Study On Panel Data Unit Root Tests With The Impact Of Initial Condition

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).With the panel data model has been widely applied in many research fields, people begin to pay more and more attention to stability problem of panel data, especially in the recent20years, the panel data unit root test has become a hot research field of international economics. However, studies have shown that panel data unit root tests are affected by many factors, therefore, this paper mainly considers the existing portion of the more popular panel unit root test methods.With panel data model has been widely applied in many research fields, people started getting attention problems of stationary panel data, especially in the last20years, the research of panel data unit root test has become a hot research the number of international economists. However, previous studies indicate that panel data unit root test method is affected by many factors, therefore, this paper mainly from the perspective of the initial conditions of the existing portion of the more popular panel unit root test methods of data analysis.In this paper, based on combing and summarizing the advantages and disadvantages of the research literature on existing panel data unit root tests and initial conditions affect them, and doing some of our own work. Specifically, the first analysis of the impact of initial conditions on LLC test, and IPS test that is affected by the initial conditions are discussed, then based on inadequacies on the LLC and IPS tests, we propose LR test and examine wether the impact of the initial conditions affect the efficacy of LR test or not. In addition, after analyzing the influence of the initial conditions on power of panel data unit root test, we also consider whether the initial conditions will affect the size of panel data unit root test. Research work of this paper is to explore the theoretical in nature, mainly apply the two methods of mathematical and stochastic simulation, the power and size of the asymptotic properties and finite sample test of the corresponding to different situations are considered, draws some conclusions with theoretical significance.The paper is organized as follows:Chapter1Introduction to the thesis, the main description of the problem, the background and significance of the study; research at the idea, structure and major innovations and lack of research.Chapter2is the literature review and mainly reviews the existing literature mainly related research, including panel data unit root tests (fixed and random coefficient panel data unit root tests, and describes the different types of panel data unit root test methods and ideas), from Effect of initial conditions on the time series unit root test study the effects of initial conditions on panel data unit root tests, and then come out of this paper is to study the problem. And from the perspective of theoretical and empirical analysis, describes the phenomenon of the impact for whether the study of the initial conditions affects the panel data unit root test.Chapter3studies the effects of initial conditions on fixed coefficient LLC test statistic. Firstly, when Westerlund and Breitung (2013) apply the initial conditions of Harris, Harvey, Leybourne and Sakkas (2010), explaining why the asymptotic distribution of LLC test statistic does not exist. Followed by appropriate adjustment of the order of the initial conditions, local asymptotical power of LLC is found, and study its asymptotic properties and finite sample properties of this case and compared corresponding the finite sample performance under different initial conditions.Chapter4examines the effects of the initial conditions on the first generation fixed coefficient panel data unit root tests in another of the more popular test methods-IPS test, In this case, under the alternative hypothesis, the local asymptotic distribution, local asymptotic power function and finite sample properties of the IPS test statistics are analyzed.Chapter5for a fixed coefficient panel data unit root LLC and IPS tests when their individual is explosive in panel data, the power is close to zero, we try to put a fixed coefficient panel data unit root LR test to correct, the basic idea is to construct each individual’s likelihood ratio (LR) test statistic, based on this to construct a new panel unit root LR test statistic, under the local alternative hypothesis, we consider its local asymptotic properties and apply stochastic simulation experiments to study the corresponding finite sample properties compared with LLC and IPS tests, in addition, further study how the initial conditions affect the LR test.Chapter6, from the perspective of the null hypothesis, studies the impact of the initial conditions on the fixed coefficient panel data unit root LLC and IPS tests and random coefficient panel data unit root joint LM test, and analyzes their asymptotic properties and finite sample properties.Chapter7, summarizes the main contents of this paper and puts forward some future worthy of further study.The main contents of this paper include the following aspects:1. Panel data unit root test is one of the theoretical study hot spot in panel data model, and less literatures on the initial conditions which affects efficacy of the panel data unit root tests. This article summarizes the most relevant research of panel data unit root tests and the latest advances in this field, and describes some of the main findings in the current study, and points out some deficiencies, and so provides some ideas for future research studies.2. Effect of initial conditions on the fixed coefficient panel data unit root test power of LLC. On the basis of drawing on existing research, this paper, after adjusting the order of the initial conditions, derives the limiting distribution and local asymptotic limit power function of LLC test statistic under the alternative hypothesis, finds that the local asymptotical power of panel data unit root LLC test statistic is a monotonically increasing function of the initial conditions under the homogeneous alternative hypothesis; finite sample Monte Carlo simulation results show that if the initial conditions are assumed to be zero, then the power of panel data unit root LLC test statistics may be underestimated.3. Effect of initial conditions on the power of fixed coefficient panel data unit root IPS test. We derive asymptotic distribution and local asymptotic potential function of the IPS test statistic under the local alternative hypothesis, find the local asymptotical power of IPS test is a monotonically increasing function of the initial value under the local heterogeneity alternative hypothesis; finally finite sample Monte Carlo simulation results show that if the initial value is zero, the power IPS may be underestimated.4. Panel data unit root likelihood ratio (LR) test. Unlike the existing data on the study panel unit root tests using information of likelihood ratio test statistic, the starting point of this paper is that each individual unit root likelihood ratio test rather than the entire panel data statistic. By standardizing to get new test statistic, denoted panel data unit root LR test statistics. Under the local alternative hypothesis, we derives its asymptotic distribution, and stochastic simulation experiments reveals that the method performed well in a limited sample, and compared with IPS test, the size of LLC test is a more robust.5. Effect of initial conditions on the size of fixed coefficient and random coefficient panel data unit root test. As we all know, the commonly indicators to examine the efficacy of the test statistic are the power and size, it can be found from the study that we focus on the effect of initial conditions on the power of panel data unit root test only, however, as to whether the initial conditions will affect the size of panel data unit root has not been involved. If the initial conditions affect the panel data unit root test statistic distribution under the null hypothesis, then while still using the default asymptotic distribution to do statistical inference is feasible? On the one hand, we examine the impact of the initial conditions on the size of fixed coefficient panel data unit root LLC and IPS tests. Under the null hypothesis H0, i.e. there is unit root process in model, for a category initial value of data we compare the statistics of DF type IPS and LLC in panels, and we derive the asymptotic distributions for them, respectively. While the distribution of DF type LLC still converges in distribution to N(0,1), we find that the distribution of DF type IPS may be non-standard Gaussian, which means the property of DF type LLC test is more stable than IPS test statistic under the null hypothesis. The result of simulation for large sample demonstrates, if the initial value is assumed to be a variable uncorrelated with T and N, then it is ease to make error of the first kind when the asymptomatic distribution of DF type IPS moves left and error of the second kind under the distribution moving right. On the other hand, when initial condition zi0does not satisfy the Assumption of Westerlund and Larsson (2012), i.e. zi0≠Op(1), we mainly consider the joint LM testing for a unit root in a random coefficient panel data model proposed by Westerlund and Larsson (2012) and study the asymptotic distribution of the LM test statistic. We find the distribution of LM test has changed and is related with the initial condition zi0, therefor, which implies the LM test may be unstable. Monte Carlo simulation indicates that it is likely to lead to the LM test statistic size distortion, that is, the joint LM testing for a unit root in a random coefficient panel data model is unstable and could be affected by zi0easily, when the Assumption of their paper is not satisfied.In this paper, the initial conditions on the study of panel data unit root tests, we believe to be innovative in the following points:First, under the local alternative hypothesis, after the adjustment of the order of the initial conditions, when the initial conditions can not be asymptotic ignored, the asymptotic distribution, local asymptotic power and the limited nature of the sample of the fixed coefficient panel data unit root LLC and IPS test statistics, the results show that the initial conditions may affect the power of panel data unit root LLC and IPS tests, if initial conditions are assumed to zero, the power of the test will be underestimated.Second, because of inadequacies of the two test methods of LLC and IPS tests, panel data unit root LR test proposed attempts to compensate some of the deficiencies of LLC and IPS test. Relative to the panel data unit root LLC and IPS test panel when individual in panel data is explosive, panel data unit root test LR test has a higher power, and stochastic simulation results show that the size of panel data unit root LR test is more stable than that of LLC and IPS tests.Third, under the conditions of the null hypothesis, this paper studies the effect of initial conditions on the size of panel data unit root tests, the study shows that the initial conditions have an impact on size of panel data unit root tests, some of the unit root tests have serious szie distortions, that is if the original distribution is assumed and used to make statistical inference, the test results are not reliable.