Recent Developments in Modelling Nonstationary Vector Autoregressions

In this paper we review some recent developments in the modelling of nonstationary vector autoregressions (VARs) which we feel have great potential for furthering applied researchers understanding of the relationships linking the variables making up a VAR. The developments surveyed are the use of model determination criteria in selecting lag length, trend order and cointegrating rank, causality testing in vector error correction models, FM-VAR estimation of levels VARS, common trends and cycles analysis, permanent and transitory decompositions, impulse response asymptotics, and the links between cointegrated VARs and structural models. The techniques are illustrated by applications to the modelling of U.K. equities, dividends and interest rates.     

Mixed Causal–Noncausal Autoregressions: Bimodality Issues in Estimation and Unit Root Testing1

This paper stresses the bimodality of the likelihood function of the Mixed causal–noncausal AutoRegressions (MAR), and it is shown that the bimodality issue becomes more salient as the causal root approaches unity from below. The consequences are important as the roots of the local maxima are typically interchanged, attributing the noncausal component to the causal one and vice‐versa. This severely changes the interpretation of the results, and the properties of unit root tests of the backward root are adversely affected. To circumvent the bimodality issue, this paper proposes an estimation strategy which (i) increases noticeably the probability of attaining the global MLE; and (ii) selects carefully the maximum used for the unit root test against a MAR stationary alternative.     

Tests of Predictive Ability for Vector Autoregressions Used for Conditional Forecasting

Many forecasts are conditional in nature. For example, a number of central banks routinely report forecasts conditional on particular paths of policy instruments. Even though conditional forecasting is common, there has been little work on methods for evaluating conditional forecasts. This paper provides analytical, Monte Carlo and empirical evidence on tests of predictive ability for conditional forecasts from estimated models. In the empirical analysis, we examine conditional forecasts obtained with a VAR in the variables included in the DSGE model of Smets and Wouters (American Economic Review 2007; 97 : 586–606). Throughout the analysis, we focus on tests of bias, efficiency and equal accuracy applied to conditional forecasts from VAR models. Copyright © 2016 John Wiley & Sons, Ltd.     

Testing for Granger Causality in Moments

In this paper, we consider a generalized approach which is flexibly applicable to testing Granger causality in various moments and in both the full‐sample and out‐of‐sample contexts. We further use this approach to establish a class of cross‐correlation tests for financial time series analysis, and show the advantages of this class of tests in unifying and generalizing Box–Pierce‐type Granger causality tests. We also conduct a Monte Carlo simulation to show the validity of our tests, and provide an empirical example to demonstrate the flexibility of our tests in exploring various types of Granger causality.     

Interpretation of Cointegrating Coefficients in the Cointegrated Vector Autoregressive Model*

Regression coefficients are interpreted by a counterfactual experiment. For simultaneous equations this experiment can be implemented if the coefficients are identified, and throws some light on the role of instruments and the method of indirect least squares. This paper discusses another counterfactual experiment in the vector autoregressive model in order to interpret the coefficients of an identified cointegrating relation. The dynamics of the model is used to implement a long‐run change by changing the current values. The counterfactual experiment can be conducted precisely when the cointegrating relation is identified.     

General‐to‐Specific Model Selection Procedures for Structural Vector Autoregressions*

Structural vector autoregressive (SVAR) models have emerged as a dominant research strategy in empirical macroeconomics, but suffer from the large number of parameters employed and the resulting estimation uncertainty associated with their impulse responses. In this paper, we propose general‐to‐specific (Gets) model selection procedures to overcome these limitations. It is shown that single‐equation procedures are generally efficient for the reduction of recursive SVAR models. The small‐sample properties of the proposed reduction procedure (as implemented using PcGets) are evaluated in a realistic Monte Carlo experiment. The impulse responses generated by the selected SVAR are found to be more precise and accurate than those of the unrestricted VAR. The proposed reduction strategy is then applied to the US monetary system considered by Christiano, Eichenbaum and Evans (Review of Economics and Statistics, Vol. 78, pp. 16–34, 1996) . The results are consistent with the Monte Carlo and question the validity of the impulse responses generated by the full system.     

Estimation Bias and Inference in Overlapping Autoregressions: Implications for the Target‐Zone Literature*

Samples with overlapping observations are used for the study of uncovered interest rate parity, the predictability of long‐run stock returns and the credibility of exchange rate target zones. This paper quantifies the biases in parameter estimation and size distortions of hypothesis tests of overlapping linear and polynomial autoregressions, which have been used in target‐zone applications. We show that both estimation bias and size distortions of hypothesis tests are generally larger, if the amount of overlap is larger, the sample size is smaller, and autoregressive root of the data‐generating process is closer to unity. In particular, the estimates are biased in a way that makes it more likely that the predictions of the Bertola–Svensson model will be supported. Size distortions of various tests also turn out to be substantial even when using a heteroskedasticity and autocorrelation‐consistent covariance matrix.     

Testing Granger Causality in the presence of threshold effects

This paper proposes a Granger Causality test allowing for threshold effects. The proposed test can be conducted on the basis of the threshold autoregressive distributed lag model or the augmented logistic smooth transition autoregressive model. The proposed test is applied to the U.S. civilian unemployment rate, and it is shown that real investment, real GDP and real interest rate are helpful for improving the in-sample fit of unemployment.     

Confidence Sets for the Break Date in Cointegrating Regressions

In this paper, we propose constructing confidence sets for a break date in cointegrating regressions by inverting a test for the break location, which is obtained by maximizing the weighted average of power. It is found that the limiting distribution of the test depends on the number of I(1) regressors whose coefficients sustain structural change and the number of I(1) regressors whose coefficients are fixed throughout the sample. By Monte Carlo simulations, we then show that compared with a confidence interval developed by using the existing method based on the limiting distribution of the break point estimator under the assumption of the shrinking shift, the confidence set proposed in the present paper has a more accurate coverage rate, while the length of the confidence set is comparable. By using the method developed in this paper, we then investigate the cointegrating regressions of Russian macroeconomic variables with oil prices with a break.     

基于分组的异方差检验和两阶段估计

本文提出了一种基于分组的异方差检验法，并给出了存在异方差时的两阶段估计。     

似无关动态协整模型中的水平扭曲与校正

本文在解析似无关动态协整模型及其动态最小二乘估计的基础上,从理论上揭示了关于协整参数的假设检验存在严重的水平扭曲,即对协整参数约束的Wald检验统计量的渐近卡方分布存在严重的有限样本扭曲。进一步,本文应用自举抽样技术对水平扭曲进行了有效校正。基于本文的发现,我们建议在对似无关动态协整模型中的参数进行假设检验时,为保证结论的准确性,应使用自举抽样推断技术产生统计量值并由此来形成检验结论。     

存在自相关时自回归模型的估计和检验

讨论存在自相关情况下自回归模型中随机解释变量的内生性,指出目前的计量经济理论所存在的问题,证明了随机误差存在自相关情况下一阶自回归模型和高阶自回归模型的随机解释变量与随机误差都不相关,同时改进了自回归模型的估计和检验方法。     

Causality in qualitative and quantitative research

We are flooded with a wave of writings on causality in the social sciences during the last decades. The same holds for the relationship between quantitative and qualitative research in the social sciences. An enormous amount of texts appears on (causality in) qualitative research, mostly in a controversy with quantitative research. These writings induced us to develop the thesis of “unity in diversity”, i.e., that there is no difference “in principle” between causality in qualitative and quantitative research, because both are supported by what I will call an “experimental logic”. In developing this thesis a plea is being made for going back to the sources. A historical overview of theories of causality is presented, which develops into two prominent views: INUS-causation and causal realism. A historical framework is also outlined for the opposition between quantitative and qualitative research, in which French positivism and British empiricism are opposed to German neo-kantianism and neo-hegelianism. After having developed the thesis of “unity in diversity” for this historical framework, the same is being done for the recent literature: “mixed methods research”, the book DSI of KKV, the reactions of David Collier and “QCA” of Charles Ragin. At the end the question of small-n research and the case n = 1 is examined.     

中国三大都市圈经济增长趋于收敛还是发散?——基于协整分析和Granger因果检验

本文采用Engle和Granger(1987)提出的协整检验方法和Im、Pesaran和Shin(1997)的方法,从时间序列分析角度入手,研究目标是在不同的空间尺度上(全国和三大都市圈),从不同的时间尺度上揭示中国区域经济差异的演化规律。探索改革开放以来三大都市圈区域经济不平衡程度的演化历程与变化趋势。主要结论:长三角和珠三角具有收敛趋势而环渤海都市圈内不存在收敛;三大都市圈之间不存在收敛趋势,在长期受两个共同冲击的影响。     

Exponential Tilting with Weak Instruments: Estimation and Testing*

This article analyses exponential tilting estimator with weak instruments in a nonlinear framework. Our paper differs from the previous literature in the context of consistency proof. Tests that are robust to the identification problem are also analysed. These are Anderson–Rubin and Kleibergen types of test statistics. We also conduct a simulation study wherein we compare empirical likelihood and continuous updating‐based tests with exponential tilting (ET)‐based ones. The designs involve GARCH(1,1) and contaminated structural errors. We find that ET‐based Kleibergen test has the best size among these competitors.     

物流系统中一类向量优化问题弱有效解集非空紧性的刻画与研究

向量优化问题在物流系统中有着广泛的应用,在向量优化问题中,决策者为了选择一个“最好的”可行方案,需要综合考虑各个目标因素。由于向量优化问题的解和决策者的偏好紧密联系,所以最优解的概念在这里是没有意义的。通常研究的是有效解和弱有效解。它们和决策者的控制结构密切相关。文章研究了当目标空间的控制结构为多面体锥时,锥约束凸向量优化问题的弱有效解集的非空紧性的各种刻画,从而为向量优化问题计算方法的发展提供了很好的理论基础。     

Statistical Causality and Strategic Behavior in Industrial Markets

This paper proposes a simple test of the leader-follower model of strategic behavior. This test relates the temporal notions of leadership central to such models to the empirical methods of statistical causality. This test is performed using data from the US softwood plywood industry of the last three decades. Others have productively explored the spatial pricing practices of this industry by applying a leader-follower model. Similarly, we find that a leader-follower model explains well the temporal relations between key strategic variables (prices) in the industry. We conclude that the leader-follower model imposes meaningful restrictions on observable time-series data and that statistical causality is a useful method for testing these restrictions.     

Minimum Distance Estimation and Testing of DSGE Models from Structural VARs*

The aim of this paper is to complement the minimum distance estimation–structural vector autoregression approach when the weighting matrix is not optimal. In empirical studies, this choice is motivated by stochastic singularity or collinearity problems associated with the covariance matrix of impulse response functions. Consequently, the asymptotic distribution cannot be used to test the economic model's fit. To circumvent this difficulty, we propose a simple simulation method to construct critical values for the test statistics. An empirical application with US data illustrates the proposed method.     

空间加权矩阵设置与空间面板参数估计效率

总结了常用的空间加权矩阵的一般构建方法和研究领域内新提出的空间加权矩阵的构建方法,从宏观与微观层面,量化分析了空间加权矩阵设置对于空间面板参数估计效率、空间效应识别的影响效应。结论表明：宏观数据层面,随着空间加权矩阵复杂程度的提高,无论是空间面板固定效应模型还是空间面板随机效应模型,参数估计的有效性与一致性都显著提高并且广义矩参数估计方法优于拟极大似然估计方法,复合的空间加权矩阵条件下,拉格朗日乘子检验方法的功效更高;微观数据层面,回归结果表明四种不同类型的空间加权矩阵的设置,对于聚集外部性引致的企业全要素生产率增长的空间边界的识别具有显著影响,复合的空间加权矩阵更有效。