Hansen’s work aims to incorporate that uncertainty into economic models in tractable ways. “For example, suppose there is uncertainty about long-term macroeconomic growth. Agents—consumers or investors—have a model to predict growth, but they may also have suspicious or doubts about whether their model is right. They may have multiple models of this growth, but they don’t know how to weight the various models.
“We want to see what happens when agents start struggling with doubts about possible misspecification in their model,” Hansen said.
Drawing on insights from decision theory (including the work of famed former Chicago economists Frank Knight and Tjalling Koopmans), Hansen used formal models and simple games to understand responses to ambiguity.
He started with the recursive utility model of Koopmans, Kreps, and Porteus, to highlight how uncertainty about future events affects asset valuation. “Expectations about future growth rates influence risky claims to consumption,” he explained. “Consumption today reflects thoughts about consumption tomorrow. The forward-looking nature of the recursive utility model provides an additional channel through which sentiments about the future matter.”
To illustrate this, he gave a simple coin-flipping example, where a coin could be flipped every day in the future, with a high payoff for heads and a low payoff for tails. Alternatively, the coin could be flipped once and the result would determine payoffs in all future dates.
“With standard discounted expected utility, you are indifferent between the two options. With recursive utility, when you start thinking about joint distribution, you may prefer the first option. There’s an intertemporal component.”
Presenting the formal model for recursive utility, Hansen explained, “It puts on the table the intertemporal dimension of risk. Preferences become more sensitive to the intertemporal characterization of an uncertain future. It’s incredibly revealing and useful.”
To illustrate the idea of ambiguity aversion, Hansen described the Ellsberg Paradox, a well-studied game where agents choose between gambles based on drawing a given colored ball from one of two urns. Some people tend to avoid the urn where the chances of drawing the right color are less clear, violating expected utility principles by choosing the perceived “safer” bet over the more ambiguous one.
Hansen explained robustness (the topic of his recent book with Thomas J. Sargent), which deals with investors’ doubt over the accuracy of their model. Decision makers who are uncomfortable with ambiguity try to cover themselves by using a family of models. They start with a benchmark model, consider all the ways it might not be correct, and assess the consequences of the errors. He outlined a model where decision makers use exponential tilting toward bad outcomes to factor in caution when they are uncertain.
With useful models to understand how investors confront uncertainty about macroeconomy growth, we can reassess asset pricing puzzles. Using a model with learning and a concern for model misspecification to estimate the price of uncertainty, Hansen showed a historical pattern that echoes observations from finance: in bad economic times, the uncertainty premium goes up.
He concluded by noting fruitful areas for more work: on models with learning and continuous observation about conditions and models where investors have heterogeneous beliefs. “There’s a rich literature, questions are first order and fundamental, but there is still a lot of exciting work to be done.”
- “Beliefs, Doubts and Learning: Valuing Macroeconomic Risk” (Lars Peter Hansen)
- “Risk, Uncertainty, and Value” (Lars Peter Hansen and Thomas J. Sargent)
- “Probability and Uncertainty in Economic Modeling” (Itzhak Gilboa, Andrew W. Postlewaite, and David Schmeidler)
- “Challenges in Identifying and Measuring Systemic Risk” (A chapter on systemic risk by Hansen)