YIXIAO SUN

Home Address:   113 Sachem Street   New Haven, CT 06511   Tel: (203) 624-6159 Office Address:   Department of Economics   Yale University   Box 208268   New Haven, CT 06520-08268   Tel: (203) 432-3722   Fax: (203)432-6167 Birth Date: October 2, 1971 Citizenship: P.R. China

Fields of Concentration

Econometric Theory Applied Econometrics Financial Economics Empirical Macroeconomics

Desired Teaching:

Econometrics Financial Economics Microeconomics Empirical Macroeconomics

Comprehensive Examinations Completed:

October 1999 (Oral) Econometrics (with Distinction) May 1999 (Oral) Financial Economics (with Distinction) May 1999 (Written) Microeconomic Theory (with Distinction) August 1998 (Written) Macroeconomic Theory

Dissertation Title:

Econometrics of Panel Structure Models and Fractional Component Processes

Committee:

Professor Peter C. B. Phillips (co-chair) Professor Donald W. K. Andrews (co-chair) Professor Christopher Udry

Expected Completion Date:

May 2002

Degrees:

M. Phil., Economics, Yale University, 2001 M.A., Economics, Yale University, 2000 M.A., Management (Summa Cum Laude), Wuhan University, China, 1996 B.S., Mathematics (Summa Cum Laude), Wuhan University, China, 1993

Fellowships, Honors and Awards:

Dissertation Fellowship, Yale University, 2001-2002 Graduate Student Fellowship, Cowles Foundation, Summer 2001 John Perry Miller Fellowship, Yale University, 2000-2001 Carl Anderson Fellowship, Cowles Foundation, 2000-2001 Graduate Student Fellowship, Cowles Foundation, Summer 2000 Graduate Student Fellowship, Cowles Foundation, Summer 1999 University Fellowship, Yale University, 1998-2000 Ford Foundation Scholarship, Wuhan University, 1994-1995 Excellent Academic Achievement Awards, Wuhan University, 1993-1996 Meritorious, Mathematical Contest in Modeling, Sponsored by SIAM, China, 1993

Teaching Experience:

Teaching Assistant, Econometrics III (Graduate), Fall, 2001, Yale Teaching Assistant, Mathematical Economics, Fall, 2000, Yale Teaching Assistant, International Economics, Spring, 1997, SUNY Albany Teaching Assistant, Intermediate Microeconomics, Fall, 1996, SUNY Albany

Papers and Publications:

"Catching up, Forging ahead, and Falling behind: A Panel Structure Analysis of Convergence Clubs," August 2001 [job market paper]. "Asymptotic Theory for Panel Structure Models," May 2001 [job market paper]. "Finite Sample Comparisons of Semiparametric Estimators of the Long Memory Parameter," March 2001, (with Donald Andrews). "Regression with an Evaporating Logarithm Trend," December 2000 (with Peter Phillips), forthcoming in Econometric Theory P&S. "Nonlinear Log-periodogram Regression Estimation of Long-Range Dependence for Perturbed Fractional Processes," (with Peter Phillips), October, 2000, Submitted to Journal of Econometrics. "Perturbed Fractional Process, Fractional Cointegration and the Fisher Hypothesis", (with Peter Phillips), February 2000, under revision for Journal of Applied Econometrics. "Efficient Detrending in the Presence of Fractional Errors," (with Peter Phillips and C. C. Lee), September 1999. "Local Polynomial Whittle Estimation of Long-range Dependence," (with Donald Andrews), November 1999, (Revised October 2001), Submitted to Econometrica. "Non-orthogonal Hilbert Projections in Trend Regression," (with Peter Phillips), Econometric Theory, P&S, Vol. 17(4), 2001.

Conference Presentation:

"Local Polynomial Whittle Estimation of Long-range Dependence," Presented at the North American Summer Meeting, College Park, Maryland, 21-24 June 2001

Referee for:

Econometric Theory Journal of Applied Econometrics

Professional Affiliations:

The Econometric Society American Statistics Association Institute of Mathematical Statistics

References:

Professor Peter C. B. Phillips Cowles Foundation Yale University Box 208281 New Haven, CT 06520-8281 Phone: (203) 432-3695 Fax: (203) 432-6167 E-mail: peter.phillips@yale.edu Professor Donald W. K. Andrews Cowles Foundation Yale University Box 208281 New Haven, CT 06520-8281 Phone: (203) 432-3698 Fax: (203) 432-6167 E-mail: donald.andrews@yale.edu Professor Christopher Udry Economic Growth Center Department of Economics Yale University Box 208269 New Haven, CT 06520-8269 Phone: (203) 432-3637 Fax: (203) 432-3898 E-mail: christopher.udry@yale.edu

Dissertation Abstract:

This dissertation has two themes, one dealing with the econometric detection of group structure in panel data, the second dealing with the econometric estimation of long memory when the time series is perturbed by weakly dependent fluctuations. These themes are considered in two separate parts of the dissertation. Each part has two or three chapters, introducing the new model, developing a framework of asymptotic analysis and providing an application to an important empirical question. I. Panel Structure Model: Asymptotic Theory and Applications This part proposes and implements a tractable approach to detect group structure in panel data. The mechanism is via a panel structure model, which assumes that individuals form a number of homogeneous groups in a heterogeneous population. Within each group, the (linear) regression coefficients are the same, while they may be different across different groups. The econometrician is not presumed to know the group structure. Instead, a multinomial logistic regression is used to infer which individuals belong to which groups. The panel structure model has a wide variety of potential applications in economics. Direct applications include models of multiple equilibria and their history dependence. Other applications include empirical sample splitting when the sample division is determined by multiple variables, including both continuous and discrete variables. In addition, the panel structure model may be used to control parameter heterogeneity in panel data modeling. In fact, it can be regarded as a bridge between a model with homogenous coefficients and one with completely heterogeneous coefficients. To some extent, the panel structure model avoids the shortcomings of both models while retaining their advantages. Chapter 1 is concerned with developing an asymptotic theory for the panel structure model described above. This chapter shows that there always exists a local maximizer of the likelihood function, which is consistent and asymptotically normal, even if the likelihood function is unbounded. In addition, the chapter establishes the consistency and asymptotic normality of a global maximum likelihood estimator (MLE) under the assumption that the time dimension is larger than the number of regressors in the linear regression. This is a novel way to overcome the problem of an unbounded likelihood function, a well-known problem in the maximum likelihood estimation of a mixture model. An EM (Expectation and Maximization) algorithm is presented to estimate the system. A simulation study shows that the MLE performs quite well and the proposed approach detects the underlying structure with due precision. Chapter 2 employs the panel structure model and the asymptotic theory developed above to investigate the convergence club hypothesis. Many studies suggest that the world is polarizing into convergence clubs of rich and poor nations (e.g., Quah, 1996, 1997). However, few papers have attempted to formally investigate the convergence clubs. Chapter 2 helps to fill this gap. By using the panel structure model, this chapter is able to classify countries into different clubs and estimate the parameters of each club in a cohesive manner. The clubs are characterized by balanced growth paths. Within each club, the balanced growth paths parallel each other whereas the paths may intersect across different clubs. The findings in this chapter suggest that the world economy consists of three convergence clubs: an advanced club, an underdeveloped club and a developing club. These convergence clubs exhibit different convergence behavior in terms of both speed of convergence and steady state growth rate. In particular, the steady state growth rates for the three clubs are 2.09, 0.27%, and 2.90% per year, respectively. The difference in long run growth implies that some countries will catch up and even forge ahead and some countries will fall behind. It is envisaged that catching up, forging ahead, and falling behind happen simultaneously as individual economies interact with each other. II. Bias-reduced Estimators of Long-range Dependence The memory parameter is often a focus of empirical studies that investigate persistence in economic and financial time series. Not surprisingly, various approaches have been proposed to estimate this parameter. Among them, the semiparametric approach is especially appealing to empirical analysts as it allows for various types of long run behaviors while retaining generality with respect to short run fluctuations. The semiparametric approach relies on approximating the short-run component of the spectrum by a constant around the origin. This often results in a considerable finite sample bias. Part II of the dissertation proposes a natural way to reduce this bias that involves replacing the constant in the approximation by a constant plus an even polynomial with either integer or fractional powers. Using a polynomial with integer powers in the approximation, Chapter 3 generalizes the local Whittle estimator to the local polynomial Whittle (LPW) estimator. Following the work of Robinson (1995), the chapter establishes the asymptotic bias, variance, mean-squared error (MSE), and normality of the LPW estimator. These results show that the bias of the LPW estimator goes to zero at a faster rate than that of the local Whittle estimator under some smoothness condition, but that its variance is only inflated by a multiplicative constant. In consequence, the rate of convergence of the LPW estimator is faster than that of the local Whittle estimator, given an appropriate choice of the bandwidth. Using a polynomial with fractional powers in the approximation, Chapter 4 proposes a new estimator of long-range dependence for a fractional component process, which is the sum of a fractional process and a weakly dependent process. A fractional component process may model certain time series better than a purely fractional process as some economic variables may be affected by both persistent shocks and temporary shocks. One example of a fractional component process is the long memory stochastic volatility model. The proposed new estimator resembles Geweke and Porter-Hudak’s log-periodogram regression estimator (sometimes called the GPH estimator) but has frequencies to the fractional power 2d as an additional regressor. Under some smoothness assumptions around the origin, Chapter 4 shows that the bias of the new estimator goes to zero at a faster rate than that of the GPH estimator, but that its variance is only inflated by a multiplicative constant. As a consequence, the optimal rate of convergence to zero of the asymptotic MSE of the new estimator is faster than that of the GPH estimator. Some simulation results demonstrate the viability and bias-reducing feature of the new estimator relative to the GPH estimator. The final chapter employs fractional component processes to model the inflation rate and real interest rate, and provides a plausible explanation for an empirical puzzle found by Phillips (1998). According to the Fisher identity, the nominal interest rate equals the sum of the real interest rate and the inflation rate. The degree of persistence of the nominal interest rate is thus necessarily the same as that of the dominant component of the real interest rate and inflation rate. Phillips found that the nominal interest rate is more persistent than both the real interest rate and the inflation rate. This chapter argues that small sample biases of the existing long memory estimators are large enough to account for this empirical incompatibility. The argument is supported by evidence from various sources. In particular, the bias-reduced estimator proposed in Chapter 4 produces estimates that are compatible with the Fisher identity.