If you want to know the returns on a college education, you might look at earnings, comparing the average wages of those who attend college to those who don’t. The problem with this approach is that it doesn’t account for the complications of self-selection—kids with greater innate ability may be more likely to choose to attend college, for instance. How would you know if higher wages were due to college or ability?

“We would end up overestimating the actual effect of college because part of that difference in average wages is attributable to innate talent,” says Francesca Molinari, Economics/Statistics and Data Science. “Labor economists have long confronted the problem that once we realize there is selection in going to college, we have a situation where we can’t learn the returns to education based on this data.”

Enter Molinari’s specialty: econometrics. Econometrics is a field that studies how to use economic or social science data that is often limited in what it reveals. “Econometrics provides statistical methods to analyze data that comes from various aspects of an individual’s life,” Molinari says. “We try to come up with methods that anyone working with social science data can use, often to answer questions of economic interest.”

### Questioning Classical Methods

The field has historically worked with limited data by finding additional variables to round it out or by making assumptions. “We would combine the data with various assumptions about how individuals make decisions, for example, to obtain what is called point identification of the objects of interest,” Molinari says.

In the example of returns on college education, labor economists and econometricians would make assumptions about why people decide to go to college and write a model that incorporates them.

Molinari’s research area within econometrics—called partial identification analysis—proposes an alternative to the classical methods. “The partial identification approach to econometrics provides ways to estimate effects of interest—when the classical assumptions that are often made or the way in which we try to enrich data—are not warranted,” she says. “We might not have additional variables we can draw on, and sometimes the modeling assumptions we make are driven by convenience rather than economic theory. This strains the credibility of the results.”

The partial identification approach trades the strength of the conclusions that researchers can draw in favor of their credibility. For example, it acknowledges that it’s not possible to know exactly the returns on a college education, given only the wages of students and non-students. “Instead, we can represent the returns of a college degree in an interval (or range) of values, which are all consistent with the data we observe. Then, this interval may be very informative about the economic question of interest,” Molinari explains.

This approach also enables a more accurate analysis of any data in range form—a popular survey technique. For example, the University of Michigan’s Health and Retirement Study, a large longitudinal survey, asks baby boomers to report their wealth within a range. This encourages participation, because people had previously been reluctant to give details about their wealth.

“But then you have interval data and that becomes problematic,” says Molinari. “If you allow for every possible value in the interval, you won’t get a unique prediction for whatever relationship you’re trying to learn, the relationship between wealth and savings rate, for example. The partial identification approach says this: Let’s take all the possible values of wealth in an interval, learn the parameter or range associated with all of the possible values, and report that, because that’s the only thing that we can say for sure.”

“You want to put emphasis on what the data is really saying as opposed to some transformation of your original assumption, which could be true or not.”

Molinari fell in love with partial identification because of the beauty of the logic and the rigor. “It’s a real exercise in being rigorous about what comes from the data and what is your assumption,” she says. “You want to put emphasis on what the data is really saying as opposed to some transformation of your original assumption, which could be true or not. From the beginning, this was very appealing to me.”

### An Everyday Experience of Risk Preference

Molinari’s work in partial identification had been mostly theoretical, until a recent empirical project took an unexpected turn.

The empirical project had quotidian origins. When Molinari and her colleague and husband Levon Barseghyan, Economics, were hired at Cornell, they moved from Chicago, where they had been graduate students at Northwestern University. Heading to Ithaca, one of the many things they needed to do was purchase a car and insurance for the car. It was the first time Barseghyan and Molinari, both born and raised abroad—Armenia and Italy, respectively—had insured a car in the United States. The experience sparked a series of research questions for Barseghyan about how people make decisions in the face of risk, and the two eventually started working together to find answers.

“We’re constantly making choices where the outcome is uncertain because life is uncertain. This is why we care about risk preferences. They are also at the heart of economics,” Molinari says. “What is the mechanism that determines what people decide when there are uncertain outcomes? How can we model these choices and estimate the parameters behind these models?”

Molinari, Barseghyan, colleague Ted O’Donoghue, Economics, and Cornell alumnus Joshua C. Teitelbaum (Georgetown University) have been analyzing data from a very common real-life event: choosing a car insurance deductible from a menu of options. Molinari says we can think about this like choosing among lotteries, with some probability that we would have an accident (in other words, will have to pay the deductible) and some that we would not. Applied economists already have a model for how people make these kinds of decisions—called the Expected Utility Theory Model—but Molinari says it’s based on some problematic assumptions.

“The classical way to model this is to say that people choose the deductible option that maximizes their expected utility,” Molinari says, which is based on the actual chance that they will or will not have an accident. “But years and years of research in psychology and experimental economics shows that people tend to overweight small probabilities, in this case overweight their risk of an accident.”

Molinari and her collaborators showed how to estimate an alternative model, called the Non-Expected Utility Model, which incorporated these biases. “In that line of work, under commonly maintained assumptions, we showed that the model was point-identified,” she says.

However, as Molinari and her team, including graduate students Maura Coughlin and Matthew Thirkettle, continued to study the problem, they began questioning their own assumptions. “In our previous work, we were assuming that if you are offered five options, you consider all five. What we came to realize by looking at the data, reading the literature, and thinking on our own is that sometimes people don’t consider all of the options,” Molinari says. “Now, things become quite complicated, because there is nothing in the data that tells me what options people considered.”

The team has been able to write a model that accommodates the unobservable heterogeneity in consideration sets—differences in the set of options people consider, which the data doesn’t reveal. “It recognizes that you may actually look at a subset of the full set of options,” Molinari says. “And it turns out the problem is partially identified.”

What began as more classical, empirical research looped and tied to Molinari’s theoretical work in partial identification. “It’s an important extension of my research—not a small step,” she says. “I see this new paper as bringing all of my research life so far together. It has been a nice journey for me.”

While researchers need the complex math and modeling, Molinari says her work also points to some simple advice on insurance. “When insuring small or moderate losses, people tend to buy too much,” she says.