August 2020 | Working Paper

Making Decisions Under Model Misspecification

Simone Cerreia-Vioglioa, Lars Peter Hansen, Fabio Maccheronia, 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 simpli…fications, and hence, as misspeci…fied. We extend min-max 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 misspeci…fication concerns.

Series Name: Becker Friedman Institute Working Paper Series |Tags: Uncertainty|
July 2020 | Working Paper

Uncertainty and Decision-Making During a Crisis: How to Make Policy Decisions in the COVID-19 Context?

Loïc Berger, Nicolas Berger, Valentina Bosetti, Itzhak Gilboa, Lars Peter Hansen, Christopher Jarvis, Massimo Marinacci, Richard D. Smith


Policymaking during a pandemic can be extremely challenging. As COVID-19 is a new disease and its global impacts are unprecedented, decisions need to be made in a highly uncertain, complex and rapidly changing environment. In such a context, in which human lives and the economy are at stake, we argue that using ideas and constructs from modern decision theory, even informally, will make policymaking more a responsible and transparent process.

View Working Paper

Tags: Uncertainty, Uncertainty and Valuation|
May 2020 | Working Paper

Working Paper and Associated Code – “Robust Identification of Investor Beliefs”

Xiaohong Chen, Lars Peter Hansen and Peter G. Hansen

This paper develops a new method informed by data and models to recover information about investor beliefs. Our approach uses information embedded in forward-looking asset prices in conjunction with asset pricing models. We step back from presuming rational expectations and entertain potential belief distortions bounded by a statistical measure of discrepancy. Additionally, our method allows for the direct use of sparse survey evidence to make these bounds more informative. Within our framework, market-implied beliefs may differ from those implied by rational expectations due to behavioral/psychological biases of investors, ambiguity aversion, or omitted permanent components to valuation. Formally, we represent evidence about investor beliefs using a novel nonlinear expectation function deduced using model-implied moment conditions and bounds on statistical divergence. We illustrate our method with a prototypical example from macro-finance using asset market data to infer belief restrictions for macroeconomic growth rates.

Tags: Uncertainty|
March 2020 | Working Paper

Structured Uncertainty and Model Misspecification

Lars Peter Hansen and Thomas J. Sargent

An ambiguity averse decision maker evaluates plans under a restricted family of what we call structured models and unstructured alternatives that are statistically close to them. The structured models can include parametric models in which parameter values vary over time in ways that the decision maker cannot describe probabilistically. Because he suspects that all parametric models are misspecified, the decision maker also evaluates plans under alternative probability distributions with much less structure.

Tags: Risk, Robustness and Ambiguity, Uncertainty|Export BibTeX >

title={Structured Uncertainty and Model Misspecification},
author={Hansen, L. P. and Sargent, T. J.},
journal={SSRN Working Paper},

February 2020 | Article

New Published Paper and Python Code Posted – “Pricing Uncertainty Induced by Climate Change”

Michael Barnett, William Brock, and Lars Peter Hansen

Geophysicists examine and document the repercussions for the earth’s climate induced by alternative emission scenarios and model specifications. Using simplified approximations, they produce tractable characterizations of the associated uncertainty. Meanwhile, economists write simplified damage functions to assess uncertain feedbacks from climate change back to the economic opportunities for the macroeconomy. How can we assess both climate and emissions impacts, as well as uncertainty in the broadest sense, in social decision-making? We provide a framework for answering this question by embracing recent decision theory and tools from asset pricing, and we apply this structure with its interacting components in a revealing quantitative illustration.

Online Appendix 

Associated Results and Python Scripts – GitHub

Journal: The Review of Financial Studies |Volume: 33|Issue Number: 3|Pages: 1024-1066|Publisher: Oxford University Press|Tags: Climate, Risk, Robustness and Ambiguity, Uncertainty and Valuation|Export BibTeX >


Author = {Michael Barnett and William Brock and Lars Peter Hansen},

Date-Added = {2019-11-08 10:47:02 -0600},

Date-Modified = {2019-11-08 10:49:54 -0600},

Journal = {Review of Financial Studies},

Title = {Pricing Uncertainty Induced by Climate Change},

Year = {March 2020, The Review of Financial Studies}}

February 2020 | Working Paper

Newly Published Paper: “Twisted Probabilities, Uncertainty and Prices”

Lars Peter Hansen, Thomas J. Sargent, Balint Szoke and Lloyd S. Han

A decision maker constructs a convex set of nonnegative martingales to use as likeli-hood ratios that represent alternatives that are statistically close to a decision maker’s baseline model. The set is twisted to include some specific models of interest. Max-min expected utility over that set gives rise to equilibrium prices of model uncertainty expressed as worst-case distortions to drifts in a representative investor’s baseline model. Three quantitative illustrations start with baseline models having exogenous long-run risks in technology shocks. These put endogenous long-run risks into con-sumption dynamics that differ in details that depend on how shocks affect returns to capital stocks. We describe sets of alternatives to a baseline model that generate countercyclical prices of uncertainty.

Keywords— Risk, uncertainty, relative entropy, robustness, asset prices, exponential quadratic stochastic discount factor

JEL Classification— C52, C58, D81, D84, G12


Associated Paper Results and Code

Journal: Journal of Econometrics|Volume: 216|Issue Number: 1|Publisher: Elsevier|Tags: Financial Market Linkages to the Macroeconomy, Risk, Robustness and Ambiguity, Uncertainty and Valuation|Export BibTeX >
  title={Sets of Models and Prices of Uncertainty},
  author={Hansen, Lars P. and Sargent, Thomas J.},
  institution={National Bureau of Economic Research}
November 2019 | Working Paper

New Paper Revision 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: forthcoming in the Journal of Econometrics|Tags: Econometrics, Financial Market Linkages to the Macroeconomy, Uncertainty and Valuation|Export BibTeX >
  title={Prices of Macroeconomic Uncertainties with Tenuous Beliefs},
  author={Hansen, Lars Peter and Sargent, Thomas J},
October 2018

Wrestling with Uncertainty in Climate Economic Models

Lars Peter Hansen and William Brock

As we all know, the human and economic impact on the climate has been a topic that has recently received substantial attention.

While there is considerable evidence documenting impacts of climate change, a full understanding of the magnitude and the timing of this impact remains uncertain.  Moreover, we still seek to comprehend  better the economic consequences of climate change. The construction of quantitative models that connect economics and climate impacts currently confront uncertainty in simplistic ways.  They serve as valuable illustrations, but there is much to be done in terms of developing models that are fully fledged quantitative tools for policy assessment.

Our aim is to take inventory on some of the challenges for building better models, models that can provide a more rigorous defense for say measurements of the social cost of carbon while recognizing that there are limits to our understanding of climate economic linkages.  We will not provide precise answers but instead suggest a productive quantitative modeling agenda going forward.

This paper uses insights from decision theory under uncertainty to explore research challenges in climate economics. We embrace a broad perspective of uncertainty with three components: risk (probabilities assigned by a given model), ambiguity (level of confidence in alternative models), and misspecification (potential shortfalls in existing models). We survey recent climate science research that exposes the uncertainty in climate dynamics that is pertinent in economic analyses and relevant for using models to provide policy guidance. The uncertainty components and their implications for decision theory help us frame this evidence and expose the modeling and evidential challenges.

Title of book: forthcoming in Climate Change Economics: The Role of Uncertainty and Risk|Editor(s): V.V. Chari and Robert Litterman|Tags: Climate, Uncertainty|Export BibTeX >

title={Wrestling with Uncertainty in Climate Economic Models},
author={Brock, W.A. and Hansen, L. P.},
journal={SSRN Working Paper},

August 2018 | Article

Aversion to Ambiguity and Model Misspecification in Dynamic Stochastic Environments

Lars Peter Hansen and Jianjun Miao

In many dynamic economic settings, a decision maker finds it challenging to quantify the uncertainty or to assess the potential for mistakes in models. We explore alternative ways of acknowledging these challenges by drawing on insights from decision theory as conceptualized and implemented in statistics, engineering, and economics. Building on prior research, we suggest tractable and revealing ways to incorporate behavioral responses to uncertainty, broadly conceived. Our analysis adopts recursive intertemporal preferences for decision makers that allow them to be ambiguity averse and concerned about the potential misspecification of subjective uncertainty. By design, these representations have revealing implications for continuous-time environments with Brownian information structures.   Problems where uncertainty’s structure is obscure such as macroeconomics, finance and climate change are promising areas for application of these tools.


Supplemental Index

Journal: Proceedings of the National Academy of Sciences of the United States of America |Publisher: PNAS|Tags: Risk, Robustness and Ambiguity|Export BibTeX >

title={Aversion to Ambiguity and Model Misspecification in Dynamic Stochastic Environments},
author={Hansen, L. P. and Miao, J.},
journal={Proceedings of the National Academy of Sciences},
publisher={National Academy of Sciences}

December 2017

Time Series Econometrics in Macroeconomics and Finance

Lars Peter Hansen

Ninety years ago, Slutsky (1927) and Yule (1927) opened the door to the use of probability models in the analysis of economic time series. Their vision was to view economic time series as linear responses to current and past independent and identically distributed impulses or shocks. In distinct contributions, they showed how to generate approximate cycles with such models. Each had a unique background and perspective. Yule was an eminent statistician who, in the words of Stigler (1986), among his many contributions, managed effectively to invent modern time series analysis.” Yule constructed and estimated what we call a second-order model and applied it to study the time series behavior of sunspots. Slutsky wrote his paper in Russia in the 1920s motivated by the study of business cycles. Much later, his paper was published in Econometrica, but it was already on the radar screen of economists, such as Frisch. Indeed Frisch was keenly aware of both Slutsky (1927) and Yule (1927) and acknowledged both in his seminal paper Frisch (1933) on the impulse and propagation problem. Building on insights from Slutsky and Yule, Frisch pioneered the use of impulse response functions in economic dynamics. His ambition was to provide explicit economic interpretations for how current period shocks alter economic time series in current and future time periods. The Journal of Political Economy (JPE) provided an important platform for research that confronts Frisch’s ambition in substantively interesting ways. Read full paper here.

Journal: “The Past, Present, and Future of Economics: A Celebration of the 125 Year Anniversary of the JPE and of Chicago Economics,” Journal of Political Economy 125|Publisher: University of Chicago Press |Tags: Econometrics|Export BibTeX >

title={Time-Series Econometrics in Macroeconomics and Finance},
author={Hansen, L. P.},
journal={Journal of Political Economy},
publisher={University of Chicago Press Chicago, IL}