非平稳面板数据的非线性共同周期检验

经济变量的协同波动是学术界、宏观政策制定者长期关注的重要问题,本文将时间序列数据的共同周期检验方法扩展至面板数据,提出非平稳面板数据的非线性共同周期检验方法。本文根据数据特征,将共同周期划分为强降秩结构共同周期和弱降秩结构共同周期,分别在强降秩结构数据和弱降秩结构数据中提出共同周期检验统计量,并提出区分强降秩结构数据和弱降秩结构数据的统计量。研究结果表明,本文检验统计量的极限分布都是卡方分布,并且各检验统计量都表现出良好的有限样本性质,因此,本文提出的非平稳面板数据的非线性共同周期检验方法具有较高的实用性。     

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.     

PRACTITIONERS CORNER: Tests for Cointegration in Models with Regime and Trend Shifts

ABSTRACT Recently Gregory and Hansen (1996) proposed a number of residual-based tests for cointegration in models with the possibility of a structural break. They considered three models: (i) level shift; (ii) level shift with trend; and (iii) regime shift (both level shift and slope coefficients can change). We introduce a more general model that permits a trend shift as well as a regime shift and we provide the critical values appropriate for testing this hypothesis.     

Variance Decomposition Analysis for Nonlinear Economic Models1

In this paper, we propose a new method called the total variance method and algorithms to compute and analyse variance decomposition for nonlinear economic models. We provide theoretical and empirical examples to compare our method with the only existing method called generalized forecast error variance decomposition (GFEVD). We find that the results from the two methods are different when shocks are multiplicative or interacted in nonlinear models. We recommend that when working with nonlinear models researchers should use the total variance method in order to see the importance of indirect variance contributions and to quantify correctly the relative variance contribution of each structural shock.     

Density Forecasts With Midas Models

We propose a parametric block wild bootstrap approach to compute density forecasts for various types of mixed‐data sampling (MIDAS) regressions. First, Monte Carlo simulations show that predictive densities for the various MIDAS models derived from the block wild bootstrap approach are more accurate in terms of coverage rates than predictive densities derived from either a residual‐based bootstrap approach or by drawing errors from a normal distribution. This result holds whether the data‐generating errors are normally independently distributed, serially correlated, heteroskedastic or a mixture of normal distributions. Second, we evaluate density forecasts for quarterly US real output growth in an empirical exercise, exploiting information from typical monthly and weekly series. We show that the block wild bootstrapping approach, applied to the various MIDAS regressions, produces predictive densities for US real output growth that are well calibrated. Moreover, relative accuracy, measured in terms of the logarithmic score, improves for the various MIDAS specifications as more information becomes available. Copyright © 2016 John Wiley & Sons, Ltd.     

Generalized Forecast Error Variance Decomposition for Linear and Nonlinear Multivariate Models

We propose a new generalized forecast error variance decomposition with the attractive property that the proportions of the impact accounted for by innovations in each variable sum to unity. Our decomposition is based on the generalized impulse response function, and it can easily be obtained by simulation. The new decomposition is illustrated in an empirical application to US output growth and interest rate spread data.     

Cointegration in a macroeconomic system

This paper investigates the long-run relationships within a set of six quarterly time-series on the Austrian economy by means of cointegration. After analysing the univariate properties, especially with respect to the appropriate seasonal filter, the maximum-likelihood method proposed by Johansen (1988) is applied to estimate and test the cointegrating relationships. We found three such relations, implying that the system is driven by three independent stochastic time trends. In a next stage we investigate whether the empirically determined cointegrating relationships are compatible with implications derived from the neoclassical growth model with exogenous stochastic technical progress. It is found that the Austrian data strongly reject the propositions that the real interest rate and the log ratios of consumption to output, investment to output, and the real gross wage sum to output are stationary.     

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。     

Cointegration in a historical perspective

We analyse the impact of the Engle and Granger (1987) article by means of its citations over time, and find evidence of a second life starting in the new millennium. Next, we propose a possible explanation of the success of this citation classic. We argue that the conditions for its success were just right at the time of its appearance, because of the growing emphasis on time series properties in econometric modelling, the empirical importance of stochastic trends, the availability of sufficiently long macroeconomic time series, and the availability of personal computers and econometric software for carrying out the new techniques.     

Trends and Cycles in GDP

The recent experience in the UK of substantial growth in GDP following the recession of the early 1980s has led to renewed interest in the measurement and explanation of business cycles. Development of economic as well as econometric theory has improved our ability both to measure the cycle more accurately and to offer a better explanation of its behaviour. In this Briefing Paper we present an analysis of these two developments.     

Cointegration and distance between differenced processes

In this note, it is argued that cointegration augments the distance between the differenced series. If two series, x _t and y _t , are integrated of order one and cointegrated and v _t and w _t are integrated of order one but not cointegrated then, under certain conditions, the distance between ??x _t and ??y _t is more than the distance between ??v _t and ??w _t .     

Cointegration and models of exchange rate determination

The application of new techniques in testing for cointegration indicate the inappropriate- ness of the pure monetary model to explain movements in the nominal exchange rate. In general the fundamental variables are found to be integrated of different orders and there is a lack of cointegration between the exchange rate variables in the monetary model and relative prices. Estimation of other dynamic models are found to give rise to parameter estimates which do not support the monetary model. The results are broadly consistent across five countries. These results imply that it is not worthwhile to forecast from the monetary model and its main variants.     

Bias Reduction in Dynamic Panel Data Models by Common Recursive Mean Adjustment*

The within‐group estimator (same as the least squares dummy variable estimator) of the dominant root in dynamic panel regression is known to be biased downwards. This article studies recursive mean adjustment (RMA) as a strategy to reduce this bias for AR(p) processes that may exhibit cross‐sectional dependence. Asymptotic properties for N,T→∞ jointly are developed. When ( log ²T)(N/T)→ζ, where ζ is a non‐zero constant, the estimator exhibits nearly negligible inconsistency. Simulation experiments demonstrate that the RMA estimator performs well in terms of reducing bias, variance and mean square error both when error terms are cross‐sectionally independent and when they are not. RMA dominates comparable estimators when T is small and/or when the underlying process is persistent.     

Inference of Seasonal Cointegration: Gaussian Reduced Rank Estimation and Tests for Various Types of Cointegration*

An extension of Gaussian reduced rank estimation of Ahn and Reinsel (Journal of Econometrics, Vol. 62, pp. 317–350, 1994) to seasonal periods other than four is presented. Simple adjustments for estimation that are necessary because of complex‐valued seasonal unit roots are presented in detail and the asymptotic distribution of the estimators that takes the same form as that in Ahn and Reinsel (1994) is derived. Tests for contemporaneous cointegration and common polynomial cointegrating vectors (PCIVs) for different seasonal unit roots are presented. Finite sample properties are briefly examined through a small Monte Carlo simulation study and a numerical example is presented to illustrate the methods.     

Testing for Unit Roots and Cointegration in Spatial Cross-Section Data

Abstract

Spatial impulses are derived for SAR models containing a spatial unit root. Analytical solutions are obtained for lateral space where the number of spatial units tends to infinity. Numerical solutions are obtained for finite regular lattices where edge-effects are shown to influence spatial impulses, and for irregular lattices. Monte Carlo simulation methods are used to compute critical values for spatial unit root tests in SAR models estimated from spatial cross-section data for regular and irregular lattices. We also compute critical SAC values for spatial cointegration tests for cross-section data that happen to be spatially nonstationary. We show that parameter estimates in spatially cointegrated models are ‘superconsistent’.

RÉSUMÉ On dérive des impulsions spatiales de modèles SAR contenant une racine unité spatiale. On obtient des solutions analytiques pour l'espace latéral lorsque le nombre d'unités spatiales tend vers l'infini. On obtient des solutions numériques pour des réseaux réguliers finis, où l'on relève l'influence d’«?edge effects?» sur les impulsions spatiales, et pour des réseaux irréguliers. Des méthodes de simulation Monte Carlo sont utilisées pour calculer des valeurs critiques pour des tests de racine unité spatiale dans des modèles SAR estimés sur la base de données transversales spatiales pour réseaux réguliers et irréguliers. Nous calculons également des valeurs critiques de SAC pour essais de co-intégration spatiale, concernant des données transversales qui s'avèrent être spatialement non stationnaires. Nous démontrons que les estimations de paramètres dans des modèles spatialement co-intégrés sont «?ultra cohérentes?».

EXTRACTO Se derivan impulsos espaciales para modelos SAR que contienen una raíz unitaria espacial. Se obtienen soluciones analíticas para espacio lateral donde el número de unidades espaciales tiende al infinito. Se obtienen soluciones numéricas para retículos finitos regulares que demuestran que los efectos de borde influyen sobre los impulsos espaciales, así como para retículos irregulares. Se utilizan métodos de simulación de Monte Carlo para computar valores críticos destinados a las pruebas espaciales de raíces unitarias en modelos SAR, estimados a partir de datos espaciales de corte transversal para retículos regulares e irregulares. También computamos valores SAC críticos destinados a pruebas de cointegración espacial para datos de corte transversal que no son espacialmente estacionarios. Mostramos que las estimaciones de parámetros en modelos espacialmente cointegrados son ‘superconsistentes’.

     

自举法与协整参数的FMOLS估计

考虑静态和动态两类数据生成过程,利用蒙特卡罗模拟方法,从估计偏差、实际检验水平和检验功效三个方面对FMOLS(Full Modified Ordinary Least Square)估计的渐近分析和自举分析进行全面比较.结果表明,与渐近分析相比,自举分析可以减小实际检验水平对名义水平的偏差,但要以检验功效的降低为代价.严格意义上,自举分析是降低了"拒真"错误出现的概率.相对稳健的选择是结合两方面的信息,渐近检验通过则接受原假设,自举检验拒绝则接受备择假设,对于其他情况,具体结论取决于人们的研究态度.     

The Environmental Kuznets Curve,Cointegration and Nonlinearity

This paper clarifies some conceptual shortcomings of the empirical environmental Kuznets curve (EKC) literature that arise because of the hitherto inadequate application of unit root and cointegration techniques. The literature to date has ignored the fact, and a fortiori the consequences, that powers of integrated processes are themselves not integrated processes. The paper explains why standard methods should not be applied and discusses some recently proposed viable estimation and testing approaches for cointegrating polynomial regressions. The application to CO₂ and SO₂ emissions data shows that using appropriate methods leads to strongly reduced evidence for a cointegrating EKC compared to typical but conceptually not sound findings. Copyright © 2014 John Wiley & Sons, Ltd.