Jonathan B. Hill

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Home Page of Jonathan B. Hill

Assistant Professor of Economics

University of North Carolina – Chapel Hill

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CONTACT INFORMATION

Dept. of Economics

Gardner Hall 200G

University of North Carolina

Chapel Hill, NC 27599-3305

jbhill at email dot unc dot edu.

RESEARCH INTERESTS

Robust M-, GMM-, and GEL-Estimation

Several projects involve developing a theory of robust Minimum Distance Estimation for nonlinear models of the conditional mean and variance with arbitrarily (or nearly arbitrary) heavy tails. The theory covers Tail Trimmed versions of GMM, QML, and GEL estimation under trivial assumptions on the GARCH component. This research includes asymptotic theory for tail-trimmed sums of dependent and heterogeneous processes, self-normalized by a kernel variance estimator, and several new robust estimators that can achieve greater than root-n consistency. Finally, this work includes methods of heavy tail robust inference including kernel tail-trimmed variance estimation, robust moment condition tests, tests or functional form and volatility spillover.

Extreme Value Theory

My current research involves functional central limit theory for “tail arrays”. The theory allows for substantial generality in analyzing the properties of tail index estimators, tail dependence measures, and tail quantile functions when the data are dependent (short or long memory) and heterogeneous. Non-extremes are left unrestricted.

A related problem is the analysis of nonparametric tail dependence measures without relying on a bivariate tail shape, on a conditional volatility structure, or memory and heterogeneity properties of non-extremes. I look at extensions of projection theory based dependence measures to the tails, including Extremal-NED and Extremal-L₀-Approximabilty properties, as well as estimable tail correlations of exceedances and events. I explore the relationships between each measure, which classes of processes satisfy these tail dependence properties, and how they relate to the index of bivariate regular variation.

Applications include measures of extremal volatility spillover in asset and exchange rate markets, tests of exremal white noise and extremal nonlinearity, and the exact shape and decay rate of joint (serial and bivariate) GARCH and stochastic volatility tails.

Model Specification Tests

In other research I have studied consistent tests of functional form. Projects include analyses of when such tests are not degenerate, are never in-consistent (“super consistent”), have strictly integer or rational-valued nuisance parameters, and are robust to heavy tails and arbitrary plug-in choice.