Papers

October 2018 | 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|
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|
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|
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|
December 2017 | Working Paper

The Price of Macroeconomic Uncertainty with Tenuous Beliefs

Lars Peter Hansen and Thomas J. Sargent

A dynamic extension of max-min preferences allows a decision maker to consider both a parametric family of what we call structured models and unstructured alternatives that are statistically close to them. The decision maker suspects that parameter values vary over time in unknown ways that he cannot describe probabilistically. Because he suspects that all of these parametric models are misspecifi ed, he evaluates decisions under alternative probability distributions with much less structure. We characterize equilibrium uncertainty prices by confronting a representative investor with a portfolio choice problem. We offer a quantitative illustration that focuses on the investor’s uncertainty about the size and persistence of macroeconomic growth rates. Nonlinearities in marginal valuations induce time variations in market prices of uncertainty. Prices of uncertainty fluctuate because a representative investor especially fears high persistence in bad states and low persistence in good ones.

 

For the Non-Expert:

The Price of Macroeconomic Uncertainty with Tenuous Beliefs

Tags: Econometrics, Financial Market Linkages to the Macroeconomy, Uncertainty and Valuation|Export BibTeX >
@article{hansen:2016,
  title={Prices of Macroeconomic Uncertainties with Tenuous Beliefs},
  author={Hansen, Lars Peter and Sargent, Thomas J},
  year={2016}
}
June 2017

Uncertainty in Economic Analysis and the Economic Analysis of Uncertainty

Lars Peter Hansen

This essay was written for the inaugural issue of a journal Called KNOW, published in conjunction with the Stevanovich Institute for the Formation of Knowledge. I explore why addressing uncertainty in our knowledge is especially important in economic analyses when we seek a better understanding of markets, economic outcomes, and the impact of alternative policies. I also provide some historical context to the formalization of the alternative components to uncertainty and their impact in economic analyses. It has been important in economic scholarship to take inventory, not only of what we know, but also of the gaps in this knowledge. Thus, part of economic research assesses what we know about what we do not know and how we confront what we do not know. Not only does uncertainty matter for how economic researchers interpret and use evidence, but also for how consumers and enterprises we incorporate in models confront the future.

Journal: KNOW |Volume: 1|Issue Number: 1|Publisher: University of Chicago Press |Tags: Uncertainty and Valuation|
March 2017

Stochastic Compounding and Uncertain Valuation

Lars Peter Hansen and Jose A. Scheinkman

Exploring long-term implications of valuation leads us to recover and use a distorted probability measure that reflects the long-term implications for risk pricing. This measure is typically distinct from the physical and the risk neutral measures that are well known in mathematical finance. We apply a generalized version of Perron-Frobenius theory to construct this probability measure and present several applications. We employ Perron-Frobenius methods to i) explore the observational implications of risk adjustments and investor beliefs as reflected in asset market data; ii) catalog alternative forms of misspecification of parametric valuation models; and iii) characterize how long-term components of growth-rate risk impact investor preferences implied by Kreps-Porteus style utility recursions.

Pages: 21-50|Title of book: After the Flood: How the Great Recession Changed Economic Thought |Publisher: The University of Chicago Press |Tags: Uncertainty and Valuation|Export BibTeX >

@incollection{hansenscheinkman:2017,
Author = {Hansen, Lars Peter and Scheinkman, Jose},
Booktitle = {After The Flood},
Pages = {21-50},
Publisher = {The University of Chicago Press},
Title = {Stochastic Compounding and Uncertain Valuation},
Year = {2017}}

January 2017 | Chapter

Term Structure of Uncertainty in the Macroeconomy

Lars Peter Hansen, Jaroslav Borovička

Dynamic economic models make predictions about impulse responses that characterize how macroeconomic processes respond to alternative shocks over different horizons. From the perspective of asset pricing, impulse responses quantify the exposure of macroeconomic processes and other cash flows to macroeconomic shocks. Financial markets provide compensations to investors who are exposed to these shocks. Adopting an asset pricing vantage point, we describe and apply methods for computing exposures to macroeconomic shocks and the implied compensations represented as elasticities over alternative payoff horizons. The outcome is a term structure of macroeconomic uncertainty.

 

You can find a verbal description of this research here.

Volume: 2B, Chapter 20|Pages: 1641-1694|Title of book: Handbook of Macroeconomics|Editor(s): John B. Taylor, Harald Uhlig|Place of Publication: Netherlands and Great Britain|Publisher: Elsevier|Tags: Financial Market Linkages to the Macroeconomy, Uncertainty and Valuation|Export BibTeX >
@article{borovivckahansen:2016,
  title={Term Structure of Uncertainty in the Macroeconomy},
  author={Borovi{v{c}}ka, Jaroslav and Hansen, Lars Peter},
  journal={Handbook of Macroeconomics},
  volume={2},
  pages={1641--1696},
  year={2016},
  publisher={Elsevier}
}
March 2016 | Article

Misspecified Recovery

Jaroslav Borovička, Lars Peter Hansen, José A. Scheinkman

Asset prices contain information about the probability distribution of future states and the stochastic discounting of those states as used by investors. To better understand the challenge in distinguishing investors’ beliefs from risk‐adjusted discounting, we use Perron–Frobenius Theory to isolate a positive martingale component of the stochastic discount factor process. This component recovers a probability measure that absorbs long‐term risk adjustments. When the martingale is not degenerate, surmising that this recovered probability captures investors’ beliefs distorts inference about risk‐return tradeoffs. Stochastic discount factors in many structural models of asset prices have empirically relevant martingale components.

Journal: Journal of Finance|Tags: Econometrics, Uncertainty and Valuation|Export BibTeX >
@article{bhs:2016misspecified,
  title={Misspecified Recovery},
  author={Borovi{v{c}}ka, Jaroslav and Hansen, Lars Peter and Scheinkman, Jos{'e} A},
  journal={The Journal of Finance},
  year={2016},
  publisher={Wiley Online Library}
}
December 2015 | Working Paper

Sets of Models and Prices of Uncertainty

Lars Peter Hansen and Thomas J. Sargent

A decision maker constructs a convex set of nonnegative martingales to use as likelihood ratios that represent parametric alternatives to a baseline model and also nonparametric models statistically close to both the baseline model and the parametric alternatives. 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. We offer quantitative illustrations for baseline models of consumption dynamics that display long-run risk. We describe a set of parametric alternatives that generates countercyclical prices of uncertainty.
NBER Working Paper No. 22000

Tags: Financial Market Linkages to the Macroeconomy, Risk, Robustness and Ambiguity, Uncertainty and Valuation|Export BibTeX >
@techreport{hansensargent:2016sets,
  title={Sets of Models and Prices of Uncertainty},
  author={Hansen, Lars P. and Sargent, Thomas J.},
  year={2016},
  institution={National Bureau of Economic Research}
}