We introduce new measures of Granger causality in quantiles that are able to detect and quantify nonlinear causal effects between random variables. The measures are based on nonparametric quantile regressions and defined as logarithmic function of restricted and unrestricted expectations of quantile check loss functions. They can be easily and consistently estimated by replacing the unknown expectations of check loss functions by their nonparametric kernel estimates. We derive a Bahadur-type representation for the nonparametric estimator of the measures.We provide the asymptotic distribution of the this estimator, which one can use to build tests for the statistical significance of the measures. We also examine the properties of the latter tests under some local alternatives. Thereafter, we establish the validity of a smoothed local bootstrap that one can use in finite sample settings to perform statistical tests. A Monte Carlo simulation study reveals that the bootstrap-based test has a good finite sample size and power properties for a variety of data-generating processes and different sample sizes. Finally, the empirical importance of measuring Granger causality in quantiles is illustrated. We quantify the degree of nonlinear predictability of quantiles of equity risk premium using the variance risk premium, unemployment rate, inflation, and the effective federal funds rate. The empirical results show that the variance risk premium and effective federal funds rate have strong predictive power for predicting the quantiles of risk premium, compared to the predictive power of the other two macro variables. In particular, the variance risk premium is able to predict the centre, the lower and the upper quantiles of the distribution of risk premium, whereas the effective federal funds rate only predicts the lower and upper quantiles. However, unemployment rate and inflation have no effect on the quantiles of risk premium.