Research Statement. Zhongwen Liang

Transcription

1 Research Statement Zhongwen Liang My research is concentrated on theoretical and empirical econometrics, with the focus of developing statistical methods and tools to do the quantitative analysis of empirical problems and justification of economic theories more accurately. The major question I am trying to answer is how can we estimate and test economic relationships more practically and efficiently. In practice, we want to estimate the quantitative effects or test the economic theories based on economic models using data from the real world. In order to do so, we have to make some assumptions either on the functional relationship between economic variables such as linear or nonlinear, or on the distribution of the unobserved errors. In reality, these assumptions may not be very reasonable. If the assumptions are violated, the results obtained will be very misleading. The main goal of my research is to give deeper understanding of the existing methods, make the assumptions as flexible as possible, and propose new methods to achieve better results. In particular, I work on a strand of new techniques which are called nonparametric and semiparametric methods. The main idea is to remove the unreasonable assumptions and make the estimation and testing as flexible and applicable as possible. I have 8 publications so far, two papers under review and several working papers, which are close to be submitted. I work in two broad areas in econometrics, which are time series and panel data models. My contributions are summarized in the following. Time Series The first field I have been working on for the past a few years is time series analysis, especially nonstationary time series. Nonstaionarity is a type of feature that is different from stable properties. This feature is commonly observed in most of financial and macroeconomic time series, for example stock prices, exchange rates, etc. Since the seminal works of Granger (1987), Engle and Granger (1987) and Johansen (1988), the nonstationarity has attracted much attention. In 2003, Granger was awarded the Nobel memorial prize in economics based on his work on nonstationarity. The traditional approach to understand the nonstationarity is through the linear autoregression, which means the current status is determined by the past statuses in a linear way. However, the real world is not quite linear. There are more and more evidence that nonlinearity is more essential in reality. The nonlinear nonstationary models have received much 1

2 attention recently. Researchers are trying to combine the nonlinear and nonparametric models with the nonstationary time series, which would enjoy more flexibility and weaker restrictions. However, this increases the complexity of the problem. The properties of the estimation and testing are quite different from the classical ones and are difficult to reach. I have done some work in this area. When we deal with the nonstationary economic variables, one question is whether there does exist any reasonable relationship among these variables. This is answered for a specific yet flexible class of relationships in Gu and Liang (2014), which was published in the Journal of Econometrics. We considered the problem of testing for a class of semiparametric relationship among nonstationary time series, which includes the traditional linear model as a special case. Based on the recent development in the field, we developed two tests to verify the relationship we are looking for. Further, we applied the proposed test to examine the purchasing power parity (PPP) hypothesis between the U.S. and Canada, which shows evidence that a nonlinear PPP may hold between the U.S. and Canada and different from the existing results obtained from linear models. Another question we need to answer is when there indeed exists the nonlinear relationship, how do we figure out the quantitative effects we are interested in. This question is answered for different setups in the following papers. The theoretical results we obtained provide good guidance for practitioners in the empirical applications. In Li, Li, Liang and Hsiao (2017) which was published in Econometric Reviews, we considered a combination of partially linear and partially varying coefficient model between nonstationary economic variables. This model is quite general and nests some other semiparametric models, which makes it more applicable in practice. We proposed the newly developed estimation methods for both the constant coefficients and the functional coefficients, and established the theoretical properties of these estimators under some mild conditions. Further, these estimators are shown to enjoy the wellknown super-consistency property, which makes them more preferred in empirical applications. Wang, Liang, Lin and Li (2015) published in Annals of Economics and Finance complements Li, Li, Liang and Hsiao (2017) with a different estimation method, which is a convenient method for practical use but was ruled out by the conditions imposed in Li, Li, Liang and Hsiao (2017). The theoretical property of this method is studied with a novel proof. Liang, Lin and Hsiao (2015) published in Econometric Reviews, considered the estimation of the general nonlinear relationship between nonstationary economic variables with a newly developed method. The detailed examination of the performance of this estimation method is given in the paper. The simulation results showed that the estimation we proposed enjoys substantial efficiency gain over another commonly used estimator, which provided a guidance for empirical applications. 2

3 Time trend is also an important component in macroeconomic analysis, which is used to capture the important pattern such as economic growth. There was a debate in nonstationarity literature in whether to model the time trend as the deterministic trending or stochastic trending. Therefore, it s also interesting to know the properties of nonlinear and nonparametric trending models which could lead to very different results compared with the traditional ones, and provide better understandings. In Liang and Li (2012) which was published in the Journal of Econometrics, we considered the problem of estimating a semiparametric time series model with a time trend. We showed that one of commonly used estimation methods leads to an inconsistent estimation result, while the alternative method can yield consistent estimation. We established the theoretical properties of our proposed estimators. In addition, we considered the estimation of another flexible specification and established the theoretical properties of our proposed estimators. Furthermore, the testing of the linearity against partially linear time trend structures was also considered. Panel Data The second field I have been working with is the identification and estimation of nonlinear and nonparametric panel data models, since the nonparametric structures have the advantage to capture the nonlinear effects or correlations. I have done some work in this area. The results give practical tools for empirical analysis. In Li and Liang (2015) which was published in the Journal of Econometrics, we considered the flexible nonparametric and semiparametric panel data models and their estimations. The method we use is very different from the traditional linear panel models. We established the theoretical properties of the method we discussed. We also considered the estimation of a partially linear fixed effects panel data model using the similar method. Nonparametric methods are also capable to capture the nonlinear or heterogenous correlations. This is reflected in a series of papers I have done on the so-called correlated random coefficient (CRC) panel data models. In Gao, Li and Liang (2015) which was published in the Journal of Econometrics, we considered binary response CRC panel data models which are frequently used in the analysis of treatment effects and demand of products. We focused on the nonparametric identification and estimation of panel data models under unobserved heterogeneity which is captured by random coefficients and when these random coefficients are correlated with regressors. We based our identification strategy on a particular method which was proposed to solve the heterogeneity and endogeneity problem in the binary response models. With the help of this, we constructed a semiparametric estimator for the average slopes and establish its properties. Furthermore, we proposed a nonparametric method to test the correlations between random coefficients and regressors. 3

4 I have two other working papers on the CRC panel data models. In Hsiao, Li, Liang and Xie (2016), we considered a random coefficient model where the coefficients exhibit individual heterogeneity, and allow for these individually heterogenous coefficients to be arbitrarily correlated with the regressors. If only cross sectional data is available, we show that the identification of the mean parameter requires stringent conditions. However, if panel data are available, identification becomes feasible when the number of regressor is greater than T, the number of time periods. Even in the case T is less than the number of regressors, we showed that under certain condition the conventional fixed effects estimator can provide a consistent estimate of the mean effects. We also proposed a least squares estimator and a semiparametric estimator for the mean coefficients. In Liang (2016), I considered a truncated CRC panel data model which is commonly used in empirical analysis when we don t have complete observation of the population. I obtained the identification and estimation results based on the special regressor method. I constructed the theoretical properties for the estimator of the population mean of the random coefficient. Nonstationary Panel Data Another filed I am working on is the combination of the previous two fields, which is the nonstationary issues in panel data. Recently, I obtained some new results in the classical panel unit root tests literature by myself and with my coauthors. In Lahiri, Liang and Peng (2016), we investigated the local power of the Im, Pesaran and Shin (2003) (IPS) test which is one of the most cited and influential panel unit root tests, when both the incidental initial point and trend are present. We found a new result which is important but cannot be obtained by the existing method. We derived the analytical expression of the asymptotic local power of the IPS test with both initial conditions and incidental trends, which fills the gap in the literatue. Moreover, we found least squares de-trending will effectively take care of the initial condition by canceling out its dominant components asymptotically, thereby eliminating its effect on the local asymptotic power, which provides guidance for practitioners. In Liang (2017a), I propose a unified method to derive the exact local asymptotic power for panel unit root tests, especially Levin, Lin, Chu (2002) (LLC) and IPS tests. The approach is general and could also be used to provide the exact local powers to other panel unit root tests, where few results exist in literature. Other Researches I have broad research interests. I have some other work besides my main research field. In a recent paper Liang (2017b), I considered the estimation and inference of the structural changes 4

5 in the serially correlated time-varying coefficient regression models with regard to both the smooth structural changes and abrupt changes. The structure change is a very important issue in policy analysis. I systematically extended some existing estimation and testing methods to the serially correlated time-varying coefficient regression models. I established the theoretical properties of our estimators and tests. Moreover, I apply my methods to a time-varying beta coefficient relationship between an individual stock and the market index to understand both smooth changes and abrupt changes in risk premium. I have one other paper on the important issues of nonparametrics. In Ju, Li and Liang (2009) which was published in Advances in Econometrics, we constructed a nonparametric kernel estimator for the joint multivariate cumulative distribution function (CDF) of mixed discrete and continuous variables, which are frequently encountered in practice. We proposed a data-driven cross-validation method to choose optimal smoothing parameters, and established its validity. The theoretical properties of the proposed estimator were also derived. Furthermore, we provided conditions to ensure the optimality of the smoothing parameters. I also talk about the idea from this paper in the course Econometrics III which I am teaching right now. Future Reseearch My future research will be in the similar directions. I am working on some papers right now. In one of them, I consider the estimation of the semiparametric partially linear cointegration model. This type of model gives much flexibility of functional relationship and interpretation, which is one of the most widely used semiparametric models. The estimation of partially linear model under cointegration is not fully understood. I study the estimation using the profile least squares estimation and establish the theoretical properties. In a paper on varying index model, I consider a more flexible index setup for treatment effect estimation when the endogeneity is present in the treatment. I adopt the estimation strategy based on a nonparametric estimation method combined with the semiparametric instrumental variable methods. For panel data models, I will further study the identification and estimation of the nonparametric and semiparametric panel data models with sample selection problems. I will also work on the estimation and testing of the diffusion processes, which is the workhorse model in financial econometrics. I will teach a Financial Econometrics course in Spring 2018, which provides a good chance to think about teaching and research at the same time. I am also interested in applying nonparametric econometric methodologies to solve the empirical problems in the real world, for example policy evaluation and demand analysis. Publications and Working Papers 5

6 1. Kunpeng Li, Degui Li, Zhongwen Liang and Cheng Hsiao, Estimation of Semi- Varying Coefficient Models with Nonstationary Regressors. Econometric Reviews 36, Luya Wang, Zhongwen Liang, Juan Lin, and Qi Li, Local Constant Kernel Estimation of a Partially Linear Varying Coefficient Cointegration Model. Annals of Economics and Finance 16-2, Yichen Gao, Cong Li and Zhongwen Liang, Binary Response Correlated Random Coefficient Panel Data Models. Journal of Econometrics 188, Cong Li and Zhongwen Liang, Asymptotics for Nonparametric and Semiparametric Fixed Effects Panel Models. Journal of Econometrics 185, Zhongwen Liang, Zhongjian Lin, Cheng Hsiao, Local Linear Estimation of a Nonparametric Cointegration Model. Econometric Reviews 34, Jingping Gu and Zhongwen Liang, Testing Cointegration Relationship in a Semiparametric Varying Coefficient Model. Journal of Econometrics 178, Zhongwen Liang and Qi Li, Functional Coefficient Regression Models with Time Trend. Journal of Econometrics 170, Gaosheng Ju, Rui Li and Zhongwen Liang, Nonparametric Estimation of Multivariate CDF with Categorical and Continuous Data. Advances in Econometrics 25, Kajal Lahiri, Zhongwen Liang and Huaming Peng, The Local Power of the IPS Test with Both Initial Conditions and Incidental Trends. Working paper. 10. Zhongwen Liang, 2017a. A Unified Approach on the Local Power of LLC and IPS Tests, Working paper. 11. Zhongwen Liang, 2017b. Estimation and Inference of Structural Changes in Time Varying Coefficient Models. Working Paper. 12. Zhongwen Liang, A Truncated Correlated Random Coefficient Panel Data Model. Working paper. 13. Cheng Hsiao, Qi Li, Zhongwen Liang and Wei Xie, Correlated Random Coefficient Panel Data Models. Working paper. References Engle, R., Granger, C.W.J., Cointegration and error and correction: Representation, estimation and testing. Econometrica 55,

7 Granger, C.W.J., Developments in the study of cointegrated economic variables. Oxford Bulletin of Economics and Statistics 48, Im, K.S., Pesaran, M.H., Shin, Y., Journal of Econometrics 115, Testing for unit roots in heterogeneous panels. Johansen, S., Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control 12, Levin, A., Lin, C., Chu, C.-J., Unit root tests in panel data: Asymptotic and finitesample properties. Journal of Econometrics 108,