Forthcoming Paper in the Proceedings of the National Academy of Sciences (PNAS): “Robust Inattentive Discrete Choice”
When people make decisions they often have a large volume of information at their disposal. Faced with this challenge, in practice they focus their attention on a more limited amount of salient information. To assess what information should be exploited in decision-making, we extend a modeling approach that is called “rational inattention.” This approach assumes that the decision maker has a subjective prior that is used in determining how to direct attention across the vast set of information at the decision-maker’s disposal. The resulting solution can be highly sensitive, however, to the choice of the prior. We relax this assumption and allow the decision-maker to confront subjective uncertainty when taking discrete actions, thereby making the decisions more robust.
Abstract
Rational inattention models characterize optimal decision-making in data-rich environments. In such environments, it can be costly to look carefully at all of the information. Some information is much more salient for the decision at hand and merits closer scrutiny. The inattention decision model formalizes this choice and deduces how best to navigate through the potentially vast array of data when making decisions. In the rational formulation, the decision-maker commits fully to a subjective prior distribution over the possible states of the world that could be realized. We relax this assumption and look for a robustly optimal solution to the inattention problem by allowing the decision-maker to be ambiguity averse with respect to this prior. We feature a setup that is deliberately simple by a) assuming a discrete set of choices, b) using Shannon’s mutual information to quantify attention costs, and c) imposing relative entropy with respect to a baseline probability distribution to quantify prior divergence. We provide necessary and sufficient conditions for the robust solution and develop numerical methods to solve it. In comparison to the rational solution with no prior uncertainty, our decision-maker slants priors in more cautious or pessimistic directions when deducing how to allocate attention over the range of available information. This approach implements a form of robustness to prior misspecification, or equivalently, a form of ambiguity aversion. We explore some examples that show how the robust solution differs from the rational solution with a commitment to a subjective prior distribution and how it differs from imposing risk aversion.
Forthcoming in the Proceedings of the National Academy of Sciences (PNAS).
New Working Paper: “Uncertainty, Social Valuation, and Climate Change Policy”
Uncertainty, as it pertains to climate change and other policy challenges, operates through multiple channels. Such challenges are commonly framed using social valuations such as the social cost of climate change and the social value of research and development. These valuations have contributions that vary across horizons. We propose decompositions when the nature of this uncertainty is broadly conceived. By drawing on insights from decision theory, stochastic impulse response theory, and the pricing of uncertain cash flows, we provide novel characterizations. We use these methods to illustrate when and why uncertainty leads to more proactive policy approaches to climate change.
@article{barnett2024uncertainty,
title={Uncertainty, Social Valuation, and Climate Change},
author={Barnett, Michael L and Brock, William A and Zhang, Hong and Hansen, Lars Peter},
journal={University of Chicago, Becker Friedman Institute for Economics Working Paper},
number={2024-75},
year={2024}
}
✕ New Working Paper: “Making Decisions Under Model Misspecification”
We use decision theory to confront uncertainty that is sufficiently broad to incorporate “models as approximations.” We presume the existence of a featured collection of what we call “structured models” thathave explicit substantive motivations. The decision maker confronts uncertainty through the lens of these models, but also views these models as simplifications, and hence, as misspecified. We extend the max-min analysis under model ambiguity to incorporate the uncertainty induced by acknowledging that the models used in decision-making are simplified approximations. Formally, we provide an axiomatic rationale for a decisioncriterion that incorporates model misspecification concerns. We then extend our analysis beyond the max-min case allowing for a more general criterion that encompasses a Bayesian formulation.
JEL codes- C54, D81
This research received the Best Paper Award at the 1st MUSEES Conference, as presented by my co-author, Fabio Maccheroni.
@article{cerreia2020making,
title={Making decisions under model misspecification},
author={Cerreia-Vioglio, Simone and Hansen, Lars Peter and Maccheroni, Fabio and Marinacci, Massimo},
journal={University of Chicago, Becker Friedman Institute for Economics Working Paper},
number={2020-103},
year={2020}
}
✕ Newly Published in the Annual Review of Financial Economics: “Comparative Valuation Dynamics in Production Economies: Long-run Uncertainty, Heterogeneity, and Market Frictions”
Abstract:
We compare and contrast production economies exposed to long-run uncertainty with investors that have possibly different preferences and/or access to financial markets. We study the macroeconomic and asset-pricing properties of these models, identify common features and highlight areas where these models depart from each other. Our framework allows us to investigate more fully the impact of investor heterogeneity, capital heterogeneity, and fluctuations of the growth components to the capital evolution as they affect the dynamics of macroeconomic quantities and asset prices. In our comparisons, we employ an array of diagnostic tools to explore time variation and state-dependencies in nonlinear environments.
Published in the Annual Review of Financial Economics.
The Annual Review of Financial Economics is online at financial.annualreviews.org https://doi.org/10.1146/annurev-financial-082123-105652
JEL codes: C68, D45, D53, D81, G12
New Working Paper: “Carbon Prices and Forest Preservation Over Space and Time in the Brazilian Amazon”
Abstract:
Some portions of land in the Brazilian Amazon are forested, and other portions are used in agricultural activities, principally cattle-ranching. Deforestation emits carbon, and reforestation captures it. Both are consequential for the global climate. The social and private productivities for the alternative land uses vary across locations within the Amazon region. In this research, we build and analyze a spatial/dynamic model of socially efficient land allocation to establish a benchmark for ad-hoc policies. We incorporate the stochastic evolution of cattle prices into our analysis, and we explore the consequences of ambiguity in the location-specific productivities on the socially efficient policy. Finally, we assess the consequences of imposing alternative social costs of carbon emissions on the spatial/dynamic allocation of land use. Our results indicate that even modest transfers per ton of net CO2 would incentivize Brazil to choose policies that produce substantial capture of greenhouse gases in the next 30 years. Our analysis points to the management of tropical forests as an important contributor to climate change mitigation in the near future.
We thank Pengyu Chen, Bin Cheng, Patricio Hernandez, João Pedro Vieira, Daniel (Samuel) Zhao for their expert research assistance and to Joanna Harris and Diana Petrova for their helpful comments.
@article{assunccao2023carbon,
title={Carbon Prices and Forest Preservation Over Space and Time in the Brazilian Amazon},
author={Assun{\c{c}}{\~a}o, Juliano J and Hansen, Lars Peter and Munson, Todd and Scheinkman, Jos{\’e} A},
journal={Available at SSRN 4414217},
year={2023}
}
✕Newly published in the Journal of Econometrics: “Robust Inference for Moment Condition Models without Rational Expectations”
Abstract
Applied researchers using structural models under rational expectations (RE) often confront empirical evidence of misspecification. In this paper we consider a generic dynamic model that is posed as a vector of unconditional moment restrictions. We suppose that the model is globally misspecified under RE, and thus empirically flawed in a way that is not econometrically subtle. We relax the RE restriction by allowing subjective beliefs to differ from the data-generating probability (DGP) model while still maintaining that the moment conditions are satisfied under the subjective beliefs of economic agents. We use statistical measures of divergence relative to RE to bound the set of subjective probabilities. This form of misspecification alters econometric identification and inferences in a substantial way, leading us to construct robust confidence sets for various set identified functionals.
JEL Classification: C14, C15, C31, C33, G40
Keywords: Subjective beliefs, bounded rationality, misspecification sets, nonlinear expectation, divergence, Lagrange multipliers, stochastic dual programming, confidence sets
@article{chen2021robust,
title={Robust Inference for Moment Condition Models Without Rational Expectations},
author={Chen, Xiaohong and Hansen, Lars Peter and Hansen, Peter G.},
journal={Journal of Econometrics, forthcoming},
year={2021}
}
New Working Paper: “A Deep Learning Analysis of Climate Change, Innovation, and Uncertainty”
Abstract:
We study the implications of model uncertainty in a climate-economics framework with three types of capital: “dirty” capital that produces carbon emissions when used for production, “clean” capital that generates no emissions but is initially less productive than dirty capital, and knowledge capital that increases with R&D investment and leads to technological innovation in green sector productivity. To solve our high-dimensional, non-linear model framework we implement a neural-network-based global solution method. We show there are first-order impacts of model uncertainty on optimal decisions and social valuations in our integrated climate-economic-innovation framework. Accounting for interconnected uncertainty over climate dynamics, economic damages from climate change, and the arrival of a green technological change leads to substantial adjustments to investment in the different capital types in anticipation of technological change and the revelation of climate damage severity.
@article{barnett2023deep,
title={A Deep Learning Analysis of Climate Change, Innovation, and Uncertainty},
author={Barnett, Michael and Brock, William and Hansen, Lars Peter and Hu, Ruimeng and Huang, Joseph},
journal={arXiv preprint arXiv:2310.13200},
year={2023}
}
Newly published in the Journal of Applied Econometrics: “Risk, Ambiguity, and Misspecification: Decision Theory, Robust Control, and Statistics”
Abstract
What are “deep uncertainties,” and how should their presence influence prudent decisions? To address these questions, we bring ideas from robust control theory into statistical decision theory. Decision theory has its origins in axiomatic formulations by von Neumann and Morgenstern, Wald, and Savage. After Savage, decision theorists constructed axioms that formalize a notion of ambiguity aversion. Meanwhile, control theorists constructed decision rules that are robust to some model misspecifications. We reinterpret axiomatic foundations of decision theories to express ambiguity about a prior over a family of models along with concerns about misspecifications of the corresponding likelihood functions.
Keywords— deep uncertainty, ambiguity, misspecification, variational preferences, statistical divergence, relative entropy, prior, likelihood
JEL Codes— C10, C14, C18
@article{hansen2022risk,
title={Risk, Ambiguity, and Misspecification: Decision Theory, Robust Control, and Statistics},
author={Hansen, Lars Peter and Sargent, Thomas J.},
journal={University of Chicago, Becker Friedman Institute for Economics Working Paper},
number={2022-157},
year={2022}
}
Published paper in the Journal of Economic Theory: “Asset Pricing under Smooth Ambiguity in Continuous Time” with Jianjun Miao
Abstract
We study asset pricing implications of a revealing and tractable formulation of smooth ambiguity investor preferences in a continuous-time environment. Investors do not observe a hidden Markov state and instead make inferences about this state using past data. We show that ambiguity about this hidden state distribution alters investor decisions and equi-librium asset prices. Our continuous-time formulation allows us to apply recursive filtering and Hamilton-Jacobi-Bellman methods to solve the modified decision problem. Using such methods, we show how characterizations of portfolio allocations and local uncertainty-return trade-offs change when investors are ambiguity-averse.
Keywords— Risk, ambiguity, robustness, asset pricing, portfolio allocation, continuous time
Related: Read Research Reflection by Hansen – “Navigating Uncertainty” March 11, 2022
@article{hansen2022asset,
title={Asset Pricing Under Smooth Ambiguity in Continuous Time},
author={Hansen, Lars Peter and Miao, Jianjun},
journal={Economic Theory},
volume={74},
number={2},
pages={335--371},
year={2022},
publisher={Springer}
}
Published paper in the University of Chicago Press for the National Bureau of Economic Research: “Climate Change Uncertainty Spillover in the Macroeconomy”
Abstract
The design and conduct of climate change policy necessarily confronts uncertainty along multiple fronts. We explore the consequences of ambiguity over various sources and configurations of models that impact how economic opportunities could be damaged in the future. We appeal to decision theory under risk, model ambiguity and misspecification concerns to provide an economically motivated approach to uncertainty quantification. We show how this approach reduces the many facets of uncertainty into a low dimensional characterization that depends on the uncertainty aversion of a decision-maker or fictitious social planner. In our computations, we take inventory of three alternative channels of uncertainty and provide a novel way to assess them. These include i) carbon dynamics that capture how carbon emissions impact atmospheric carbon in future time periods; ii) temperature dynamics that depict how atmospheric carbon alters temperature in future time periods; iii) damage functions that quantify how temperature changes diminish economic opportunities. We appeal to geoscientific modeling to quantify the first two channels. We show how these uncertainty sources interact for a social planner looking to design a prudent approach to the social pricing of carbon emissions.
View on the NBER Macroeconomics Annual – The University of Chicago Press Journal Website
@article{barnett2021climate,
title={Climate Change Uncertainty Spillover in the Macroeconomy},
author={Barnett, Michael and Brock, William and Hansen, Lars Peter},
journal={Prepared for the 2021 Macoreconomics Annual},
year={2021}
}
✕