## Amid Great Uncertainty

Economist Lars Peter Hansen confronts—and quantifies—the unknowns of market behavior.

** **In 1898, Impressionist Camille Pissarro peered out his hotel window in Rouen, France, and discovered his newest subject. “I found an excellent place from which I can paint the Rue del’Épicerie and even the market, a really interesting one, which is held there every Friday,” he wrote to his son. Depicting an elaborate dance of bargaining and buying, hawking and haggling, his rendering has long been admired for its reflection of contemporary life.

Economist Lars Peter Hansen sees something else: uncertainty.

“When vendors come to that market, they don’t know how much demand there will be for their goods,” says Hansen, the David Rockefeller Distinguished Service Professor in Economics, Statistics & the College. “They can make guesses. They can use previous experiences. But they really don’t know exactly.”

Hansen has made a career of investigating the dynamics of not knowing—and creating powerful statistical tools that help estimate how decision-makers act amid uncertainty. Winner of the 2013 Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel for his work on asset pricing, he sums up his approach with one sentence: “You can do something without having to do everything.”

It’s a simple idea that’s transformed how economists model complex financial markets. “We think of financial markets as forward-looking,” Hansen says. “By their very nature, they encode peoples’ beliefs about the future,” as well as concerns about uncertainty. The economist crafts models that reflect both the impact of uncertainty faced by the people economists seek to model and by the economists and other analysts who use the models. Through this approach, economists can achieve a better understanding of how, for example, tax policy or economic and political upheaval will influence economic outcomes.

**Acknowledging Imperfection**

Doing so is no easy task. “The models we have are simplifications, and, thus, they’re imperfect,” says Hansen, whose interest in using mathematics to investigate larger social issues started during the Vietnam era when he was an undergraduate. Today he brings together economics, statistics, and mathematics to confront gaps in our understanding of the macroeconomy.

“While uncertainty is unavoidable and pervasive in our lives,” he says, “in many discussions of economic analysis and policy, it unfortunately takes a backseat. We should instead push uncertainty to the forefront of our thinking.”

A starting point is acknowledging the interplay between the actors inside an economic model and the economist on the outside. One of Hansen’s favorite lecture slides splices together Pissarro’s busy market, buyers and sellers full of uncertainty, with a portrait of famed 17th-century Swiss statistician Jacob Bernoulli assessing the drama. “I like to think about Bernoulli looking in on this scene saying, ‘Here’s this model, but I need to use evidence to figure out unknown features of it.’”

It’s a complicated investigation of a market with many competing interests and visions of the future. As the late Frank Knight, one of Hansen’s University of Chicago economics predecessors, wrote in 1921: “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 or complete.”

That reality drives Hansen to design rigorous analytical frameworks that can help decision-makers navigate the uncertainties they face. His best known statistical methodology, the Generalized Method of Moments, incorporates uncertainty without requiring researchers to specify the economic environment fully or all of the information used by investors inside the economic model.

“Rather than dismiss imperfect models,” he says, “I prefer to use them in sensible ways.” But what does it mean to be sensible?

**Being Sensible, Quantifying Uncertainty**

Just how much uncertainty exists in any given scenario? And how can economists even begin to approximate it?

At its most basic level, uncertainty is a game of chance, a story of known probabilities. Think of a coin toss or an urn filled with colored balls, four red and four yellow. There’s risk on any given turn, because you don’t know which color you’ll draw, but at least you know your chances.

Now imagine that same urn filled with eight balls, but this time you don’t know how many of each color are inside. Uncertainty isn’t just about probabilities anymore; it’s about ambiguity. You don’t have the information you need to understand your chances. Be it a game or buying and selling on the market, how can you make predictions about outcomes when the probabilities are unknown?

“This is where Bernoulli steps in,” Hansen says. With his so-called law of large numbers, the statistician “pushed us from a situation where probabilities are known to a situation where you have to use evidence to figure out probabilities.” If you draw a ball at random from an urn with a large number of balls, for example, drawing over and over again, you can begin to figure out approximately which fraction are red and which are yellow. Once you gain a sense of these percentages, you can begin to make better guesses about the probability of the next color you draw.

“In many respects, that’s a very simplified statement of what motivates the field of statistics,” Hansen says. “You have these overall models of things, like the question of what’s happening inside the urn, but you don’t know probabilities.”

So what happens when probabilities aren’t just unknown, but also change over time, as in real-life financial systems? What if the number of balls in the urn fluctuates while you are drawing them? Here Bernoulli’s law of large numbers falls short because even if you have evidence from the past, the future can shift on you in unexpected ways.

“One way to think about a financial crisis is as something small magnifying into something big,” Hansen says. Indeed uncertainty, like interest rates, compounds over time. Whereas many past economic models had a linear character, there has been a growing focus on non-linear (more flexible) models. In these models, Hansen says, “little jiggles within the system today can have a big impact in the future.”

By quantifying the impact of uncertainty, Hansen aims to make it a more accepted part of modeling and policymaking, particularly in areas like climate science where problems are urgent, but unknowns abound. “There’s often a big bias in public perception that if you acknowledge uncertainty to your answers, then people take you less seriously,” he says. That, he stresses, creates the danger that people who have unwarranted confidence will become the most influential policy advisors.

His advice? “Instead of pretending like you can have some omniscient view of what might happen in the future, don’t be afraid to acknowledge the uncertainty. It’s a little more complicated of a calculation, but more circumspect because it doesn’t pretend to know what will happen and this can lead to smarter decisions.”

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*–Brooke O’Neill*