July 2014 | Article

Uncertainty Outside and Inside Economic Models (Nobel Lecture)

Lars Peter Hansen

“We must infer what the future situation would be without our interference, and what changes will be wrought by our actions. Fortunately, or unfortunately, none of these processes is infallible, or indeed ever accurate and complete.”  Knight (1921)

Journal: Journal of Political Economy|Volume: 122|Issue Number: 5|Pages: 945-987|Tags: Econometrics, Financial Market Linkages to the Macroeconomy, Risk, Robustness and Ambiguity, Uncertainty and Valuation|Export BibTeX >

Author = {Hansen, Lars},
Date-Added = {2016-03-28 00:37:47 +0000},
Date-Modified = {2016-03-28 00:40:13 +0000},
Journal = {Journal of Political Economy},
Number = {5},
Pages = {945 – 987},
Title = {Nobel Lecture: Uncertainty Outside and Inside Economic Models},
Url = {},
Volume = {122},
Year = {2014},
Bdsk-Url-1 = {}}

January 2013 | Chapter

Risk Pricing over Alternative Investment Horizons

Lars Peter Hansen

I explore methods that characterize model-based valuation of stochastically growing cash flows. Following previous research, I use stochastic discount factors as a convenient device to depict asset values. I extend that literature by focusing on the impact of compounding these discount factors over alternative investment horizons. In modeling cash flows, I also incorporate stochastic growth factors. I explore dynamic value decomposition (DVD) methods that capture concurrent compounding of a stochastic growth and discount factors in determining risk-adjusted values. These methods are supported by factorizations that extract martingale components of stochastic growth and discount factors. These components reveal which ingredients of a model have long-term implications for valuation. The resulting martingales imply convenient changes in measure that are distinct from those used in mathematical finance, and they provide the foundations for analyzing model-based implications for the term structure of risk prices. As an illustration of the methods, I re-examine some recent preference based models. I also use the martingale extraction to revisit the value implications of some benchmark models with market restrictions and heterogenous consumers.

Pages: 1571-1611|Title of book: Handbook of the Economics of Finance|Editor(s): George M Constantinides, Milton Harris, and René M Stulz|Place of Publication: Amsterdam|Publisher: North Holland|Tags: Uncertainty and Valuation|Export BibTeX >
  title={Risk Pricing Over Alternative Investment Horizons},
  author={Hansen, Lars Peter},
November 2012 | Chapter

Challenges in Identifying and Measuring Systemic Risk

Lars Peter Hansen

Sparked by the recent “great recession” and the role of financial markets, considerable interest exists among researchers within both the academic community and the public sector in modeling and measuring systemic risk. In this essay I draw on experiences with other measurement agendas to place in perspective the challenge of quantifying systemic risk, or more generally, of providing empirical constructs that can enhance our understanding of linkages between financial markets and the macroeconomy.

Title of book: Risk Topography: Systemic Risk and Macro Modeling|Editor(s): Markus Konrad Brunnermeier and Arvind Krishnamurthy|Place of Publication: Chicago|Publisher: University of Chicago Press|Tags: Financial Market Linkages to the Macroeconomy|Export BibTeX >
  title={Challenges in Identifying and Measuring Systemic Risk},
  author={Hansen, Lars Peter},
  institution={National Bureau of Economic Research}
October 2012 | Article

Proofs for Large Sample Properties of Generalized Method of Moments Estimators

Lars Peter Hansen

I present proofs for the consistency of generalized method of moments (GMM) estimators presented in Hansen (1982). Some basic approximation results provide the groundwork for the analysis of a class of such estimators. Using these results, I establish the large sample convergence of GMM estimators under alternative restrictions on the estimation problem.

Journal: Journal of Econometrics|Volume: 170|Issue Number: 2|Pages: 325-330|Tags: Econometrics|Export BibTeX >
  title={Proofs for Large Sample Properties of Generalized Method of Moments Estimators},
  author={Hansen, Lars Peter},
  journal={Journal of Econometrics},
October 2012 | Article


Manuel Arellano, Lars Peter Hansen, Enrique Sentana

We develop methods for testing that an econometric model is underidentified and for estimating the nature of the failed identification. We adopt a generalized-method-of moments perspective in a possibly non-linear econometric specification. If, after attempting to replicate the structural relation, we find substantial evidence against the overidentifying restrictions of an augmented model, this is evidence against underidentification of the original model. To diagnose how identification might fail, we study the estimation of a one-dimensional curve that gives the parameter configurations that provide the greatest challenge to identification, and we illustrate this calculation in an empirical example.

Journal: Journal of Econometrics|Volume: 170|Issue Number: 2|Pages: 256-280|Tags: Econometrics|Export BibTeX >



author={Arellano, Manuel and Hansen, Lars Peter and Sentana, Enrique},

journal={Journal of Econometrics},







July 2012 | Article

Three Types of Ambiguity

Lars Peter Hansen, Thomas J. Sargent

For each of three types of ambiguity, we compute a robust Ramsey plan and an associated worst-case probability model. Ex post, ambiguity of type I implies endogenously distorted homogeneous beliefs, while ambiguities of types II and III imply distorted heterogeneous beliefs. Martingales characterize alternative probability specifications and clarify distinctions among the three types of ambiguity. We use recursive formulations of Ramsey problems to impose local predictability of commitment multipliers directly. To reduce the dimension of the state in a recursive formulation, we transform the commitment multiplier to accommodate the heterogeneous beliefs that arise with ambiguity of types II and III. Our formulations facilitate comparisons of the consequences of these alternative types of ambiguity.

Journal: Journal of Monetary Economics|Volume: 59|Issue Number: 5|Pages: 422-445|Tags: Risk, Robustness and Ambiguity|Export BibTeX >
  title={Three Types of Ambiguity},
  author={Hansen, Lars Peter and Sargent, Thomas J.},
  journal={Journal of Monetary Economics},
July 2012 | Article

Recursive Utility in a Markov Environment with Stochastic Growth

Lars Peter Hansen, Jose A. Sheinkman

Recursive utility models that feature investor concerns about the intertemporal composition of risk are used extensively in applied research in macroeconomics and asset pricing. These models represent preferences as the solution to a nonlinear forward-looking difference equation with a terminal condition. In this paper we study infinite-horizon specifications of this difference equation in the context of a Markov environment. We establish a connection between the solution to this equation and to an arguably simpler Perron–Frobenius eigenvalue equation of the type that occurs in the study of large deviations for Markov processes. By exploiting this connection, we establish existence and uniqueness results. Moreover, we explore a substantive link between large deviation bounds for tail events for stochastic consumption growth and preferences induced by recursive utility.

Journal: Proceedings of the National Academy of Sciences|Volume: 109|Issue Number: 30|Pages: 11967-11972|Tags: Financial Market Linkages to the Macroeconomy, Uncertainty and Valuation|Export BibTeX >
  title={Recursive Utility in a Markov Environment With Stochastic Growth},
  author={Hansen, Lars Peter and Scheinkman, Jos{'e} A},
  journal={Proceedings of the National Academy of Sciences},
  publisher={National Acad Sciences}
May 2012 | Article

Dynamic Valuation Decomposition Within Stochastic Economies: Fisher–Schultz Lecture

Lars Peter Hansen

I explore the equilibrium value implications of economic models that incorporate responses to a stochastic environment with growth. I propose dynamic valuation decompositions (DVD’s) designed to distinguish components of an underlying economic model that influence values over long investment horizons from components that impact only the short run. A DVD represents the values of stochastically growing claims to consumption payoffs or cash flows using a stochastic discount process that both discounts the future and adjusts for risk. It is enabled by constructing operators indexed by the elapsed time between the trading date and the date of the future realization of the payoff. Thus formulated, methods from applied mathematics permit me to characterize valuation behavior and the term structure of risk prices in a revealing manner. I apply this approach to investigate how investor beliefs and the associated uncertainty are reflected in current-period values and risk-price elasticities.

Journal: Econometrica|Volume: 80|Issue Number: 3|Pages: 911-967|Tags: Uncertainty and Valuation|Export BibTeX >

  title={Dynamic Valuation Decomposition Within Stochastic Economies},
  author={Hansen, Lars Peter},
  publisher={Wiley Online Library}
April 2012 | Article

Small Noise Methods for Risk-Sensitive/Robust Economies

Evan W. Anderson, Lars Peter Hansen, Thomas J. Sargent

We provide small noise expansions for the value function and decision rule for the recursive risk-sensitive preferences specified by Hansen and Sargent (1995), Hansen et al. (1999), and Tallarini (2000). We use the expansions (1) to provide a fast method for approximating solutions of dynamic stochastic problems and (2) to quantify the effects on decisions of uncertainty and concerns about robustness to misspecification.

Journal: Journal of Economic Dynamics & Control|Volume: 36|Issue Number: 4|Pages: 468-500|Tags: Risk, Robustness and Ambiguity|Export BibTeX >
  title={Small Noise Methods for Risk-Sensitive/Robust economies},
  author={Anderson, Evan W. and Hansen, Lars Peter and Sargent, Thomas J.},
  journal={Journal of Economic Dynamics and Control},
January 2012 | Article

Pricing Growth-Rate Risk

Lars Peter Hansen, José A. Scheinkman

We characterize the compensation demanded by investors in equilibrium for incremental exposure to growth-rate risk. Given an underlying Markov diffusion that governs the state variables in the economy, the economic model implies a stochastic discount factor process S. We also consider a reference growth process G that may represent the growth in the payoff of a single asset or of the macroeconomy. Both S and G are modeled conveniently as multiplicative functionals of a multidimensional Brownian motion. We consider the pricing implications of parametrized family of growth processes G , with G0 = G, as is made small. This parametrization defines a direction of growth-rate risk exposure that is priced using the stochastic discount factor S. By changing the investment horizon, we trace a term structure of risk prices that shows how the valuation of risky cash flows depends on the investment horizon. Using methods of Hansen and Scheinkman (Econometrica 77:177–234, 2009), we characterize the limiting behavior of the risk prices as the investment horizon is made arbitrarily long.

Journal: Finance and Stochastics|Volume: 16|Issue Number: 1|Pages: 1-15|Tags: Uncertainty and Valuation|Export BibTeX >
  title={Pricing Growth-Rate Risk},
  author={Hansen, Lars Peter and Scheinkman, Jos{'e} A},
  journal={Finance and Stochastics},