The figure implies that the estimated VaR-implied correlation is very unstable around the center and goes beyond 1 frequently. The estimated ES-implied correlation is higher than the estimated linear correlation in the left tail and lower than the estimated linear correlation in the right tail for all the countries, consistent with the empirical findings that dependence increases during market downturns and decreases during market upturns. Among all countries, the tail dependence between the US and Canada and Japan increases least. It is also noteworthy that although the US exhibits a higher linear correlation with Canada during normal times, the downside dependence does not increase much. For example, the tail dependence between the US and the UK is even higher than the tail dependence between the US and Canada, emphasizing the importance of estimating tail dependence.

Table 3 reports the _H_ statistics and _AH_ statistics for measuring correlation asymmetries. Panel A reports the results of the _H_ statistics. The _H_ statistics between the US and other countries are positive for VaR-implied and ES-implied correlations, implying that the linear correlation underestimates the dependence in the left tail and overestimates the dependence in the right tail. Rows 1 and 2, labeled " _HVaR_<sup>−"and "</sup><sup>_H_</sup> _ES_<sup>−",respectively,report the value of downside</sup><sup>_H_statistics using</sup> the VaR-implied correlation and the ES-implied correlation, respectively. The results show that the VaR-implied correlation tends to produce higher but less significant correlation asymmetries than ES-implied correlation. In particular, the VaR-implied correlation indicates that relations between the US and Italy, France, and Japan in the left tail increase significantly at 5% level, and the ESimplied correlation implies significant relations between the US and the UK, Italy, Germany, and France. Compared to rows 1 and 2, rows 3 and 4, labeled " _HVaR_<sup>+" and "</sup><sup>_H_</sup> _ES_<sup>+", reveal that the degree</sup> that correlation decreases during market upturns is generally less than the degree that correlation increases during market downturns.

Panel B reports the results of the _AH_ statistics. Signs of the _AH_ statistics using the VaR-implied correlation are incongruous, but only the positive statistics are significant. The _AH_ statistics using the ES-implied correlation are all positive and significant at 10% level and higher, implying that correlations are generally higher during market downturns and lower during market upturns than the linear correlation. The downside _AH_ statistics using the VaR-implied correlation are significant at 5% level only for the relation between the US and Canada and the relation between the US and Japan. The downside _AH_ statistics using the ES-implied correlation imply that correlations between the US and Canada, the UK, Italy, and France during market downturns are significantly underestimated by the linear correlation at 1% level, and correlations between the US and Germany and Japan during market downturns are underestimated by the linear correlation at 10% level. The upside _AH_ statistics using the VaR-implied correlation demonstrates a positive and significant relation between the US and Germany, and the upside _AH_ statistics using the ES-implied correlation show that all correlations decrease significantly at 10% and higher.

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