Generalized long memory processes,failure of cointegration tests and exchange rate dynamics

This paper presents evidence that the equilibrium relationship in a system of nominal exchange rates is best described as a stationary GARMA process. The implementation of the GARMA methodology helps explain conflicting and puzzling results from the use of linear cointegration and fractional cointegration methods. Furthermore, we use Monte Carlo analysis to document problems with standard cointegration tests when the attraction process is distributed as a long memory GARMA process. Copyright © 2006 John Wiley & Sons, Ltd.     

Testing for cointegration using partially linear models

A partially linear model of cointegration is developed where stationary covariates enter nonparametrically. We propose tests for cointegration using singular values of the estimated autoregressive matrix. The tests are based on eigenvalues of standardized matrices and are relatively simple to compute. Asymptotic theory of the proposed test is developed. It is shown that the limiting distribution of the proposed test is similar to that of several tests in the recent literature. A Gamma approximation of the distribution is discussed to facilitate inference. Finite sample properties of the proposed procedure are illustrated in some limited Monte Carlo experiments. An empirical application to US macroeconomic time series is conducted to highlight the approach.     

股市理性泡沫的检验方法比较研究

首先在理性预期和无套利条件下得到理性泡沫模型;然后基于实证对理性泡沫的四种典型检验方法:方差界检验、设定检验、单位根和协整检验、内在性泡沫检验方法进行比较分析,并得出结论。     

Threshold Effects in Cointegrating Relationships*

In this paper, we introduce threshold‐type nonlinearities within a single‐equation cointegrating regression model and propose a testing procedure for testing the null hypothesis of linear cointegration vs. cointegration with threshold effects. Our framework allows the modelling of long‐run equilibrium relationships that may change according to the magnitude of a threshold variable assumed to be stationary and ergodic, and thus constitutes an attempt to deal econometrically with the potential presence of multiple equilibria. The framework is flexible enough to accommodate regressor endogeneity and serial correlation.     

Bootstrap testing for the null of no cointegration in a threshold vector error correction model

We develop a test for the linear no cointegration null hypothesis in a threshold vector error correction model. We adopt a sup-Wald type test and derive its null asymptotic distribution. A residual-based bootstrap is proposed, and the first-order consistency of the bootstrap is established. A set of Monte Carlo simulations shows that the bootstrap corrects size distortion of asymptotic distribution in finite samples, and that its power against the threshold cointegration alternative is significantly greater than that of conventional cointegration tests. Our method is illustrated with used car price indexes.     

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.     

Distribution approximations for cointegration tests with stationary exogenous regressors

The distribution of a functional of two correlated vector‐Brownian motions is approximated by a Gamma distribution. This functional represents the limiting distribution for cointegration tests with stationary exogenous regressors, but also for cointegration tests based on a non‐Gaussian likelihood. The approximation is accurate, fast and easy to use in comparison with both tabulated critical values and simulated p‐values. The proposed procedure is applied to a UK model investigating purchasing power parity. Copyright © 2005 John Wiley & Sons, Ltd.     

面板协整检验有限样本性质的模拟比较

面板协整检验是基于渐近分布的检验,有限样本下统计量的检验水平和检验功效的表现涉及检验的可靠性。本文针对目前实证研究中应用最广的一类基于残差的统计量及文献中最新提出的基于准残差的统计量进行蒙特卡罗模拟,比较10个检验统计量在不同DGP设定下的检验水平和检验功效,尤其是在DGP误设时的表现。模拟结果表明:基于准残差的面板协整检验大多数情况下有着更好的检验水平和检验功效表现。这一研究为解决实证中面临的统计量可靠性甄别与选择问题提供了依据。     

The Price-Wage Mechanism in Poland: An Endogenous Switching Model

This paper proposes a two-equation price-wage model that enables to test whether the inflationary pressure on wage rate is only present when the rate of inflation is greater than some threshold value. Since the likelihood function for this model is very nonstandard, we develop a small-sample Bayesian approach to estimate its parameters. Our empirical results for Poland, 1962–1993, give support to the hypothesis of the price- wage spiral with a positive threshold value of inflation. This revised version was published online in July 2006 with corrections to the Cover Date.     

Determining the cointegrating rank in nonstationary fractional systems by the exact local Whittle approach

We propose to extend the cointegration rank determination procedure of Robinson and Yajima [2002. Determination of cointegrating rank in fractional systems. Journal of Econometrics 106, 217–242] to accommodate both (asymptotically) stationary and nonstationary fractionally integrated processes as the common stochastic trends and cointegrating errors by applying the exact local Whittle analysis of Shimotsu and Phillips [2005. Exact local Whittle estimation of fractional integration. Annals of Statistics 33, 1890–1933]. The proposed method estimates the cointegrating rank by examining the rank of the spectral density matrix of the d$d$th differenced process around the origin, where the fractional integration order, d$d$, is estimated by the exact local Whittle estimator. Similar to other semiparametric methods, the approach advocated here only requires information about the behavior of the spectral density matrix around the origin, but it relies on a choice of (multiple) bandwidth(s) and threshold parameters. It does not require estimating the cointegrating vector(s) and is easier to implement than regression-based approaches, but it only provides a consistent estimate of the cointegration rank, and formal tests of the cointegration rank or levels of confidence are not available except for the special case of no cointegration. We apply the proposed methodology to the analysis of exchange rate dynamics among a system of seven exchange rates. Contrary to both fractional and integer-based parametric approaches, which indicate at most one cointegrating relation, our results suggest three or possibly four cointegrating relations in the data.     

The long-run relationship between private and public savings: An empirical note

This empirical note extends the recent work by Holmes (2006) in examining the long-run relationship between private and public savings in the U.S. over the post-World War II period. Standard Engle-Granger cointegration tests fail to reject the null hypothesis of no cointegration; however, once allowance is made for an endogenous break in the cointegrating relationship, the weak form of the Ricardian equivalence proposition is supported.     

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。     

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.     

A review of Phillips-type right-tailed unit root bubble detection tests

Recent developments on the right-tailed unit root tests of Phillips et al., which are used to date stamp the origination and collapse dates of asset price bubbles, have generated considerable interest. This paper provides a review for both empirical researchers that adopt these new econometric tools to detect the presence of asset price bubbles, and theoretical papers that extend these testing procedures. This paper also uses the psymonitor package in R to demonstrate the practical use of such tests using an example based on data for British Railway Mania of the 1840s.     

Prices,wages, and import prices in Israel: 1970–1983

This paper presents an empirical investigation of the dynamics of prices, wages and import prices in a small open economy using data for Israel in the accelerating inflationary period of 1970–1983. The appropriateness of the specification of a price equation as a function of import prices and wages is critically reviewed using Sims's methodology. The main finding is that the only significant lags in the representation of the rate of change in prices, wages and import prices are the lags of the rate of change in prices (the rate of inflation). Other factors in the representation are attributed to market forces influencing real wages and the real exchange rate. Testing the correlation of the estimated VAR residuals leads to the conclusion that a short-term inflation equation specified as a function of present and past wages is not acceptable. A further decomposition of the VAR residuals presents evidence in favour the hypothesis that price shocks contribute to the explanation of the inflationary process in Israel. A rational expectation interpretation of the results is proposed, followed by some policy implications.     

On the cointegration of international stock indices

This paper investigates the cointegration relationship among a group of international stock indices in light of new developments of econometric methods. Kasa (1992) first documented strong evidence for cointegration relations among five national stock indices, which suggests that there exists a common trend among those stock indices. Using Johansen multivariate cointegration test, we find that his findings are persistent in a sample of longer periods and more countries. In order to investigate whether these results are driven by statistical biases related to the sample size, we apply to our tests the Johansen’s small sample correction factor. The results still point toward the existence of a cointegration relationship but the evidence becomes much weaker. We next examine the empirical patterns emerged from different lag specifications and argue that Kasa’s findings are more likely due to the size distortion in extreme long lag VAR models. Indeed, when we employ a newly developed non-parametric test that does not require estimation VAR models, the null hypothesis of no cointegration cannot be rejected for the original sample of Kasa’s five-country stock indices from 1974 to 1990, nor for the extended period from 1970 to 2003.     

Credit in the euro area: An empirical investigation using aggregate data

This paper uses multivariate cointegration techniques to estimate a model of aggregate bank lending in the euro area. The model provides a quantitative benchmark for assessing conjunctural developments in loans to the area-wide private sector. Large and protracted deviations of realised loans from the paths implied by the model may reveal information about the emergence of financial imbalances as well as about the state of the economy, particularly about the strength of inflationary pressures. A specific application of the model shows that its error-correction term contains information on future changes in inflation over forecast horizons of relevance for monetary policy.     

On forecasting cointegrated seasonal time series

We analyze periodic and seasonal cointegration models for bivariate quarterly observed time series in an empirical forecasting study. We include both single equation and multiple equation methods for those two classes of models. A VAR model in first differences, with and without cointegration restrictions, and a VAR model in annual differences are also included in the analysis, where they serve as benchmark models. Our empirical results indicate that the VAR model in first differences without cointegration is best if one-step ahead forecasts are considered. For longer forecast horizons however, the VAR model in annual differences is better. When comparing periodic versus seasonal cointegration models, we find that the seasonal cointegration models tend to yield better forecasts. Finally, there is no clear indication that multiple equations methods improve on single equation methods.     

Asymmetry and nonstationarity for a seasonal time series model

Tests for symmetry and seasonal unit roots are developed for an extended model of Hylleberg et al. (1990. Seasonal integration and cointegration. Journal Econometrics 44, 215–238.) which can represent both partial seasonal unit roots and threshold effects. Methods based on ordinary least squares (OLS) estimation and instrumental variable (IV) estimation are proposed and compared. For adjusting mean functions, ordinary mean adjustment and recursive mean adjustment are both considered. Several tests are constructed from various combination of estimation schemes and mean adjustment schemes. Among the tests, the tests based on IV-estimation are recommended because they have very simple limiting null distributions and have finite sample power properties comparable to those based on the OLSE. The recommended tests are applied to a US unemployment rate data set and find evidences for both nonstationarities associated with zero frequency and threshold effects.