Econometric Theory
Applied Econometrics

Econometrics
Financial Economics
Microeconomics

(Oral) November 2000, Econometrics; May 2000, Financial Economics (with distinction)
(Written) May 1999, Microeconomic and Macroeconomic Theory

Econometric Essays on Generalized Empirical Likelihood, Long-memory Time Series, and Volatility

Professor Donald W. K. Andrews
Professor Peter C. B. Phillips
Professor Joseph Altonji

May 2003

M. Phil., Economics, Yale University, December 2001

M.A., Economics, Yale University, December 1999

Diplom, Mathematics (with minor in Economics), University of Bonn (Germany), August 1998 (with distinction), Thesis title: The -equation on unbounded domains in Cⁿ. A first approach.

Diplôme d’Etudes Approfondies (DEA), Mathematics, Paris VI, Pierre et Marie Curie (France), September 1996 (mention bien), Thesis title: Le problème de parité dans les matroïdes.

Vordiplom, Mathematics (with minor in Economics), University of Konstanz (Germany), August 1994 (best grade possible)

Carl Arvid Anderson Prize Fellowship in Economics, Yale University, 2002-2003
Enders Fellowship, Yale University, Summer 2002
Dissertation Fellowship, Yale University, 2002
Graduate Student Fellowship, Cowles Foundation, 1999-2001
University Fellowship, Yale University, 1998-2000
Teaching Assistantship, SUNY Albany, 1997-1998
Scholarship German Merit Foundation (Studienstiftung des deutschen Volkes), 1992-2002
Erasmus Stipend, 1995-1996

Teaching Assistant, Game Theory, Yale University, Fall 2001
Teaching Assistant, Financial Markets, Yale University, Spring 2001
Instructor, Introduction to Calculus, SUNY Albany, 1997-1998

Research Assistant to Professor Donald W. K. Andrews, Yale University, 1999-2001
Research Assistant to Professor Judy Chevalier, Yale School of Management, January 2002 (project: "Measuring prices and price competition online: Amazon and Barnes and Noble")

"Generalized Empirical Likelihood Tests under Partial, Weak, and Strong Identification", mimeo, Yale University, 2002 [job market paper].

"A Biased-reduced Log-periodogram Regression Estimator for the Long-memory Parameter" (with Donald W. K. Andrews), 2003, Econometrica 71, forthcoming. Also Cowles Foundation Discussion Paper No. 1263.

"Efficiency Properties of Labor Taxation in a Spatial Model of Restricted Labor Mobility" (with Ashok Kaul and Martin Kolmar), 2002, Regional Science and Urban Economics 32(4), 447-473.

"Dynamic Combination of Models and an Application to Conditional Variance Prediction in Stock Market Time Series", mimeo, Yale University, 2001.

Work in Progress:

"Rate of Convergence of Positive-Semidefinite Kernel HAC Estimators of the Long-Run Covariance Matrix".

"GEL Methods for Time Series Models when Identification is Weak" (joint work with Richard J. Smith).

Inter-University Graduate Student Conference at Princeton, October 18, 2002
Invited junior scholar at the NSF Symposium on Identification and Inference for Econometric Models, U.C. Berkeley, August 2-7, 2001
Invited junior scholar at the workshop "New Directions in Time Series Analysis" held at the CIRM, Luminy, France, April 23-27, 2001

Co-organizer of the Graduate Summer Workshop at Yale, June-August 2002

Econometric Theory

The Econometric Society
Institute of Mathematical Statistics

Internship at Daimler-Chrysler, Stuttgart, Germany, February-April 1995

German (native language), English, French (fluent), Spanish (basic knowledge), Latin

The dissertation has three parts. The first part introduces Generalized Empirical Likelihood (GEL) based test statistics for the structural parameters in a linear model. The second part is concerned with bias-reduced estimation of long-range dependence. The third part introduces a flexible approach to combine econometric models. The approach can be viewed as a generalization to the Markov-switching literature. I apply it to the prediction of conditional variance in stock market time series.

I. Generalized Empirical Likelihood Tests

In instrumental variables regression, the instruments available to empirical researchers are often only weakly correlated with the endogenous variables. That is, identification of the model is weak. It is well known that classical asymptotic approximations to the finite sample distributions of the main instrumental variables statistics can be very poor under weak identification. For example, even though the likelihood ratio and Wald test statistics are asymptotically , use of critical values can lead to extreme size-distortions in finite samples in weakly identified situations. I therefore propose two new, computationally simple, test statistics for the structural parameters in a linear model whose sizes are robust to the strength or weakness of identification. In fact, the asymptotic null distribution of these statistics is under partial (Phillips (1989)), weak (Staiger and Stock (1997)), and strong identification. An additional important advantage of these test statistics is their robustness to conditional heteroskedasticity in the data.

Both test statistics are based on GEL methods. GEL can be viewed as an alternative to Generalized Method of Moments (GMM). It has received considerable attention in the recent literature due to its competitive bias properties. The first statistic GELR is constructed from the criterion function of the GEL estimator. The second statistic K generalizes the K statistic in Kleibergen (2001) from GMM to GEL. This statistic is given by a quadratic form in the first-order condition of the GEL estimator evaluated at the true parameter value. I show how GELR and K can be modified to test a hypothesis involving a subvector of the structural parameter vector. I perform Monte Carlo simulations and find that the new tests have very competitive size and power properties under both weak and strong identification. Their main advantage lies in their robustness to certain features of the error distribution like conditional heteroskedasticity, asymmetry, and thick tails. In over-identified problems, the statistic K is generally more powerful than GELR.

Finally, I derive the asymptotic distribution of the GEL estimator for the structural parameters in the linear model under weak identification. Similar to the findings of Phillips (1989) and Stock and Wright (2000) for 2SLS and GMM, the resulting estimators have non-standard asymptotic distributions and are in general inconsistent. Therefore, inference based on the classical normal approximation is inappropriate under weak identification.

II. Bias-reduced Estimators of Long-range Dependence (joint with Donald Andrews)

The memory parameter (d) has been the focus of many recent empirical studies investigating persistence in economic and financial time series. Among the various econometric estimation procedures, that have been proposed, the semiparametric approach based on Geweke and Porter-Hudak (1983) (GPH) has received particular attention from applied researchers since it makes only minimal assumptions on the short run component of the time series and allows for various types of long run behavior. Because the semiparametric approach is based on a potentially imprecise approximation of the short run component of the time series by a constant around the origin, it can result in considerable finite sample bias.

We therefore propose a simple bias-reduced estimator that eliminates the first- and higher-order bias of the GPH estimator. The bias-reduced estimator is the same as the GPH estimator except that one includes frequencies to the power 2k (for k = 1, …, r, for some integer r) as additional regressors in the pseudo-regression model that yields the GPH estimator. We establish the asymptotic bias, variance, and mean-squared error (MSE), determine the MSE-optimal choice of the number of frequencies to include in the regression, and establish asymptotic normality. Under general assumptions, these results show that the bias goes to zero at a faster rate than that of the GPH estimator but that its variance only is increased by a multiplicative constant. In consequence, the optimal rate of convergence to zero of the MSE is faster than that of the GPH estimator. Extensive Monte Carlo simulation results for stationary Gaussian ARFIMA(1, d, 1) and (2, d, 0) models show that the bias-reduced estimators perform well relative to the GPH estimator.

III. Dynamic Combination of Models and an Application to Conditional Variance Prediction in Stock Market Time Series

ARCH type models have been criticized for their poor predictive performance and their high persistence of volatility. These deficiencies might well result from structural changes in the ARCH process over time. As a possible remedy to these problems, I introduce a general method that links variable length Markov chain models for discrete time series, with real-valued time series models. The resulting model class, which I call Dynamic Combination of Models (DCM), incorporates the idea of model mixing and model switching and thus allows the parameters of the model to change over time. The transition probabilities for the regime in the next period depend on a possibly long history. Unlike the Markov-switching approaches in the literature I do not restrict the length of the history to a certain fixed number of periods. I present an efficient computational method to estimate DCM using the so-called context algorithm.

I then apply a particular GARCH(1,1) DCM to the prediction of the conditional variance in stock market time series. The study shows that the new DCM estimator has competitive in-sample and out-sample performance for various loss functions. The new estimator's volatility forecasts are less persistent to individual shocks than are those of GARCH.