Faculty research continues to be an integral part of Department activity and is critical to our Departmental mission. For this year’s newsletter we asked Professor Jonathan Hill to share his research with our readers.
Mid-way through graduate school, I discovered a real-world phenomenon that was both ubiquitous and poorly understood: the extreme volatility of financial data. Two questions have driven my research since then. First, what are the causes of such extreme volatility? Second, what are the consequences for economic choices? While I was first introduced to the concept through the financial markets (stock prices, exchange rates, interest rates), I’ve discovered that the extreme-volatility phenomenon is observed in economic outcomes as disparate as auction results and urban sprawl.
The definition of extreme volatility is most evident from comparison to the standard normal distribution. The “bell curve” picture that we have in mind represents a standard amount of volatility. When extreme volatility is observed, the distribution is flatter and “fatter” or “heavier” in the tails of the distribution. Because of these differences from the standard normal distribution, all of the hypothesis tests we learned in statistics class based on the normal distribution will be biased or imprecise. This fascinated me. How does this feature arise in financial markets? What the implications for conventional econometric tests? How can we create tests that are unaffected by or are robust to such volatility? My first project concerned a way to test whether an econometric model was correctly specified when data were extremely volatile, with an eye toward modeling financial bubbles. My job market paper itself concerned pure prediction theory for these heavy-tailed data. Interesting applications of extreme value theory are not simply for financial data: I have also published a co-authored paper in which the focus is on observed prices in first-price auctions. I find it fascinating that the theoretical underpinnings of extreme values naturally arise in many places: these include how financial volatility evolves over time, and how auction bids clump near a reserve price. Theory predicts this will happen, and observed financial and auction bid data verify that these data are indeed “heavy tailed”.
After graduate school my interests branched into other areas: • the econometric specification of causality tests, typically applied to macroeconomic and financial data. My own applications concerned whether spikes in money growth influenced future income growth, possibly many months or quarters in the future. • The robustness of statistical tests, typically applied to heavy-tailed data. • The appropriate hypothesis tests for “big data” questions: practical and theoretical concerns when an economist has far more data variables at hand than can possibly be used for an economic or econometric model. This can be very important in practice, since analysts have publicly available data sets like the Current Population Survey that offer hundreds of variables to use but no guidance on which variables belong in the regression. The typical approach to this problem is to assume that only a limited number of variables matter for a particular model and focus on those variables. My research focuses on testing the validity of that premise.
Most recently, I’ve become interested in quantile methods of estimating the properties of a distribution. The determinants of spending of the very rich, for example, may differ from those of the very poor; quantile analysis allows us to identify those differences. Similarly for health care: policy-makers may be more interested in why some people have very low (low quantile) health care expenditures, while others (with the same underlying health) have very high (high quantile) health care expenditures.
My teaching has had a major impact on my research interests. As I develop the syllabus and lecture notes for a course, I have time and time again been forced to rethink why some issues are discussed the way they are in text books and in scholarly articles. When I find a discrepancy between the textbook approach and my own approach, I have a new research project to pursue. At the same time, my research has had a important impact on how I work with undergraduates who are developing seminar papers or honors theses. I know that undergraduates can understand the newest methods, and I like to challenge them to contribute new ideas. The result, every time, has been wonderful.
A complete list of Professor Hill’s works and proper citations can be found on his website, http://www.unc. edu/~jbhill