摘要
基于综列数据的单位根和协整分析,不仅有助于改善检验的有限样本性质和提高检验势,而且能够反映个体特征和经济关系的内在结构特征。综列数据各截面单元之间大多存在或强或弱的相关性,但现有的第一代综列单位根检验都是基于截面不相关假定的,第二代基于截面相关假定的检验要么对截面之间的相关性有特殊的假定,要么在相关性较强时存在严重的分布扭曲,从而缺乏普适性。综列协整可以基于残差的平稳性也可以基于综列向量误差纠正模型(PVECM)来检验。但基于残差的综列协整检验无法考察多个协整向量的情形,并且无法考察截面单元之间的长期均衡关系和短期动态调整之间的相互影响。Groen和Kleibergen(2003)建立了基于PVECM综列协整检验的基本分析框架,但其模型受到各截面单元变量之间不能存在协整关系的约束。所以,在全面系统地分析现有综列单位根和综列协整检验的优点以及局限性的基础上,本文对现有检验方法进行了有效的修正和扩展。
就综列单位根而言,本文的主要目的是在对现有检验统计量进行修正的基础上,建立对截面相关具有普适性的新的检验方法。首先,由于Maddala和Wu(1999)以及Choi(2001)的联合p值检验中包含了从t检验值到其p值的非线性变换,从而大大减弱了截面单元之间的相关性,所以,本文构造了基于ADF检验的联合p值检验统计量,并考察其在截面弱相关下的有限样本性质和检验势。仿真结果显示,该检验在截面单元弱相关时仍有良好的表现;其次,Chang(2002)提出用非线性工具变量估计来消除截面单元之间的相关性并实现检验统计量的正态性,但本文的研究显示Chang(2002)的SN检验仅适用于截面单元之间的相关性非常弱的情形,并且在含确定性趋势时是有偏的,本文首先基于仿真实验结果对检验统计量的有偏性进行了修正,使其可以被用于含截距和时间趋势的综列数据,大大扩展了该检验的应用范围。进而,鉴于现有检验在截面相关下的表现均差强人意,本文结合SUR型的可行广义最小二乘(FGLS)估计和非线性工具变量(NIV)估计,建立了广义非线性工具变量(GNIV)检验统计量;即通过FGLS来消除截面单元之间的相关性,进而通过NIV估计来保证估计的一致性,从而得到不受截面相关性影响并且渐近分布为标准正态分布的GNIV检验统计量。仿真结果显示,GNIV检验在截面不相关、弱相关、中等程度相关、直至强相关设定下均有良好的有限样本性质和较高的检验势,显著优于Chang(2002)的SN检验、Pesaran(2003)的CIPS检验、以及Levin,Lin和Chu(2002)的LLC检验。
就综列协整而言,鉴于基于残差的综列协整检验存在诸多的局限性,本文主要考察基于PVECM的综列协整检验。首先,Groen和Kleibergen(2003)并没有给出其有约束综列协整检验的具体临界值,而其检验统计量的极限分布为布朗运动随机积分的泛函形式,临界值问题严重制约了该检验方法在实证分析中的应用。本文通过大规模的仿真实验给出了该检验统计量在各种设定形式下的临界值,显著提高了该检验的实际应用价值。其次,由于截面单元之间的相互影响是普遍存在的,本文基于Johansen(1988,1991,1995)的似然比检验,通过混合各截面单元的变量(并不是混合各截面单元的数据)来引入各截面单元之间的协整关系和动态调整的相互影响,在无约束假定下提出了基于PVECM的似然比检验统计量。由于该无约束模型的待估参数个数依截面单元个数快速增加,根据似然比检验统计量渐近分布的临界值进行判定将是不可靠的,所以,本文提出了基于bootstrap仿真的似然比检验程序,并通过小规模的仿真实验考察了其在有限样本下的表现。
最后,作为综列单位根和综列协整的应用,本文分别以我国工业能源消费、人民币均衡汇率、我国证券市场的弱有效性作为研究对象,从基于残差的综列协整分析、基于PVECM的综列协整分析、和单独应用综列单位根检验分析实际经济问题三个方面,为综列单位根和综列协整对我国的应用性研究提供了完整的范例。为全面反映不同检验技术在实证分析中的应用,工业能源消费分析所采用的是现有的McCoskey和Kao(1998)的LM综列协整检验、我们新提出的GNIV综列单位根检验和Im, Pesaran和Shin (2003)的IPS检验;而人民币均衡汇率分析则根据本文的方法论研究成果,采用了Groen和Kleibergen(2003)的综列协整检验和我们所提出的修正的SN综列单位根检验;证券市场弱有效性研究采用联合p值检验和我们的GNIV检验。研究结果显示,工业各主要行业能源消费和行业经济增长之间、人民币对美元和日元的实际汇率与基本经济要素之间均存在长期稳定的均衡关系,我国证券市场在总体上具备弱有效性的特征。
The panel unit root and panel cointegration analysis can not only improve the finite sample size and test power, but also provides more information about the individuals and that between each other. It is well known that cross-sectional dependency must be considered in most panel data, but the first-generation panel unit root tests are based on the cross-sectional independency. The second-generation panel unit root tests are either based on the special specification for the cross-sectional dependency, or characterized by serious size distortion when the dependency is strong. Panel cointegration test can be achieved based on the residuals or on the panel vector error correction model (PVECM). The panel cointegration test based on residuals is not valid for cases with more than one cointegration vectors, and does not allow for the interaction of short-run dynamics and cointegration relationship among individuals. Groen and Kleibergen (2003) proposed the panel cointegration test based on PVECM, but it also suffer from the assumption that there is no cointegration between individuals. Based on the comprehensive analysis of the current literature on panel unit root tests and panel cointegration tests, some existing tests are modified or developed, and some new test statistics are provided
In view of the panel unit root test, one purpose of this paper is to construct the new test for panel data with general cross-sectional dependency by modifying or developing the existing tests. The combing p-value test by Maddala and Wu (1999) and Choi(2001)employs the nonlinear transformation from the t-statistics to its p-value, and then the cross-sectional dependency is weakened significantly. Therefore, the combing p-value test based on ADF statistic can be extended to panel data with weak cross-sectional dependency, and the simulation result argues for its wonderful performances. Chang (2002) suggests removing the cross-sectional dependency and ensuring the asymptotic standard normality of her test statistic by using the nonlinear instrumental variables. However, we found that her SN test can only be used for panel with very weak cross-sectional dependency and would become biased when determinant component is included. To expand its application, the SN test has been modified based on our simulation results. For the lower power of the existing test in panel data with cross-sectional dependency, finally, we combined the SUR type feasible GLS and Nonlinear Instrumental variable (NIV) estimator to construct the generalized NIV (GNIV) test statistic available for panel data with none, weak, moderate or even strong cross-sectional dependency, where the FGLS is for removing the cross-sectional dependency and the NIV is for bringing about the consistent estimates. the simulation result offered the evidence that the GNIV test is superior to the SN test by Chang (2002), the CIPS test by Pesaran(2003)and the LLC test by Levin, Lin and Chu (2002).
In view of panel cointegration, for the limitations of panel cointegration tests based on residuals, this paper focus most attention on the PVECM based. Firstly, Groen and Kleibergen (2003) have not proposed the critical values for their test statistics with asymptotic distribution as the functional of Brown motion, which would hamper its application. This paper provided those critical values under varied setting based on a set of simulation to enable the test in applications. Secondly, since the interaction among individuals is popular, we pooled the variables (not pooled data) in different cross-sectional units to include the cointegration relationship among individuals, and then constructed the panel likelihood ratio (LR) test statistics based on Johansen (1988,1991,1995). However, the number of parameters to be estimated for such a test would increase with a rate N, the number of the cross-sectional units, so the critical values obtained from the asymptotic distribution cannot be used in finite sample. To solve such a problem, we propose a LR test produce based on the bootstrap simulation, and then investigate the performance of the test based on bootstrap procedure by a small-scale simulation design.
Finally, as the examples of empirical study employing panel cointegration test based on residuals, panel cointegration test based on PVECM, or panel unit root test only, respectively, the energy consumption of Chinese industries, Renminbi real equilibrium exchange rate, and weak effectiveness of Chinese securities market are investigated based on panel data. To show how the different test techniques are carried out, the example of energy consumption is based on LM panel cointegration test by McCoskey and Kao (1998),our GNIV test and the IPS panel unit root test by Im, Pesaran and Shin (2003). While, Renminbi real equilibrium exchange rate is discussed based on panel cointegration test by Groen and Kleibergen (2003) and our modified SN panel unit root test. To test the weak effectiveness of Chinese securities market, the combing p-value test and our GNIV test are employed. The analysis result implies the existence of the long-run equilibrium relationship between energy consumption and growth in industries, and between Renminbi real exchange rates and the fundamental economic factors; evidence for weak effectiveness of Chinese securities market is also observed.
引文
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