面板数据非线性阈值协整的检验方法

非线性阈值协整是线性协整的后续发展。本文使用两机制TR模型对Westerlund和Edgerton(2005)的面板数据协整向量结构突变模型进行扩展,提出截距项具有阈值效应、截距项和斜率系数都具有阈值效应的面板数据非线性阈值协整模型。在此基础上,本文进而分别构造Zc、Ztc、Zr、Ztr统计量检验阈值协整,并对上述统计量的极限分布进行了数学推导,发现它们都收敛于随机泛函。仿真实验结果表明,有限样本下上述检验统计量具有较小的水平扭曲和较高的检验势。     

基于参数空间的ST-ECM模型的协整检验问题研究

在非线性平滑转移误差修正模型（ST-ECM）的协整检验中,由于存在未识别参数而使协整检验统计量构造困难,同时由于目前文献普遍使用的泰勒展开近似法并不能精确替代原始非线性模型,从而导致协整检验统计量功效较低。本文首先在遍历未识别参数的参数空间的基础上构造了ST-ECM模型协整检验的supF统计量,推导了supF统计量的极限分布并说明了其收敛性质。接着,蒙特卡洛仿真模拟结果显示,supF统计量在ST-ECM模型协整检验中具有良好的检验水平和功效,且supF统计量的功效明显优于EG统计量、F*NEC统计量和inft统计量。最后,本文对亚洲六个国家的利率期限结构预期假说进行了验证,结果表明中国、新加坡和泰国三个国家的利率期限结构预期假说成立且存在非线性调整效应,supF统计量较其他统计量具有更高的检验功效。     

平滑转移误差修正模型的转移函数选取问题研究

针对非线性平滑转移误差修正模型转移函数选取中存在的统计量极限分布非标准、检验统计量功效较低的问题,本文在推导非线性平滑转移协整检验统计量极限分布的基础上构造了如下转移函数选取步骤。首先,计算F_NST统计量,进行非线性平滑转移协整检验;其次,计算t_EST和t_LST统计量及相依概率P_est和P_lst;最后,比较P_est和P_lst大小并与临界值相比,得出结论。蒙特卡洛仿真模拟结果显示,转移函数选取中各统计量具有良好的功效和势,且转移函数选取中各统计量的功效明显优于其他统计量的功效。实证分析表明我国利率期限结构具有明显的非线性对称调整效应,非线性平滑转移误差修正模型中转移函数应该选取指数函数。     

协整向量、调节参数同为非线性的阈值协整检验

针对经济变量的长期均衡和短期调节关系可能同时存在非线性的事实,本文扩展现有阈值协整模型,提出了协整向量、调节参数都为非线性的阈值协整模型,并着重探讨了该模型的检验方法。研究表明,在协整关系的检验中,Wald统计量有较好的有限样本性质。在协整关系的非线性检验中,LMW和LMG统计量的水平扭曲和检验势都较好。在调节参数的非线性检验中,当调节参数具有显著的非线性时,LMH统计量表现出较好的有限样本性质。     

面板数据协整关系检验的一个简明蒙特卡洛实验框架

体现处于考察中的面板数据之问的样本关联性，本文设计出一个简明蒙特卡洛实验框架以生成单一方程式面板数据之间协整关系检验统计值之有限样本密度分布及对应临界值。本文的蒙特卡洛实验框架提供了一个简明的可操作平台，可以运用于涉及面板数据协整关系检验的相关实证研究。为检测所发展的计量分析方法的可操作性与适用性，本文给出了相关应用实例。     

基于结构突变和截面相关的面板协整检验

本文基于Westerlund和Edgerton（2008）,考虑了无时间趋势和有时间趋势的面板协整检验。在检验协整时,本文不仅允许误差项存在异方差、序列相关以及截面相关,而且还允许各截面在截距和协整斜率上存在未知时点的多个突变点。蒙特卡洛模拟结果表明,（1）该检验的具有较小的水平扭曲和较高的检验势,（2）将模型拓展到不含有趋势项的情形是必要的。在此基础上,使用基于动态最小二乘估计量的新统计量对国际CO2排放和经济增长关系进行检验,发现在考虑了突变和截面相关的情形下,两者间的长期均衡关系确实存在。     

关于机理变化型变结构非线性协整的研究

变结构非线性协整是协整理论发展的必然的趋势,也是经济系统复杂多变的必然需求,文章补充了变结构非线性协整的定义,并提出了机理变化型变结构非线性协整,指出其本质问题即单位根的结构突变检验,总结了几种结构突变的单位根检验方法,讨论了变结构点的估计方法,给出了基于Chow统计量的变结构协整检验和建模方法。     

Enders-Granger方法在协整检验中的应用研究

本文将协整检验由传统的线性协整检验扩展到线性协整检验和阈值协整检验,并在Enders和Granger(1998)方法的基础上提出了一个新的检验协整是否存在的Sup-F和Sup-F*统计量。通过MC仿真研究发现:在线性协整下,ADF方法比Sup-F法具有更高的检验势,但在"持久性"较强时,Sup-F检验比ADF检验法具有更高的检验势;Sup-F统计量在Three-Regime的阈值协整检验中比ADF法有更高的检验势;Sup-F*在检验协整(包括线性协整和阈值协整)时都具有较低的检验势;随着在不同Regime中自回归系数差距的增大(非对称程度增大),sup-F统计量的检验势提高很快,且比ADF法的检验势高。     

人民币实际汇率与中国进出口贸易结构变迁(1997～2007年)——基于多种模型的动态分析

为分析人民币实际汇率对中国进出口贸易结构变迁的影响,基于1997～2007年季度SITC二位数水平下的中国进出口贸易面板数据、人民币实际汇率和中国及其贸易伙伴GDP季节时序数据,本文对相关变量进行了异质面板和单时序季节单整和协整检验,并进一步构建异质面板季节误差修正模型,对人民币实际汇率对中国进出口贸易结构变迁的长短期动态影响进行了实证分析,并针对中国当前的对外经贸和宏观经济发展现状提出了相应的政策建议。     

初始条件对LLC检验局部渐近势的影响研究

本文研究了DF类面板数据单位根LLC检验势受时序数据初始值的影响,推导了DF类面板单位根LLC检验统计量在局部备择假设下的极限分布和局部渐近势函数,发现了面板数据单位根LLC检验统计量局部渐近势在同质性局部备择假设下是初始条件的单调递增函数;小样本蒙特卡罗模拟结果表明,若假定初始条件为零,LLC统计量的检验势将被低估。     

Testing for Error Correction in Panel Data*

This paper proposes new error correction‐based cointegration tests for panel data. The limiting distributions of the tests are derived and critical values provided. Our simulation results suggest that the tests have good small‐sample properties with small size distortions and high power relative to other popular residual‐based panel cointegration tests. In our empirical application, we present evidence suggesting that international healthcare expenditures and GDP are cointegrated once the possibility of an invalid common factor restriction has been accounted for.     

Panel cointegration tests of the Fisher effect

Most empirical evidence suggests that the Fisher effect, stating that inflation and nominal interest rates should cointegrate with a unit slope on inflation, does not hold, a finding at odds with many theoretical models. This paper argues that these results can be attributed in part to the low power of univariate tests, and that the use of panel data can generate more powerful tests. For this purpose, we propose two new panel cointegration tests that can be applied under very general conditions, and that are shown by simulation to be more powerful than other existing tests. These tests are applied to a panel of quarterly data covering 20 OECD countries between 1980 and 2004. The evidence suggest that the Fisher effect cannot be rejected once the panel evidence on cointegration has been taken into account. Copyright © 2007 John Wiley & Sons, Ltd.     

Savings and investments in the OECD, 1970–2007: A test of panel cointegration with regime changes

In this paper we test for the existence of a long-run relationship between investment and savings (the Feldstein–Horioka puzzle) in a panel of 18 OECD countries, 1970–2007, allowing for heterogenous breaks in the coefficients. For this purpose we develop a bootstrap panel cointegration with breaks robust to cross-section dependence, shown by simulation to enjoy good size and power properties provided that some care is applied in its use. The tests suggest that, even allowing for parameter shifts in the countries where capital control regulations changed in the sample period, there is no evidence of an investment–savings long-run relationship for the panel as a whole.     

Likelihood based testing for no fractional cointegration

We consider two likelihood ratio tests, the so-called maximum eigenvalue and trace tests, for the null of no cointegration when fractional cointegration is allowed under the alternative, which is a first step to generalize the so-called Johansen’s procedure to the fractional cointegration case. The standard cointegration analysis only considers the assumption that deviations from equilibrium can be integrated of order zero, which is very restrictive in many cases and may imply an important loss of power in the fractional case. We consider the alternative hypotheses with equilibrium deviations that can be mean reverting with order of integration possibly greater than zero. Moreover, the degree of fractional cointegration is not assumed to be known, and the asymptotic null distribution of both tests is found when considering an interval of possible values. The power of the proposed tests under fractional alternatives and size accuracy provided by the asymptotic distribution in finite samples are investigated.     

Cointegration Testing in Panels with Common Factors*

Panel unit‐root and no‐cointegration tests that rely on cross‐sectional independence of the panel unit experience severe size distortions when this assumption is violated, as has, for example, been shown by Banerjee, Marcellino and Osbat [Econometrics Journal (2004), Vol. 7, pp. 322–340; Empirical Economics (2005), Vol. 30, pp. 77–91] via Monte Carlo simulations. Several studies have recently addressed this issue for panel unit‐root tests using a common factor structure to model the cross‐sectional dependence, but not much work has been done yet for panel no‐cointegration tests. This paper proposes a model for panel no‐cointegration using an unobserved common factor structure, following the study by Bai and Ng [Econometrica (2004), Vol. 72, pp. 1127–1177] for panel unit roots. We distinguish two important cases: (i) the case when the non‐stationarity in the data is driven by a reduced number of common stochastic trends, and (ii) the case where we have common and idiosyncratic stochastic trends present in the data. We discuss the homogeneity restrictions on the cointegrating vectors resulting from the presence of common factor cointegration. Furthermore, we study the asymptotic behaviour of some existing residual‐based panel no‐cointegration tests, as suggested by Kao [Journal of Econometrics (1999), Vol. 90, pp. 1–44] and Pedroni [Econometric Theory (2004a), Vol. 20, pp. 597–625]. Under the data‐generating processes (DGP) used, the test statistics are no longer asymptotically normal, and convergence occurs at rate T rather than as for independent panels. We then examine the possibilities of testing for various forms of no‐cointegration by extracting the common factors and individual components from the observed data directly and then testing for no‐cointegration using residual‐based panel tests applied to the defactored data.     

Combination of Tests for Cointegration in Cross‐Correlated Panels

In this paper, Cheng and Sheng's (2017) combination of ‘combinations of P‐values’ (CCP) is extended to a combination of more than two tests and applied for cointegration testing in cross‐correlated panels. In a Monte Carlo experiment, power and size of the different combinations of combinations are investigated. If uncertainty about the panel configuration is taken into account, the results indicate that a multi‐test combination can minimize power losses. Furthermore, the usefulness of the combinations studied is illustrated by an application to international interest rate linkage. Cross‐sectional dependencies in both the simulation and the empirical studies are accounted for by using the block bootstrap.     

Cointegration in Panel Data with Structural Breaks and Cross‐Section Dependence

The power of standard panel cointegration statistics may be affected by misspecification errors if structural breaks in the parameters generating the process are not considered. In addition, the presence of cross‐section dependence among the panel units can distort the empirical size of the statistics. We therefore design a testing procedure that allows for both structural breaks and cross‐section dependence when testing the null hypothesis of no cointegration. The paper proposes test statistics that can be used when one or both features are present. We illustrate our proposal by analysing the pass‐through of import prices on a sample of European countries. Copyright © 2013 John Wiley & Sons, Ltd.     

Size and Power of the Error Correction Model Cointegration Test. A Bootstrap Approach

The size and power of the ECM cointegration test are investigated by using the 'bootstrap critical values'. The purpose of this paper is to show the ability of the bootstrap technique to produce critical values which are much more accurate than the asymptotic ones. The properties of the test have been studied, using Monte Carlo methods, for three different data generating processes. As regards the size of the test, we find that the ECM cointegration test together with the bootstrap critical values perform better than the ECM cointegration test based on the asymptotic critical values. While as regards the power of the tests, the results prove to be similar for the different versions.     

Testing cointegration relationship in a semiparametric varying coefficient model

In this paper, we develop two cointegration tests for two varying coefficient cointegration regression models, respectively. Our test statistics are residual based. We derive the asymptotic distributions of test statistics under the null hypothesis of cointegration and show that they are consistent against the alternative hypotheses. We also propose a wild bootstrap procedure companioned with the continuous moving block bootstrap method proposed in  Paparoditis and Politis (2001) and  Phillips (2010) to rectify severe distortions found in simulations when the sample size is small. We apply the proposed test statistic to examine the purchasing power parity (PPP) hypothesis between the US and Canada. In contrast to the existing results from linear cointegration tests, our varying coefficient cointegration test does not reject that PPP holds between the US and Canada.