Aversion to Ambiguity and Model Misspecification in Dynamic Stochastic Environments
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.
@article{hansen:2018aversion,
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},
volume={115},
number={37},
pages={9163–9168},
year={2018},
publisher={National Academy of Sciences}
}
Time Series Econometrics in Macroeconomics and Finance
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.
@article{hansen:2017time,
title={Time-Series Econometrics in Macroeconomics and Finance},
author={Hansen, L. P.},
journal={Journal of Political Economy},
volume={125},
number={6},
pages={1774–1782},
year={2017},
publisher={University of Chicago Press Chicago, IL}
}
Uncertainty in Economic Analysis and the Economic Analysis of Uncertainty
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.
@article{hansen:2017uncertainty,
title={Uncertainty in Economic Analysis and the Economic Analysis of Uncertainty},
author={Hansen, L. P.},
journal={KNOW: A Journal on the Formation of Knowledge},
volume={1},
number={1},
pages={171–197},
year={2017},
publisher={University of Chicago Press}
}
Stochastic Compounding and Uncertain Valuation
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.
@incollection{hansenscheinkman:2017,
Author = {Hansen, Lars Peter and Scheinkman, Jose},
Booktitle = {After The Flood: How the Great Recession Changed Economic Thought},
Pages = {21-50},
Publisher = {The University of Chicago Press},
Title = {Stochastic Compounding and Uncertain Valuation},
Year = {2017}}
Ambiguity Aversion and Model Misspecification: An Economic Perspective
How to accommodate potential model misspecification is a challenging topic. On the one hand, if we have very precise information about the nature of the misspecification, then presumably we would fix or repair the model. On the other hand, if we allow for too large of a set of possible ways for a model to be misspecified, we may find that little can be said of value in confronting the decision problem. The interplay between tractability and conceptual appeal is a central consideration when producing tools that aid in statistical decision making. Our comment will describe other important advances in decision theory within the economics discipline that are designed to confront uncertainty conceived broadly to include an aversion to ambiguity and a concern about model misspecification. We will also delineate some special challenges for applications in the social sciences.
@article{hansenmarinacci:2016,
title={Ambiguity Aversion and Model Misspecification: An Economic Perspective},
author={Hansen, Lars Peter and Marinacci, Massimo},
journal={Statistical Science},
year={2016}
}
✕ Term Structure of Uncertainty in the Macroeconomy
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.
@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}
}
✕ Misspecified Recovery
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.
@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}
}
✕ Four Types of Ignorance
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.
@article{hansensargent:2015,
title={Four Types of Ignorance},
author={Hansen, Lars Peter and Sargent, Thomas J.},
journal={Journal of Monetary Economics},
volume={69},
pages={97--113},
year={2015},
publisher={Elsevier}
}
✕ Examining Macroeconomic Models Through the Lens of Asset Pricing
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.
@article{borovivckahansen:2014,
title={Examining Macroeconomic Models Through the Lens of Asset Pricing},
author={Borovi{v{c}}ka, Jaroslav and Hansen, Lars Peter},
journal={Journal of Econometrics},
volume={183},
number={1},
pages={67--90},
year={2014},
publisher={Elsevier}
}
✕ Shock Elasticities and Impulse Responses
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.
@article{bhs:2014,
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},
volume={8},
number={4},
pages={333--354},
year={2014},
publisher={Springer}
}
✕