.pdf]
• Reactions to the Berkeley Story (October, 2002).   This paper is my discussion of a paper at the 2002 Jackson Hole Conference by Christina and David Romer.   The Romers paper uses narrative evidence to support and extend an interpretation of post war Fed policy that has also been explored by Brad DeLong and others.  The basic story is that the Fed has a pretty good model in the 50s, forgot it under the influence of advocates of an exploitable Phillips curve in the late 60s, then came to its senses by accepting Friedman and Phelps’s version of the natural rate hypothesis in the 1970s.  The Romers extend the story by picking up Orphanides’s idea that the Fed misestimated potential GDP or the natural unemployment rate in the 1970s. The Romers story is that the Fed needed to accept the natural rate hypothesis (which it did by 1970 according to them) and also to have good estimates of the natural rate (which according to them it didn’t until the late 70s or early 80s).  The Romers story is about the Fed’s forgetting then relearning a good model.  My comment features my own narration of a controversial paper by Professors X and Y’.   [ romers3.pdf]
• European Unemployment and Turbulence Revisited in a Matching Model (with Lars Ljungqvist). (September, 2003).  This paper recalibrates a matching model of den Haan, Haefke, and Ramey and uses it to study how increased turbulence interacts with generous unemployment benefits to affect the equilibrium rate of unemployment.  In contrast to den Haan, Haefke, and Ramey, we find that increased turbulence causes unemployment to rise.  We trace the difference in outcomes to how we model the hazard of  losing skills after a voluntary job change.   [ dhhr8.pdf]
• Robust control and filtering of forward-looking models (with Lars Hansen). (November 19, 2002) This is a comprehensive revision of an earlier paper with the same title. We describe an equilibrium concept for models with multiple agents who, as under rational expectations share a common model, but all of whom doubt their model, unlike rational expectations.  Agents all fear model misspecification and perform their own worst-case analyses to construct robust decision rules.  Although the agents share the approximating models, their differing preferences cause their worst-case models to diverge.  We show how to compute Stackelberg (or Ramsey) plans where both leaders and followers fear model misspecification.   [ king6.pdf]

·   Knowing the Forecasts of Others’
(with Joseph G. Pearlman) , April 10, 2004.  This paper uses recursive methods to compute an equilibrium of the notorious model in section 8 of Townsend’s 1983 JPE paper Forecasting the Forecasts of Others’.  The equilibrium is of finite (and even low) dimension.  Market prices fully reveal traders’ private information, making the equilibrium equivalent with one in which traders pool their information before trading.  This means that the problem of forecasting the forecasts of others disappears in equilibrium.  There is no need to keep track of higher order beliefs.  [main paper (pdf)]

• Drifts and Volatilities:  Monetary Policies and Outcomes in the Post WWII U.S.
(with Tim Cogley) , August 26, 2002. This paper answers criticisms of our 2001 NBER Macro Annual paper made by Sims and Stock. We enrich our specification of a drifting coefficient VAR to allow stochastic volatility and study whether our earlier evidence for drifting coefficients survives this generalization. It does. We investigate the power of various tests that have been used to test time invariance of the autoregressive coefficients of VARs against alternatives like ours. All except one have low power. These results about power help reconcile our results with those of Sims and Bernanke and Mihov. We also study evidence that monetary policy rules have drifted.   [main paper (pdf)]
• Certainty equivalence’ and model uncertainty’
(with Lars Hansen) , July 2002. Prepared for an August 2002  conference in honor of Henri Theil. The paper reviews how the structure of the Simon-Theil certainty equivalence result extends to models that incorporate a preference for robustness to model uncertainty.  A model of precautionary savings is used an example.  [main paper (pdf)]
• A Quartet of Semi-Groups for Model Specification, Robustness, Prices of Risk, and Model Detection,
(withEvan Anderson and  Hansen) April 2003.  This paper supercedes Risk and Robustness in Equilibrium’, also on this web page. 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, that 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.
• The European Employment Experience  (with Lars Ljungqvist , Aug 13, 2002). A general equilibrium model of stochastically aging workers whose human capital depreciates during spells of unemployment and appreciates during spells of employment. There are layoff costs and government supplied unemployment compensation with a replacement ratio attached to past earnings, the product of human capital and a wage draw. The wage draw changes on the job via  Markov chain, inspiring some quits.  We use a common calibration of the model with “European” and “American” unemployment compensations to study the different unemployment experiences of Europe and the U.S. from the 1950s through 2000.    [pdf file ]
• European Unemployment: From a Worker's Perspective
(with Lars Ljungqvist) , Sept 17, 2001. Prepared for an October 2001 conference in honor of Edmund Phelps. Within the environment of our JPE 1998 paper on European unemployment, this paper conducts artificial natural experiments that provoke conversations'' with two workers who experience identical shocks but make different decisions because they live on opposite sides of the Atlantic Ocean.] [main paper (pdf)
• Optimal Taxation without State Contingent Debt
(with Rao Aiyagari, Albert Marcet and Juha Seppala) , Sept 29, 2001. An extensively revised version of a paper recasting Lucas and Stokey's analysis of optimal taxation in a market setting where the government can issue only risk free one-period government debt. This setting moves the optimal tax and debt policy substantially in the direction posited by Barro. The paper works out two examples by hand, another by the computer. [Postscript file ] [pdf file ]
• Time Inconsistency of Robust Control?
(with Lars Peter Hansen) , October 1, 2001. Responding to criticisms of Larry Epstein and his coauthors, this paper describes senses in which various representations of preferences from robust control are or are not time consistent. [Postscript file ] [pdf file ]
• Robust Control and Model Uncertainty (with Lars Peter Hansen) (January 22, 2001). Paper prepared for presentation at the meetings of the American EconomicAssociation in New Orleans, Jan 5, 2001. This paper is a summary of results presented in more detail in Hansen, Sargent, Turmuhambetova, and Williams (2001) -- see below. That paper formulates two robust control problems -- a multiplier problem from the literature on robust control and a constraint formulation that looks like Gilboa-Schmeidler's min-max expected utility theory. [Postscript file ] [pdf file ]
• Robust  Pricing with Uncertain Growth (with Marco Cagetti, Lars Peter Hansen, and Noah Williams) (January 2001). A continuous time asset pricing model with robust nonlinear filtering of a hidden Markov state. [pdf file ]
• Evolving Post-World War II U.S. Inflation Dynamics (with Timothy Cogley) (Final Version, June 2001) This paper uses Bayesian methods and post World War II data on inflation, unemployment, and an interest rate to estimate a drifting coefficients' model. The model is used to construct characterizations of the data that make contact with various points in Lucas's Critique and Sargent's The Conquest of American Inflation published by Princeton University Press. The paper constructs various measures of posterior means and variances of inflation and unemployment and studies their relationships. This paper will appear in the 2001 Macroeconomic Annual. [Postscript file ] [pdf file ]
• Escaping Nash Inflation (with In-Koo Cho and Noah Williams) (Very Revised, May 31, 2001) This paper analytically computes the escape route' for a special case of the model in my Marshall lectures The Conquest of American Inflation published by Princeton University Press. We show that theoretical computations of the mean dynamics and escape dynamics do a good job of explaining simulations like those in The Conquest of American Inflation. The paper uses the mysterious insight of Michael Harrison: If an unlikely event occurs, it is very likely to occur in the most likely way' . [Postscript file ] [pdf file ]
• Acknowledging Misspecification in Macroeconomic Theory (with Lars Peter Hansen, December 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
• Coment on Christopher Sims's Fiscal Consequences for Mexico of Adopting the Dollar' (June 13, 2000). A comment prepared for a conference on dollarization at the Federal Reserve Bank of Cleveland, June 1-3, 2000. sims10.ps sims10.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 ]
• 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
• Optimal Taxation without State Contingent Debt
(with Albert Marcet and Juha Seppala) , June 5, 2000. An extensively revised version of a paper recasting Lucas and Stokey's analysis of optimal taxation in a market setting where the government can issue only risk free one-period government debt. This setting moves the optimal tax and debt policy substantially in the direction posited by Barro. The paper works out two examples by hand, another by the computer. [Postscript file ]
• Laboratory Experiments with an Expectational Phillips Curve (with Jasmina Arifovic), August 22, 2001. Experiments with human subjects in a Kydland-Prescott Phillips curve economy. Postscript file PDF file
• Discussion of Can Market and Voting Institutions Generate Optimal Intergenerational Risk Sharing, by Antonio Rangel and Richard Zeckhauser (March 25, 1999). NBER Florida conference on social security. Postscript file
• Optimal Fiscal Policy in a Linear Stochastic Model (with Francois Velde) (April 29, 1998
[ Postscript file [ PDF file ]
• Policy Rules for Open Economies (January 1998)
(Discussion of Laurence Ball) Postscript file ]
• Projected U. S. Demographics and Social Security (November 1, 1998)
(with Mariacristina De Nardi and Selahattin Imrohoroglu [ Postscript file ]
• The Big Problem of Small Change (August 1998)
(with François Velde) [ PDF file ] [ Postscript file ]
• Accounting Properly for the Government's Interest Costs
(with George Hall) [ Postscript file ]
• Neural Networks for Encoding and Adapting in Dynamic Economics
(with In-Koo Cho) [ Postscript file ]
• Learning to be Credible  (with In-Koo Cho) [ Postscript file ]
• Robust Permanent Income and Pricing (April 30, 1999)
(with Lars Peter Hansen and Thomas Tallarini) [ Postscript file ]
• Robust Permanent Income and Pricing (April 1997)
(with Lars Peter Hansen and Thomas Tallarini) , old version with preference shock specification of model[ Postscript file ]
• Mechanics of Forming and Estimating Dynamic Linear Economies
(with Evan Anderson, Lars P. Hansen and Ellen McGrattan)[ Postscript file ]
• Two Computational Experiments to Fund Social Security
(with He Huang and Selo Imrohoroglu) Postscript file ]
• Coinage, Debasements, and Gresham's Laws
(with Bruce Smith) [ Postscript file ]
• The European Unemployment Dilemma, Revised May 1997
(with Lars Ljungqvist) Postscript file ]

• Alternative Monetary Policies in a Turnpike Economy
(with Rodolfo Manuelli)
• An Appreciation of A. W. Phillips
(with Lars Peter Hansen)
• Expectations and the Nonneutrality of Lucas
• Discounted Linear Exponential Quadratic Gaussian Control
(with Lars Peter Hansen) [ Postscript file ]