The aim of this paper is to show that measures on tail dependence can be estimated in a convenient way by regression analysis. This yields the same estimates as the non-parametric method within the multivariate Extreme Value Theory framework. The advantage of the regression approach is contained by its straightforward extension to the estimation of higher dimensional tail dependence. We provide an example on international stock markets. The regression approach to tail dependence can be applied to estimate several measures of systemic importance of financial institutions in the literature.