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This paper investigates the impact of the US stock market on the co-movements among the BRIC stock markets using conditional Granger causality which allows a comprehensive exploration on direct and indirect causality. The results from linear conditional causality test show a strong influence of the US stock market on the co-movements of BRIC. Our findings identify the US stock market which is the main inner factor making major contributions to the co-movements among the BRIC stock markets. Further, this study provides robust evidence that the co-movements cannot be significantly influenced by the common information factor. These findings show a more complete picture of the relationships between the US and the BRIC stock markets, offering important implications for policymakers and investors.

The aim of this paper is to explore how the US stock market affects the co-movements of the BRIC stock markets. Lehkonen and Heimonen [

BRIC is an acronym for the combined countries of Brazil, Russia, India and China. Proposed originally by Jim O’Neill of Goldman Sachs in 2001, it is considered as the fastest growing market economies. Before being grouped as the BRIC countries, these countries were for a long time on the periphery of the global economy. Following Bekiros [

In contrast to these previous studies, in this paper we first investigate whether the price of US stock market can affect the linkages among the BRIC stock markets. The prime motivation for choosing the US stock market comes from the fact that it plays a critical role in the global economy as a representative leading mature market [

Granger causality now provides a flexible, efficient and powerful method for exploring the co-movements of stock markets [

As compared with previous studies, the main contribution in this paper is following: we apply unconditional and conditional Granger causality approach to explore the linkages among the BRIC countries. Comparing the differences between the results of unconditional and conditional methods, we address the following questions: whether the price of the US stock market has a significant influence on the co-movements of BRIC countries? How the US stock market impact the co-movements of the BRIC stock markets? To the best of our knowledge, there are no papers answering the two questions above.

The remaining part of this paper is organized as follows. Section 2 introduces the methodology applied in the paper. Section 3 shortly describes the data used. Section 4 provides and discusses the empirical results. Finally, Section 6 offers conclusions.

Granger causality analysis was proposed by Granger [_{X}_{,t} and F_{Y}_{,t} denote the information sets including the past values of X_{t} and Y_{t} before time t + 1. Then {X_{t}} is said to Granger cause {Y_{t}} if, for k ≥ 1:

( Y t + 1 , ⋯ , Y t + k ) | ( F X , t , F Y , t ) ~ ( Y t + 1 , ⋯ , Y t + k ) | F X , t (1)

where “ ~ ” is equivalence in distribution.

The unconditional Granger causality testing introduced above can show spurious causality between X and Y if there is an apparent impact of a third variable, Z say, on X and Y. For instance, if there is no direct causal relationship from X to Y but there are strong dependencies of X and Y on Z, then a spurious causality from X to Y may be reported under the influence of Z. The spurious causality from X to Y may be eliminated by the dependencies between X and Z and between Y and Z subtracted. To deal properly with the general spurious case, the conditional Granger causality was introduced by Geweke [

To explain the conditional case, { X t , Y t , Z t ; t ≥ 1 } denote three stationary and ergodic time series processes, and we wish to eliminate any joint impact of Z on the inference of the Granger causality from Y to X. Next we can consider the full and reduced regressions as follows with the conditioning variables Z_{t} included in both regressions

X t = ∑ k = 1 p A x x , k ⋅ X t − k + ∑ k = 1 p A x y , k ⋅ Y t − k + ∑ k = 1 p A x z , k ⋅ Z t − k + ε x , t (2)

X t = ∑ k = 1 p A ′ x x , k ⋅ X t − k + ∑ k = 1 p A ′ x z , k ⋅ Z t − k + ε ′ x , t (3)

where matrices A.,_{k} are the regression coefficients, and the stochastic process ε.,_{t} are the residuals. Technically, the null hypothesis of zero causality is as follows:

H 0 : A x y , 1 = A x y , 2 = ⋯ = A x y , p = 0 (4)

Similarly to the definition of the unconditional Granger causality statistic as the appropriate log-likelihood ratio [_{t} to X_{t} conditioned on Z_{t} is defined as following:

F Y → X | Z ≡ ln | Σ ′ x x | | Σ x x | (5)

where Σ x x = cov ( ε X , t ) and Σ ′ x x = cov ( ε ′ X , t ) are the residuals covariance matrices of the regression models Equations ((2) and (3)), respectively. F Y → X | Z in Equation (5) is considered as a log likelihood ratio test, comparing models with and without the directed causal relation from Y to X.

If the causal effect from Y to X is entirely subtracted by the third time series Z, the test F Y → X | Z = 0 , which means that no more improvement in the predication of X can be expected by including the past of Y conditioned on Z. On the contrary, the test F Y → X | Z > 0 if the direct causal effect from Y to X exists, which indicates that the past of Y conditioned on Z can help to improve the predication of X.

The standard large-sample theory [

The data in this study consist of five time series of daily stock price indices denoted relative to United States (US), Brazil (BR), Russia (RS), India (IN) and China (CH), respectively. The sample covers the period from September 18, 2007 to September 30, 2015, with 1696 observations for each stock market. All indices were all taken from the Yahoo! website (http://finance.yahoo.com), and the stock returns are expressed as r_{t} = lnP_{t} − lnP_{t−}_{1}, where P_{t} is the stock price index at time t. In order to compensate for missing values in the returns for each of the countries, we exclude the corresponding observations in all of the returns.

Mean | Maximum | Minimum | S.D | Skewness | Kurtosis | J-B | ADF | PP | |
---|---|---|---|---|---|---|---|---|---|

US | 0.00015 | 0.0913 | −0.0947 | 0.0144 | −0.5234 | 9.576 | 3131.8*** | −26.7222*** | −46.2120*** |

BR | −0.00011 | 0.1687 | −0.1209 | 0.0195 | 0.1565 | 10.732 | 4229.2*** | −26.1905*** | −41.8285*** |

RS | −0.00052 | 0.2020 | −0.2119 | 0.0265 | −0.3815 | 13.140 | 7302.9*** | −23.4252*** | −37.1160*** |

IN | 0.00033 | 0.1503 | −0.1752 | 0.0167 | −0.7276 | 17.027 | 14046.0*** | −23.7181*** | −39.8264*** |

CH | −0.00034 | 0.0925 | −0.1918 | 0.0193 | −1.0823 | 13.785 | 8545.8*** | −22.2638*** | −41.4320*** |

Notes: J-B is the empirical statistic of the Jarque-Bera test for normality.ADF and PP are the empirical statistics of the Augmented Dickey-Fuller unit root test and the Phillips and Perron unit root test, respectively.

standard deviations of all returns range from 0.0167 to 0.0265. Russia exhibits comparatively higher risk. On the contrary, the US stock market displays the lowest volatility level among the selected stock markets. The stock market of Russia shows the maximum and the minimum returns among the BRIC markets, which implies a strenuous fluctuation. Negative skewness are observed for all BRIC countries with the exception of Brazil which has a positive skewness. All return series exhibit excess kurtosis. Furthermore, the J-B test shows that the null of normality is strongly rejected for all returns. Finally, the results of time series stationarity test, by applying the ADF and PP statistics, identify all of time series are stationary.

To examine the co-movements among the stock returns, we employ the Pearson correlation coefficient to calculate correlations between the BRIC stock markets, which can be expressed as:

ρ ( i , j ) = 〈 r i − μ i 〉 〈 r j − μ j 〉 σ i σ j (6)

where r_{i} and r_{j} are the returns for stock i and j, μ_{i} and μ_{j} are the means, σ_{i} and σ_{j} are the standard deviations, and 〈 〉 is defined to be the average over time.

Since all of the returns are stationary, the VAR model is first applied to model the bivariate data of the BRIC stock returns. The lags are determined by minimizing AIC for the VAR model.

BR | RS | IN | |
---|---|---|---|

Panel A:unconditional | |||

RS | 0.499*** | ||

IN | 0.330*** | 0.432*** | |

CH | 0.196*** | 0.227*** | 0.273*** |

Panel B:conditional | |||

RS | 0.288*** | ||

IN | 0.184*** | 0.353*** | |

CH | 0.184*** | 0.207*** | 0.258*** |

Notes: *** indicates statistical significance at 1% level.

BR | RS | IN | CH | |
---|---|---|---|---|

BR | c | |||

RS | 1 | - | 2 | 5 |

IN | 1 | 1 | - | 9 |

CH | 1 | 1 | 1 | - |

Notes: Unconditional linear Granger causality (above diagonal) and conditional linear Granger causality (below diagonal).

unconditional Granger causality(UGC) and conditional Granger causality(CGC) among the BRIC stock markets, where the F-statistics are provided. The results from the unconditional Granger causality show that the significant causality is found between the BRIC. The significant bidirectional causality is only observed in the case of Brazil and Russia, Brazil and India, China and India, and China and Russia. At 1% level of significance, results indicate the causality from Brazil to China and from Russia to India, respectively.

Moreover, we find a remarkable difference between the results of the unconditional and conditional Granger causality. Comparing the results from the unconditional Granger causality, the following significant unidirectional linear causal relationships do not exist in the results of the conditional Granger causality: from Brazil to China, from Russia to India, and from China to Russia. For instance, the Brazilian stock market exhibits a strong unconditional linear effect on the Chinese stock market. However, this causal relationship does not exist when the effect of the US stock market subtracted, which implies the causality can change from direct to indirect. The results show that when we examine the co-movements, we cannot ignore the effect of the US market, which definitely have a great influence on the linkage among the BRIC stock markets. This finding reflects the leading role of the US stock market in the international financial market, since it is considered as a “global factor” influencing all countries [

As shown in

BR | RS | IN | CH | |||||
---|---|---|---|---|---|---|---|---|

UGC | CGC | UGC | CGC | UGC | CGC | UGC | CGC | |

BR | 23.2826*** | 0.0044*** | 16.7573** | 2.4500 × 10^{−4} | 8.6479 | 7.5808 × 10^{−7} | ||

RS | 92.4775*** | 0.0144*** | 1.06576 | 6.9221 × 10^{−5} | 12.0172** | 4.8059 × 10^{−4} | ||

IN | 81.0052*** | 0.0029*** | 17.8488*** | 4.6742 × 10^{−5} | 22.9761*** | 0.0025*** | ||

CH | 76.7734*** | 3.7667 × 10^{−4} | 31.1568*** | 0.0055*** | 35.7090*** | 0.0059^{∗∗∗} |

Notes: Significant (***, ** or*) entries indicate that stock market X (top row) has a causal linear relationship with stock market Y (left column), i.e. X → Y. *, ** and *** indicate statistical significance at 10%, 5% and 1% levels, respectively.

fect the relationships across the BRIC stock market. The results are similar to Mensi et al. [

According to Asimakopoulos et al. [

We detect the nonlinear causal relationships among the BRIC stock market in the GARCH (1, 1) filtered residual series by using BDS test. The BDS test can help to explore the nonlinear serial dependence in time series. The results of BDS test in

This paper provides fresh new insights into the co-movements among the BRIC stock markets from 2007 to 2015, applying the novel conditional Granger causality analysis. The existing literature concentrates on the relationships among the BRIC markets but, in reality, the co-movements may be affected by the US stock market. Using conditional linear Granger causality test, we examine how the US stock market impacts the co-movements among the BRIC stock markets, which allows a comprehensive exploration on direct and indirect causality. We provide evidence that there is conditional causality among the BRIC markets,

Embedding dimension(m) | BDS statistics for the US and BRIC | ||||
---|---|---|---|---|---|

BR | RS | IN | CH | US | |

2 | 0.0137*** | 0.0265*** | 0.0215*** | 0.0138*** | 0.0226*** |

3 | 0.0302*** | 0.0509*** | 0.0419*** | 0.0314*** | 0.0505*** |

4 | 0.0402*** | 0.0703*** | 0.0580*** | 0.0483*** | 0.0726*** |

5 | 0.0468*** | 0.0828*** | 0.0689*** | 0.0581*** | 0.0874*** |

6 | 0.0509*** | 0.0892*** | 0.0737*** | 0.0628*** | 0.0952*** |

Notes: *** Represents significant nonlinear dependencies at 1% level of significance.

BR | RS | IN | CH | |||||
---|---|---|---|---|---|---|---|---|

UGC | CGC | UGC | CGC | UGC | CGC | UGC | CGC | |

BR | 16.1253*** | 0.0146*** | 15.9924^{∗} | 5.4387 × 10^{−4} | 7.3876 | 1.2869 × 10^{−7} | ||

RS | 90.4195*** | 8.1959 × 10^{−4}** | 0.5711 | 6.4264 × 10^{−5} | 10.0208** | 7.4022 × 10^{−6} | ||

IN | 71.2210*** | 0.0012** | 16.0341*** | 4.4591 × 10^{−5} | 15.4877** | 0.0021*** | ||

CH | 72.5070*** | 4.6307 × 10^{−4} | 21.6095*** | 0.0041*** | 33.4177*** | 0.0028*** |

Notes: Significant (***, ** or*) entries indicate that stock market X (top row) has a causal linear relationship with stock market Y (left column), i.e. X → Y.

which reveals more complex interaction relations on a deeper level.

Our results show a strong influence of the US stock market on the co-movements of BRIC. We also uncover evidence of wide variation in causal relations across the BRIC stock markets without taking into account the influence of the US. This identifies the US stock market is the main inner factor making major contributions to the linkage mechanism among the BRIC countries. The global dominance of the US stock market may have significantly affected the co-movements among emerging markets. In particular, we find that some of the causal relationships still remain unchanged regardless of the impact of the US stock market. A possible explanation is that there exists a limited effect of the US stock market on the co-movements, since there exist other major global economic and financial factors that can affect the relationships among the BRIC markets, e.g., the oil prices, the gold prices and VIX. Further research is needed to examine what impact the co-movements of the BRIC stock markets.

Overall, our findings in the paper have two key implications for international investors and portfolio managers. First, the asset allocation decisions should not ignore the influence of the US stock market on the co-movements among the BRIC countries, which can remind the investors to be more cautious when they plan to invest in simultaneous financial markets that exhibit pure contagion. Second, awareness of the impact of the US stock market is important for policymakers to pay more attention to the directions and degrees of the co-movements in order to better manage and control market risks to prevent future financial crises.

This research was supported by the MOE Project of Humanities and Social Sciences (17XJCZH002) and Student Research Training Program in Southwest Jiaotong University (201710613075).

Wang, L., Yang, Y. and Ma, Y.H. (2017) The Impact of US Stock Market on the Co-Movements of BRIC Stock Markets―Evidence from Linear Conditional Granger Causality. Open Journal of Statistics, 7, 849-858. https://doi.org/10.4236/ojs.2017.75060