Markov switching causality and the money–output relationship

The causal link between monetary variables and output is one of the most studied issues in macroeconomics. One puzzle from this literature is that the results of causality tests appear to be sensitive with respect to the sample period that one considers. As a way of overcoming this difficulty, we propose a method for analysing Granger causality which is based on a vector autoregressive model with time‐varying parameters. We model parameter time‐variation so as to reflect changes in Granger causality, and assume that these changes are stochastic and governed by an unobservable Markov chain. When applied to US data, our methodology allows us to reconcile previous puzzling differences in the outcome of conventional tests for money–output causality. Copyright © 2005 John Wiley & Sons, Ltd.     

混频Granger因果关系检验的功效和稳健性分析

研究目标：分析混频Granger因果关系检验的功效及其稳健性。研究方法：以货币与产出间的因果关系为例,比较分析不同情形下,混频和同低频Granger因果关系检验功效的差异性和检验结果的稳健性。研究发现：货币与产出间的因果关系不是一成不变的,混频Granger因果关系检验的水平和功效随着不同层次的货币供给、模型滞后阶数、预测期长度,变量的多寡,以及样本量的大小和所处的经济阶段的变化而呈现异质性和非对称性。研究创新：将混频技术与Granger因果关系结合起来,从不同角度全面系统地检验了货币与产出的因果关系,并分析了该方法的稳健性。研究价值：进行货币政策调控时,须评估不同情形下货币政策的作用效果,选取恰当的时机,采用更加合理的调控手段和方法。     

基于波动率的货币与产出关系检验——来自分位数回归模型的新证据

本文使用1991年1月到2012年3月的样本数据对货币波动率和实际产出波动率之间的关系进行了检验。首先,应用GARCH模型度量货币波动率和产出波动率,进而对二者进行了Granger因果关系检验,发现我国货币供给增长率及其波动率对实际产出增长率及其波动率具有解释和预测能力。其次,使用分位数回归模型研究产出波动率在较小(低分位数)和较大(高分位数)时对货币供给量M0和M1波动率的不同反应程度。最后,提出了稳定产出增长,防止产出剧烈波动的货币政策建议。     

Testing for linear and nonlinear granger causality in the stock price-volume relation: Korean evidence

In this paper, linear and nonlinear Granger causality tests are used to examine the dynamic relationship between daily Korean stock returns and trading volume. We find evidence of significant bidirectional linear and nonlinear causality between these two series. ARCH-ype models are used to examine whether the nonlinear causal relations can be explained by stock returns and volume serving as proxies for information flow in the stochastic process generating volume and stock returns respectively. After controlling for volatility persistent in both series and filtering for linear dependence, we find evidence of nonlinear bidirectional causality between stock returns and volume series. The finding of strong bidirectional stock price-volume causal relationships implies that knowledge of current trading volume improves the ability to forecast stock prices. This evidence is not supportive of the efficient market hypothesis. Another finding is that the nonlinear relationship is sensitive to institutional, organizational, and structural factors. The results of this study should be useful to regulators, practitioners and derivative market participants whose success precariously depends on the ability to forecast stock price movements.     

Short and long run causality measures: Theory and inference

The concept of causality introduced by Wiener [Wiener, N., 1956. The theory of prediction, In: E.F. Beckenback, ed., The Theory of Prediction, McGraw-Hill, New York (Chapter 8)] and Granger [Granger, C. W.J., 1969. Investigating causal relations by econometric models and cross-spectral methods, Econometrica 37, 424–459] is defined in terms of predictability one period ahead. This concept can be generalized by considering causality at any given horizon h$h$ as well as tests for the corresponding non-causality [Dufour, J.-M., Renault, E., 1998. Short-run and long-run causality in time series: Theory. Econometrica 66, 1099–1125; Dufour, J.-M., Pelletier, D., Renault, É., 2006. Short run and long run causality in time series: Inference, Journal of Econometrics 132 (2), 337–362]. Instead of tests for non-causality at a given horizon, we study the problem of measuring causality between two vector processes. Existing causality measures have been defined only for the horizon 1, and they fail to capture indirect causality. We propose generalizations to any horizon h$h$ of the measures introduced by Geweke [Geweke, J., 1982. Measurement of linear dependence and feedback between multiple time series. Journal of the American Statistical Association 77, 304–313]. Nonparametric and parametric measures of unidirectional causality and instantaneous effects are considered. On noting that the causality measures typically involve complex functions of model parameters in VAR and VARMA models, we propose a simple simulation-based method to evaluate these measures for any VARMA model. We also describe asymptotically valid nonparametric confidence intervals, based on a bootstrap technique. Finally, the proposed measures are applied to study causality relations at different horizons between macroeconomic, monetary and financial variables in the US.     

Granger因果关系检验应用中的若干问题

分析了实践中应用Granger因果关系检验存在的一些问题,如信息遗漏,变量变换改变因果关系的性质、变量单整性对检验程序的影响以及检验模型的选择等,并提出在线性投影上有初步证据的因果概念。进而,应用单整变量之间Granger因果关系的一般检验程序对1978~2013年我国货币供给量与价格水平、产出之间的Granger因果性重新进行检验。     

A Bootstrap Method for Identifying and Evaluating a Structural Vector Autoregression*

Graph‐theoretic methods of causal search based on the ideas of Pearl (2000), Spirtes et al. (2000), and others have been applied by a number of researchers to economic data, particularly by Swanson and Granger (1997) to the problem of finding a data‐based contemporaneous causal order for the structural vector autoregression, rather than, as is typically done, assuming a weakly justified Choleski order. Demiralp and Hoover (2003) provided Monte Carlo evidence that such methods were effective, provided that signal strengths were sufficiently high. Unfortunately, in applications to actual data, such Monte Carlo simulations are of limited value, as the causal structure of the true data‐generating process is necessarily unknown. In this paper, we present a bootstrap procedure that can be applied to actual data (i.e. without knowledge of the true causal structure). We show with an applied example and a simulation study that the procedure is an effective tool for assessing our confidence in causal orders identified by graph‐theoretic search algorithms.     

A consistent nonparametric test for nonlinear causality—Specification in time series regression

Since the pioneering work by Granger (1969), many authors have proposed tests of causality between economic time series. Most of them are concerned only with “linear causality in mean”, or if a series linearly affects the (conditional) mean of the other series. It is no doubt of primary interest, but dependence between series may be nonlinear, and/or not only through the conditional mean. Indeed conditional heteroskedastic models are widely studied recently. The purpose of this paper is to propose a nonparametric test for possibly nonlinear causality. Taking into account that dependence in higher order moments are becoming an important issue especially in financial time series, we also consider a test for causality up to the Kth conditional moment. Statistically, we can also view this test as a nonparametric omitted variable test in time series regression. A desirable property of the test is that it has nontrivial power against T^1/2-local alternatives, where T is the sample size. Also, we can form a test statistic accordingly if we have some knowledge on the alternative hypothesis. Furthermore, we show that the test statistic includes most of the omitted variable test statistics as special cases asymptotically. The null asymptotic distribution is not normal, but we can easily calculate the critical regions by simulation. Monte Carlo experiments show that the proposed test has good size and power properties.     

Searching for the Causal Structure of a Vector Autoregression*

We provide an accessible introduction to graph‐theoretic methods for causal analysis. Building on the work of Swanson and Granger (Journal of the American Statistical Association, Vol. 92, pp. 357–367, 1997), and generalizing to a larger class of models, we show how to apply graph‐theoretic methods to selecting the causal order for a structural vector autoregression (SVAR). We evaluate the PC (causal search) algorithm in a Monte Carlo study. The PC algorithm uses tests of conditional independence to select among the possible causal orders – or at least to reduce the admissible causal orders to a narrow equivalence class. Our findings suggest that graph‐theoretic methods may prove to be a useful tool in the analysis of SVARs.     

GMM Estimation with Non‐causal Instruments*

This note provides a warning against careless use of the generalized method of moments (GMM) with time series data. We show that if time series follow non‐causal autoregressive processes, their lags are not valid instruments, and the GMM estimator is inconsistent. Moreover, endogeneity of the instruments may not be revealed by the J‐test of overidentifying restrictions that may be inconsistent and has, in general, low finite‐sample power. Our explicit results pertain to a simple linear regression, but they can easily be generalized. Our empirical results indicate that non‐causality is quite common among economic variables, making these problems highly relevant.     

Money as a Potential Anchor for the Price Level: a Critique of the P* Approach

A number of recent articles have attempted to restore the use of a simple measure of the money supply as an indicator of future price levels and to re-establish a causal link from money to prices. Most notably Hallman, Porter and Small (HPS) (1989a), (1989b) originated the approach using US data and Hannah and James(1989) have applied it to the UK The approach broadens the traditional idea of a constant velocity of money by introducing the notion of V* and Q*, the long-run value of velocity and income. These are then used to define P from the traditional quantity theory of money as the long-run equilibrium price level. The analysis then proceeds to estimate a standard Error Correction Model (ECM) for price determination with the levels effect given by (P-P*)t-1. The conclusion drawn is that 'a measure of money that determines the long-run future level of prices is useful in determining the proper monetary policy for attaining price stability. We have shown, through the construction of P*, that M2 can serve as this determinant for the price level' (Hallman, Porter and Small (1982a) p. 23).
We argue in this paper that the P* approach is flawed. It is certainly more complex than traditional monetarist approaches but the fundamental questions of causality are in no way either affected or resolved. The P* analysis is a variant on more conventional cointegration analysis (Engle and Granger (1987), Johansen (1988), Hall (1989)) and we argue that the Johansen framework allows us to address the question in a formal and more complete way. When this approach is applied to the US data used by HPS, we find that while the P* relationship does indeed represent a cointegrating one, it does not have a causal link with prices but rather the causality runs from prices to money - this result conforms well to the work of Hendry and Ericsson (1990) or Hall, Henry and Wilcox (1990), which use this form of relationship to model the demand for money.     

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.     

The linkage between insurance activity and banking credit: Some evidence from dynamic analysis

This paper investigates the long-run and short-run linkages between insurance activity and banking credit for G-7 countries. To minimize the pretest bias and overcome the structural changes, we adopt the bootstrap Granger causality test applied to full sample and subsamples with a fixed window size. The Johansen cointegration test with GMM-IV estimator finds a long-run positive relation between the series. The full sample results of bootstrap Granger causality test show that there is predictive power from life insurance activity to banking credit only for France and Japan, while the short-run causal relationships between nonlife insurance activity and banking credit are country-specific. However, parameter stability test results suggest that the short-run results in full sample are unreliable. The results of rolling VAR models report that the causal linkages between them are time-varying across various subsamples. These findings offer some useful insights for achieving the co-evolution between insurance and banking credit markets.     

On economic uncertainty,stock market predictability and nonlinear spillover effects

This paper uses a k-th order nonparametric Granger causality test to analyze whether firm-level, economic policy and macroeconomic uncertainty indicators predict movements in real stock returns and their volatility. Linear Granger causality tests show that whilst economic policy and macroeconomic uncertainty indices can predict stock returns, firm-level uncertainty measures possess no predictability. However, given the existence of structural breaks and inherent nonlinearities in the series, we employ a nonparametric causality methodology, as linear modeling leads to misspecifications thus the results cannot be considered reliable. The nonparametric test reveals that in fact no predictability can be observed for the various measures of uncertainty i.e., firm-level, macroeconomic and economic policy uncertainty, vis-à-vis real stock returns. In turn, a profound causal predictability is demonstrated for the volatility series, with the exception of firm-level uncertainty. Overall our results not only emphasize the role of economic and firm-level uncertainty measures in predicting the volatility of stock returns, but also presage against using linear models which are likely to suffer from misspecification in the presence of parameter instability and nonlinear spillover effects.     

The cycle of violence in the Second Intifada: Causality in nonlinear vector autoregressive models

We contest Jaeger and Paserman's claim (Jaeger and Paserman , 2008. The cycle of violence? An empirical analysis of fatalities in the Palestinian–Israeli conflict. American Economic Review 98 (4): 1591–1604) that Palestinians did not react to Israeli aggression during Intifada 2. We address the differences between the two sides in terms of the timing and intensity of violence, estimate nonlinear vector autoregression models that are suitable when the linear vector autoregression innovations are not normally distributed, identify causal effects rather than Granger causality using the principle of weak exogeneity, and introduce the “kill‐ratio” as a concept for testing hypotheses about the cycle of violence. The Israelis killed 1.28 Palestinians for every killed Israeli, whereas the Palestinians killed only 0.09 Israelis for every killed Palestinian.     

Empirical Modelling of Money Demand in Periods of Structural Change: The Case of Greece*

This paper examines the behaviour of the demand for money in Greece during 1976Q1 to 2000Q4, a period that witnessed many of the influences that cause money‐demand instability. Two empirical methodologies, vector error correction (VEC) modelling and second‐generation random coefficient (RC) modelling, are used to estimate the demand for money. The coefficients of both the VEC and RC procedures support the hypothesis that the demand for money becomes more responsive to both the own rate of return on money balances and the opportunity cost of holding money because of financial deregulation. In general, both procedures also support the hypothesis that the income elasticity of money demand declines over time as a result of technological improvements in the payments system and the development of money substitutes, which lead to economies of scale in holding money.     

Nonlinear causality testing with stepwise multivariate filtering: Evidence from stock and currency markets

We examine the spillovers of the US subprime crisis to Asian and European economies and in particular to what extent currency and stock markets have been affected by the crisis. Linear and nonlinear dependencies are detected after pairwise and system-wise causality analysis. A new stepwise multivariate filtering approach is implemented after controlling for conditional heteroskedasticity in the raw data and in VAR/VECM residuals using multivariate GARCH models. Significant nonlinear causal linkages persisted even after the application of GARCH-BEKK, CCC-GARCH and DCC-GARCH modelling. This indicates that volatility effects might partly induce nonlinear causality. Perhaps new short-term asset-pricing models could be developed to explain this stylized fact. These results might also have important implications for hedging, trading strategies and financial market regulation.     

Okun's Law Revisited*

In the light of modern theoretical studies, the negative relationship between output and unemployment may take a nonlinear form, in the sense that changes in output can cause asymmetric changes in the unemployment rate. A regime‐dependent specification of Okun's law, where the inverse relationship between cyclical unemployment and cyclical GDP is allowed to differ across recessions and expansions, is estimated for the US economy. Using both the Hodrick–Prescott filter and a bivariate structural time series model to isolate the cyclical component of the variables of interest, the nonlinear specification is highly significant when tested against the linear alternative independently of the method used for extracting the cycle of unemployment and GDP. The estimation results imply that the contemporaneous effect of growth on unemployment is asymmetric and significantly higher in recessions than in expansions, and shocks to unemployment tend to be more persistent in the expansionary regime.     

浙江省区域物流与经济增长的实证研究

基于浙江省1990~2012年统计数据,运用ADL模型及格兰杰因果检验对浙江省区域物流与经济增长的相互关系进行了研究。结果表明:从长期来看,浙江省GDP、全社会货物周转量及港口货物吞吐量三者之间存在着单向的因果关系。港口货物吞吐量是全社会货物周转量增加的格兰杰原因,全社会货物周转量和港口货物吞吐量平均每增长1%,分别带动浙江省GDP增长0.8672%和0.9903%。     

Visiting the effects of oil price shocks on exchange rates: Quantile-on-quantile and causality-in-quantiles approaches

We employ the relatively novel quantile-on-quantile and causality-in-quantiles approaches to empirically address the effects of oil price shocks on exchange rates of developed and developing countries. We find the evidence of the effects of oil shocks on exchange rates vary across quantiles. In addition, the effects and causality of oil price shocks are asymmetric and the slope of the coefficient in quantile-on-quantile analysis shows a relatively extreme fluctuation. Furthermore, for the developed currencies, the Granger causal relationship in both the mean and the variance running from oil shocks to exchange rates is always evident at all quantiles, while for the developing countries, the causal flow in the first and second moments is insignificant at middle quantiles.