Chinese / English
Sun Yixiao

A Selective Review of

Xiaohong Chen’s Research Contributions

 

Yixiao Sun

Professor of Economics, UC San Diego

Changjiang Chair Professor, Wuhan University

 

It is my greatest honor and pleasure to describe some of Xiaohong Chen’s research. Her research is so broad and profound that very few, if any, econometricians can provide an authoritative description of all her research contributions to Econometrics. For this reason, I will focus on one of her many contributions to nonparametric econometrics.

 

Xiaohong is one of the most influential scholars in nonparametric econometrics in the world. She is personally responsible for most of the asymptotic results in the method of sieves, one of two nonparametric methods. All of her contributions in this area have been fundamental, innovative, and of extremely high quality. It is now virtually impossible to use the method of sieves without citing her work or being influenced by her ideas. The estimation and inference methods proposed by Xiaohong have been employed in many areas of economics including macroeconomics, finance, industrial organization, labor economics, and international trade.

 

A hallmark of Xiaohong’s work is the generality of her results. She always considers the most general settings and strives for the most general results under the weakest possible conditions. It is often the case that after she establishes the most general results under some high-level conditions that reflect the essence of the problem, other researchers, some of whom are prominent econometricians themselves, would follow her research and consider a specific model and obtain simplified versions of her general results. Every piece of Xiaohong’s work is masterfully done with deep insights and profound results. It is no wonder that she has received so many awards for her publications. This includes the Journal of Nonparametric Statistics Best Paper Award, the Richard Stone Prize in Applied Econometrics, and the Arnold Zellner Award in Theoretical Econometrics, among others. Winning just one such award would be deemed by most scholars as the accomplishment of a lifetime. Repeated winnings are a testimonial of her efforts to obtain the most elegant results that have extraordinary influence.

 

I have had the distinct honor to work with Xiaohong on the paper “Sieve Inference on Possibly Misspecified Semi-nonparametric Time Series Models.” The paper was joint with Zhipeng Liao of UCLA, one of Xiaohong’s former students, and was published in the Journal of Econometrics in 2014. Through working with Xiaohong very closely, I witnessed first-hand her extremely careful approach to research and her highest intellectual and technical standards. In search for simple and powerful practical methods, she would leave no stone unturned.

 

While our joint paper is highly technical, I will try my best to provide some intuition on the problems we tackle.

 

The main theme of the paper is the method of sieves with application to time series data. Previously, the method of sieves for iid data has been thoroughly investigated in Xiaohong’s ground-breaking work with Chunrong Ai (Econometrica, 2003). Using the method of sieves to estimate an unknown function is analogous to using a sieve, i.e., a woven screen familiar to farmers, to separate wanted elements, such as seeds, from unwanted nuisances, such as small particles of soil, by moving the sieve in a certain way. From an econometric point of view, the unwanted nuisance is the noise in our sample, and the wanted element is the main signal, i.e., the unknown function, that we want to extract from the data. The key premise here is that we do not impose any parametric functional form on the function and we let data speak for itself. That is, we do not assume that the wanted elements and unwanted nuisances are different in any obvious way. For this reason, the mesh size of the sieve should not be too small or too large. If it is too small, unwanted pieces of larger size cannot sift through the mesh, and the wanted portion will still contain many unwanted nuisances. Econometrically, the estimated functions will be too noisy. On the other hand, if the mesh size is too large, we fail to retain some wanted but smaller elements that sift through the mesh. From an econometric point of view, the estimated function will be inconsistent. While the analogy is not perfect, it is quite revealing: it is important to have some information on the relative size of the wanted element and unwanted nuisance in order to design a sieve with optimal mesh size. Almost all aspects of the method have been investigated in Xiaohong and her coauthors’ earlier work. This includes adaptive design of the sieves (see Xiaohong’s paper with Tim Christensen, which is forthcoming in Quantitative Economics) and the most difficult cases when there is endogeneity (see a sequence of important publications by Xiaohong and her authors Richard Blundell, Dennis Kristensen, Demian Pouzo, etc). Here the endogeneity problem is analogous to the case where the wanted elements and unwanted nuisances are intertwined and stuck together, and a special instrument (i.e., instrument variable) is needed to break them apart.

 

Our paper aims at inferring some aspect of the unknown function. For example, if the unknown function is the demand function, we may be interested in consumer surplus, which is an integral of the unknown function. The proposed procedures are very general as they are applicable to any aspect of the unknown function, be it an integral or the value of the function at a point. The M-estimation framework adopted also allows for a wide range of different estimation methods.

 

Serial dependence in time series data poses additional challenges in inference. Consider as an example where we want to estimate the level of a time series. If the observations are strongly positively correlated with each other, then the confidence in our estimate should be lower compared to the case when the observations are independent from each other. Intuitively, if there is a positive shock to the observation in one year, and it persists to some degree over the next ten years, we are likely to get a high estimate. On the other hand, if we happen to start with a negative shock that persists over a long horizon, then we are likely to get a low estimate. The higher the persistence, the wider the range of possible values our estimate will take. That is, higher persistence implies higher variation and extra uncertainty of our estimate. Any method that ignores the extra uncertainty will likely give rise to a wrong conclusion. Our paper takes the extra uncertainty into account and develops convenient and accurate F and t tests that also reflect the difficulty in estimating the extra uncertainty.

 

Perhaps because of our shared experiences, Xiaohong and I have become very close friends. We had numerous conversations in 2008 when I was on leave at Yale. We have been discussing research ever since, no matter whether we work on a project together or not. She has been an invaluable source of advice and guidance over many years. Both Xiaohong and I graduated from the mathematics department of Wuhan University, and both of us were fortunate enough to pass the second “Chow test” and become a member of the Ford class at Renmin University of China. (For this, I am deeply indebted to Professor Gregory Chow who made the class possible. I also applaud the National Economics Foundation for selecting Professor Chow as a co-winner of the prize.) Our paths literally crossed later in that Xiaohong obtained her Ph.D. from UCSD and is now a titled professor at Yale, while I got my Ph.D. from Yale and now teach at UCSD. I can testify that all her former professors here at UCSD have very fond memories of her and take great pride in her wonderful achievements.

 

Even though Xiaohong has become a prominent figure in econometrics, she is friendly, approachable, and down-to-earth. She has nurtured many young scholars in the economics profession in general and in econometrics in particular. Many of these scholars have already become well established in the profession. The record that Xiaohong has set on the world stage will inspire generations of Chinese scholars, especially those who got their college education from Mainland China. Xiaohong Chen, together with Professor Gregory Chow, is the best choice for the China Economics Prize.

 



◆please indicate the source if authorized: National Economics Foundation

◆photo:National Economics Foundation