Before revision:  The test performs well under different data generating processes, even when the underlying model is not very sparse. Additionally, we investigate two empirical applications : the money-income causality relation using a large macroeconomic dataset and networks of realized volatilities of a set of 49 stocks. In both applications we find evidences that the causal relationship becomes much clearer if a high-dimensional VAR is considered compared to a standard low-dimensional one .
After revision:  The test performs well under different data generating processes, even without sparsity. In two applications on money and income and on volatility spillovers we find evidence that causal relationships become clearer in high-dimensional VAR is considered compared to a standard low-dimensional one .