August 2022 | Working Paper

New Working Paper: “Risk, Ambiguity, and Misspecification: Decision Theory, Robust Control, and Statistics”

Lars Peter Hansen and Thomas J. Sargent


We connect variational preferences with the likelihood functions and prior probabilities over parameters that are building blocks of statistics and econometrics. We use relative entropy and other statistical divergences as cost functions in the variational preferences of someone who is ambiguous in the sense of not having a unique prior over a discrete set or manifold of statistical models (i.e., likelihood functions) and who suspects that each statistical model is misspecified. We connect variational preferences to theories of robust control and statistical approximation.

Keywords— Variational preferences, statistical divergence, relative entropy, prior, likelihood, ambiguity, misspecification

Tags: Econometrics, Risk, Robustness and Ambiguity|
May 2022 | Article

Newly published research in the University of Chicago Press for the National Bureau of Economic Research: “Climate Change Uncertainty Spillover in the Macroeconomy”

Michael Barnett, William Brock, and Lars Peter Hansen


The design and conduct of climate change policy necessarily confronts uncertainty along multiple fronts. We explore the consequences of ambiguity over various sources and configurations of models that impact how economic opportunities could be damaged in the future. We appeal to decision theory under risk, model ambiguity and misspecification concerns to provide an economically motivated approach to uncertainty quantification. We show how this approach reduces the many facets of uncertainty into a low dimensional characterization that depends on the uncertainty aversion of a decision-maker or fictitious social planner. In our computations, we take inventory of three alternative channels of uncertainty and provide a novel way to assess them. These include i) carbon dynamics that capture how carbon emissions impact atmospheric carbon in future time periods; ii) temperature dynamics that depict how atmospheric carbon alters temperature in future time periods; iii) damage functions that quantify how temperature changes diminish economic opportunities. We appeal to geoscientific modeling to quantify the first two channels. We show how these uncertainty sources interact for a social planner looking to design a prudent approach to the social pricing of carbon emissions.

View on the NBER Macroeconomics Annual – The University of Chicago Press Journal Website 

Journal: The University of Chicago Press for the National Bureau of Economic Research|Volume: 36|Tags: Climate, Uncertainty|Export BibTeX >
  title={Climate Change Uncertainty Spillover in the Macroeconomy},
  author={Barnett, Michael and Brock, William and Hansen, Lars Peter},
  journal={Prepared for the 2021 Macoreconomics Annual},
May 2022 | Working Paper

Making Decisions Under Model Misspecification

Simone Cerreia-Vioglioa, Lars Peter Hansen, Fabio Maccheroni, and Massimo Marinacci

We use decision theory to confront uncertainty that is sufficiently broad to incorporate “models as approximations.” We presume the existence of a featured collection of what we call “structured models” that have explicit substantive motivations. The decision maker confronts uncertainty through the lens of these models, but also views these models as simplifications, and hence, as misspecified. We extend the max-min analysis under model ambiguity to incorporate the uncertainty induced by acknowledging that the models used in decision-making are simplified approximations. Formally, we provide an axiomatic rationale for a decision criterion that incorporates model misspecification concerns.

This research received the Best Paper Award at the 1st MUSEES Conference, as presented by my co-author, Fabio Maccheroni. 

Series Name: Becker Friedman Institute Working Paper Series |Tags: Uncertainty|Export BibTeX >
  title={Making decisions under model misspecification},
  author={Cerreia-Vioglio, Simone and Hansen, Lars Peter and Maccheroni, Fabio and Marinacci, Massimo},
  journal={University of Chicago, Becker Friedman Institute for Economics Working Paper},
March 2022 | Working Paper

New Working Paper: “Asset Pricing under Smooth Ambiguity in Continuous Time”

Lars Peter Hansen and Jianjun Miao


We study asset pricing implications of a revealing and tractable formulation of smooth ambiguity investor preferences in a continuous-time environment. Investors do not observe a hidden Markov state and instead make inferences about this state using past data. We show that ambiguity about this hidden state distribution alters investor decisions and equi-librium asset prices. Our continuous-time formulation allows us to apply recursive filtering and Hamilton-Jacobi-Bellman methods to solve the modified decision problem. Using such methods, we show how characterizations of portfolio allocations and local uncertainty-return trade-offs change when investors are ambiguity-averse.

Keywords— Risk, ambiguity, robustness, asset pricing, portfolio allocation, continuous time

Related: Read Research Reflection by Hansen – “Navigating Uncertainty” March 11, 2022

View on SSRN

Journal: forthcoming in the Journal of Economic Theory|Tags: Risk, Robustness and Ambiguity, Uncertainty|
January 2022 | Article

Newly published paper in the Journal of Monetary Economics: “Central Banking Challenges Posed by Uncertain Climate Change and Natural Disasters”

Lars Peter Hansen


Climate change poses an important policy challenge for governments around the world. The challenge is made all that much more difficult because of the multitude of potential policymakers involved in setting the policy worldwide. What then should be the role of central banks? How are climate change concerns similar to or distinct from those of other natural disasters? Clarity of ambition and execution will help to ensure that central banks maintain credibility. By adhering to their mandated roles, they retain their critically important distance from the political arena. Their credibility will be further enhanced by avoiding the temptation to exaggerate our understanding of climate change.

Journal: Journal of Monetary Economics|Volume: 125|Pages: 1-15|Tags: Climate, Uncertainty, Uncertainty and Valuation|Export BibTeX >
  title={Central Banking Challenges Posed by Uncertain Climate Change and Natural Disasters},
  author={Hansen, Lars Peter},
  journal={University of Chicago, Becker Friedman Institute for Economics Working Paper},
January 2022 | Article

Newly published research in the Journal of Economic Theory: “Structured Ambiguity and Model Misspecification”

Lars Peter Hansen and Thomas J. Sargent

A decision maker is averse to not knowing a prior over a set of restricted structured models (ambiguity) and suspects that each structured model is misspecified. The decision maker evaluates intertemporal plans under all of the structured models and, to recognize possible misspecifications, under unstructured alternatives that are statistically close to them. Likelihood ratio processes are used to represent unstructured alternative models, while relative entropy restricts a set of unstructured models. A set of structured models might be finite or indexed by a finite-dimensional vector of unknown parameters that could vary in unknown ways over time. We model such a decision maker with a dynamic version of variational preferences and revisit topics including dynamic consistency and admissibility.

Journal: Journal of Economic Theory|Volume: 199|Pages: 105-165|Tags: Risk, Robustness and Ambiguity, Uncertainty|Export BibTeX >
  title={Structured ambiguity and model misspecification},
  author={Hansen, Lars Peter and Sargent, Thomas J},
  journal={Journal of Economic Theory},
October 2021 | Working Paper

New working paper: “Robust Inference for Moment Condition Models without Rational Expectations”

Xiaohong Chen and Peter G. Hansen


Applied researchers using structural models under rational expectations (RE) often confront empirical evidence of misspecification. In this paper we consider a generic dynamic model that is posed as a vector of unconditional moment restrictions. We suppose that the model is globally misspecified under RE, and thus empirically flawed in a way that is not econometrically subtle. We relax the RE restriction by allowing subjective beliefs to differ from the data-generating probability (DGP) model while still maintaining that the moment conditions are satisfied under the subjective beliefs of economic agents. We use statistical measures of divergence relative to RE to bound the set of subjective probabilities. This form of misspecification alters econometric identification and inferences in a substantial way, leading us to construct robust confidence sets for various set identified functionals.

Tags: Bounded Rationality, Confidence Sets, Divergence, Lagrange Multipliers, Misspecification Sets, Nonlinear Expectations, Stochastic Dual Programming, Subjective Beliefs|
August 2021 | Article

Newly published paper in the Annual Review of Economics: “Uncertainty Spillovers for Markets and Policy”

Lars Peter Hansen


We live in a world surrounded by uncertainty. In this essay, I show that featuring this phenomenon more in economic analyses adds to our understanding of how financial markets work and how best to design prudent economic policy. This essay explores methods that allow for a broader conceptualization of uncertainty than is typical in economic investigations. These methods draw on insights from decision theory to engage in uncertainty quantification and sensitivity analysis. Uncertainty quantification in economics differs from most sciences because there is uncertainty both from the perspective of an external observer and from people and enterprises within the model. I illustrate these methods in two example economies in which the understanding of long-term growth is limited. One example looks at uncertainty ramifications for fluctuations in financial markets, and the other considers the prudent design of policy when the quantitative magnitude of climate change and its impact on economic opportunities is unknown.

View Paper in the Annual Review of Economics 

View Paper on SSRN

Journal: Annual Review of Economics|Tags: Uncertainty|Export BibTeX >
  title={Uncertainty Spillovers for Markets and Policy},
  author={Hansen, Lars Peter},
  journal={Annual Review of Economics},
  publisher={Annual Reviews}
July 2021 | Article

Published paper and Jupyter Notebook Available: “Macroeconomic Uncertainty Prices When Beliefs are Tenuous”

Lars Peter Hansen and Thomas J. Sargent

Investors face uncertainty over models when they do not know which member of a set of well-defined “structured models” is best. They face uncertainty about mod-els when they suspect that all of the structured models might be misspecified. We refer to worries about the first type of ignorance as ambiguity concerns and worries about the second type as misspecification concerns. These two types of ignorance about probability distributions of risks add what we call uncertainty components to equilibrium prices of those risks. A quantitative example highlights a representa-tive investor’s uncertainties about the size and persistence of macroeconomic growth rates. Our model of preferences under concerns about model ambiguity and misspec-ification puts nonlinearities into marginal valuations that induce time variations in market prices of uncertainty. These reflect the representative investor’s fears of high persistence of low growth rate states and low persistence of high growth rate states.

For the Non-Expert:

Vox EU: Acknowledging and pricing macroeconomic uncertainties by Lars Peter Hansen and Thomas J. Sargent

Journal: Journal of Econometrics|Volume: 223|Issue Number: 1|Pages: 222-250|Tags: Econometrics, Financial Market Linkages to the Macroeconomy, Uncertainty and Valuation|Export BibTeX >
  title={Macroeconomic uncertainty prices when beliefs are tenuous},
  author={Hansen, Lars Peter and Sargent, Thomas J},
  journal={Journal of Econometrics},
May 2021 | Preliminary Paper

New preliminary paper: “Confronting Uncertainty in the Climate Change Dynamics”

Michael Barnett, William Brock, and Lars Peter Hansen


In designing policy to combat climate change, there are many calls for immediate action. However, there has also been some apprehension expressed about acting prematurely based on existing limits to our understanding of the timing and the quantitative magnitude of climate change and its impact on economic and social outcomes. We approach this problem from the perspective of a decision maker who confronts uncertainty in a setting in which there will be future information about damage severity. The value of further empiricism in the near term will be limited as the climate-economic system moves into uncharted territory. The decision maker’s concerns about uncertainty go beyond the standard risk considerations. There is ambiguity over how much credibility to assign to alternative models of climate change and economic damages and all such models are potentially misspecified. These uncertainties add to the challenge of projecting how economic damages in the future will be enhanced with current and future fossil fuel emissions. The solution to the decision problem we pose shows some initial caution until future damage possibilities are more fully revealed. With the more refined information, the decision maker may be either more wary of climate change, or more bullish, and act accordingly depending on what is revealed. We provide a quantitative illustration drawing in part on cross-model ambiguity revealed by pulse experiments conducted by geoscientists.

Tags: Climate, Uncertainty|Export BibTeX >
  title={Confronting Uncertainty in the Climate Change Dynamics},
  author={Barnett, Mike and Brock, William and Hansen, Lars Peter},