July 2017

Wrestling with Uncertainty in Climate Economic Models

Lars Peter Hansen and William Brock

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.

Journal: SSRN working paper |
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|
May 2017 | Working Paper

Prices of Macroeconomic Uncertainties with Tenuous Beliefs

Lars Peter Hansen and Thomas J. Sargent

A decision maker expresses ambiguity about statistical models in the following ways. He has a family of structured parametric probability models but suspects that their parameters vary over time in unknown ways that he does not describe probabilis- tically. He expresses a further suspicion that all of these parametric models are misspecified by entertaining alternative unstructured probability distributions that he represents only as positive martingales and that he restricts to be statistically close to the structured parametric models. Because he is averse to ambiguity, he uses a max-min criterion to evaluate alternative plans. We characterize equilibrium uncertainty prices by confronting a decision maker with a portfolio choice problem. We offer a quantitative illustration for structured parametric models that focus uncertainty on macroeconomic growth and its persistence. There emerge nonlinearities in marginal valuations that induce time variation in market prices uncertainty. Prices of uncertainty fluctuate because the investor especially fears high persistence in bad states and low persistence in good ones.

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},
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 >

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 >
  title={Term Structure of Uncertainty in the Macroeconomy},
  author={Borovi{v{c}}ka, Jaroslav and Hansen, Lars Peter},
  journal={Handbook of Macroeconomics},
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 >
  title={Misspecified Recovery},
  author={Borovi{v{c}}ka, Jaroslav and Hansen, Lars Peter and Scheinkman, Jos{'e} A},
  journal={The Journal of Finance},
  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 >
  title={Sets of Models and Prices of Uncertainty},
  author={Hansen, Lars P. and Sargent, Thomas J.},
  institution={National Bureau of Economic Research}
January 2015 | Article

Four Types of Ignorance

Lars Peter Hansen, Thomas J. Sargent

This paper studies alternative ways of representing uncertainty about a law of motion in a version of a classic macroeconomic targetting problem of Milton Friedman (1953). We study both “unstructured uncertainty” – ignorance of the conditional distribution of the target next period as a function of states and controls – and more “structured uncertainty” – ignorance of the probability distribution of a response coefficient in an otherwise fully trusted specification of the conditional distribution of next period׳s target. We study whether and how different uncertainties affect Friedman׳s advice to be cautious in using a quantitative model to fine tune macroeconomic outcomes.

Journal: Journal of Monetary Economics|Volume: 69|Issue Number: January|Pages: 97-113|Tags: Risk, Robustness and Ambiguity|Export BibTeX >
  title={Four Types of Ignorance},
  author={Hansen, Lars Peter and Sargent, Thomas J.},
  journal={Journal of Monetary Economics},
November 2014 | Article

Examining Macroeconomic Models Through the Lens of Asset Pricing

Jaroslav Borovička, Lars Peter Hansen

Dynamic stochastic equilibrium models of the macro economy are designed to match the macro time series including impulse response functions. Since these models aim to be structural, they also have implications for asset pricing. To assess these implications, we explore asset pricing counterparts to impulse response functions. We use the resulting dynamic value decomposition (DVD) methods to quantify the exposures of macroeconomic cash flows to shocks over alternative investment horizons and the corresponding prices or compensations that investors must receive because of the exposure to such shocks. We build on the continuous-time methods developed in Hansen and Scheinkman (2010), Borovicka et al. (2011) and Hansen (2011) by constructing discrete-time shock elasticities that measure the sensitivity of cash flows and their prices to economic shocks including economic shocks featured in the empirical macroeconomics literature. By design, our methods are applicable to economic models that are nonlinear, including models with stochastic volatility. We illustrate our methods by analyzing the asset pricing model of Ai et al. (2010) with tangible and intangible capital.

Journal: Journal of Econometrics|Volume: 183|Issue Number: 1|Pages: 67-90|Tags: Financial Market Linkages to the Macroeconomy, Uncertainty and Valuation|Export BibTeX >
  title={Examining Macroeconomic Models Through the Lens of Asset Pricing},
  author={Borovi{v{c}}ka, Jaroslav and Hansen, Lars Peter},
  journal={Journal of Econometrics},
September 2014 | Article

Shock Elasticities and Impulse Responses

Jaroslav Borovička, Lars Peter Hansen, Jose A. Scheinkman

We construct shock elasticities that are pricing counterparts to impulse response functions. Recall that impulse response functions measure the importance of next-period shocks for future values of a time series. Shock elasticities measure the contributions to the price and to the expected future cash flow from changes in the exposure to a shock in the next period. They are elasticities because their measurements compute proportionate changes. We show a particularly close link between these objects in environments with Brownian information structures.

Journal: Mathematics and Financial Economics|Volume: 8|Issue Number: 4|Pages: 333-354|Tags: Financial Market Linkages to the Macroeconomy, Uncertainty and Valuation|Export BibTeX >
  title={Shock Elasticities and Impulse responses},
  author={Borovi{v{c}}ka, Jaroslav and Hansen, Lars Peter and Scheinkman, Jos{'e} A},
  journal={Mathematics and Financial Economics},