July 2017

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.

Journal: SSRN working paper |Tags: Climate, Uncertainty|
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},
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}
October 2010 | Working Paper

Modeling and Measuring Systemic Risk

Markus Brunnermeier, Lars Peter Hansen, Anil Kachyap, Arvind Krishnamurthy, Andrew W. Lo

An important challenge worthy of NSF support is to quantify systemic financial risk. There are at least three major components to this challenge: modeling, measurement, and data accessibility. Progress on this challenge will require extending existing research in many directions and will require collaboration between economists, statisticians, decision theorists, sociologists, psychologists, and neuroscientists.

Tags: Financial Market Linkages to the Macroeconomy|Export BibTeX >
  title={Modeling and Measuring Systemic Risk},
  author={Brunnermeier, Markus K. and Hansen, Lars Peter and Kashyap, Anil K. and Krishnamurthy, Arvind and Lo, Andrew W},
November 2005 | Working Paper

Nonlinear Principal Components and Long-Run Implications of Multivariate Diffusions

Xiaohong Chen, Lars Peter Hansen, José A. Scheinkman

We investigate a method for extracting nonlinear principal components. These principal components maximize variation subject to smoothness and orthogonality constraints; but we allow for a general class of constraints and densities, including densities without compact support and even densities with algebraic tails. We provide primitive sufficient conditions for the existence of these principal components. We also characterize the limiting behavior of the associated eigenvalues, the objects used to quantify the incremental importance of the principal components. By exploiting the theory of continuous-time, reversible Markov processes, we give a different interpretation of the principal components and the smoothness constraints. When the diffusion matrix is used to enforce smoothness, the principal components maximize long-run variation relative to the overall variation subject to orthogonality constraints. Moreover, the principal components behave as scalar autoregressions with heteroskedastic innovations. Finally, we explore implications for a more general class of stationary, multivariate diffusion processes.

Journal: Annals of Statistics|Tags: Econometrics|Export BibTeX >
  title={Principal Components and the Long Run},
  author={Xiaohong Chen, Lars Peter Hansen, and José A. Scheinkman},
March 1998 | Working Paper

Risk and Robustness in Equilibrium

Evan W. Anderson, Lars Peter Hansen, Thomas J. Sargent
Tags: Risk, Robustness and Ambiguity|Export BibTeX >
  title={Risk and Robustness in General Equilibrium},
  author={Anderson, Evan W and Hansen, Lars Peter and Sargent, Thomas J},
  journal={Preprint University of Chicago},