| This dissertation is supported by National Natural Science Funds—Stationary and Nonstationary Linear Panel Data Modeling Research under Cross-sectional Dependence and Non-spherical Disturbances Conditions (No.71071130).Recently, panel data modeling has attracted considerable interest in the theoretical analysis and practical application. The number of literature can even use voluminous to describe. An important reason is that panel data has two dimensions of time and section. Pooling information of those two dimensions can help us to overcome the multicollinearity problems in traditional time series analysis, and provides more information, more variation, less collinearity, more freedom and greater estimating efficiency. On the other hand, scholars have gradually recognized the problem that it must ensure all variables to have the same relationship between different sections (time) when we fuse the information, which also means that data from each sections (time) must be poolable. Therefore, poolability test becomes an important part in the procedure of panel data modeling. It has specific meaning for poolability testing in panel data model. While just as in the case of linear model, the poolability test tends to be concentrated in testing for slope coefficients'homogeneity between individuals. Thus, for linear panel data, there is no clear distinction between the poolability test and the slope coefficients' homogeneity test.In this dissertation, we comb and summarize the advantages and disadvantages of existing tests for poolability, and then put forward our own points of view. Specifically, the poolability test is first discussed in the framework of stationarity and non-stationarity. Afterwards, we introduce cross-sectional dependence to each framework. Through such steps, the poolability test is expected to be dealt with comprehensively and systemically. Moreover, we also study the cross-sectional dependence test after studying the poolability systematically. Research in the dissertation is a purely theoretical discussion, in which two methods are mainly used including mathematical derivation and Monte Carlo experiments respectively for asymptotical properties and finite sample performance, and thus a number of results with theoretical significance are obtained.The structure in the dissertation is as followed:Chapter1is introduction, in which the discussing problem, backgrounds and significance are introduced.In chapter2, the existing results in relevant research are reviewed including: study on cross-sectional dependence (the influence, the diagnosis, and the specification, in which the factor models is high lightened); estimation methods for non-stationary panel data model in cross-sectional independence and dependence (especially focused on fully modified OLS and bias-adjusted estimator); various types of methods and thoughts for poolability testing.In chapter3, poolability test is considered in the stationary panel data model. Firstly we analyze commonly used poolability testing methods and point out their inadequacies.Secondly, through studying individual Lagrange Multiplier (LM) statistic, we construct a new poolability test statistic, and scrutinize its properties both in large and small samples as well as compare it with existing poolability tests. Finally, the new statistic based on individual LM statistic is applied to SPSM algorithm, which is proposed by Kapetanios (2003), and a new method is proposed for panel data grouping.In chapter4, the new idea based on individual LM statistic is extended to testing for poolability in non-stationary panel data. We discuss how to apply the idea proposed in chapter3to the non-stationary panel, and also examine the asymptotic properties and performance in finite samples.In Chapter5, the poolability test is considered in stationary panel data with cross-sectional dependence. Based on the existing thoughts, a new poolability test is proposed for panel data with cross-sectional dependence. The basic idea is that we first estimate the common components through principal components analysis procedure, and then construct a new poolability test based on individual LM statistic after removing the estimated common components. Meanwhile, the resulting test statistic is analyzed in approximation as well as in local asymptotic power. Monte Carlo experiments are also conducted to examine its performance of size and power. During above analysis, we pay particular attention to the comparison with the counterparts under cross-sectional independence.In chapter6, we study the poolability test for non-stationary panel data with cross-sectional dependence. We first analyze the influence of cross-sectional dependence to the poolability under the framework of the non-stationary, and then propose the corresponding test statistics as well as scrutinize its properties just the same way as previous sections.In chapter.7, the cross-sectional dependence test is studied in panel data model. On the basis of ideas and drawbacks in usual existing methods of cross-sectional dependence, we propose a new cross-sectional dependence test, and discuss the properties both in large and small samples.In Chapter8, we summarize main contents of the dissertation and propose some valuable issues for further study.Research contents in the dissertation include the following aspects:1. The current theoretical study in panel data model theory concentrates in the unit root test, cointegration, etc., and there has been relatively little work done in poolability test. In this dissertation we systematically summarize the related works and latest developments for poolability testing in panel data, and introduce some mainly used methods in this filed as well as point out several deficiencies for subsequent study.2. Poolability test in stationary panel data. Reference to predecessors'ideas, we attempts to construct poolability test based on Lagrange Multiplier principle.Different from existing methods, we study individual score rather than the entire one. In order to be applicable to the situation N??, we use standardization to obtain a new statistic. Mathematical derivation shows that the new method has as good asymptotic properties as PY test which was proposed by Pesaran and Yamagata (2008b). Monte Carlo experiments reveal that the proposed method has good and robust performance in finite samples. Moreover, we combine the new test and SPSM algorithm to obtain a novel method for panel data grouping3. The poolability test in non-stationary panel data model. Non-stationary panel data has great difference with the stationary panel data. Because, on one hand, we are confronted with the problems of endogeneity; On the other hand, the derivation for asymptotic properties of non-stationary panel data is very different with that of the stationary one, which leads to a different way to get the asymptotic properties. Under the framework of non-stationary. We use the idea of FMOLS to overcome the endogenous problem and construct poolability test based on individual LM statistic. It can be seem that the resulting test has a limit distribution of standard normal and performs well in finite samples.4. The poolability test in panel data model with cross-sectional dependence. We propose poolability tests for stationary and non-stationary panel data respectively. To get rid of cross-sectional dependence, the PCA method is used to estimate factors and factor loadings. New poolability test based on individual LM static is constructed under both frameworks of stationarity and non-stationarity. After that the achieved asymptotic properties and performance in finite samples confirm the effectiveness of our tests.5. The cross-sectional dependence test. Considering the defects of exiting tests, we propose a new testing statistic for cross-sectional dependence based on the sample covariance based on Schott's statistic (2004) which is proposed for testing independence of high dimension data from the perspectives of accumulative error and finite sample problem. Careful Mathematical derivation and Monte Carlo experiments show that the proposed test performs well and robustly, which provide a novel alternative approach for testing cross-sectional dependence.In the dissertation, innovations of this research are following:1. Under the condition of cross-sectional independence, we propose corresponding poolability tests to stationarity and non-stationarity for panel data respectively:poolability test statistic for stationary panel data based on the individual LM statistic, and the poolability test statistic for non-stationary panel data based on the idea of fusing the thoughts of individual LM and FMOLS. We also conduct theoretical analysis and simulations, which show that the two types of testing statistics both have better statistical property when compared with existing tests.2. Under the condition of cross-sectional dependence, we propose corresponding poolability tests to stationary and non-stationary for panel data respectively:poolability test for stationary panel data based on individual LM by defactoring estimated common components, and poolability test for non-stationary panel data based on individual LM through fusing the ideas of PC A and FMOLS. Theoretical analysis and simulations are also conducted. Results show that the two types of tests both perform well when compared with existing tests.3. We propose a new testing statistic for cross-sectional dependence based on the merits and demerits of existing tests. Afterwards, we analyze its asymptotic properties and investigate the performance in the respects of size and power in finite samples. The test is found to converge to standard normal distribution asymptotically and avoid the problem of low power of Pesaran(2004) CD test as well as perform well in the respect of size. Meanwhile, we combine the new idea of poolability test based on individual LM and SPSM algorithm to obtain a novel method of panel data grouping... |
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